I I; ~ 9 {'2 .‘i' E? 3. 3'3 § .5. ,nfl. _. no _ ."ifi 'h .u I. an ‘I 1 i. ‘ o .. - . 4-5 _ J} Illllllll‘llllmllllllllllllll * l, WAN 3 1293 01005 0627 Michigan State University ‘ This is to certify that the thesis entitled THE STRUCTURE OF RESERVE REQUIREMENTS AND MONETARY CONTROL presented by Carol Ann Leisenring has been accepted towards fulfillment of the requirements for Ph. D. degree in Economics Major professor Date 5 0:707%/?/ /7757 0-7539 © COPyright by Carol Ann Leisenring 19 78 THE STRUCTURE OF RESERVE REQUIREMENTS AND MONETARY CONTROL By Carol Ann Leisenring A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Economics 1978 i9“ ab”) ABSTRACT THE STRUCTURE OF RESERVE REQUIREMENTS AND MONETARY CONTROL By Carol Ann Leisenring This study is an empirical investigation of the extent to which nonmember banks and the structure of Federal Reserve reserve require— ments interfere with precise control of the money stock. The theo- retical framework employed is a Brunner-Meltzer money supply model in which the money multiplier links the net source base, which the Fed- eral Reserve is assumed to control, to the money stock. Variation in the money multiplier therefore impedes accurate monetary control. One source of its variation is variation in the reserve ratio, base- absorbing reserves divided by the demand-deposit component of the money stock. This study assesses the size, sources, and predictability of variation in the reserve ratio. Several institutional arrangements built into Federal Reserve re- serve requirements introduce variation into the reserve ratio. These include differential reserve requirements which apply different reserve ratios to different banks, the prescription that member banks hold re- serves against liabilities that are not money, and the conventions of lagged reserve requirements and excess reserves. Finally, nonmember banks cause the reserve ratio to vary. Since an increasing proportion of commercial banks are nonmembers, the control problem posed by none member banks is believed to be of growing severity. Carol Ann Leisenring The data used here cover the period January 1, 1961 through December 31, 1974. For member banks, this is weekly averages of actual daily deposit figures; for nonmember banks, the figures are estimated. The sample period encompasses several structural changes in Federal Reserve reserve requirements which have increased the number of cate— gories of deposits to which different reserve ratios are applied. It is frequently claimed that these changes and lagged reserve requirements have introduced greater variability into the reserve ratio. The reserve ratio is specified as a combination of nine parameters, each of which represents one of the aforementioned institutional as- pects of reserve requirements. The historical behavior of each paramr eter is investigated, as well as the variation in the reserve ratio under the various Federal Reserve reserve sobemes. Using the formula for the variation of a linear combination of random variables, the variation in the reserve ratio induced by each parameter is isolated. The effects of the introduction of lagged reserve requirements, the increased number of reserve categories, and the growing proportion of nonmember banks are inferred. If the parameters in the reserve ratio are variable yet predic- table, then the variation they cause is not detrimental to monetary COD? trol. To test predictability, two forecasting experiments are performed. First, a naive forecasting model of the reserve ratio is constructed in which each component parameter is assumed in week t to equal its value in week (t-l).- The error of this forecast is compared to that for an- other naive model in which perfect knowledge of one parameter is assumed, while retaining the no-change assumption for all other parameters. This implies the loss, in terms of accurate forecasts of the reserve ratio, Carol Ann Leisenring associated with a no-change forecast of each parameter. Second, fore- cast values for each parameter are derived from models based on the time-series analysis of George E. P. Box and Gwilym M. Jenkins.l These forecasts are substituted for the naive ones and the resulting errors are compared. The results indicate that the sources of greatest variation in the reserve ratio are nonmoney deposits and lagged reserve requirements. Nonmember banks are a relatively minor, and not increasing, source of variation. Differential reserve requirements have also not been a serious control problem. The results support the contention that the increased number of reserve categories cause increased variation in the reserve ratio. The Boerenkins forecasts of the parameters repre- senting lagged and differential reserve requirements, interbank de- posits, and nonmember banks are all quite accurate. The most trouble— some sources of unpredictability in the reserve ratio are excess re— serves, and time and government deposits. 1George E. P. Box and Gwilym M. Jenkins, Time Series Analysis: Forecasting and Control, Revised Edition (New York: Holden-Day, Inc., 1976). To my parents iii ACKNOWLEDGMENTS I would like to thank the members of my Committee, especially Robert H. Rasche and Carl M. Gambs, for their help throughout this project. I am particularly grateful to my Chairman, Bob Rasche, for his patience and assistance; without his continued support this dis- sertation would probably not have been finished. Thanks are due to Darwin Beck, Neva Van Peski, and their asso- ciates in the Banking Section, Division of Research and Statistics, at the Board of Governors of the Federal Reserve System, who compiled much of the data used in this study. I also thank my mother, who typed most of the first draft, and Mrs. Hope Burd, who typed the final copy, for their fast, accurate typing of a difficult manuscript. Finally I am indebted to many people who offered their moral and emotional support for the completion of this task. I thank Christine, who has endured a lot and remained a true and enduring friend through it all. I thank Defina for her continuing faith and encouragement. I thank Steve for helping me create the equilibrium in my life that was needed to finish this project. I owe a special thanks to my family, especially my mother, whose quiet support, and unfaltering patience and confidence have been my mainstay. iv TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . . CHAPTER 1 INTRODUCTION TO THE PROBLEM . . . 2 REVIEW OF THE LITERATURE . . . . . Brunner-Meltzer . . . . . . . . . Benston . . . . . . . . . . . Poole and Lieberman . . . . . . . Starleaf O O O O O O O O O O O 0 Summary and Recommendations . . 3 THE THEORETICAL MODEL . . . . . . . Introduction . . . . . . . . . Factors that Affect the Value of the r-Ratio The Madel O O O O O I O O O O O O 4 BEHAVIOR OF THE PARAMETERS OF rt . . Data, Definitions, and Assumptions Lagged Reserve Requirements . . . 3) Demand Deposits . . . . . b) Time Deposits . . . . . . Differential Reserve Requirements . a) Demand Deposits . . . . . b) Time Deposits . . . . . . Nonmember Banks . . . . . . . . a) The Level of Nonmember Bank Deposits . . b) Differential State Reserve Nonmoney Deposits . . . . . . . . a) Government Deposits . . . b) Interbank Deposits . . . . c) Time Deposits . . . . . . Nondeposit Liabilities . . . . . Excess Reserves . . . . . . . . . 5 THE'VARIATION IN rt . . . . . . . . Historical Variation in r . . . "Partial Variation" of r . A Naive Forecasting Model . . . . Summary of Findings . . . . . . . v Requirements Page vii 14 17 22 26 28' 33 36 36 40 70 76 76 82 82 88 95 95 99 106 106 118 126 128 130 133 136 152 156 156 168 176 181 vi Table of Contents (Continued) CHAPTER Page 6 ESTIMATION OF ARIMA MODEL FOR THE PARAMETERS IN rt . . . . 184 Introduction . . . . . . . . . . . . . . . . . . . . . 184 Lagged Reserve Requirements (AP and A? ) . . . . . . 195 a) Demand Deposits . . . 9’? . . .lit. . . . . . . 195 b) Time Deposits . . . . . . . . . . . . 209 Differential Reserve Requirements (6? t and 6E ) . . . 220 9 a) Demand Deposits . . . . . . . . . . . . . . . 220 b) Time Deposits . . . . . . . . . . . . . . . .'. 231 Nonmember Banks (vD and vT) . . . . . . . . . . . . . . 236 Nonmoney Deposits EY , 1 E It) . . . . . . . . . . . . 246 a) Government Deposifs . . . . . . . . . . . . . . 246 b) Interbank Deposits . . . . . . . . . . . . . . . 256 c) Time Deposits . . . . . . . . . . . . . . . . . 259 Excess Reserves (at) . . . . . . . . . . . . . . . . . 262 Summary . . . . . . . . . . . . . . . . . . . . . . . . 266 7 AN ARIMA FORECASTING EXPERIMENT FOR rt . . . . . . . . . . 274 8 SUMMARY AND RECOMMENDATIONS . . . . . . . . . . . . . . . 283 APPENDIX A: SUMMARY OF MODELS OF THE MONEY SUPPLY PROCESS . . . 290 APPENDIX B: DERIVATION OF THE SOURCE BASE . . . . . . . . . . . 312 APPENDIX C: STATE AND FEDERAL RESERVE RESERVE REQUIREMENTS . . 315 APPENDIX D: SUPPLEMENTAL TABLES TO CHAPTER 4 . . . . . . . . . 325 APPENDIX E: DERIVATION OF THE EQUATIONS FOR THE PARTIAL VARIANCE OF rt . . . . . . . . . . . . . 333 BIBLIOGRAPHY O O O O O O O O O O O O O O O O O O O O O O O O O 339 Table 10. ll. 12. 13. 14. 15. 16. LIST OF TABLES Lagged Federal Reserve Reserve Requirements, Demand Deposits . . . . . . . . . . . . . Lagged Federal Reserve Reserve Requirements, Demand Deposits . . . . . . . . . . . Annual Figures for j = l, 11 . D A j.t. Lagged Federal Reserve Reserve Requirements, Time Deposits . . . . . . . . . . . . Lagged Federal Reserve Reserve Requirements, Time Deposits . . . . . . . . . . . . . Differential Federal Reserve Reserve Requirements, Demand Deposits . . . . . . . . . . . . . Differential Federal Reserve Reserve Requirements, Demand Deposits . . . . . . . . . . . . . Annual Figures for 6? , j = 1, ll . . . ,t Differential Federal Reserve Reserve Requirements, Time Deposits . . . . . . . . . . . . . Differential Federal Reserve Reserve Requirements, Time Deposits . . . . . . . . . . . . . T i,t’ 1 = 3, 5 . . . Annual Figures for 6 Level of Nonmember Banks Deposits . . . . . Annual Figures for v2 . . . . . . . . . . . Annual Figures for v: . . . . . . . . . . . Nonmember Bank Holdings of Vault Cash . . . Effects of Nonmember Bank Holding of Vault Cash December 31, 1960-December 31, 1974 . . . vii Page 83 86 89 92‘ 93 96 97 100 103 105 107 109 110 116 121 122 viii List of Tables (Continued) Table 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. Nonmoney Deposits . . . . . . . . . . . . . . . . . Annual Figures for Yt . . . . . . . . . . . . . . . Annual Figures for It . . . . . . . . . Annual Figures for Tt . . . . . . . . . . . . . Summary of the Specification of the Nondeposit Liability Portion of the Equation for rt . . Effects on rt of Nondeposit Liabilities . . . . . Excess Reserves . . . . . . . . . . . . Annual Figures for 8t . . . . . . . . . . . . . . Historical Specification of the Expression for rt . Historical Record of the Variation in rt . . . Specification of Equations for the Partial Variance Partial Variance of rt . . . . . . . . . . . . . . Errors Resulting from the Naive Forecasting Model . ARIMA Results for A? t j=1,11 . . . . . . . . . . 3 ARIMA Results for A: t, i=1,5 . . . . . . . . . . . 9 ARIMA Results for 6? , j=l,ll . . . . . . . Jst ARIMA Results for 5: t’ i=3,5 . . . . . . . . . 9 ARIMA Results for v2 and v: . . . . . . . ARIMA Results for Yt’ It, TC and St . . . . . . Summary of Estimated ARIMA Models . . . . . . . Error Resulting from the ARIMA Forecasting Model . Calculation of the Source Base, December, 1977 . State Reserve Requirements for Nonmember Banks, May, 1977 Summary of Changes in Federal Reserve Reserve Requirements 1961 - 1964 . . . . . . . . . . . . Page 127 129 131 134 140 144 153 154 158 161 171 174 178 197 212 222 233 239 249 267 276 313 315 321 ix List of Tables (Continued) Table Page D-l. Annual Figures for IT i,t’ 1=l,5 . . . . . . . . . . . . . . 325 D-Z. Annual Figures for the Proportion of Commercial Banks that are Member Banks . . . . . . . . . . . . . . 327 D—3. Annual Figures for 3-Month Treasury Bill Rate . . . . . . 328 D—4. Quarterly Figures for v2 . . . . . . . . . . . . . . . . . 329 D—5. Quarterly Figures for Tt . . . . . . . . . . . . . . . . . 330 D-6. Quarterly Figures for at . . . . . . . . . . . . . . . . . 332 CHAPTER 1 INTRODUCTION TO THE PROBLEM The Federal Reserve's increased emphasis in recent years on mone- tary aggregates in the formulation of monetary policy is well docu- mented in the literature as well as in Federal Reserve publications.1 While, according to some spokesmen, the Federal Open Market Committee has always paid attention to the behavior of monetary aggregates, the weight attached to them in the policy process has been growing since 1960. Beginning in 1966 with the inclusion of the "proviso" clause, the Federal Open Market Committee Directive has given explicit con- sideration to the path of at least one monetary aggregate. Since 1970, the Directive has used the rate of growth of at least one monetary aggregate as a specific policy target. This new policy emphasis has stimulated considerable discussion as to whether the Federal Reserve has the technical capability to control the money stock or some other monetary aggregate, with the desired degree of accuracy.2 Doubts about the Federal Reserve's capacity to control the money stock arise over 1See, for example, Jack M. Guttentag, "Discussion," in Controlling Monetary Aggregates II: The Implementation (Boston: Federal Reserve Bank of Boston, 1972), pp. 69-72; Alan R. Holmes, "A Day at the Trading Desk," Monthly Review, Federal Reserve Bank of New York 52 (October 1970):234—8; Arthur Burns, "The Role of the Money Supply in the Conduct of Monetary Policy," Monthly Review, Federal Reserve Bank of Richmond (December 1973):2-8; Milton Friedman, "Letter on Monetary Policy," Monthly Review, Federal Reserve Bank of Richmond (May—June l974):20-23. 2See, for example, Alan R. Holmes, "Operational Constraints on the Stabilization of Money Supply Growth," in Controlling Mbnetary Aggre- gates (Boston: Federal Reserve Bank of Boston, 1969), pp. 65-78; Thomas Mayer, "A Money Stock Target," in Current Issues in Mbnetary Theory and Policy, ed. Thomas M. Havrilesky and John T. Boorman (Arlington Heights, 111.: AHM Publishing Company, 1976), pp. 548-555; and Milton Friedman, "Statement on the Conduct of Monetary Policy," in Current Issues in Monetary Theory and Policy, ibid., pp. 556-565- 1 2 a number of issues but one of the most frequently discussed control problems is that posed by the structure of reserve requirements. It is this problem that is the subject of this study. If the Federal Reserve is to control the money stock (or the demand-deposit component of it) what affords it that control is the basic relationship between bank reserves and deposits. The reserve- deposit relationship is expressed in the demand-deposit multiplier for- mula found in any introductory economics text. The level of deposits (D) is the product of the reciprocal of the average legal reserve ratio, r, and the level of reserves, R. Thus, __1_ (1-1) D — r(R). Through open market operations and its power to change legal reserve ratios, the Federal Reserve has control (though not complete) over the level of R and the value of r. Therefore, it is through this reserve- deposit linkage that the Federal Reserve can presumably control the level of bank deposits and hence the money stock or some closely— related monetary aggregate. There are several shortcomings in this avenue of control. One problem lies in the fact that the Federal Reserve does not have complete control over the level of bank reserves. While this issue is a frequently-discussed one, it is not of concern in this study. The prob- lem that this study addresses is variation in the reserve ratio, r, caused by the structure of reserve requirements. Even if precise con- trol of bank reserves is assumed, exact control of the level of deposits is precluded by changes in r. The structure of reserve requirements causes variation in r for a number of reasons. 3 First, there is no single required reserve ratio, but a number of different reserve ratios that are applicable to different kinds of de- posits and different classes of member banks ("differential reserve requirements"). Second, a majority of the commercial banks in this country are not members of the Federal Reserve System and are, there— fore, allowed to hold reserves in a form that is not under the control of the Federal Reserve. These two institutional aspects of the reserve requirement system are potential impediments to precise control of the level of deposits, regardless of the Federal Reserve's ability to con— trol the level of reserves. Their existence allows changes in the distribution of a given level of deposits between time and demand de- posits, between classes of member banks or between member and nonmember banks to alter the reserve-deposit relationship. This can be seen explicitly by rewriting equation (1—1) in the form, (1-2) r = R/D. A shift in the distribution of, for example, a given amount of member bank deposits in favor of small banks will allow a lower level of required reserves to be held against the same level of deposits; the value of r will fall. The result will be the same if a shift in the distribution of deposits occurs toward time deposits or nonmember banks. A change in the distribution of deposits will therefore allow a change in the level of deposits that can be supported by a given quantity of reserves.. Changes in the level of deposits may therefore occur even if the Federal Reserve does not alter the level of reserves; changes in dis- tribution of deposits may mitigate intentional changes in the level of reserves 0 4 The level of deposits that may correspond to a given level of re- serves will also vary depending on the level of excess reserves that member banks choose to hold. In addition, controlling the level of deposits on a short-run basis may be impeded by the institution of lagged reserve requirements, whereby current required reserves are based on deposit levels two weeks earlier. If, however, the Federal Reserve had perfect control of the level of deposits, there are additional features of reserve requirements that would interfere with its controlling the money stock with equal pre- cision. This is because there are several kinds of deposits against which reserves must be held but which are not included in the money stock ("nonmoney deposits"). Since only privately-owned demand deposits are included in the money stock, any variation in the ratio of total deposits to privately-owned demand deposits will mitigate precise con— trol of the money stock. The institutions of differential and lagged reserve requirements, the existence of nonmember banks and excess reserves, and the prescrip- tion that member banks must hold reserves against certain nonmoney de- posits are all factors that cause slippage in the reserve-deposit link- age; or, in terms of equation (1—2), they cause the value of r to vary. In contrast, if there were one uniform reserve ratio applied contempor- aneously only to privately—owned demand deposits at all commercial banks, then the value of r would vary only when the Federal Reserve changes the legal reserve ratio or the level of excess reserves changed. Uhder such a "uniform" reserve scheme, it is claimed that control of the level of reserves would allow the Federal Reserve more accurate cone trol of the demand-deposit component of the money stock. 5 Models of the money supply process recognize that the structure of reserve requirements causes variation in the r-ratio and potentially prohibit precise money stock control.3 Furthermore, discussions of theories and techniques involved in money stock control typically cone cern themselves with the control problems introduced by the current structure of reserve requirements. Specifically, many authors lament the seeming erosion of control in recent years represented by: 1) a growing proportion of commercial banks that are nonmembers; 2) the introduction of lagged reserve requirements; 3) the increased number of member bank reserve classes; and 4) the increased number of cate— gories of nonmoney deposits.4 Early empirical investigations of the importance to the money supply process of variation in r revealed that, relative to other dis- turbances, changes in the value of r have been a minor source of dis— ruption. Friedman and Schwartz,5 for example, found that from 1867 to 1960, secular and cyclical changes in the money stock were dominated by changes in high-powered money and institutional changes. They report that both the money multiplier and the reserve ratio have been "remark- ably stable," especially since 1902. In a complementary study, 3See Appendix A. 4See, for example, Albert E. Burger, The Money Supply Process (Belmont, CA: Wadsworth Publishing Co., Inc., 1971), pp. 50-58; Sherman Maisel, "Controlling Monetary Aggregates," in Controllirngonetary Aggregates (Boston: Federal Reserve Bank of Boston, 1969), p. 160, 165- 65; and John H. Kareken, "Discussion," in Controlling Monetary A re- gates II: The Implementation (Boston: Federal Reserve Bank of Boston, 1972), p. 143. 5Milton Friedman and Anna Jacobsen Schwartz, A Monetary History of the United States, 1867-1960 (Princeton, N.J.: Princeton Univers- ity Press, 1971). 6 Cagan6 also concluded that variation in the r-ratio has contributed little to either secular or cyclical changes in the money stock; any changes in the value of r have been overwhelmed by changes in high— powered money. Despite evidence that variation in the r—ratio has been relatively minor, there has been no shortage of proposals to reform reserve re- quirements in order to reduce the variation in r. According to Arthur Burns, ". . . the present structure of reserve requirements leaves much to be desired. Reforms are needed to increase the precision and the certainty with which the supply of money and credit can be con- trolled."7 Proposals to abolish differential and lagged reserve require- ments and reserves against nonmoney deposits have been made by a num- ber of authors as well as official commissions and study groups. Poole and Lieberman, for example, recommend that required reserves against government deposits and time and savings deposits, as well as lagged reserve requirements be eliminated.8 In the report of the President's Commission on Financial Structure and Regulation (The Hunt Commission), the commission proposed that the Federal Reserve impose a uniform 6Phillip Cagan, Determinants and Effects of Changes in the Stock of Moneyrr1875-l960 (New York: Columbia University Press, 1965). 7Arthur F. Burns, "The Structure of Reserve Requirements," a speech presented to the Governing Council Spring Meeting, American Bankers Association, White Sulphur Springs, West Virginia, April 26, 1973; reprinted in the Federal Reserve Bulletin (May l973):340. 8William Poole and Charles Lieberman, "Improving Monetary Control," Brookingg Paper on Economic Activity (2:1972):335. 7 reserve requirement on all classes of member banks and that required reserves against time and savings deposits be abolished.9 By far the most common target for reform, however, has been non- member banks. Much of the enthusiasm for subjecting nonmember banks to Federal Reserve reserve requirements has been generated by reports of the declining proportion of commercial banks that are member banks.10 As the portion of the country's demand deposits that are in nonmember banks grows, an ever-increasing part of the nation's money stock falls outside the control of the Federal Reserve. This erosion of the Fed- eral Reserve's monetary control can only be stopped, it is claimed, by placing the reserves of all commercial banks under the Federal Reserve's control. This is the recommendation of a number of authors as well as the position taken by the Commission on Money and Credit, the President's Committee on Financial Institutions, and the Hunt Commission. Every year since 1964, the Federal Reserve itself has requested that Congress put nonmember banks under their control for reserve purposes. The Federal Reserve states that, "Because demand deposits held by an insti- tution are part of the country's money supply just as are those in mem— ber banks, applying the same demand-deposit reserve requirements to all 9The Report of the President's Commission on Financial Structure and Regulation (Washington, D.C.: U.S. Government Printing Office, 1971), p. 65. 10See, for example, Edward G. Boehne, "Falling Fed Membership and Eroding Monetary Control: What Can Be Done?", Business Review, Federal Reserve Bank of Philadelphia (June 1974):3-15; William Burke, "Primer on Reserve Requirements," Business Review, Federal Reserve Bank of San Francisco (Winter 1974):3-16; Arthur F. Burns, ibid., p. 340—41; Annaul Report of the Board of Governors of the Federal Reserve System, 1972, (Washington, D.C., 1972), pp. 195-96. 8 such institutions would facilitate the effective implementation of monetary policy."11 The fact that various kinds of nonbank financial intermediaries have recently begun to issue deposits that are subject to withdrawal by check has created a control problem analogous to that represented by nonmember banks. Since the deposits of these institutions that are transferable by check function like demand deposits, they constitute another part of the nation's payments system that is not currently con— trollable by the Federal Reserve. Since the provisions of such ser- vices by nonbank financial institutions is becoming more prevalent, it seems apparent that the control problem they represent will be an increasing one in the future. Recognition of this trend has led some to recommend that Federal Reserve reserve requirements be extended, not only to nonmember banks, but to all financial intermediaries that issue deposits subject to checking privileges. The Hunt Commission proposed that Federal Reserve membership "be required of all commercial banks, savings and loan associations and mutual savings banks that offer third party payments services."12 In the last few years, the Federal Reserve Board has taken the position that, ". . . reserve requirements set by and held with the Federal Reserve be made applicable to all financial institutions that offer money-transfer services in essentially the same manner as do member banks. This would provide the most rational and 11Annual Report of the Board of Governors of the Federal Reserve System, 1971 (Washington, D.C., 1971), p. 212. 12The Report of the President's Commission on Financial Structure and Ragulation, p. 65. 9 equitable system of reserve requirements, particularly in view of the evolution toward the use of check-type transfers by thrift institu— tions."13 The desire to extend Federal Reserve reserve requirements to cover nonmember banks is, however, by no means unanimous. Opponents of the proposal claim that the gain in terms of monetary control would be negligible; that so many other factors cause variation in the r—ratio that relatively little would be achieved by placing nonmember banks under the control of the Federal Reserve. In addition, it is usually claimed that such a reform would jeopardize the dual banking system and correspondent banking.14 It is easy for those who support retaining the current system of state reserve requirements for nonmember banks to point to the Federal Reserve scheme of lagged and differential reserve requirements and required reserves against nonmoney deposits, all of which also generate variation in r. The fact that the Federal Reserve has only recently increased the number of reserve classes for member banks, fuels the claims that reform could be made within its own reserve requirements system that would also improve monetary control. In a paper written for the Conference of State Bank Supervisors, Robertson and Phillips take the popular position that, "The existence of different reserve requirements for member and nonmember banks does not complicate the 13Annual Report of the Board of Governors of the Federal Reserve System, 1972, ibid., p. 195. .14Ira Kaminow, "The Case Against Uniform Reserves: A Lost pre- spective," Business Review, Federal Reserve Bank of Philadelphia (June 1974): 16-21. 10 problem of monetary controls to any significant degree; Federal Reserve could make far more important changes for more precise control of the money stock by altering its own reserve rules for member banks."15 Despite many claims about the relative sources of variation in the reserve ratio and the proposals for reform, there is little empirical evidence to support or refute them. What empirical evidence there is, which is reviewed in the next chapter, is often not comprehensive or not completely reliable because of data problems. This study investi- gates the extent to which lagged reserve requirements, differential reserve requirements, nonmember banks, reserves against nonmoney de- posits and excess reserves introduce variability and unpredictability into the reserve ratio. The theoretical basis for this study is a standard Brunner—Meltzer nonlinear money supply model16 in which the money stock is related to the net source base by the money multiplier. The money-multiplier model presumes that the Federal Reserve attempts to control the money stock by controlling'fhe source base; a prerequisite of precise monetary con— trol is therefore a stable, or at least predictable, money multiplier. The money multiplier is determined by several variable parameters, one of which is the reserve ratio. 15Ross M. Robertson and Almarin Phillips, Optional Affiliation With the Federal Reserve System for Reserve Purposes is Consistent With Effective Monetary Policies (Washington, D.C.: Conference of State Bank Supervisors, 1974), p. 5. 16See Appendix A. ll Aside from changes in legal reserve ratios, all variation in the reserve ratio comes from one of the aforementioned institutional aspects of reserve requirements or excess reserves. In Chapter 3, the reserve ratio is therefore expressed as the product of nine parameters (or groups of parameters) so that each parameter reflects the impact on the reserve ratio of lagged or differential reserve requirements, nonmember banks, reserved against nonmoney deposits, or excess reserves. In Chapter 4, the historical behavior of each of the parameters in the reserve ratio is described. The relative variability of each parameter implies the relative severity of the control problem attrib- utably to each institutional aspect of reserve requirements. In some cases, secular or seasonal patterns are discernible in a parameter's behavior; in some cases, a parameter's behavior can be related to some independent economic or institutional occurrence. In Chapter 5, the historical variation in the reserve ratio and its component parameters are assessed; the variation in the reserve ratio attributable to each component parameter is isolated. Variability in the reserve ratio, whatever its source, is not necessarily troublesome to control if the variation is predictable. To assess the predictability of the reserve ratio and its component param- eters, two different forecast experiments are performed. For control purposes, the simplest way to forecast the reserve ratio is to assume no change from the previous week in its component parameters. The first forecast experiment utilizes this naive assumption of no—change in the parameters of the reserve ratio. The error in the reserve ratio that is caused by the naive forecasts of its parameters is calculated. 12 Using the time series methodology of Box and Jenkins,17 models are estimated to represent each of the parameters in the reserve ratio. The development of these models is described in Chapter 6. These models are then used to derive another, more SOphisticated forecast, of each of the parameters comprising the reserve ratio. These forecast values are then substituted for the naive forecasts and the resulting errors are compared. The relative loss, in terms of accurate forecasts of the reserve ratio, of using the naive or Box-Jenkins forecast of each parameter is determined. These results are reported in Chapter 7. In all of the empirical results, it is interesting to note the validity of the claims made about the relative severity of the control problems caused by the different institutional aspects of reserve requirements. The following common claims are evaluated: 1) That the growing proportion of banks that are nonmembers is resulting in an increasingly troublesome control problem; 2) That the control problem caused by nonmember banks is not as severe as that caused by lagged reserve requirements, differential reserve requirements, and other structural aspects of Federal Reserve reserve requirements; 3) That the Federal Reserve‘s introduction of lagged reserve re- quirements has introduced a source of great variability into the re- serve ratio and has created a much more serious control problem than nonmember banks; 17George E. P. Box and Gwilym M. Jenkins, Time Series Analysis: Forecastigg and Control, Revised Edition (New York: Holden-Day, Inc., 1976). l3 4) That the increased number of deposit categories defined by the Federal Reserve has made the monetary control problems of lagged and differential reserve requirements more difficult. CHAPTER 2 REVIEW OF THE LITERATURE The variation in the reserve-deposit relationship caused by non- uniform reserve requirement is a control problem which has been recog- nized by authors since the deposit-expansion process was first detailed by C. A. Phillips1 in 1920. Beyond recognizing the existence of the problem however, the earliest analysis of the effects of nonuniform reserve requirements is in Laughlin Currie's The Supply and Control of Money in the United States,2 first published in 1934. While Currie's empirical analysis of the problem is limited by the inadequacies of the data available at the time, he does recognize and discuss the control problems represented by nonmember banks, differential Federal Reserve reserve requirements and reserve requirements against nonmoney deposits, especially time deposits. Currie states, "Indeed it will be found that so many and diverse are the forces causing variations in the reserve ratio against demand deposits that it is quite impossible to predict the magnitude of a change in the volume of money that will result from any given change in the volume of commercial banks."3 To assess the control problem represented by time deposits, Currie compares estimates of changes in total required reserves with estimated changes in required reserves against time deposits, using call report data for 1921 through 1933. The results show that a "considerable 1C. A. Phillips, Bank Credit (New York: The MacMillan Company, 1920). 2Laughlin Currie, The Supply and Control of Money in the United States (New York: Russell and Russell, 1968). 3ibid., p. 71 14 15 proportion"4 of the annual changes in required reserves are due to changes in the level of time deposits. Currie also recognizes the con- trol problem represented by nonmember banks, but minimized its impor- tance. He claims that the two systems are so interdependent that shifts of deposits between member and nonmember banks largely offset each other and their overall effect on the money stock is neutralized. He does recognize that, "Over a period of time, however, the relative volume of member and nonmember banks deposits do change, and this causes changes in the ratio of member bank reserves to total demand deposits."5 It was however his view that nonmember banks would grad- ually choose to join the System and therefore that the problem posed by nonmember banks would soon disappear. To determine the effects of interbank deposits and cash items in process of collection, Currie calculated the ratio of adjusted demand deposits to net demand deposits, using call report data for 1922 through 1932. Since both these asset items are deducted from demand deposits before required reserves are calculated, there is always a dis- crepancy between net demand deposits (on which reserves are based) and adjusted demand deposits (the money-stock component). Currie finds that the ratio is quite unstable, indicating the variation in the levels of interbank deposits and cash items in process of collection also disrupt the money-reserve ratio. With regard to differential reserve requirements between classes of member banks, Currie notes that the net expansion or contraction of “ibid., p. 69. 5ibid., p. 74. 16 money resulting from a redistribution of deposits between classes of member banks will generally be in opposition to intended monetary con- trol. For example, during a business expansion, larger, city banks are apt to lose deposits to smaller, country banks, allowing an expansion of the money stock at a time when discretionary policy would be aimed in the opposite direction.6 Currie calculates reserve ratios for classes of member banks, for all member banks, and for all commercial banks. While he finds that these reserve ratios vary little, he claims that it is misleading to conclude that nonuniform reserve requirements are not a control problem; very small changes in the reserve ratios translate into relatively large changes in the money stock. Comparing changes in member bank reserves to: 1) member bank adjusted demand deposits; 2) adjusted demand deposits for all commercial banks; and 3) the money stock, shows that given changes in member bank reserves have historically corres- ponded to a wide variety of changes in adjusted demand deposits and the money stock. Currie concludes that, "Actually an increase in util- ized reserves may correspond with almost any multiple expansion or con— traction of money."7 In their development of a modern theory of the money supply pro- cess, Karl Brunner and Allan H. Meltzer and their followers have incor- porated sufficient institutional detail that the models include the effects of nonuniform reserve requirements. A description of Brunner- Meltzer's well-known nonlinear money supply theory as well as Brunner's earlier linear theory are contained in Appendix A. They are discussed 61131.1. , pp. 75-6. 7ibid., p. 82. 17 below only briefly and only with reference to the specific issue under consideration in this study. Following the development of modern money supply theories, a number of empirical studies were undertaken to meas- ure the control problem caused by nonuniform reserve requirements. Each of these empirical studies is also discussed below. Brunner-Meltzer Brunner's linear theory8 is based on the notion of surplus reserves, defined as available reserves less desired available reserves. As sur- plus reserves appear in an individual bank's portfolio, it expands its earning assets, thereby increasing the money stock in the process of ridding itself of surplus reserves. Brunner identified eight ways in which surplus reserves may be generated for an individual bank. Four of those eight sources of surplus reserves are pertinent to this study. 1) Shifts between demand and time deposits, to the extent that either legal or desired reserve ratios on time and demand deposits are not equal; 2) Redistribution of existing deposits or the distribution of newly-created deposits among banks subject to different reserve ratios; 3) Reallocation of a bank's cash assets between interbank deposits and assets that satisfy legal reserve requirements; 4) An individual bank may gain or lose surplus reserves as other banks in the system reallocate their cash assets as described in para— graph (3). 8KarliBrunner, "A Schema for the Supply Theory of Money," Inter- rLational Economic Review 2 (January l961):79-109. 18 The expression which explains the generation of aggregate surplus reserves therefore includes four terms that are of interest here. First, the quantity of surplus reserves released or frozen by shifts between time and demand deposits is represented by, (using Brunner's notation), (2-1) 1 di 1- = 32 Second, loss or gain M5 [(rdi + wi)(l - g .) - (rt1 + wi)]n1, where (for n banks), 1 l 21 2 2 the legal reserve ratio against demand deposits for the ith bank; the marginal propensity of the ith bank to hold additional reserves against demand deposits; the legal reserve ratio against time deposits for the ith bank; the marginal propensity of the ith bank to hold added reserves against time deposits; the marginal propensity of the ith bank to adjust its balances at other banks because of a change in its deposit liabilities; the deposit flow representing a shift from demand deposits to time deposits at the ith bank. the term Brunner identifies as 2’ represents the aggregate of surplus reserves resulting from a redistribution of existing deposits among different classes of banks. Specifically, (2-2) 1 8331 n d . i 1 1i 2 ~1:1[(1 - g3i) - (r + wl)gli]n3 , where, the proportion of the ith bank's clearing balance that is settled by the Federal Reserve mechanism; the proportion of the ith bank's clearing balance that is settled by debiting its deposit liabilities to other banks; the net deposit inflow to the ith bank resulting from the redistribution of existing deposits among different banks. “11 (Z n =0)- i=1 3 19 In order for this term to affect the aggregate level of surplus reserves, the value of the bracketed expression must be different for different banks. Finally there are two terms in the expression for surplus reserves incorporating the influence of interbank deposits. One deals with the distributional effect of interbank deposits. Dividing banks into four classes (central reserve city, reserve city, country, and nonmember banks), the net interbank position for the 3th class of banks is an aggregation over all banks in that class and is represented by, s s bs (2-3) ho - (l - gz)do where hS = interbank deposits that represent assets of banks in the 3th class; bs . th do 8 demand dep031ts of the 3 class that are owned by other banks. The average interbank position for all classes of banks, weighted by legal and desired reserve ratios, is therefore defined by 2 (rd + ws)[hs - (1 - S)dbs] s=l l o 8z o (2-4) 80 = - (rds + ws) 1 l S IIM-L‘ s The rate of change in the average distribution of interbank deposits will absorb or release surplus reserves. This is defined by, 4 (2-5) 2 (rd s=l s s . + wl)€o, where to is the rate of change in so. The second term dealing with interbank deposits defines the scale effect of the quantity of inter- bank deposits in the system. The term Yo is defined, 20 n (2-6) Y =2 d . summing over all n banks in the system. The rate of change in Y0 there- fore determines the surplus released or absorbed by a change in the level of interbank deposits in the system. Although Brunner has done empirical work in connection with the linear money supply hypothesis, little of it is pertinent to the issues of this study and what is pertinent has been rather sketchily reported by Brunner. Brunner minimizes the effect differential reserve require- ments have had in the money supply process and believes that the dis- turbance from this source has been overrated by Federal Reserve offi— cials. While "there is little doubt that volatile redistribution of deposits among classes of banks could seriously impair the degree of control exercised by the monetary authorities over the money supply, . . . (I) investigation of the variations generated in the average requirement ratio on demand deposits attributable to a shifting distri- bution of existing deposits, however, yields no support for the conten- tion that volatile shifts in deposit distribution actually impairs the degree of control over the money stock." In An Alternative Approach to the Monetary Mechanism, Brunner and Meltzer assess the importance of the disturbance represented by the term, 21. For subperiods when legal reserve ratios remained constant, they computed for each month in the period June, 1945 through September, 1962, the change in required reserves from the same month in the preced- ing year. These calculations reveal, according to Brunner and Meltzer, 9U.S., Congress, House, Committee on Banking and Currency, subcomr udttee on Domestic Finance, An Alternative Approach to the Monetary Mechanism, by Karl Brunner and Allan H. Meltzer, 88th Congress, 2nd Ses- sion (Washington, D.C.: Government Printing Office, 1964), p. 18 21 that the amount of reserves released or absorbed by shifts in the dis- tribution of deposits has been small, regular, and has declined since World War II. In the 41-month subperiod ending in September 1962, the average monthly release of required reserves was $43 million. That same subperiod displays the largest range of monthly values: a maximum value of $141 million and a minimum value of -$111 million. Assuming a money multiplier of 2.5, Brunner and Meltzer infer that changes in reserves attributable to a changing distribution of deposits amounted to an average annual change in the money supply of $87 million in the early 1960's (down from $175 million in the subperiod right after World War II). In percentage terms, the source of reserves was, on the average, responsible for .06% of the growth in the money stock in the early 1960's or for an annual rate of change in the money stock of .22 in the last 15 years. Furthermore, Brunner and Meltzer claim that the average monthly values behave in a regular pattern, implying that the irregular influence of the distribution of deposits on the money stock.would be even smaller. Since the size of the disturbance from this source appears smaller than the effects of random forces on the money stock, Brunner and Meltzer conclude that "removal of differential requirement ratios cannot be justified in terms of the degree of con- trol over the money supply."10 Brunner and Meltzer also conclude that the effect on the money stock of changes in either the level or distri— bution of interbank deposits is very small. Changes in interbank de- posits, even changes that are large relative to observed changes, would have minimal impact on the money stock. For example, a 1% change in the loibid. 22 money stock would require a reallocation of interbank deposits of $8 billion from central reserve city banks to country banks and of $28 billion from reserve city banks to country banks. Since total member interbank deposits were $15 billion at the end of 1962, shifts in deposits of such magnitude seem highly unlikely. Brunner and Meltzer conclude therefore that variations in the money stock due to changes in interbank deposits are so small they are indistinguishable from random variations in the money stock and that omitting their effects on the money stock does not cause significant error.ll Benston . . 12 . . . Benston s 1969 article is the first systematic attempt to empir- ically investigate the extent to which the reserve requirement system interferes with monetary control. He considers three sources of varia- tion in the reserve-demand deposit relationship: (1) differential reserve requirements for different classes of member banks; (2) the imposition of different reserve ratios on demand and time deposits; and (3) the tendency of different banks to hold different levels of excess reserves relative to deposits. The basis of Benston's empirical investigation is the equation, n n -1 (2-7) DDt = TRt 2 (rd dd + re ddi) + Z rt td, i-l i i i j=1 j J ’ where rd = the legal reserve ratio against demand deposits for the ith class of banks; llibid., p. 27. 12George J. Benston, "An Analysis and Evaluation of Alternative Reserve Requirement Plans," Journal of Finance XXIV (December 1969): 849-70. 23 rt. = the legal reserve ratio against time deposits for the jth J class of banks; ddi = the ratio of demand deposits in the ith class of banks to total member banks demand deposits; th re. = the ratio of excess reserves to demand deposits at the i class of banks; td. = the ratio of time deposits of the jth size to total demand 3 deposits at all member banks. Benston's analysis centers on the demand deposit multiplier, the expres- sion inside the bracket in equation (2-7). Except for rdi and rtj, the values of the terms in the demand deposit multiplier are not known. The values of ddi’ rei, and td must be predicted; they may, however, vary i so little or be so predictable, that effects of changes in their values can be easily offset. Benston attempts to compare the predictability of a change in net demand deposits arising from a change in total reserves, under various reserve requirement systems. He considers the following three systems: 1) the country bank-city bank system; 2) a graduated system, based on bank size; and 3) a uniform reserve requirement scheme. Benston was unable to obtain deposit data distributed by banks size, so he uses the country-city reserve city distinction as a proxy for size for both de- mand and time deposits. The tdj terms actually reflect two influences on the demand deposit multiplier-~the distribution of time deposits among classes of member banks and the ratio of member bank time deposits to member bank demand deposits. Benston does not distinguish between these two effects. The data he uses is semimonthly averages of daily figures for member banks for the period January 1, 1951 to August 1967. 24 13 The mean change in dd from one period to the next is .021%. i Expressed as a percentage of ddi,l4 the mean change in the ratio is only .0612 for country banks and -.033% for city banks. Therefore while the series ddi exhibits a few large period-to-period changes and extreme values, the overall variation in ddi has not been large. The Fed may therefore be able to predict total demand deposits successfully while ignoring any shift in deposits between classes of member banks. To test this possibility, Benston "predicts" total demand deposits for each period, using the value of dd for the previous period. The overall 1 error in estimating DDt in this manner proved to be quite small, though there were a few periods for which the errors were substantial. Benston therefore concludes that Changes in dd are small and predictable. i Benston uses the same simple prediction model to test whether changes in dd are offset by differences in re When the ddi term is i i' lagged, the prediction errors are smaller, implying that unexpected changes in dd are offset some by different re Benston concludes that i i' a system of differential reserve ratios may actually be superior to uni- form reserve ratios. However, there is little difference in excess reserve behavior between bank classes so the possible advantage of dif- ferential reserve ratios is apparently small. Finally, Benston estimates total demand deposits by the simple model, DDt = DD The errors encountered with these predictions are t-l' large and ten times larger than the errors involved when DDt were 13 [dd dd .100 i,t ' i,t-l] 1“ = dd - 100 [ddi,t - ddi,t-1] ' i,t-1 25 estimated u51ng ddi,t = ddi,t-l' larger problems involved in estimating total demand deposits that are This implies that there are other, not accounted for by shifts in ddi' Therefore, Benston finds no sig- nificant evidence to recommend one reserve requirement system over another. The tdj terms show much larger changes for all classes of bank than the ddi terms. But since the ratio of time to demand deposits for all banks grew during the sample period, Benston concludes that the changes in tdj were primarily the result of movements into time deposits rather than the result of shifts in deposits among classes of banks. The tdj ratio as it is constructed does not allow Benston to disentangle the two movements. Assuming tdj,t = tdj,t-l in his prediction model for DDt results in errors that are as much as nine times larger than those resulting from assuming ddi,t = ddi,t-1' When two or three lagged error terms are added to the prediction model, the prediction errors are reduced by two-thirds. Benston therefore concludes that changes in time deposits need not hamper monetary control either. Benston sees nonmember banks presenting two control problems. First, is the erosion of control over the total deposits of the nation as more and more banks leave (or fail to join) the System. He considers this problem unimportant, claiming, "the shifts of deposits of this sort are gradual and obviously can be predicted and accounted for easily."15 The second and, in Bestons's regard, more significant problem is the transitory shifts in deposits between existing member and nonmember banks. Benston compares the Federal Reserve's estimate of nonmember 15ibid., p. 859. 26 bank demand deposits to nonmember bank call data and concludes that estimation between call dates of nonmember bank deposits is a much more serious problem for the Fed than predicting shifts in deposits between classes of member banks. Poole and Lieberman In "Improving Monetary Control," William Poole and Charles Liebermanl6 investigate the variation in the ratio of member bank re- serves to member bank adjusted demand deposits. They ignore the con- trol problem created by nonmember banks. They calculate the member bank reserve ratio using weekly data for individual member banks for the period October 7, 1970 to November 3, 1971. The ratio proves to be more stable under the new graduated reserve requirement system than under the old city-country system. The ratio has a standard of devia- tion of .44 and a coefficient of variation of .018 under the city- country bank reserve plan, compared to .37 and .017 for the graduated reserve system. Poole and Lieberman decompose the member bank reserve-demand de- posit ratio into the sum of required reserves against private demand deposits, government demand deposits, interbank deposits, time deposits and nondeposit liabilities (Eurodollars and commercial paper). Total required reserves and each of its components are then divided by total member bank demand deposits. (This ignores excess reserves). The var— iance of the total required reserve ratio is then the sum of the vari- ance of each of the component required reserve ratios plus twice the covariances of the component ratios. 16William Poole and Charles Lieberman, "Improving Monetary Control," Brookinga Papers on Economic Activiry (2:1972):293—342. 27 Their results indicate that differential reserve requirements cause little variation in the total reserve ratio: the variance of the total required reserve ratio is .1403 while that for its demand deposit com- ponent is .0021. The greatest source of variation in the total required reserve ratio comes from time deposits (its reserve ratio has a vari— ance of .1101) followed by government deposits (.0308) and interbank deposits (.0209). The reserve ratio for the nondeposit liabilities show even smaller variances. The same calculations for changes in deposits yield the following results: total required reserve ratio, .0931; government deposits, .0306; interbank deposits, .0406; time deposits, .0091; demand deposits, .0020. When first differences are considered then, time deposits cause much less disturbance in the reserve ratio, and the major control problems are changes in government and interbank deposits. Poole and Lieberman therefore conclude that neither gradu— ated reserve requirements nor reserve requirements against nondeposit liabilities causes serious disturbance in the required reserve ratio; changes in the level of time deposits and the reserves needed to back them are substantial, but those changes are apparently more predict- able than are changes in either government or interbank deposits. While Poole and Lieberman present no quantified measure of the disturbance introduced in the reserve ratio by lagged reserve require- ments, they do present theoretical arguments to support the view that, "The lagged reserve requirement system in all probability reduces the stability of short run functional relationship and to that extent the precision of week-by-week control."17 While it is true that lagged 17ibid., p. 311. 28 reserve requirements provide member banks and the Federal Reserve with perfect certainty about the level of required reserves, they provide no one with information on the amount of reserve adjustment that is neces— sary. Hence, it is the contention of Poole and Lieberman that some reserve adjustment is necessary with either lagged or contemporaneous reserve requirements, but that lagged reserve requirements preclude any reserve adjustment through manipulation of deposit levels. More of the adjustment is therefore forced into the money market. To assess their impact in the money market, Poole and Lieberman examine three indi- cators of money market stability (weekly change in the money stock, fed- eral funds rate, and the level of free reserves) for 296 weeks before the introduction of lagged reserve requirements and 197 weeks after their introduction. In each case, they find slightly more instability with lagged reserve requirements. Starleaf The most recent investigation of this problem is a study by Dennis Starleaf18 in which he systematically removes other sources of variation in the reserve ratio in order to assess whether or not nonmember banks present a serious control problem. He defines the reserve ratio, R + V n _._J£____. where R.In is member bank reserves, Vh is nonmember bank vault cash and DD is the demand-deposit component of the money supply. 18Dennis R. Starleaf, "Nonmember Banks and Monetary Control," The Journal of Finance XXX (September l975):955-975. 29 Initially Starleaf dismisses three of the causes of variation in the r-ratio, assuming that they can be accurately predicted by the Fed. These include changes in legal reserve ratios, changes in the distri— bution of deposits between classes of member banks,19 and changes in the level of nondeposit liabilities. Under these assumptions, the artificial reserve ratio r* is constructed which excludes the effects of nondeposit liabilities and incorporates constant effective reserve ratios for all member banks. Thus, * .147 NDD + .04T + ER + v 20 (2_9) r = m m m n , DDA + DDA + DD + CIP - FLT + FORN m n f m,f where NDDm = member bank net demand deposits; Tm = member bank time deposits; ER.In = member bank excess reserves; DDAm = member bank demand deposits adjusted; DDAn = nonmember bank demand deposits adjusted; DDf = demand deposit balances at branches and agencies of foreign banks in New York City plus such balances at international investment corporations in New York City; CIPm f = member bank cash items in process of collection associated ’ with foreign agency and branch transfers; FLT 8 Federal Reserve Float, and FORN = deposits at Federal Reserve Banks due to foreigh official institutions. 19He relies on Benston's findings for this conclusion. 20 After the introduction of lagged reserve requirements in Septem— ‘ it = — ber, 1968, R m’t .147 NDDm’t_2 + .o47m,t_2 + ERm,t + (vm’t vh,t_2). 30 He then constructs a reserve ratio, rfn, derived from r* by exclud— ing the influence of nonmember banks. This is accomplished by first, subtracting Vn from the numerator and DDAn from the denominator of r*. Second, the reserves that member banks must hold against net interbank deposits due to nonmember banks is deducted from the numerator of r*. The data needed to make this adjustment however is not available so instead he adds net interbank deposits at member banks due to all com- mercial banks21 to the denominator of r* to obtain, .147 NDD + .047T + ER m m m _. * = , (2 10) r_n DDA + NBD + DD + CIP - FLT + FORN m m f m,f where NBD = member bank deposits due other commercial banks less deposits due member banks from other commercial banks. Starleaf claims that changes in the level of time and government deposits can be foreseen perfectly, because of lagged reserve require- ments. Therefore he removes the variation in r* and rfn from these two sources, resulting in the following definitions, .147NDD - .147DG + R. + V m m m n _. * = ’ (2 11) r_t,_g DDA + DDA + DD + CIP - FLT + FORN m n f m,f .147NDD - .147DG + R m m m + CIP - FLT + FORN m,f _ * = (2 12) r -n,-t,-g DDA + NBD + DD m m f 21The rationale for adding NBDm to the denominator of (2-10) is as follows: if there were no nonmember banks, NDDm (on which R5 is based) would exceed DDAm (the money supply component) by the amount of govern- ment demand deposits; here NDD exceeds (DDAm + NBDm) by the same smount. Thus adding NBDh to the denominator of rrn counters the reserves member banks hold against their net balances due nonmember banks. This assumes that member bank balances due to other member banks equal member bank balances due from other member banks (which is in theory true). 31 Finally Starleaf removes the affects of float and foreign deposits CI represented by the DD FLT and FORN terms in the denominator f’ Pm,f’ of equation (2-12). This results in, .147NDD - .147DG + ER m m m (2-13) r* = ° m DDA + NBD m m The only remaining sources of variation in r; are excess reserves and lagged reserve requirements. The values of these reserve ratios are then calculated for June 30 and December 31 for the years, 1961 through 1973. For nonmember banks, call report data are used; for member banks, weekly data for the week nearest the call data are used. Comparing first r* and rfn, both ratios follow the same basic pattern and it is difficult to determine from a plot of them whether one series varies more than the other. The first and second differences of the series r* and rfn indicate that r* is slightly more stable than r: ; the mean of the absolute values of the second differences of r* is .00332, compared to .00420 for rfn. These results imply that the existence of nonmember banks has been sta- bilizing to a small degree. Using r* and rfn to calculate money multi- pliers, mg and mS,-n’ respectively, Starleaf finds that both mg and m§’_n display considerable variability. The m§’_n multiplier is slightly more variable than mg; the mean of the absolute values of the second differences is .03097 for m§’_n and .02833 for mg. Starleaf concludes that nonmember banks have at least not been a source of instability and may be a minor source of stability. Comparing rft,-g and rfn,-t,-g again shows less variation in the ratio that includes nonmember banks. The mean of the absolute value of 32 the second differences is .00212 for rft -g compared to .00368 for D 9 rin,-t,-g' Again the empirical evidence implies that nonmember banks have been a minor source of stability. Values of r; exhibit considerable variation; the mean of the abso- lute values of the second differences of r; is .00274. This indicates that excess reserves and lagged reserve requirements alone account for much of the variance in the r-ratio. Finally, Starleaf investigates the stability of the r; ratio with excess reserves also removed (r;,-er)' Since the rH,-er ratio displays considerable variation, Starleaf is able to conclude that lagged reserve requirements alone contribute considerable variation to the r-ratio. Starleaf's study can be criticized on a number of grounds. A pri- mary deficiency is his unavoidable reliance on call report data for nonmember banks. The numerous discontinuities and distortions in call report data are a well—known problem which renders results based on call report data somewhat unreliable. It is possible that the small differences that Starleaf finds between the variation in r* and rfn are due to errors and distortions in the data. Second, Starleaf dismisses as unimportant differential Federal Reserve reserve requirements and requirements against nondeposit liabil— ities as sources of variation in the reserve ratio. In the case of dif- ferential reserve requirements, he relies on Benston's results as a justification. In the second case, he merely assumes that changes in nondeposit liabilities can be perfectly predicted with lagged reserve requirements. This assumption could of course be made about many things that disrupt the reserve ratio: time deposits, government deposits, interbank deposits, and the distribution of deposits among classes of 33 member banks. In actuality, the Federal Reserve does not have the data needed to perfectly predict these items nor the capabilities to per- fectly offset their changes. Starleaf ultimately compares the ratio of reserves to adjusted demand deposits for all commercial banks with that for member banks and concludes that since the latter ratio varies more, nonmember banks are a source of stability. Kopecky22 has shown that, under certain circumr stances, Starleaf's results for r* and rfn are trivial. In a more complete model specifying bank behavior, Kopecky includes the institu- tional arrangement whereby member banks provide reserve assets to non- member banks through interbank deposits. Member banks' excess reserves are then taken to be a stochastic function of demand deposit liabil- ities owed to the public and to nonmember banks. Under these conditions, Kopecky shows that the mean of the absolute value of the second differ- ences of r* (which is the measure of variability Starleaf uses) is always larger than that for rfn.23 Summary and Recommendations The control problems generated by differential reserve require- ments appear, according to the empirical work reported to date, to be minimal. Some of the earlier writers, such as Currie, recommended that uniform reserve requirements be placed on all demand deposits. In addi- tion, much of the theoretical work done on the money supply process 22Kenneth J. Kopecky, "Nonmember Banks Revisited: A Comment on Starleaf.f Unpublished manuscript, Board of Governors of the Federal Reserve System, Washington, D.C. 23ibid., pp. 11-12. 34 implies that differential reserve requirements introduce troublesome variation in the reserve ratio.24 Empirical results do not however support this popular contention. Both Benston's and Poole and Liberman's results indicate that the distribution of demand deposits among classes of member banks changes little and, in comparison to other sources of variation in the reserve ratio, have relatively insig- nificant effects. Comparing a graduated reserve scheme, a uniform reserve plan, and the city-country classification system, Benston con— cludes that none of the reserve systems can be recommended on the basis of improved monetary control. It should be noted, however, that since Benston uses data on city and country banks as a proxy for data dis- tributed by size of bank, his results with respect to a graduated re- serve system are not totally reliable. Poole and Lieberman are also not able to conclude that removing differential reserve ratios on classes of member banks would improve monetary control. Their results also show that the variation in the reserve ratio caused by differen- tial reserve requirements is slightly smaller under the graduated re- serve scheme than under the previous city-country system. Most authors agree that monetary management would be improved if nonmember banks were placed under Federal Reserve reserve requirements, but no one has presented convincing empirical evidence to support that view. Poole and Lieberman include universal reserve requirements in their list of proposed reforms. Benston however claims, "The absence of a Federally controlled, single reserve ratio applied to the demand 24See, for example, Albert E. Burger, The Money Supply_Process (Belmont, California: Wadsworth Publishing Company, Inc., 1971), pp. 57-580 35 deposits of nonmember banks has resulted in a few fairly large errors of prediction, but these may be a function of discontinuous reporting by nonmember banks rather than their noncontrol."25 Therefore he is unable to recommend universal membership. Starleaf does not recommend universal membership either, inferring from his empirical results that nonmember banks have been a source of stability, rather than instabil- ity. Removal of reserve requirements against time deposits is also a common recommendation for reform. Currie recommended that this reform be enacted in order to prevent "distortions" of the money supply caused by consumers' shifts in and out of time deposits. On the other hand, some authors have proposed that the distinction between demand and time deposits be removed for reserve purposes, and the same reserve ratio be applied to each. From his empirical results, Benston concludes that changes in time deposits are sufficiently predictable that the question of the best reserve ratio for them cannot be answered on the grounds of monetary control. Poole and Lieberman, however, recommend that reserve requirements on both time deposits and government deposits be eliminated, their empirical results imply that these two nonmoney items introduce significant variation into the reserve ratio. There is virtual agreement among all authors that lagged reserve requirements should be eliminated. Poole and Lieberman reason that lagged reserve requirements are a major source of disruption and Starleaf's results support this contention. 25Benston, p. 869. Chapter 3 THE THEORETICAL MODEL Introduction The theoretical model employed in this study is a standard money multiplier model like that originally formulated by Karl Brunner and Allan H. Meltzerl and modified and refined by Albert E. Burger2 and others.3 The underlying assumption of such a model is that the mone— tary authorities have relatively precise control over the net source based and that they control the net source base in an attempt to con- trol the money stock. The relationship between the net source base, Ba’ and the narrowly defined money stock, M1, is conventionally denoted, (3—1) M1 = mBa, where m represents the money multiplier. The multiplier m is not a lKarl Brunner and Allan H. Meltzer, "Liquidity Traps for Money, Bank Credit, and Interest Rates," Journal of Political Economy 76 (January/February l968):1-37. 2Albert E. Burger, The MoneyrSupply Process (Belmont, CA: Wadsworth Publishing Company, Inc., 1971). 3For a more detailed presentation of Brunner and Meltzer's "non- linear" money supply model, see Appendix A. 4The net source base is defined as the sum of Federal Reserve holdings of U.S. Government securities, the gold stock, treasury cur- rency outstanding, Federal Reserve float, and "other Federal Reserve Assets" minus treasury cash holdings, treasury deposits at Federal Reserve Banks, foreign deposits at Federal Reserve Banks, other deposits at the Federal Reserve, and other Federal Reserve liabilities and cap- ital. For a more detailed description and derivation of the net source base, see Appendix B. 36 37 constant; it is dependent on factors representing the behavior of the public, commercial banks, and the federal government. The monetary authorities supply a specific quantity of "base money" (set the net source base at some prescribed level), but theo- retically any size money stock may be generated from that level of base money. The level of the net source base, plus various institu- tional factors, act as constraints on the size of the money stock, but there is no exact or constant relationship between the net source base and the money stock. The inexactness or variability in the base- money stock relationship is reflected in variation in the money multi- plier. Any variation in the value of m causes variation in the money stock, given a constant level of base money. When the monetary authorities determine the level of the net source base, presumably they have some estimated value of m in mind.5 If the value of m turns out to be larger than predicted, the money stock will be larger, given the controlled level of the net source base. Thus, variation in the value of m hinders control of the money stock. Variation in the value of m can be best analyzed using a more de— tailed definition of m. This can be derived as follows. The net source base is completely absorbed by the sum of member bank unborrowed re- serves, nonmember bank vault cash, and currency in the hands of the public. This is the channel through which the base acts as a constraint 5Assuming of course that their aim is to control the money stock by controlling the net source base. 38 on the money stock. The money stock is defined here as currency held by the public plus privately-owned demand deposits.6 Schematically, (3-2) Ba=(Rm-B)+VCn+Cp=(R-B)+Cp, (3-3) M = (2" + D", where Rm = member bank reserves B = member bank borrowing VCn = nonmember bank vault cash Cp = currency held by the public R = total bank reserves that absorb base money Dp = privately-owned demand deposits. Substituting the expression for Ba and M into (3-1) gives, Cp+Dp=m(R=B)+Cp, = Cp+Dp (R - B) + CP m s The following parameters are defined, R/Dp, bank reserves that absorb base money relative to Dp r = k = Cp/Dp, currency holdings of the public, relative to Dp b = B/Dp, member bank borrowing, relative to Dp Substitution yields, kDp+ Dp m = ' er - pr + k1)" 6This "conventional" definition of the money stock will be used throughout this study, unless otherwise indicated. Foreign deposits at Federal Reserve Banks are also included in this definition of the money stock but are ignored here. The rationale for this is first, that the item is quantitatively very small and second, that it has no effect on the issues being investigated in this study. 39 Dividing the numerator and denominator of the right hand side of the equation by Dp gives ___1_+__k__ (3-4) m - b + r - k ° As can be seen in equation (3—4), the value and stability of m is dependent on the value of stability of l) the public's decision with regard to currency holdings (k); 2) member bank borrowing behavior (b); and 3) various behavorial and institutional factors that govern the level of bank reserves relative to privately-owned demand deposits (r). Variation and unpredictability will occur in m as a result of varia- tion and unpredictability in k, b, or r. Consider first the parameter k. As equation (3-2) shows, every dollar of the net source base becomes a part of either bank reserves or currency in the hands of the public. Every dollar of the net source base that is held as currency by the public adds exactly one dollar to the money stock. But every dollar of the net source base that is absorbed into bank reserves can potentially support (% -$1) of demand deposits, where r represents the weighted-average reserve requirement. Therefore, how the net source base is apportioned between Cp and (R.— B) is one important determinant of the size of the money stock which will ensue from a given amount of base money. Any variation in the portion of the net source base that the public elects to hold as cash will therefore cause variation in m. The second factor that causes variation in m is member bank borrow- ing (b). 'By adding to member bank reserves, borrowing in effect extends 40 the net source base7 and gives member banks the potential to expand demand deposits above the level that would be possible without borrow- ing. Therefore an increase in the level of member bank borrowing will increase the size of m (as can be seen in equation (3—4)) and a larger money stock will correspond to a given level of base money. Finally, m may vary because of variation in the relationship be— tween bank reserves and privately-owned demand deposits (r). The pur- pose of this study is to investigate the behavior of the parameter r and thereby infer its effect on m. The parameter r summarizes the effects on m of a number of factors determined by bank, public, and federal government behavior in combination with the current reserve requirement systems. The parameter r is examined in more detail in the next section. Factors that Affect the Value of the r-Ratio The level of reserves that absorb base money relative to privately- owned demand deposits (r) can, given the current reserve requirement systems, be affected in two basic ways. One way is through changes in the distribution of deposits among classes of banks that are subject to different required reserve ratios. Changes in the distribution of de— posits may cause base money to be absorbed or released by increasing or decreasing the amount of reserves that must be held per dollar of 7The net source base plus member bank borrowing is defined as the source base. The monetary authorities exercise some control, though imprecise, over member borrowing through administration of the discount window. Furthermore, it is usually claimed that the Fed can offset member bank borrowing with enough precision to exactly control the source base. In light of this, the source base could be used as the controlled variable as validly as the net source base. 41 privately-owned demand deposits. The value of r is, therefore, cur- rently affected by the distribution of total deposits between member and nonmember banks; by the distribution of member demand and time deposits among member banks of different reserve categories; by the distribution of nonmember demand and time deposits among nonmember banks in different states;8 and by the distribution of net interbank deposits and cash items in process of collection between members and nonmembers, members of different reserve categories and nonmembers in different states. The second way that the value of r is altered is by things that are not part of the money stock, against which member banks must hold base-absorbing reserves. By adding to reserves, these factors reduce the amount of net source base available to back the money stock; they increase the value of r and lower m. Five factors affect the value of r in this manner. They include: excess reserves, government demand deposits, interbank deposits, time deposits, and several categories of nondeposit liabilities against which member banks are required to hold reserves. In addition, the value of r is affected by weekrto—week changes in either the level of member bank demand or time deposits, or their distribution among reserve classes. Each of these factors is dealt with separately below. (i) Nonmember banks: The existence of nonmember banks introduces variation in r in three ways each of which stems from the institutional 880me states subject their nonmember banks to differential reserve requirements, based either on bank size or geographical location. In those states, the distribution of deposits among nonmembers subject to different reserve ratios is also germane. 42 arrangement which places nonmember banks under different sets of re- serve requirements than member banks. Nonmember banks are subject to reserve requirements imposed by the state in which they are chartered. These state-imposed reserve requirements vary widely from state to state; Illinois has no reserve requirements at all, seven states impose reserve ratios that are the same as those of the Federal Reserve System. Table C—l in Appendix C is a listing of state reserve requirements as of May, 1977. In general state reserve requirements are quantitatively smaller than those of the Federal Reserve. In addition, there are a number of qualitative differences between state and Federal Reserve reserve requirements. First, while member banks must meet reserve requirements every week, nonmember banks in many states are required to meet their requirements much less frequently. In addition, different assets qual- ify as legal reserves for nonmember banks than for member banks. As can be seen in Table 0-1, at least part of required reserves can be satisfied with holdings of federal or state government securities in 26 states and by cash items in process of collection in 22 states. Non- member banks' voluntary holdings of vault cash qualify for required reserves in every state; the remainder of required reserves can in every state be held in the form of demand deposits in other commercial banks. In contrast, Federal Reserve reserve requirements require all member banks to hold their required reserves as vault cash or deposits at the Federal Reserve Bank. This means that nonmember banks' reserves can be held in a form that is at least useful to nonmember banks and often, a form.which is interest-bearing. Member banks, however, must hold their reserves in noninterest bearing assets. 43 These quantitative and qualitative differences between Federal Reserve and state reserve requirements have caused discussion and crit- icism on the grounds of equity. There is no doubt that Federal Reserve reserve requirements put member banks at a cost and competitive disad- vantage vis e vis nonmember banks. This is reflected in the diminish- ing proportion of the nation's commercial banks which choose to be mem- bers. The inequity caused by the existence of dual reserve require- ments in each state is not, however, an issue here. The important issue here is the control problem that may be caused by the qualitative differences between Federal Reserve and state re— serve requirements. The two assets in which member banks must hold their required reserves are, as can be seen in Appendix B, both base- absorbing. The level of member bank reserves is therefore limited by the size of the net source base and can be controlled by the Federal Reserve. Under the existing state reserve systems, nonmember banks are not specifically required to hold base money as reserves. Only the vault cash portion of nonmember bank reserves absorbs base money di- rectly. The part of nonmember bank reserves made up of interbank deposits may indirectly absorb base money as member banks reserves must be held against those interbank balances. This is one of the ways that nonmember banks affect the value of the r-ratio: by altering the level of interbank deposits in member banks and thereby affecting the level of member bank reserves. This will be discussed more in the section below on interbank deposits. As a whole, however, nonmember bank re- serves are not constrained or controlled as are member bank reserves. If bank reserves are defined as those that absorb money, most nonmember 44 bank reserves are actually reserves only in a legal sense; only the vault cash portion of nonmember bank reserves are base-absorbing. Nonmember bank "reserves" can be expressed as, 9 R = VCn + Dn + Dn , m n where R = nonmember bank "reserves;" VCn = nonmember bank vault cash; D; = demand deposits due nonmember banks from member banks;10 D: = demand deposits due nonmember banks from other nonmember banks. Both member and nonmember banks are required to hold reserves against net demand deposits, defined as total demand deposits minus cash items in process of collection and demand deposits due from other domestic commercial banks. Total nonmember bank "reserves" are then, R9 = z d (D - 1'"h - DP’h - Dn’h) + z t T , + ERP; h n,h n m r n,r h k where, Rn = nonmember bank "reserves;" the legally required reserve ratio against nonmember demand deposits in the hthstate;ll sP‘ ll 9Security reserve requirements are ignored throughout this anal- ysis, i.e., it is assumed that nonmember bank reserves are reduced by the amount of those reserves that can be held in securities. 10The notation Dx will be used to denote an interbank deposit that is the asset of bank y x and the liability of bank y. 11'When nonmember banks within one state are subject to differential reserve requirements, the expression for nonmember bank reserves will have to be fragmented further to account for the additional reserve categories. U 8 ll RR“ = Member bank 111 R: Rm= where, 45 the legally requirfid reserve ratio against nonmember time deposits in the k state; gross nonmember bank demand deposits in the hth state; gross nonmember bank time deposits in the kth state; - cash {gems in process of collection for nonmember banks in the h state; interbank balances due to nonmember banks in the hth state from all other nonmember banks in the nation; interbank balances due to nonmember banks in the hth state from all member banks in the nation; total nonmember bank "excess reserves." reserves may be express as, VCm + Fm, and 7. d.(D .- Im’J - 13“"J - Dm’J) + 2 t,T ,+ ER , . j m, m n . 1 m,1 J 1 member bank reserves; member bank vault cash; member bank deposits at Federal Reserve Banks; the legally required rese ve ratio against demand deposits for member banks in the j reserve category; the legally required reserge ratio against time deposits for member banks in the i reserve category; gross member bank demand deposits in the jth reserve category; gross member bank time deposits in the ith reserve category; c h items in process of collection for member banks in the j reserve category; interbank balances due to member banks subject to dj from all other member banks; 46 DE’J = interbank balances due to member banks subject to d. from all nonmember banks in the nation; J ERm = total member bank excess reserves. Using the expression DD j and DDn h for net demand deposits gives, (3—5) DD . = (D . - Im’J - Dm'J - Dm’J) for member banks, and m,j m,j m n = _ n,h _ n,h _ n,h . . (3-6) DDn,h (Dn,h I Dn m ) for nonmember banks. Substitution gives,- (3—7) vcm + Fm = ‘2: deDm j + EtiTm i + ERm for member banks, and j 9 i 9 (3-8) vc“+nn+bn=2d m n DDn + Et Tn + ERn for nonmember banks. h h Equation (3—7) shows how the net source base constrains the deposit expansion of member banks. Member bank net demand deposits, DD , can increase only as long as member banks can increase m,f! (VCm + Fm) by d (DD ). Since VCm + Fm are both uses of the net 3 111.3 source base, member banks can only increase their demand deposits if the monetary authorities allow the source base to increase, if banks are willing to reduce excess reserves, or if the public is induced to hold lower levels of currency or time deposits. Equation (3-8) however demonstrates that nonmember banks are not necessarily constrained in their expansion of the money supply by the monetary base because the quantity (VCn + D: + D2) is not entirely 47 base money. In the extreme case,12 if all privately-held demand de— posits were held in nonmember banks, the expansion of privately-held demand deposits would be constrained by the base if, and only if, non- member banks held all their reserves as vault cash or as deposits at member banks. In that case, when the entire base was absorbed by non- member bank vault cash or member bank reserves against interbank de— posits liabilities, privately-owned demand deposits (and the money stock) would be constrained. But since nonmember banks can hold re- serves in the form of interbank deposits at other nonmember banks, privately-held demand deposits at nonmember banks (and therefore the money stock) is not theoretically constrained at all by the size of the base. As can be seen by equation (3—8), nonmember banks can increase (DDn,h) to infinity by increasing (D2) infinitely. That is, nonmember banks can trade interbank deposits and using the (D2) as legal reserves, increase demand deposits forever. In reality, of course, this does not occur because the public has no such clear—cut preference for demand deposits at nonmember banks over demand deposits at member banks. As nonmember banks expand their deposits, there is leakage of deposits to member banks by the normal process of loss of deposits to other com— mercial banks. As this leakage of deposits to member banks occurs, privately-held demand deposits are constrained, because member banks are definitely constrained by the level of the base. Nonmember banks 12It is also possible that the level of privately-held demand de— posits would be constrained if all base money was absorbed into cur- rency in the hands of the public. That is, as nonmember banks expand demand deposits, the public will also increase their holdings of cur- rency (represented by the k-ratio discussed above). Once currency in the hands of the public grows to absorb all base money, demand deposit expansion would stop due to lack of demand. 48 are in effect then not constrained at all by legal reserve ratios, but only by the lack of demand for their deposits as opposed to member bank deposits and currency. It is for this reason that many authors have assumed the level of nonmember bank deposits to be some stable function of member bank deposits.13 This is the second way in which nonmember banks affect the r—ratio. Since nonmember banks are not required to hold base money in a fixed proportion to the demand deposits they issue, the higher the propor- tion of the nation's bank deposits that are in nonmember banks, the lower will be the value of r and the larger will be the value of m. More importantly, variation in the proportion of bank deposits held at nonmember banks causes variation in the value of r and therefore in m. (ii) Differential state reserve requirements: The third way that nonmember banks can affect the value of r is through the impact of differential state reserve requirements. Nonmember banks in different states are, of course, subject to different required reserve ratios. Therefore the level of nonmember bank "reserves" required behind a given level of nonmember bank deposits will depend on how those deposits are distributed among states.14 However, since not all nonmember "reserves" are base-absorbing reserves, the effect on r of the distribution of nonmember bank deposits among states cannot be translated with precision from its affect on nonmember "reserves." 13See for example, Ronald L. Teigen, "Demand and Supply Functions for Money in the United States: Some Structural Estimates," Econometrics XXXII (October l964):476-509. l4When nonmember banks within one stare are subject to differential reserve requirements, the distribution of nonmember deposits between those groups of banks is also pertinent to this discussion. 49 If nonmember deposits are concentrated in states with relatively high required reserve ratios, total nonmember "reserves" will be rela- tively high. Due to the nature of nonmember "reserves" however, it cannot be inferred that the value of r will increase, without knowl- edge of how the composition of nonmember "reserves" may change as their level grows. If, for all h, the group of nonmember banks subject to dh holds a constant and uniform ratio of vault cash of total de- posits, the distribution of nonmember bank deposits across state lines does not affect the aggregate level of VCn, reserves that absorb base, r, or m. On the other hand, if each group of nonmembers holds an amount of vault cash to keep the vault cash to required "reserves" ratio constant, the distribution of nonmember deposits across states affects the aggregate level of vault cash, reserves that absorb base money, r and m. In that case, if nonmember deposits are concentrated in states with high (low) d VCn will be high (low), r will be larger h’ (smaller), and m will be smaller (larger). The only other channel by which a change in nonmember "reserves" affects r is the indirect one mentioned above whereby nonmember inter— bank deposits in member banks affect the level of member bank reserves. If, because their required reserves change, nonmembers change the level of their deposits in member banks, member bank (base—absorbing) reserves will change, affecting the value of r. The conclusion then is the same as that for vault cash. If each group of nonmembers holds a uniform and constant ratio of deposits at member banks to total deposits, the dis- tribution of nonmember deposits among states has no effect on r. If each group of nonmembers holds a constant ratio of deposits at members of required "reserves, the distribution of nonmember deposits among 50 states affects r through its effects on member bank reserves against interbank deposit liabilities. (iii) Differential Federal Reserve reserve requirements: The amount of base money that members banks are required to hold per dollar of deposits is not the same for every bank or for every dollar of de- posits. The value of r therefore depends on how a given level of time and demand deposits are distributed among member banks in different reserve categories. More importantly, changes in the distribution of deposits across reserve categories induces changes in the value of r and thereby in the value of m. During the sample period under consideration in this study (1961— 1974), the number of different reserve categories for time and demand deposits has increased from three to nine. This can be seen in Table 0-2 of Appendix C. Until 1966, member banks were categorized as reserve city or country banks and the two classes were subject to dif- ferent required reserve ratios on demand deposits; all member banks were subject to the same single level reserve ratio on time and savings de- posits. In 1966,15 time and savings deposits were divided into three categories for reserve purposes: savings deposits, time deposits less than $5 million, and time deposits greater than $5 million. This in- creased the number of separate Federal Reserve reserve categories to five. In 1968,16 the number of member bank reserve categories was 15Board of Governors of the Federal Reserve System, Federal Reserve Bulletin (July 1966):979. 16ibid., (January l968):95-6. 51 increased to seven as demand deposits less than $5 million and demand deposits over $5 million at both reserve city and country banks were each subjected to a different legal reserve ratio. In November, 1972,17 the reserve city—country distinction was discarded for reserve purposes and a system of graduated reserve requirements was adopted in which required reserve ratios depend on the deposit-size of the bank. Five separate deposit-size groups were defined: less than $2 million, $2 million to $10 million, $10 million to $100 million, $100 million to $400 million, and over $400 million. Finally in 1974,18 the reserve category for time deposits over $5 million was divided into two reserve categories: time deposits maturing in 30 to 179 days and those matur- ing in 180 days or more. Thus by the end of the sample period, there were four separate reserve categories relating to time deposits and five relating to demand deposits. Given some level of member bank deposits, the level of base- absorbing reserves, and therefore the value of r, will vary with the distribution of those deposits among member banks subject to different required reserve ratios. Critics of the Federal Reserve's reserve structure therefore point to the increased number of reserve categories as a potential source of more variation in r. This increased "splinter- ing" of reserve requirements, in light of the Federal Reserve's appar- ent increased concern over their ability to control the money supply, seems contradictory. "Increased splintering of reserve requirements . . . 17ibid., (November 1972):994. 18ibid., (November l974):799-800. 52 tended to introduce greater variability in the reserve ratio, therefore making it more difficult for the Federal Reserve to predict the results of any policy action."19 (iv) Lagged Federal Reserve reserve requirements: Beginning September 18, 1968,20 the Federal Reserve introduced a system of lagged reserve requirements under which a member bank's required reserves are based on its average daily close-of—business deposit holdings two weeks earlier. At the same time all member banks were put on a weekly report- ing and reserve-settlement schedule. Under the lagged system, a mem— ber bank's reserves consist of its average daily close-of—business de- posits at the Federal Reserve in the current week plus its average daily close-of-business vault cash holdings two weeks earlier. In addi- tion, any excess or deficiency in required reserves may be "carried over" into the next settlement week to the amount of 2% of required reserves; no excess or deficiency may be carried over more than one week. Since the introduction of lagged reserve requirements, member banks, at time t, hold reserves based on DD and T but the money m,t-2 m,t-2’ supply existing in the system at time t, is based on current demand deposit levels. If DD . m,j,t-2 = DDm,j,t for all j, and T = T m,i,t-2 m,i,t for all i, the lag in member bank reserve requirements has no effect on the parameter r. If the ratios Tm,i,t-2/Tm,i,t and DDm,j,t-2/DDm,j,t 1'9Albert E. Burger, The Money Supply Process, p. 57. 20Board of Governors of the Federal Reserve System, Federal Reserve Bulletin (May 1968): 437-8. 53 vary for some i,j, lagged reserve requirements induce variation in r, m i . s nce R depends on DDm,j,t-2 and Tm,k,t-2 For example, if DDm,j,t-2/ DDm j t < l, for any j, r will be smaller and m will be larger than 9 9 would be possible without lagged reserve requirements. Apparently the rationale for instituting lagged reserve require— ments was to reduce uncertainty for member banks, provide the Federal Reserve with better information and reduce weekly reserve adjustment pressure. Whether or not lagged reserve requirements have actually served these goals is in question. As burger21 points out, the fact that the Federal Reserve has more accurate information on required reserves each week is obvious: since required reserves are based on deposit levels two weeks earlier, the Federal Reserve knows with pre— cision the level of required reserves well before each settlement date. They do not, however, know total reserves with any more accuracy; since reserve adjustment pressure is generated by the difference between re- quired and total reserves, there is no evidence that the Federal Re- serve is better equipped to ameliorate or exaggerate reserve adjustment pressure now than before lagged reserve requirements existed. Specif- ically, Burger finds that the Federal Reserve has had more difficulty estimating total reserves since lagged requirements were introduced. In addition, Burger finds that by three different measures, the amount of reserve adjustment experienced in the systemuhas actually increased since the advent of lagged reserve requirements. He therefore concludes, ". . . the evidence indicates that after lagging the Federal Reserve has 18Burger, pp. 55-6. 54 been less able to accurately determine the extent to which it should intervene in the money market to prevent short-term pressures."22 Burger raises other objections to lagged reserve requirements. Lagging procedures have created comparability problems in published bank data relating to reserves and excess reserves. The carry-over convention in itself has, by Burger's findings, introduced greater variation in excess reserves and the excess reserves-deposit ratio. Not only does this create problems with the data series, but more importantly increased variation in the excess reserve ratio introduces additional variation in m and the money supply process. Whether or not lagged reserve requirements have fulfilled their prescribed functions of reducing uncertainty and reserve adjustment pressure, there is no question that they have introduced an additional element of variation in r and therefore in the base-money supply rela- DD T tionship. "Because-—B%L£:g and _%§£;£ . . . do not remain constant, m,t m,t but exhibit considerable variability, an additional unpredictable source of variation is now included in the reserve ratio. Therefore to this extent the Federal Reserve . . . made the prediction of changes in the money stock more difficult."23 (v) Excess reserves: As an addition to bank reserves above those legally required, excess reserves absorb part of the net source base, without supporting or adding to any part of the money stock. Therefore the higher the level of excess reserves member banks choose to hold, the 22ibid., p. 56. 23ibid., p. 53. 55 larger the value of r, and the lower the value of m. Variation in the level of excess reserves causes r and therefore m to vary also. (vi) Government demand deposits: Banks are required to hold base— absorbing reserves against government deposits, but they are not included in the money stock. Therefore a higher level of government deposits means that more of the net source base is absorbed and less base money is left to support money stock items. An increase in the ratio of government demand deposits to privately-owned demand deposits therefore increases the value of r and decreases the value of m. (vii) The level and distribution of interbank deposits: Letting the superscripts p and g refer to privately-owned and government-owned deposits, respectively, and letting the notation D: refer to interbank deposits as defined above, gross demand deposits can be expressed as, (3-9) D , = Dp , + Dg , + D: . + D: j’ for member banks in the jth m’J m’J m’J ’3 ’ reserve category, and P 8 n m th .. = + (3 10) Dn,h Dn,h + Dn,h + Dn,h Dn,h’ for nonmember banks in the h state. Substituting equations (3-9) and (3-10) into the expressions for net demand deposits, equations (3—5) and (3—6) above, gives, _ = g __ maj m _ msj + n _ msj (3 11) DDm’j Di’j + ij I + (Dm’j Dm ) (Dm,j I)n ) for member banks; _. 3 P g _ n,h _ n _ n,h m _ n,h (3 12) DDn,h Dn,h + Dn,h I (Dn,h Dn ) + (Dn,h Dm ) for nonmember banks. 56 In the aggregate all interbank balances cancel out and total net demand deposits equal total privately-owned and government demand deposits, less cash items in process of collection. That is, 2(1):: . - 132:3) = 0, j : 2(D: h - Dg’h) = o, and h 9 n _ m,j + m _ n,h = §(Dm,j Dn ) §(Dn,h Dm ) 0' In general however, for each individual bank or for the group of banks subject to one required reserve ratio, (Dm _ m,j . m,j Dm ) ¥ 0 for all j, n (Dn,h n (”m,j - Dz’h) # for all h, and _ m,j m _ n,h , Dn ) + (Dn,h Dm ) ¥ 0 for all j,h. Therefore, an individual bank or group of banks subject to the same required reserve ratio may be required to hold reserves against inter- bank balances. For example, if (D: - Dg’j)>0 for some j, at least 9 j one bank subject to d. will be required to hold reserves against inter- bank deposits. Conversely, if (D: - DE’J)<0 for some j, then some 9 j bank's required reserves will be less than they would be without the presence of interbank deposits. Therefore, when commercial banks are subject to differential required reserve ratios, both the level of interbank deposits and their distribution among banks affect the value of r. The following numerical example illustrates this. For simplic- ity, the example deals with two member banks, but the results are generalized to include all commercial banks below. Assume banks A and B hold Dp (DS = 0 here) and interbank deposits owned by the other mem— ber bank as follows: EXAMPLE 1 m B Dm(DA) DD Case 1) No interbank deposits: Bank A $150. 0. 150. Case 2) Interbank deposits Allowed: Bank A $150. 100. 50. 200. Bank B Dp $300. Dm 0 m A B (DB - DA) 0 DDB 300. Bank B up $300. m A Dm(DB) 50. A B (DB - DA) -50. DDB 250. Case 3) Change in the distribution of interbank deposits: Bank A $150. 50. -50. 100. Bank B Dp $300. 02(03) 100. (of; - D2) 50. DDB 350. 58 Case 4) Change in the level of interbank deposits: Bank A Bank B DP $150. DP $300. m B m A Dm(DA) 75. Dm(DB) 150. B A A B (DA - DB) -75. (DB - DA) 75. DDA 75. DDB 375. Uniform 10% Reserve Graduated Reserve Reqpirement Requirements r = R/Dp r = R/Dp Case 1) $45/$450 = .1 $27.50/$450. = .061 Case 2) 45/450 = .1 25/450 = .056 Case 3) 45/450 = .1 30/450 = .067 Case 4) 45/450 = .l 31.25/450 = .069 Case 1 shows the system where there are no interbank deposits at all; Case 2 introduces $150 of interbank deposits; in case 3, the distri- bution of that $150 of interbank deposits has been changed and in Case 4, the level of interbank deposits has increased 50%. In all four cases, the money stock (=DP here) is $450. The member banks are assumed to be subject first to a uniform reserve requirement of 10%; secondly, to a graduated reserve requirement system in which 5% of the first $200 of deposits, and 10% of any additional deposits, must be held as legal reserves. Comparing the four cases, it can be seen that as long as member banks are subject to uniform reserve requirements, neither the level nor the distribution of D: affect the level of reserves relative to privately-owned demand deposits. As the chart shows, r is .l for all 59 four cases and therefore interbank deposits have no impact on the value of I. If member banks are subject to graduated reserve requirements as they are in reality, a change in either the distribution of D: (Case 3) or a change in the level of D: (Case 4) will alter the value of r. The reason that D: affect the value of r under graduated reserve require- ments is that their level and distribution alter the distribution of net demand deposits among banks that are subject to different required reserve ratios. This changes the level of reserves while Dp remains the same, so that the value of r varies. Comparing the four cases, it can be seen that as long as member banks are subject to uniform reserve requirements, neither the level nor the distribution of D: affect the level of reserves relative to privately-owned demand deposits. As the chart shows, r is .1 for all four cases and therefore interbank deposits have no impact on the value of m. If member banks are subject to graduated reserve require— ments as they are in reality, a change in either the distribution of D: (Case 3) or a change in the level of D: (Case 4) will alter the value of r. The reason that D: affect the value of r under gradu— ated reserve requirements is that their level and distribution alter the distribution of net demand deposits among banks that are subject to different required reserve ratios. This changes the level of re- serves while Dp remains the same, so that the value of r varies. The terms (D: - D:.j) for all j, measure the amount by which 3 net demand deposits are redistributed by D: among reserve categories. a , d j ,j D? for all j an no redistribution will occur. In that case, D: does not affect the value If (om - Dm’j) = o for all j, then DD m, m m of r. However, if (D: - Dz’j) # O for some j, net demand deposits 9 j 60 are redistributed from the group of banks for whom (D: . 9 - Dg’j)>0. This can be seen in the numerical example. With no D: present (Case 1), the distribution of net demand deposits between banks A and B is identical to the distribution of Dp. By com- parison, in the other three cases, the distribution of net demand de- posits between the two banks is altered by both the level and distribu- tion of D: and is no longer identical to the distribution of DP. When the deposits of the two banks are not subject to the same required reserve ratios, the change in the distribution of net demand deposits alters the level of required reserves while total DDm and Dp remain constant. Therefore the value of r is affected, causing variation in m. Whether r is increased or decreased by a change in D: depends on whether the resulting redistribution of net demand deposits is toward banks subject to larger or smaller required reserve ratios. If m (Dmsj (Case 3 or 4, compared to Case 1). If (D: 9 - Di’j)>0 for banks subject to relatively high d , r increases, 3 — DE’J)>0 for banks sub- :1 ject to relatively low dj’ the value of r falls (Case 2, compared to Case 1). The effects of interbank deposits are the same as those described above whether the banks involved are members or nonmembers or a com- bination of both, as long as they are subject to different required reserve ratios. The problem is dealing with nonmember "reserves" that are not necessarily reserves in the base—absorbing sense. When non- member banks are involved, determining the effect of interbank deposits on the distribution among banks of net demand deposits reveals only the levels of legally required reserves for the banks involved. 61 Just as in example 1, a change in the level or distribution of interbank deposits redistributes net demand deposits and, as long as the banks involved are subject to different required reserve ratios, alters the level of legally required reserves. The effect on base— absorbing reserves (and therefore on I) however, is indeterminate. When nonmember banks are involved, the crucial determinant of reserves that absorb base money is how nonmember banks apportion their reserves between vault cash and interbank deposits. The following numerical example illustrates. Assume bank A is a member bank and B a nonmember and first, that both banks are subject to a uniform reserve require- ment of 10% and secondly, that member banks are subject to a 15% required reserve ratio. EXAMPLE 2 The numerical information used in Example 2 is presented on the following two pages. 62 C E G E c E mm.eom an no.moa no me.moa an em.mom an .mHN an .me an E G C E E G G E E C Q 5 mos €9.58 mos- Asauee 3:7 accuse 33+ Assume .2 accuse .3: finance t E a E c . 8 .mm so eo.om so .mm so om.o~ so .mm so oH an .oon on .oon on .oomm on .oomm an .oomn ea .oomw an m some < some m some < some m some < some Ao an an Amm>ummou + cam u m xcmm .mmw u < xcmmv "voBOHHm muHmoaoo xcmnuoucH AN ommu c a II II II II .oom no .oom an I: II II II o as a a E snuenv o Aennaav : a I: II II II 0 Em C an -- -- l -- .83 as some as m xcmm < xcmm m xcmm < xcmm m xamm < xcmm .meo uH=m> :H Nm .muwmoaow mufimoamo some xcmoumuaa :H muwmoamm oamaoo xcmnuousfi cw :mo>uomou: uHJm> aw :mm>uomou: um: mo Nu vac: muonfiofidoz Au Ham vac: muonfimscoz An Haw mac: muonamecoz Am muamoaom JamQHOucH oz AH ommu N mqmzma oSu :H omcmsu Aw ammo Nw.Hmm .me Nw.Hm .mHI Nw.He .OH .oon .oomn «flow. am An Amo>uommu + mmm n m xcmm .on u < xcmmv ”muamoaov xcmououce mo sowuonwuumwo onu :« mwcmno Am ammo .owH .oml .om .oomm a some .mHN .mH .oomn < seem an 64 Uniform reserve requirements: 19% Value of r = R/Dp .3. 2.. a Case 1) $40/$400 = .10 -- -- Case 2) 40/400 = .10 $20.45/$400 = .051 $25.66/$400 = .064 Case 3) 40/400 = .10 23.18/400 = .058 27.90/400 = .070 Case 4) 40/400 = .10 19.09/400 = .048 24.95/400 = .062 Differential reserve requirements, member bank: 15%, nonmember bank: 10% Value of r = R/Dp 3.. _.b_ _9_ Case 1) $50/4OO = .125 -- -- Case 2) 49.25/400 = .123 $30.67/$400 = .077 $35.41/$4OO = .089 Case 3) 50.75/400 = .127 34.77/400 = .087 39.26/400 = .098 Case 4) 48.50/400 = .121 28.64/400 = .072 34.21/400 = .086 Cases 1 - 4 correspond to the cases described in example 1. In addition example 2 divides each case into three subcases each of which corres- ponds to a different composition of nonmember bank reserves. In sub- case a, it is assumed that nonmember banks hold all their legal reserves as vault cash; in subcases b nonmember banks hold all their "reserves" in interbank deposits and in subcases c, they hold 3% of their required reserves as vault cash and the remainder as interbank deposits. In subcases a, all of nonmember bank "reserves" absorb base money so they are qualitatively identical to member bank reserves. If, in addition, member and nonmember banks are subject to the same required reserve ratio, the presence of interbank deposits will merely redis- tribute net demand deposits among banks, leaving total reserves 65 unaltered. Neither the level nor distribution of interbank deposits therefore affects r. On the other hand, if the two banks are subject to different required reserve ratios, changes in either the distri— bution or level of interbank deposits causes variation in r like that caused by D: when member banks are subject to graduated reserve requirements (Example 1). If (D: - D:)>0, net demand deposits are redistributed toward the member bank, and reserves rise here, since the member bank is subject to the higher reserve requirement. In subcases b, nonmembers hold no base-absorbing reserves. There- fore regardless of the level or distribution of interbank deposits, reserves, and therefore r, are lower under reserve option b than any other. Nonmember bank "reserves" affect r only indirectly if by decid- ing to hold all "reserves" as interbank balances, D: is increased, forcing member banks to hold more reserves (Cases 2b, 2c, and 4b). Under reserve option c, reserves increase above their level under option b, because nonmembers now absorb some base money as vault cash. Under both reserve options b and c, the level of distribution of inter- bank deposits affect total reserves and therefore the value of r, whether the banks involved are subject to uniform or differential re— serve requirements. This is because "uniform" reserve requirements are uniform only in that they subject both banks to the same percentage required reserve ratio; they do not guarantee that all banks hold the same amount of base money per dollar of deposits as reserves. Therefore as long as members and nonmembers are subject to qualitatively differ- ent reserve requirements, not only will the level and distribution of interbank deposits affect r, their precise effect on r cannot be deter- mined without knowledge of how nonmembers apportion their required 66 reserves between vault cash and interbank balances. For example, assume deposit levels dictate that the system is represented by case 2-a and the distribution of interbank deposits changes such that it should move to case 3-a. The value of r would be expected to rise. But if non- members simultaneously choose to alter the composition of their required reserves, moving the system to case 3-b or 3—c, the value of r would fall, not rise. Therefore the predictable and determinable effects of a change in the level or distribution of interbank deposits can be com— pletely reversed by a change in nonmember banks' reserve policy. In summary, unless member and nonmember banks are subject to uni- form reserve requirements and nonmembers hold all their required re- serves as vault cash, the level and distribution of interbank balances somehow affect the value of r. Without knowledge of how a nonmember might alter its reserve composition in response to a change in the absolute or net level of its balances due to other banks, the effect of DE and D; on base-absorbing reserves and on r is indeterminate. The effects of D: on nonmember bank required reserves are compar— able to the effects of D: on member bank reserves. That is, if non- members are subject to different required reserve ratios and (D:,h - Dz’h) # 0 for some h, net demand deposits are redistributed and the level of nonmember bank "reserves" is altered accordingly. However, the effect that D: has on reserves that absorb money is again not determinable, without knowledge of the form in which nonmembers hold their reserves. If the level and distribution of D: are such that h their presence increases nonmember reserves (i.e., (D: - DE’ )>0 for ,h relatively large dn), it could be inferred that base-abosrbing reserves 67 would also rise (nonmembers' vault cash rise and D; rise, increasing members' reserves), but this cannot be determined with certainty or accuracy. Furthermore, since D: themselves act as their legal reserves, nonmembers could theoretically increase deposits infinitely and meet legal reserves with increased D: alone, with no need to absorb addi- tional base money. In that case, the value of r would approach zero and m would approach infinity. (viii) The level of time deposits: Since the reserve requirements on time deposits are uniformly lower than those on demand deposits, a dollar of time deposits absorbs less base money than a dollar of demand deposits. Therefore, if the money supply is defined to include time deposits, M2, a given level of source base can support a larger money stock the greater the proportion of bank deposits that are time de- posits. On the other hand, if money is defined narrowly, M1’ the pre- sence of time deposits in the system absorbs base money, while adding nothing to the money stock. Throughout this study, the money stock is defined to exclude time deposits, so the more time deposits there are in the system, the larger the value of r and the smaller m is. (ix) The level and distribution of cash items in process of col- lection: Both member and nonmember banks are allowed to deduct cash items in process of collection from gross demand deposits before fig- uring their reserve liabilities. Therefore the amount of such cash items in the bank system and their distribution among different reserve classes affect the value of r. With a given level of privately-owned demand deposits, a change in the level of cash items in process of 68 cellection or changes in their distribution between groups of banks sub- ject to different required reserve ratios will cause variation in the value of r. (x) The level of member bank nondeposit liabilities: Beginning in 1969, the Federal Reserve made various kinds of nondeposit sources of funds subject to reserve requirements. Specifically, the liability items involved are: liabilities arising out of Eurodollar transac- tions, large certificates of deposit, funds obtained through issuance of debt by affiliate ("bank-related commercial paper"), and funds raised through sales of finance bills (banker's acceptances that are ineligible for Federal Reserve discount). Liabilities arising out of Eurodollar transactions were originally subject to a 10 percent reserve requirement on October 16, 1969.24 The original imposition of reserve requirements exempted certain base amounts of Eurodollar-related liabilities from reserve-requirements computation. On June 21, 1973, the definition of this base amount was changed to the following: loans aggregating $100,000 or less to U. S. residents and total loans of a bank to U. S. residents if they do not exceed $1 million. Before June 21, 1973, certificates of deposits of $100,000 or more and funds obtained through issuance of bank-related commercial paper were subject to the reserve requirement on time deposits over $5 million. Beginning on that date, an 8 percent reserve requirement was imposed on increases in the two liability categories above the level of May 16, 24Board of Governors of the Federal Reserve System, Federal Reserve Bulletin (August l969):655-6. 69 1973 or $100 million, whichever is larger.25 On July 12, 1972,26 the marginal reserve requirement was extended to cover funds raised through sales of finance bills, which were previously subject to no reserve requirement. Beginning September 19, 1974,27 large certificates of deposit, bank-related commercial paper, and funds from the sales of finance bills were divided into two subcategories for reserve purposes: those of maturity length less than four months and those maturing in four months or more. The short—term maturity group continued to be subject to the 8 percent marginal reserve requirement, but the long- term category for all three types of liabilities were reverted to the original (5 percent) reserve requirement on time deposits greater than $5 million. The maturity distinction was retained until December 12, 1974,28 when all time deposits in excess of $5 million were divided into maturity-length subclasses. These structural changes, as well as changes in the required reserve ratios are detailed in Table C-2 in Appendix C. These four types of nondeposit liabilities (liabilities arising out of Eurodollar transactions, large certificates of deposit, bank- related commercial paper, and sales of finance bills) all represent additional reserve-absorbing liabilities that are not included in the money stock and therefore their level will affect the value of r. The 25ibid., (May l973):375-7. 26ibid., (July 1973):549. 27ibid., (September l974):680. 28ibid., (November 1974):799-800. 70 higher the level of nondeposit liabilities, the higher the value of r and therefore the lower the value of m. In addition, if the different categories of nondeposit liabilities are subject to different reserve ratios, the distribution of a given level of nondeposit liabilities among the various reserve categories will affect the value of r in the same way that differential reserve requirements for demand deposits affect the value of r. The Federal Reserve has for some time periods applied the same reserve ratios to different categories of nondeposit liabilities; this can be seen in Table C-2. The Model The parameter r can be expressed so that the impact of each of the factors discussed above can be seen explicitly. First the following sums are defined for period t: Gross member bank deman deposits in p g m n = + + + the j reserve Dm,j,t m,j,t Dm,j,t Dm,j,t Dm,j,t’ category: Gross member bank D = ED . demand deposits: m,t j m,j,t P 8 m n - + + Dm,t + Dm,t Dm,t Dm,t’ Net member bank m j m j m j deman deposits in DD . = D — I ’ — D ’ - D ’ the jgh reserve m,j,t m,j,t t m,t n,t cate o : m,j,t m,j,t t :jst m9t n m,j + (Dm,j,t I)n,t)’ Net member bank _ demand deposits: DDm,t - EDDm,j,t = p g _ m‘+ n _ hm Dmrj D , It (Dm,t n,t)’ Member bank time deposits in the i reserve category: Member bank time deposits: where j = l - 5, i = Gross nonmember bank demand t deposits in the h state: h Gross nonmember bank demand deposits: Member bank non— deposit liabilities in the qth reserve category: Nonmember”bank deposit liabilities: Net nonmember bank demand de osits in the ht state: Net nonmember bank demand deposits: Nonmember bank time deposits: 71 T = ET , ; m,t i m,i,t l - 4, for the current Federal Reserve reserve requirement system; P g n m = D + + , Dn,h,t n,h,t Dn,h,t Dn,h,t + Dn,h,t D = ED n,t h n,h,t =Dp +Dg +Dn +Dm, n,t n,t n,t n,t ND , m9q9t ND = END , m,t m,q,t q = _ n,h _ n,h _ n,h DDn,h,t Dn,h,t It Dn,t Dm,t p g n,h n n,h - + - + - Dn,h,t Dn,h,t It (Dn,h,t Dn,t) m n h + _ 9 (D ,h,t Dm,t)’ DDn,t = EDDn,h,t h p g n m n + — + — D Dn,t Dn, It (Dn,t m,t)’ = ET Tn,t k n,k,t’ where h = l - 100, k = l - 56, for the current state reserve requirement systems; Total gross demand deposits: Total net demand deposits: Total time deposits: Total gross deposits: Total net deposits: t m,t n,t =Dp+Dg+Dm +Dn +D“ +Dm t t m, m,t n,t n,t =Dp+Dg+le, t t t where le = Dm + Dn + Dn + Dm , t m,t m,t n,t ,t DD = DD + DD II U ”'13 + U HOG l H NTD = DD + T . t t t Using the definition of r and equations (3-7) and (3-8), rt can be expressed as, Ed DD + z T + En ND ER'n + vcn ij m,j,t-2 iti m,i,t-2 qrq m,q,t-2 - t t p Dt Ed DD + T + En ND j j m,j,t-2 iti m,i,t—2 q m t-2 D: D: Dp 73 Successively multiplying the numerator and denominator of each term by the same quantities yields, p 8 1b - DDm,j,t-2 DDm,jrt DDm,t DDt (Dt + Dt + Dt ) rt 7 zdj DD DD DD D j m,j,t mat t t D: + Et TmriLt-Z Tm,i,t Tm,t_3£ + En NDm,q,t-2 NDm,q,t NDm,t i 1 Tm,i,t Tm,t Tt D: q q NDm,q,t NDm,t D: m n,h + ERt TDm,t + VCt TDn,h,t TDn,t. TDm,t D: TDn,h,t TDn,t D: Substitution yields, D D D T T T - = + + + (3 l3) rt §djxj,t 6j,t vt €t(l yt 1t) itixi,t 61,t Vt It N N m n ing q,t 6q,t 0't + Etot + lph,tmh,tpt where. AD . DDm,j,t-2 AT _ Tm,i,t-2 AN NDm,g,t-2 o . "" 3 .- 9 j,t Dm,j,t i,t Tm,i,t q,t NDm,q,t 6D g DDm,j,t,6T = Tm,i,t, 5N _ NDm,q,t j,t DDm,t i,t Tm’t q,t ND ,t vD g DDm,t vT _ Tm,tz t DD ’ t T t t DDt E =‘fi-r t D8 “Y a: J— t Di ib I 8 74 T T =-—5 t Dp t ND 0, -41.; t Dp t ER:1 E = t TDm,t TD TD m _ at n 21: p "" 9 p t p t p D D t t VCn,h w = t h,t TDn,h,t = TDn,h,t “h,t TD ' n,t The contribution the the size, variability and predictability of rt of each of the factors discussed earlier can be seen explicitly in equation (3-13). The terms in equation (3-13) account for the follow- ing factors: at : level of excess reserves; Y : level of government demand deposits; 1 : level of interbank deposits; a : level of nondeposit liabilities; t It : level of time deposits; 6D , GT and 6N : distribution of member bank deposits i,t i,t’ q,t and nondeposit liabilities among reserve categories; 75 period-to-period changes in the level or distribution among reserve categories of member bank deposits and nondeposit liabilities; vD, and VT : the proportion of bank deposits held in t t member banks; T : nonmember bank holdings of vault caslgFl relative to total deposits, in the h state; wh : the distribution of nonmember bank ,t deposits among states. There are two factors that affect the value and variability of r that are not specifically accounted for in equation (3-13), though they were discussed in the preceding text. They are: the distribu- tional effect of interbank deposits and the effect of the level and distribution of cash items in process of collection. They are not explicitly included in equation (3-13) because the data needed to test and isolate their impact on rt are not available. CHAPTER 4 BEHAVIOR OF THE PARAMETERS OF rt Data, Definitions, and Assumptions The structure of Federal Reserve reserve requirements was changed several times during the sample period. At the beginning of the sample period member banks were categorized as city and country banks, based on their geographical location; so there were initially two demand de— posit reserve categories, and the same required reserve ration was applied to all time and savings deposits. This system of three cate- gories of member bank deposits was in effect until July 14, 1966,1 when three different reserve ratios were applied to savings deposits and to time deposits less than and greater than $5 million. Disaggregated data for savings deposits and time deposits are however available only beginning September 7, 1966; they are available for time deposits less than and greater than $5 million only beginning January 11, 1968. Beginning January 11, 1968,2 city and country bank demand deposits, were subdivided into two size categories, less than $5 million and greater than $5 million. This change resulted in four demand deposit reserve categories and three categories of savings and time deposits. On November 9, 1972,3 a graduated reserve requirement system.was adopted for demand deposits; this scheme defined five categories of demand 1Board of Governors of the Federal Reserve System, Federal Reserve Bulletin (July 1966):979. 2ibid., (January l968):95-6. 3ibid., (November 1972):994. 76 77 deposits based on bank size and eliminated the old city—country distinc- tion. Finally, on December 12, 1974,4 time deposits greater than $5 million were divided into two subcategories based on maturity length, those maturing in thirty to 179 days and those maturing in more than 179 days. In addition a number of kinds of nondeposit liabilities were subjected to reserve requirements during the sample period; these changes are described below in the section on nondeposit liabilities. On September 18, 1968,5 a number of the administrative rules gov— erning the calculation of required reserves were changed. Beginning on that date, all member banks were placed on a weekly reserve settle- ment system under which required reserves are based each Wednesday on a weekly average of daily close-of—business deposit levels, two weeks earlier. Before that date, not all member banks were on a weekly settlement basis and required reserves were based on contemporaneous opening—of—business deposit levels. Required reserves against demand deposits are based on net demand deposits (DDt above), defined to be total demand deposits less cash items in process of collection and de- mand deposits due from other domestic commercial banks. At the same time that lagged reserve requirements were instituted a procedure known as reserve carryover was also introduced. Under reserve carryover, a reserve excess or deficiency, up to 2 percent of required reserves, may be carried ahead to the next reserve computation week. This causes excess reserves to be negative for some weeks after 1968. 4ibid., (November l974):799-800. 5ibid., (May l968):437—8. 78 With a few exceptions noted below, the data used in this study are weekly averages of daily figures (Thursday through Wednesday) for the period January 1, 1961 through December 31, 1974. Until September, 1968, the data are "opening of business" figures, and "close of busi- ness" figures thereafter; this reflects the change in the definition of deposits used to calculate required reserves. For nonmember banks, the only actual data collected are call report data which occur every June 30 and December 31.6 The Federal Reserve's weekly estimates of nonmember bank deposits are used whenever possible in this study. The Federal Reserve makes weekly estimates of three portions of non- member bank deposits: time deposits, government demand deposits, and "adjusted demand deposits." "Adjusted demand deposits" is the demand- deposit component of the money stock, designated as D: above. Initially these estimates are based on the deposits of a sample of country member banks. When call report data become available, the weekly estimates are benchmarked to these actual deposit figures.7 The changes in ad- justed demand deposits resulting from the benchmark procedure have been substantial in recent years.8 Since the information from call reports 6For part of the sample period, data from call reports for March 31 and September 30 are also available. 7The benchmarking procedure currently followed for adjusted demand deposits consists of calculating from each call report, the ratio R, where R 8 nonmember bank adjusted demand deposits/country bank adjusted demand deposits. The difference between the actual value of R and its estimated value is then distributed over the 26—week period ending at the call report date. 8Darwin Beck and Joseph Sedransk, "Revision of the Money Stock Measures and Member Bank Reserves and Deposits," Federal Reserve Bulle— tin (February l974):81-89. 79 is single-day data, and it is commonly conceded that call report data contain substantial aberrations, the benchmark process may introduce, rather than remove, errors into the nonmember deposit series. Not only is the actual weekly value of nonmember bank deposits never known, given the deficiencies of call report data, there are no reliable fig— ures available to judge the accuracy of the estimates.9 It is there— fore very difficult to assess the direction and extent of errors in the estimation and benchmarking procedures. The nonmember bank portion of D: in the denominator of Yt’ L , and t Tt is an estimate; the nonmember bank parts of time and savings deposits (Tt)’ included in the numerator of Tt and the denominator of v: is an estimate, as is the nonmember bank part of the numerator of Yt' In addition, not all of the components of nonmember bank deposits needed to calculate the parameters listed above are estimated. D . The parameters Yt’ 5t, and 1 require measures of commerc1al bank 1: deposits for which the nonmember bank portion is not available, except for call report dates. The nonmember bank part of net demand deposits (DDt)’ gross demand deposits (Dt) and interbank deposits (Dib) are not known or estimated on a weekly basis. These nonmember bank data have been partially constructed by using the definitions given below. 9There is daily deposit data available for a sample of insured commercial banks which was collected by the F.D.I.C. for the Advisory Committee on Monetary Statistics (The "Bach Committee"). The data cover the period from fall, 1974, through spring, 1975. Based on this experience, it appears that revisions in money stock figures could be reduced substantially if the Federal Reserve had better and more frequent information on nonmember bank deposits. The Bach Commit- tee therefore recommended several improvements in the data-collection procedures for nonmember banks. See, Advisory Committee on Monetary Statistics, Irproving the Monetary Aggregates (Washington, D.C.: Board of Governors of the Federal Reserve System, 1976). 80 (4-1) Net demand deposits = Gross demand deposits - demand deposits due from other domestic com- mercial banks - cash items in pro- cess of collection; (4-2) Adjusted demand deposits Gross demand deposits — demand deposits due to other domestic com- mercial banks — cash items in pro- cess of collection - government demand deposits - Federal Reserve float. Federal Reserve float is ignored here because it is quantitatively small. Rearranging the terms in definition (4-2) gives the following expression for gross demand deposits: (4-3) Dt = Adjusted demand deposits + demand deposits due to other domestic commercial banks + cash items in process of col- lection + government demand deposits. Subtracting the definition of adjusted demand deposits from that of net demand deposits and rearranging terms gives the result that net demand deposits is: (4-4) DDt = Adjusted demand deposits - demand deposits due from other domestic commercial banks + demand deposits due to other domestic commercial banks + government demand deposits. Since not all of the items involved in the definitions of net and gross demand deposits are available for nonmember banks, the nonmember bank portions of both net and gross demand deposits are approximated by nonmember bank adjusted demand deposits plus government demand de- posits. As can be seen from expression (4—3), this measure of gross demand deposits is less than actual gross demand deposits by the amount of nonmember bank demand deposits due to other domestic commercial banks and nonmember bank cash items in process of collection. As expression (4—4) shows, the figures used here for net demand deposits are greater than actual net demand deposits by the net amount of non- member bank demand deposits due to other domestic commercial banks less 81 those due from other domestic commercial banks. In addition, since no weekly data are available on nonmember bank holdings of interbank deposits, total commercial bank interbank deposits are not known. The deficiencies in the data affect two of the parameters that com- prise rt: v2 and It 10 Both 02 and It were calculated in two ways. First, v: and It were calculated using call report data for the missing nonmember bank interbank deposits figures. The weekly calculations of D . Vt and 1t then include the most recent quarterly or semiannual nonmember bank interbank deposit data. Second, 02 and It were recalculated leav- ing out the unavailable nonmember bank components of net and gross de- mand deposits and interbank deposits. The estimated denominator of v: is therefore larger and the estimated numerator of It is smaller here D than the actual values. These alternative calculations of vt and 1t s s are denoted V2 and It'll In addition, the ratio of nonmember bank vault cash to total de- posits for each state, w , and the proportion of total nonmember bank h,t deposits in each state, ah t’ must be calculated using call report data. 9 10The value of E is also affected but since 5 has no particular economic meaning, the misspecification of the data has no real consequence. An alternative definition of ED, 5:, may be defined that is analogous to v2* and It. 11It is, of course, the variation in vD and 1 rather than their levels that is most important. If the missing components of the data cause any problem it is not the problem of altering the size of VD and 1 but of masking some of their variation. But since the size of the missing components are small relative to their totals, the effects of the deficiencies in the data are probably not very important. The shortcoming of using call report data to calculate VD and 1 is that by adding the same call report figures into consecutive weekly obser- vations, some of the actual variation in the parameters may be smoothed out. Again, since the components for which call report data are used are small relative to the totals, the effects are probably minor. 82 Call report data are the only source of nonmember bank data, distrib— uted by state. Lagged Reserve Requirements The effect on rt of lagged Federal Reserve reserve requirements is D i,t one means that deposit levels in period (t-2) are larger than those in T and Xi t 9 reflected by the parameters A A value of It greater than period t; member bank required reserves relative to current deposit levels are therefore higher than legal reserve ratios. Therefore, the value of rt is larger than if the At parameters were equal to one. If the value of At is less than one, member bank required reserves rela- tive to current deposit levels are lower than legal reserve ratios and the value of rt is smaller. More importantly, variation in the value of the At parameters above and below one introduces variation in rt. a) Demand Deposits Lagged reserve requirements were introduced on September 18, 1968, but values of the A-parameters have been calculated for the entire sample period. Table 1 gives statistics for the parameters, A§,t' The first part of Table l is based on the entire sample period and gives D and 1D 1 t 2 ts referring to demand deposits in city banks 9 9 results for l and demand deposits in country banks, respectively. The second part of Table 1 is based on the subperiod 1968 - 1974. Part 2A refers to the second reserve requirement scheme for demand deposits and part 2B refers to the graduated reserve requirement scheme. As can be seen in the first column of Table l, the mean of all but one AD-parameter is less than one, indicating the overall growth in deposits in each reserve category during the sample period. Columns 2 83 «memo. Hmooo. wwaoo. Nawom. A u. Nev soaaaaa an soap Houmoew .mxsmm anucsoo u eemoo. oabao. aoooo. omens. A mAV aoaaaaa mm Amman mama .mxamm .CuESU moons. mamas. Amoco. momma. A oAv soaaaaa an amao HWummuw .mxamm auwo ammoo. mmqao. maooo. maooo.a A Dav aoHHHfia mm :mnu mama .mxamm xuau mufimonon menace AchHum>uomoo womV aAAm~\~Humo\HH\H .ooanoe oaeaom .N u. mmmao. ommao. Hoaoo. ommaa. A MAW.Hnaanm aoonaoo omm~o. emaoo. wmcoo. «mama. A aAv mason Aoau mnemoamn nausea Amaowum>uomno ommv eaoanaooa .ooanoe oameom .A cowumfium> No.H Eoum Ho.H Eoum coo: mo aowuma>mo soaumfi>oo uaofiofimmooo umowpmq mwmuo>< as :3 r A . o>ummom Hmuoomm oomwmg .H oaomfi mx mumuoEmumm ocu mo osam>v muHmoama onmfima .mucmEoufisvom o>uomom .umwuma we Ho>onuas3 ._ooam> Esaacae I o.H_ no _m=Hm> Eaaqua I o.H_ same I o.H 84 H . . . . o.HH cameo aoema mHHoo mamas A oAV soaaaas ooam span a. OH Houmouw .mnam ufimoaoa obese. mambo. emooo. booms. A oAV aoaaaaa coon scam . _, Aom a .onam uamoeon maAHo. Amwao. mNAoo. names. nAV soaaaas ooamuoam o. w .onam oamoeoo Noses. AoAmo. assoc. mamas. A V eoaaaas osmumm o. A .onam osmoeon Aaaoo. mmeoo. eoooo. oaooa. A AV aoaaaas Na coco mama .oNHm uwmomon moamoeon nomads .m coaumwum> No.H Eoum Ho.H Scum com: mo coaumw>oa cowumfi>oo ucmwoawmooo umomumq owmuo>< ooaaaoeoo .H oases 85 and 3 of Table 1 give measures of the deviation of the AD-parameters from their neutral value of one. Column 2 gives the absolute value of the difference between one and the mean; column 3 gives the largest deviation from one. The last column gives the coefficient of varia— tion of each lD-parameter. While none of these measures of variation in the AD-parameters is large on an absolute scale, they are also not zero, indicating that lagged reserve requirements do introduce variation in rt that would otherwise not be present. As would be expected, the reserve categories corresponding to larger deposit levels show more variation: city banks under the first scheme; both categories of demand deposits greater than~ $5 million under the second scheme; and the larger the deposit cate- gory, the larger the variation under the graduated scheme. Table 2 shows statistics for the first differences of each 1D- parameter. The first two columns of Table 2 show the mean of (1D — i,t D D1 D Aj,t-l) and 'Aj,t - Aj,t-l' for all j. Column 3 is the standard devi- ation of the first differences of each A? t and the last column shows 9 D i,t The mean of the first differences of A? t is small for all j. The D _AD jat jst-l the largest weekly change in A for all j. mean of IA 1 is much larger for all j, indicating that each I? t fluctuates considerably from week to week, producing successively 9 D ID j t - j t-l) which cancel each other 9 9 positive and negative values of (1 out. D _ AD jst jat-l an absolute scale; they are, however, slightly larger than the standard deviation of A? t for all j, indicating that the values of A? t deviate 9 9 considerably from week to week. The largest weekly changes are also The standard deviations of (A ) are also not large on 86 moooo.I Au me coaaaaa mm can» «Hone. oomNo. NHHNO. umMummuw .mxcmm muucnoo oooao. mamoo. qnqoo. ooooo. A DAV QOHHHHE mm amnu moo .mxsmm anussou u.e H momao. «ammo. ammmo. ooooo.I A 94V :OHHHHE mm amnu uwumoum .mxamm Aufio Homes. Ammoo. assoc. ooooo. A AV soaaaaa mm amnu mama .mxamm mufio mufimoeon vsmaon .< aA\mN\NHIw6\HH\H deoauoe cannon .N a mnemo. Nomao. Hmmao. aoooo.- Au MAV o.H.meamm eucaoo maomo. qumo. eamao. ooooo. A QAV oxamm Aufio mnemonon panama .< Amcowum>uomno mmmv eAaHIHcmH dooaooe oaeamm .H mwcmnu sowumfi>mn osam> amp: Haaxowz oummcmum ounaomo< umowumq mo use: a.” AHH.H n h . ox .muouoamumm osu mo moucmuowwan umuwmv muamoaon panama .muaoEouasqu o>ummom m>ummom Hmuowom common .N manna 87 “in Aa u ma aaV mo msam> musaomnm ummwumaa msoea. oaoao. acamo. oaooc.- Ao H“AV aoaaaaa comm ones umummuw .mnam uamommn bombs. mAAHo. mamas. aoooo.- Ao OWAV soaaaaa ooemIooamu.mmmam uamoemo oo~mo. emwao. owmao. Noooo.- A eAV soaaaas ooamIoamu.wmuam uamommn cccmo. cameo. amoao. Hocoo.u A aAV aoaaaas o.AoamI~m onam canoeon memos. Anaoo. aqaoo. ooooo. A 94V :oaaaaa mm amen mmma .mnam uamoema muamoemn vamamn .m wwcmeu coauma>mn msam> ammz amaxmmz vumocmum munaomnm ummwuma mo cmmz eoaaaoaoo .N manna 88 not large, but they are much larger than the average weekly changes in ; apparently most week-to-week changes in A? are small, but there 9 lg’t have occasionally been large weekly jumps in 1?,t. The last two col- umns of Table 2 again show the tendency for the AD-parameters corres- ponding to larger deposit levels to exhibit more variation and larger weekly changes. Table 3 gives annual figures for the lD—parameters which show that their variation has increased during the sample period. The stand- ard deviations of AI,t and Ag’t have increased quite steadily, especi- ally since 1965. Annual figures for the other nine AD-parameters also indicate more variation in the latter years of the sample period; this trend is more pronounced in the reserve categories corresponding to larger deposit levels. The increased variation in Ag’t implies that the rate of growth (or decline) of deposits in the jth reserve category has increased during the sample period. b) Time Deposits Table 4 presents figures 1: , i = l, 5. The first part of Table 9 t 4 has statistics for A: t’ referring to total time and savings deposits 9 for the entire sample period. Part 2 is based on the subperiod begin- T T 2,t and A3,t ring to time and savings deposits, respectively. This was the only part ning September 9, 1966 and contains statistics for 1 , refer- of the sample period for which separate data were available for time de- posits and savings deposits. Further disaggregation of time deposits was available only after January, 1968, as indicated in Part 3 of Table 4. The division of time deposits by maturity length is only appropriate (and the data only available) after December 12, 1974. 89 oncoo. mmaoo. waooo.a oflmqo. mmamo. woooo.a moomo. waamc. aeooo.a qnma mmmoo. aowoo. Noooo.a cenqc. «ammo. awwmm. Anamo. mmoNo. waooo.a muma wqmoo. Acaoo. onmmm. mammo. mammo. «comm. Naono. omoao. Nmnmm. Numa ammoo. mmaoo. moooo.a wmmeo. aommo. mmmmm. mmwno. «Awao. mmwmm. amma mmooo. mmmoo. mmooo.a cacao. mammo. mmwmm. commo. monao. komm. ohma wmmoo. mwaoo. Noooo.a ammqo. mwomo. oummm. Nmvo. mmoao. Anwmm. 1Nmoma mmqao. omqoo. omooo.a mammo. mammo. amomm. Amaoo. Amqao. anmm. nwoma commo. wmmmo. mcnmm. Acamo. mmeao. wnnmm. mama mANNo. meewo. mmmmm. moaoo. momao. ooooo.a coma aommo. mwNNo. cmnmm. ooomo. qoaao. wommm. mama mmnmo. mmmao. omwmm. omqqo. Amaao. mommm. qeoma «Ammo. mmomo. cawmm. cmmmo. wnaao. maooo.a mcma mwmao. NoAao. mqwmm. «memo. aooao. «coco.a Noma mmmao. omoao. wmwmm. ommqo. owwoo. commm. aoma mo.a Scum coauma>mn cam: mgg mo.a a? coauma>mm mumvamum aoauma>mn mumwamum coauma>mn cummamum ummwuma ummwuma ummwuma To; Naa a n ma you mmuswam aamsca< .m manme 90 Aaw«o. w«o~o. m«ooo.a mommo. mamao. 0aooo.a ma«oo. mmaoo. mmmmm. «Ama a~N«o. mNmao. nmmmm. a«mmo. amuao. Aanmm. mmmoo. Naaoo. ~«mmm. mnma «a«mo. wnmao. oaamm. mmamo. «muao. mmnmm. mo«oo. mAaoo. mammm. NAma «wm«o. «NAao. anmmm. mammo. wNmao. mowmm. aamoo. omaoo. wwmmm. anma owm«o. maaao. aammm. mNaNo. NwNao. «mmmm. mm«oo. aomoo. amooo.a onma mmm«o. «Anao. mmmmm. aaomo. Naoao. ammmm. w«moo. onaoo. omooo.a «mama mammo. «w«ao. mmwmm. mmoNo. mmwoo. oommm. aa«oo. oAaoo. ammmm. maama o.mA o.MA - o.MA amaao. o«w~o. aoaoo.a Amoao. ammoo. mmmmm. a«amo. mmamo. a«ooo.a «Ama momao. aanmo. Nommm. oomao. amaoo. aammm. mammo. emnmo. waooo.a mmma Naa«o. mmmmo. «Ammm. mamao. Namoo. owmmm. omano. o««~o. ammmm. NAma Nmaao. aammo. «mamm. amaao. aNaoo. Nammm. Namno. mammo. amwmm. amma anmao. mA«~o. wmwmm. owmao. maaoo. maooo.a mammo. a«a~o. mawmm. oAma aoaao. mo«No. «ommm. ammoo. ma«oo. awmmm. mmaAo. wmamo. mmamm. «mama am«mo. maamo. mmamm. «Naoo. «~«oo. «ommm. aomao. «m«~o. «mamm. mmama a. mo.a scum coauma>ma cam: mo.a Eoum coauma>mn com: mo.a scum soauma>mn cum: coaDMa>mQ aumaamum soauma>mo unmasmum soauma>mn aumvsmum ummwuma ummmuma ummwuma eoaaaooou ..m canoe 91 .mcoaum>ummoo an no ammmmm « .umwuma ma um>m£oa53.émsam> anacaE I o.a_uo_m=am> Esaaxma.IOnaam .maoaum>ummno mm so ammmm .soaaaaa oo«m amen umummum muamomma aamama n aa macaaaaa oo«m cmcu mmma mam coaaaae 00am amzu umummuw muamomma asmama u oa “aoaaaaa 00am amnu mmma was ceaaaae cam amen umummuw muamoama aamama u m “coaaaaa cam cmcu mmma mam coaaaaa um cmnu umummuw muamoama acmEma u m “coaaaae mm amen mmma muamoama acmfima u A mmxcmn muussou ca coaaaaa mm cmcu Hmummuw muamomma acmEma u a mmxcmn muuaooo ca coaaaas aw cmcu mmma muamomma acmama u m mmxcmn muao ca coaaaaa mm cmeu umummuw muamoama acmEma u « “magma muau ca coaaaae mm amnu mmma muamomma acmama u m ”magma muucsoo n N mmxcmn muau u a "mmauowmumo uamoama acmama waa3oaaom mnu cu mumamu h unauomasm msH N .amumoaaCa mmaspmnuo mmmaa: ummm uma mcoaum>ummno Na no ammmma amoma. «mamo. maooo.a mmaao. maNNo. amaoo.a «Ama «o«ma. oam«o. maooo.a mamao. awamo. amooo.a mnma am«ma. m«o«o. mmnmm. nam«o. sumac. amnmm. Numa wmANa. amm«o. Nawmm. mmomc. nomao. mowmm. anma mmomo. «am«o. «Ammm. omm«o. ammao. aoamm. oAma waoma. oan«o. Nowmm. ana«o. wNwao. mmmmm. «mama mmooa. Nmm«o. ommmm. maw«o. Nmnao. aawmm. maama o. o. awa oma mo.a Eoum coauma>ma ammz mo.a Eoum coauma>ma cum: mo.a Eoua soauma>mn com: coauma>mo aumaamum coauma>mn aumacmum coauma>mo aumacmum ummwuma ummwuma ummwuma ooaeaoaou .m oases .«A\mN\NaI«A\Na\Na .aoaumm man now mcoaum>ummno 03u mmasausa 92 a .umummuw ma pm>mnoa53 ._m:am> E:Eaaae I o.a_ no _m=am> asaaxms I o.a_N ammE I o.aa amooo. emaao. caaao. aamma. amaoo aaa amnu muoa mo mmauauaumz mamas. mamas. Hammo. aAHAa. memos aaauoaomm noaoasasoz acoao. mamas. Amoco. aaaaa. A AV soaaaaa am cmcu umummu .muamommn mEaH Amoco. assoc. eaooo. momma. ammoo mAA cmnu muoa mo mmauHHSumz mmaoo. oAaoo. Amoco. mmmaa. moans mAanaomm noaaasaomz cmaoo. omaao. mamoo. momma. A H.VAV soaaaaa ma cmnu mmma .muamoamo maaa Amaoaum>ummao «any aAAa~\~a.mo\HH\H .ooauom panama .a u. assoc. eamao. aaaoo. Aomma. A MAVD.Nnoanomoo nwaapom mmaoo. Aameo. macoo. Amaam. A HAV moanomon osam Amaoaum>ummao «m«V aAAaN\~HIoc\A\a .ooauom daemon .N m ameoo. Aaoao. eceoo. omama. Au WAV moanoeoa mea>mm cam maae amuoa Amcoaum>ummoo ommv eaaauaoma .ooauom panama .A coaumaum> No.a Scum ao.a Eoua cmmz mo coauma>mn coauMa>mQ ucmauaaamou ummwuma mwmum>< Am.a n a .u.ma .mumumamumm ma» mo mmaam>v muamoamn mEaH .musmfimuasmmm m>ummmm m>ummmm amumamm amwwma .« maomH 93 The results for A; t are similar to those for A? t' The means 9 9 of A: t are less than one, indicating the overall growth in all cat— 9 egories of time deposits during the sample period. Neither the coeffi- cient of variation nor the measures of deviation from one are large on an absolute scale; on the other hand, they are not zero either. Like those for Ag’t the coefficients of variation for Ai,t are in general larger for larger deposit-size categories. That is, the variation in time deposits (A§,t) is much larger than that in savings deposits (Ag’t) and the AT-parameter for time deposits greater than $5 million is much larger than that for time deposits less than $5 million. The excep- tion to this pattern is the coefficient of variation for total time and . savings deposits, AI,t’ which is relatively low. D T j,t’ the variation in Al,t coefficient of variation (A; t) is less than all but three of those for In comparison to A is small; the largest A? t’ and those three correspond to the smallest demand deposit reserve 9 categories. The largest weekly deviations from one for A: t are also 9 in general smaller than those for A? t except for the smallest cate- 9 gories of demand deposits. The average weekly deviations from one are T than for most A? ; this is because the means of AT larger for A1,t j,t i,t are in general smaller, reflecting the more rapid rate of growth in time deposits. Table 5 presents statistics on the first differences of the AT- parameters. Like the AD-parameters, the mean of the first differences of Ai,t is small for all 1. Again the means of the absolute value of the first differences are much larger than the means of the first dif- ferences, reflecting sizable weekly fluctuation in the AI-parameters. 93 m m .AaIu Ha I D May mo msam> muoaomnm ummwumAa u.m Haemo. memoo. momma. ooooo.I A sAV aoaaaas mm coco umummuw o.a .moamoeoo ease oAHoo. oaaoo. vooo. ooooo. A HAV soaaaaa am amen mmma .muamoemn maae Amcoaum>ummoo mama aA\a~\~H.mc\aa\a mooasom panama .a m mm«ao.I ommoo. NNNoo. ooooo. Au MaVu.Nmuamoamn mmca>mm ANw«o. ammoo. owmoo. moooo.I A Hay muamommo mEaH Amcoaum>ummno mm«v eA\mN\~aIcc\A\a .ooaaom panama .N m maaao. cANoo. oomoo. Noooo.u Au MAV moamomon mmaaemm mam mBaH amuoe Amaoaum>ummno mmmv aeaauaomaIdooasom damaum .H mwdmno coauma>mn maam> com: amaxmmz cumaCMum musaomo< ummwuma mo :mmz Am.a u m a u WA .mumumemumm mnu mo mmocmumaman umuamv muamommn mEaH .mucmamuasmmm m>ummmm m>ummmm amumamm amwwma .a oases 94 The standard deviations and largest weekly values for (A: t - A: t-l 9 9 T i,t again show greater variation. ) are all small; the A corresponding to larger deposit categories The results for the first differences of the AT-parameters again imply that they vary less and may therefore be more predictable than the AD—parameters. The means of the absolute value of the first dif— ferences and the largest weekly changes are all larger for the AD- parameters than for the AT-parameters, except for the smallest demand- deposit categories. The standard deviations of the first differences T T D 3180 show that (Ai,t Ai,t—l) in general vary less than do (Aj’t - D Aant-1" T Annual figures for A show no important secular trends that can i,t be identified by simple observation. The only discernible pattern is in the AT-parameter for time deposits less than $5 million; the stand- ard deviation of Az,t declines during the sample period. Since a decrease in the variation of a A—parameter indicates a fall in the rate of deposit growth (or decline), the drop in the variation of Az’t occurs because most of the possible growth of deposits in that category is achieved by 1968. After 1968, the increasing stability of Az,t reflects the overall slow-down in the growth of that deposit category. Varia- bility in the other AT-parameters also show changes over time but those patterns are probably traceable to changes in Regulation Q interest rate ceilings and market interest rates; these influences are difficult to isolate by observation and will therefore be dealt with in Chapter 6. The AT—parameters corresponding to the larger deposit-level categories tend to vary more at the end of the sample period, but this may well be 95 due to the effects of interest rates. Annual figures for A: t are 9 reported in Table D-l of Appendix D. Differential Reserve Reqpirements The effect on rt of differential Federal Reserve reserve require- ments is summarized in the parameters 6? t and 6? t' The parameters 9 9 6? t and 6: t represent the proportion of member bank demand and time 9 9 deposits in the jth and ith reserve category, respectively. If the distribution of member bank deposits shifts in favor of banks or deposit categories subject to relatively high (low) legal reserve ratios, the value of rt will rise (fall). More importantly, variation in the distribution of deposits, represented by variation in the 6-parameters, will induce variation in rt. a) Demand Deposits Table 6 gives the results for 6? t' Neither the standard deviation 9 nor the coefficient of variation of 6? t for any j are large on an ab- 9 solute scale. The coefficient of variation of 6D is in general larger i,t than that for A? for all j, except for 6D There is a tendency 9t 11,t. for the standard deviation of 6? t to increase as the size of the jt 9 reserve category increases, although the relationship is not as consis- h D tent as it was for the A -parameters. D j.t° mean of the first difference of 6? t is not large for any j, but in 9 general is larger than that for the AD-parameters. Like the AD- Table 7 gives statistics for the first differences of 6 The parameters, the mean of the absolute value of the first difference is D ; this indi- i,t cates that the 6? t fluctuate considerably from week to week. Neither 9 larger than the mean of the first difference for all 6 96 Table 6. Differential Federal Reserve Reserve Requirements, Demand Deposits (Values of the Parameters 6? t’ j = 1,11) 9 Coefficient Standard of Mean Deviation Variation 1. Sample Period, 1961-1974 (730 observations) A. Demand Deposits City Banks (61 t) D .59001 .02071 .03510 Country Banks (62 t) .40999 .02071 .05051 2. Sample Period, 1/11/68-12/25/74 (364 observations) A. Demand Deposits City Banks, less than $5 million (69 ) .00617 .00061 .09887 City Banks, moreD ’Ehan $5 million (6D) .56823 .01046 .01841 Country Banks, less than $5 million (6D) .14256 .00792 .05556 Country Banks, m6re than $5 million (6D t) .28303 .01671 .05904 B. Demand Deposits Deposit Size, less than $2 million (6D t) .07452 .00681 .09138 Deposit Size $2’t to $10 million (6%) .14381 .00357 .02482 Deposit Size,’t$10 to $100 million (6 .27583 .00426 .01544 Deposit Size, $108’ E0 $400 million (6D ) .21687 .00386 .01780 10,t Deposit Size, more D than $400 million (6 .28898 .01028 .03557 ll,t) 97 AM. ”AV soaaaaa am mwoao.I ma«oo. ««moo. aaooo. amnu muoaunmxcmm muonsoo mmaoo. maaoo. Aaaoo. aoooo.- A oaV aoaaaaa mm swam mmma u.« .mxamm muuasoo mamas. aaaoo. oeeoo. aooo.u A aaV aoaaaaa am amzw.muoa .mxamm muao amooo.- moooo. Amoco. cocoa. A aV aoaaaaa an smnu mmma .mxsmm moan muamoamn asmama .< Amaoaum>ummno mamV aA\aN\~HImc\HH\H .ooasom oaeanm .N Um aoaao.I aa«oo. mmmoo. oaooo. A Mavu.amx:mm mpucsoo oocao. comma. aaaoo. oaooo.- A aaV manna Aoao muamoemn acmama .< Amcoaum>ummao mNAv aamauaoma .ooasom panama .a mwdmso coauma>mo maam> ammz amaxmmz aumasmum musaomn< ummwuma mo :mmz n Aaa.a u m ma mumumamumm mnu mo mmocmumwman umuamv muamoama ocmEmQ .musmamuasumm m>hmmmm m>ummmm amumamm amaucmummman .A manna Huo.a o.a 98 A ma Gav mo msam> musaomnm ummwumAa . . . . o.aa momma Aaaoo aaaoo moooo A eaV soaaaas ooem smnu muow.mwnam uamommn Hoaoo.u maaoo. Aoaoo. aoooo.u A oaV soaaaaa oceanooamonwnam manomen momao.u aaaoo. aaaoo. cocoa. A oaV eoaaaas ooaanoamonmnam sarcoma avoo. mamoo. moaoo. Hoooo. A aeV aoaaaaa oamummo.A .onam oamoeoo Aaaoo. Hoaoo. mmoco. aoooo.I A aoV aoaaaas mm amsu mmma .mmam uamoema ooaoomoo cannon .m wwwwnu coauma>mn m=am> :mmz amaxmmz aumacmum munaomo< ummwuma mo smmz ooasaosou .A oases 99 the standard deviation nor the largest weekly change in 6D indicate i,t any weekly fluctuation that is large on an absolute scale. By all three of these measures of variation, the variation in (6? - 6D Jat jab-1 D D is much smaller than that in (Aj’t - Aj,t-l ) ) for all j. In addition, unlike the AD-parameters, the standard deviation of (6? - 6D Jst jst-l) 13 much smaller for all j than the standard deviation of 6 ; the be- i,t havior of the 6D-parameters may therefore be relatively easy to pre- dict. The first differences of 6? t show the same tendency for vari- 9 ation to rise with the size of the deposit category. Annual figures for 6?,t are presented in Table 8. The standard deviations of GI,t and 6§,t have risen slightly during the same period, although this has not been a consistent or strong tendency. The pro- portion of member bank demand deposits in city banks has fallen; this D i,t’ 5 is reflected in the decline in the mean of 6 , and 62 . This D 3,t ,t is no doubt the result of the growth in the size and number of country banks. As would be expected, the behavior of the 6D-parameters in the graduated reserve scheme reflects the overall growth of deposits dur- ing the same sample period. The mean of the 6D-parameter for the smallest deposit-size category falls during the sample period and that for the largest deposit-size category rises. b) Time Deposits T i t’ i = 2, 5. Of the 9 Table 9 gives figures for the parameters 6 6T-parameters for the four major time deposit categories, that for time deposits greater than $5 million shows the largest standard devi- ation; that for savings deposits has the largest coefficient of vari- ation, although all four coefficients of variation are close in size. The standard deviation and coefficient of variation for all four 100 aammm. maooo. mmamm. ammao. mmamm. aammm. aammm. mmamm. moama. mama aammm. maooo. aammm. moaao. ammoo. aammm. maaam. ammoo. moama. mama mmamm. maooo. aaaoo. mamao. aomoo. ammme. mamao. aomoo. mmaaa. mmaa ommmo. aammm. aammm. mmaao. mmamm. momma. mamao. mmamm. mamaa. amaa mmamm. maooo. oamoo. maoao. mmamm. mmmam. mmamm. mmamm. mamma. mama mmmmm. maoom. mammo. mmamm. aammm. mamas. aammm. mmamm. amoma. mamma mamamo. emaooo. mmammo. mmmao. mmamm. mamas. maoao. maaoo. mmmma. mmma moaao. aammm. mmaaa. mmamm. aammm. mmmma. amaa ammao. mmamm. mamas. aaaom. mmamm. mmama. mmma ammao. mmamm. aammm. mmamm. mmamm. aomma. amaa mammo. mmmoo. ammam. mmamm. mmmoo. ammom. momma ommao. mmamm. mmmmm. mmmoo. amaoo. maaam. mmaa mmmao. amaoo. amamm. mmmoo. mmamm. aammm. mmaa manom. ommoo. mmamm. mmamm. mmmoo. amomm. amaa ”imam flamam oMaam coaumaum> coauma>mn :mmz coaumaam> coauma>mo :mmz coaumaam> coauma>mn sum: «0 aamacmom mo aamacmum mo aumacmum oeoaoammooo oooaoammoom sooaoammoom aa.a u a .u.am mom monomam anaoa< .m mamas N D a 101 mmmao. oAmoo. mmamm. mamao. mwmoo. wma«a. «mmmo. oaaoo. mmaao. «Ama wm«ao. mmmoo. a«mmm. «ammo. mmmoo. om««a. ammmo. amaoo. ammao. mmma mmmao. mamoo. mmamm. omomo. Ammoo. o«a«a. mw«mo. mmaoo. mamao. mama w«mao. a«moo. mammm. omamo. momoo. ««o«a. mamao. a«aoo. ammmo. amma awaao. mmmoo. mmmmm. wmmao. mmmoo. amm«a. ommmo. mmaoo. aommo. omma «m«ao. mmmoo. mmamm. mamao. ommoo. «mm«a. mmamo. «Aaoo. «mama. mmama amaao. ommoo. «waam. Omamo. omwoo. aam«a. mwomo. amaoo. oomwo. «mama u.Mm Dame mama mmmao. ammoo. anmom. aammo. mmmoo. ammma. mmmoo. a«moo. mammm. «Ama om«ao. a««oo. «a«om. mm«mo. ammoo. oa«ma. aomao. naaoo. mmamm. mmma ammao. aamoo. mmmmm. ammao. mamoo. aaama. aaoao. moaoo. «amaa. mama mommo. a«aoo. mmowm. mmmao. «mmoo. mao«a. aamao. ammoo. ««mmm. amma mm«ao. ammoo. mmmam. nomao. mamoo. oma«a. ammoo. am«oo. mmamm. omma ma«ao. owmoo. amwam. «amao. aamoo. maoma. awwoo. momoo. m«mmm. mmama Ammmc. mwmoo. mwaam. aa«ao. mamoo. aa«ma. mamoo. aamoo. A«amm. «mama D.Mm D.Mm u.mm coaumaam> COauma>mQ cmmz soaumaam> coauma>ma com: coaumaum> coauma>ma cmmz mo aumacmum wo mamasmum mo vumaamum mamaoammmoo oaoaoammmou mauaoammooo moaoaosoo .m oaoma 102 .mcoaum>ummno am no ammmm« .mcoaum>pmmno mm :0 ammmmm .coaaaas oo«w smnu mace u aa msoaaaaa oo«m amaa mmma mam coaaaae ooaw swam mace n ma mcoaaaae ooam amaa mmma mam coaaaae cam amaa muoa u m “coaaaaa cam amen mmma mam coaaaae mm smsu mace u m ”coaaaaa mm amaa mmma u A mmxcmo maucooo um coaaaaa mm amnu “mummum muamoama aamEma n a mmxcma mausaoo um coaaaaa mm amaa mmma muamoama asmama u m mmxamn muao um scaaaae mm amaa umummum muamommm acmama u « mmxcmn Auao um coaaaae mm amnu mmma muamomma aamEma n m mmxamo aauaooo u m “manna muao n a "mmaaommumu uamoama aamama maazoaaoa mcu cu mamama n umauumasm mnem .amumoaaca mmashmnuo mmmaas mmma amm maoaum>ummno mm no ammmm a ammmo. ammoo. a«mmm. oaoao. mamoo. ammom. «Ama aoamo. mamoo. mmmmm. mm«ao. mamoo. mmmam. mmma m«mmo. Amaoo. mommm. mmaoo. «maoo. mmamm. mmma mmmmo. mmaoo. Ammmm. om«oo. moaoo. oaomm. amma mmmmo. m«aoo. Ammmm. m«aoo. a«aoo. amnam. mmma mmamm. «ammo. maamm. aamoo. mmaoo. Amaam. mmama ommoo. mmaoo. aammm. mmamm. m«aoo. mmmam. «mama coaumaum> coauma>mm smmz coaumaum> acauma>mm ammz coaumaam> coauma>mm cmmz mo aumacmum mo aamacmum mo aumacmum sooaoammoom ucoaoammooo usoaoammoom moaoaoaom .m oamoa 103 Table 9. Differential Federal Reserve Reserve Requirements, Time Deposits (Values of the Parameters 6? t’ i = 2, 5) 9 Coefficient Standard of Mean Deviation Variation 1. Sample Period, 9/7/66-12/25/74 (434 observations) Time Deposits (63 t) T .56395 .07147 .12702 Savings Deposits ’ (63 t) .43605 .07147 .16390 9 2. Sample Periodr_l/ll/68-12/25/74 (363 observations) Time Deposits, less than $5 million (62 t) .09704 .01348 .13891 Maturities of 30-179 days1 .30062 .00155 .00516 Maturities of more than 179 daysl .07243 .00032 .00442 Time Deposits, greater than $5 million (6; t) .48574 .07390 .15214 f 7 ’ Maturities of 30-179 days1 .40082 .00181 .00452 Maturitief of more than 179 days .19345 .00020 .00103 1Includes 2 observations for the period, 12/12/74-12/25/74. 104 T D T 6 -parameters are much larger than for any 6 —parameter or A -parameter. The smallest coefficient of variation for the 6T-parameters is .12702 (for 6; t) which is more than three times the largest coefficient of 9 variation for the 6D-parameters (.03557 for 631 t); the largest coef- 9 ficient of variation for the 6T-parameters (.16390 for 6g t) is more 9 than four times the size of the largest 6D—parameter coefficient of variation. The coefficient of variation for 6: t’ i = 2, 5, is at 9 least 12 times the size of that for each corresponding lT-parameter; the coefficient of variation for 6: t is seventy-four times the size of 9 T that for A4,t° Table 10 gives the results for the first differences of 6: t’ 9 i = 2, 5. The mean of the first differences of 6: t is large for all i, 9 relative to that for the AT-parameters or the 6D-parameters. The mean of the absolute value for the first differences of 6i,t is larger than the mean of the first differences for all i; this is the same result reported for the parameters discussed above, but the difference between the two means is smaller for 6T . Therefore, while the weekly fluc— i,t T D and 6 are also present in tuations present in the behavior of A i,t lit 6: t’ they are apparently much smaller. Even though the mean of 9 T T T D (61,t - 61,t-l) is in general larger than that for A1,t or 6j,t’ the T T T D mean of l6i,t di,t-1' is smaller than it is for xi,t or 6j,t' T _ 6T i,t i,t—1 the standard deviation of 6T for all i. The standard deviation and i,t T _ 6T i,t i,t-l The standard deviation of (6 ) is much smaller than the largest weekly value of (6 ) are small for all i and are smaller than the same measures of variation in A: t and 6? t' 9 9 Comparing 6T with AT or 6D therefore yields the following i,t i,t j,t 105 Hun.“ u.a . I > s on m woman A He gov we «saw on H p u ad . . . . u.m ammoo NmHoo mNHoo «coco A gov aoHHHHa mm amaa mmammuw .muHmOQMQ mafiH u. «mace. Nmooo. omooo. noooo.l A Nov :OHHHHB mm amaa mmma .muamomon maHH AmaOHum>uowno momV q5\m~\maumo\afl\a .voaumm mflaemm .N u. mmwoo. oqaoo. oaaoo. ooooo. A va mufimoamn mwcfi>mw a amwoo.- oqaoo. assoc. ooooo. Au Mao muamoama mafia Amaowum>ummno mmcv «N\m~\mfiueo\s\m .eoaumm oaqamm .H osam> :owumfi>mn o=Hm> com: Axum: wumwamum ouaaomn< ummwqu mo cmmz a An .N u H .u We mumumamumm m:u mo moocmumMMHa umuamv mufimoamm mafia .mucmamuHSUmm m>ummmm m>ummmm Hmumvmm HmwucmumMMHn .OH manna 106 conclusions: while the levels of 6: t vary more and the mean change of 9 6: t is in general larger, the standard deviation, mean of the absolute 9 value of the first differences, and the largest weekly change in 6: are ,t smaller than the corresponding measures of changes in A: t and 6? t' 9 9 Thus it would appear that predicting the value of 6: t is an easier task. 9 T Table 11 gives annual figures for 61 t' The overall growth in time deposits that occurred during the sample period is reflected in the behavior of the mean of 6T for all i. As would be expected, the means i,t of 6T and 6T both decline and that for 6T rises. Furthermore the 3,t 5,t [at decline in 6T and 6T and the increase in 6T is well-explained by 3,t 4,t 5,t changes in the level of time deposits (Tt). That is, years of large T (small) decreases in 63 t and 6§,t and increases in 5:,t are also years of large (small) increases in Tt. The year for which the 6T-parameters have consistently high coefficients of variation is 1970; 1970 is also a year of unusually high variation in It. Therefore it is inferred that the behavior of 6:,t reflects influences such as market interest rates and Regulation Q ceilings which affect the overall rate of growth of time deposits. The impact of these variables will be dealt with in Chapter 6. In addition, quarterly figures indicate that seasonal fac- tors strongly affect the behavior of 5:,t; these also will be consid- ered in detail in Chapter 6. Nonmember Banks a) The Level of Nonmember Bank Deposits The parameters v2 and V: represent the proportion of the nation's demand and time deposits, respectively, that are in member banks and are therefore under the direct control of the Federal Reserve. Changes in 10? .oHamHHm>m uo: mama o .m:0Hum>ummno mm so vwmmmm .maoHum>ummno Hm do vmmmmc .maOHum>ummno NH do vmmmmm .GOHHHHE mm amaa mmammuw .muHmoamv mEHu u m “:0HHHHE mm amaa mmmH .muHmoaoo wEHu n q “muHmoamv mwaH>mm u m "mmHuowoumo uHmoamv mEHu wcH3oHHow mnu ou muomou H uaHuomnsm onem .omumoHvaH mmqumcuo mmcho Mama you mcoHum>ummno am so wmmmmH comma. Hquo. monoc. manna. mwmoo. Omens. ommmc. mHHHo. mmmHm. can mmmmo. mmmHo. women. oqqmo. cwmoo. mHmwo. mmweo. NHNHO. mmmmm. man NoHNo. meHo. NNmOm. memo. oewoo. mmuoo. qumo. wowoo. meoq. Nan NooHo. monoo. «mane. omemo. nqmoo. HwOOH. mquo. Hoooo. momHe. Han wmqeo. nqnmo. Hnomq. Hoqqo. momoo. manH. oquo. mqmmc. «mmma. OmmH nmqmo. oquo. nOOHq. momma. mmmoo. umOHH. nuuHo. Hmwoo. oawmc. maomH MHHmo. mmmHo. Hoaoq. mmOHo. OHHoo. wHOOH. nmowo. wwNHo. omomq. «womH o o o o o o HHQNO. moNHo. Nmmmm. nomH o o c o o o momoo. mmmoo. cmoom. moomH oi u. u« No Me Me :oHumHum> :OHumH>mo com: coHumHum> coHumH>mm com: coHumHum> :oHumH>mn com: mo wumwcmum mo vuqumum mo wumwcmum ucoHonwooo ucmHonmmoo uamHommmmou mm .m n H .u We now moustm HHmsaq< .HH oHan 108 the distribution of deposits between member and nonmember banks will cause v2 and v: to vary which will induce variation in rt. Table 12 gives the results for the levels and first differences of v? and v: as well as the alternative specification of v2, v2*, described above. Consider first the behavior of v2. As can be seen from Table 12, the mean of v2 for the entire sample period is .82484 and its stand- ard deviation is .02653. The standard deviation and coefficient of variation for v? are not large on an absolute scale. As would be ex- pected, the alternative definition of v2*, which leaves out nonmember bank interbank deposits (call report data), shows slightly more vari— ation than V? but the difference is small. Presumably it makes little difference which definition of v? is used. The mean of the week-to-week change in VD is -.00014 and the standard deviation is .00202. Therefore the average disturbance caused by v? from one week to the next is small, as is the variability of the disturbance. The mean of the absolute value of the first differences of v? is much larger than the mean of the first differences, implying that v? fluctuates considerably from.week to week, although the size of those fluctuations is apparently not large. The standard deviation of the changes in v? is much less (.00202) than the standard deviation of the levels of v? (.02653); therefore, the variation in the first dif- ference of V2 is small. The largest weekly change in v2 occurring dur- ing the sample is also small. The mean of v? has, of course, fallen during the sample period, as can be seen in Table 13, which gives annual figures of v2. The mean of v2 has decreased steadily each year from a high of .86252 in 1961 to 109 To u HI”. u . > I e no 9 I > 0 ms m> ummwum AH av An new H 4H u mHmoo. oqooo. amooo. cocoo.l AH>V muHmonQ maHH u mmmoo.l wwHoo. HmHoo. «Hooo.I «a? u mmmoo. Nomoo. NoHoo. «Hooo.l An>v muHmoamn panama Am:0Hum>ummno mNNV W? vam m? wumuoamumm mnu mo mmoaoumMMHn umuHm .N u Hsomo. oaqmo. Nessa. AH>V muHmoawn maHH u commo. oqwmo. Hqcmm. «a? u oHNmo. mnemo. qwqmm. An?v muHmonmn panama u u AmcoHum>ummno ommv H? mam a? mumumamumm may mo mmsHm> .H Hmwcmsu aOHumHum> coHumH>oo osHm> com: szmmz mo vumvcmum musHomn< ummwuma ucmHonmmoU mo com: AqanIHomHv muHmoamn mxcmm umnawacoz mo Hm>MA .NH mHan 110 Table 13. Annual1 Figures for V2 Percentage Change from Previous Year Standard Standard Mean Deviation Mean Deviation 1961 .86252 .00302 -- -- 1962 .85682 .00310 -.661% 2.648% 1963 .85072 .00291 -.712% - 6.129% 19642 .84567 .00316 -.594z 8.591% 1965 .84140 .00552 -.505% 74.684% 1966 .83509 .00442 -.750% -l9.928% 1967 .83360 .00349 -.l78% -21.041% 1968 .82788 .00610 -.686% 74.785% 19692 .81805 .00519 -l.l87% -l4.918% 1970 .81389 .00384 -.509% -26.012% 1971 .80746 .00684 -.790% 78.125% 1972 .79520 .00659 -l.518% -3.655% 1973 .78444 .00724 -1.353% 9.863% 1974 .77469 .00618 —l.243% -l4.641% 1Based on 52 observations per year unless 2Based on 53 observations. otherwise indicated. 111 a low of .77469 in 1974. Over the same period the standard deviation of v: has more than doubled from its 1961 value of .00302 to its 1974 value of .00618. Therefore, the variability of v2, though small, is rising. Neither the overall decline in v2 nor the increase in its stand- ard deviation occurs smoothly during the sample period. The largest declines in the mean of v? occur in 1969 and in every year after 1971. A plot of v? indicates that it has declined more and varied more since 1965. Particularly large increases in the standard deviation of v? occurred in 1965, 1968, and 1971; since 1971 the standard deviation of v? has remained at or near that higher level. Presumably much of the behavior of v? should be attributable to changes in the number of member banks relative to the total number of commercial banks in the country. Information on this variable is con— tained in Table D—2 in Appendix D. As can be seen in the last column of Table D—2 the largest decline in the proportion of banks that are members occurred during 1969 and 1970. While 1969 was a year when v2 fell a lot, 1970 was not a year of unusual decline in v2. Overall the decline in the proportion of commercial banks that are members is greater in the later years of the sample and this mirrors the decline in v2 and the increase in its variation after 1965. The behavior of v? however does not consistently reflect the member banks-commercial banks ratio; there are years of exceptional decline in V? which are not matched by years of unusual exit of banks from the System and vice versa. Apparently shifts of deposits between member and nonmember banks occur that are independent of the attrition of banks from the System. 112 Much more of the behavior of v? is explained by movements and levels of interest rates.12 The analysis here will be based on the interest rate on newly-issued three—month Treasury bills, used as an indicator of the short-term interest rate. Information on this vari- able is contained in Table D-3, in Appendix D. The years of the larg- est declines in v2, 1969, 1972, 1973, and 1974, are each also years of historically high (1969, 1973, and 1974) or rapidly rising (1972) interest rates or both, as can be seen in Table D—3. During the early years of the sample period, while interest rates rose considerably each year, they were not at historically high levels; during the same years, v? fell but not at record rates. As rates con- tinued to rise in the mid-sixties, the decline in v2 gained momentum. The only two years since 1965 that v? did not drop at a substantial rate were 1967 and 1970; these were also the only two years in the sample period when interest rates were not either rising rapidly or already at record-high levels. A relationship between high and/or rising interest rates and de- clining values of v? is not surprising considering the cost differen- tials between member and nonmember bank reserve requirements described above. It is puzzling, however, that the effects of high or rising interest rates do not show up as clearly in the member banks-commercial banks ratio. During years of marked decline in the relative number of member banks which were not also years of an unusual fall in v2, one of two other factors had to be at work: either some independent shift of 12The relative number of member banks is no doubt related to the behavior of interest rates too, so there is probably considerable inter- relation between both factors and VD. This will be dealt with in Chapter 6. t 113 deposits toward remaining member banks was occurring or the banks that were leaving (not joining) the System were of below-average size. By the same reasoning during years of exceptional decline in v2 not matched by a fall in the relative number of member banks, either an independent shift of deposits away from member banks was at work or the banks leaving the System were of above-average size. The latter situ— ation would be consistent with the close correspondence between falling v2 and high interest rates if it is assumed that larger banks are more responsive to high interest rates. Therefore when interest rates rise, large banks are more apt to react by leaving the System, causing a proportionally larger fall in v2 than in the relative number of member banks.13 It may be that this is the case and that in the years of large decline in the relative number of member banks not matched by any exceptional drop in v3, some independent (or lagged interest rate) effect was causing a disproportionate number of small banks to leave the System. The two years in the sample period that interest rates were not high or rising (1967 and 1970) were also years when the standard devi— ation of v2 fell and the year after each of those years was a year of exceptional increase in the standard deviation of VS. It may be that the years of relative interest rate ease (1967 and 1970) caused bankers to ease up in changing their membership-status (and the standard devi— ation of VS fell), while the return to high and rising rates in each of 13While it is rational to believe that large banks would be more apt to recognize and react to the cost of membership during periods of high interest rates, to the extent that large banks are also national banks, large banks should find it costlier and should require more time to exit the System, since charter conversion would be necessary. 114 the next years reinforced bankers' expectations and increased their pro- pensity to change membership status (thereby causing the variance of v? to rise). It cannot be concluded here that this is a very strong relationship however since there are other years when the standard deviation of v? rose or fell, unaccompanied by any particular interest rate behavior. In 1965, for example, the standard deviation of v2 rose substantially and it fell in 1966, while interest rates behaved similarly in both years. The values of v? display a discernible seasonal pattern. Despite the secular decline in vi, a plot of v? shows that its value increases during the first quarter of every year in the sample period. During the second quarter of each year, the increase in v2 slows, flattens out, and the overall decline in v? is accomplished during the third and fourth quarters of each year. This pattern is more pronounced dur— ing the years since 1964. This seasonal pattern can be seen in Table D-4 in Appendix D, which gives quarterly figures for v2. Referring to Table 12, the mean of v: is .79442 and its standard deviation is .02416. The mean of v: is less than that of VS, indica- ting that on the average over the sample period, member banks hold a larger proportion of the nation's demand deposits than time deposits. This is probably due to the tendencies of large, metropolitan banks to be member banks and have deposit structures where demand deposits are relatively important. Part 2 of Table 12 also indicates that v: varies less than v2. T t-l) each of which is small on an absolute scale and is less than one-half The mean of (v: - v is -.00006 and its standard deviation is .00040, the magnitude of comparable figures for v2. The mean of Iv: - vE-ll 115 is .00029 and the largest value of (v: - vE_1) is .00315, both of which T are much smaller than comparable figures for v2. A plot of (v: - Vt-l) is virtually flat; the absolute value of the change in v: equals or exceeds .0005 only 126 weeks out of the 729 weeks in the sample period and exceeds .001 only four times. Like v2, the value of v: falls overall during the sample period but the decline in v: is smaller. The value of v: drops 11.99% during the sample period, compared to 8.66% for VE' Furthermore, the decline of v: does not occur as regularly and smoothly as does that of v2. As the annual figures in Table 14 show, the value of v: rises during the first five years of the sample period and does not begin to fall until 1966. It continues to decline in 1967 and 1968, and then drops drastic- ally during 1969; nearly half of the overall decline of V: is accom- plished in 1969. The mean of v: falls again in 1970 but during that year, the value of v: actually increases; this shows up the next year as the 1971 mean rises. The decline in v: is resumed and it falls slightly during 1971 and 1972. During the last two years of the sample period, the behavior of v: becomes more erratic. It shows its char- acteristic relative stability during the first half of 1973, but rises during the third quarter, then falls during the fourth quarter. This decline continues into the first quarter of 1974, followed by an ins crease in the second quarter, a leveling off and resumed decline dur- ing the third and fourth quarters. While the standard deviation of VI does not rise as steadily and consistently as did that of vi, the overall result is that it increases more than it decreases, and the later years of the sample period dis— play consistently larger variability in v: than do the early years. 116 Table 14. Annual1 Figures for v: Percentage Change from Previous Year Standard Standard Mean Deviation Mean Deviation 1961 .81070 .00381 -- - 1962 .81376 .00138 .377% —63.780% 1963 .81680 .00099 .374% -28.261% 19642 .82009 .00088 .403z -11.111% 1965 .82046 .00054 .045% -38.636% 1966 .81643 .00275 -.491% 409.259% 1967 .81139 .00121 -.6l7% —56.000% 1968 .80365 .00241 -.954% 99.174% 19692 .78379 .00885 -2.471% 267.220% 1970 .77132 .00281 -l.591% -68.249% 1971 .77280 .00198 .192% -29.537% 1972 .76514 .00202 —.991% 2.020% 1973 .76046 .00201 -.612% .495% 1974 .75478 .00217 -.747% 7.960% 1Based on 52 observations per year unless otherwise indicated. Based on 53 observations. 117 As can be seen in Table 14, most of the increase in the standard devi- ation of v: occurs in 1966 and 1969. By the same reasoning applied to v2, the behavior of v: over time should be at least partially attributable to the relative number of memr ber banks and interest rates. In addition, the effectiveness of Regula- tion Q interest-rate ceilings may influence v: via their impact on the growth of total time deposits. As Regulation Q ceilings encourage or impede the growth of time deposits, v: will also be affected, to the extent that the change in the level of time deposits is unevenly di- vided between member and nonmember banks. Since member banks dominate the market for large, negotiable certificates of deposit and this cate-. gory of time deposits is apt to be most interest-elastic, the effects of Regulation 0 ceilings will likely be felt most heavily by member banks. The Regulation Q ceiling relative to the Treasury bill rate appears to have an important impact on v:. The increase in v: at the beginning of the sample period occurred while the Regulation Q ceiling was not effective; this was the period of time when the market for large certif- icates of deposit grew rapidly so the member bank portion of time de- posits also grew. The decline in v: began in 1966 when Regulation Q ceilings became effective, and accelerated as the Treasury bill rate rose further above the ceiling. The decline in v: and the increase in its variation is consistently larger the larger the gap between market and ceiling rates and abates (or v: grows) when the gap is smaller or the ceiling ineffective. While the number of member banks and cost-of-membership issue rep- T resented by high interest rates no doubt exert some influence on vt’ 118 the effect of interest rates relative to Regulation Q ceilings appears to be dominant. The relationship between v: and interest rates indi- cates that member banks lose time deposits more rapidly than nonmem- bers when Regulation Q ceilings are effective. This is no doubt because of the member bank dominance of the interest-elastic market for certif- icates of deposit. The complex relationships between vi, membership attrition and market interest rates will be analyzed with more SOphis- ticated techniques in Chapter 6. b) Differential State Reserve Requirements As discussed in Chapter 3, the existence of nonmember banks can also affect the value of rt through the impact of differential state reserve requirements. Since nonmember banks in different states are subject to different required reserve ratios, the ratio of nonmember bank reserves to total deposits will vary depending on how a given level of deposits are distributed among states. If nonmember bank total deposits are concentrated in states with relatively high (low) required reserve ratios, the level of reserves per dollar of total de- posits held by nonmember banks will be relatively large (small). Hence as the distribution of nonmember bank deposits among states changes, the reserves-to-total deposits ratio for nonmember banks will vary. This phenomenon is analogous to the effect of differential Federal Reserve reserve requirements. Whatever the effect of differential state reserve requirements on the ratio of nonmember bank reserves-to-total deposits, the impact on the value of rt cannot be inferred directly. Since nonmember bank vault cash is the only part of nonmember bank reserves that is base- absorbing, it is nonmember bank vault cash relative to total deposits 119 that is relevant to the value of rt; it is‘changes in the ratio of vault cash to total deposits, rather than the reserve-deposit ratio, that will cause variation of rt. If the behavior of nonmember banks is such that the vault cash-total deposits ratio is relatively constant in every state, then differential state reserve requirements have no effect on rt. On the other hand, if the vault cash-total deposit ratio is not approximately equal for nonmember banks in different states, then the distribution of nonmember bank deposits among states will effect the value of rt. In this latter case, any variation in either the ratio of vault cash to total deposits for each state or in the distribution of nonmember bank deposits among states will cause variation in rt. In the equation for rt, the nonmember bank reserves portion of the expression for rt is given by, 51 m glwlhthtpt’ th where wh t = nonmember bank vault cash in the h state: ’ nonmember bank total deposits in the hth state ’ = nonmember bank total deposits in the hth state:. wh,t nonmember bank total deposits ’ n a nonmember bank total deposits. pt privately-owned demand deposits' The effects of changes in the level of vault cash relative to total de- posits in the hth state is represented by WE t and uh t represents the 9 9 proportion of total nonmember bank deposits in the hth state. The only data available from which to calculate w and uh are h,t ,t Federal Deposit Insurance Corporation call report data. Until June, 1963, call report data are available on a quarterly basis; for the last eleven years of the sample period, data are available on a semiannual 120 basis only. Table 15 gives the mean and standard deviation for wh,t between states for each of the thirty—four call report dates in the period December 31, 1960 through December 31, 1974. Table 16 presents the mean and standard deviation of wh,t and wh,t for each state based on all thirty-four call report dates. As can be seen from Table 15, the mean of wh,t has declined dur- ing the sample period and does vary from one call date to the next. Thus, the average ratio of vault cash to total deposits for all nonmem— ber banks is not constant. The standard deviation of w reported in h,t Table 15 implies that the variation in wh,t between states is not con- sistently high, but it is relatively high for some call dates. Further-. more, Table 16 indicates that the vault cash-total deposit ratio is not uniform between states, since the mean of wh,t for the thirty-four call dates ranges from .01144 for California to .03352 for Arkansas. The standard deviation of wh,t reported in Table 16 measures the variation in wh,t that has occurred through time for each state. The standard deviation of wh,t is small for most states but varies considerably be- tween states; it ranges from .00151 for Vermont to .04584 for Arkansas. All of this implies that the ratio of nonmember bank vault cash to total deposits is not particularly stable; it apparently has varied consid— erably over time and is not especially uniform between states. A number of factors may cause the variation in wh,t between states. It may be that nonmember banks choose to hold a relatively constant proportion of their legal reserves in the form of vault cash. If this is so, differential state reserve requirements would account for differ- ent values of Wu t for different states. Variation in the ratio between 9 states is no doubt influenced by state institutional and demographic 121 Table 15. Nonmember Bank Holdings of Vault Cash VC whtg'fiimzi \p ’ h,n,t __ h,t Call Standard Call Standard Date Mean Deviation Date Mean Deviation 12/31/60 .02135 .00652 12/31/66 .02042 .00500 4/12/61 .02479 .00686 6/30/67 .01876 .00421 6/30/61 .02220 .00581 12/31/67 .01953 .00479 9/30/61 .02646 .00702 6/30/68 .01805 .00412 12/31/61 .02329 .00621 12/31/68 .02103 .00598 3/26/62 .02395 .00563 6/30/69 .01929 .00605 6/30/62 .02112 .00512 12/30/69 .02073 .00818 9/28/62 .02201 .00578 6/30/70 .02022 .00675 12/31/62 .02389 .00640 12/31/70 .01785 .00600 3/18/63 .02858 .03109 6/30/71 .02046 .01528 6/29/63 .02603 .03055 12/31/71 .01680 .00487 12/31/63 .02051 .00522 6/30/72 .01610 .00775 6/30/64 .02326 .00605 12/31/72 .01629 .00557 12/31/64 .02424 .02128 6/30/73 .01455 .00512 6/30/65 .02291 .00583 12/31/73 .01735 .00625 12/31/65 .02295 .02007 6/30/74 .01364 .00341 6/30/66 .02142 .00512 12/31/74 .01680 .00500 Data Source: Federal Deposit Insurance Corporation, Assets, Liabilities and Capital Accounts, Commercial Banks and Mutual Savings Banks, Report of Call Nos. 54-84, December 31, 1960-December 31, 1968; and Federal Deposit Insurance Corporation, Board of Governors of the Federal Reserve System, and Office of the Comptroller of the Currency, Assets, Liabil- ities and Capital Accounts, Commercial Banks and Mutual Savings Banks, June 30, 1969-December 31, 1974. 122 Table 16. Effects of Nonmember Bank Holding of Vault Cash December 31, 1960-December 31, 1974 (34 observations) wh,t = ::h n t mh,t = ::h n t h,n,t n,t Standard Standard State Mean Deviation Mean Deviation Alabama .02372 .00423 .01379 .00109 Alaska .02047 .00871 .00126 .00077 Arizona .02200 .02723 .01008 .00075 Arkansas .03352 .04548 .01186 .00050 California .01144 .00155 .04473 .00294 Colorado .01828 .00291 .00903 .00058 Connecticut .02558 .02541 .01280 .00219 Delaware .01908 .00206 .01537 .00273 District of Columbia .01542 .00321 .00627 .00356 Florida .02142 .00419 .04467 .00498 Georgia .02501 .00396 .02614 .00199 Hawaii .02543 .00653 .01305 .00258 Idaho .01741 .00379 .00206 .00023 Illinois .01519 .00241 .07014 .00411 Indiana .01959 .00392 .03240 .00214 Iowa .01511 .00282 .03744 .00239 Kansas .01396 .00229 .02421 .00123 Kentucky .02213 .00364 .02325 .00065 Louisiana .02473 .00464 .02442 .00150 Maine .02751 .00561 .00375 .00046 Maryland .02495 .00364 .02220 .00097 123 Table 16. Continued wh,t =¥.§h&£ ”h,t =:—:ELQLE h,n,t n,t Standard Standard State Mean Deviation Mean Deviation Massachusetts .02607 .00457 .01409 .00101 Michigan .02028 .00344 .02849 .00217 Minnesota .01504 .00300 .03228 .00220 Mississippi .02511 .00316 .01817 .00194 Missouri .01739 .00285 .05065 .01975 Montana .01551 .00279 .00297 .00015 Nebraska .01873 .02501 .01257 .00042 Nevada .02852 .00925 .00350 .00120 New Hampshire .01355 .00178 .00323 .00040 New Jersey .02114 .00268 .01911 .00072 New Mexico .02228 .00491 .00471 .00020 New York .01370 .00249 .02905 .00494 North Carolina .03014 .00440 .02979 .00271 North Dakota .01189 .00234 .00738 .00074 Ohio .02151 .00270 .02875 .00432 Oklahoma .02001 .00353 .01227 .00172 Oregon .01783 .00238 .00662 .00048 Pennsylvania .02110 .00365 .05437 .00444 Rhode Island .02888 .01133 .00676 .00365 South Carolina .03081 .00475 .00964 .00052 South Dakota .01223 .00241 .00578 .00107 Tennessee .02242 .00306 .02284 .00093 124 Table 16. Continued W = VCh,n,t g TDh,n,t h,t TD “h,t TD haflgt njt Standard Standard State Mean Deviation Mean Deviation Texas .01971 .00398 .06234 .00593 Utah .02012 .00406 .00435 .00086 Vermont .01532 .00151 .00520 .00051 Virginia .02475 .00438 .01640 .00095 Washington .02450 .00422 .00520 .00045 West Virginia .02526 .00515 .00844 .00020 Wisconsin .01727 .00266 .04465 .00233 Wyoming .01781 .00340 .00148 .00014 Data Source: Federal Deposit Insurance Corporation, Assets, Liabilities and Capital Accounts, Commercial Banks and Mutual Savingszanks, Report of Calls Nos. 54-84, December 31, 1960-December 31, 1968; and Federal Deposit Insurance Corporation, Board of Governors of the Federal Reserve System, and Office of the Comptroller of the Currency, Assets, Liabil- ities and Capital Accounts, Commercial Banks and Mutual Savings Banks, June 30, 1969-December 31, 1974. 125 features such as branching laws, average bank size and urban-rural mix. Variation in wh,t through time is partially attributable to the effects of high and rising interest rates during the sample period. Whatever the cause of variation in w the fact that nonmember banks do not h,t’ hold a constant amount of vault cash per dollar of deposits means that changes in the distribution of nonmember bank deposits among states affects rt. Consequently variation in either wh,t or wh,t will gener- ate variation in rt. Table 16 also gives the results for wh,t which indicate the extent to which the distribution of nonmember bank deposits between states has changed historically. The standard deviations of wh,t are all small; thus shifts in the distribution of deposits among states has apparently been minimal. The infrequency of available nonmember bank data seriously limits analyzing the impact of state reserve requirements on rt.14 To the extent that nonmember bank deposits within a state are subdivided into categories for reserve purposes, the distribution of deposits among these categories will also affect rt. State deposit data that are dis- aggregated into these additional reserve categories are not available at all. The lack of weekly nonmember bank deposit data makes it impos- sible to analyze the nonmember bank reserves portion of rt in a way 14In addition, some authors have questioned the reliability of the data that are available. This study however is concerned with the amount and source of variation in measured r , which is by necessity calculated with available data. The only available measure of r therefore incorporates whatever errors or inadequacies are in the deposit data. The deficiencies of the data, while possibly trouble- some, are therefore not at issue here. t 126 that is comparable to the analysis of the member bank portion. There— fore, the analysis in the following chapters does not include the nonmember bank part of rt. Nonmoney_Deposits Since member banks are required to hold base-absorbing reserves against deposits that are not included in the money stock, the base money supplied by the monetary authorities will support a smaller money stock, the higher the levels of nonmoney deposits. The nonmoney de— posits include deposits of the U. S. Government, interbank deposits, and time deposits. Their influence is reflected here in the param— eters, Yt’ It, and Tt’ respectively, where each category of nonmoney deposits is expressed as a ratio to privately-owned demand deposits. , and T and Table 17 gives statistics for the parameters Yt’ It t their first differences. Of the three types of nonmoney deposits, Tt has the largest standard deviation but Yt has the highest coefficient of variation. The standard deviations and coefficients of variation for Yt’ 1 , and It are all large relative to the parameters discussed t above. For example, the coefficients of variation of v? and v: are less than one-third the level of the lowest coefficient of variation of the three nonmoney items (It). The mean of the first differences for Yt and it are small, -.00003 and .00002, but as expected Tt shows a considerably larger average weekly change (.00193). The standard deviation and largest weekly values of (It - ) are also larger than for either Yt or t . The Tt-l t mean of the absolute value of the first differences is, for all three parameters, much larger than the mean of the first differences; thus u Namac. mamao. maaoo. A 9V muamoama mafia mnemo. Acmmo.l cacao. mnqoo. Noooo. «a u commo.| wqooo. cuqoo. Noooo. A av mufimoawa xamnumuaH comma. wmoao. cameo. moooo.| Au>v muHmoaon uaoaauo>ou Amaoaum>ummno amsv up wow .u# .u> cw momamnu vowummIOulwowuom .N 7. mmamm. awsom. Hsow~.H Aupv muamoamn mafia 2 1‘ Nwsaa. Namao. Hamma. *u u oqwaa. mqoao. owwma. A av mufimooma xamnuouaH u aoomm. mmqao. mqaqo. A >v muwmoamn unmeaum>ou u u u Amcowum>ummpo omNV P van . p . r mumumamumm mnu mo mooam> .H mwcmno coHumwum> coaumfi>ma m=Hm> coo: magmas mo vumvcmum ousaoma< ummwumA uamwofiwwmoo mo cmmz u u u Acnoalaomav A P . a . > .mumuoEmumm onu mo mmocmumwman umuwm mam mosam>v mafimoamo hmaoaaoz .NH manna 128 Yt’ 1 , and Tt apparently all fluctuate considerably. The mean of t IT t - Tt-l' is much larger than that for Yt or 1t’ indicating that It indeed varies considerably more. The statistics on the first differ- ences also indicate that the size of, and variation in, the weekly change of Yt’ It, and Tt are larger than that for the parameters dis- cussed earlier. a) Government Deposits A plot shows that the behavior of Yt is dominated by its contin- ual fluctuations rather than any discernible systematic pattern. The standard deviation of (Yt ) is nearly as large as the standard — Yt-l deviation of Yt itself and the plot of the first differences exhibits as many and as large fluctuations as the one of the levels of Yt' Table 18 gives annual figures for Yt' During the first five years of the sample period, Yt rose slightly, reaching its high in 1965, and declined thereafter, especially in 1966, 1973, and 1974. The standard deviation has also declined some; the early years of the sample in gen- eral show more variation for Yt' While Yt displays large week-to-week variation, a plot of Yt indi- cates that it follows the same pattern of fluctuation within the same quarter of nearly every year of the sample. Given the regularity of this seasonal pattern, it appears that the behavior of Yt may reflect institutional factors such as tax payment dates. If this is the case, the behavior of Yt should be predictable even though it displays a lot of variability. This issue will be considered in the regression analy- sis in Chapter 6. 129 Table 18. Annual1 Figures for Yt Percentage Change from Previous Year _ Standard Standard Mean Deviation Mean Deviation 1961 .04263 .01169 -- 1962 .05174 .01513 21.370 29.427 1963 .05006 .01567 ~3.247 3.569 19642 .04799 .01484 -4.135 -5.297 1965 .05061 .01906 5.460 28.437 1966 .03760 .01533 —25.706 -l9.570 1967 .03749 .00944 —.293 -38.421 1968 .03987 .01128 6.348 19.492 19692 .03716 .01243 -6.797 10.195 1970 .04145 .00941 11.545 —24.296 1971 .03961 .01141 -4.439 21.254 1972 .04025 .01118 1.616 —2.016 1973 .03617 .01363 —10.137 21.914 1974 .02822 .01036 -21.980 -23.991 1Based on 52 observations per year unless othe wise indicated. 2Based on 53 observations. 130 b) Interbank Deposits As can be seen in Table 17, there is little difference between the behavior of It and its alternative definition 1:, which excludes call report data on nonmember bank interbank deposits. By all measures, the variation in I: is slightly smaller than in It. The behavior of It is dominated by large weekly changes. The standard deviation of the first differences of It is much smaller than that of its level, so (It - lt-l) displays much smaller weekly fluctuations than It. The value of It has increased overall during the sample years. Table 19 gives annual figures for It and shows that the mean of It has grown slightly each year since 1964 except in 1966, 1972, and 1973. A plot shows that most of the rise in the value of 1t was accomplished during 1968, 1969, 1970, and 1973. As can be seen in Table 19 there is also a tendency for the variation in It to rise during the sample per— iod; since 1967 the standard deviation of It has been larger. The larg- est increases in the standard deviation occurred in 1968 and 1972. There have been two occurrences during the sample period that would logically influence It. One is the decline in the relative number of member banks. Since nonmember banks can hold legal reserves in the form of interbank balances, It might be expected to rise as the relative num- ber of nonmembers grows. Gilbert15 however has found that member banks hold more interbank deposits than nonmembers of comparable size. Con- sequently It may fall as relatively more banks are nonmembers. 1SAlton Gilbert, "Utilization of Federal Reserve Bank Services by Member Banks: Implications for the Costs and Benefits of Membership," Review, Federal Reserve Bank of St. Louis 59 (August 1977):12. 131 Table 19. Annual1 Figures for It Percentage Change from Previous Year Standard Standard Mean Deviation Mean Deviation 1961 .12961 .00460 -- -- 1962 .12756 .00581 -1.582 26.304 1963 .12428 .00483 -2.571 -16.867 19642 .12272 .00455 -1.255 -5.797 1965 .12457 .00415 1.507 -8.791 1966 .12452 .00442 -.040 6.506 1967 .12847 .00432 3.172 -2.262 1968 .13335 .00652 3.799 50.926 19692 .14565 .00733 9.224 12.423 1970 .15529 .00733 6.619 4.366 1971 .16792 .00779 8.133 1.830 1972 .15441 .01154 -8.045 48.139 1973 .14433 .00756 -6.528 —34.489 1974 .16156 .00744 11.938 -1.587 1Based on 52 observations per year unless otherwise indicated. 2Based on 53 observations. 132 The second phenomenon that should be at work on It is the record of high and/or rising interest rates during the sample years. Since interbank deposits are noninterest bearing, high and/or rising inter- est rates should cause banks to economize on their holdings of inter- bank deposits and the level of It should fall.16 Although the results are not clear cut, Table 19 and Table 13 indicate that in general the increase in It mirrors the decline of v? and the variation in both parameters rises. The years when It is high or rises (1968 through 1974) are, except 1970, also years when v2 de- clines substantially. The first year of unusual decline in v2 was 1969 and that was also the year of the first large increase in It. There are, however, years when v? falls substantially and It also falls (1963, 1966, 1972, and 1973, for example), so the relationship between It and the relative decline in member banks is not clear. Any impact of mar- ket interest rates on It is difficult to discern from observation (comparing Tables 19 and D—3). The general tendency of interest rates to rise or be high during the sample period and the increase in 1t con— tradicts the expected relationship between 1t and interest rates. The influence of both of these independent variables on It will be con- sidered further in the regression analysis in Chapter 6. In addition, the analysis in the next chapter will deal with the seasonal behavior of It which appears to be strong. 16Banks, of course, earn a "return" on interbank balances in the form of services rendered. Banks typically hold a level of interbank balances necessary to "pay" for the services needed from a correspondent. To determine the required level of interbank balances, correspondents often apply a market interest rate to the level of interbank balances and compare this to the cost of services provided. Therefore, higher market interest rates allow lower interbank balances to pay for a given level of correspondent services. 133 c) Time Deposits The value of Tt’ of course, rises continually throughout the sample period. Table 20 gives annual figures for Tt and shows that the annual mean rises every year but 1969; the mean of Tt more than triples its value between 1961 and 1974. As expected, Tt also displays considerable variation; as can be seen in Table 17, its standard deviation is .36787 which is higher than that for Yt’ 1t, v2, or VE' The coefficient of variation of It is .28726, exceeded only by the coefficient of varia- tion of Yt' The standard deviation of (It - ) is only six percent Tt-1 of the standard deviation of Tt’ indicating that a large portion of the variation in Tt is due to its upward trend. A plot of (It - Tt-l) still displays considerable weekly fluctuations however; the mean of (Tt - rt_1) is .00193 and the mean of lrt - rt_1| is .01399, both of which are much higher than comparable statistics for Yt’ It, v2 or YE' As can be seen in Table 20, the variation in Tt has also increased; the standard deviation of Tt is larger after 1968, except for 1972. Table 20 shows that the largest increases in the mean of Tt occurred during 1962, 1963, 1965, 1970, 1971, 1973, and 1974. The best explanation of the behavior of Tt ought to be market interest rates and interest rates relative to Regulation Q ceilings. The relationship between the Treasury bill rate as an indication of short-term interest rates and Tt is, however, ambiguous. If an increase in the Treasury bill rate represents a general increase in all rates including that paid on time deposits, It should be expected to rise as consumers shift out of cash and demand deposits into all interest-bearing instruments, in- cluding time deposits. If, on the other hand, an increase in the Treasury bill rate represents more attractive terms being paid on an 134 Table 20. Annual1 Figures for It Percentage Change from Previous Year Standard Standard Mean Deviation Mean Deviation 1961 .69941 .02543 -- -- 1962 .79322 .03792 13.413 49.115 1963 .89351 .03379 12.643 —10.891 19642 .98015 .03157 9.697 -6.570 1965 .09300 .04096 11.514 29.743 1966 .17717 .04142 7.701 1.123 1967 .28536 .04187 9.191 1.086 1968 .34193 .03330 4.401 -20.468 19692 .32260 .04932 -1.440 48.108 1970 .35303 .07401 2.301 50.061 1971 .56403 .05120 15.595 -30.820 1972 .64276 .03842 5.034 —24.961 1973 .78432 .07819 8.617 103.514 1974 .00300 .09062 12.256 15.897 1Based on 52 observations per year unless otherwise indicated. 2Based on 53 observations per year. 135 instrument that is an alternative in time deposits, Tt would be expected to fall. Whenever market interest rates are below the Regulation Q ceiling, Tt should rise more rapidly; when Regulation Q ceilings are effective, Tt would be expected to fall (or rise more slowly). The limited analysis here indicates no particular relationship between It and the Treasury bill rate. While five of the years of exceptional increase in It (1962, 1963, 1965, 1973, and 1974) were also years of high or rising interest rates, the other two years during which It increased a lot, 1970 and 1971, were years of falling and low (respectively) rates. In addition, many other years in the sample per- iods recorded equally high or rising rates, when Tt did not rise ex- ceptionally, including 1969 when Tt actually fell. The behavior of Tt is more closely related to the effectiveness of Regulation Q ceilings. The rapid growth in It in the early years of the sample occurred when Regulation Q ceilings were not effective. The slow-down in its growth in the late 1960's corresponds to effective Regulation Q ceilings, the decline in It in 1969 occurred when the dif— ference between interest rates and ceilings was large. A more sophisti- cated analysis of the effects of interest rates and ceilings on It is included in the regression analysis in Chapter 6. The values of Tt display a distinct seasonal pattern of behavior; Table D—5 gives quarterly figures for It. Substantial increases occur in Tt during the first quarter of every year; this is reflected by the fact that the first quarter of every year (except 1969) has the largest quarterly standard deviation and the lowest quarterly mean. During the second quarter, the rise in Tt continues but at a slower pace; in the last seven years of the sample period, It has fallen first during the 136 second quarter, then rises again, above the level reached at the end of the first quarter. During the third quarter, the level of Tt stabilizes at a level above that of the first and second quarters and fluctuates around that level but its level does not change much. During the fourth quarter of all but one year, Tt drops drastically; but, except 1969, It never drops back to the level of the first quarter of the same year, so that the overall increase in Tt continues unabated from year to year. Nondeposit Liabilities The data available for the various categories of nondeposit liabil— ities are deficient in a number of ways which hamper analyzing the effects of lagged and differential reserve requirements against nonde- posit liabilities. In addition, the structure of reserve requirements against these liabilities has been changed so many times that it is difficult to isolate the effects of lagged and differential reserve requirements for any reasonably long period of time. What follows is gdzag) of rt, as it should be analyzed (i.e., assuming perfect data). This specifi- a specification of the nondeposit liability portion (Enql cation will then be compared with what analysis is possible, given the available data. As was indicated in Chapter 3, the first nondeposit reserve require- ment was a marginal reserve requirement imposed on liabilities arising out of Eurodollar transactions which began on October 16, 1969. At the time this study began no data on this liability were available and therefore the "Eurodollar" category of nondeposit liabilities is ignored below. 137 Beginning June 21, 1973,17 a marginal reserve requirement was applied to certificates of deposit in excess of $100,000 (CDt) and funds obtained through issuance of commercial paper (CPt)° Beginning on that date then the nondeposit liability portion of rt would be represented by: N N “1,:A1,t“1,c’ where nl t = the marginal required reserve ratio against (CD + CP)t’ 9 + AN g (CD CP)t-2, l,t (CD + CP)t 03 = (CD + CP)t. l,t DP t Beginning July 12, 1973, the marginal reserve requirement on CDt and CPt was extended to cover funds from the sale of sales finance bills (SFt) and therefore nondeposit liabilities should be represented in the equation for rt by: N N n2,tA2,ta2,t’ where n2 t = the marginal required reserve ratio against (CD + CP + SF)t’ 9 N = (CD + C? + SF)t-2 2,t (CD + CP + SF)t A 17Since all reserve requirements against nondeposit liabilities were introduced after lagged reserve requirements were instigated, changes in reserve requirements are imposed on one date, but applied to nondeposit liabilities two weeks earlier. In each case, the dates referred to here are the dates when the reserve requirement was changed. For example, the reserve requirement which became effective June 21, 1973, was first applied to nondeposit liability levels as of June 7, 1973. 138 (CD + C? + SF)t a = ' 2,t DP t Beginning September 19, 1974, all three liability categories (CDt’ CPt’ and SFt) were divided into two maturity-length categories: those maturing in less than four months and those maturing in more than four months. The shorter-maturity group continued to be subject to the marginal reserve requirement against nondeposit liabilities, but the longer-maturity group was reverted to the original reserve requirement against time deposits in excess of $5 million (Tt,>$5)' After this change then the nondeposit liability portion of rt should be revised to: n A N N N N N N 3,t 3,t61,ta3,t + na’tk4’t62,ta4,t, where :3 ll marginal required reserve ratio against nondeposit liabilities maturing in less than 4 months; n = required reserve ratio against time deposits in excess of $5 million plus nondeposit liabilities, maturing in more than 4 months; AN _ (CD + CP + SF)t-2,_$4 months; 3,t (CD + 08 + SF)t , < 4 months (CD + CP + SF)t 6N = L154 months; l,t (CD + CP + SF)t dN = (CD + C? + SF)t; 3,t DP t AN 3 Tt-2, >$5m + (CD + CP + SF)t-Z, >4 months; 4,t Tt, >$5m+ (CD + CP + SF)t, >4 months SN 3 Tt, >$5m + (CD + GP + SF)t,>4 months ; 2,t (T>$5m + CD + CP + SF)t GN = (T>$5m + CD + CP + SF)t . 4 P D t 139~ The special reserve requirements against nondeposit liabilities were dropped on December 12, 1974, and were combined with time deposits in excess of $5 million. At that time the reserve category, time deposits over $5 million plus the three categories of nondeposit liabilities, was divided into two subcategories based on maturity-length: 30 to 179 days and over 179 days. For this scheme, the nondeposit liability specification is represented by: N N N N N + (“5,tA5,t53,t n6,t)‘6,t64,t)a5,t’ Where n5 t = the required reserve ratio against (T>$Sm + CD + CP + SF)t’ ’ maturing in 30-179 days; n6 t = the required reserve ratio against (T>$5m + CD + CP + SF)‘, ’ maturing in more than 179 days; A8 = (T>$5m + CD + GP + gnu-2L 30-179 days; 5,t (T>$5m + CD + CP + SF)t, 30-179 days 5N = (T>$5m + CD + GP + SF)t, 30-179 days; 5,t (T>$5m + CD + CP + SF)t AN = (T>$5m + CD + CP + SF)t-2, >179 days; 6,t (T>$5m + CD + CP + SF)t, >179 days 6N = (T>$5m + CD + CP + SF)t:_,>l79 days; 6,t (T>$5m + CD + CP + SF)t 6N = (T>$5m + CD + CP + SF)t. 5,t DP 1: Table 21 is a summary of the four different reserve schemes that have applied to nondeposit liabilities. The first deficiency in the data available for nondeposit liabil- ities arises from the fact that many of the reserve requirements imposed on them are marginal. That is, the required reserve ratios are applied 140 Am>onm wmcwmmvv u «26 “Aam + no + gov u so menace 6v dram + .8 + a8 .42 mnucoE «v .u 6 669. .336. + B + So n Me ms??? + M8 “a we? :55 I .53; 5 av Armm + mo + Gov « a x k .m maozom m>wmmom HQ 6 8 I m. Aam + no + nov 4 u Nuufiam + so + gov n .m« M6 New: qs\aa\m I m~\ma\s Amm + mo + gov « 8 N mamnom m>wwmmm I I I I I I I I I I I I I I I IuI I I I I I I I I IIIII I I I I I I I IIIIIIIII an H u n 25 Eu + 28 .4 u N636 + 8c ... 4T 4%.“? ES: - 2:26 Amo + Gov H memnom m>wmmmm d U U U U mumumamwmm mo coauawuumma u mo coauuom zozwzx aw mmumn m>wuoommm mnu mo cowumoflmwomam u w you coaumswm mnu mo aofiuuom Auwawaqu ufimommpcoz mnu mo coaumuwmwummm m£u mo humaanm .HN magma 141 mama oAHA .0 name mAHA . ammAev amWAav Aam + mo + no + NIn Aam + no + no + u Aam + so + no + av ammA mama mAHIom .0 Aam + no + so + av mama mAHIoM .0Amm + no + no + emwAHv mmma mAHIom .NI0Aam + no + no + ammxev I I I I I I I I I I I I I I m IIIIII an I 0 e I Aam + no + no + mmAHV U E flaw + so + no + mmAeV I m cos 3, E I :0 6A 0Amm + an + no + mmAav m :05 . E :0 «A 0Amm + mo + no + maxev I . I 0:0:68 «A N 0Aam + so + so + ammAev mHQUOENHmm MO GOHUHQflWQQ a 24 m 20 We “sawmmaoa + flamenco qt\m~\~0 I 65\N0\~0 Q QEMSUW 0>Hmmmm Md Z N 26 6 24 .v.uaoo I m mamnom m>ummmm u v a a can mwum m> uom 9 mo cowuwom zoz©ZA w a. a mum man mo nowumUMMAomam 605600860 .HN 60069 142 0a m a u Aam + mo + no + av u Aam + no + no + av a II ‘0 mam a.“ E 6 AAHA Aam + no + no + mmAev z .v.u:oo I e oEwLom m>ummmm muwuoEmpmm mo cowuficfimwa u a 6 a 6:6 u o no no 6 w an m z zozx w mnu mo coaumowmaumam mmumn m>wuommwm vmsnwucou .HN 60069 143 to changes in the liability items rather than their levels; or, pre- scribed base amounts of the liabilities are exempted from reserve requirements. In each case, the data that are available reflects levels of nondeposit liabilities. Therefore the data cannot be used to show changes in, or increases above a base level of nondeposit lia- bilities for an individual bank, which is the relevant figure for the determination of required reserves. This problem arises in calcula- ting the parameters for nondeposit liability Reserve Schemes 1, 2, and three of the parameters in Scheme 3. The marginal aspect of these reserve requirements is denoted by the asterisks attached to the appropriate parameters in Table 21. In all of the empirical work that follows, the marginality of these reserve requirements is ignored due to the lack of data. The empirical results for the 1:, 62, and aE-parameters are summarized in Table 22. The two parameters in Reserve Scheme 1 can- not be calculated because the data do not distinguish between funds arising from issuance of commercial paper and those from sales finance bills; Schemes l and 2 therefore are combined into the same Reserve Scheme. In Scheme 3, the breakdown of (CP + SF)t into those matur— ing in less than four months and those maturing in more than four months is not available. The only data available for (CP + SF)t are for those maturing in more than thirty days; the needed maturity-length break- down is available for CDt only. In calculating the AN- and 6N? parameters, the only data available for (CP + SF)t’ those maturing in more than thirty days, are used in both maturity—groups. In general, dates quoted in Table 22 do not match those defining the reserve schemes 144 mzm . a imam. 6 30A 0Aam + .6 + no + 3A5 I 64 mNmI «II a I 6 6N0A N 0Aam + no + no + mwxav z mxm I . a 6NNN6. 6 6N0 om 0Aam + 66 + no + mmxev I 60 mAm I I0 I I 6 6N0 on N 0Aam + no + no + smwxev z Amco006>06606 NV 6N\mN\N0 I 6N\6o\N0 .w wamfium Guru—0mg m o . a 66066. :0: 8 WA 0Aam + 660+ so + mmkav I 6‘ Nme0coa 6A NI0Aam + no + so + ammxwv z naucoa «v .u 6660.0 Amm + 66 + gov I 60 m :06 . Iu N :0 «v N Amm + no +.eov 0666006>06606 O06 6N\NN\00 I 6N\00\6 m mamzom o>uwmmm «z u Amwwm. Amm + no + gov n 0 NA NI0Amm + no + gov «z «z 0666006>06606 va 06N\NN\00 I mN\m0\6 NwH mmamnom oaommm AvAV mucmEouwnumm m>ummom wowwmg .0 cowumfi>ma cowumwum> coaumfi>ma 06606066666 mmucmwmmwwa umwfim ammz u A mo mumumEmwmm wnu mo mosam>v mmfiufiawanA ufimomwvcoz mo 0 :o muomwmm .NN macaw 145 0Amm + mo + no + 66 I m 6mooo. ANNoo. NNNoo. 6666c. momoo. NmoO6. 666 I I4I a 6 6 6N0 on 0066 + No +.ao + mwxav z 0666006>06666 6v 6NN6NNNO I 6N\66ANO & mausom m>wwmmm 0 603A + + no + a N 66660. NNmoo. NNmoo. Nm6mo. No6No. meac. N 660666 6 A .0A6m mu 666A 6 u 26 066 + no + no + av 0Amm +.mu + gov 0 omooo. onoo. onoo.I mmNNo. Nwmmo. N0o6N. 660666 6v .0 I6z6 N A66 + 66 + 666 66MM6HMM6 0666006606666 N06 6N\NN\00 I 6N\00\6 v c w m mamnum m>wwmmm Amov mucmEmufiavom m>uomom Hmwucmummwfio .N A666006>66666 m6Nv 0Aam + 666 600N0. mmooo. 0Nooo. m6MNO. 0Nwoo. 0Nwoo.0 6N\mN\N0 I a6\NN\o0 NI0gm + 66v 0Aaov 66606. NNwoo. m0ooo.I N660o. 6m00c. Nowma. 0666006506666 6N6 MHMIIII 6N\NN\00 I 6N\m0\6 A666 mmeowoumo Auwaanqu uawommwcoz umnuo cowumfi>ma msam> :mmz cowumwwm> o.H Eoum cmmz mumwcmum munaomn< mo GOHumw>mn mo cum: uCMwuwmwmoo mwmum>< mmucmummmwn umufim 666600666 .NN 6066a 146 ommao. ommHo. wONoo. «HAMH. HNqAH. ONNNO. ommao. ammoo. NNmHo. mmqmo. mmHAo. ommoo. womoo. momma. Hoano. Nqooo. Nmooo. maooo.l mmaoo. omooo. mNOAN.H ommmo.a Omoom. momma. u a a I 66 z m 0Amm + 60 +.mu + 00 Am60006>ummno HANV 6A\m~\~0 I mo\mm\oa q mamnom m>wmmmm u an m "5 ammAav z 0Amm + 60 + no + AmSOHum>Hmm£o NHV ¢N\NN\HH I ¢N\HH\m m mamnom m>uommm u 6 0I 6 100.66% Amm + mu + nov 6 Amc000m>ummno Amv 46A\A~\HH I mm\m0\o me mmamnom m>uommm 6 0266 66000006600 0066666662 .6 0Amm + 60 + 60 + 0v I 66 ma .0 a 0 66 6N0A A66 + mu + 60 + 66606 7 .v.0=ou I c maoaom o>ummmm cowumw>mo maam> can: wumvamum musaomn< wo one: £0006006> noflumfi>on mo vumvamum 0cmwofimwooo mmocmwmwwaa umuwm cmmz 666600660 .NN 60660 147 .606000060 00 600006>06600 0060000006 002 i .0600 .NN 0600000 w00000w60 .600006>06600 6006006>6 006 00 66660 60 6006> 600 000 .6500 .6 06086060 w00000w60 006>6060 0000 00060006 60 N0 060686060 6009a .6066 000000 0600 6008 00 w0000068 .Amm + muv 000 606 6060686060 006 w0006000060 00 6660 6066 6:0 600060600 M600600m>6 000 606 600008 0000 06:0 6006 00 606 650008 0000 06:0 6660 00 w000006e 66000 0000 60000 6006000 66066 606 06060 0600065500 00 00006w60mw6606 6:0 000 6066 608m .600006>06600 6006006>6 006 00 66660 606 6060606060 600 00 66006> 600 000 .qnm0 .00 06086006m 00 66000000 00060006 600686000060 6>06660 00 6w06£0 0600000006 60H 0 0: A600006>06600 0nmv 0 Nm0oo. 06000. 00000. mo0mo. mfiqoo. nonoc. 60\mN\N0 I mo\~N\O0 .0Amm + 00V 0 A600006>06600 why an . . . . . . .mIIII. No00o m0moo oANoo omm~0 mmmmo moAmm 6A\AN\00 I mn\m0\6 Anuv 6600ow6060 h00000600 0060066002 06000 000060>6Q 6006> 066: 00006006> 000060>60 0662 6066060m 6000060< 00 6066060m 00 066: 00600000600 66006060009 0600b 666600660 .NN 60660 148 in Table 21. In some instances this is merely because of lagged re- serve requirements; in other cases, it is because the dates for which data are available do not match the dates for which reserve schemes were in force. In each case, all available observations of data were used to calculate the parameters. It should be noted that all of the parameters calculated for Reserve Scheme 3 and the AN— and 6N- parameters in Reserve Scheme 4 are based on very few observations of data. Some authors18 have asserted that the various categories of non- deposit liabilities are quite volatile and therefore that application of reserve requirements in general to nondeposit liabilities, and spec-. ifically lagged and differential reserve requirements, introduces highly variable parameters into the reserve ratio. Given the many definitional and data problems described above, it is difficult to pre- sent any conclusive evidence on the behavior of Az’t, 6:,t’ and a:,t. It is however possible to compare the results for lagged and differ- ential reserve requirements against nondeposit liabilities to similar parameters for demand and time deposits to see whether A: and 62 are highly variable. Consider first the AN—parameters which are reported in the first part of Table 22. The results in Table 22 indicate that the variation in AN has not been large on an absolute scale. The coefficient of 9 variation is largest for Ag t’ corresponding to all three categories 9 of liabilities; the coefficients of variation for Ag t and A? t in 9 9 18See, for example, Burger, p. 57. 149 Reserve Scheme 3 are both smaller and when nondeposit liabilities are N combined with time deposits over $5 million in Reserve Scheme 4 (AS t 9 and A2 t) the AN—parameters are even more stable. The mean of A: t 9 9 is considerably below one for all but q = 3 (corresponding to nondeposit liabilities maturing in less than four months); this reflects the over- all growth in nondeposit liabilities. Thus the average deviation of A: t from its neutral value of 1.0 has been relatively large for all 9 but q = 3. The average deviation from one of AN q t is many times larger than 9 that for any AD- or AT-parameter (see Tables 1 and 4) for all q. This is due to the unusually high rate of growth in nondeposit liabilities in comparison to any category of deposits. The coefficients of vari- ation for A: t are however not large relative to those for A? t or 9 9 AT . Except for AN , the coefficients of variation for AN are of i,t i,t q,t the same general size as those for A? t and A: t; even the coefficient 9 9 of variation for A? t is exceeded by that for five of the AD- 9 parameters. The mean of the first difference of Ag t indicates sizable weekly 9 for all q. The mean of (A: - AN ,t q,t-l) is much larger N changes in Aq,t for all q than the mean of the first difference of any AD- or AT- parameter (see Tables 2 and 4). The mean of the absolute value and the standard deviation of the first differences of A: t are both small 9 D J.t' changes in the rate of growth) in nondeposit liabilities has been high for all q relative to A It appears that the rate of growth (and relative to any deposit category and therefore the average deviation N N N of Aq,t from one and the mean of (Aq’t Aq,t-l) are large relative to 150 other A—parameters. The weekly fluctuations that are characteristic of AD and AT however are smaller for AN so that the variation j,t i,t q,t in the level and first differences of AN t is not large relative to other X-parameters. The end of part one of Table 22 gives statistics for two additional categories of nondeposit liabilities, certificates of deposit and the sum of commercial paper and sales finance bills. As would be expected, these two categories show a lot of variation relative to the other A: t categories. This is true for both levels and first differences 9 and is especially true of commercial paper and sales finance bills. The results for 6: the parameters representing the application 9t, of differential reserve requirements to nondeposit liabilities, are presented in part two of Table 22. The 6N-parameters for Reserve Scheme 3, vary more than those for Reserve Scheme 4. This is apparent from the coefficient of variation for the levels of 6: t’ as well as 9 from the size and standard deviation of the first differences of 6: t' 9 Of course the small number of observations involved in both reserve schemes makes this a tenuous result. Comparing part two of Table 22 vary more than AN t for all q; to part one indicates that the 6N q,t q, this is, in general, true for levels as well as first differences. The coefficient of variation for 6: t’ for all q, is not large on 9 an absolute scale or relative to the coefficients of variation of 6? J9t E t' The mean of the first differences of 6: t is however quite 9 9 or 6 large and is much larger than the mean of the first differences of D T 63,t or 61,t' standard deviation of these changes is not particularly large relative Thus the weekly changes in 6: t are large but the 9 151 to that for 6? . The mean of I6N — 6N I is the same as the mean Jat q,t q,t-1 of (6N - 6N ) so that weekly fluctuations characteristic of the q,t q,t-1 other 6-parameters do not occur in 6: t' f Part 3 of Table 22 gives the results for a: t which denote the 9 ratio of each category of nondeposit liabilities to privately-owned demand deposits. The 0N t show considerable variation on an absolute scale as well as relative to the nonmoney deposits parameters, Yt’ It, Tt (see Table 17). Only the standard deviation of Tt exceeds that for a:,t for all q. The mean of the first differences of a:,t is also large for all q, larger than that for any of the nonmoney deposit parameters. The mean of the absolute value and the standard deviation , of the first differences of 6N t are also large; they consistently ex- 9 ceed comparable measures of variation for Yt and 1t and are close to or larger than those for T except under Reserve Scheme 1. t It is apparent that the categories of nondeposit liabilities rela- tive to privately-owned demand deposits vary considerably relative to other nonmoney items and therefore the application of reserve require- ments may well have introduced highly variable parameters into the reserve ratio. It does not appear however that the AN— and 6N- parameters are any more variable than comparable parameters for deposit categories. The limited analysis here however does not represent con- clusive evidence, especially in light of the data problems discussed above. Unfortunately the lack of comprehensive, consistent data on these liabilities makes further analysis difficult; consequently in the empirical work that follows reserve requirements against nondeposit liabilities are ignored. 152 Excess Reserves Since member bank excess reserves absorb base money like required reserves without "supporting" any part of the money stock, changes in the level of excess reserves will cause variation in rt. A given level of base money will correspond, all other things equal, to a smaller money stock, the higher the level of excess reserves member banks choose to hold. The control problem presented by excess reserves is reflected here in the parameter at. A plot of at shows it is extremely stable relative to the other parameters. As can be seen in Table 23, 8t and its variation are both very small. Its standard deviation is only .00093, the mean and stand-. ard deviation of (e - Et-l) are small, -.00001, and .00061, and the t mean of let - is only .00047. The relative stability of St is et-ll demonstrated by the fact that (St - Et-l) equalled or exceeded .00015 only 21 times in the 729 observations and never exceeded .0027. Thus at and its first differences vary much less than any of the other parameters in rt. Due to the small mean of 6t, its coefficient of variation is high relative to the other parameters. The trend during the sample period has been for St to decline. This can be seen in Table 24 which gives annual statistics for e ; the t mean of 8t dropped every year except 1973. A plot of 6t displays a tendency for the standard deviation of at to be larger after 1968; the average deviation of e from its mean is no larger in the latter years t of the sample period, but the frequency of such deviations is much higher. The best explanation of the fall in at is no doubt the overall increase in interest rates during the sample period. With the exception 153 womoo.l 00900. 06000. 0oooo.I A60m006>06690 mwnv 6 .060686069 600 00 66006060009 06009 .N 6NN00. 06666. 0N0oo. 0 0666006>06666 0000 6 .060606069 600 00 66006> .0 6w0600 00006006> 000060>69 6006> 0662 0%00663 mo 6066060m 6000060< 066w060 00600000600 00 066: A6590 I 0oa0v .060656069 6:0 00 66006060009 06009 606 66006>V 66>0666m 666009 .mN 6006B 154 Table 24. Annual1 Figures for 6t Percentage Change from Previous Year Standard Standard Mean Deviation Mean Deviation 1961 .00320 .00061 -- —- 1962 .00254 .00033 —20.625 -45.902 1963 .00206 .00050 -l8.898 51.515 19642 .00172 .00043 —16.505 -14.000 1965 .00149 .00036 -13.372 -16.279 1966 .00132 .00046 -11.409 27.778 1967 .00127 .00040 -3.788 -13.043 1968 .00107 .00043 -15.748 7.500 19692 .00075 .00043 —29.907 0.000 1970 .00056 .00030 -25.333 -30.233 1971 .00052 .00035 -7.143 16.667 1972 .00047 .00038 -9.615 8.571 1973 .00048 .00040 2.128 5.263 1974 .00034 .00025 -29.167 -37.500 1Based on 52 observations per year unless otherwise indicated. 2Based on 53 observations per year. 155 of 1970, each of the years showing the largest drop in 6t was also a year of high and/or rising interest rates. The two years in the sample period during which interest rates were low and did not rise, 1967 and 1971, were also years of relatively small declines in at. This relationship will be explored further in Chapter 6. Both the decline in 8t and its increased variation may however be artificially caused by the carry-over procedure introduced in the re- serve requirement system in 1968. Since the carry-over practice has been allowed, the weekly figures for excess reserves are often nega- tive which would exaggerate both the fall in 6t and the increase in its variation. The fact that the mean of at fell drastically in 1969 and 1970 seems to support that hypothesis. 0n the other hand, annual in- creases in either the standard deviation or coefficient of variation display no pattern to indicate that their increases were distorted in 1968 by the introduction of the carry-over procedure. In addition, the procedures used in 1972 to ease member banks into the new graduated reserve requirement structure also caused distortion in the data on excess reserves. The values of 8t follow a discernible seasonal pattern, as can be seen from the quarterly figures given in Table D-6. The largest quarterly mean occurs in the first quarter of nine years and the small- est quarterly mean occurs in the fourth quarter. The first and fourth quarters show the most fluctuation in st; those two quarters record the highest standard deviation and coefficient of variation in all but three and four years, respectively. This seasonal behavior will be further analyzed in Chapter 6. CHAPTER 5 THE VARIATION IN rt Historical Variation in rt Five different reserve requirement schemes were imposed on member bank deposits during the sample period; these reserve systems will be referred to below as Reserve Schemes A through E. In Reserve Scheme A, demand deposits are divided into two categories, those at city banks and at country banks, and all time and savings deposits are in- cluded in one reserve category. Reserve Scheme B uses the same two reserve categories for demand deposits, but introduces different re- serve ratios for time and for savings deposits.1 Under Reserve Scheme C, demand deposits at city banks and at country banks are each divided into those less than $5 million and greater than $5 million; there are three time and savings deposits categories, saving deposits, and time deposits less than and greater than $5 million. Reserve Scheme D employs the same seven reserve categories as Scheme C, but includes lagged reserve requirements. Reserve Scheme E, consists of the grad- . 2 uated reserve scheme for demand depo31ts. 1This does not correspond to the structural changes in reserve requirements. (See Table C-2, Appendix C). Time and savings deposits were divided into three categories (savings deposits, time deposits less than $5 million, and time deposits greater than $5 million) on July 14, 1966, but data for these categories are only available beginning Januaryju1,1968. Separate data on time deposits and savings deposits are available beginning September 7, 1966. Hereafter Scheme B is de- fined to correspond to available data rather than actual reserve cate- gories. 2On December 12, 1974, time deposits were divided further, based on maturity length. But since the sample period only includes four obser- vations after this change, it is ignored. 156 157 The dates defining the subperiods covered by each reserve scheme and the appropriate expression for rt are summarized in Table 25. Each of these five subperiods represents a period of time during which no structural changes in reserve requirements occurred. It is, there- fore, interesting to compare the amount of variation that has occurred in rt under the various reserve schemes. Table 26 gives the mean, standard deviation and coefficient of var— iation for rt and each of the parameters in the expression for rt for each reserve scheme. Comparing the standard deviation of rt for each of the five reserve schemes shows variation in rt fell when the first two structural changes were enacted. Upon the introduction of lagged reserve requirements in Reserve Scheme D, however, the variation in rt increased and it increased again under Reserve Scheme E, after gradu- ated reserve requirements were instituted. This result indicates that the latest structural changes in Federal Reserve reserve requirements, especially lagged requirements, have generated more variation in rt.3 As can be seen in Table 26, neither the standard deviations nor the coefficients of variation for v2 and v: are large relative to those for the other parameters in rt. This indicates that the existence of non- member banks has not been a major source of variation in rt for any of 3The comparability of the variation in r between subperiods may be questioned because changes in legal reserve ratios cause variation in r too and of course the number of magnitude of those changes is not the same in each subperiod. No changes in legal reserve ratios occurred in subperiods A or C. In the other three subperiods however, the vari— ance of d is at most .000006 and variance of t is at most .000002. Furthermoféf it is not clear whether more or less ’ variation in r for a particular reserve scheme can be attributed to the structural aspects of the reserve scheme alone, or to the particular time period it covers. 158 Table 25. Historical Specification of the Expression for rt Dates Reserve (Number of Es re i f Scheme Observations) p $3 on or rt A 1/1/61-9/7/66 r = Z (296) A’t j= -l ,Zdj,t6 j,t vtgt<1 + Yr + 1 t) + 51 T m E n tl,tvtTt+€tpt + wh,twh,tot h=1 B 9/7/66-1/11/68 r = Z (70) B’t j= =1,2dj,t(S j,t vtgt (1 + Yt: + 1t)+ T T m ._2 ti,t61,tVtTt + €tot + 1-2,3 51 Z w 6h on h=1 h,t ,t t 6 6D C 1/11/68-9/18/68 rC t = jZ djé t tvt Dgt (l + Yr 4 1t) (36) ’ =3 3 5 T 521 n ii3t 1, :51, tvtTt + 5 do +h= leh,twh,tpt 6 D D 9/18/68-11/9/72 r = Z d A ng (1 + y + 1 ) + (217) D,t j=3 j, t j,t 6j,t vt t t t 5 T T VT 2 ti, tXL téL t VtTt + 6to + 1= 3 51 n hilwh,twh,tpt 11 D D VD E 11/9/72-12/25/74 rE t = 2 dj tAj th t vt€t(l + Yt + 1t) + (111) ’ j=7 ’ ’ ’ 5 m T T T 1:3ti,txi,tai,tvtTt + 5:9 + 51 n 2 wh,twh,tpt 159 Definitions of Symbols for Table 25 Subscripts j and 1 Reserve Category Reserve Scheme j = 1,11; j = 1 city banks A & B j = 2 country banks j = 3 city banks, <$5 million j = 4 city banks, >$5 million C & D j = 5 country banks, <$5 million j = 6 country banks, >$5 million 3 = 7 <$2 million j 8 $2 million - $10 million j 9 $10 million - $100 million E j = 10 $100 million - $400 million j = 11 >$400 million i = 1,5; 1 1 total time and savings deposits A i 2 total time deposits B i 3 total savings deposits B, C, D & E. i = 4 time deposits, <$5 million C, D & E i = 5 time deposits, >$5 million C, D & E dj t required reserve ratio against the jth demand deposit category; 9 ti t required reserve ratio against the 1th time deposit category; 9 member bank net demand deposits in the jth reserve category, AD lagged twopperiods ; j,t member bank net demand deposits in the jth reserve category, current period member bank time deposits in the ith reserve category, lagged AT two periods 3 i,t member bank time deposits in the itfi reserve category, current period 6D member bank net demand deposits in thepjth reserve category. j,t member bank net demand deposits ’ 6T member bank time deposits in the ith reserve categppy. i,t member bank time deposits ’ vD member bank net demand deposits t net demand deposits in all commercial banks’ vT member bank time deposits t time deposits in all commercial banks’ 6t net demand deposits in all commercial banks gross demand deposits in all commercial banks’ 160 Definitions of Symbols for Table 25 - continued U. S. government demand deposits. privately—owned demand deposits ’ interbank demand deposits privately-owned demand deposits’ time deposits in all commercial banks. privately-owned demand deposits ’ member bank excess reserves. member bank total deposits ’ member bank total deposits privately-owned demand deposits; nonmember bank vault cash in the hthstate nonmember bank total deposits in the hth state 9 nonmember bank total deposits in the hth state. nonmember bank total deposits ’ nonmember bank total deposits = privately-owned demand deposits 161 mmmmo. 00000. «m000m. «600000. «*mmmoo. 0N000. 00000. mm000. 00N00. «6N0000. 00600. 00000. 00000. 00000. «600000. «*00N00. 00000. «000N0. «000N0. 00000. 00000. 00N00. . ._. 66660 6 U 66660. 6 U 66666. > U . 0 N/ 66006 0 U . 9 66666 «6 6666. 66 6 6 . 6.6 66666 06 . 6.6 66666 66 . 6.6 60606 66 . 6.0 66666 66 66660. 6 66 6666 6660060u666666 um GEMSUW 0>H0mmm 06000. 00N00. «60000. 6600000. 66000. «£05000. 06000. «6000N0. 000N0. . 0. 66660 6 U 66666. 6 U 06666. 6 o u 66606 06 U . 9 66666 66 . u 66666 66 . 6.6 66666 66 66666. 6.66 Q A 66660. 6 66 66666 666666-066060 6< 606006 6>0666m 0O0u6006> MO 66606660600 0o0060>60 00600606 0662 u 00066006> HO 66606066660 000060>60 0662 6 :0 66066066> 6:6 0o 66oumm 06666o6m06 .66 60660 162 00000. 05000. 05000. ««00000. 00000. 00000. 05000. 05000. 00000. 00000. ««00000. 00000. 00000. 00000. 55050. 50000. 50500. 00000. 00000. 00000.0 00050. 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P c00um0um> c006m0>m0 cmmz :00uw0um> a00um0>m0 ammx we 00m0GMum mo vumvamum . uam0u000moo ucm000mmmoo wmsa0ucoo .00 m00ma 163 u 660666. 66006. 66666. 6» 666666. 600006. 66666. 6 u u 66606. 66606. 66666. 66 6666666. 66666. 66666. 66 u u 66606. 66606. 66066. 666 6666666. 66666. 66666. 66> u 0. 66606. 66666. 66606. 69 66666. 60666. 06666. 69 . 6.6 . . . 6.6 66666 666666. 66666. 66 66606 66666 66666 66 . . . 6.6 . . . 6.6 60666 66666 66660 66 66606 6666066 60660 66 . . . 6.6 . . . 6.6 66066 666066 66666 66 66606 66666 66666 66 . 6.6 66006 06006. 66666. 60 . . 6.6 ««00000 ««00000 00500. H0 . 6.0 6666666 66666. 60666. 60 . . . 6.6 . . . 6.6 66666 66666 66666 66 66606 06666 66666 66 . . . 6.6 6.6 66666 66666 66660 66 66006. 66066. 66660. 66 :00um0um> :00uM0>w0 cmmz :00um0um> c00um0>m0 cam: 00 vumwawum mo wuvaMum . 66606066666 66606066606 666606666 66 60666 164 00000. 00000. 00000. ««00000. 00500. u600 00666. 66666. 60 66606. 66666. 6.M0 66606. 66666. 6.M0 6666066. 06666. 6.M0 66666. 66660. 6.66 60000.66666660u6666600 "6 666666 6>66666 6. u 66666. 60606. 06606. 0 666066. 660606. 06606. 03 u .6 66666. 66666. 66606. 0 66666. 06666. 66606. 06 u 666066. 6666666. 66666. 666666. 6666666. 60066. 66 u u 660666. 666660. 06666.0 66666. 666066. 66666.0 6 u 66666. .66006. 66660. M 66666. 66666. 66660. 66 u 06666. 66006. 60660. 66666. 66666. 66660. 60 c00um0um> :006m0>w0 cmmz :00uw06m> a00um0>m0 can: 00 vumvamum mo UnawaMum 66606066666 66606066666 66:6066oo .66 60666 16S 00000. «00000. 00000. 80 6.0 50000. 00000. 00000. 90 6..6 05050. 00000. 00000. 90 . 6.6 00000 00000. 00000. 90 . . 6.0 ««00000 ««00000 00000. H0 6.6 ««00000. 00000. 00000. H0 0 00000. 00000. 00000. u 0M0 66606. 60666. 66606. 6 6M6 6.6 00000. 00000. 00050. 00 6.6 00000. 05000. 00000. 00 6.6 00000. 00000. 00000. 00 66666. 666666. 66666. 6 0M0 :00uM0um> a00uM0>m0 ammz a00uM0um> c00um0>mn emu: mo vumvamum mo vumvamum . 66606066666 66606066666 666606666 .66 60666 166 .mms0m> umm00mam mmunu mmumo00c0«« .mms0m> ummwum0 manna moumu00a0 um .m memnum m>ummmm you mmuMum 00 so mco0um>ummno 0 60 mamnom m>hmmmm wow mmumum 00 so m=O0um>ummno 0 so 0mmmm .0 mamnom m>6wmmm now mmumuw 00 co mc00um>ummno 0 60 mamnom m>6mmmm How mmumum 00 co m:00uw>ummno 0 m< mamsom m>ummmm How mmumum 00 so mao0um>ummno 50 co 00mm0 0 60666. 06606. 06606. N3 66666. 66666. 66606. “6 606666. 6666666. 66666. 66 666666. 666660. 66666.0 66 U 66666. 66006. 66660. 66 66666. 66006. 00660. 60 666666. 66606. 66666. 6» 66666. 66666. 66666. “6 00606. 66666. 66666. 6M6 66606. 66666. 66666. “6 c00um06m> :00uMH>00 ammz mo vumvamum 66606066666 666606666 .66 60666 167 the four reserve schemes. In the first three reserve schemes, v? and v: have lower coefficients of variation than any of the other parameters in the expression for rt. In Reserve Schemes D and E, the coefficients of variation for V2 and v: are smaller than those of all other param- eters except some of the A-parameters and one G-parameter in Reserve Scheme D. The coefficients of variation for v2 and v: are however exceeded by those for two A-parameters in Reserve Scheme D and by those for four A—parameters in Scheme E. The variation of the A- and 6- parameters for individual reserve categories understates the total var- iation generated in rt by lagged and differential reserve requirements. Therefore the above results show that in each of the reserve schemes, v2 and v: display less variation than do the other parameters in rt. There is also no support here for the claim that nonmember banks have become a more serious problem in recent years. The standard deviations of v? and v: are largest under Scheme D; their standard deviations in the time period covered by Scheme E are however smaller than during Scheme A. The parameters that show the consistently largest coeffic- ients of variation for all reserve schemes are Tt’ Yt’ and et’ repre- senting time and government deposits and excess reserves, respectively. In the first three reserve schemes, the variation of wt, representing the distribution of nonmember bank deposits between states, is also large. While the variation of the parameters in the expression for rt pro- vides a way of comparing their relative variation, it does not measure the variation that each parameter causes in rt. This is because each of the parameters is combined multiplicatively with the other parameters in the expression for rt so that any change in a given parameter is 168 first multiplied by several other parameters before it is translated into variation in rt. That is, the variation in any given parameter causes variation in rt that is first weighted by the parameters by which it is multiplied in the expression for rt. In the next section a method is devised which deals with this problem. "Partial Variation" of rL L Variation in rt is caused by simultaneous variation in all param- eters in the expression for rt. To isolate the effects on rt of vari- ation in each of the parameters alone, the values of all other param— eters are held constant at their means, so that only the variation in one parameter causes variation in rt. This will be referred to as the partial variance of rt. The following result for the variance of a linear combination of random variables is employed in deriving the partial variance of r : I: If g is a function of random variables such that, n g(xl, x2, ...xn) = Z aixi + c, then 2 4 a. var (x ) + Z a a cov(x , x.) . 1 i i i,j=l i j i J i#j (5-1) var (g) = i "Mt-'5 Consider the following expression, taken from Table 25 above, for rt for Reserve SCheme A with the A-parameters included: (5-2)r=2 DDD + IT + A" j=l,2dj,txj,t5j,tvtgt (1 + Y: + 1t) tl,tAl,tvl,tTt m51 n etpt + hilwb,twh,tpt ° 4Maurice-G. Kendall and Alan Stuart, The Advanced Theory of Sta- tistics, Volume 1 (London: Charles Griffin and Company Limited, 1963), p. 231-3. 169 To derive the partial variance of r due to lagged reserve require— A,t ments, denoted by var A (r ), the values of all parameters in r A,t A,t D but A1, t’ A2,t and Al t are held constant at their means. Represent- ing the means of variables by a (-) over them, equation (5-2) for rA t 9 then becomes, _ - D -D —D— - (5-3) rA,t - .E dj,t Aj,t6j,tvtgt (l + Yt + 1 ) + J-l,2 51 ‘ 63T¥+25+zwap l,t l,t t t t t h=1 h,t h t t Employing the result represented by equation (5—1), the partial vari- ance of rA t due to lagged reserve requirements is then, 9 2 (5-4) var A (rA,t) = [V?St(1 + Yt + 1 tfl [;E 1 235 t(3j t)2 var (Ag’t) - -D D D + 2(‘11,‘1 c 2, 1:51, :32, t CW (11, t’ 12,9] 2 + (5T ¥)2 [2:48:19 var (1T )] tt - - -D D T [3'21 zdjn: ti,t‘sjnz CW ”j,t-$1.9] + + [2v 5 (l + Yt 1t) vt Tt] The partial variance of r due to differential reserve require— A,t ments is analogously represented by: - _ _ 2 -132 (5-5) var 6 (ra ) = [VDEtU + Yt + 18] L21 2 d? txj t var (Git) - - D D D + 2“1, td2, txl, tXZ, t C°V (61, t’ ’52 ,t% 170 Table 27 shows the expressions for varA(rt), var6(rt), varv(rt), varY(rt), var1(rt), varT(rt), and var€(rt), the derivations for which are presented in Appendix E. The expressions for the partial variance of rt are different for different reserve schemes as the definitions of j and i vary. This is detailed in the bottom part of Table 25. Table 28 gives the results for the partial variance of rt for each reserve scheme. The partial variance due to lagged reserve require— ments is calculated for all reserve schemes even though lagged reserve requirements were not instituted until September 18, 1968. Schemes C and D are therefore combined into one subperiod, labelled Scheme D', containing 253 observations. Using the alternative definitions of VE*, 1*, and 5: described above, the figures for varv*(rt) and var1*(rt) t are also given in Table 28; using the values of v2*, 1: and 5: however makes very little difference in the calculation of the other partial variances. As can be seen in Table 28, the variation in rt caused by lagged reserve requirements has increased steadily with each new reserve system.5 Differential reserve requirements however caused the great- est variation in rt under Reserve Scheme D' although the partial vari- ance is larger under the current graduated reserve system than under either scheme based only on the city-country distinction for demand deposits.6 The partial variance in rt contributable to nonmember banks 5This is true on an absolute scale, but not if varx(r ) is expressed relative to var(r ). The ratio var (r )/var(r ) is largesE for Scheme B and smallest for Scheme E. This is because var(rt) is larger for the periods of time covered by Schemes D' and E. 6The ordering between reserve schemes is again changed if var (rt) is expressed relative to var(r ). Var6(rt)/var(rt) is largest for Reserve Scheme B and smallest for E. 171 u. m.- 6u6fl u. flu.“- Haw. \ >ou \ \ um> A no any OK OK w m w +A may 6.6 6.6 m u u .u u u 6 mucmEmuwncmm m>ummmm Hmwucmummmwa NA mwva .mvw A w + m + Hy w 0 n A My um> 6.0 6.6 00 .6 6.6 666.. 6.6 6.6 n.6u66n66 n pu>Au0 + u» + 0vuw69. + 6.6 66 - -66-- - .6-6 \6*6 66.-06 .6.666>666.-666.036.-066.06 -w W + 6 6 6- .66 - - 6 6.6 6.6 6.6 on u > 6 666 6. 66 6.6666 666 6 6667 .6666 66.66 6.6 6>666.-6 6.6 6.-666.66 -M M + ex ex ale am | I 6.6 6.6 6.6 6 u u on u .6 mucosouwsvmm w>ummmm wmwwmq A mxvum>~A nmvNA mvw A w + m + HV mam n A My nm> N Op 652 up we moamfium> Hmwuumm u 6 mo mocmfium> Hmwuumm wcu you mCOHumsvm mo cOHum06maumam .NN magma 172 6.6 6 a a muwmoamn unmecuw>ou A6>Vum> A66 + Hvuwu>u “mu nK um n Aunv>um> N .l IQI 0' Q In 6 H 9. 9 >00 66 66 6 6.0 6.0 6.6 6 6 6 6.6 6.6 6.6 m w 6m 66 N66 6 + w + 0ww .m K .6 66 + 6 a a a Au9vum> uPu we» H&u Haw + H N I HI HI I a a a mxcmm umnEmEcoz Am>vum> Auw + 6» + Hvuw6 Mmu MHu mwnw n Auuv?um> N 6.6 .6.6 > o A He any 0 6.666.6 6.666.66w M 66.6> 666 + 666 + 066669 + 6- ex - .- -6- - - .6- \6mfi H 9 HM BK I I 66.63....» 66.666 66.066“ 66.66 + H N HI N I N IHI 06 man up mo woam66m> Hmfiuumm 666606666 .66 60666 173 mm>memm meUXm— mufimoamn 6869 muflmoama xcmnumucH 6666666 66.66 . . . 6 6 6 6 6 6 6 6 6 6 66..» 66 66 66 66 N A6» + 066M696.6 6.6 6.6 6 Auuvw6m> Auuvvum> AuMV6Hm> 06 man 6 mo ouamwum> Hmfiuumm .NN maan 174 Table 28. Partial Variance of r (All amounts are expressed in the form E -05) Reserve Scheme (Number of Observations) A and B (366) D' and E (364) A (296) B (70) D' (253) E (111) varA(rt)l .3396 .4066 .4593 .5560 var6(rt) .0299 .0668 .1000 .0880 varv(rt) .1391 .0260 .5646 .1374 varv*(rt) .1416 .0602 .6221 .1354 var (rt) .2538 .1181 .1003 var1(rt) .0289 .1873 .0874 var1*(rt) .3156 1.9411 1.1106 varT(rt) 3.1964 .4377 6.1066 var€(rt) .2312 .0935 .0819 var(rt)2 1.298 1.212 2.793 3.864 1.310 3.533 1 . . The sample period for each reserve scheme contains the indicated number of observations, minus two. 2The calculations of r here includes the A—parameters for every reserve scheme, so the variance of rt in Table 26 above. given here does not match that 175 was also highest under Reserve Scheme D'; this was a period during which the variance and covariance of v? and v: were especially large. Since 1972, however, the variance of v? and v: has declined so that varv(rt) under Reserve Schemes A and E are nearly identical. The same pattern of results occurs for varv*(rt) of rt when the alternative definition of V2* is used. The variance of rt attributable to government deposits is largest for the first half of the sample period (for Reserves Schemes A and B), and is only half as large after January, 1968. The disturbance in rt caused by interbank deposits is greatest during the latter part of the sample period, especially during the 1968-1972 period. The same pattern shows up in the results for var1*(rt), but the variation in rt caused by interbank deposits is much greater when the alternative definition, I: is used. The variation in rt caused by time deposits is also greater for the latter years of the sample period. The dis- turbance attributable to excess reserves, however, is smaller during the end of the sample period, reflecting the relative low levels of (and therefore little variation in) excess reserves after 1967-68. It can be seen from Table 28 that under every reserve scheme the major source of variation in rt is variation in It. In addition, dif- ferential reserve requirements are a minor source of disturbance in rt under all four reserve schemes. Under both Reserve Schemes A and B, the second largest source of variation in rt is lagged reserve re— uirements, followed by government demand deposits (or interbank de— posits, if the alternative definition, 1:, is used). Under both of those schemes, the partial variance in rt caused by nonmember banks is relatively small. 176 Under Reserve Scheme D', the disturbance in rt caused by nonmember banks is much larger: varv(rt) is larger than either varA(rt) or var6(rt) and is only exceeded by the partial variance of rt due to time deposits or to interbank deposits if the 1: definition is used. Under Reserve Scheme E, varv(rt) is again smaller and is again exceeded by varA(rt) as well as varT(rt) and var1*(rt). In summary the partial variance of r caused by nonmember banks is t of major importance only under Reserve Scheme D', during a period when v2 and v: were particularly unstable. In each of the other reserve schemes the disturbance caused in rt by nonmember banks is smaller than that caused by lagged reserve requirements and time deposits. 0n the other hand, varv(rt) is not zero; the existence of nonmember banks clearly introduces some variation in rt. The variation in rt caused by differential reserve requirements is small for all reserve schemes; nonmember banks cause more disturbance than differential reserve require- ments except during the very short life of Reserve Scheme B. The par- tial variance of rt caused by both government deposits and excess re- serves is much less during the latter years of the sample period, in- creasing the relative importance of varv(rt). A Naive Forecasting Mbdel It is possible that while the parameters in rt vary, any one of them may vary in a sufficiently predictable fashion to pose no serious control problem. To investigate the predictability of the parameters in rt, two different forecast models are employed. First, a naive fore- casting model is used to calculate the error in r that results from 1'. assuming there is no change in each of the parameters. Second, in the 177 next chapter a model is estimated for each of the parameters in rt, which then provides a more sophisticated forecast for each parameter. The two forecasting experiments are then compared, using the loss in terms of accurate predictions of rt as a criterion. In a control situation, the simplest solution in week t to the lack of knowledge of the actual values of the parameters that comprise rt, is to make a no-change assumption. This naive model provides a forecast value of r , denoted ? , t l,t . _ D D D (5'6) r1,: ‘ §dj,txj,t-16j,t-lvt-lgt-l (1 + Yt-l + 1 ) t—l T T T m + Eti,txi,t-l i,t-lvt-th-l + Et-1pt-1+ :wh,t-l n 7 wh,t-lpt-l' The average error in predicting rt by this method is represented by the mean square error defined as, (5-7) MSE1 = ZHFJ IIMZ A N I > V V t l where N is the number of observations. The value of MSEl for each re- serve scheme is given in the first part of Table 29. The loss, in terms of accurate forecasts of rt, attributable to the naive forecasts of one parameter (or set of parameters) is then cal- culated by assuming perfect knowledge of it (them), while retaining the no-change assumption for the other parameters. For example, for lagged 7The calculation of r , 21 t and f (defined below) includes the A—parameters for all reserve schemes, ’ even though lagged reserve requirements were not in effect until Reserve Scheme D. 178 Table 29. Errors Resulting from the Naive Forecasting Model (Results of the Calculation of El) Reserve Scheme (Number of Observations) A (100) B (69) D' (100) E (111) MSEl .7235 E-OS .7837 E—05 .7767 E-OS .9376 E-05 E: -.0086 .2534 .2014 .3826 8? —.0333 .0110 .0199 .0294 E: -.0077 .0245 .0527 .0214 E: .1858 .1266 .0577 .0930 E; -.O672 - 0510 -.1808 -.0666 E: .2666 .3117 .2677 .2903 E: .2612 .1643 .1246 .2103 179 reserve requirements it is assumed that the current value of each X-parameter is known, but that the best available estimate for the other parameters is their value in the previous week. Thus, ?: t is defined as 1 _ d D D 0 — 2 + 2,t j j,t j,t j,t-1Vt-1g (1 Yt-l + I t—l t-l) T T T m + + iti,txi,t6i,t-lvt-1Tt-l E:-;-1"-;-1 n + Ewb,t-lwh,t-lpt-l° The error associated with this forecast of rt is given by N A _ 1 AA 2 (5-9) MSE2 - N Z (rt r2,t) t=l Comparing MSE; with MSEl shows the benefit (in terms of more accur- ate predictions of rt) accruing from perfect knowledge of the 1- parameters. The value of MSE: relative to MS'E1 also implies the error introduced into the forecast of rt by the naive forecasts of the A's. To facilitate this comparison, the error-coefficient EA is defined as 1 X MSEl - MSE; (5-10) E1 = MSEl MSEl 1 - MSE2 . 1 A value of E: close to one implies that the damage (in terms of poor forecasts of rt) done by assuming no change in the A's is large; or that the gain from perfect knowledge of the A-parameters is large. A near- zero value of EA indicates that a no-change assumption for the A- 1 parameters contributes only small errors to the forecast of rt, or that 180 the benefits of forecasting rt from perfect knowledge of the A's are small. A negative value of El will occur if MSE2>MSE1, which implies that the error in rt is smaller with a no-change assumption for the A's than with perfect knowledge of them. The concepts MSE2 and B1 are defined analogously for the other parameters in rt. The value of El for each of the parameters in rt for each reserve scheme is given in Table 29. For Reserve Schemes A and D', only the last 100 observations are used. Because of programming limitations, only 100 of the observations in Reserve Scheme A and D' could be used in the forecasting model described in succeeding chapters; the same limitation is therefore imposed here to make the results of the two forecasting experiments comparable. None of the error-coefficients are especially close to one so apparently the error resulting from the naive forecasts is not large on an absolute scale for any of the parameters. The value of £1.13 rela- tively large for Schemes B and E; for Reserve Scheme E, the error- coefficient for the A-parameters is larger than that for any other parameter. The partial variance of rt also showed that lagged reserve requirements caused more disturbance in Reserve Scheme E than the others. The value of E6 is very small for all reserve schemes, although it 1 is larger for each successive reserve scheme. The value of E: is also uniformly low for every scheme; it is largest under Scheme D', as is var§(rt). These results indicate that the distribution of deposits be- tween classes of member banks and between member and nonmember banks is relatively stable; therefore assuming no change in the G-parameters and v2 and v: introduces very little error in the forecast of rt and even perfect knowledge of them provides little net benefit. 181 1 Several of the E-coefficients are negative under Scheme A and E1 is consistently negative for all schemes. In these cases, perfect knowledge of the parameter(s) in question results in poorer forecasts of rt than assuming no-change. The error-coefficient for the other nonmoney deposits and excess reserves are relatively large for all reserve schemes. The value of EY is smaller for each successive re- 1 serve scheme, as is vary(rt). Except for Reserve Scheme A, the larg- est error—coefficients are consistently Bi, E1’ and E This implies E 1. that the variation in time deposits, excess reserves, and the 1- parameters causes the largest errors in forecasting rt by a no-change procedure; therefore the most benefit can be gained from more accurate forecasts of the A's, Tt and €t° Summary of Findings Comparing the three measures described above for the variation and predictability of the parameters in rt, the results are not always con- sistent, but some general conclusions may be drawn. It is frequently claimed that the increase by the Federal Reserve in the number of classes of member banks has introduced increases variability into rt. The results reported in this Chapter support this claim. The value of varA(rt) is consistently larger for each successive reserve scheme; var6(rt) in general rises as more reserve categories are added, although var6(rt) for Scheme E is smaller than for D'. In addi- tion E: is largest under the graduated reserve scheme and E? is con- sistently larger with more deposit categories. This means that the naive forecasts of the A- and G-parameters result in the largest errors under the graduated reserve scheme. Thus under the graduated scheme, 182 more variation is introduced in rt via the A- and G-parameters and easy forecasts of these parameters are less successful than under previous schemes. It is also commonly claimed that nonmember banks cause less dis- turbance in rt than do lagged and differential Federal Reserve reserve requirements. The results given in the first section of this Chapter support this contention; the standard deviations of v2 and v: are in general smaller in all reserve schemes than those of the A- and 6- parameters. The partial variance of rt is also smaller for nonmember banks than for lagged reserve requirements, except under Reserve Scheme D'. The value of Ev is also much smaller than EA for all re- 1 l serve schemes; the naive forecasts of v? and v: are therefore much more successful than for the A-parameters and much more can be gained from better forecasts of the A's. It is concluded that lagged reserve re- quirements have in general caused more variation and unpredictability in rt than nonmember banks. For differential reserve requirements the results are less consis- tent. The varv(rt) is larger than var6(rt) for every reserve scheme except B. The naive forecasts of the d-parameters also result in smaller errors than those for VD and VT except under Reserve Scheme E when E6 t t 1 V and E1 are nearly equal. In general the disturbance in rt caused by differential reserve requirements is small and there is no convincing ' evidence here that they represent a more serious control problem than nonmember banks. These results do not support the view that the disturbance caused by nonmember banks has increased in recent years. The standard devia- tions of v? and v: are smaller for the period covered by Reserve Scheme 183 A. The value of varv(rt) is nearly equal for Schemes A and E. The value of E: is largest under Reserve Scheme D', but is nearly the same for Schemes B and B. All three measures of variation show that nonmoney deposits, especially time deposits, and excess reserves are consistently serious sources of disruption in rt. All three measures also imply that lagged reserve requirements are a more serious control problem than differ- ential reserve requirements. CHAPTER 6 ESTIMATION OF ARIMA MODELS FOR THE PARAMETERS IN rt Introduction In this chapter a more sophisticated forecast equation is esti- mated for each parameter; these forecast results are then compared to the results in the last section of Chapter 5. The technique employed here is the time series analysis developed by George E. P. Box and Gwilym M. Jenkins.1 The first step in developing a time series model is to achieve stationarity in the series to be described. Stationarity requires that the series remain in equilibrium about a constant mean; that is, displacement through time has no effect on the joint probability dis— tribution of any set of observed values. Consider, for example, a time series of observed values of yt. The series yt is said to be station- ary if the joint probability distribution for m observations, yl, y2...yt , is the same as that for the m observations, m y1+k’ y2+1<, . . . ytm+k, where k is some integer. In practice, stationarity is achieved by differencing the data. Thus even though the original series yt may not be stationary, some degree, d, of ordinary differencing will in general make the series Adyt stationary. The differenced series Adyt may also be represented by the backward shift operator, B. The Opera- tor B is defined such that (l - B)y = yt - yt_1. 1George E. P. Box and Gwilym.M. Jenkins, Time Series Analysis: Forecasting and Control (San Francisco: Holden — Day, Inc., 1976). 184 185 Therefore the dth ordinary difference of yt can also be represented by (l - B)dyt. Most of the series analyzed in this study show pronounced seasonal behavior and therefore seasonal differences of the data also must usually be taken to ensure stationarity. The degree 3 of seasonal differences of yt is denoted ASyt; here the seasonal period is 52 so that, S = .- A yt yt yt—52' Henceforth, zt will be used to represent the differenced series AdAS where d and s are of necessary degree to achieve stationarity in yt. t In practice, d and s are usually less than or equal to two. The Box-Jenkins methodology consists of representing zt by either i a moving average model or an autoregressive model or a combination of both (referred to as an ARIMA model). In a moving average model the stationary process zt is represented by the weighted sum of current and past disturbances, denoted here by at. That is, the moving average process is written, (6-1) 2 = a - 9 — 6 t y lat—1 Zat-Z - "°" where 81 are called the moving average parameters from zt. Typically it is assumed that Bi = O for i > q where q is known as the order of the moving average process. Equation (6-1) then reduces to, (6-2) 2 = a — e - e t t lat-l Zat-Z "°° eqat-q° A moving average process of order q is often denoted MA(q). In terms of the backward shift operator, an MA(q) process may also be written _ _ _ 2 _ _ q (6 3) 2t - (l 91 B 62B ... GqB )at. 186 The invertibility condition for a MA(q) process is that the roots of equation, (6-4) (1 - e B - e 32 - - 6 sq) = o 1 2 ... q lie outside the unit circle.2 There are no restrictions on the 8i parameters needed to insure stationarity for the MA(q) process. The autoregressive process is one in which zt is represented by the current disturbance and a weighted sum of past observations of zt. That is, (6-5) zt = ¢lzt-l + ¢ZZt-2 + ¢32t-3 .... + at. The autoregressive parameters ¢1 are assumed to be equal to zero for i > p, where p is the order of the autoregressive process. Thus the autoregressive process of order p, AR(p), is, + a . (6-6) 2 = ¢lzt-l + ¢22t-2 + .... + ¢pzt-p t t The AR(p) process may also be written using the backward shift oper- ator, P _ (6-7) (1 - ¢l B - ¢2B - .... - ¢pB ) zt - at. In order for an AR(p) process to be stationary the roots of the equa- tion, 2 p- (6-8) 1 - $1 B ¢2 B .... - ¢p B - 0, Bi must satisfy the condition IBiI < 1. No restrictions are required on the parameters ¢i to ensure invertibility.3 The stationary series 2 may also be represented by a mixed ARIMA t process which is a combination of MA(q) and AR(p) processes so that, 21bid., p. 67. 3ibid., pp. 53-54. 187 .. = + +.... + "' ' (6 9) Zt ¢lzt-1 ¢22t-2 epzt-p at 91at_l 62at_2 a O ¢q t-q Equation (6-9) may also be written in terms of the backshift operative B so that, 2 p _ _ _ 2 _ _ (6-10) (1 - ¢1B ¢ZB — ... - ¢pB )zt - (1 91B 62B ... Oqu)at. To ensure stationarity and invertibility of a mixed process, the roots of equations (6-4) and (6-8) above must all lie outside the unit circle.4 Moving average, autoregressive or mixed processes will be denoted here by (p,d,q)(d,s), where p and q represent the orders of autoregres-p sive and moving average processes, respectively; d is the degree of ordinary differing and s is the degree of seasonal differing needed to achieve stationarity. Identification of the orders p and q is made by examining the auto- correlation and partical autocorrelation functions of zt. The autocor- relation of zt a lag k is defined to be E[(zt - u) (zt k - u)] pk “ 2 2 «flat - u) 1»: [(zt+k - u) 1 (6-11) "' E[(zt - u) (zt+k - 11)] 0' Z where u is the mean and Oz is the standard deviation of the series zt. The estimated value of pk is given by, 4ibid., pp. 73-74. 188 (6-12) rk = c , o 1 N-k _ _ ck ='fi til (zt - z)(zt+k — z) for k = O, l, 2 ... K, and E is the sample mean of 2t and N is the number of observations on zt. The partial autocorrelation function comes from expressing an AR(P) process as p nonzero functions of the autocorrelations.5 These func- tions are the Yule-Walker equations which may be written, (6-13) pl - $1 + $201 + ...__ ¢pop_1 '0 ll ¢lpl + ¢2 + ... + ¢ppp-2 = + +...+ . op ¢lop11 ¢20p_2 ¢p The partial autocorrelations are then estimated by substituting the estimated values rk for 0k and solving recursively for ¢i° The values of p and q are implied by the autocorrelations and par- tial autocorrelations. In general the values of the autocorrelations will be large for k < q only, so a standard for "largeness" is needed. It can be shown6 that the variance of the estimated autocorrelation rk can be approximated by, 5For a more detailed derivation of the partial autocorrelation function see Box and Jenkins, ibid., pp. 54-56, 64—66. 61bid., pp. 34-36. 189 (6-14) var (rk) = l + 2 k > q. ZIH n nun H i l The standard error of the estimated partial autocorrelation is approxi- mated by -—i- .7 The size of the autocorrelations and partial autocorrelations, relative to their standard errors, are then used to determine the size of p, q, d, and shy following these general rules: 1) If both the autocorrelations and partial autocorrelations fail to tail off (remain large relative to their standard errors even at large values of k), the series needs further differencing. 2) A moving average process of order q is implied if the autocor- relations are large at lag l, 2...q only and the partial autocorrela- tions tail off. 3) An autoregressive process of order p is implied if the auto- correlations decay exponentially and the partial autocorrelations are large at lags l, 2...p only. 4) A mixed process of order p, q is implied if the autocorrela- tions decay exponentially after lag q and the partial autocorrelations tail off after lag p. Once the values of p, q, d, and s are identified the values of $1 and 91 are estimated by an iterative nonlinear least squares procedure. The estimation procedure required initial values for the parameters which represents a starting point for the estimation process. The 7ibid., pp. 65-66. 190 preliminary parameter estimates used here were obtained by solving the equations provided by Box-Jenkins.8 The estimation results for an ARIMA model are evaluated like those for any regression model. The overall goal of the ARIMA process how- ever is to specify the model so that all systematic behavior in the series, zt, is removed and that the residuals of the ARIMA process, at, be "white noise.’ White noise is a series of random drawings from a fixed Normal distribution with zero mean and variance 0:. The ade- quacy of an ARIMA process is therefore tested by determining whether or not its residuals are indeed white noise. This is done by examin— ing the autocorrelations of the residuals of the model, denoted here by raa(k). "small," relative to their estimated standard error which is approximated by 4L-. It In general it is desirable that the raa(k) be has been shown however that this approximation of the standard error is not very reliable,9 especially at short lags, and should be con— sidered an upper bound only. A more reliable and comprehensive test of whether at is white noise is to examine the first K autocorrelation raa(k) (k = l, 2....K). The quantity, Q, is defined as, K 2 Q = n 2 raa(k), n = N - d - s. k=l It has been shown10 that Q is distributed as x2(K-p-q). The value of Q is usually calculated for lags k = l - 10, k = 11 - 20, and k = 21 - 30. If the values of Z are less than the x2(K - p - q) values, the at 8ibid., pp. 176-77, 187-93, and Charts B, C, and D, pp. 518-20. gibid., p. 290. loibid., p. 291. 191 can be considered white noise. If, however, the values of Q are large relative to the critical x2 values, there is reason to suspect that the model is not appropriately specified. If there is reason to suspect the adequacy of the model, one way to improve it is through overfitting. Overfitting consists of refit- ting the data to a more elaborate model and comparing its results to the original results. Thus an autoregressive or moving average vari- able is added to the model, or the degree of ordinary differencing is changed to see if the model can be improved. Multivariate ARIMA models consist of a noise model like that de- scribed above, which hopefully converts the dependent variable zt to white noise, plus relevant independent variables. The independent vari- ables are introduced in the form of a "transfer function" which hope— fully converts the independent variable, x to white noise while i,t including in the process of impact of xi t on zt. Each transfer func— 9 tion may contain autoregressive and/or moving average variables of its own. The procedure is to use the autocorrelations and partial autocor- relations of each independent variable to identify an ARIMA process that transforms xi t to white noise (or as close to white noise as is 9 reasonably possible). This ARIMA transformation is then applied to both xi t and the dependent variable zt, and the cross correlations 9 between 2t and x1 t are calculated and used to identify the nature of 9 the transfer function for x Applying the same whitening transfor- i,t' mation to-xi t and 2t is known as "pre-whitening" the input x , i,t 192 The cross correlations between xi t and 2t are defined by 3 E[(xt - ux)(yt+k - HY)] (6-15) ox y(k) = , for k = o, 1.1, i 2... Ox Cy where the u's denote the means of the series and ox Cy is the covariance between x and y. Unlike the autocorrelations of a series, the cross correlations are not symmetric about zero and must therefore be calcu— lated for both positive and negative lags. The estimated cross corre- lations are then calculated by, c (k) (6-16) r (k) = -391——-, k = o, + 1, + 2, .., where xy 5 s -— -— x Y n-k _ _ ny(k) = — E (xt - x)(yt+k - Y): R = O: 19 2 ° t-l n+k _1_ z (xt-k - x)(yt - 3'): k = O, '19 -2: '00: n t=l where x and y are the sample means and Sx =‘/ cxx(0), sy = chy(0). The estimated cross correlations between 2t and the "prewhitened" input x give clues as to the form of the transfer function for x i,t i,t' Consider the general form of a transfer function model with one inde- pendent variable. It can be written in the form, (6-17) zt = 6-1(B)N(B)Xt_b + Nt’ where Nt is the noise model for 2t and _ 2 r 6(B) - 1 61B 62B ... GrB u w(B) mo - wlB - ... - wuB . The parameter b is a delay parameter representing the delay in the effect of xt on 2t. The transfer function for xt can therefore be represented by v(B) which is the ratio of two polynomials, in B, 193 2 u mo wlB sz - ... - wuB 2 l — 61B - 62B - ... - 5 B (6-18) v(B) II N 2 (v0 + le + v2B + '°')xt-b' It can be shown that the values of vj are proportional to the cross correlations between 2t and the prewhitened input xt.11 Using the cross correlations, estimates of the v , 95 for j = 0, l, 2... can :1 be obtained and used to identify the values of r, u, and b in the transfer function. The series oj will behave according to the follow- ing general rules:12 1) v will have b zero values, v0, v v j 1’ ... b-l; 2) followed by u - r + l nonzero values, vb, vb+l’ ... vb+u-r’ which follow no particular pattern (no such values occur if u mNm. u mm commas om-a Aako.av As-.mv Amo.aauv mom mm omla mun Nun Hun u u.m mma.aa oHIH «macho. + mamemm. + paaome. . p u pa mm a 0 A u A m Axv prp x Ask\HM\~H.wo\oH\Hv Aa ovam o as pa moa.H n oaumaumpm pompmzupapppa scum spam. u mamppampa up upcpapm> Nam. a Na oma.am omHH Asam.~v Aakm.~V Asm.oauv mam NN cm a m-“ Nuu Hun u p.~ om~.o caua weaned. + mmqoaa. + «HsMNm. a m n me as . . . u.~ Axe «pup x ma\oa\anaa\a\av AH cvam 0 av ax saN.Om onus aoa.a~ oNIH ask.q oaua mm Axe «pap x aka.a u uapmapmpm compmsnaapppa moum mafia. a mapppammm up pupmapp> ans. n we Asma.mV Amaq.suv Aooaa.v Aowm.sv Aomm.Huv Ammoa.-v no no ..u L n u . n . mm momeaa. + an pNNmNH. . m posNao. + N mwawmm. + H ppmmawm. u p + p Maewaflm.a a Na Amo\oa\auao\a\av mm ppm ma mmma up maappapp> Hmcommpm asap Aa.ovam.o.av u MK .n Awoummh Home: <2Hm< ummm man you muHommm oowmmmuwmmv HH.Hnn .u m« you muaomom <2Hm< .om manma 198 me.a u paumapmum comumzupapppo mo-m sans. n mamspammm mo mupmapp> has. a we assume omna aksm.~v Asm.kauv was mm omla N-u H.“ u u.n owa.ca oa-a panama. + panama. . p a ma mm a a . uafi Axe Npmp x Ase\am\ma.wo\oa\av as ovam o ov me Hmo.~ u pappapppm aomumzupapppo scum maNm. u mapppammm up moppapm> Ham. n we amknmm om-a Awa.ssv AmNmN.-v mme mm omua N-p Hnu p “.0 oaa.NH oH-H «aammm. + pnmmoo. . m n pea mm A a a “.0 Ass pra a AQN\HM\NH-wa\OH\HV AH HVAN a es mi oma.a u papmapmum pomumsupapppo «one Hmma. u mamapammm mo muapapm> Now. a Na omo.mm onus . . . . . Anus NV Awam av Asa «fiuv «mm Hm ON H mus Nuu any . u u.m Ns~.w oana mwowma. + «semen. + pommm~.u p n ma mm all . . . u.n Axe Np“: a Aa~\am\ma.wo\oa\av AH ovam o ov a« omm.a n oaumwumum aomumzlcwnudo melm Noam. n mamovawmm mo moamaum> «no. a Na www.mm mmum Assm.s-v Amaaa.o amaa.mv Assam.-v imam.~-v . Qua . muu . no . To . u Tué . u...» mom ca oa-a mstwH - pmNmmo + mNNmNS + «sooma . p + ma ”amaa . n ma mm a .. . UAW.» Axe Np“: a Aq~\HM\~Huwo\OH\HV ma mpa up pappapp> Hmpommmm a mpaa AH seam o av a4 puppaucou .om magma 199 .umumsmuma sumo you coauaauumoc Am.wvaa.v.av mau ca wouoomv ma moaoaouommav Hmoommmm mo oouwmv mnH .mooaumsvm m>fimmmuwou mnu Eouw wmuufiao ma Am Nae. u Na oaa.aa oauH amaa.~-v HHaaa.uv am~.aHv Aaao.Hv amaa.auv aa~.oa oanH . . L ..o up no u no u amH.a oHuH aH paamOH. . a maHaao. . a moaoaa. + H mpwHaH. + p+H HMH Naoaa.u n HMH pm . . . u.HH Axe mums x Haa\Ha\NHnwa\oH\Hv mH pr pm memem> proapom a mpHa aH oVAa 0 Ho pH moo.~ u pHumeapm :oapmzuaprpa aoum HaNH. u mespHmpa mo moapHpm> mac. u we aH~.aa oaHH aaHo.auv aHo.mav aaom.~V now am am H aHlp «up Hnu p p.oH aao.oH OHuH mMNNHH. + mHaHNa. + «Haaoo. + a u an pm - . . . u.OH Axe Name a AaaHHa\NHuaa\OH\HV aH mpH up pHpaHpap Hmaoaapa p apHa aH Hvaa H as pH aaa.H u pHpaHuapm pompm3.pprpa scum HmHa. u meppHmmm up pupmep> aaa. a Na oam.aa oaHH Amaa.av HaHo.aV flea.aHuv aaa ON ON H auu aup Hug a p.a aaa.a oHaH amaaoa. + «momma. + «macaw. . a a pa pm . . . p.a Axe mum: a Haa\Ha\~Hnma\oH\Hv aH ovaa o av ma aoo.a u pHuaHumpm compm3-pprpa aoum Haas. u aHm=UHmmm mo muamep> Naa. n ma OHN.Ha oa-H Haoa.Hv Haaa.av aaHa.av aa~.aH-v aaa.a oH-H pHaHao. + «momma. + paomaa. + paaaaa. . a n ma mm a .a . 0am Axe «pm: a Haa\Ha\~H.aa\oH\Hv aH pr up oprHpm> prommma m apHa aH ovaa o as ea puppHupoo .oa «Hams 200 the sample period, from January 10, 1968 through December 31, 1974. The autocorrelation and partial autocorrelation functions for AD im- 3,t ply that the following models are potentially useful in describing the D behavior of A3,t' (0,0,3)(0.0) (0,0,3)(0.1) (0.0.2)(0.2) (0.1.2)(1.0) (0.1.2)(l.l) (0.1.2)(1.2) (0,2,3)(2.0) (0,2,3)(2.l) (0,2,3)(2,2)- Each of the above models was fitted to A? t; the best results 9 occur with (0,0,3)(0,l), (O,l,2)(1,0) and (0,2,3)(2,0). Each of the models have a relatively high R2, significant coefficients, and the variance of residuals is small, but none of them transform 1? t to 9 white noise. Each of the three models have therefore been overfitted by the following models: (0,0,3)IOJ)= (0,1,3)(l,1) (1,1,3)(1.1) (l,0,3)(0,1); (0.1.2)(1LQ)= (0.2.2)(2.0) (0.0.2)(0.0) (1.1.2)(1.0) (0,1,3)(l.0) (1,1,3)(1.0) (2.1.3)(1.0); (0,2,3)(2,0): (1.2.3)(2.0) (2.2.3)(2.0) (3,2,3)(2,0). None of the models overfitted to (0,0,3)(0,1) give better results than it does, even when variables are added at the seasonal lags indi- cated by the residual autocorrelations. The autocorrelations of 201 residuals for (0,0,3)(0,1) are large at lags 3 and 12 so the process (3,0,3)(0,1) was fitted, as well as (0,0,3)(O,1) plus a variable at lag 12; neither of these models is however at all successful. Consider now the models overfitted to (0,1,2)(l,0); (l,l,2)(l,0), (O,l,3)(l,0), and (1,1,3)(1,0) are all improvements in that their resid— uals are closer to white noise, but the estimated coefficients of all three models violate the invertibility condition. Even if relevant seasonal variables are added, the invertibility condition is violated. The estimated coefficients of the models overfitted to (0,2,3)(2,0) also violate invertibility conditions. Of all the processes tested for AD only (0,0,3)(0,l), (0,1,2) 3,t (2,0), and (0,2,3)(2,0) satisfy invertibility conditions. The best model among these three is (0,0,3)(0,l); its results are given in Table 30. Although it does not result in white noise, this is appar- ently the best invertible model than can be constructed for A? t' 9 iv) A The autocorrelation and partial autocorrelation func- «“U n 9 tions for A imply that the following ARIMA models may describe the #0 ,t behavior of 12,t: (0.0 3)(0 1) (2,0, 3)(0, 1) (0, 1,2)(1, l) (0.1 2)(l.2) (0 2.3)(2.1) (0 2 3)(2,2). Each of the above models were fitted to the series A2 t; the best re- sults occur with the first seasonal difference of the series so the. other two models are not pursued further. The R2 for all models is however quite small and none transforms A? t to white noise at long 9 lags. 202 Each of the four models that uses the first seasonal difference has therefore been overfitted by the following models: (020:3)(021): (0,1,3)(l,1) (l,0,3)(0,1) (1,1,3)(lyl); (2,0,3)(O,1): (2.1.3)(1.l) (3.0.3) (0.1); (0,1,2)(1,1): (0.0.2)(0.l) (0.2.2)(2.1) (l,l,2)(l.1) (1.0.2)(0.1); (0.2.3)(2.}): (1,2,3)(2,1). Of all these processes, the best results are obtained with (l,0,3)(0,1), (2,0,3)(O,1), and (1,0,2)(0,1). The results for these three models are quite similar; none converts Ag’t to white noise ex— cept at short lags. The autocorrelations of the residuals are large at or near seasonal lags such as 13 and 26, so all three models were refitted including moving average variables at the appropriate sea- sonal lags. Adding the seasonal variables improves the performance of each model slightly. The best model is (l,0,3)(0,1) plus a variable D 4 t to white noise at the 5% level of signif- at lag 13; it converts A icance for all lags and its estimated coefficients satisfy the invert- ibility condition. Its results are given in Table 30. D O 5,t' tions for A: t reveal that the following models are of interest: _ 2 v) A The autocorrelation and partial autocorrelation func- 203 The second seasonal differencing of A? t in general yields poor 9 results; of the remaining three models, the best results are obtained with (0,1,3)(l,1) and (0,0,2)(0,l). They both have significant coef- ficients and low residual variances, but neither converts A? t to white 9 noise. These two processes have therefore been overfitted in the following ways: (OLOLZ)(O,1): (0,1,2)(1,1) (1.0.2)(0.1) (0,0,3)(0.1) (l,l,2)(1,1); (021:3)(lal): (1,1,3)(1,1) (l,0,3)(0,1). Of these models, (1,0,2)(0,1), (0,0,3)(0,l), (l,0,3)(0,1), and (1,1,3)(1,1) all convert A? t to white noise. The model with the high— est R2 and lowest residual variance is (0,0,3)(0,l) so it is judged superior to the other three; the estimated process is invertible. Its results are given in Table 30. vi) A2 t: Examination of the autocorrelation and partial auto- 9 correlation functions for AD indicates that the following ARIMA models 6,t may be appropriate: (0,0,3)(0.1) (0,1,2)(l.1) ' (0.1.2)(1.Z) (0,2,3)(2.1) (0,2,3)(2.2)- 204 Of these five models, the best results occur with (O,l,2)(l,l) and (0,2,3)(2,1). Both models have a relatively high R2 and both convert A2,t to white noise. The estimated coefficients of (0,2,3)(2,l) how- ever violate the invertibility condition; those of (0,1,2)(1,1) satisfy the condition, so (0,1,2)(l,l) is chosen as the model to represent A2 t' Its results are given in Table 30. Its first moving average 9 parameter is not significantly different from zero, but this result is not surprising because the autocorrelation at lag 1 for the (1,1) dif- ferenced data is also not significantly different from zero. 0 O D I O v11) A7 t: The autocorrelations and partial autocorrelations in— 9 D dicate that the following models may describe the behavior of A7 t: (0.0.1)(0,1) (0.0.1)(0.2) (0,1,2)(1.l) (0,1,2)(1.2) (0,2,3)(2.l) (0,2,3)(2.2)- Each of the three process performs better with the first season differ- ence of the data. Each of these models has a high R2 and reduces the variance of residuals to a very low level. None of the models however transforms AD to white noise so there is reason to suspect inadequa— 7,t cies in the models. Therefore each of the models has been overfitted with the following processes: (9)0,1)(0.1)= (1.0.1)(0.1) (0,0,2)(0.l) (1.0.2)(0.1) (0,0,3)(0,l); ' (0.1.2211 :3: (0,2,2)(2.1) (l,l,2)(l.1) (0,1,3)(l,1) (1,1,3)(1,1); 205 (0,2,3)(211)= (l,2,3)(2,1)- Of the models overfitted to (0,0,1)(0,1), only (0,0,2)(0,l) is an improvement, but it still does not result in white noise. The auto- correlations of residuals is large at lag 10 but adding a variable at that lag causes an:a(k) to rise. Considering the models overfitted to (0,1,2)(1,l), both (1,1,2)(1,l) and (1,1,3)(l,l) give better results, but the estimated coefficients of the latter violate the invertibility condition. The estimated coefficients of (l,l,2)(1,l) satisfy the invertibility con- dition but the process does not convert Ag’t to white noise. The auto- correlation of residuals is large at lag 10 but adding a variable at that lag increases an:a(k). The coefficients estimated for (0,2,3)(2,1) and (l,2,3)(2,1) violate the invertibility condition; even when appropriate seasonal variables are included, the estimated models are not invertible. Thus of all the models tested for AD those that give the best 7,t’ results do not satisfy the invertibility condition. 0f the few that are invertible, the best is (0,0,2)(0,1); its results are given in Table 30. The model has as good R2 and low variance of residuals but does not result in white noise. 3 t: The behavior of the autocorrelation and partial auto- 9 correlation functions for Ag t imply that the following models need to 9 viii) A be investigated: ' (0,0,2)(091) (0,0,2)(0.2) (0,1,3)(l,1) (0,1,2)(1.2) (0,2,3)(2.1) (0,2,3)(2.2)- 206 D 8,t' best results occur with (0,0,2)(0,1) and (0,1,3)(l,1). Each of the Each of the models listed above were fitted to the series A The models has significant coefficients and very low residual variance, although neither process results in white noise or has a very large R2. Consequently, the specification of the models is in question and they have been overfitted with the models listed below: (010,2)(0.1)= (0,1,2)(l.l) (1.0.2)(0.1) (0,0,3)(0.1) (l,l,2)(1.1); (011.3) (1.1): (1,1,3)(1.1) (l,0,3)(0,1)- Comparing the results for these models (0,0,3)(0,l), (1,1,3)(1,1), D 8,t model remains low. The autocorrelations of the residuals of each model and (l,0,3)(0,1), all convert A to white noise, but the R2 for each are large at lag 14, so they are rerun including a moving average var- iable at that lag. Adding this variable improves only the results for D A8,t. mated coefficients satisfy the invertibility condition; the results are (0,0,3)(0,l) which is chosen as the best model for Its esti- reported in Table 30. ix) A; t: Its autocorrelations and partial autocorrelations indi- cate that the following models will be useful in explaining the behavior D of Ag’t. (0,0,3)(0.1) (0,0,3)(0.2) (0,1,2)(1.1) - (0,1,2)(1.2) (0,2,3)(2.1) (0.2.3)(2.2). 207 Both (0,0,3)(0,l) and (0,2,3)(2,1) have high R2's and low residual var- iance; in addition, each process transforms Ag t to white noise. The 9 (0,0,3)(0,l) process is chosen since it has a slightly higher R2 and lower residual variance; its results are given in Table 30. The esti- mated coefficients of the process satisfy the invertibility condition. D o 10,t' D 10,t (0,1,2)(l.0) (0,1,2)(l.l) (0,1,2)(1.2) (0.2.2)(2.0) (0,2,3)(2.1) (0,2,3)(2.2)- x) A Autocorrelations and partial autocorrelations for the parameter A show that the following ARIMA processes are important: The processes (0,1,2)(1,1) and (0,2,3)(2,1) give the best results. The model (0,1,2)(l,l) converts A? to white noise at short lags and D 10,t however has an especially high R2. To attempt to account for more of 0,t (0,2,3)(2,l) converts A to white noise at all lags. Neither model the variation in A30 t’ the following models were overfitted: 9 (0,1,2)(l,1)= (l,l,2)(1.1) (1.2.2)(2.1) (0,1,3)(l,1) (1,1,3)(1.l); (0.2.3)(2.1)= (l,2,3)(2,1)- Of all these models, (l,l,3)(l,l) appears to be the best; it results in white noise at all lags and has a higher R2 than (0,1,2)(1,1) and (0,2,3)(2,1). The estimated coefficients of (1,1,3)(l,l) however do not satisfy the invertibility condition; even when variables at pertinent seasonal lags are added, the invertibility condition is violated. The coefficients of (0,2,3)(2,l) also violate the invertibility condition; 208 with or without relevant seasonal variables. The best model that can be devised for Ago t is therefore (O,l,2)(l,1); it converts AD to 10,t white noise at all lags when a variable is included at the seasonal lag 13. Its estimated coefficients satisfy the invertibility condi- tion, but the R2 for the model is not very high. The results are given in Table 30. xi) A21 t: From the autocorrelation and partial autocorrelation 9 functions for Afl t’ it appears that the following models are pertinent: 9 (0,0,3)(0,1) (0,1,2)(1.1) (0,1,2)(l.2) (0,2,3)(2.1) (0,2,3)(2,2)- The (0,0,3)(0,l), (O,l,2)(l,1), and (0,2,3)(2,l) processes perform best but none of the models has a very high R2 or result in white noise. Therefore each of the models is apparently inadequate and has been over- fitted with the models listed below: (Q10.3)(0,1)= (0,1,3)(l,1) (l,0,3)(0,1) (1,1,3)(1.l); (0,1,2)(0el)= (0,0,2)(0.1) (0.2.2)(2.1) (l,l,2)(1.1) (1.0.2)(0.1); (0.243)(2.L)= (l,2,3)(2,1)- The model that performs best of those listed above is (l,0,3)(0,1), but it converts A21 t to white noise at short lags only. The autocorre- 9 lation of the residuals is large at the seasonal lag 13 and adding a moving average variable at that seasonal lag improves the model's per- formance somewhat. It still only results in white noise at short lags 209 and does not have a very high R2, but it is apparently the best model that can be devised for Ail t' The estimated model is invertible. Its 9 results are presented in Table 30. b) Time Deposits The A-parameters for time deposit categories have each been fitted first to an ARIMA noise model and second, to a multivariate ARIMA model that also includes transfer functions for three input variables. The input variables are designed to capture the effects of market interest rates and interest rate ceilings on the rate of growth in the various categories of time and savings deposits. They include the three-month Treasury bill rate15 (denoted TBt)’ the percentage change in the Treasury bill rate (ZTBt), and the difference between the Treasury bill rate and the Regulation Q interest rate ceiling16 (Qt)° T The relationship between A1 t 9 and TBt and ZTBt is not totally clear. When market interest rates are high or rising, savings and time deposits should be attractive to the public relative to cash and demand T i,t the ith category of time deposits, A: t 9 deposits and, since A is inversely related to the rate of growth of would be expected to fall (reflecting an increased growth in time and savings deposits). Thus, 15The rate on new issue of three-month U.S. Government Securities; data are weekly. Source: Board of Governors of the Federal Reserve System, Federal Reserve Bulletin, various dates, p. A—33. 16For parameters relating to savings deposits, Qt is the Treasury bill rate minus the Regulation Q ceiling for savings deposits; when that quantity is negative, Q - 0 is used. For parameters relating to other categories of time deposits, Q is the Treasury bill rate minus the Regulation Q ceiling for time deposits maturing in one year or more until July 20, 1966, and for time deposits less than $100,000 maturing in two years or more thereafter; when the quantity is negative, Q = 0 is used. Source: Board of Governors of the Federal Reserve System, Federal Reserve Bulletin, various dates, p. A210. 210 TBt and ‘ZTBt would be expected to vary inversely with A:,t. On the other hand, if high or rising market interest rates imply that other interest-bearing assets are more attractive than time and savings de- posits, large values of TBt and ZTBt would be coupled with relatively high values of Ai’t (indicating a decline, or slowdown in the rate of growth, of time and savings deposits). A positive value for the in- put variable Qt indicates that market interest rates are above the allowable rates on time and savings deposits so Qt and A:,t should be directly related. The estimation program used here does not allow different degrees of seasonal differencing for the input and dependent variables in a multivariate model. The parameters in rt all require some degree of seasonal differencing to achieve stationarity. This necessitates, in the multivariate processes described here and in the following sections, that the input variables be subjected to the same degree of seasonal differencing as the dependent variable, regardless of what their iden- tification procedures imply. In what follows, the description of the transfer functions will indicate the degree of seasonal differencing desired for each transfer function but in the estimation process all variables are seasonally differenced to the degree required for the noise model. T T l,t' Since A1,: Reserve Scheme A, its ARIMA model is based on the first half of the i) A is used in the equation for rt only under sample period only. The autocorrelations and partial autocorrelations imply that the following noise models are relevant for A: t: 9 211 (0,1,2)(1.l) (0,2,3)(2.1) (0,1,3)(1.2) (0,0,2)(2.2)- Each of these four models were fitted to the series AI,t and the best results were obtained with (O,l,2)(l,l) and (O,l,3)(l,2). The model (0,1,3)(l,2) results in white noise at all lags but its R2 is not very high. On the other hand, the process (0,1,2)(l,l) has a healthy R2 but does not result in white noise. The (0,1,2)(1,l) model seems prom— ising so it has been overfitted with the models (l,l,2)(l,l) and (0,1,3)(l,1). Both models have a high R2 and both convert A§,t to white noise at all lags but (0,1,3)(l,1) is chosen as the best model. The noise model (0,1,3)(l,1) was therefore used in a multivariate ARIMA model with transfer functions for the three independent variables described above. The cross correlation functions between AI,t and the independent variables imply the following transfer functions: TBt 3 (091:0)(190); zrst : (0,2,0)(0.0); Qt : (0,3,0)(0,0). Adding the input variables increases the model's R2 and reduces its residual variance somewhat, but Qt is the only input variable whose coefficients are statistically significant. The other two independent variables were therefore excluded and the model was reestimated; the results are given in Table 31. The model has a high R2 and low residual variance and the values of an:a(k) indicate that it converts Af’t to white noise. The cross correlations of residuals are also small so the transfer function ap- pears to be adequate. Three of the four coefficients in the transfer function are not of the expected sign, but the one positive coefficient 212 ameH.av enessssss. : aassa.s Hasas.-s AsHa.Ns aHNa.Ns ass.HNs als . Nne . . 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Nsaasas. + ssHasH. + H AeN\aNANHuss\sH\HV AH.ssHs.a.sv "so asN sap sH aseH . u .H a a a e o a a a o a a nu es aeHspHee> asHs aH.HsAs s HV . sea .sH wsH up oHsers> s msHa HH Hvas.H so . ma .AH Hvaa.H.Hv . as asa.H n eHssHsees somee3.sHspss asus sass. u sHessHmes so essers> sHa. n Na HN.sH ssa.aN smuH Ha.sH ass.sH anH as.N mae.e . sH:H am so u. 318 News E News s manpowmom mo meowumaouuoo mmouo mamswammm mo mcowumamuuooous< wag Hsss.av AssaH.uv Assa.Nuv AasH.H-V Haas.as Has.sHv aasa.anv no to no u to to no u u. a saNNss. + N seasss..w sNasss. - sHsts. . a esaNaN. + N ssssaa. + H esasee. . e n Has a a a .u a a a. . .uaH ss\sH\HuHs\H\Hs aH seas a sv . s .aH Haas H so . as .u.H Ammumow Home: <2Hm< ummm mnu HOW muasmom coammouwomv m .H n a H a new msHsmmm <2Hm< .Hm mHssa noo.~ u owumflumum comumziaaausa «elm 55mm. u mamowwmmm mo madman“; can. u M N sa.s ma.sH aa.NH sas.aH sauH sa.H He.aH Hs.aH aHN.HH sNuH sN.s as.a as.a aaN.a sHuH do . do am mm | HastV News HesHsaas News HasHsas use Ass News a mamoowmmm mo mcoaumaouuou mmouo mamooamom mo mcowumHouu000u5< wmq AaNaa.v Asses.-v Haas.Ns Aaas.aus AsHH.H-s AaNaN.V no no no ..u ..u a smasss. + a ssssss. . N saasss. + H saHNss. - ssasHss. . N maNNssss. + aHss.as HaNa.NV Aaeaa.s Haas.Ns mammaMN maMMNww + H HI... . . u o . Hlu . u . on N c + q u.N < n“ saaNNsss + seastss + sasaasss + sasHsts + aNaN.ss aHaH.Ns . 9H 9. Nssaaaa. + mamasN. + H a A a U a a a a u 0 A a 0 a u A 0 0 “A aN\Ha\NH-ss\a\Ns As sols a so u s .As sols N so u see .As Haas H so . as .Hs.stN H No “ MH sHs.N u eHseHsesa someezusHspss msns Naas. n aHessHmea so esseHees Has. n Na Ns.NH ma.sa sN.sN seH.sN smuH sN.s Na.aN Ns.NH NHa.aH sN-H ma.H Ha.aH sN.s aNs.N sHuH sow .. on do so I “sagas News HealeeNV News Assxsas News Ass News s mHmnmuHmmm WC mCOHUNHUh—HOU mmOHU mHmswfimmm NO WCOHUNHQHHOUOU5< wmg sessHssos .Ha eHspa 214 Aammoo.uv umH< manomm + H assess.“ Amoooo.a mmcooo. + cacao. Aasaas.h Hassss.Hs Asmsss.e I. .I II u A + a esssNes. + N eessems. + H eeNaHaN. . a n s was a a A 0“ a A a a 0U&Q eeN\Ha\NH-ss\sH\Hv HH Haas H Hv . ma .HH HsHa H so . aHs .ssss. sH HuesaN so useHeHNseeu seemaHsae use st.N u eHemHsess somumzusHspss sous Hsaa. u sHmseHmes so meseHee> Haa. a Na Na.s sa.HN NH.NN NsH.sa sauH Ha.a sa.sH aH.NH mHH.NN sNuH sN.s Ha.NH aN.NH Naa.s sHuH do u do do no .I HesHsv News HsVHsa\s News Assasas News Has News a ..mamooamom mo mcowumaouuou mmouo mamoofimom mo mcoaumamuuooouo< mod aHsHs.-v Haass.us amaa.Hus HNNe.H-V asses.-v an no u no a N saNsss. - H sNNsss. . ssmsss. . a saNassss. - eN usaNHssss. . HasH.HV Assa.Huv Haae.Ns HHss.ans Asa.aNV aaNNa.uv u no o no u 1 o . saNassss. + H sassasss. . sasHasss. + a eNsamH. . N sesNHHs. + H usHNsHs. . s u e Mas u HaN\Ha\NHuss\a\Nv HH.ssHs.N.sv ” s “HH.sVHs.a.sv ” mas “HH.HVAs.H.sV ”use axH.HVHa.H.sV n u.aH u H sessHssos .Ha mHssa 215 .uoumEduma some you coauafiuummv Am.oVAu.o.av msu ca dmuocoo ma woaosoummmao Hmaommmm mo oouwoo may .maoaumoco GOHmmopwmu msu Eouw douuaao ma Amoa mucosamaawwm Nmm ecu um .muomwowmmooo man now muHEHH Hosoa and moan: mum wucmHUHmwoou onu 3oHoo mmmosusoumd :« madness one .muaommu coammouwmu onu so :oHumau0mca mama osu aHaaom uoc meow .um>mso£ .Emuwmma mane ..Emuwoua ocooom mnu Sofia woudaaumoou mm3 Hobos o:u ma Hawmwoouom whoa mum muaomootummooHOM may .mx demo WK Mom .uonuocm Sufi? doummoouow odd Emumoum woo nuH3 mouse A A Iaumo dam vowmaucooH mums mHoooE <2Hm< HH< .u MK wow u ex u0w ooow>oua soauoauomca odouowmao ma ouony H « ssns aHHsN. u sHeseHmes so messHpes aaa. a Na NHs.sN sam.Ha smnH Nas.aH sam.aH sNuH saN.s Nas.sH sHuH do on I. page News as NpNs s mHdewmmm mo mcowumaowuou mmouo mamoowwom mo mcowumaouuooouo< wag AsaHss.h Asasss.H AssHss.h Assass.s HsNNHH.p HsHsas.Hs In ..u no no ..u u u. N ssNNss. + H saNHss. + essaass. + a eastH. + N pNNaaa. + H saaaNm. . s u Was A a A U A A u. eHaN\Ha\NH-ss\sH\Hs HH seas N sv " s .e weH es eHseHeee s ssHs HH HVHN.H.ss ” MK sons mamas. n mHessHmes so essere> aaa. a Na st.aa «NH.sa sauH ass.as Haa.am sN-H asa.eN aas.sm sH-H do on . I. Eat News 8 News s mamoofimom mo mcowumamupou mmouo mamovfimmm mo muowumaouuooous< won sessHssos .Ha mHssa 216 is also statistically significant. Furthermore, there are very few non- zero observations of QC in the time period used here so the measured relationship between A; t and Qt is probably not very reliable. 9 ii) A; t: The parameter A; t (corresponding to total time de- 9 9 posits) enters the equation for rt only under Reserve Scheme B. That scheme covers only 70 weekly observations of data, but with so few ob- servations, the ARIMA identification and estimation procedures fail. The ARIMA model for A; t is therefore based on all available observa- 9 tions, which cover the period July 9, 1966, through December 31, 1974. T The autocorrelations and partial autocorrelations for A 2,t sug- gest the following ARIMA noise models: (2.1.2)(1,0) (0,2,2)(2,0) (0.1.4)(1.1) (0.1.4)(1.2) (0.2.4)(2.1) (0.2.4)(2.2)- Several of these models convert Ag’t to white noise but (2,1,2)(1,0) appears to be the best since it has the highest R2 and lowest resid— ual variance. The noise model is used in a multivariate model along with the input variables TBt’ %TBt, and Qt' After prewhitening each input variable, their cross correlations with A; t suggest the following transfer functions: TBt 3 (0,1,0)(1,0); ZTBt : (0,2,0)(0,0), MBt : (0,4,0)(0,0). Each of the transfer functions has at least one statistically signif- icant coefficient; the model including all three input variables results in white noise and the cross correlations of residuals.imply that all three transfer functions are adequate. The signs of the coefficients 217 of TBt and °/.TBt show that A; t is directly related to interest rates; 9 the nature of its relationship with Qt is not clear from these results. T T 3,t 3,t rt under Reserve Schemes B, C, and D' so its ARIMA model is based on iii) A The parameter A (savings deposits) is included in all available observations of data for the period, July 9, 1966 to December 31, 1974. The autocorrelation and partial autocorrelation functions for Ag t imply that the following processes are important: 9 (0,1,2)(1.0) (0,1,3)(l,1) (O,l,3)(l.2) (0,2,3)(2.0) (0,2,3)(2.l) (0,2,3)(2.2)- Of these six models, the best results occur for (0,1,3)(l,1) and (0,2,3)(2,0); each model has a high R2 and low residual variance. The best model appears to be (0,1,3)(l,1) because it converts Ag’t to white noise at lags 1-10 and 1-30; the value of an:a(k) is large at lag 13, but adding a variable at that lag does not improve the results. The noise model (0,1,3)(l,1) was therefore used, along with the three independent variables given above, in a multivariate ARIMA model. The cross correlations between A§,t and the independent variables imply the following transfer functions: TB : (0,1,0)(1.0); ZTB: (0,3,0)(0.0); Qt 3 (0,2,0)(0,0)- Adding the input variables to the (0,1,3)(l,1) process increases the R2 and lowers the residual variance. Only the transfer function for TBt has a statistically significant coefficient, but when Qt and ZTBt are excluded the results are not as good, so all three input variables are retained. The values of an:a(k) indicate that the model converts 218 T A3,t to white noise and the cross correlations for each independent var- iable are less than the critical x2 values, implying that each transfer function is adequately specified. The results are reported in Table 31. The signs of the coefficients in the transfer functions for TBt are not consistent, although the statistically significant coefficient implies a direct relationship. The signs of the coefficients of %TBt are mixed, but they are not statistically significant. None of the coefficients of Qt are of the expected sign but they are also not statis- tically significant. iv) AT The parameters AT and AT are included in rt under 4,t‘ 4,t 5,t Reserve Schemes C and D' so their ARIMA models are based on the corres—' ponding time period, January 11, 1968, to December 31, 1974, 364 obser— vations. The autocorrelation and partial autocorrelation functions for A: 5 (time deposits less than $5 million) indicate that the following models may represent the noise function for A: t: (0,1,3)(l,1) (0,1,3)(1.2) (0.2.2)(2.l) (0,2,2)(2,2). For both processes, the first seasonal difference of A: t gives better 9 results than the second. Both (0,1,3)(l,1) and (0,2,2)(2,l) have high RZ's and low residual variances; (0,1,3)(l,1) appears to be the best model since it converts Az’t to white noise at all lags. The noise model (0,1,3)(l,1) is therefore included in a multivar- iate ARIMA model along with the three input variables mentioned above. The cross correlation functions of AZ,t and the independent variables imply the following transfer functions: 219 TBt : (1.1.0)(l.0); ZTBt : (0,2,0)(1.1); Qt : (0,2,0)(0,0). Only the transfer function for TBt has statistically significant coef- ficients so the other two input variables were eliminated and the model reestimated; the results are presented in Table 31. When the transfer functions are added the process does not result in white noise; the cross correlations of residuals for the transfer function are large, indicating that the function is not adequately specified. The cross correlation is large at lag 13 but adding a var- iable at that lag does not improve the model's performance. The model was also refitted with several modifications of the transfer function but in no case are the cross correlations lower.l7 This is apparently the best model that can be constructed for Az’t. The signs of the coefficients of TBt consistently show a direct relationship between it and Az’t implying that at high interest rates, time deposits in this reserve category grow at a slower rate. T O S,t° (time deposits greater than $5 million) indicate that the follow- v) A The autocorrelations and partial autocorrelations for T 5,t ing noise models should be considered: A (0,1,2)(1.1) (0,1,2)(1.2) (0,2,3)(2.0) (0,2,3)(2,2). The second seasonal difference of A: t gives very poor results in both 9 of the above models; each of the other three models has a respectable l7 tried. The transfer functions (0,1,0)(1,0) and (l,2,0)(l,0) were also 220 R2 and low residual variance, but neither results in white noise. The model (O,l,2)(l,1) converts Ag’t to white noise at lags 11-30, but not at short lags because the autocorrelation of residuals is large at lag 4. For (0,2,3)(2,0), the autocorrelation of residuals is large at lag 13. Adding the seasonal variable to (0,2,3)(2,0) improves the perfor- mance but it still does not result in white noise. The model (O,l,2)(l,1) plus a variable at lag 4 does result in white noise so it appears to be the best noise model. This noise model was then included in a multivariate process with the same three independent variables. The cross correlations functions for A; t and the prewhitened input variables indicate the following 9 transfer functions: TBt . (1.1.0)(1.0); ZTBt : (0,2,0)(1,l); Qt ' (0.2.0)(0.0). Qt is the only input variable that has statistically significant coef- ficients so the model was rerun excluding the other two transfer func- tions. The results are reported in Table 31. T . The process converts A5 t to white noise and the transfer function 9 for Qt appears to be adequate. The coefficients of Qt imply the ex- pected direct relationship between Qt and A: t' D Differential Reserve Requirements (dj t 9 T and Gi,t)l a) Demand Deposits By definition, the sum of the 6D for each reserve scheme is one. 3,t Therefore an ARIMA model is not needed for one 6? t 9 its value can be derived directly from the values of the other 6 in each reservescheme; D i,t' For the first demand deposit reserve scheme, the ARIMA models for 6? t 9 221 and 63 t are identical. For the last two demand deposit schemes, ARIMA D D models are not estimated for 66,t and 611,t. D . D D D i) 6 and 52 t' Like Al and A 6 D l9t 9 gt 2,t, l,t in Reserve Schemes A and B, so their ARIMA models are based on the first D . and 52,t appear in rt part of the sample only. The autocorrelation and partial autocorrela- tion autocorrelation functions indicate that the following models . D D should be conSldered for 61,t and 62,t' (3.1.0)(1.1) (0,2,2) (2.1) (0.2.1) (2.2) (2.1.2) (1.2). When these four models are fitted to 5? t’ the (3,1,0)(l,l) pro- 9 cess performs best, but it does not transform the series to white noise except at short lags. Examination of the autocorrelations of the residuals shows high correlations at the seasonal lags l3 and 26. The model was therefore rerun including moving average variables at these lags and this modified model does convert 6?,t to white noise at all lags. All five coefficients are statistically significant and they satisfy invertibility and stationarity conditions; the model has a high R2 and low residual variance. The results are given in Table 32. g t: The ARIMA m°d913 for 5? t’ j = 3,11 are based on all , 9 the available observations; they cover the last half of the sample, ii) 6 January 10, 1968 through December 31, 1974. Examining the autocorrela- D 3,t ing ARIMA models may be useful in explaining its behavior: tions and partial autocorrelations for 6 indicates that the follow- 222 aaN.Na sauH aNs.aN sNuH aaN.a anH w Hstpws a saa.H u eHssHsees spasmsusHsess sous NsHa. n eHessHaes so esseres asa. a Na xNaNs.-V HNs.sNV HNNN.HV Asas.Nus Aaam.suv I . I . - .l a I. a . I“. U. aH UssaNNs. . H seasNaa. + as + a e assaasss. + N e MsseaHaH..mH MssssaNs.n a Mss ‘ e. HaN\Ha\NH.ss\sH\HV aH weH es eHssHees Hesoeepe e ssHs HH.HVHH.H.av Ms ass.aN sauH Nas.sN sNuH Haa.s sHuH m Heszse s sss.N u eHeaHssss soaessusHsess asls some. n mHessHaes so peseHess Nsa. u Na HasH.a-v Hana.a-v Haam.Nv Ases.av asam.ss us no u ..u. no. no. u. sN ssassN. - aH eNaNaN.a s + a MssNasaH. + N “ssasaHN. + H MesaHeNa. u “as Ass\sH\HuHs\H\HV sN esp aH emmH up seHsers> Hmsospme ssHs HH.HVHs.H.as u Ms .u .n Aboummm. Homo: <25? ummm me.» ..How muaomwm cowmmopwmmv Ha .H u n we .Hom muaommm £52 1% man—mm. 223 ssH.sN ssuH sss.aH sNuH saH.s sH1H m HesNese e ssa.H n eHesHesss somes3-sHspss sols ssss. u sHsssHsss so eessHpss Nsa. u Na HsHs.ss HHNs.HV AssN.an HNsH.snv Asst.V AasN.ss up no no u no. ..u. ..u. u. s stNsN. + N sstsH. + H smassN. . s + s MssaHNss. . N Msstsss. + H MssHasss. u Mss . . . e.N HsNHHsNNHussHsH\Hs HH HsHs H as ss ssa.H u eHsmHssss soass3-sHspss asus assN. u sHsssHses so pessHpss asa. a Na ssN.ss sNHH HaaN.H-s Haa.HHs Asaa.Hs HNss.H-s AsNN.ans aaa.a sH-H ssssss. . sssHHs. + s + sssssNNH. + sssssHHH. - ssssssss.un sss s s . . . e.s Hstpss HaNHHs\NH-ss\sH\Hs sH ssH es eHserse Hssesses s ssHs aH HVHH H as ss Nsa.H u essaHeses soaps; sHspss as.s sssH. n sHsssHses so messHpss ass. a Np HsH.aN ss-H aas.sH sN-H Hsss.ss Hasa.s-s Hass.Ns AaaN.Hs Aass.ss . n no L ..o no no u o. asass sH H sH sasssN. + sH stsss. I s staNH. + N ssaaas. + H sssaas. + s n Nss AssNess s a 7 Us asN\Hs\NHsss\sH\Hv sH sss sH mssH as seHssHes> Hssosses ssHs HH HVHs.H.sV Ms sessHesos .Ns eHssa 224 .uouosopma sumo Mom coaoawuommv Am.ovac.o.dv onu as douoCmo ma masocoumMMHo Hmcommom mo summon one .wooHudooo ooammouwou onu Eouw douuHEo mH Am sHs. u Ns AssN.sus HNNNs.-v Hsss.sv n n no sH UssHHNH. . s esstNs. . N ssNHss. + Assas.us Haas.Hv Hass.N-s AasN.Hs I» u lua I a I“. u. H assass. . s + a sMssassNN. + N u sMsstaaN. . H sMsssssHs. n JMss m . u. HsVNpNs a HsN\Hs\NHuss\sH\HV sH ssH as mHssHpse Hssssses s ssHs HH.HVHs.H so sMs aaa.H u eHssHsses semeszusHspss ss-s sass. u sHsssHses so eessHess ssa. a Na Hass.suv HasH.Nv Hass.sv u u ..n sH ssssasN. . s ssssNNN. + N sssHss. + NNs.sN ssHH HasH.N-V AHssa.-v Assss.-v HsHs.aV NsN.a sH-H saaass. . s + sssssssH. . sssaHNHH. . sssssssa. a sss N a HstpNs s HsN\Hs\NH.ss\sH\Hs sH ssH us sHssHes> Hssosspa s msHs HH.HVHs.H.sV e Ms sNa.H u eHssHsses seseszusHspss asus HssN. u sHsssHses so messHps> sNN. n s aaH.ss ss-H N saN.sN sNuH Hess.an asN.Hss Asas.ss . u ..u as u no. u. aHs a sH H sH assass. . H sstsa. + s + H MststsN. . Mst m AssNese e , A HsN\Hs\NHuss\sH\Hs sH ssH us mHssHps> Hssosses s ssHs HH.NVHH.N.HV u Ms sessHssos .Ns eHssa (0.1.1)(1.1) (0.1.1)(1.2) (3,1,1)(1.l) (l,l,l)(l.l) (l,l,l)(1.2) (0,2,2)(2.1) (0.2.1)(2.2)- The best results occur with the models (3,1,1)(l,l), (l,l,l)(l,l), and (0,2,2)(2,l). All three models result in a high R2 and very low resid- D 3,t only. The last two models have therefore been overfitted in the fol- ual variance and they all convert 6 to white noise, but at lags l—lO lowing ways: (Islel)il,l)} (1.2.l)(1.1) (2,1,1)(1.1) (l,l,2)(l.l); (0,2,2)(2,l)2 (O,l,2)(l,1) (1.2.2)(2,1)- None of the overfitted models however perform better than their orig- inal formulations or (3,1,1)(l,l). The autocorrelations of the residuals for all three models are large at the seasonal lag 13 so the three models were all refitted ins cluding a moving average variable at that lag. Adding the seasonal variables improves each model slightly. The best model appears to be (3,1,1)(l,l), the results of whiCh are presented in Table 32. The seasonable variable in (3,1,1)(l,l) does not have a significant coef- D 3,t lags at the 5% level of significance and its estimated coefficients ficient but the augmented model does convert 6 to white noise at all satisfy the conditions for stationarity and invertibility. iii) 62 t: The autocorrelations and partial autocorrelations for 9 62 t imply the following processes: 9 226 (0,1,3)(l,1) (l,l,l)(l.1) (0,2,2)(2.l) (0,2,2)(2.2) (0.1.l)(1.2) (l,l,l)(1.2)- Each of the six models listed above was fitted to the series 62 t' The 9 second seasonal difference of the data is consistently less success- ful than the first so those three models are not pursued further. Each of the remaining three models has a relatively high R2 and transforms D 4,t transforms 62 t to white noise at long lags each was overfitted with 9 the following models: 6 to white noise for lags l-lO. Since none of the three models (0.1.3)(1.1)= (1,1,3)(l.l); (l,l,l)(l,l)= (l,l,2)(1.1) (2.1.1)(l.1); (0.2.2)(2,llfi (0,2,3)(2.1) (1.2.2)(2.1)- None of the overfitted models however is an improvement over the orig- inal formulation. For each of the original models, the autocorrelations of the resid- uals are large at or near the seasonal lags l3 and 26. Each model was therefore refitted including moving average variables at these seasonal lags. Adding the seasonal variables to (l,l,l)(l,l) and (O,2,2)(2,l) does not reduce an:a(k) to the level required for white noise. For (0,1,3)(l,1), adding variables at lags l3 and 14 reduces its residual autocorrelations so that the model results in white noise at all lags. The estimated process is also invertible, so it is chosen as the best D model for 64,t' Its results are given in Table 32. 227 O D C 1v) 65 t: From the autocorrelation and partial autocorrelation 9 functions for 6? t’ the following ARIMA processes appear to be relevant: 9 (0.1.l)(l.1) (0,1,1)(1.2) (l,l,l)(l.1) (l,l,l)(l.2) (0.2.2)(2.1) (0,2,1)(2,2)- The models (l,l,l)(l,l), (0,2,2)(2,l), and (0,2,1)(2,2) give better re- sults than the other three listed above. Each of these three models D have a respectable R2 and significant coefficients, but transforms 65 t 9 to white noise at short lags only. Therefore these three models have been overfitted in the following way: (1.1e1)(1,1)= (2,1.l)(l.1) (3,1,1)(1.1) (l,l,2)(l.l) (1.2.1)(2.1); (0.2.2)(Zel)= (1.2.2)(2.1) (0,2,3)(2.l); (0.211)(2,2)= (1.2.l)(2.2) (0.2.2)(2,2). Of all these models, the best results occur with (3,1,1)(l,l) and (0,2,2)(2,l); both models still only convert 62’t to white noise at short lags. The autocorrelations of the residuals for both are large at the quarterly lag 13, so both models were rerun including a moving average variable at that lag. Adding the seasonal variable reduces the resid- ual autocorrelations of both models. With the variable at lag 13, (3,1,1)(l,l) results in white noise at all lags and its estimated coefficients satisfy the stationarity and invertibility conditions. 228 It is therefore chosen as the best model to describe 6? t; its results 9 are given in Table 32. D O 7,t' tions for 63 t show that the models listed below are pertinent: (0.1.3) (1.1) (3,1,3)(l,1) (0.2.2)(2.1) (0.1.1)(1.2) (l,l,l)(l.2) (0,2,1)(2,2). v) 6 The autocorrelation and partial autocorrelation func- Each of the models was fitted to 63 t' Other than (O,l,l)(l,2), which 9 gives very poor results, all of the models above perform well. Each of the five models has a very low residual variance and a high R2. The model (3,1,3)(l,1) however is the best because it converts 6? t to 9 white noise at all lags; the other four models only result in white noise at lags 1-10. The estimated process (3,1,3)(l,1) also satis- fies the stationarity and invertibility conditions; its results are given in Table 32. D 0 8,t° 63 t imply that the models listed below should be considered: 9 vi) 6 The autocorrelations and partial autocorrelations of (0.1.1)(1.1) (0.1.1)(1.2) (l,l,l)(l,1) (0,2,1)(2.1) (0,2,1)(2,2). D 8,t° (l,l,l)(l,l) and (0,2,1)(2,l) processes out-perform the other models. These five models were fitted to appropriate differences of 6 The Each one results in a reasonably good R2 and a low residual variance, but (l,l,l)(l,l)'results in white noise at lags 1-10 only and (0,2,1)(1,l) does not result in white noise at all. Both models have therefore been overfitted by the following models: 229 (l,l,l)(lsl): (2.1.1)(1.1) (l,l,2)(l.l); (0.2.1)(2e1)= (l,2,l)(2.l) (0.2.2)(2.l) (1.2.2)(2.1). Each of the overfitted models is an improvement over the original; the best results are obtained with (2,1,l)(l,l), (l,l,2)(l,1), (l,2,l)(2,l), and (0,2,2)(2,l), but they all only result in white noise at short lags. The autocorrelations of the residuals for all four models are consistently large at the quarterly lags 13 and 26, so each of the models was rerun including moving average variables at lag 13 and at lags 13 and 26. The best result occurs with (l,2,l)(2,l), plus D 8,t the 5% level of significance; the other three models give white noise a variable at lag 13; it transforms 6 to white noise at all lags at only at the 2.5% level. The estimated coefficients of (l,2,l)(2,l) plus a variable at lag 13 satisfy the stationarity and invertibility conditions. Its results are given in Table 32. vii) 63 t: The characteristics of the autocorrelation and par- tial autocorrelation functions for 63 t indicate that the models listed 9 below are relevant for 63 t: (0,1,3)(l,1) (3,1,3)(l,1) (0,2,3)(2.1) (l,l,l)(1.2) (0.2.2)(2,2)- Each of these models was estimated for 63 t; (0,1,3)(l,1) and I 9 (3,1,3)(l,1) are the most promising models. Neither model converts 63 t to white noise except at short lags and neither model has an espec- 9 ially high R2. The (0,1,3)(l,1) process was therefore overfitted with 230 the following models: (0,1,3)(lll): (l,l,3)(1,l) (2.1.3>(1.1); neither model however gives better results than (0,1,3)(l,1). The autocorrelations of the residuals of both (0,1,3)(l,1) and (3,1,3)(l,1) are large at the seasonal lags l3 and 26, so the models were rerun including a moving average variable(s) at lag(s) 13 and 13 and 26. Adding the seasonal variable(s) reduces the autocorrela- tions of residuals for both models. The best model is (3,1,3)(l,1) plus a variable at lag 13; these results are given in Table 32. This augmented model results in white noise at all lags at all levels of significance and it is stationary and invertible. D O 10,t’ autocorrelations imply the following models to describe 6 viii) 6 Examination of its autocorrelations and partial D I 10,t“ (0,2,1)(2.0) (0,2,1)(2.1) (0,2,1)(2,2) (0,1,3)(l,1) (3,1,0)(1.1) (3,1,3)(l,1) (O,l,3)(l,2)- Of all the models, (0,1,3)(l,1) or (3,1,3)(l,1) appear to be most promr ising; both (0,1,3)(l,1) and (3,1,3)(l,1) convert 6:0 t to white noise 9 at lags l-lO. Since many of the coefficients in (3,1,3)(l,1) are not statistically significant, the models listed below have also been tested: (1,1,3)(1.1) ' (2.1.3)(1.1) (3,1,1)(1.1) (3.1.2)(1.1)- 231 Of the above four models (3,1,1)(l,l) and (2,1,3)(l,1) perform best; along with (3,1,3)(l,1), these models all have very similar Rz's and they all transform 6D to white noise at lags l—10 only. The auto- 10, t correlations of the residuals are uniformly large at lag 13 so each of these three models was refitted including a moving average variable at lag 13. Adding the seasonal variable results in a more successful model for each one; the seasonal variable has a significant coefficient in all three models and all three models transform 630’t to white noise. Since its R2 is highest and residual variance is lowest, (3,1,3)(l,1) is chosen as the best model. Its estimated coefficients satisfy the stationarity and invertibility conditions; its results are given in Table 32. b) Time Deposits Like A1, t’ 6; t have been fitted first to an ARIMA noise model, 9 which is then included in a multivariate ARIMA model with the three input variables, TBt’ %TBt and Qt' Hopefully the independent variables account for the effects of interest rates and interest rate ceilings on the relative growth of the various categories of time and savings T _ deposits. Since 6; +63 t l for Reserve Scheme B, and 63 t + 64 t + 6; t = 1 for Reserve Schemes D' and E, an ARIMA model is not fitted for 9 T T 18 62,t or 64,t° T T . i) 63 t: The ARIMA model for 63 t (savings dep031ts) is based on 9 9 the period July 9, 1966, through December 31, 1974, which corresponds 18Estimation of an ARIMA model was more difficult, and the results poorer, for 62 t than for 6; t’ so 62 t was chosen as the one to be de- rived from the values of the other two. 232 to the period covered by Reserve Schemes B, D', and E. The autocorre- T lation and partial autocorrelations for 63 t 9 indicate the following noise models: (2.2.2)(2,0) (3,1,0)(1,1) (3,1,0)(1.2) (2,2,1)(2.1) (2.2.l)(2.2)- Each of the five models above performs well but the best results occur with (3,1,0)(1,1) which has a high R2, significant coefficients and it converts 5§,t to white noise at all lags. The noise model (3,1,0)(1,1) was therefore combined with a trans- fer function for each of the three input variables discussed above. The cross correlation functions between 6§,t and the prewhitened inde- pendent variables indicate the following transfer functions: TBt (0,2,0)(1.0); ‘ZTBt (0,2,0)(0,0). Qt (0,2,0)(0,0). None of the coefficients in the transfer function for Qt is statistic- ally significant so the model was rerun with only TBt and %TBt as input variables. Its results are presented in Table 33. The combined noise- T 3,t although only at the 5% level of significance for long lags. The cross transfer function model has a high R2 and converts 6 to white noise, correlations of residual at positive lags for both input variables are much smaller than the critical values of x2 so the transfer functions are apparently adequate. Since 6; t measures the proportion of member bank time and savings 9 deposits that are savings deposits, it is not clear what the relation— ship should be between 6§ t and market interest rates. The regression 9 T 3,t and the Treasury results indicate a direct relationship between 6 233 Hsssa.IV xNNN.HIs HNst.v HsHN.NIV I In Iu u a essaNss. I N ssHNss. I H sssts. + sHNsHs.I H.ssNHs HH.NNNIV Hsas.Nv aNaN.Nv e. sasss.H + H s sstHs.H I H as NsssssH. + sHNNaH. + H I e.s sass ass.NHs + mas HsH.aHs HsH.aHuHI + H ass NNsss. sHNseH. + sassH.I A A u A A A A u A AI A A u A OUA sNNHs\NHIss\sH\Hs Hs.sVH s.a so u s .HH HVHs s Hs “ saN .aH HVHs H Hv “ ma “HH HsHs.H.NV . Ms Hsa.H u UHssHeses semessIsHsess ssIs sssH. I sHsssHses so eessHpss aaa. u Na ss.NH Ns.NH sas.as ssIH HN.s as.s sss.sN sNIH Ns.s sa.s sss.s sHIH . do do mm I. Assamese News assasas NpNs Has News 3 mamooamom mo moowuoamuuoo mmouo mamoosmom mo muowumamuu000u5< woq Hst.NIV Hass.NIv Hsass.s I“ I N saNassss. I H esaNsssss. I usaNNssss. + . .I . HNaH.sv aNss.sv HNsN.sV NIs Hsss Hs HID Assas v s Ast No D ssstsH. + Nsassss. + sHsasN. + H s.s sassssss. + sassssss. + sasasss. + s I. H I H.ss A A A a“ A A A A a“ A A A. A ouAm HsN\Hs\NHIss\a\Ns aH seas N sv . mas .HH HVHs N ss . ma .HH HVAs H as . as AUA Admumwy Home: <2Hm< umom ocu pow muaswom coammopwomv m .m n a We MOM muaomom 42Hm< .mm GHAMH 234 .uouoEmuda some now doaumauomoo Am.oVAv.v.nv was as owuocoo wH masocmHMWMHo Hoaomdwm mo mouwov may .mcoaumdvo coawmouwou onu Eoum douuaao ma Am aaa. I Na Hs.N ss.sN sN.aN ssH.sN ssIH sN.H ss.sH sa.sH st.sH sNIH aN.s NH.s sN.s NHs.sH sHIH dd u do dd do .I HesHss Nese issHsHNV Nth NesHses Nsse Hes Npse s wamooammm mo meowumamuuoo mwouu mamooamom mo maoaumamuuoooud< . wag sessHssos .ss eHssa 235 bill rate; the significant coefficients of %TBt imply an inverse rela- tionship between 6T 3 t and changes in the Treasury bill rate. g t: The ARIMA m0d31 for 5g t (time deposits greater than ’ 9 $5 million) is based on the period January 10, 1968, through December 31, ii) 6 1974, which corresponds to Reserve Schemes D' and E. The autocorrela- tions and partial autocorrelations for 6: imply the following noise ,t models: (2.1.0)(1.0) (2.1.0)(1.1) (2.1.0)(1.2) (3.2.l)(2,0) (2.2.1)(2,1) (2.2.1)(2.2)- For both (2,1,0) and (2,2,1), the best results are obtained with the g t. The models (2,1,0)(1,l), (2,2,l)(2,l), and (3,2,1)(2,0) all have a very high R2 and a low vari- first seasonal difference of 6 ance of residuals and all three models transform 6; t to white noise at 9 all lags. Since it has the fewest coefficients to estimate, (2,1,0)(l,l) is chosen as the best model. The noise model (2,1,0)(l,l) is included with the input variables in a multivariate ARIMA process. The cross correlation function for T 5,t transfer functions: 6 and the prewhitened independent variables imply the following TBt 3 (19190)(1:0); zrst : (1.0.0)(1.0); Qt : (0.3.0><0.0). Combining (2,1,0)(l,l) with the input variables does not improve its R2 or residual variance, but at least one coefficient in every transfer function is statistically significant. The autocorrelations of resid- uals show that the model results in white noise and the cross 236 correlations of residuals for each input variable are small relative to the critical values of x2 so there is no reason to question their specification. Again the coefficients in the transfer functions do not have consistent signs and therefore do not provide much insight into T 5 t and the input variables. the relationship between 6 Nonmember Banks(v2 and vi) The rest of the parameters are used in the equation for rt during all four reserve schemes. There are 730 observations available but since the estimation program cannot accept that many observations, the sample is divided into two parts and separate ARIMA models are esti— mated for each subperiod. For all the remaining parameters except Et’ the sample is divided at January 10, 1968; this date almost divides the sample in half and also corresponds to one of the major structural changes in Federal Reserve reserve requirements described earlier. a) Demand Deposits For v2, the autocorrelation and partial autocorrelation functions for the first part of the sample imply that the following ARIMA models may be useful: (3,1,0)(1,1) (3.1.2) (1.1) (3,1,1)(IIZ) (0,2,1) (2.1) (0,2,1)(2,2)- The first three models all give very good results; each has a very high R2, low residual variance and each converts v? to white noise at all lags. The (3,1,0)(1,1) process is judged superior however because it has the highest R2 and the fewest coefficients to estimate. 237 It is hypothesized that the behavior of v2 is affected by the num- ber of member banks and by interest rates. The number of member banks is represented here by the number of member banks divided by the number of commercial banks (MBt);19 the behavior of interest rates is again summarized by the level and percentage change in the Treasury bill rate (TBt and %TBt). There should of course be a direct relationship between V2 and MBt and it is expected that both TBt and %TBt are negatively re- lated to v2. This latter hypothesis is based on the reasoning that dur- ing times of high or rising interest rates, membership is costlier and the tendency will be greater for banks to leave the System, and for v? to therefore fall. Transfer functions have been fitted for these three input vari- ables and are combined with the noise model for v2, (3,1,0)(1,1). After prewhitening each input variable, the cross correlation functions be- tween them and v2 imply the following transfer functions: MBt : (1,4,0 ,0); )(0 TBt : (0,1,00)(l.0); %TB : (0,2, 0)(l,0). t In the combined transfer function-noise model, none of the vari- ables in the transfer function for %TBt has a significant coefficient, so the model was refitted excluding %TBt. In that version, the trans- fer function for TBt has no statistically significant coefficient and the coefficients are of the wrong sign; the transfer function for TBt has therefore also been excluded. Excluding these two input variables has no harmful effects on the model's R2 or residual variance; the 19The variablem is based on monthly data (last Wednesday of each month) on the numfier of member banks and commercial banks. Source: Board of Governors of the Federal Reserve System, Federal Reserve Bulletin, various dates, p. Arl8. 238 results for the model with MBt as the sole input variable are presented in Table 34. The coefficients in the transfer function for MBt are in general of the expected sign although only one is statistically signif- icant.20 The model converts v? to white noise at all lags and the cross correlations are small relative to the critical x2 values, so the transfer function appears to be adequately specified. For the second part of the sample period, the autocorrelation and partial autocorrelation functions indicate the following ARIMA pro- cesses to describe the behavior of VS: (3,1,0)(1,1) (0,2,1)(2,l) (0,2,1)(2,2) (l,l,l)(l,2). In the (0,2,1) process, the second seasonal difference of V2 performs better than the first. The remaining three models all reduce the resid- ual variance to a low level, have significant coefficients, and high R2's; each however results in white noise at short lags only. They have therefore been overfitted with the following models: (3Ll20)(1,12= (3,1,1)(l,l)3 (0e2 .1) (2e2): (0.2.2)(2.2) (l,2,l)(2.2). (1.2.2)(2.2); (1 Llel) (1 .2): (1.1.2)(1.2). (2.1.1)(1.2) (2.1.2)(1.2). 20Since the coefficients in the numerator of the transfer function for MB are not statistically significant, the model was also estimated using lower-order formulations of the transfer function, but the results are not as successful. 239 u HsN.st HNs.NsIs e . stsss.H + H d saNNaa. IH .saas HssH.Hs + sss HssH.NsIHsaa.HIqI+ sssss. stHss. + ssHss.I HHs.ass Hst.HIV HasN.HIV HsaN.sIV saaNss.H + H p ssssts. Nssasss. I ssNNNN. I H u . m «/ Hass.sIs Asss.Ns HssN.HIs Haas.Hv Hass.Hs + asN.NIs HHas.sImII aNsH.ssII s s ssNHss. I ssssNN. + sssHss.H I ssasHs.H + Hsass. ssHasH. I sssHHN.I sHasaH. + H a a N NN sH He d d HsNNHs\NHIss\sH\HHIHH HHas s Hs d u . m2.38.13 " ms “HH.ssHs.s.Hv s: .NN sss sH HH sssH as sstsHps> ssHs aH. Hsas H .ss us» sss.N I eHsstsds sessszIsHspss ssIs assH. I sHsssHsds so ddssHess ssa. Ns am.o om~.sm IqomIH Ns.s asa.sH sNIH ss.s HNN.N sHIH o: Edema? Assamese s mamooamom mo maoHumHmuuoo mmouo mamooamom mo muoaumaouuooou5< wmm as.HsHIs Assa.HIv Hass.sIv asas.sIs . stHHH. I sssssN. I ssNHsN. I H ssHsaa I H + as s N ass s: HssH.Hs HsNaN.s Hsst.V Hass.HIs HHNss.s H s sssHsNN. + sssaaas. + NsHsst. + ssssHN. I NsNas. a a a U . A a o“ HssHsH\HIHs\H\HV HH sVHs a He s: “HH.HsHs H as .s> Aomumme Hobo: <2Hm< ummm ago How muasmom :oawmmuwmmv M? com “9 now wuHSmom ¢2Hm< .qm mHQMH 240 aaa.H I dHemHsses sosdssIsHspss ssIs saNH. I sHsssHmdm so ddssHpes aaa. I Ns sa.sH as.N asH.aH ssIH as.sH Ns.s ssN.sH sNIH sa.N as.s aaN.s sHIH do do mm .I AssHss Nhss Assisss Nhss Hes News s mHmDonom mo maowumaouuoo mmoum. mamovammm mo mcowumamuuooouo< wmq HaHs.NIs AasN.NV HNsN.NIs HHss.NIs I I I u s ssNHHss. I N essaNss. + H ssasts. I ssasss. 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I Ns aH.ss as.ss ss.aN ss.aH sNH.NN ssIH ss.sH ss.ss ss.HN sN.N sss.sH sNIH Na.N ss.sH Ha.a sH.s Has.a sHIH dd w dd dd I. dd dd .l Hessss Np HessseNV NeNs AssHsas Npse Assasss News Hes Nhss s dadsvfimmm mo maowudaouuoo mmouo madoonom mo chHudeHHOUOua< wdq Has.ssIv s sssNaa. I H + s: HsHHs.V HsNas.V HsNNN.IV Hess.HIv IIaNsssds aaas.Hs aaasaww ssassss. + ssassss. + sNNsHs. I sssHssH. I Nstst. + saHHNHq + sHsas. HsHs.Hv HsHN.NIs HNNa.Nc HasN.NIv HsHs.HIV In In In In u sassss. + s ssssss. I N ssssss. + H sassss. I sstss. I Aasa.sv AssH.ss HHa.Nas HsHs.HIV . . ssass sNaNaa. + H + uses sasssN. I H + as NssaNHs + ssHsss + H I e> s . Hass.NIs HHaN.HIs HsHs.Ns, Assa.HIs INas.sHs a N Nssss.I sassss. I Nasss. sHsHNst. I sstss.H + H A A A U A d d d AsN\Hs\NHIss\sH\HV HH seas a ss " s :HH HsHs s HV u sas ”HH.HVHs.H.HV " ss ”HH.ssAs.s.HV ” s: asH ssH as stsHes> Hssessds s ssHs aH. NVaH N.Ns "as edsstsos .ss stss 242 The model (3,1,1)(l,l) is not an improvement over (3,1,0)(1,1); the coefficient of the moving average variable is not significant. The model (0,2,2)(2,2) gives better results than (0,2,1)(2,2) and the other two models overfitted to it. Of the models overfitted to (l,l,l)(l,2), the best is (2,1,l)(l,2). The most promising models are therefore (3,1,0)(1,1), (0,2,2)(2,2), and (2,1,l)(1,2); each one has a high R2 but results in white noise at lags 1—10 only. The autocorre— lations of the residuals of all three models are large at lags, ll, 13, and 27, so each was rerun including moving average variable(s) at those lag(s). With the seasonal variables added, the results for all three processes are very similar. The (3,1,0)(1,1) process plus variables at lags 11, 13, and 27 is chosen as the best since it has the highest R2; it transforms v2 to white noise except at short lags. This noise model plus transfer functions for MBt’ TBt’ and %TBt were included in a multivariate model. After prewhitening each input variable, their cross correlations with v2 imply the following trans- fer functions: MB: = (1,4,0>(0.0>; TBt : (1,1,0)(1,0); %TBt (l,0,0)(l,l). Each independent variable has at least one statistically significant co- efficient and the cross correlations of residuals for each transfer function are small, implying that they are adequately specified. The multivariate process does not however result in white noise. The auto- correlations of residuals are large at lags 7, 9, and 15 but when vari- ables at those lags are added, the model's results are poorer. The other two successful noise models described above, (0,2,2)(2,2) and (2,1,1)(l,2) were also used in the multivariate process, but they both 243 perform more poorly than (3,1,0)(1,1). This noise model plus the three transfer functions therefore appears to be the best model that can be constructed for v2; its results are given in Table 34. The signs of coefficients for MBt are not consistently positive but the majority of them do imply the expected direct relation between MBt and v2. The co- efficients of TBt are also of mixed sign and those for %TBt are not of the expected sign. b) Time Deposits The autocorrelations and partial autocorrelations for v: for the first part of the sample period indicate that the following ARIMA models are relevant: (3,2,0)(2,0) (3,2,3)(2,l) (3,2,2)(2,2). All three models give very good results; both (3,2,0)(2,0) and (3,2,3)(2,l) result in white noise at all lags. The (3,2,0)(2,0) pro- cess appears to be preferable since it has fewer coefficients to esti- mate and its R2 is slightly higher; both (3,2,0)(2,0) and (3,2,3)(2,l) were however used in the multivariate process described below. The behavior of v: is presumably also affected by MBt’ TBt’ and %TBt. In addition, Qt’ the difference between the Treasury bill rate and the Regulation Q ceiling for time deposits is relevant. Transfer functions for these four independent variables are therefore fitted and included in a multivariate process with the noise model (3,2,0)(2,0) and.with (3,2,3)(2,l). After prewhitening each independent variable, their cross correlations with v: indicate the following transfer functions: 244 MBt : (1.4.0)(0.0); TBt : (0.1.0)(l.0); ”..TBt : (0,2,0)(0,0); Qt : (0.3.0)(0.0). The best results are obtained using (3,2,3)(2,l) as the noise model. The transfer functions for TBt and %TBt contain no statistically signif- icant coefficients so the model was refitted excluding these input var- iables. These results are reported in Table 34. The model has a high R2 and low residual variance. The model converts v: to white noise at all lags and the cross correlations of residuals for both transfer functions are small, indicating that the functions are adequately specified. The transfer function for MBt would be expected to have positive coefficients, so two of the coefficients in its numerator are of the wrong sign. The a priori relationship between v: and Qt is not clear. When Qt is large, time deposits in commercial banks will decline (or not grow as fast). The impact on v: of this situation will depend on the relative ability of member and nonmember banks to attract (or fail to lose) time deposits as their overall level grows more slowly or falls. The coefficients in the transfer function for Qt’ all of which are sta- tistically significant, indicate that VT t and Qt are inversely related; this implies that when market conditions make time deposits relatively unattractive, member banks fail to effectively compete and their share of the nation's time deposits falls. Since member banks dominate the interest-elastic market for large certificates of deposit, this result seems appropriate. The negative coefficients for Qt may also be the result of contemporaneous rise in Qt and fall in v: during the sample period, without the existence of any causal link. 245 For the second part of the sample period, the autocorrelation and partial autocorrelation functions for v: show that these ARIMA models should be considered: (3.2.0)(2.0) (2.2Il)(2.l) (2.2.l)(2.2)- The (2,2,l)(2,1) process performs best; it has a very high R2, low resid- ual variance, significant coefficients and converts v: to white noise at all lags. The noise model (2,2,l)(2,l) is combined with transfer functions representing MBt’ TB %TBt, and Qt' After prewhitening each t9 input variable, the following transfer functions are implied by their cross correlations with vT: t MBt : (1,6,0)(0,0); TBt : (1,1,0)(1,0); %TBt : (1, 0,0)(1, 0); Qt = (0. 4.0)(0 0) There are statistically significant coefficients in all four trans- fer functions so all of the input variables are retained; the results for the model are given in Table 34. The noise model does not result in white noise; the autocorrelation of residuals is large at lag 13 so a moving average variable is added at that lag. With this addition, the model does transform v: to white noise at all lags. The cross correlations of residuals for MBt are small so the trans- fer function is apparently adequate. None of the seven coefficients in the numerator are statistically significant and would therefore appear to be redundant, but a transfer function of lower order results in much larger cross correlations. The signs of the coefficients for MBt in general reflect the expected direct relationship between MBt and vi, although two are negative. 246 The relationship between V: and TBt or %TBt is complicated and there is no.3 priori way to characterize it. As discussed earlier, large values of TBt or %TBt may correspond to either increases or de- creases in the level of time deposits; furthermore, whatever the rela- tionship between the Treasury bill rate and the rate of growth in time deposits, the relationship between the growth of time deposits and v: is also not clear. In addition, there may be some tendency for high or rising interest rates to encourage banks to leave the System, imply- ing an inverse relationship between VT t and TBt and %TBt. The results here reflect an inverse relationship between %TBt and vi; the rela- tionship between TBt and V: is not clear, although the statistically significant coefficient implies a direct relationship. Both transfer functions result in white noise, although for %TBt, at the 2.5% level of significance only. The coefficients of Qt are also mixed; the majority are negative, implying the inverse relationship between Qt and v: also reported for the first part of the sample period. The cross correlations of resid- uals are large, implying that the transfer function for Qt is not ade- quate, but no reasonable modification of it gives any better results.2 T) Nonmoney Deposits (Yt, It, t a) Government Deposits The autocorrelation and partial autocorrelation functions for the parameter Yt indicate that for the first part of the sample period the 21The transfer function used here results in white noise except at lags 21-30. The cross correlation is large at and near lag 28, but in- cluding variables at these lags does nOt remedy the situation. 247 following models should be considered: (3,1,0)(1,1) (3,1,0)(IIZ) (0,2,3)(ZII) (0,2,3)(2.2)- For both models, the first seasonal difference of the series gives better results than the second. However neither (3,1,0)(1,1) nor (0,2,3)(l,l) converts Yt to white noise. These two models have there- fore been overfitted in the following ways: (3.1e9)(l.1)= (3,1,1)(1II) (3.1.2)(l,l); (0i213)(2 i1): (l,2,3)(2,1) (2.2.3)(2.1)- Both models overfitted to (3,1,0)(1,1) give poorer results than it does. The models overfitted to (O,2,3)(2,l) are both slight improvements but neither results in white noise, even at short lags. The most promising model appears to be (3,1,0)(1,1) since it does convert Yt to white noise at short lags. Its residual autocorrelation is large at the seasonal lag 13 and when a moving average variable is added at that lag, the resulting model transforms the series to white noise at all lags at the 5% level of significance. This is apparently the best model that can be devised. It is presumed that the value of Yt is strongly affected by the schedule of payments dates for federal taxes. A dummy variable (Gt) was constructed to represent tax payment dates22 and is included as an 22The dummy variable is defined as G = l for the first wednesday after every tax payment date and Gt = 0 otherwise. The tax payment dates used are January 15, March 15, April 15, June 15, September 15, and December 15. 248 input variable for Yt’ along with the noise model (3,1,0)(1,1) plus a variable at lag 13. Since the series Gt varies so little from week to week, the process for prewhitening and identification of its transfer function fails. Therefore the simple transfer function (1,0,0) is used. The coefficients in the transfer function for Gt have the proper signs but they are not statistically significant. In addition, inclu- sion of the transfer function has no effect on the model's performance. Since these results show no important relationship between Gt and Yt the input variable is dropped. It may be that Gt is not a good repre- sentation of the tax-payment date cycle or it may be that the seasonal variable at lag 13 in the noise model (which is statistically signif- icant) is related to that cycle and therefore the introduction of Gt does not add to the explanatory power of the model. The univariate process (3,1,0)(1,1) plus a variable at lag 13 is apparently the best model that can be constructed for Yt for this time period. The esti- mated coefficients satisfy stationarity and invertibility conditions. The results for the model are given in Table 35. For the second part of the sample period, the following models appear to be promising: (3,1,3)(l,1) (0,2,1)(2,l) (0,2,1)(2,2) (3,0,3)(0,2). Of these models, the best results are obtained with (3,1,3)(l,1) and (0,2,1)(2,l), but neither model results in white noise at long lags. The latter model has therefore been overfitted with the following models: 249 saa.H I oHomHaoos somossIsHsoas aNH.ss ssIH sss.aH sNIH asIs sass. I sHsasHsos so dossHass sHN.N sHIH . n dd I. NsN Ns Has News a madooamom mo duosudamuuoooud< wda HNNN.ss sNIasssHNN. + Hsaa.aIs Hst.ss AHNsa.v Assss.s Hssss.v Haas.Hs In I In I a In In D sH sNasaN. + s omNsNNN. + N massHH. + H ostsss. + s + N > sHa.Ns I ssIH Nss.aN sNIH aaa.H I oHaaHasos soaaszsHssas ssa.a sHIH I . u m do mm 0 wood ad dd .I as s sass H sH s s H > Ass News a sum. H mm madoowmom mo maowudaouuooouo< wdA HaHN.aIV sass.sv HssH.ss Assa.ss In D In In In H. sH sassaN. I a + s asNNNaN. + N ssassNH. + H sstNHN. 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I Ns ss.sH ss.Hs Ns.aa aHs.aN ssIH sN.HH ss.sN Na.aN NaN.sH sNIH sH.a sH.sH aH.s aas.HH sHIH dd . dd dd dd I aasHss Name HasHseNHNass ass Haas Name ass News a madodamom mo mcoaudaduuoo mmouo madavflmdm mo macaudaouu000u5< wdq aNssa.s AssN.NIs Hsaa.ss ,Hsss.NV aaNss.Is I I Iu u I a asHaass. + N saast. I H sstas. + sNNsHs. + sH ossNaNsss..I NIa aNNs.Hs HI. aHaa.HIs a assa.Hs aHIa AeaH.Hs NIa aaaN.Ns saNHNsss. + saNNssss. I ssNNssss. + sssNHaHs. + sasssNNs. + . . Hsasa.Is HHssN.IV assa.HIv HIa Aaas No a HaasH s o assasss. I NsHaHsH. I ssssss. I H a I 0 m " P sasasass + sasaasss + HNsN.HIs aHsa.Hs AasH.HIs Nasaa.Is s sHsstHH. I ssHaass. + NsHNsNN. I sassss. I H ass\sH\HIHs\H\Hs aN.sVHs.a.sso ”as maH ssH as oHsoHss> s msHa aN.sVAs.N.sV.NossN a n3 seH as oHsoHas> o msHs sN.HVHs.N.sV a ss aaH ssH as oHssHss> Hssomsos s ssHs sN.Hvas.H.ss a e smasHosos .as oHssa 253 Hmm.H n oaumaudum domudchHnuda cOIm meH. u deodeom mo oucdaud> mun. a mu ss.aN sNN.sN . saIH sN.aH sNa.sH sNIH as.a sNN.s sHIH dd dd II Assasss News Has News a deooadoM mo mcoaudaouuoo mmouo madaofimom mo mcowudamuuooouo< wdq HHNs.NV HNHH.NV HssN.HIs Assa.HIv HHH.sNV .Iu . Iu Iu I u u H sssassss..Issssaasss. + a sstss. I N saHNaH. I H ooassss.H + a I as A A 0 U A A A 0“ Hss\sH\aIHs\H\Hs AH.HsHs H so . ss .AH.HsHs H so . m aaa.H I oHoaHasds sodomsIsHssss asIs Nsss. I sHossHsds so mosmHss> Haas I Ns sH.sa Ha.sa aas.sa saIH sN.HN ss.aH NsN.NH sNIH sa.s as.a Hsa.s sHIH u dd dd dd II lasaseNV Name Assases Nose ass Nose a madowwmdm mo msoaudadunoo mdouo mfidoofimdm mo m:0fiudaouu000us< wdd HsN.ass AaNa.NIs sassa.s HaHa.Hv a sNHHss.H + md ssssss. I H a NsasHaa. + sssasa. + H o + d u H< aaHsaIMI HsHHH.s AssN.Hs o u peas aasN.HIs ._+ sas INNsas.Is sNNsas. + NsHsaas. + saaaaa. + H quoo.l camoo.l m AsN\Ha\NHIss\sH\Hs HN.HsAs.s.Hs asses “sN.HsHs.s.Hs "use “HN.HsHs.H.Ns "up soasHusos .as oHsos 254 .Hmumeduda aodm pom soauaauodmo Am.dvav.o.av mad as dmuoomo dH masocmummwad Hdcomdmm mo mmuwmo may .mcoaudovm aoammmuwmu mau Eoum omuusao ma Am . .o Hs.sVHs s.ss .os aH.Hsas.s.Hs noses o.a msmH HHm ssa. HH.HVAs.H.HV a s9 HH.Hsas.H.Ns as ommy mmHoz muHaz mm Am.dvaa.o.uv Am.owamddamv umumsdudm COHoooom ummmoduy Hmooz mmHoz Hose: smssaHoms smastsos .ss oHsms 270 aH.sVas.s.Hs Hoses . msoH HHm NaH. aH.HsHs s.Hv " se HH.ssAa.s Hs HN u assH HHs aNN. aH.Hsas.H.ss “use HH.HsHs.H.ss HH o A A ..U o sN.HsAs s Hs .osea mssH HHs HNa. aN.HsAs.s.Hv “use sN.Hsaa.H.Nv aN HN.ssas.s.ss " s aH ssH a + HN.ssHs.N.ss a sea yHoo «H wdH u u ssIHH assH Naa. + sN.HsHs.N.ss " se sH ssH + sN.HsHs.H.as aH e omoe omHoz opens s as.ssas.s.sv am.sst.s.av sososdeme N :oHuocom emmmcdey Hmooz mmHoz Hose: smooeHoms smasHosos .ss oHsae 271 coefficients and those that are significant do not always have the expected signs. Market interest rates would logically be a major determinant of the growth rate of the various categories of time and savings deposits, but the direction of their influence is not clear. The regression re- sults presented here show that TBt is a statistically significant inde- pendent variable for three of the AT-parameters and %TBt is signif- icant for A2,t only (total time deposits). The results show that Af’t and TBt vary directly, so as interest rates rise the rate of growth in the various categories of time and savings deposits falls; the rate of change in interest rates is apparently not an important influence on rates of growth in time and savings deposits. The effectiveness of Regulation Q interest rate ceilings is also a statistically signif- T and AT are l,t 5,t directly related to Qt’ but the relationship between A: t and Qt is not 9 icant variable for three AT-parameters; as expected, A clear. For 6T and 6T , both TB and %TB are statistically signif- 3,t 5,t t t icant, but Qt is significant for 6: t only. The rate of growth in sav- 9 ings deposits (A; t and 6g t) therefore does not appear to be affected 9 9 by Qt’ but is directly related to interest rates. It was hypothesized that v2 and v: are directly related to the relative number of member banks and inversely related to interest rates. In the regression results, MBt is statistically significant for both v2 and v: and in general the expected direct relationship is verified. Interest rates are not significant variables for either v2 or v: in the first half of the sample; they are significant for both parameters in the second part of the sample, but the signs of the coefficients imply no consistent relationship between interest rates and attrition 272 from the Federal Reserve System. In addition, Qt is a significant var- iable for v: for both halves of the sample period. The signs of the coefficients consistently show vT t and Qt are inversely related; this is attributed to the member bank dominance of the highly interest-elastic market for large certificates of deposit. The ARIMA models for It indicate that it is directly related to the relative number of member banks, but in general the behavior of market interest rates is not a significant determinant of It. This inr plies that member banks hold fewer interbank balances as assets; this supports the result reported by Gilbert.27 Regulation Q ceilings and interest rates would be expected to influence Tt’ although the direction of influence for the latter is not _a priori clear. Both TBt and %TBt are statistically significant in both models for Tt; for the first half of the sample the signs are mixed, but for the second half they are consistently negative. The latter re— sult indicates that high and rising interest rates cause the growth of time deposits to slow, as other assets become more attractive. Qt ought to be inversely related to It, but it is concluded here that there is no strong causal link between the two. Qt is statistically signif- icant in the first model for Tt only, the majority of its coefficients are not of the expected sign; furthermore, this result is based on very few nonzero observations of Qt' It is hypothesized that 6t and interest rates are inversely re- lated but the results reported here show the opposite to be true. As 27Gilbert, p. 12. 273 discussed above however, the model for at for the last half of the sample is probably not very reliable. CHAPTER 7 AN ARIMA FORECASTING EXPERIMENT FOR rt The problem of nonuniform reserve requirements arises in a week- to-week control situation when the Federal Reserve does not know the value of rt or its component parameters. The simplest solution to this lack of knowledge is to assume each week that there is no change in the value of each parameter. This is the basis of the naive forecasting model described in Chapter 5. The ARIMA models described in Chapter 6 are now used to forecast values for each of the parameters in rt. These more sophisticated forecasts are used as an alternative to the naive forecasts to predict values of rt, and the resulting error is calculated. Following the techniques developed by Box and Jenkins,1 forecast values for the parameters in rt are derived from their estimated ARIMA models.2 The ARIMA forecast for each parameter is then substituted for the naive forecasts in the first forecast equation for rt (equation 5—6). Denoting the ARIMA forecasts with an asterisk, this model pro- vides a forecast value for rt, defined as, 1George E. P. Box and Gwilym M. Jenkins, Chapter 5. 2Forecasts of the univariate models were calculated using Computer Programs for the Analysis of Univariate Time Series Using the Methods of Box and Jenkins, Supplementary Program Series No. 517 (Madison, WI: The University of Wisconsin Computer Center, revised May, 1975); the multivariate processes were forecast with the computer program, Analysis of Time Series Models Using the Box-Jenkins Philosophy by David J. Pack (Columbus, Ohio: The Ohio State University, revised January,_1978). 274 275 A _ D* D* D* * * (7-1) r3,t g dj,t Aj,t 6j,t vt €t_1 (l + yt + 1t) T* T* T* * * In + + E ti,t Ai,t éi,t Vt Tt Et pt-l n 3 + E l”h,t wh,t—1 pt-l' The average error in rt caused by the ARIMA forecasts is given by, A 2 (rt ' r3,t) ’ IIMZ -.l (7-2) MSE3 - N t 1 where N is the number of observations. The value of MSE3 for each reserve scheme is given in the first part of Table 37; it measures the error in rt associated with the ARIMA forecasting experiment. Following the procedure used for the naive forecasting model, the ARIMA forecasts for each parameter (or set of parameters) in rt is (are) in turn replaced by its (their) actual value(s) in week t. Consider, for example, the parameters representing lagged reserve requirements. The actual current values of Ag’t and A:,t are substituted for their ARIMA forecasts in equation (7-1); this yields another forecast of rt, 7 3 “A - 2 d AD dD* D* g l + * + * ( — ) r4,t — j j,t j,t j,t Vt t-l ( YI; 1t) T T* T* * * m + i ti,t Ai,t 51,t vt TI; + 8t t-l n + i wh,t-l mh,t—l pt-l' The difference between this and the actual value of rt is measured by, 3The definitions of r the A-parameters for all (defined below) all include reserve schemes. A and f t’ r3,t’ 4,t 276 Table 37. Error Resulting from the ARIMA Forecasting Model (Results of the Calculation of E2) Reserve Scheme (Number of Observations) A (100) B (52) D' (97) E (111) MSE3 .551523-05 .l3263E-04 .ll96lE-02 .110152-02 E; -.o3351 .60452 .01237 .01562 E3 -.01770 .62686 -.Ol655 .01253 E: -.01777 .61659 .01597 .00690 E: .3809l .66564 -.00150 .00209 E; .02486 .64610 .01129 .00527 3:1 .03574 .66410 .35685 .00236 E 32 .21559 .64444 .36265 .99445 1Based on a univariate forecasting model. (7-4) MSEX = 4 X(r - r t 4,t zhH where N is the number of observations. Comparing MSEZ and MSE3 indicates the loss, in terms of accurate forecasts of rt, from using the ARIMA forecasts of the A-parameters. To facilitate this comparison, the error-coefficient EA is defined as, 2 MSE - MSEA (7_5) EA = 3 4 2 MSE 3 MSEA =l_-———-—li MSE3 If the ARIMA forecasts of the A—parameters are very poor, then replacing them with their actual values will reduce the error in the forecasted rt; MSEZ will be smaller than MSE3 and B? will be close to one. Therefore the closer the value of E: to one, the poorer the ARIMA forecasts of the A-parameters and the larger the error they cause in forecasting rt. 0n the other hand, if the ARIMA forecasts of the A-parameters are good, then using their actual values will reduce the error in rt very little; MSE: and MSE3 will be similar and E; will be close to zero. Therefore the smaller the value of E3, the D smaller the error in rt caused by the ARIMA forecasts of Aj t E t 9 9 It is possible for E2 to be negative; this occurs when MSEz > MSE3. This indicates that the error in rt is smaller with the ARIMA forecasts for the A-parameters than when their actual values are used. The con- cepts of MSE4 and E2 are defined analogously for the other parameters in r . t The results for E2 for each parameter in rt for all four reserve schemes are given in Table 37. Because of programming limitations, the 278 forecasting experiment is limited to the last 100 observations of Schemes A and D'.4 Some of the values forecasted for A: t and 6: t 9 9 T i 6 under Scheme D', had to be deleted from the under Scheme B, and for A calculation of E2 because the forecast equation gives nonsensical re- sults. For Reserve Scheme B, the erratic results probably occur because there are no observations available for A: t and 6: t before the fore- 9 9 cast origin. Under Scheme D' the erratic forecasts of A: t are trace- 9 able to erratic behavior in the independent variables. As can be seen in Table 37, the E -coefficients are consistently 2 large under Scheme B; the EZ-coefficients for B are also about the same size for all parameters. This indicates that the mean square error in rt falls considerably when the actual value of each (set of) parameter(s) is substituted for its (their) ARIMA forecasts. The loss therefore from using the ARIMA forecasts is substantial for each parameter and the loss is approximately equal for each one. This result is probably due to the small number of observations left for Scheme B. For the period covered by Reserve Scheme A the poorest ARIMA fore- falls most when they are replaced by the actual values of Yt and €t° The value of E3, E3, and casts are for Yt and Et’ since the error in rt EV are all negative, implying that the error in rt is smaller with the 2 ARIMA forecasts than when the actual values of the parameters are used. The values of Bi, f, and E: are also all negative (see Table 29, Chap- Y ter 5). None of the E2 2 on an absolute level so the error resulting from using the ARIMA fore- E -coefficients, including E and E3, are large casts is not large for any parameter. 4The forecasting programs used here allow at most five different forecast origins per run. 279 For Reserve Scheme D', the E -coefficients are largest for T 2 and 6t and very small or negative for the other parameters. Even E: and E; are not very close to one. Again, using the ARIMA forecasts apparently does not cause very large errors in rt and perfect knowledge of the parameters yields little gain. Under Reserve SCheme E, E: is very close to one so the mean square error in rt falls considerably when the ARIMA forecast of 8t is re- placed by its actual value. Thus the ARIMA forecasts of st are appar— ently very poor for this period of time and the loss from using a: is significant. The Ez-coefficients for the other parameters are all very small so their ARIMA forecasts are apparently quite good. In the naive forecasting experiment described in Chapter 5, E: is larger under the later reserve schemes, especially the graduated scheme. Ignoring Scheme B, EA is small for all schemes and is not appreciably 2 larger for Scheme E. Therefore while the naive forecasting model is less successful with more reserve categories, this is not true for the ARIMA model. In the last two reserve schemes, E: is much smaller than Bi, so the error associated with the ARIMA forecasts of the A-parameters is smaller than with the no-change forecasts. The errors resulting from the naive forecasts of the 6-parameters also increase slightly with the number of reserve categories. Ignoring 6 again Reserve Scheme B, E also increases for successive reserve schemes, 2 although E2 is negative for Schemes A and D'. Except for Scheme B, E3 is less than E? so the ARIMA forecasts result in smaller losses than the naive forecasts for the 6-parameters. Both the naive and ARIMA forecasts of v? and v: result in very small errors. The largest value of E: is for Reserve Scheme D' and, 280 except for Scheme B, E: is also largest during that period. Apparently v2 and v: vary most during Scheme D' and are therefore difficult to suc— cessfully predict during that period, regardless of the methodology. Except for Schemes B, E: is smaller than Bi, so the ARIMA forecasts of D vt and v: are better than their naive forecasts. Except for Scheme B, E3, E2, and E: are all small so the ARIMA fore- casts introduce only small errors in rt. For the last reserve scheme, Ev is however smaller than EA and E indicating that laggedand differen- 2 2 2’ tial reserve requirements cause more unpredictable variation in rt than do nonmember banks. This is not true under Scheme D', when E: is rela- tively large, or under Scheme A, when all three coefficients are nega- tive. A The gain from perfect knowledge of Yt over its ARIMA forecasts is large for the first half of the sample but falls drastically for the last half. The values of E: show the same pattern so apparently Y1 is more predictable in the first half of the sample. In addition, ARIMA forecasts for Yt in the first half of the sample are relatively poor, Y Y 2 1° ARIMA forecasts are more successful and result in smaller losses than since E is larger than E For the second part of the sample, the the naive forecasts of Yt' Except for Scheme B, the ARIMA forecasts of It yield small errors, ; is consistently larger than E; schemes. The ARIMA experiment for Tt is very successful during Schemes A although E which is negative for all and E; E; is small and much smaller than E: so the ARIMA experiment results in smaller errors than the naive model. The ARIMA model for Tt is less successful during Scheme D' however; E; is relatively large 281 and larger than E Due to programming limitations,5 the ARIMA fore- T 1' casts of Tt had to be derived from the noise model alone, excluding the transfer functions. The poor results in Reserve Scheme D' prob- ably occur because the effects of interest rates and Regulation Q on It have been excluded and Reserve Scheme D' corresponds to the time period when the behavior of these independent variables were most cru- cial to the behavior of Tt' Considering the small losses during Schemes A and E from using the ARIMA forecasts even though the transfer func- tions are excluded, it appears that Tt could be very successfully fore- casted with a multivariate ARIMA model. Using the ARIMA forecast for Ct causes relatively large losses in. rt for all reserve schemes and this is especially true for Reserve 8 € 2 is larger than E1 ARIMA forecasts are apparently very poor and, except during Scheme A, Scheme E. Furthermore, E except for Scheme A. The the 8t - €t_1 surprising result, especially for the last part of the sample, consid- assumption represents a better forecast. This is not a ering the very low R2 of that ARIMA process. As discussed earlier, it appears that after reserve-carryover was introduced, the behavior of 6t is erratic (especially, relative to its low level) and difficult to successfully forecast with an ARIMA model. In summary, the ARIMA methodology causes the largest losses in accuracy of rt when used to forecast at for all schemes, Tt during Re- serve Scheme D', and Yt during Scheme A (this ignores the result for Scheme B). The ARIMA forecasting experiment for the X- and 6-parameters, 5For both parts of the sample period, the second seasonal differ- ence of T was required for stationarity. The program used here to forecast the multivariate models would not allow for the second seasonr al difference of order 52. 282 v2 and vi, and It, It for Schemes A and E, and Yt for the last half of the sample yields small errors in rt; the ARIMA forecasts for these parameters cause smaller losses than the naive forecasts. Comparing MSE to MSEl (Table 29, Chapter 5) shows whether the 3 ARIMA forecast experiment is more successful than the simple no-change model. For Reserve Scheme A, MSE3 < MSEl so the ARIMA forecasts of the parameters in rt provides a better forecast for rt than the naive fore- casting model. For the other reserve schemes however, this is not true. Especially during Schemes D' and E, the error in f3 t estimated with , the ARIMA models, is much larger than the error in f , estimated with l,t the naive model. Considering the values of the Ez-coefficients for the individual parameters, it seems likely that this poor ARIMA perfor- mance is due almost entirely to bad forecasts of Tt and 6t in Scheme D' and St alone in Scheme E. To test this proposition, MSE is recalculated for Schemes D' and 3 E, using Et-l instead of 6:. The results are .80908E-03 and .80425E—05 for each scheme, respectively. The naive forecasts of at therefore result in smaller errors than e: for both schemes. For Scheme E, the error falls below MSE1 so when the ARIMA forecasts for 8t are excluded, the ARIMA forecast experiment is more successful than the naive one. For Scheme D', the error associated with the ARIMA forecasts is still * larger than MSEl, even when the 8t values are not used. WHERB SUMMARY AND RECOMMENDATIONS The behavior of the individual parameters in rt shows that those representing the categories of nonmoney deposits have varied most dur- ing the sample period; both the levels and first differences of Yt’ It, and It show more variation than the other parameters. Of these three parameters, It has varied most. In addition, the variation in Tt and It have increased during the sample period; the variance of Yt however has decreased over time. While the parameters representing lagged reserve requirements do not vary much on an absolute scale, they all display considerable week-- to—week fluctuations about one; in some instances these weekly fluctu- ations are large. This is indicated by the fact that in general the standard deviation of the first differences is larger than that of the levels, and the mean of the absolute value of the first differences of the X-parameters is larger than the mean of the first differences. T. These patterns occur for A as well as AD although, by all measures i,t j,t T i,t' The parameters corresponding to differential reserve requirements of variation, A? t vary more than A , behave much like the A-parameters: the variation in the d—parameters is not large on an absolute scale, but they do fluctuate considerably from week-to-week. The levels of the 6-parameters vary more, and the mean of the first differences is larger than for the A-parameters, but variation in the first differences is smaller for the 6-parameters; this pattern holds for both demand and time deposits. Therefore, while the d-parameters vary more, they appear to be more easily predicted 283 284 than the A—parameters. The ST-parameters also vary more than the 6D- parameters, but the average size and variation in their weekly changes is smaller; this implies that while differential reserve requirements applied to time deposits causes considerable variation in rt, it is more predictable variation than that caused by the 6D-parameters or XT-parameters. The variances of v2 and v: are small on an absolute scale and the variation in their first differences is even smaller. They do not therefore show the sizable weekly fluctuations characteristic of the A- and 6-parameters. This implies that the distribution of deposits between member and nonmember bank does not vary much from week-to—week and that v? and v: do not vary in an unpredictable fashion. 0f the two parameters, V: is the most stable. Both v2 and v: have, of course, declined during the sample period; the decline is more pronounced in v2 and in addition, the standard deviation of v? more than doubled between 1961 and 1974. The changes in v: appear to be closely tied to the effectiveness of Regulation Q ceilings. The statistics for wh,t indicate that the base-aborbing money per dollar of deposits held by nonmember banks varies considerably from state to state; this implies that differential state reserve require- ments are potentially a serious control problem. On the other hand, wh,t shows that shifts in the distribution of deposits between states have been minimal. Further investigation of these parameters is hame pered by lack of data. Data problems also seriously limit analysis of the variation caused by reserve requirements against various categories of nondeposit liabil- ities. The parameters representing the application of lagged reserve 285 requirements to nondeposit liabilities do not fluctuate from.week to week as much as the other A-parameters, but the erratic rates of growth in the categories of nondeposit liabilities result in relatively large changes in the AN-parameters. The GN-parameters also show large weekly changes but the variation in these parameters is not large relative to the other 5-parameters. Therefore the application of lagged and dif- ferential reserve requirements do not appear to introduce particularly variable parameters into rt. The aN-parameters, representing the ratio of nondeposit liabilities to privately-owned demand deposit do vary a great deal; their variance is only exceeded by It. The application of reserve requirements themselves to nondeposit liabilities therefore does introduce additional, highly variable, parameters into rt. The level of excess reserves has of course declined during the sample and the variation in at has increased, especially since 1968, when the reserve-carryover procedure began. The coefficient of varia- tion of 8t is large, but by other measures of variation, 8t is very stable relative to the other parameters. The sample period is divided into five subperiods corresponding to the various reserve plans that have been in effect. The variation in rt is larger during later reserve schemes. Successive changes in Federal Reserve reserve requirements that have introduced more cate- gories of deposits and lagged reserve requirements into the reserve structure have apparently also introduced increased variation in rt. In some reserve schemes, the standard deviation of some A— or 6- parameters for individual deposit categories are among the largest of all the parameters. The parameters that have consistently varied most are Yt’ Tt, Et and in one reserve scheme, wt. In no reserve scheme 286 is the variation in V2 and v: large relative to other parameters, and in some schemes the standard deviations of v2 and v: are among the smallest of all the parameters. Thus the historical record of rt under the various reserve plans shows that the largest sources of dis- turbance have been time deposits, government deposits, and excess re- serves; lagged and differential reserve requirements have been a moder— ate, but increasing, source of variation in rt. Changes in the dis- tribution of deposits between member and nonmember banks have been only a minor source of variation. The partial variance of rt is used here as a device to decompose the variation in rt into its sources. The partial variance due to TC is consistently the largest for all reserve schemes and varT(rt) in- creases during the sample period. The partial variance shows that lagged reserve requirements have also been a major source of variation in rt; varA(rt) is larger for each successive reserve Soheme so as more reserve classes have been added, lagged reserve requirements have caused more variation in rt. Vary(rt) and var€(rt) are also large for the first half of the sample, but both decline in the second half. Var6(rt) increases only slightly with the number of reserve classes. The value of var5(rt) is small for all reserve classes so shifts of deposits between classes of member banks have not been a major source of variation in rt. According to varv(rt), shifts of deposits between member and nonmember banks have also been only a minor source of var- iation in rt and there is no convincing evidence that nonmember banks are an increasing source of disruption. Varv(rl is largest for Scheme D', but nearly equal for Schemes A and E. 287 To test the relative predictability of each parameter, two fore- casting experiments on rt are performed. One is a simple model which assumes no change in the value of each parameter; the second uses fore— casts of each parameter derived from models estimated using the time series methodology of Box and Jenkins. Results of the naive forecasting experiment support the general results described above. The naive forecasts of Tt’ Et’ and the A- parameters cause the largest forecast error in rt; the naive forecasts of VS, VI, and the 6-parameters result in small errors in rt only. In addition the Yt = Yt-l forecasts cause large errors in rt in the first half of the sample. Thus Tt’ 8t, the A—parameters, and Yt for the first part of the sample, are the parameters that are the most diffi- cult to forecast using this simple technique; v2, VE’ and the 5- parameters can be quite successfully forecasted, even with this simple no—change procedure. The errors associated with the naive forecasts of the X-parameters and the 6-parameters increase with the number of reserve classes; the error caused by using no-change forecasts for v? v: does not increase through time. The ARIMA forecasting experiment provides more sophisticated fore— cast values for each of the parameters. Substituting the ARIMA fore- casts for the naive ones, however, reduces the overall forecast error in rt only during Reserve Scheme A. The results reported for the E2- coefficients show that the ARIMA forecasts are most successful for the A-parameters and the 6-parameters, v: and v3, and It. The error in rt caused by the ARIMA forecasts of these parameters is very small. In addition, the ARIMA forecasts of Yt are very good for the last half of the sample and those for Tt are successful except during Scheme D'. 288 The ARIMA forecasts of 6t result in large error in rt for all reserve schemes. The ARIMA forecasts on most of the parameters are therefore quite successful. The fact that the error in rt is larger for the ARIMA forecasts than for the naive forecasts in most reserve schemes is attributable to the poor ARIMA forecasts of at, Yt during the first half of the sample, and It during Scheme D'. When the naive forecasts are used for at instead of its ARIMA forecasts, the error in rt falls substantially. Thus the major impediment to successfully forecasting the parameters of rt with the ARIMA methodology appears to be the dif- ficulty of describing at with an ARIMA process. None of the evidence presented here indicates that declining mem— bership in the Federal Reserve System has caused increased variation or unpredictability in rt. Relative to the other parameters in r D Vt and v: vary little and are easily predicted. The variation in v? t, and v: are of course not zero, so presumably the variability in rt could be reduced if nonmember banks were subjected to Federal Reserve reserve requirements. In addition, vD and v: do not reflect the total t impact of nonmember banks on rt; wh,t and “h,t also represent the influence of nonmember banks. It is often contended that the Federal Reserve could make struc- tural changes within their own reserve requirements that would remove more troublesome sources of variation and/or unpredictability in rt than nonmember banks; this claim is in some cases supported here. According to the results of this study, removal of lagged reserve require- ments and reserves against some categories of nonmoney deposits, espec- ially time deposits, would remove more variable and unpredictable param- meters from rt than v2 and vi. The distribution of deposits among 289 classes of member banks however, apparently does not shift much, so removal of differential reserve requirements would have little effect on the stability or predictability of rt; there is no evidence that removing differential Federal Reserve reserve requirements would be a more fruitful institutional change that universal membership. The claim is also supported here that as the Federal Reserve has increased the number of categories of deposits, more variation has been introduced into rt through lagged and differential reserve requirements. In general, the variation and unpredictability in rt has increased with the number of Federal Reserve reserve categories, especially because of the increased number of A-parameters. The greatest gain in terms of reducing the variation in rt would accrue from removing reserves against time deposits, government de- posits, and interbank deposits, and lagged reserve requirements. In addition, it appears that the introduction of reserve requirements against nondeposit liabilities and the reserve-carryover procedure have increased the variability of rt. Since 1t and the A-parameters are successfully forecasted with the ARIMA procedure, the greatest gain in terms of easy predictability of rt would come from removing reserves against time deposits, government deposits, and the reserve-carryover procedure. APPENDICES APPENDIX A SUMMARY OF MODELS OF THE MONEY SUPPLY PROCESS APPENDIX A SUMMARY OF MODELS OF THE MONEY SUPPLY PROCESS Brunner Brunner's first formulation of a theory of the money supply pro- cess is his linear money supply theory.1 It is based on the notion that a commercial bank will adjust its assets to absorb any surplus reserves that emerge in its portfolio. Surplus reserves, 6, are de- fined as the excess of actual available reserves over desired avail- able reserves where available reserves are total cash assets less required reserves. This gives, _ d s - v - v , where total cash assets - required reserves, < ll wO + w1 dl + w2 2, and W0 is a part of desired reserves that a bank will hold independent of its level of deposits and depends on an index of loan and bond yields, borrowing from the Fed, and the bank's loan-investment ratio; w and w are the bank's marginal prOpensities to hold reserves against 1 2 demand and time deposits, d and d2, respectively. 1 As surplus reserves appear in a bank's portfolio, the bank is in— duced to expand its earning assets and as it does so, its surplus re- serves are drained away for four reasons. First, part of the asset expansion will be held by borrowers as cash and therefore as earning 1Karl Brunner, "A Schema for the Supply Theory of Money," Inter- national Economic Review 2 (January l961):79-109. 290 291 assets are expanded, surplus reserves are reduced by a currency drain. Second, part of the asset expansion will become deposits at other com- mercial banks. Third, part of the asset expansion will be held by the public in time deposits, thereby increasing required reserves and re— ducing surplus reserves. Fourth, part of the expansion will become demand deposits at the expanding bank; again, this increases required reserves thereby diminishing surplus reserves. The function describing the generation of funds by a bank is of the form, (A-l) aS = %-(s), where aS denotes the supply of bank funds, and _ t d A- [c+(r +w2)t+(1 f3)p3+ (r +wl) (l - c - t - flp3)]. Each term in the definition of A corresponds to one of the chan- nels listed above by which surplus reserves are dissipated. The cur- rency drain is accounted for by c, which represents the portion of the bank's asset expansion that the borrower holds as cash. The time de- posit drain is represented by (rt + w2)t, where rt is the legal re- serve ratio and t is the fraction of the asset expansion the borrower holds in time deposits; (rt + w2)t then is the amount by which the bank's required and desired reserves rise, as its asset expansion in— duces an increase in time deposits. The last two terms in A account for the amount of s absorbed by increased demand deposits at other banks and at the expanding bank. In accounting for these factors, Brunner's scheme includes explicit consideration of the institutional procedure by which interbank claims are settled. Let 292 p1 = the amount of demand deposits the borrower must hold as a compensating balance at the expanding bank; p2 = additional demand deposits redeposited in the expanding bank; p3 = demand deposits held at other banks; f = the proportion of p collected from the expanding bank via Federal Reserve Funds; f = the proportion of p collected by debiting the expand- ing bank's balances at other banks; f = the proportion of p collected by crediting other banks' balances at the expanding bank. The surplus reserves that are lost to increased demand deposits at other banks then amounts to p3, minus the part (f3) of p3 that are col- lected by increasing other banks' deposits at the expanding bank. If f3 = l, the expanding bank will have traded publicly-owned demand de— posits for other bank-owned demand deposits so that no surplus reserves are lost at all. The net amount of surplus reserves lost to deposits at other banks is therefore (1 - f3)p3. Finally, the expanding banks' own demand deposits will increase because of the asset expansion, thereby increasing its required re- serves and further depleting its surplus reserves. The amount by which their own demand deposits will increase can be derived algebraically. For every dollar of asset expansion, the expanding bank's own demand deposits must increase by l - c - t - (l — f3)p3, plus any change in its balance at other banks, which is equal to f2p3 per dollar of asset expansion. Thus the net increase in the expanding banks' demand deposits is, 293 l - c - t - (1 - f3)p3 + f 3 or, 2P ) since f + f + f = l. (1 ' C ’ t ' 1 2 3 f1P3 This term must be multiplied by (rd + wl), the legal and desired level of required reserves, to determine the increase in reserves (depletion of s) the bank will hold against the new demand deposits. Having completely specified the form of A, the aS = 1/A s func- tion describes the process by which a bank generates money as it ad- justs its portfolio to eliminate any surplus reserves (or acquire re- serves if s < O). The other major relationship of Brunner's linear money supply hypothesis explains the process by which surplus reserves are gener- ated. Brunner discusses eight ways in which the surplus reserves of an individual bank may be generated. 1) A bank may experience a net current inflow, designated by n1, which will increase surplus reserves by the amount of the inflow less the increase in required reserves caused by the inflow. This currency inflow is independent of any portfolio changes by the bank. Surplus reserves generated from this source is therefore denoted by, [1- (rd+w)(1—g>1n l 2 l’ where g2 represents the marginal propensity of the bank to adjust its balances at other banks because of the change in its deposit liabil- ities represented by the cash inflow, n1. 2) A bank may experience shifts between demand and time deposits that are independent of its own asset expansion discussed above. Such a shift will generate surplus reserves for the bank to the extent that 294 different levels of reserves are held against time and demand deposits. We have, [- (rt+w>1n 1 2 2 2’ denoting the surplus reserves generated by a demand deposit-time de- posit shift. 3) A bank may acquire or lose surplus reserves as existing de— posits are redistributed among banks or as a result of the distribur tion among banks of new deposits generated by an asset expansion by some bank in the system. Brunner designates n3 as the net inflow to a bank resulting from the redistribution of existing deposits and the distribution of newly generated deposits. The surplus reserves ac- quired by that bank is then given by, [(1 - g ) - (rd + w )g ]n where 3 l l 3’ g1 = the proportion of the bank's clearing balance settled by debiting its deposit liabilities to other banks; = the proportion of the bank's clearing balance settled by the Federal Reserve mechanism. g3 4) A bank may experience an increase in surplus reserves as a result of its dealings with the Federal Reserve. Brunner divides this source of surplus reserves into two parts. The first, denoted by n4, is the net increase of cash assets coming from transactions with the Fed that involve a banks nondeposit liabilities (such as borrowing from the Federal Reserve or the bank's earning assets). The second part, represented by n is the net accrual of cash assets resulting 5’ from transactions with the Federal Reserve having to do with the bank's 295 deposit liabilities (such as open market operations). Surplus re- serves resulting from transactions with the Fed are then represented by. n + (l — v)n5, 4 where V involves an assumption regarding the bank's behavior toward deposits generated in dealings with the Fed (i.e., perhaps A = v, but perhaps not). 5) A bank will gain or lose surplus reserves when legal reserve ratios are changed. This is measured by, d t -A r d1 - Ar d2. 6) A bank may reallocate its cash assets between those that satisfy legal reserve requirements and interbank deposits. Because of the definition of "net demand deposits" used in determining legally required reserves, this reallocation will generate or absorb surplus reserves. This is measured by d (r + wl) Aho, where Aho represents the reallocation of the bank's cash assets. 7) A bank may also be the recipient of surplus reserves as other banks reallocate their cash assets as described in (6). Letting d be the portion of d that is owned by other banks, the change in sur- 1 plus reserves involved here is represented by, d b _[l - (r +w1)(l - g2)] Ado . 8) A bank may gain or lose surplus reserves because of a change in the level of reserves it desires to have on hand, independent of the level of its deposits. This factor is represented by changes in wo. 296 These eight sources of surplus reserves together determine 5, <1 - g2>1n1 + [ E = x< ) M* 1., rC S where r represents the return to banks from making loans and rc is the cost for commercial banks of lending. When, for example r rises, banks will be enticed to extend relatively more loans, causing M to rise rela- * tive to M . The obvious criticism of Teigen's model is the artificial distinc- tion between exogenous and endogenous parts of the money stock. Member 305 bank borrowing is of course not entirely outside the control of the Federal Reserve, nor is the portion of the money stock he labels exogenous completely under their control. The important implication of Teigen's work for this study is his assumption that nonmember bank de- posits are a constant, predictable fraction of the total money stock and his lack of consideration for the behavior of and components of the average required reserve ratio, k. Teigen's treatment of these param- eters of the money supply process is deficient; it is important in that succeeding authors have often followed him and adopted the same assump- tions. Brunner-Meltzer Brunner and Meltzer's (B-M) nonlinear money supply theory6 incor- porates less institutional detail than Brunner's original theory, but it places greater emphasis on the role of interest rates in the money supply process. Brunner and Meltzer's original version of their non— linear money supply process has been refined and expanded by Albert E. Burger.7 The model consists of a function describing banks' supply of assets to the public and a function accounting for the public's supply of assets to the banking system. In equilibrium, the two determine an 6Karl Brunner and Alan H. Meltzer, "Some Further Investigations of Demand and Supply Function for Money," Journal of Finance XIX (May 1964): 240-283; and "Liquidity Traps for Money, Bank Credit, and Interest Rates," Journal of Political Economy 76 (January/February l968):1—37. 7Albert E. Burger, "An Analysis and Development of the Brunner- Meltzer Non-Linear Money Supply Hypothesis," Project for Basic Monetary Studies, Working Paper No. 7, Federal Reserve Bank of St. Louis, St. Louis, Mo., 1969; and The Money Supply Process (Belmont, CA: Wadsworth Publishing Company, Inc., 1971). 306 interest rate and the money stock. The nonlinear money supply hypoth- esis is strictly a macro-theory and therefore sidesteps the complica- tions of moving from a micro- to a macro-theory encountered with Brunner's linear theory. In the B-M system, the banking system demands earning assets as it adjusts its portfolio to rid it of surplus reserves. The rate of port- folio adjustment is therefore a function of the divergence between desired and actual reserves. The level of desired reserves is taken to be a function of the level of deposits, a vector of interest rates and the discount rate. Required reserves are of course determined by legal reserve requirements and member bank deposits. Excess reserves are a function of interest rates, the discount rate, and the level of deposits. Schematically this is represented by: (A—l7) is h(R - Rd), with (A-18) R = f(DaTaj-9p)9 (Arl9) R = R? + R? + v“, (A-20) R = rddD + rtTT, and (A-21) R = e(i,p,fl)(D + T), where E = banks' demand for earning assets; R = actual reserves; R = desired reserves; R = required reserves; R = excess reserves; D = demand deposits; T -= time deposits; 307 i = vector of interest rates; 0 = discount rate; vn = nonmember bank vault cash; rd = required reserve ratio against demand deposits; rt = required reserve ratio against time deposits; 5 = the portion of total demand deposits in member banks; T = the portion of total time deposits in member banks; n1 = composite variable representing interest rate vari- ability, deposit flows, and anticipated reserve re- quirement changes. Member banks determine two behavioral coefficients. The first defines the ratio of excess reserves to total deposits, e, and is described by equation (A221) above. The level of excess reserves is taken to be a function of interest rates, the discount rate and a composite variable, n1, which represents interest rate variability, deposit flows, and anticipated reserve requirement changes. The second behavioral coef-' ficient, b, defines borrowing from the Fed, A, relative to total deposits, TD, represented by A b - TD — f(i,p’Tr2)’ where U2 indicates the Fed's administrative policies with regard to the discount window. The public's supply of assets to banks, Ed, is given by (15.-22) Ed = f(i,W,E), where E - earning assets of commercial banks; W = wealth. 308 The public also determines two behavioral coefficients, k and t. The amount of currency the public wishes to hold relative to demand deposits is represented by k which obeys the function, P k =-—§- = f(q, Y/Y , Tx, S, W), where DDp P Kp = currency in the hands of the public; DDp = privately-owned demand deposits; q = service charges on demand deposits; Y/Yp = the ratio of current to permanent income; Tx = the public's tax liability; U) II a variable representing population mobility and seasonal factors. B—M do not make currency holdings a function of interest rates, though the influence of interest rates on k could easily be incorporated into the analysis. The public also determines the distribution of bank de— posits between time deposits and demand deposits, represented by the coefficient t, where (A-23) t = -lE-= f(if, it,-EL;3L), where D1)p Pa Yp Tp = privately-owned time deposits; if = index of interest rates paid on financial assets; it = index of interest rates paid on time deposits; %%:= real value of nonhuman wealth. The rate paid on time deposits, it, is determined by banks and is pos- tulated to be dependent on if and Regulation Q restrictions. 309 Finally, U. S. Treasury policy determines the ratio, d, of govern- ment deposits, DDg, relative to publicly-owned deposits, DDt d =-——— . DDp The d ratio has been known to fluctuate considerably, however it is determined by Treasury policy and therefore is exogenous to the model. The following identities and definitions complete the system: (A—24) M1 = DDp + KP, where M1 represents the money supply; (A—ZS) B = B8 + A, where B represents the monetary base and B8 is the adjusted base; (A-26) B = Rm + Kp + Vn, where Rm is member bank reserves; m r e (A—27) R = R + R ; R (A-28) r ’71-'13, vn (A-29) V =TD; (A-30) DD = DDP + DDt. Assuming Ba and W to be exogenous, the money multiplier can be derived. Substituting equations (A-26) and Ar27) into equation (Ar25) yields: Ba = R” - A.+ KP + v“, Ba = R? + R? - A + KP + v“, Ba = R - A + KP. Dividing both sides by privately-owned demand deposits gives, P .111. DDp DDp DD DDp 310 Substituting for the definitions of r, b, and k yields: Since, by definition, TD is comprised of privately-owned deposits plus government deposits plus time deposits, the above equation can be re- written. Ba = r(DDp + DDt + I) _ h(DDp + DDt + T) —_ +ko DDp DDp DDp Substituting for the definitions of d and t, and factoring yields: (A—3l) .§f_ = (r - b)(l + d + t) + k. DDp Dividing both sides of equation A—24) by DDp and substituting k for P -——— gives, DDp M1 = l + k; hence, = DDP. Substituting this result for DDp in equation (Ar31) yields; 9&1 =(r-b)(l+d+t)+k. 1 + k Manipulation gives, g 1+1: (r=b)(l+d+t)+k (A—32) Ml Ba. 311 Equation (Ar32) describes the relationship, m1, between Ba and M1. The multiplier, ml, is dependent on interest rates because of the de- pendence of the t and b ratios and the level of excess reserves on interest rates. When the bank credit market is in equilibrium (ES é Ed), an interest rate is determined. This equilibrium interest rate then determines values t, b, and the level of excess reserves which, along with the values of r and d, determine the equilibrium value of m A 1' value for the multiplier ml, or for any of the parameters on which it depends, can of course be calculated at any point in time. But an equilibrium value of m and its parameters implies complete portfolio 1 adjustment by both the banks and the public. That is, equilibrium requires that the public holds the desired levels of currency, demand and time deposits and earning assets, given its wealth, income, and interest rates; banks hold the desired levels of earning assets, bor- rowed and nonborrowed reserves, given the interest rate, discount rate, and deposit levels. The value of the money multiplier, = l+k 1 (r-b)(l+t+d)+k’ (A-33) m is of course dependent on the size of the r-ratio. The dependence of r on the distribution of deposits between member and nonmember banks, nonmember bank vault cash and member bank excess reserves can be seen by writing r explicitly as: = rd6(1+_d)+ rtT t + e + v here l+d+t ’w v = ratio of nonmember banks vault cash to DDp; e = ratio of member bank excess reserves to DDp. APPENDIX B DERIVATION OF THE SOURCE BASE APPENDIX B DERIVATION OF THE SOURCE BASE The source base is defined as the net monetary liabilities of the Federal Reserve System and the U. S. Treasury and can be derived from their consolidated balance sheet. The net source base is the source base less member bank borrowing. Table B-1 shows the calculation of the source base for December, 1977. The right side of the table computes the source base as the sum of the net liabilities of the Federal Reserve and the Treasury; the source base is therefore the sum of member bank deposits at the Federal Reserve plus all currency and coin held by commercial banks and the public. This defines the source base in terms of its uses; all base money is absorbed by member bank reserves, nonmember bank vault cash, and currency in the hands of the public. The left column of Table B-1 calculates the source base by sum- ming all the sources of base money. This derivation is simply a re- arrangement of the balance sheet of the Federal Reserve System, plus three modifications to allow for the monetary activities of the U. 8. Treasury. The items involved in these modifications are identified with an asterisk. First, the currency issued by the Treasury must be added into the source base ("Treasury Currency Outstanding") since it circulates and can be used as bank reserves just as currency issued by the Federal Reserve. On the other hand, the Treasury holds currency (its own or Federal Reserve notes) in its vaults, thereby holding base money out of the system; Treasury cash holdings are therefore subtracted in the BL: 313 .m<|q¢“Awan humouoomv :«uoHHom o>uomom Hmuoomm .Emumzm o>uomom HmumoMm onu mo muoauo>ou mo oumom "mousom .smmo uH=m> xcmn nooaoecoc movaaooH m .mucoSmmuwm mmmnouooou wood: was: mmfiufiuoomm mo .omqam moooaocHN moonwam wafizmun Hmfiooema mam.o~am ommm mousom .mHmNaNHw mmma mouoom .mas.m Hmueemo new hmeueaeemeo .m .e hmeuo .omm o>uommm Hmumoom um muamoaon nosuo .oco.m o>uomom Hmumomm um muwmoaoo xusmmoua .moq mwcfioaom ammo huommmuw um "mmma .cnm.HH wofioamumuoo %odmuuoo >uammouH k .qu.~ muomm< o>ummmm Houston Honuo .wom.m umoam .wmm women .Ham.mm moOfiumHoouHo aw honouuoo .omm _ mooamummoo< .wqm.noa mofiuauooom unmaaho>ou .m .D .Hmm.m :«oo mam hoamuuso N uavouo o>uomom Haywoom .mmo.n~ w o>uowom Hmhmmvmnw 0;“ UN WUHmOQwQ owONoH mQUNUHWHUHmU Hem-Q om o>ummmm zoom noose: .cao.HH m «sooum taco mmmm mo mom: ommm mo moouoom AmumHHoa mo macaaawz .mmuowwm %Hamn mo mowmuo>< zanuaozv nnma .uonfiooom .ommm oouoom mnu mo coaumaooamo .Hum manna 314 calculation of the source base. Included in the item Treasury cash holdings is also the part of the nation's gold against which gold certi- ficates have not been issued. The net result of adding the gold stock and subtracting the gold portion of Treasury cost holdings is there— fore the amount of gold certificates owned by the Federal Reserve. With these modifications, the left column merely sums the assets of the Federal Reserve System and deducts its liabilities and capital accounts to isolate the items that comprise the source base. The Fed- eral Reserve's control of the base comes from complete control of its portfolio of government securities, which is the dominant source of base money. APPENDIX C STATE AND FEDERAL RESERVE RESERVE REQUIREMENTS ««.m a H umcamwo mo>uommu HOW mom: on coo m..o.o oowooaaao pom mowuwuooom owansm ponuo .mmo» H casuas wofipsuma mowuw luooom ucoeauo>oo .m.D «swan uwcfimwm mo>uomou mo New on a: MOM com: on coo m..a.u wowomaaoo moan .umox H awnuwz wofiuaume .mmwuwuooom ucoaouo>ou .m.: m ma mfiwuoou .mofiufiuoomm Axocowm uov ucoacuo>ou .m.D mufimoaov Hououlom mkuoam .cOHHHHE ooamMWa «.umHo m coaaawa ooawVIh mumsmaon .mmpuomou .aoHHHHa mWAJM.~H wo Nno.ca cu m: .uooaaum>oo .m.: o :OHHHHE mvaNH usofiuomacoo «.mofiuwusomm ucoecuo>ow .m.: mufimommv Hmuoulma oomuoaoo «.m w H umowmwo mo>nomow mo Now cu m: .mmfiufiuoomm uooecu0>oo .m.D m mm mfiauowwamo .cOHHHwE mmA .Hnm .GOAHHHE ooamAImm.~H MGOHHHHE ooamloawlmh.HH «63333352 wee Sonia 9V 4% 83:5 ShumwMa IfiHOmom no oEmm CH mxcmn co camuv .omHo mum “Gowaafia NwVIn mmmcmxw< *.m£ucos o afisufi3 wawuoume m..n.o mHomHuowoz .omHo monocoe o cmsu whoa no: ca mafiuSumE mowuwuouom uamacuo>oo .m.D a CH mcoufiu< m cm mxmma< m 0H meanwa< 30Hom omumowocH omwsuonuo oEwH ocmaoa ouMum woman: mxcmm Eouw moo mooomamm no mufimoaom mo unmoumm some uH=m> mm xaco pawn mo>ummom msma .mmz .mxamm umoEoEcoz you muamaouwoomm m>uomom monum .HIU mHan o “354me 315 .mo>uomow mo Now cu a: How mom: on :mo Amo>uomou mo NON coco mmoav mowuwuooom owaofim Moguo moan .mowuauooom ucmsauo>ou .m.D mufimoooo Hmuoe oxamn MosuOImH oxamn coumomlom muuomonommmmz .mowuausomm oaansm ponuo .mmfiuwuooom ucoaauo>oo .m.: m ma camamumz k.vHom mm 91¢ .mofiufiuoomm uooacum>oo .m.D mum 0H mafia: .aoaaawa ooquIqH macadafis ooqmlooawlma chHHHHB ooawloamlwa .mo>ummou mo “coaaafia oawlmmloa Now cu m: .wowuwuooom uameauo>ou .m.: m maowaafia wwwrw mamfimfiooa .mo>uom Ion mo Nmm cu a: wow mom: on coo mxcmo %xUSucmM mo cosmmfi m..a.o mam omHo moan .mmwufiusoom oHHooa Honuo moan .umo> H cfinuwa wawuauma .mowu Iwuouom Azocowm uov ucmscuo>ou .m.: m n %xooucox ”m .coHHHHa ooamhnma “3 MGoHHHHE ooamloawlua ..T mm 28335 oaumm :3 mum .mcoaaaea ~mv:m.~ mmmamx « m n msoH .QmHo m m mamHoaH omuaovmu mo>uommu Hmwoa on mfiocfiHHH * n ma osmoH «.QQ umdwmwm mm>hmmou mo Nom oo o: .mxcmo uofiuo Eoum moo woodmamm m NH Hfim3mm Boawm mouwowocH omwsuonuo mafia madame oumum woman: mxcmm Scum woo mooomamm no ammo uaom> mm %Hco oaom mo>uomom mufimomoo mo unwoumm vengeance .Huo «Home 317 .umHo mm mm Hue» 3oz .mm>ummou mo Non cu m: .mmmo ooH cHsuHs waHuoumE .moHuHuooom unsecuo>oo .m.D m NH oonoz 3oz «.oeHo mm mm shapes smz .mm>uomou mo Noe cu m: .mumom N aHsuHB maHnoumE .moHuHuoomm ucoacuo>oo .m.D m NH oanmaamm 3oz «.UmHo m CH mom>oz .mm>ummou mo Now on a: .mmHuHuooom unmacum>oo .m.: q mH mxmmunoz .aOHHHHE NwAHwo.OH « m McOHHHHE NwVINm.N mangoes .GOHHHHB OOHmAImH “:0HHHHE OOHmIOHwINH nooHHHHE OHwamIOH «« ¥.UmHo m McOHHHHB NwVIm.N Huoommwz .mm>uomou mo Non cu m: u0w mom: on coo Amo>uomou mo NmH cu gov mxamo HoonmHmmHz so emsmme m..n.o haae oeoo mon .umoh H :HnuHa wcHuoumE .moHuH lusoom A%ocow< uov ucoaouo>oo .m.D mm mm HaaHmmHmmHz .mo>uomou mo Non cu a: How mom: on one omHu moHa .umo% H aHsuHa wcHuoumE .moHuHuooom ucoaouo>ow .m.D N N muomocaHz «.mo>uomou mo Mom cu a: HON mom: on coo .omHo moHa mmHuH Iuooom Amoaow< uov ucoEGHo>ou .m.: 0 HH omenon onwm woumoHocH omHshofiuo oSHH panama muMum mmchD oxamm Eouw one moocmHmm no ammo uHom> mo %Hoo oHom mo>uomom muHmooon mo unmouom emeceuaoo .Hno mHema 318 .mm>uommn No New cu a: wow mom: on coo omHo moHa moHu IHuoomm Ahooow< uov ucoeoum>oo .m.D .mhmo OH oHLuHS oHnmuomHHoo .umHo .mmmv Ho coco whoa uoc aH waH undone .moHuHuooom unsecuo>oo .m.= .mo>uommu «0 New cu a: wow com: on coo omHo mon moHuH muHmoaoo Hmuoeum.NH m N o ma .eoeHHHe mmeeum meoeaaee mwv.e-m muoxmn nusom moHHoumo eusom ocmHmH moonm Iwooom Azooow< uov opossum>oo .m.= mum NH MHom>Hchcom .m a H umchwm mo>uomou you omHu moHa .umoz H cH unqu wcHnouma .moHuHuooom ucoaauo>ow .m.: man umchwm mo>uomou How umHo q NH cowouo .uonuo HHmnm mzmo owH amaa mmoH :H waHuoumE e.suee mama men as macho no names .oeHu .coHHHea mmA.eue win an mEosmeo .uonuo HHmlm .m w H umaHmwm MmNmo owH cmsu mo>uomou mo Noe cu a: now pom: mmmH :H wcHuoumE on coo mmHuHusoom ucoaaum>ou .m.: .cOHHHHE mmA.Hlo . N oHno a N w muoxma :uuoz .uonuo HHmIm .aOHHHHa ooquImH “:0HHHHE ooquOOHmIMH .msme owe ewes neOHHHHa ooemuOHmu~H mmoH :H onusuma maOHHHHE OHmINMHbH mcHHoumu «.oeHo .coHHHHe mah.eue maoeHHHe vanw euuoz aoHom omumonoH omHsumnuo mEHH panama oumum mmoHGD mxamm Boom ova mmocmHmm no : muHmomoo mo uaoouom ammo uH=m> mm NHco onm mm>ummmm poocHuaou .Hlo oHomH 319 .mxamn nonuo Eonm moo mmoomHmo pom ammo uH=m> pH on amaa mo>nomon HmuOu «0 Now ummmH no “on umaHmwm o>nomon mo Now on as now mom: on coo .mmHanouom nooeono>ou .m.: CH ON wcHEONB .w a H umcwmwm mo>nowmn mo Nwm mum on umaHmwm mo>nomon mo Nmm on a: now mom: on coo moHansoom oHHoam nonuo moHa mnuaoe wH :HnuH3 wcHnsumE .moHanooom nomaano>ow .m.: NH 0N aHmaoomHz .Acmmo uHsm> mm oHon on umns mo>nomon mo NONV omHu m N mHannH> umoB {.NuHo mama :H mxcmn co o3mnp UAHU mm mm nouwcHnmm3 .m a H umchwm mm>nomon now omHo mon .nmmz H cHnqu waHnoqu .moHanooom unmecno>ou .m.D “on umchwm mo>nomon now omHo m 0H chHwnH> .moHanoomm oHHoom nonuo .nmw» H aHnuH3 wcHnoume .mmHuH Inooom Azocmw< nov uooacno>oo .m.: m.o NN uaoano> Mm mm nous «.omHo m mH mmme m OH oommoacoa 30Hom woumUHocH omHanosuo oaHH panama mumum mmoH:D mxcmm Eonm one moocmHmm no ammo uHom> mm NHco oHoz mm>nomom muHmomon mo ucmonmm emeenuaoo .H.oxmaemn 320 .mu< enema .< sneamee< .NNmH .ocoh ..o.a .oouwaHnmma :.mo>nomom co umonouoH mo uaoaxmm woo woo .muaaooo< .3.o.z .eHnmnooEmz o>nommm Hmnmomm mo coonom one: .Eoumxm o>nmmmm Honooom msu mo mnoono>ou mo vnmom "monoom .mvoom Hmnovom n .m.m .o>nomom Honovom mm meow n .m.m .uHmoaoa mo mwumonHunmU u m..n.o .coHuooHHoo mo mmooonm oH mamuH ammo n umHo .muHmoaoo mwaH>mm n m .muHmoaon oEHH u H .muHmoomn mwaH>om one oBHH n m w a .muHmomon panama n on .NHco mUHmoaoo HmoonoHoon we um: one mxcmo nmcuo aonm moo muHmoamw oHnHwHHm « a» .mxcmo NnouHmoaoo oo>onmom cH oHo: on umns mHCMA nosuo aonw mow muHmoamn . a New channeeoo .Hno ensue Table C—2 Summary of Changes in Federal Reserve Reserve Requirements 1961 - 1974 I. Structural Changes 1. Beginning July 14, 1966 (reserve city banks) and July 21, 1966 (country banks), the following reserve categories for time deposits became effective: a) savings deposits; b) time deposits, less than $5 million; c) time deposits, greater than $5 million. Beginning January 1, 1967, time deposits such as Christmas and vacation club accounts were defined as "savings deposits" for reserve purposes. Beginning January 11, 1968 (reserve city banks) and January 18, 1968 (country banks), the following reserve categories for net . demand deposits became effective: a) reserve city banks, less than $5 million; b) reserve city banks, greater than $5 million; c) country banks, less than $5 million; d) country banks, greater than $5 million. Beginning September 18, 1968, lagged reserve requirements became effective whereby a bank's required reserves are based on its average deposit holdings two weeks earlier. Average deposits figures are based on a seven day (Thursday through Wednesday) average of daily close-of-business figures, where Friday's fig- ures are used for Saturday and Sunday if the bank is not open over the weekend. With this change, all National Banks were put on a weekly reporting and reserve settlement schedule. A bank's reserve balance is the sum of its average daily close- of—business deposit balance with its FRB during the current settlement week plus its average daily close-of—business hold- ings of currency and coin during the week two weeks earlier. Under this new scheme, a member bank is allowed to carry over any excess or deficiency of required reserves into the next settlement week, provided the carry—over does not exceed 2 percent of required reserves. No part of an excess or defic- iency not offset in the next week may be carried over into addi— tional settlement weeks. Prior to this change, required re- serves were based on contemporaneous beginnings-of-day figures every Wednesday for banks designated as weekly reporting member banks and every other Wednesday for all other member banks. Reserve~ balances were also measured by contemporaneous levels of deposits at Federal Reserve Banks and vault cash. 321 322 Beginning July 31, 1969, the definition of gross demand deposits was changed to include outstanding checks or drafts arising from Euro-dollar transactions. Beginning October 16, 1969, member banks were required to hold reserves amounting to 10 percent against their net balances due from domestic offices to their foreign branches, foreign branch loans to U. S. residents, and borrowings from foreign banks by domestic member banks. On January 7, 1971, the reserve ratio was increased to 20 percent. On June 21, 1973, the reserve ratio was reduced to 8 percent and the following loans were exempted from required-reserve calculations: loans aggregating $100,000 or less to U. S. residents and total loans of a bank to U. S. residents if they do not exceed $1 million. Originally cer- tain base amounts were exempted from required-reserve computa- tion but these items were gradually eliminated beginning July 5, 1973 and were completely eliminated by March 14, 1974. Effective November 9, 1972, reserve requirements on net demand deposits were restructured to be based on a bank's deposit- size. The following five deposit size categories were defined for the calculation of required reserves: less than $2 million; more than $2 million and less than $10 million; more than $10 million and less than $100 million; more than $100 million and less than $400 million; and greater than $400 million. Each deposit interval applies to that designated portion of a bank's net demand deposits. Beginning June 21, 1973 (based on deposits as of June 7, 1973), a marginal reserve requirement of 8 percent was imposed on increases in a) certificates of deposit of $100,000 or more, b) outstanding funds obtained through issuance by an affiliate of obligations subject to the existing reserve requirements on time deposits ("bank related commercial paper"). The reserve ratio was applicable to increases in the total of both types of funds above the level held during the week of May 16, 1973 or $10 million, whichever is larger. Since both categories of funds were previously subject to a 5 percent reserve require- ment on time deposits, the marginal reserve requirement repre- sents a 3 percent increase in reserve requirements on addi- tions to such funds. Beginning July 12, 1973 (based on deposits of June 28, 1973), the reserve requirement described in (8) above was extended to include funds raised through sales of finance bills. Funds sub- ject to this reserve requirement are those used in the institur tion's banking business which were obtained through banker's acceptances that are ineligible for Federal Reserve discount. Since there was previously no reserve requirement on such funds, this change placed all outstanding financial bills under the basic 5 percent requirement on time deposits, plus the addi- tional 3 percent requirement on increases in such funds above the level held during the week of May 16 or $10 million, which- ever is greater. 323 10. Effective October 4, 1973 (based on deposits of September 20, 1973), the marginal reserve requirement on large certificates of deposit, bank-related commercial paper, and funds raised in the sale of finance bills described in (7) and (8) above was raised to 11 percent. The same reserve ratio was reduced to 8 percent, effective December 27, 1973 (based on deposits of December 13, 1973). 11. Effective September 19, 1974 (based on deposits of September 5, 1974), large certificates of deposit, bank-related commercial paper, and funds from sales of financial bills were each di- vided into two categories for reserve purposes: those of maturity length less than four months and those of maturity length of four months, or more. The shorter-term categories continued to be subject to the marginal 8 percent reserve re- quirement, but the long-term categories for all three types of funds were reverted to the regular 5 percent reserve re- quirement on time deposits exceeding $5 million. 12. Effective December 12, 1974 (based on deposits of November 28, 1974), the marginal reserve requirement of 8 percent on large certificates of deposit, bank-related commercial paper and sales of finance bills, all with maturities of less than four months was removed and these funds were reverted to the 5 percent reserve requirements on time deposits in excess of $5 million. At the same time, all time deposits (including the three types of liabilities named above) with maturities of six months or more were placed under a 3 percent reserve requirement; all such funds maturing in less than six months were placed under a 6 percent reserve requirement, except the first $5 million which are subject to a 3 percent requirement. Source: Board of Governors of the Federal Reserve System, Federal Reserve Bulletin, various dates. 324 .e<.e .eNen .nmeEmuoo .Cnemnnem o>nomom Henoeom .Eoumem o>nomom Henooom o:u wo onoono>oo mo oneom .oxcep enueooo cu oHoeoHHmoe one onoonuconen an mouen Nm No NM Nm meme enn hmeo heme ennuee Nunnouez Nunnouez Nm Nm Nm No um Nm No Nm.m Nm.m No No we Nm we Ne mm no>o mwlo ouHooaoa oEHH oonomoQ mwcn>em NwH Nm.MH Nm.NH NOH Nm Nm.NH NMH NNH NOH Nw Nm.NH Nm.oH NNH NOH um ooqm no>o ooquOOHw COHmIon OHwINm leo NmH Nm.NH Nm.NH N NH Nm.NH NNH NNH Nm.eH me no>o meuo mm no>o meno NNH NoH knucoou mono o>nomom «NmH .Hm nooaoooa I «NmH .NH nonaoooa enen .nn heeaeuee - onen .n umeoeuo onen .oe nonsmeeme u Neen .en none: neen .en some: . neen .N seem: neen .n none: . eeen n.nene e hmeamuemm eeen n.nene n neeaeueee : eeen n.nn~e en ence euHooaoa oaHH seen .ne hmeaeome u neen .en enae enen .mn ence u Neen .en heeae>oz NNmH .mH nooao>oz I NNmH .m nooao>oz Nnen .e neeae>oz u eeen .Nn nnne< eeen .en nneee . eeen n.nene nn nuances eeen .Anne on sheseee 1 neen .n senaeee H ounooooo eceaoa uoz AmconHHHE on one oneHHomv monuex o>nomom eonHooom aH oomaenu “oonsom H .HH APPENDIX D SUPPLEMENTAL TABLES TO CHAPTER 4 325 HNoHo. mmmoo. omwee. eweHo. eoeoo. amemm. «NeH NqNoo. Noeoo. HHooo.H HeNHo. «Hoes. omeom. mNmH ewNHo. quoo. emcee. NNono. meoo. MNeem. NNmH emwno. memoo. NNmeo. mHeHo. mmeoo. ewmem. HNmH emeoo. Nwmoo. momma. NNONo. «coco. mHmmm. ONmH qwmoo. eemoo. NNHoo.H owHoo. NeNoo. Ncmoo.H emceH eNNNoo. eoemoo. eoemem. wmono. eemoo. OHomm. ween NeeHo. NNeoo. Nmmee. wweno. Namoo. eqeam. NeaH mHmNoo. meonoo. mmnooo.n mmNqu. mHeeoo. mnwmwm. Hweoo. meqoo. ceNmm. moan mNquo. mONNHo. mHNeoo.H eNeHo. wNmoo. emcee. mean ommHo. mNNoo. cemom. «wean Nmnno. NmNoo. oecme. moan meeno. onoo. Nmmom. Neon eeoHo. Nwmoo. “Nommm. HeeH u.mn u.Mn name mo.H Eonw GOHueH>on :eoz mo.H Eonm cOHueH>oQ aeoz mo.H aonm GOHueH>oQ aeoz :OHueH>oo oneoceum :oHueH>on oneoaeum :OHueH>oo oneeeeum umowneH uoowneH noowneH ee.n u n .e.wn hoe mensene nneeee< .nuo enema 326 .oHoeHHe>e nos euea non mooHue>nomno mm no women .neoh non ocoHue>noooo Hm co uooemo .aonHHHE mm cecu noueonw ouHmoaoe oEHu n Ioo owcn>eo n m mounmoaoo oEHu wcHSOHH0m ocu ou onomon H uoHnooASm och N mounooooe mwcH>eo one oEHu Hence n H .eoueoHeoH omH3nonuo oooHao neom non chHue>nomno Nm no women .neoN non oeonue>nomno NH so oomemm .noueonw on no>o£oH£3 ._o:He> soaHGHa I o.H_ no _o=He> aoaerE I o.H_m .neoN m mooHHHHE mm dean mooH ounooaoe oEHu a q mounooa "eunooaoe osHu mo ooHnowoueu N H NmMNo. mowoo. mema. quoo. mmHoo. «Nmmm. quH woomo. quHo. Nmomo. Oquo. ooHoo. comma. MNmH oooNo. mecca. HmNmo. mqqoo. HoHoo. Howmm. NNNH «NONO. «coco. NmHom. quoo. meHoo. HqNam. HNaH mHNco. oqNHo. quwm. onoo. HHHoo. MNNmm. ONmH omHNo. moooo. HHNoo.H HqOHo. NMNoo. omemm. commH mwwNo. mmwoc. owNmm. oNHHo. mHNoo. Nemam. owooH .1 1. ++ .1. .1. +4. . Neen ++ i. 1. ++ .1 ++ eeen u .MH New? mo.H Bonn COHueH>oQ coo: mo.H Eonw conuen>on :eoz mo.H Eonm aOHueH>oQ see: conueH>oa wneeceum conuen>oo enemaeum =0HueH>on onevneum uoowneH umowneH uoowneH 333:8 .né mneen 327 Table D—2. Annual1 Figures for the Proportion of Commercial Banks that are Member Banks Number of Member Banks/Number of Commercial Banks Percentage . PercenEage Change from High Low Change from Mean Previous Year Value Value High to Low Value 1961 .4564 —-- .458 .455 -.655% 1962 .4523 -.898% .455 .450 -l.099 1963 .4496 -.597 .450 .449 -.222 1964 .4516 .445 .453 .450 .667 1965 .4517 .022 .452 .451 —.221 1966 .4483 —.753 .450 .447 -.667 1967 .4441 -.937 .446 .442 -.897 1968 .4396 -l.013 .442 .437 -l.l3l 1969 .4337 -l.342 .437 .430 -l.602 1970 .4245 —2.121 .428 .421 —l.636 1971 .4178 -l.578 .421 .416 -l.188 1972 .4118 -l.436 .415 .409 -l.446 1973 .4063 -l.336 .408 .405 -.735 1974 .4022 -l.009 .405 .400 -l.235 1 Annual figures based on monthly data, last Wednesday of each month. Source: Board of Governors of the Federal Reserve System, Federal Reserve Bulletin, various dates, p. Ar18. 2Percentages were figured using the high value as the base year, since the direction of change was from high to low in each year except 1964 for which the low value was used as the base year. 328 Table D-3. Annuall Figures for 3-Month Treasury Bill Rate 3-Month Treasury Bill_Rat§_ Percentage Percentage? Change from High Low Change from Mean Previous Year Value Value Low to High Value 1961 .376 --- 2.62 2.27 15.419% 1962 .780 17.003% 2.95 2.69 9.655 1963 .158 13.597 3.52 2.90 21.379 1964 .553 12.508 3.86 3.48 10.920 1965 .949 11.146 4.36 3.81 14.436 1966 .882 23.626 5.39 4.54 18.722 1967 .331 -1l.286 5.01 3.48 43.966(—30.539) 1968 .345 23.413 5.92 4.97 19.115 1969 .686 25.089 7.72 6.08 26.974 1970 .437 -3.724 7.91 4.86 -38.559 1971 .338 -32.608 5.40 3.32 62.651 1972 .068 -6.224 5.06 3.18 59.119 1973 .026 72.714 8.67 5.31 63.277 1974 .873 12.055 8-74 7.06 23.796 1Annual figures based on monthly rates on new issue. Source: Board of Governors of the Federal Reserve System, Federal Reserve Bulletin, various dates, p. A933. 2Percentages were figured using the low value as the base year, since the rate rose in every year except 1967 and 1970. For 1967, the figure in parenthesis uses the high value as the base. For 1970, the figure presented uses the high value as the base, since the rate fell during that year. Table D—4. Quarterlyl Figures for v3 Standard Standard Mean Deviation Mean Deviation 1961 - 1 .86530 .00183 1968 - i .83431 .00149 ii .86400 .00166 ii .93224 .00144 iii .86227 .00143 iii .82493 .00243 iv .85852 .00154 iv .82005 .00252 1962 - i .86067 .00171 1969 - i .82425 .00184 ii .85599 .00188 ii .82090 .00262 iii .85708 .00172 iii2 .81474 .00192 iv .85358 .00173 iv .81272 .00264 1963 - i .85389 .00116 1970 - i3 .81689 .00211 ii .85161 .00109 ii2 .81715 .00198 iii .85045 .00152 iii .81269 .00209 iv .84693 .00191 iv .80915 .00187 1964 - 1 .84695 .00111 1971 - 1 .81493 .00161 112 .84832 .00129 ii .81229 .00227 iii .84637 .00200 iii .80408 .00187 iv .84099 .00158 iv .79854 .00186 1965 - i .84512 .00161 1972 - i .80243 .00147 ii .84695 .00140 ii .79975 .00219 iii .83975 .00253 iii .79167 .00284 iv .83377 .00201 iv .78696 .00188 1966 - 1 .83808 .00151 1973 - 1 .79398 .00181 ii .83969 .00167 ii .78779 .00254 iii .83278 .00198 iii .77921 .00159 iv .82980 .00227 iv .77676 .00254 1967 - i .83567 .00209 1974 - 1 .78093 .00197 ii .83712 .00127 ii .77967 .00211 iii .83189 .00205 iii .77058 .00266 iv .82973 .00201 iv .76759 .00222 1Based on 13 observations per quarter unless otherwise indicated. 2Based on 14 observations. 3Based on 12 observations. 330 Table D—5. Quarterly1 Figures for It Standard Coefficient Mean Deviation of Variation 1961 - 1 .66507** .01975* .02970* ii .70013 .01395 .01992 iii .72208 .00639** .00884** iv .71036 .01257 .01770 1962 - i .73987** .03149* .04256* ii .79229 .01654 .02088 iii .82166* .00920 .01120 iv .81904 .00893** .01090** 1963 - 1 .84734** .03028* .03574* ii .89608 .01810 .02020 iii .91920* .01057** .01150** iv .91142 .01084 .01189 1964 — i .93878** .03179* .03386* ii2 .98701 .02062 .02089 iii l.00400* .00986** .09821** iv .98896 .01116 .01128 1965 - i l.04240** .04160* .03991* ii 1.09757 .02667 .02430 iii 1.12476* .01599** .01422** iv 1.10727 .01802 .01627 1966 - i 1.12945** .03729* .03302* ii 1.17962 .03209 .02720 iii l.21588* .01618** .01330** iv 1.18372 .02159 .01824 1967 - i l.23321** .04573* .03708* ii 1.29624 .02405 .01855 iii 1.31778* .01328** .01008** iv 1.29420 .01756 .01357 1968 - 1 1.31460** .04672* .03554* ii 1.34048 .02177 .01624 iii* 1.35683 .02007 .01479 iv 1.35580 .01983** .01463** 1969 - 1 1.34606 .03989* ..02963* ii. l.36500* .02281 .01671** iii2 1.32289 .02279** .01723 iv l.26ll6** .02980 .02363 331 Table D—S. Continued Standard Coefficient Mean Deviation of Variation 1970 - 1 1.26316** .05117* .04051* ii 1.31196 .03207 .02444 iii 1.39825 .03231 .02312 iv 1.42835* .01695** .01187** 1971 - 1 1.51049** .06635* .04409* ii 1.56377 .02938 .01879 iii 1.58884 .02046** .01288** iv l.59302* .02786 .01749 1972 - i l.63l95** .05321* .03261* ii 1.64025 .03393 .02069 iii 1.66072* .02076** .01250** iv 1.63813 .03678 .02245 1973 - 1 1.68849** .08191* .04851* ii 1.78567 .03355** .01879** iii 1.83553* .04476 .02439 iv 1.82760 .03643 .01993 1974 - i 1.88549** .07729* .04099* ii 1.99584 .05876 .02944 iii 2.06534* .03477 .01684 iv 2.06532 .02884** .01396** 1 Based on 13 observations per quarter unless otherwise indicated. N Based on 14 observations per quarter. b) Based on 12 observations per quarter. * Indicates largest quarterly values in each year. ** Indicated lowest quarterly values in each year. 332 Table D—6. Quarterly Figures for 8t Standard Standard Mean Deviation Mean Deviation 1961 — 1 .00364 .00093 1970 - i3 .00051 .00020 ii .00317 .00040 ii2 .00051 .00031 iii .00315 .00031 iii .00058 .00034 iv .00285 .00031 iv .00062 .00035 1962 - i .00274 .00043 1971 — 1 .00061 .00038 ii .00247 .00028 ii .00051 .00024 iii .00257 .00025 iii .00048 .00038 iv .00240 .00029 iv .00047 .00042 1963 - i .00233 .00074 1972 - i .00044 .00033 ii .00203 .00029 ii .00040 .00026 iii .00204 .00033 iii .00046 .00049 iv .00185 .00042 iv .00060 .00039 1964 - 1 .00194 .00057 1973 - 1 .00049 .00042 ii2 .00153- .00029 ii .00043 .00039 iii .00175 .00035 iii .00047 .00045 iv .00167 .00038 iv .00052 .00038 1965 - i .00161 .00041 1974 — 1 .00033 .00024 ii .00138 .00024 ii .00034 .00013 iii .00151 .00032 iii .00032 .00020 iv .00145 .00043 iv .00034 .00039 1966 - 1 .00133 .00041 ii .00129 .00028 iii .00136 .00062 iv .00127 .00051 1967 - 1 .00140 .00054 ii .00129 .00025 iii .00127 .00039 iv .00113 .00037 1968 - 1 .00123 .00044 ii .00112 .00039 iii .00105 .00037 iv .00087 .00048 1969 - 1 .00085 .00057 ii. .00069 .00040 iii .00077 .00040 1v2 .00070 .00037 1Based on 13 observations per quarter unless otherwise indicated. Based on 14 observations per quarter. 3Based on 12 observations per quarter. APPENDIX E DERIVATION OF THE EQUATIONS FOR THE PARTIAL VARIANCE OF rt APPENDIX E DERIVATION OF THE EQUATIONS FOR THE PARTIAL VARIANCE OF rt Consider the general expression for rt, _ D D T T T (E—l) rt - g djtxj,t6j,tvtgél + yt + It) + Z ti’tAi’tdi’tvtTt i In 51 n + Etpt + hil wh,twh,tpt’ where j and i are defined appropriately for each reserve scheme. The partial variance of rt is defined here as the variance caused in rt by one parameter while all other parameters in rt are held constant at their means. The expression for rt is therefore a function of at most (j + i) random variables. The partial variance of rt can then be derived using the following result:1 If g is a function of random variables such that, n g(xl, x2,...xn) = Z aixi + c, then i=1 n 2 n (E-2) var (g) = Z a var (x ) + Z a a cov (x , x.). i=1 1 i i,j=l i j i j 1%1 1) var A (rt): Using the definition of partial variance given above, 1Maurice G. Stuart and Alan Stuart, The Advanced Theory of Statistics, Volume I, (London: Charles Griffin and Company, Limited, l963):231-3. 333 334 _ — D -D -D— — var A (rt) — var [ i dj,tAj,t5j,tvtgt (l + Yt + 1 ) 51 - T -T -T- - - - - -n + i ti,tAi,t5i,t tTt + Etpt + hil wh,twh,tpt where (-) over a variable denotes its mean. Since the last two terms in the expression are entirely constants, their variance is zero. Us- ing equation (E-2) above, var A (rt) can be rewritten as, var 1 (rt) = [32 it (1 + Vt + It)]2[T(Ej,t 'D 2 D J 6j,t) var(Aj’t) -D D D .t'j'n °°V ”j,t’ A1".t:)' -T - 2 - -T 2 T + [vt Tt] '§(ti,t6i,t) var (Ai’t) >\T -T -T + 6 ,t’ i',t 5 cov (A: 2 E E 1' i,t i',t i,t i',t )1 i! H-H-bd e -D- - --T- - — -D - + [vt Et(1 + YI; + 1t'vt Tt][§ E dj,tti,t 6j,t 6i,t ii) var 5 (rt): The partial variance of rt due to differential reserve requirements is defined as, _ -D - _ var 5 (rt) = var I? dj,t Aj’t (1 + Yt + It) 51 2 h=1 - T T -T- - -m - - -n + . + i ti,t X1,: 51,: vtTt + etpt wh,t “h,t pt] 335 The last two terms are again zero. Employing the result in equation (E-2)) _ -D — — - 2 - -D 2 D var 5 (rt) - [vt €t(1 + Yt + 1t)] [E (dj,t Aj t) var (Gj t) - - -D -D D D + g g. dj.tdj'.t'j.txj'.t C°V ('j.t"j'.t)' jfj' -T - 2 - T + [V It] [i (ti,t A , ) var (61,t) —T -T T T + i i. ti,t t1',t Ai,t"i',t cov (61,t’61',t)] i#i' -D - —D -T + [vt g (1 + yt + 1 )v Tt][§ i dJ,t i,t Aj,tli’t D T cov (Gj’t, 6i,t)] iii var r : > v < t) Using the definition of partial variance, var v (rt) is defined, var v (rt) = var [E dj,t 3,t 6j,t Vt €t(l + Yt + 1t) - -T —T T- I- -m + i i,t Ai,t 51,t Vt Tt + 8t pt 51 The variance of the last two terms is again zero and var v (rt) is rewritten, E (1 + It + It”2 var (v2) - -T -T - 2 T + [Z t. Ai’t 61,: Tt] var (Vt) - -D -D - — — -T —T - + 22 d. A + + J.t j,t 6j,t E'11 (1 Yt 1t)2ti,t)‘i,t51,t Tt D T cov (Vt, Vt)]- iv) var Y (rt) The expression for var Y (rt) is defined by, (l + Yt + It) Since they are constants, the variance of the last three terms in var Y (rt) is zero. Using equation (E—2), var Y (rt) is, XD -D ..D- _ 2 j,t j,t vt at (1 ‘" It” var (Yt). var (r ) = [Z d t . . Y 1 1.1: v) var 1 (rt): The expression for the var 1 (rt) is defined by, - -D -D -D- - = + var 1 (rt) var [g dj,t Aj,t 6j,t Vt it (1 + Yt It) 51 - -T T -T-T - - - - -n + E ti,t Ai,t ai,t Vt TI: + 8t 0t + hEl wh,t “h,t 0t" The variance of the last three terms is again zero, so var 1 (rt) can be written, 337 _ - -D -D -D- — 2 var 1 (rt) - [g dj,t j,téj,tvt Et(l + Yt)] var (It). vi) var T (rt): Using the definition of the partial variance of rt, var T (rt) is given by, _ -D -D D - - - var T (rt) - var I? 3,t Aj,t 6j,t t St (1 + Yt + It) - -T T -T -m + + i t1,t i,t Si,t Vt Tt at 0t 51 _ _ _m + Z w w p ]. h=1 h,t h,t t The first, third, and fourth terms in var T (rt) are constants so the expression can be rewritten, _ - - -T -T2 var T (rt) — [i ti,t Ai,t éi,t Vt] var (Tt). vii) var e (rt): The equation for var 6 (rt) is defined, - D -D —D — - - = + + var e (rt) var [i dj,t j,t 6j,t Vt 5t (1 Yt It) - - -T -T - -m + i ti,t i,t 6i,t vI: Tt + gt pt 51 ‘_ _ —n + hi1 wh,t mh,t pt" Only the third term in var E (rt) is nonconstant so the above expres- sion reduces to, var '8 (rt) = (01:)2 var (st). 338 For each of the expressions given above for the partial variances of rt, the indices j, j', i, and i' are defined to conform to each of the reserve schemes. BIBLIOGRAPHY BIBLIOGRAPHY Books Advisory Committee on Monetary Statistics. Improving the Monetary Aggregates. Washington, D.C.: Board of Governors of the Federal Reserve System, 1976. Board of Governors of the Federal Reserve System. Annual Report of the Board of Governors of the Federal Reserve System, 1971. Washington, D.C., 1971. Board of Governors of the Federal Reserve System. Annual Report of the Board of Governors of the Federal Reserve System, 1972. Washington, D.C., 1972. Box, George E. P., and Jenkins, Gwilym M. Time Series Analysis: Fore- casting and Control. San Francisco: Holden-Day, Inc., 1976. Burger, Albert E. An Analysis and Development of the Brunner-Meltzer Non-Linear Money Supply Hypothesis. Project for Basic Monetary Studies, Working Paper No. 7. St. Louis: Federal Reserve Bank of St. Louis, 1969. . The Money Supply Process. Belmont, CA: Wadsworth Publish- ing Co., Inc., 1971. Cagan, Phillip. Determinants and Effects of Changes in the Stock of Money, 1875-1960. New York: Columbia University Press, 1965. Currie, Laughlin. The Sppply and Control of Money in the United States. New York: Russell and Russell, 1968. Friedman, Milton, and Schwartz, Anna Jackson. A Monetary History of the United States, 1867-1960. Princeton, N.J.: Princeton University Press, 1971. Kendall, Maurice G., and Stuart, Alan. The Advanced Theory_of Statis- tics, Volume I. London: Charles Griffin and Company, Ltd., 1963. Phillips, C. A. Bank Credit. New York: The MacMillan Co., 1920. President's Commission on Financial Structure and Regulation. The Report of the President's Commission on Financial Structure and Regulation. Washington, D.C.: U. S. Government Printing Office, 1971. 339 340 Robertson, Ross M., and Phillips, Almaren. ,thional Affiliation with the Reserve System for Reserve Purposes is Consistent with Effective Monetarnyolicies. Washington, D.C.: Conference of State Bank Supervisors, 1974. Periodicals Andersen, Leonall C. "Three Approaches to Money Stock Determinations." Review, Federal Reserve Bank of St. Louis 49 (October 1967):7-13. Beck, Darwin, and Sedransk, Joseph. "Revision of the Mbney Stock Mea— sures and Member Bank Reserves and Deposits." Federal Reserve Bulletin (February l974):81—9. Benston, George. "An Analysis and Evaluation of Alternative Reserve Requirement Plans." The Journal of Finance XXIV (December 1969): 849-870. Board of Governors of the Federal Reserve System. Federal Reserve Bulletin. Tables Entitled, "Money Market Rates," "Principal Assets and Liabilities and Number, By Class of Bank," "Reserve Requirements of Member Banks," "Maximum Interest Rates Payable on Time and Savings Deposits." (Various Dates); Board of Governors of the Federal Reserve System. Federal Reserve Bulletin (July 1966):979; (January 1968):95-6; (May l968):437—8; (August 1969):655-6; (November 1972):994; (May l973):375-7; (July 1973):549; (September l974):680; (November l974):799-800. Boehne, Edward. "Falling Fed Membership and Eroding Monetary Control: What Can Be Done?" Business Review, Federal Reserve Bank of Philadelphia (June 1974):3-15. Brunner, Karl. "A Schema for the Supply Theory of Money." Interna- tional Economic Review 2 (January l961):79-109. . "Institutions, Policy, and Monetary Analysis." Journal of the Political Economy LXXIII (April 1965):197-218. Brunner, Karl, and Meltzer, Allan H. "Liquidity Traps, for Money, Bank Credit, and Interest Rates." Journal of the Political Economy LXXVI (January-February l968):1-37. . "Some Further Investigations of Demand and Supply Functions for Money." The Journal of Finance XIX (May l964):240-283. Burke, William. "Primer on Reserve Requirements." Business Review, Federal Reserve Bank of San Francisco (Winter 1974):3-16. Burns, Arthur F. "The Role of the Money Supply in the Conduct of Monetary Policy." Monthly Review, Federal Reserve Bank of Richmond (December 1973):2-8. 341 . "The Structure of Reserve Requirements." A speech before the Governing Council Spring Meeting, American Bankers Associa- tion, White Sulphur Springs, West Virginia, April 26, 1973. Reprinted in the Federal Reserve Bulletin (May l973):339-43. Federal Deposit Insurance Corporation. Assets, Liabilities and Capital Accounts, Commercial Banks and Mutual Savings Banks. Report of Call Nos. 54-64, 66, 68, 70, 72, 74, 76, 78, 80, 82, and 84. Federal Deposit Insurance Corporation, Board of Governors of the Fed- eral Reserve System, and Office of the Comptroller of the Currency. Assetsl_Liabilities, and Capital Accounts, Commercial Banks and Mutual Savings Banks. June 30, 1969, December 31, 1969, June 30, 1970, December 31, 1970, June 30, 1971, December 31, 1971, June 30, 1972, December 31, 1972, June 30, 1973, December 31, 1973, June 30, 1974, and December 31, 1974. Friedman, Milton. "Letter on Monetary Policy." Monthly Review, Federal Reserve Bank of Richmond (May-June l974):20-3. . "Statement on the Conduct of Monetary Policy." In Current Issues in Monetary Theory and Poligy, pp. 556-65. Edited by Thomas M. Havrilesky and John T. Boorman. Arlington Heights, I11.: AHM Publishing Co., 1976. Gilbert, Alton. "Utilization of Federal Reserve Bank Service by Member Banks: Implications for the Costs and Benefits of Membership." Review, Federal Reserve Bank of St. Louis 59 (August l977):2-15. Guttentag, Jack M. "Discussion." In Controlling Monetary Aggregates II: The Implementation, pp. 69-72. Boston: Federal Reserve Bank of Boston, 1972. Holmes, Alan R. "A Day at the Trading Desk." Monthly Review, Federal Reserve Bank of New York 52 (October 1970):234-8. . "Operational Constraints on the Stabilization of Money Supply Growth." In Controlling Monetary Aggregates, pp. 65-78. Boston: Federal Reserve Bank of Boston, 1969. Jordan,Jerry L. "Elements of Money Stock Determination." Review Federal Reserve Bank of St. Louis 51 (October l969):10-19. . "The Monetary Base--Explanation and Analytical Use." Review, Federal Reserve Bank of St. Louis 50 (August 1968):7-1l. Kaminow, Ira. "The Case Against Uniform Reserves: A Loss of Perspec- tive." Business Review, Federal Reserve Bank of Philadelphia (June 1974):16-21. 342 Kareken, John H. "Discussion." In Controlling Monetary Aggregates II: The Implementation, pp. 137-45. Boston: Federal Reserve Bank of Boston, 1972. Kopecky, Kenneth. "Nonmember Banks Revisited: A Comment on Starleaf." Unpublished Manuscript, Board of Governors of the Federal Reserve System. Maisel, Sherman. "Controlling Monetary Aggregates." In Controlling Monetary Aggregates, pp. 152-74. Boston: Federal Reserve Bank of Boston, 1969. Mayer, Thomas. "A Money Supply Target." In Current Issues in Mone- tary Theory and Poliry, pp. 548-555. Edited by Thomas M. Havrilesky and John T. Boorman. Arlington Heights, 111.: AHM Publishing Co., 1976. Poole, William, and Lieberman, Charles. "Improving Monetary Control." Brookings Pepers on Economic Activity (2:1972):293-342. Smith, Warren L. "Reserve Requirements in the American Monetary System." In Monetary Management, pp. 175-315. The Commission on Money and - Credit. Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1963. Starleaf, Dennis. "Nonmember Banks and Monetary Control." The Journal of Finance XXX (September l975):955-975. Teigen, Ronald L. "Demand and Supply Functions for Money in the United States: Some Structural Estimates." Econometrica XXXII (October l964):476—509. U. S. Congress, House, Committee on Banking and Currency, Subcommittee on Domestic Finance. An Alternative Approach to the Monetary Mechanism, by Karl Brunner and Allan H. Meltzer. 88th Congress, 2nd Session, Washington, D.C.: Government Printing Office, 1964. Warburton, Clark. "Nonmember Banks and the Effectiveness of Monetary Policy." In Monetary_Manegement, pp. 317-359. The Commission on Money and Credit. Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1963. General References Kmenta, Jan. Elements of Econometrics. New York: The MacMillan Com- pany, 1971. Nelson, Charles R. Applied Time Series Analyeis. San Francisco: Holden-Day, Inc., 1973. 343 Pendyck, Robert 8., and Rubinfeld, Daniel L. Econometric Models and Economic Forecasts. New York: McGraweHill Book Company, 1976. Theil, Henri. Principles of Econometrics. New York: John Wiley and Sons, Inc., 1971.