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FINES will be charged if book is returned after the date stamped below. THE RELATIVE EFFECTIVENESS OF FISCAL AND MONETARY POLICIES RECONSIDERED by Ehsan Ahmed A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Economics 1983 8 I 2013' 9 ”1 ABSTRACT THE RELATIVE EFFECTIVENESS OF FISCAL AND MONETARY POLICIES RECONSIDERED by Ehsan Ahmed There has been a widespread disagreement in macro- economic literature concerning the relative effectiveness of fiscal and monetary policies. A large part of the literature on this issue is theoretical, but unfortunately, theoretical models have not been able to resolve the dispute. The issue therefore, becomes empirical. The most well known empirical study on the relative effectiveness of fiscal and monetary policies was done by Andersen and Jordan in 1968. Andersen and Jordan conclude that the response of economic activity to monetary policy is larger, more predictable, and faster than fiscal policy. But Andersen and Jordan‘s conclusions have been widely criticized because of theoretical shortcomings, and because of statis- tical problems with empirical tests. The principal objections are: first, the use of high employment expenditures as appropriate fiscal policy variable, second, the use of Almon lag technique, third, the absence of relevant regressors, fourth, the presence of heteroschedasticity and fifth, the simultaneous equation bias. This dissertation uses the actual government spending as a fiscal policy variable, traditional monetary aggregates as monetary policy variables, and exports as third possible regressors. The primary focus is to investigate the severity of alleged simultaneous equation bias. This is done by testing the joint and individual exogeneity of all possible regressors. The primary conclusion is that the popular money supply measure MlB, actual government spending, and exports are all exogenous when the rate90f—change data are used. Therefore, it is plausible to use the ordinary least squares to estimate the reduced form, These estimates strongly support Carlson's (1970) original results, which implies that the sum of the coefficients for A log M13 is close to one. The addition of a third regressor or increasing the number of lags fails to reject the Carlson“s specification. These conclusions are also highly compatible with Milton Friedman’s ‘monetary framework- ACKNOWLEDGMENTS' I would like to express my gratitude to my dissertation advisor, Professor James M. Johannes for providing a detailed guidance during every aspect of this study. Without his help and guidance, this study would not have been completed. I am also indebted to Professor Robert H. Rasche for his helpful comments and insights during every stage of this dissertation. I would also like to thank Professors W. Paul Strassmann and Christine Amsler for reviewing the dissertation and providing valuable suggestions. I am also indebted to my colleague Richard Cervin for his suggestions on the empirical parts of this dissertation. I owe thanks to Ms. Terie Snyder for her skillful and expedient typing. I would also like to thank my parents for their support during the years of my graduate studies. Last, but not the least, my deepest appreciation goes to my wife Dotte, for her support and encouragement throughout these years. Her professional skills in Economics and insights into the material contributed a great deal in improving the manuscript of this dissertation. ii TABLE OF CONTENTS LIST OF TABLES. CHAPTER ONE - INTRODUCTION. Two - REVIEW OF THE LITERATURE. THREE - REESTIMATION OF MODIFIED VERSION OF ANDERSEN- JORDAN' S MODEL. . . . . . . . . . . . FOUR — EXOGENEITY TESTS FOR REDUCED FORMS USING TWO RIGHT-HAND SIDE VARIABLES. . . . FIVE - EXOGENEITY TESTS FOR REDUCED FORMS USING THREE RIGHT-HAND SIDE VARIABLES. . . . . . . SIX - SPECIFICATION AND ESTIMATION OF A MORE PLAUSIBLE REDUCED FORM EQUATION . SEVEN - CONCLUSIONS AND IMPLICATIONS. APPENDIX A. APPENDIX B. APPENDIX c. REFERENCES. iii Page iv 20 31 42 56 67 7O 78 84 89 LIST OF TABLES Table. ‘ Page 3.1 Original Anderseanordan Model. . . . . . . . . . 22 3.2 Ben Friedman's Estimates. . . . . . . . . . . . . 23 3.3 An Updated Version of Friedman's Model. . . . . . 24 3.4 A Modified and Updated version of Ben Friedman's Model . . . . . . . . . . . . . . . . . . . . . . 25 3.5 Modified Specification. . . . . . . . . . . . . . 26 3.6 Carlson's Original Estimates. . . . . . . . . . . 27 3.7 An Updated Version of Carlson's Model . . . . . . Z8 4.1 Joint Exogeneity of M13 and ActG. . . . . . . . . 36 4.2 Joint Exogeneity of M2 and ActG . . . . . . . . . 37 4.3 Joint Exogeneity of MB and ActG . . . . . . . . . 38 4.4 Joint Exogeneity of UBR and ActG. . . . . . . . . 39 4.5 Exogeneity of Regressors at a Glance. . . . . . . 40 5.1 Joint Exogeneity of MlB, A and ActG . . . . . . . 45 5.2 Joint Exogeneity of M2, A and ActG. . . . . . . . 46 5.3 Joint Exogeneity of MB, A and ActG. . . . . . . . 47 5.4 Joint Exogeneity of UBR, A and ActG . . . . . . . 48 5.5 Exogeneity of Regressors at a Glance. . . . . . . 49 5.6 Individual Exogeneity of MlB, ActG and X. . . . . 50 5.7 Individual Exogeneity of M2, ActG and X . . . . . 51 .8 Individual Exogeneity of.Base ActG and X. . . . . 52 5.9 Individual Exogeneity of UBR, ActG and X. . . . . 53 5.10 Exogeneity of Regressors at a Glance. . . . . . . 54 iv Ch OOOUUUUUUUU3>D>oxo~ to to la b O: bJ r4 N H p~ u: N LIST OF TABLES (cont'd.) Ordinary Least Squares with Rate of Change Data. The Updated Estimates for Carlson's Model Using ActG Instead of HEG. . . . . 1 The OLSQ Estimates after Dropping A Log Xi The OLSQ Estimates with Four Quarterly Lags. 2SLSQ (Instrumental Variables) Schmidt-Wand Min s.e. Estimates. TWOQStage Least Squares Estimates. Two-Stage Least Squares Estimates. Two-Stage Least Squares Estimates. Two—Stage Least Squares Estimates. Ordinary Least Squares Ordinary Least Squares . Ordinary Least Squares Page 62 63 64 65 75 76 8O 81 82 83 86 87 88 CHAPTER ONE INTRODUCTION There has been widespread disagreement in macro- economic literature concerning the relative effectiveness of fiscal and monetary policies. Since the great depression, Keynesian and Neo-Keynesians have believed that fiscal I policy plays the major role in determining the level of indome in industrialized and modern economies like the United States. They believe that government's fiscal tools can operate effectively in times of recession or high rates of inflation. Although the fiscal and monetary actions can be taken simultaneously, fiscal actions according to these groups, retain their effectiveness even if a supplementary monetary action is not taken by monetary authorities. . This view of the world has been seriously questioned by Milton Friedman and others who assert that the change in the Stock of money is the primary determinant of changes in nominal GNP and therefore, Should be given major attention in macroeconomic literature. This view became the point of departure Of what is now referred to as the monetarist school of thought. This challenge to the Keynesian view of the world has spawned a whole literature on exactly which policy is more effective. A large part of the literature is theoretical, but unfortunately, theoretical models have not been able to resolve the dispute. The issue, therefore, becomes empirical. As Friedman states; "One purpose of setting forth this framework is to document my belief that basic differences among economists are empirical, not theoretical....Much of the controversy that has swirled about the role of money in economic affairs reflects, in my opinion, different implicit or explicit answers to these empirical questions." [(1970), p. 237]. The importance of the empirical approach concerning the relative effectiveness of fiscal and monetary policies has been recognized in macroeconomic literature. Several economists have carried out empirical studies. [Andersen- Jordan (1968)], [Ben Friedman (1977)], [Carlson (1978)], [BarthanuiBennet (1974)], [Deleeuw-Kalchbrenner (1969)], ~[Stephone—Grapentine (1979)], [Hafer (1981, 1982)], [Schadrack (1974)], [Keran (1969)], [Friedman-Meiselman (1963)]. The most well-known study was done by Andersen and Jordan (1968). Based on their empirical results, Andersen and Jordan conclude that "the response of economic activity to monetary actions compared with that of fiscal actions is (1) larger, (II) more predictable, and (III) faster." (p. 22). Given these results Andersen.and Jordan rule out any considerable role of fiscal policy; however, the Andersen and Jordan conclusions have been widely criticized because of the theoretical shortcomings of the model and because of statistical problems with the empirical tests. The principal objections are first, the use of high employment expenditures as the appropriate fiscal variable [Blinder-Solow (1974)], second, the use of the Almon Lag technique [Schmidt-waud (1973)], third, the absence of relevant regressors [Hester (1964)], fourth, the presence of heteroschedasticity [Carlson (1978)], and fifth, simultaneous equation biases [Deleeuw-Kalchbrenner (1969)], [Hafer (1982)], [Feige-Pearce (1979)], [Geweke (1978)], [Granger (1969)], and [Sims (1972)]. Perhaps the most damaging Of these criticisms, and the one given the least attention, is simultaneous equation bias. As Sims (1972) states, "It has long been known that money stock and current dollar measures of economic activity are positively correlated. There is further evidence that money or its rate of change tends to lead income in some sense. A body of macroeconomic theory, the quantity theory, explains these empirical Observations reflecting a causal relation running from money to income. However, it is widely recognized that no degree of positive association between money and income can by itself prove that variation in money causes variation in income. Money might equally react passively and very reliably to fluctuations in income." (p. 540). Geweke (1978) develops tests of exogeneity in the ”complete dynamic simultaneous model." According to Geweke, ”the specification of exogeneity is usually made a priori. If the specification is incorrect the otherwise identifying restrictions imposed on structural equations may not be sufficient to identify these equations, estimation procedures will be inconsistent, and the model cannot adequately portray the dynamics of the system it seeks to describe. It is therefore desirable to test the exogeneity specification rather than let it remain a mere assertion." [Geweke (1978), p. 163]. The primary purpose of this dissertation is to investigate the severity of the alleged simultaneous equation bias. This can be done by directly using an extension of the theorems of Sims (1972) to multivariate time series [Geweke (1978)]. However, to do this correctly, attention must also be given to the other four problems previously mentioned. The primary conclusion of this dissertation is that the popular money supply measure MlB, and the fiscal policy variable Act G (actual government spending) are both exogenous when the rate of change data is used. The third relevant right hand side variable, namely exports, also turns out to be exogenous. Therefore, it is plausible to use the OLSQ to estimate the Friedman type reduced form equation for nominal GNP. The estimated regressions thus, strongly implies that the sum of the coefficients for A log M13 is close to one. This is significant at the .05 level. The sum of the coefficients for A log Act-G is not significantly different from zero. Moreover, the F tests do not reject the null hypotheses that the addition of the third right hand side variable, namely exports, and the addition of lags [(Schmidt-Waud (1973)] beyond the fourth quarter do not contribute to the explanation Of variations in the rate Of change in the nominal GNP. 1 There is some evidence that the money supply measure M1 (or MlB) does not turn out to be exogenous when the arithmetic first difference is used. The other two right hand side variables, namely actual G and exports are exogenous. When a change in nominal GNP (arithmetic first difference) is regressed against the change in M13, actual G, and exports, using two stage least squares, the conclusions drawn by Andersen and Jordan do not hold. The fiscal multiplier turns out to be significantly different from zero over a period of nine quarters. However, it is extremely difficult to find the instrumental variables which are statistically exogenous. Therefore, growth rate data is preferred because it is used in the original Friedman and Andersen-Jordan work. (Andersen andHJordan, however, do not report the results in their 1968 paper. The plan of this dissertation is the following: Chapter Two: Literature Review [Andersen-Jordan (1968)], [Blinder- Solow (1974)], [Barth-Bennet (1974)], [Stephens- Grapentine (1979)], [Friedman—Mieselman (1963)], [Schadrack (1974)], [Keran (1969)], [Hester (1964)], [Schmidt-Waud (1973)], [Friedman (1977)], [Carlson (1978)]. , Chapter Three: Reestimation of the modified and updated version of the Andersen—Jordan model. [Friedman (1977)], [Carlson (1978)]. 3.4 Chapter Four: Multivariate exogeneity tests for reduced forms using two right hand side variables. [Geweke (1978)], [Granger (1969)], [Johannes (1980)]. Chapter Five: Multivariate exogeneity tests using three right hand side variables. Chapter Six: A Specification and estimation of a more plausible reduced form. Chapter Seven: , Conclusions and implications. Appendix: Estimation of alternative reduced forms using alternative econometric techniques. ‘ . CHAPTER TWO REVIEW OF THE LITERATURE The most important study of the effectiveness of monetary and fiscal policies is that of Andersen and Jordan. It is of prime importance because it was the first such study and because subsequent research in this area uses Andersen and Jordan as the point of departure. In their study, the relationship between total nominal spending (GNP), the money supply, and high employment federal expenditures or full employment surplus (HEG from now on) is tested. Andersen and Jordan's pUtative reduced form can be written in the following way: AYt = Constant + ‘2 miAMt_i + .E eiAHEGt_i + Ut 1—0 1—0 (2.1) where A refers to the first differences of levels, and where Yt = Nominal GNP Mt = Monetary base or monetary aggregate like MlB. HEG = High Employment Government Sepnding (purchases). Ut = Error term. They use seasonally adjusted quarterly data for the U.S. economy from the first quarter Of 1952 to the second quarter of 1968, and employ the Almon Lag procedure using a fourth degree polynomial with two end point constraints. Using these techniques, Andersen and Jordan test the following hypotheses: 1) Estimated coefficients for AHEG-are larger and statistically more significant than the estimated coefficients for AM. 2) AHEG influences AY faster than AM. 3) The effect of AHEG is more predictable than AM. Andersen and Jordan state that "The results of the- tests were not consistent with any of these propositions. Consequently, either the commonly used measures of fiscal. influence do not correctly indicate the degree and direction of such influence, or there was no measurable net fiscal influence on total spending in the test period....Rejection of three propositions under examination and acceptance of the alternatives offered carry important implications for the conduct of economic stabilization policy. All of these implications point to the advisability of greater reliance on monetary actions than on fiscal actions. Such a reliance would represent a marked departure from.most present procedures." [Andersen-Jordan (1968), p. 22]. These controversial results were not widely accepted. Several studies have since emerged to check the robustness of Andersen and Jordan's results to changes in data, time period, methodology and definitions of fiscal and monetary policy variables. The first objection which was raised against Andersen and Jordan's study concerns the specification of the fiscal policy variable. Blinder and Solow (1974) raise objections against the use of HEG as a fiscal policy variable. There are various measures of fiscal policy. One can use an ordinary budget surplus, but this measure does not make a distinction between discretionary and automatic changes in the budget. Instead Blinder and Solow suggest that "the most obvious, and by now the most popular way to separate discretionary from automatic fiscal actions is to focus on the full employment budget.” If the budget would be in surplus at full employment, fiscal policy is termed restric- tive, if the budget would be in deficit, it is termed expansionary." (p. 14). But, HEG is subject to criticism. According to Blinder and Solow, ”Like the ordinary surplus, the FES runs afoul of the balanced budget theorem; changes in tax receipts simply do not carry as much bang for the buck as changes in government purchases. Since the FES fails to weight tax receipts by the marginal propensity to consume, it is impossible to associate a given change in the FES with a specific change in income; it depends on how the change is apportioned between taxes and spending." (p. 17). Another problem state Blinder and Solow, ”arises 10 with the full employment surplus, whether weighted or unweighted, which did not afflict the ordinary budget surplus. Suppose the tax regulations (that is, the vector of parameters, u) are altered when the economy is very far below full employment. The revenue yield of this change at actual income levels may well be very different from the hypothetical revenue yield at full employment.” (p. 17). This would make the HEG a meaningless measure during the periods of high unemployment rates. Blinder and Solow suggest using the Weighted Standardized Surplus (WSS) instead. .The WSS is derived by substracting the product of marginal propensity to consume (MPG) and marginal propensity to tax (tax parameter) from thd change in government expenditures. Blinder and Solow conclude that when AWSS is used instead of AHEG, the sum of the estimated coefficients for fiscal policy will change significantly. However, the WSS assumes that we know all the structural coefficients to begin with. If these coefficients are already known, there is no need to estimate the WSS. K, Even if HEG is used as a fiscal variable, does it really have significant influence on nominal GNP? A study by Barth and Bennet (1974) indicates that HEG does not seem to have a significant relationship with nominal GNP. Barth and Bennet's study attempts to test two important hypotheses. First, a significant empirical relationship exists between AHEG and AY (nominal GNP). Second, causation runs from AY 11 to AHEG. Based on a sample from the first quarter of 1955 to the fourth quarter of 1961 for the U.S. economy, they reject both hypotheses. This implies that there is no significant statistical evidence that a variability in AY is caused by a variability in AHEG. The rejection of the second hypothesis implies that the variability in HEG does not seem to be caused by a movement in Y, i.e.HEG is exogenous with respect to Y. However, Barth and Bennet do not include a monetary variable in their regressions. Stephens and Grapentine (1979) point out that the inclusion of a I monetary policy variable subjects the regression to error due to missing variables Stephens and Grapentine's empirical investigation, which uses data from the second quarter of 1954 to the fourth quarter of 1975, fails to Show any significant relationship between AHEG and AY. The evidence on causality from AY to AHEG is also inconclusive. In a more recent study, Hafer (1982) uses the Granger test to test the exogeneity of HEG and concludes that unindirectional causation from AY to AHEG cannot be rejected. In View of these studies, this dissertation contends that instead of AHEG or AWSS, one should use the AActG (actual government purchases) as the fiscal policy variable. The ActG is a better measure than HEG because it does not lose its usefulness during the periods of high unemployment. The ActG is easier to calculate and there is no need to introduce MPC or a tax parameter into the calculations. 12 The choice of an appropriate monetary aggregate has also been the subject of great interest in much of the literature. The well-known study of Friedman and Meiselman (1963) consider M2 as a superior monetary aggregate and say that M2 shows a significant influence on nominan GNP. The plausibility of M2 is a1So supported by Schadrack (1974), who estimates a relationship between six monetary aggregates and nominal GNP, concluding that M2 shows the most significant influence on nominal GNP. Hafer (1981), on the other hand, is concerned with the statistical exogeneity of measures like MlB and M2. He uses the Sims and Granger tests to. estimate exogeneity and M2, and concludes that the exogeneity of these two monetary aggregates cannot be rejected. Moreover, he points out that the variability in nominal GNP is better explained by MlB. An attempt is made by Keran (1969) to evaluate the plausibility of the money stock as a monetary aggregate. The money stock is defined as M = mB, where m is the money multiplier, and B the monetary base. The sources of the monetary base consists of various kinds of credit extended by the monetary authorities. The use of a monetary base is divided between currency holdings of the non-bank public and reserves of commercial banks. Keran tests the exogeneity of the monetary base by regressing it against nominal GNP. He concludes that the change in nominal GNP is not causing any significant variations in the monetary base. Therefore, 13 the monetary base is statistically exogenous and hence, can be used as an appropriate monetary aggregate. However, Keran's conclusion is not shared by Deleeuw and Kalchbrenner (1969), who believe that the exogenous variable must be subject to control by policy makers, and must not respond to movements in endogenous variables. The monetary base will be exogenous only if the sum of its components namely, currency, borrowed reserves, and unborrowed reserves, is exogenous. Deleeuw and Kalchbrenner state,"few would disagree with the proposition that, at least as the discount window was been administered for the last fifteen years, member bank borrowings have responded strongly to current movements in business loan demand andthe interest rate. The question of interest however, is not whether borrowings are endogenous, since presumably that would be a matter of common agreement, but rather whether there is a strong tendency for the movement in borrowing to be offset by movements in some other components of the base. If there is a tendency for endogenous responses in borrowing to be offset by movements in other components of the base, then the total base contains offsetting endogenous influences and preference should be the total base of the St. Louis regressions. If there is not such a tendency, then adjusting the base to remove borrowings in this latter case, might lead to statistical confusion between the effects of a high monetary base on the economy with the effects of a booming economy on borrowing and, hence on the base....Since it is 14 not hard to think of unborrowed reserves responding in either direction to a change in borrowing during the sample period of the regressions, it seems better to represent monetary policy by a variable which excludes member bank borrowing." (p. 8). A review of Deleeuw-Kalchbrenner's study indicates that the issue of an appropriate monetary aggregate is unresolved but appears to center on exogeneity. Another major weakness of all these studies stems from the fact that other relevant variables may enter into the reduced form besides money supply and government spending. [Blinder and Solow (1974)]. Hester (1964), in his response to Friedman-Mieselman's CMC paper (1963) raises the issue of other relevant regressors in the reduced form. He introduces an autonomous spending variable (L) which is comprised of net private domestic investment, government purchases, and net exports. However, Hester's (L) has some problems: First, government spending (G) should be excluded in this work from (L), since effect of G alone is of direct interest. Second, imports (M) should also be excluded from (L) because they are known to be affected by changes in income. This implies that an alternative measure should be used which eliminates these problems. The alternative is (A) which is equal to private domestic investment, exports, and capital consumption allowance. The third major weakness of the Andersen and Jordan model is attributed to another specification error. This 15 specification error occurs when a constrained Almon Lag is used. In order to estimate the relative effectiveness of fiscal and monetary policies, researchers have generally used the distributed lag scheme because the impact of any of these policy actions is expected to last beyond the current time period. From a statistical viewpoint, independent variables with lags are assumed to be stochastic and are not correlated with the disturbance term of the equation. Therefore, one can use ordinary least squares (OLSQ) to estimate their coefficients. A Special case of the distributed lag scheme is the Almon lag technique. The Almon Lag expresses the coefficients of the right-hand side variable as a function of the length of the lag and fits appropriate curves to Show the functional relationship between the two. The distributed lag regression can be written as follows: Yt " a0 + 80 X1: + 81 Xt-l + 82 Xt—Z + .... + B X + U (2.2) According to the Almon Lag procedure, the BS can be approximated by the suitable degree of a polynomial. One can specify the degree of polynomial after the length of the lag is determined. The degree of the polynomial is generally the number of turning points. Moreover, in this technique, the choice of a lag depends on the discretion of the researcher. Anderson and JOrdan use a fourth degree polynomial with two end point constraints. This supposedly 16 increases the efficiency of their estimates. But, in the words of Schmidt and Waud (1973), "imposing the restriction that the weights lie on a polynomial will lead to more efficient estimates and more powerful tests, if the restriction is true, and to biased and inconsistent estimates and invalid tests, if the restriction is false. This second possibility should be kept in mind, especially since the polynomial lag technique is often applied with little or no thought as .to why it should be the case that the polynomial restriction is true." (p. 12). The length of the lag is another A problem. If the length of the lag is over or under estimated, the regressors are subject to specification errors. Schmidt and Waud assert that unless there is an 'a priori' reason to believe that the lag is present, the polynomial distributed lag technique should be,avoided. As Schmidt-waud state, ”the presence or absence of a lag is not a testable proposition when the Almon Lag technique is used.” (It should perhaps be noted that this is a problem peculiar to the Almon Lag specification)....Actually, what is reflected in the preceding point is just the fact that the choice of the length of the lag is extremely touchy in the Almon specification. It is, of course, clear that under— stating the length of the lag (choosing n less than the true lag length) is a specification error which leads to biased and inconsistent estimates and invalid tests." (p. 13). Schmidt and Waud suggest that if the polynomial procedure is to be used, one should use a variable lag scheme for each l7 policy variable and different degrees of the polynomial should be used. Schmidt and Waud find that the minimum standard error is achieved when the length of the lags is extended to eight quarters. Although Schmidt and Waud criticize the Andersen and Jordan's use of Almon Lags, they do not attempt to evaluate the appropriateness and exogeneity of HEG or the monetary base. The issue still remains that the use of a particular econometric estimation procedure is of secondary importance. The main issue is how to specify appropriate policy variables and test whether they are truely exogenous before they can be used on the right-hand side of the reduced form. In addition to taking care of the specification errors and testing the exogeneity of right-hand side variables, there is also a need to check the robustness of Andersen and Jordan's model by increasing the sample size. Benjamin Friedman (1977) pays attention to this matter and increases the sample size up to the second quarter of 1976. However, he does not change the methodology. On the basis of this increased sample and constrained PDL technique, Friedman concludes that the sum of the coefficients for AHEG is significantly different from zero. This clearly contradicts the results of Andersen and Jordan. Since the methodology used here is the same as that used by Andersen and Jordan, and the specification of the reduced form remains the same, Friedman's estimates are also subject to specification errors . l8 Friedman's for, is also criticized by Carlson (1978), who asserts that a critical assumption in linear regression is that the variance of the error term remains constant during the estimation process. Friedman's data violate this assumption of homoschedasticity. Carlson suggests the use of a rate of change or growth in data, instead of an arithmetic first difference. This may help overcome the critical problem of heteroschedasticity. In summary, the literature raises several problems with the Andersen and Jordan model, that must be addressed formally before the real value of Andersen and Jordan model, or a derivations like the Carlson model can be judged. 1) There is a specification error in terms of the derivation of the fiscal policy variable and methodology, in particular, the Almon lag technique. [Blinder-Solow (1974)], [Schmidt-Waud (1973)]. 2) There is a possibility of missing variables, which subject the equation to specification errors. In a modified reduced form, a third exogenous variable A is recommended. A is comprised of nominal exports, private investment, and capital consumption allowance. An alternative version 1 would be with (export) instead of (A). [Dernburg- McDougal(l963)], [Hester (1964)], [Hansen (1951)], [Samuelson (1961)]. 3) The problem of heteroSchedasticity can be taken 19 care of by using a rate of change instead of arithmetic first differences. [Carlson (1978)]. Some of the preceding issues have been addressed in the literature, but the issue of exogeneity and additional variables have not been adequately covered. This disserta- tion emphasizes the exogeneity issue and uses multivariate tests (Geweke 1978) to identify the appropriate fiscal policy variables and monetary aggregates. The exogeneity tests are also carried out on other possible right hand side variables. If the joint or individual exogeneity of any of the rightahand'side variables is rejected, the use of OLSQ will produce inconsistent and biased estimates. In this case, one should use two-stage least squares or some other consistent estimator. CHAPTER THREE REESTIMATION OF MODIFIED VERSION OF ANDERSON—JORDAN'S MODEL The last chapter briefly reviewed the study of Ben Friedman's (1977) work. Friedman reestimates the original Andersen and Jordan model by increasing the sample size up to the second quarter of 1976. His conclusion was that the sum of the estimated coefficients for AHEG is signifi— cantly different from zero. His work implies that Andersen and Jordan's estimates will be altered if the sample is updated. He produces these new estimates without any change in specification of fiscal or monetary policy variables, or estimation procedures. He does not test the statistical exogeneity of any of the right-hand side variables. Friedman's model was criticized by Carlson (1978) who points out that it violates the assumption of heterosche- dasticity. The contention in this dissertation is that heterosche- dasticity is not the only problem with Friedman's model. Like Andersen and Jordan, Friedman's estimates are subject to specification errors due to the problem with fiscal variables [Blinder-Solow (1974)], and the use of Almon 20 21 Legs. [Schmidt-Waud (1973)]. 'The main argument is that the Andersen and Jordan model, the Friedman model, and Carlson's specifications may all suffer from simultaneous equation bias. Mere extension of the sample size to 1976 does not necessarily eliminate this bias. The fact is that if Friedman's model is updated (by extending the sample to the second quarter of 1980), one will actually get the original Andersen and Jordan result. This is shown in Tables 3.2 through Table 3.5. Table 3.7 produces estimates from an updated version of Carlson's model. These new regressions follow the same lag scheme as Friedman and use constrained polynomial distributed lags. In the first regression (Table 3.3), AMlB is used as monetary policy and AHEG reflects the measure of fiscal policy. The data was obtained from the SurVey of Current Business (1980)1 and the FMP (Federal Reserve—MITeUniVersity of Pennsylvania) model. Seasonally adjusted quarterly data from the first ' quarter of 1959 through the second quarter of 1980 were used. The sum of the estimated coefficients for AMlB (Table 3.3, original AndersensJordan, and Friedman estimates are in Tables 3.1 and 3.2) is larger and more significant than Friedman's original model. The sum of the estimated coeffic- ients for AHEG is only 0.86, which is Significant only at the .10 level. IFrank Deleeuw, Thomas M.'Holloway, Darwing G. Johnson, Avid S. McClain, and Charles A. Whaite, ”The High Employment Budget: New Estimates, 1955-1980,” survey of CUrrent Business, November 1980, pp. 13-75. 22 TABLE 3.1 ORIGINAL ANDERSEN-JORDAN MODEL Equation (1) M E O 1.54 40 (2.47) (l 48) -1 1.56 54 (3.43) (2 68) -2 1.44 - 03 (3.18) ( 13) -3 l 29 — 74 (2 00) (2 85) Sum 5.83 .17 (7 25 (-54) Constant 2.28 2 (2.76) R .56 s e 4.24 D W 1.54 Equation (2) M E R 0 l 51 6 .16 (2.03) (1 15) (.53) -l 1.59 3 -.01 (2.85) (2 15) (.03) -2 1 47 - 5 -.03 (2 64) ( 19) (.10) —3 27 - 78 .11 (l 82) (2 82) (.32) Sum 5.84 .07 .23 (6 57) (.13) ( 32) Constant 2.10 2 (1.88) R .58 s.e. 4.11 D.W. 1.80 Reproduced from ”Leonald C. Andersen and Jerry L. Jordan, "Monetary and Fiscal Actions: A Test of Their Relative Importance in Economic Stabilization,” Federal Reserve Bank of St. Louis Review, February, 1978. 23 TABLE 3.2 BEN FRIEDMAN'S ESTIMATES Period AMl AHEG 0 2.01 .30 (3.10) (1.3) -l 1.55 .10 (3-6) (.6) -2 .6 .09 (1.1) (.4) -3 .16 .43 (.4) (2.5) -4 .27 .71 (.4) (2.8) Sum 4.60 1.62 (4 60) (4 1) Constant = .65 R2 = .66 ( 03) s.e. = 3.99 D.W. = 1.92 Note: The numbers in parenthesis are t-values. Reproduced from Benjamin Friedman, ”Even the St. Louis Model Now Believes in Fiscal Policy," Journal of Money, Credit and Banking, May 1977. 24 TABLE 3.3 AN UPDATED VERSION OF FRIEDMAN'S MODEL AMlB AHEG o 3.24 .37 (4.73 (1.65) -1 ' 3.38 .16 .(6.93) (.93) -2 1.87 -.01 (2.70) (-.03) -3 ~ .03 .08 (.06) (.41) -4 -.95 .26 (-1.17) (1.04) Sum 7.55 .86 (6 68) (1.64) Sample 19591 - 1980II Constant = -2.64 (-l.10) R2 = .72 s.e. = 11.32 D.W. = 2.00 Note: The numbers in parenthesis are t—values. 25 TABLE 3. 4 A MODIFIED AND UPDATED VERSION OF BEN FRIEDMAN'S MODEL Period AMlB AActG 0 3.32 .21 (4.83) (1.03) -1 3.48 .97 (7.21) (.64) -2 1.96 .03 (2.85) (.15) -3 .09 .12 (.20) (.69) -4 -.92 .24 (-1.13) (1.05) Sum 7.93 A .70 (7.90) (1.55) Sample = 19591 - 198OII Constant = -2.81 R2 = .71 s.e. = 11.43 D.W. = 1.99 Note: The numbers in parenthesis are t-values. 26 TABLE 3.5 MODIFIED SPECIFICATION A MlB A ActG A A 0 1.24 .83 .96 (2.28) (5.31) (11.00) -1 1.19 .23 .19 (2.54) (1.89) (2.47) —2 .65 —.14 -.23 (1.37) (-l.13) (-3.36) -3 .23 . .10 .11 (.35) (.63) (1.31) Sum 3.35 1.02 1.03 (3.00) (3.73) (5.10) Sample 19511 - 198011 Constant = 1.27 R2 = .90 (.76) D.W. = 1.91 A = Exports + Investment (private) + Capital Consumption Allowance Note: The numbers in parenthesis are t-values. 27 TABLE 3 . 6 CARLSON'S ORIGINAL ESTIMATES Ml(A 10g Ml) HEG ( Log HEG) 0 .40 .80 (2.96) (2.26) -l .41 .06 p (5.26) (2.52) -2 .25 .00 (2.14) (.02) -3 .06 -.06 (.71) (-2.20) -4 -.05 -.O7 (-.37) (-1.83) Sum 1.06 .03 (5.59) (.40) Sample 19531 - 1976IV Constant - 2.69 R2 = .40 (3.23) s.e. = 3.75 D.W. = 1.75 Reproduced from Keith M. Carlson, "Does the St. Louis Equation Now Believe in Fiscal Policy?”, Federal Reserve Bank of St. Louis Review, February, 1978. 28 TABLE 3.7 AN UPDATED VERSION OF CARLSON'S MODEL Period . A Log MlB A Log HEG 0 .29 .11 (2.17) (2.47) -1~ .37 .04 (4.74) (1-34) -2 .27 -.02 (2.75) (-.51) -3 .11 -.01 (1.44) (-.25) —4 -.04 .04 (-.37) (.99) :Sum 1.00 .17 (4 97) (1 88) Sample 19591 - 198011 Constant = .002 R2 = .37 (1.34) D.W. = 2.03 s.e = .01 29 These results are more compatible with Andersen and Jordan's ‘mOdel. In Table 3.4 the estimates do not seem to be any different fnmn Andersen and Jordan when AActG replaces AHEG as a fiscal policy variable. What happens to the same framework when we add a third variable to the right-hand side of the equation? The addition of the autonomous spending variable (A) to the right-hand side variables changes the estimates somewhat. (See Table 3.5). The question still remains whether the right-hand variables in all these alternative versions are truly exogenous. This question Cannot be answered unless there. is clear evidence that these regressiOns do not suffer from the simultaneous equation bias. The fiscal policy multiplier is significantly different from zero, but it is smaller than the multiplier produced by Friedman's model. The next step was to estimate an updated version of Carlson's model, which uses rates of change instead of arithmetic first differences. The estimates are summarized in Table 3.7. They are very similar to the original Carlson estimates, which Show a minor role of fiscal policy. Although Carlson's specification seems straightforward and more plausible, it is imperative that the exogeneity of all of the right hand side variables must be tested. If these variables are exogenous jointly and individually with respect to nominal GNP, it will be appropriate to use the OSLQ. If the regressors are not truly exogenbus and the regressions are subject to simultaneous equation bias, it is not appropriate 30 to use OLSQ or the PDL technique. This will lead to biased and inconsistent estimates. The issue of exogeneity is considered in the next chapter, where multivariate tests for the joint and individual exogeneity are introduced. CHAPTER FOUR EXOGENEITY TESTS FOR REDUCED FORMS USING TWO RIGHT-HAND SIDE VARIABLES The reduced form equations already examined in the literature show that independent variables must be correctly specified under the control of policy makers, and statis- tically exogenous. The controllability Of a monetary aggregate or fiscal policy variable is essential from a policy point of View; For instance, if policy makers are making a change in monetary policy, the change is reflected through a monetary aggregate. If policy makers can effectively control this aggregate, it will be considered exogenous from the policy makers viewpoint. Even if an . aggregate is controllable by policy makers, if it is not statistically exogenous, it will produce inconsistent and biased results. Statistical exogeneity means that the variable in question is independent of the disturbance term of the equation. The movement in the exogenous variable is not caused by current or past movements in the endogenous variable. For example, if a policy maker is attempting to change nominal GNP using monetary policy tools, the changes in nominal GNP should be a direct result Of a change in 31 32 monetary policy. This monetary aggregate should not in turn be affected by the changes in nominal GNP. If a policy variable is not exogenous in a statistical sense, we may not know whether we measured the influence of our policy on nominal GNP or whether nominal GNP's influenced the policy variable. The exogeneity tests used in this chapter are based on Geweke's (1978) study. (Also see Granger 1969). He considers the "complete dynamic simultaneous equation model" (CDSEM). Consider the following relationship between variables Y and X: B(L) Yt + T(L) Xt ‘ ei (8xs)(8xl)(8xk)(kxl) (axl) (4.1) The vector of the disturbance term is assumed to be serially uncorrelated. The operators B(L) and T(L) are the polynomial 'matrices in the lag operator L. The Operator L describes the relationship between k exogenous variables Xt' and g endogenous variables Yt. The stability of operator B(L) requires that Xt exogenous variables and the error term Xi determine the endogenous variable Yt‘ In a stable and complete model only current and past Xt's determine Yt's. According to Geweke (1978) the Xtie;"determined outside the CDSEM which in turn is a complete description of the interaction between Xt and Yt’ a proper specification of the determination of Xt will not include any values of Yt.” 33 (1978, p. 166). Granger (1969) has derived various useful tests based on this premise. [Also see Johannes (1980), Pierce-Hough (1975)]. For example, consider the following regression in which Xt is regressed on past Xt and past Yt (Geweke 1978): (4.2) The variable Xt will be exogenous in this "complete dynamic Simultaneous equation model” if GS = 0 for all s > 0. Some important aspects of the exogeneity'test presented in Equation 4.2 are discussed in Dent and Geweke (1979) and Johannes (1980). First, the exogeneity of variable Xt can be hypothesized and subjected to testing. Second, the "complete dynamic simultaneous equation model with Xt will not exist if the implication of exogeneity is false.” (Dent and Geweke 1979). Thirdly, it is not necessary to specify a model for Xt to test its exogeneity. Fourth, due to the presence of lags on the right-hand side, the test will be biased toward non-rejection of exogeneity, if there is a contemporaneous relationship between variables. The exogeneity tests presented in this chapter rely on a reduced form frequently used by economists. Generally, economists use a reduced form with two right-hand side variables. The hypothesis tested in this chapter is that monetary aggregate and fiscal policy variables are all jointly 34 exogenous with respect to the nominal GNP. There are two relevant questions in this type of estimation (Johannes 1980). First, the choice of the lag for each variable and second, the choice of an apprOpriate statistic to test the null hypothesis that GS = 0, (Equation 4.1) which implies that putative fiscal and monetary policy variables are in fact exogenous. Geweke (1978) favors longer lag periods for putative exogenous (Xt) variables but seems to feel that a Shorter lag period is sufficient for endogenous variables (Yt). Each variable in this study will have a contemporaneous value and eight quarterly lags. As for test statistics, the Wald, the Likelihood Ratio Test, and the LaGrange multiplier are used to test the null hypothesis that G3,: 0 or Yt—S = 0. All three test statistics are asymptotically distributed as Chi Square with 16 degrees of freedom (the degrees of freedom are the number of restrictions). If the computed value is greater than,thex, Critical value, the null hypothesis that the coefficients for Yt-i are jointly zero will be rejected.2 2To test that Mt-i and Acth_i are putative exogenous varuables you estimate two alternative versions of equation (4.3). The first version which estimates the unrestricted case has three uncorrelated regressions. The first regression regresses the contemporaneous value of AM (monetary aggregate) against the past value of AM, the past values of AActG and the past values of AY (nominal GNP). The equation also includes a constant and a trend value which shows that the data possesses stationary characteristics. The second equation in the unrestricted case regresses AActG (contemporaneous) against the past values of AActG, AM, and AY. It also includes both a constant and trend value. An alternative version would omit the past values of AYt from the right-hand side of the equation. The objective is to test the hypotheSis that eight past coeffiCients of AY are jointly zero. 35 Tables 4.1 through 4.5 produce the results for the joint and individual exogeneity test. In each specification a different monetary aggregate is used with ActG. (The HEG was also used instead of ActG, but the tables do not contain these estimates.) The tables show the results both in terms of arithmetic first differences and rates of change (A log Xi). Table 4.1 shows the the joint exogeneity of MlB and ActG is rejected on all grounds when the arithmetic first difference is used. The tests also indicate that the individual exogeneity of M18 is rejected, but the individual exogeneity of ActG is not rejected. However, the joint and individual exogeneity of MlB and ActG is not rejected when a A log form is used. Table 4.2 shows that in levels, the joint exogeneity of M2 and ActG is rejected on all grounds. This can be attributed to the individual rejection of ActG. The results show that the individual exogeneity of M2 is not rejected. The A log estimates do not reject the joint or individual exogeneity of M2 and ActG. Table 4.3 has the exogeneity results for the monetary base and ActG. In the level estimates, the joint exogeneity of MB (base) and ActG, and individual MB is not rejected. The results using growth rate data do not reject the joint or individual exogeneity of MB and ActG. AS to the individual exogeneity of UBR (unborrowed reserves), the results are not conclusive. The data with levels shows that the arithmetic first difference does not reject the individual exogeneity of UBR, but A log estimates do reject it. 36 TABLE 4. 1 Wald Likelihood Ratio LaGrange Joint Exogeneity of MlB and ActG 1. Levels 77.27 60.87 49.08 (Reject) (Reject) (Reject) 2. Logs 21.59 19.46 17.65 (Do Not Reject) (Do Not Reject) (Do Not Reject) Individual Exogeneity-of MlB F-test 1. Levels 5.43 (Reject) 2. Logs 1.75 (Do Not Reject) Individual Exogeneity of ActG F-test 2‘08“ 1. Levels . (Do Not Reject) 2. Logs 0.30 (Do Not Reject) Critical value of X2 = 26.296 .05,l6 Critical value of F8,51 = 2.14 37 TABLE 4.2 Joint Exogeneity of M2 and ActG Wald Likelihood Ratio LaGrange 1. Levels 51.99 48.23 37.71 (Reject) (Reject) (Reject) 2. Logs 20.72 19 27 18.02 (Do Not Reject) (Do Not Reject) (Do Not Reject) Individual Exogeneity of M2 F-Test 1. Levels 1.62 (Do Not Reject) 2. Logs ’ 1.26 (Do Not Reject) Individual Exogeneity of ActG F-Test 1. Levels 3.39 (Reject) 2. Logs 2.07 (Do Not Reject) . . 2 _ Critical value of X 05,16 — 26.296 Critical value of F8,51 = 2.14 38 TABLE 4. 3 Joint Exogeneity of MB and ActG Wald Likelihood Ratio LaGrange 1. Levels 39.82 34.69 30.47 (Reject) (Reject) (Reject) 2. Logs 20.40 18.99 17.85 (Do Not Reject) (DO Not Reject) (Do Not Reject) Individual Exogeneity of MB F-Test 1. Levels 1.13 (Do Not Reject) 2. Logs 1.26 (Do Not Reject) Individual Exogeneity of ActG F-Test 1. Levels 2.73 (Reject) 2. Logs 0.64 (Do Not Reject) . . 2 _ Critical Value of X 05,16 — 26.296 Critical Value of F8,51 = 2.14 39 TABLE 4.4 Joint Exogeneity of UBR and ActG Wald Likelihood Ratio LaGrange 1. Levels 57.16 47.11 40.48 (Reject) (Reject) (Reject) 2. Logs 35.98 32.16 28.88 (Do Not Reject) (Do Not Reject) (Do Not Reject) Individual Exogeneity of UBR F-Test 1. Levels 1.35 (Do.Not Reject) 2. Logs 2.18 (Reject) Individual Exogeneity of ActG F-Test 1. Levels 4.21 (Reject) 2. 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