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"NH-4'" '4 REL 5?”; “1‘ $44414 with; 4" '0 “ 1'2,—"I':' 1' ‘IHII‘MII: r4] 1 ‘ 9'4 '8' I M q 4"':I"I '4‘ I M»- -1'“1982 KEVIN JAMES MURPHY All Rights Reserved AN ECONOMETRIC ANALYSIS OF THE GEOGRAPHIC DISTRIBUTION OF UNEMPLOYMENT RATES By Kevin J. Murphy A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Economics 1981 cont'OVErs/ 1350? market bEAEV‘IOr 0Y6 del‘EIOPS anj 0f “REVS!” If”? raids? W MES. ’ me "/"o / w/ I \- ABSTRACT AN ECONOMETRIC ANALYSIS OF THE GEOGRAPHIC DISTRIBUTION OF UNEMPLOYMENT RATES By Kevin J. Murphy This dissertation comprehensively examines the geographic distribution of unemployment rates in the United States. Past research identifies the dispersion of the distribution of unemployment rates both as a key policy parameter in the ongoing inflation—unemployment controversy and as an indicator of the allocative efficiency of the labor market. With these issues in mind, this study focuses on the behavior over time of several measures of unemployment rate dispersion, develops and estimates an econometric model of the geographic dispersion of unemployment rates, and analyzes the dynamic behavior of the under- lying random variables comprising the distribution of unemployment rates. The empirical work uses state data covering the l958—1978 period. The behavior of the dispersion in unemployment rates over time is first considered. The study concentrates on three principal measures of dispersion: the coefficient of variation, the variance, and the relative inter-quartile range. Regression analysis, taking cyclic and secular variation into account, shows that all three measures are invariant with respect to time. Time-series analysis of the variance Kevin J. Murphy in state unemployment rates further reveals that the variance is stationary. These results are noteworthy in that they directly contra- dict previous empirical work, based on more aggregate, regional data, that suggests that a marked increase in the geographic dispersion of unemployment rates has occurred over time. The second part of the dissertation derives, specifies, and estimates a model of unemployment rate dispersion. Both a labor supply equation, consistent with utility maximization on the part of workers, and a labor demand equation, consistent with profit maximization on the part of firms, are developed. These two equations are combined to form an unemployment rate equation, and this equation is applied to each state, yielding a system of unemployment rate equations. The unemploy- ment rates are non-linear in regression parameters. Therefore, employment rate equations, which are linear transformations of the unemployment rate equations and which are linear in the regression parameters, are estimated in place of the unemployment rates. The estimated regression equations permit a decomposition of the variance in employment rates, for each year of the sample, into component parts attributable to the explanatory variables. This decom- position indicates that cross-state differences in product market demand and in sensitivity to fluctuations in product market demand play predominant roles in determining the dispersion in employment rates. In addition, cross-state differences in frictional and structural elements in the economy exert a pronounced effect on the dispersion. Cross-state differences in factor costs and in human capital accumulation, on the other hand, exercise modest, second-order influence on the dispersion. And cross-state differences in the age and racial composition o.‘ the labor ‘ erflorent re The f behavior of s that there is which tne sta‘ change in thii in tnese long. relatively lo. Jfietployrert 1 relatively hig “Wicrent i great internal variance of U we tine Qerc Kevin J. Murphy of the labor force have very little effect on the dispersion in employment rates. The final portion of this dissertation examines the dynamic behavior of state unemployment rates. This analysis indicates not only that there is a great deal of variation in the relative positions which the states occupy over the business cycle but also that much change in this distribution occurs in the long run. Regional patterns in these long run changes are identified. Northern states, which were relatively low unemployment rate states during the 19605, become high unemployment rate states in the l970s, and Southern states, which were relatively high unemployment rate states in the l9605, become low unemployment rate states in the l970$. Notably, though there is this great internal flux within the distribution of unemployment rates, the variance of this distribution nevertheless remains stationary throughout the time period studied. In memory of my Mother Margaret Manley Murphy ii in I of debts, er: ‘O arkrfi -‘ ', W b NME‘O FT». ‘ reps: brim: v , r- . ACKNOWLEDGEMENTS In this undertaking I have accumulated a sizeable number of debts, and it is with great pleasure that I take this opportunity to acknowledge the contributions of the people and organizations who helped bring this project to fruition. My very special thanks go to Professor Daniel Hamermesh, Chairman of my dissertation committee, who not only made invaluable comments and suggestions on the substance and style of this thesis but who indeed has inspired and helped cultivate my interest in and love of labor economics in general. His contribution to my intellectual development is beyond measure and I owe him much. I would also like to thank Professors Cynthia Rence and Janet Kohlhase for many long hours spent reading the various drafts of this dissertation and for their countless insightful suggestions. In addition my thanks go to Professor Charles P. Larrowe for the generous contribution of his time and effort as the fourth member of the dissertation committee. This dissertation was fully funded by U.S. Department of Labor Grant Number DD-26-80-0l2, and I gratefully extend my thanks to the Department of Labor and to Professor Sar Levitan and the members of the National Council on Employment Policy for selecting my initial pro- posal for funding. Of course, neither the Department of Labor or the National Council are responsible for any remaining errors, nor do they necessarily subscribe to the views and policy recommendations expressed within. I also gratefully acknowledge valuable editorial comments made by Mr. Paul Murphy and the expert typing of the manuscript by Mr. Donald Lewsader. Finally, I would like to thank two very special people. To my father, Kevin T. Murphy, I owe an immense debt of gratitude for his unending support and encouragement through the years. To my wife, Alicia Aikin, I owe my deepest thanks not only for her love and her patience in awaiting the completion of this project but also for very useful comments and suggestions made with regard to the thesis itself which ultimately improved the final product. iv TABLE OF CONTENTS LIST OF TABLES ........................... vii LIST OF FIGURES .......................... x Chapter I. INTRODUCTION ......................... I II. THE DISPERSION OF STATE UNEMPLOYMENT RATES, 1961-1978 ......................... 7 2.l Introduction ..................... 7 2.2 The Relevance of the Geographic Dispersion of Unemployment for Policy .............. 7 2.3 Previous Empirical Evidence .............. ll 2.4 Analysis of the Dispersion in State Unemployment Rates--The Coefficient of Variation .......... 13 2.5 The Behavior of Alternative Measures of Unemployment Rate Dispersion: Variance and Relative Inter-Quartile Range ........... 24 2.6 Conclusion ...................... 36 III. THE DISPERSION MODEL .................... 43 3.1 Introduction ..................... 43 3.2 Specification of the State Unemployment Rate Function ....................... 43 3.3 A Two-Sector Model of Employment Rate Dispersion ...................... 53 3.4 The Full Model of Employment Rate Dispersion ..... 59 3.5 Conclusion ...................... 6l IV. EMPIRICAL ESTIMATION OF THE DISPERSION MODEL ......... 63 4.l Introduction ..................... 63 4.2 The Data Set ..................... 64 4.3 The Regression Results ................ 67 4.4 Regional Patterns in the Regression Coefficients . . . 8D 4.5 Empirical Results from the Full Dispersion Model . . . 86 4.6 Conclusion ...................... 115 V. A REFORMULATION OF THE MODEL IN A TWO-STAGE LEAST SQUARES FRAMEWORK ..................... 123 U1 U! U‘ U“ L. (A) N —-J r" T _ 1 VI. A SHAVE t‘EVCL >—< O" 0‘ '\.) -—J —4 6.3 99:52 :0 6.4 “IN-n w , m. wuL‘JSI’. l 1::ftmvn- ‘ I» ll.x.‘U‘L.J FA AbJrr.‘ V 5' ' Ly‘b‘i VI. :63'OPP'en “L QK‘NHU’NV .w. 5.l Introduction ...................... 123 5.2 The Two-Stage Least Squares Results .......... 125 5.3 Regional Patterns in the ZSLS Coefficients ....... I31 5.4 Two-Stage Least Squares and the Full Dispersion Model ......................... 134 5.5 Conclusion ....................... 145 VI. DYNAMIC ANALYSIS OF THE DISTRIBUTION OF STATE UNEMPLOYMENT RATES ..................... 149 6.l Introduction ...................... 149 6.2 The Rank Distribution of State Unemployment Rates ......................... 153 6.3 Dynamic Change in the Distribution of State Unemployment Rates ................... I65 6.4 Conclusion ....................... I93 VII. CONCLUSIONS .......................... I98 APPENDICES ............................. 203 APPENDIX A--DATA SOURCES .................. 203 APPENDIX B--DECOMPOSITION OF NET VARIANCES T0 COMPONENT VARIANCES AND COVARIANCES ....... 205 APPENDIX C--TOTAL U.S. TRANSFER PAYMENTS: 196l-l978 ..... 215 APPENDIX D--PERCENTAGE OF STATE TRANSFER PAYMENTS PAID AS UNEMPLOYMENT INSURANCE BENEFITS: l969 and 1975 .................. 216 APPENDIX E--THE MANN-WHITNEY U TEST ............. 218 BIBLIOGRAPHY ............................ 222 vi 2-7. 2-8. 2-9. 4-1. 4-3. 4-4. 4-6. 4-7. 4-8. LIST OF TABLES Average Coefficients of Variation for l96l-1964 and 1965-1973 ........................ Variance, Standard Deviation, Labor Force Weighted Average, and Coefficient of Variation in State Un- employment Rates: l96l-1978 ............... Average Coefficients of Variation for l96l-1964 and l965-l973 (State Data) ................. Regression Results: State Coefficients of Variation . . . . Unemployment Rates of Eleven Northern States: 1962-1965 . . . Sample Autocorrelation Function of Variance in State Unemployment Rates: l96l-1978 .............. Regression Results: Variance in State Unemployment Rates .......................... Relative Inter-Quartile Range: 1961-1978 ......... Regression Results: Relative Inter-Quartile Range ..... Regression Results: State Employment Rates ........ Weighted Regional t-Statistics Associated with the OLS Coefficients .................... Variance of Log Employment Rates: 196l-1978 ........ Net Variances Of the Employment Rate Contributions of the Independent Variables and of the Residual Term Rank Order_of State Personal Income Coefficients ..... Percentage Growth in Real Personal Income by State: l96l-l978 .................... Variance in Employment Rate Contributions of Transfer Payments ........................ Ten Largest and Ten Smallest Constant Coefficients and Associated Labor Force Weights ........... vii ll 15 15 T7 20 26 28 33 34 69 88 90 99 4-9 Ratio c 0f 'A'd Etiec Const S'I. ZSLS n9 5'2. "€lghte. and 2 5-1 Heighte: ZSLS ( 5-21 ZSLS Net of the 64 State an; 6-2. Neigrtej 0f Sta 6'1 Pairwise Avera; 6.4. States ll Rates IS‘ Regresst 6.6‘ States w COBff1( E ”7 REQTESSI GFOUQS .Q 6" P€rcentac 6.3 Average: the 19; ‘JP . V J Re970mg] fr0m tr 641 . Shifts In L‘ l2. RESIORa] Irons 1: 33 I Annual 1"] Rate [0 3~2. 5—1. 5-3. 5-4. 6-2. 6-3. 6-4. 6-5. 6-7. 6-8. 6-10. 6-11. 6-12. 8-1. Ratio of the Net Variance in Employment Rate Effects of Wages to the Net Variance in Employment Rate Effects of Personal Income, Transfer Payments, Constants, and Property Income for 1978 ......... ZSLS Regression Results: State Employment Rates ...... Weighted Averages, Variances, and t-Statistics of OLS and ZSLS Coefficients .................. Weighted Regional t-Statistics Associated with the ZSLS Coefficients .................... ZSLS Net Variances of the Employment Rate Contributions of the Explanatory Variables and the Residual Term State Unemployment Rate Rankings: 1961-1978 ........ Weighted Regional Averages and Standard Deviations of State Unemployment Rate Ranks (1961-1978) ...... Pairwise Mann-Whitney Test Results Comparing Regional Average Unemployment Rate Ranks (1961-1978) ...... States Most Prone to Very Low or Very High Unemployment Rates .......................... Regression Results: State Unemployment Rate Ranks ..... States with Statistically Significant Regression Coefficients in the Aggregate Unemployment Rate ..... Regression Results: Cyclic Sensitivity of Major Industry Groups (1958-1978) ................... Percentage Share of Area Income by Industry ........ Average Change in State Ranks from the 19605 to the 19705 ........................ Regional Classification of State Rank Changes from the 19605 to the 19705 ............... Shifts in State Rank from 1961 to 1978 .......... Regional Classification of State Rank Changes from 1961 to 1978 .................... Annual Variances and Covariance in the Employment Rate Contributions of Personal Income .......... Annual Variance and Covariances in the Employment Rate Contributions of Transfer Payments ........... viii 111 127 129 133 136 154 171 175 180 184 186 190 205 Annual Annual Contrl Annual Contri Annaal Contri Annual Contri Annaal Contrf 8-3. 8-5. 8-6. 8-7. 8-8. 8-9. 8-10. D-2. Annual Variance and Covariances in the Constants ....... 207 Annual Variance and Covariances in the Employment Rate Contributions of Property Income .............. 208 Annual Variance and Covariances in the Employment Rate Contributions of the Wage Rates ............... 209 Annual Variance and Covariances in the Employment Rate Contributions of Educational Attainment ........... 210 Annual Variance and Covariances in the Employment Rate Contributions of the Teenage Labor Force .......... 2]] Annual Variance and Covariances in the Employment Rate Contributions of the Non-White Labor Force ......... 212 Annual Variance and Covariances in the Employment Rate Contributions of AGNP/PGNP ................. 213 Annual Variance and Covariances in the Residual Terms . . . . 214 Percentage of State Transfer Payments Paid as Unemployment Insurance Benefits in 1969 ........... 216 Percentage of State Transfer Payments Paid as Unemployment Insurance Benefits in 1975 ................. 217 ix 2-1. 2-3. 4-1. 4-3. 4-4. 4-5. 4-7. 4-8. 4-10. 4-11. 5-2. 5-3. 5-5. 5-6. 5-7. LIST OF FIGURES A Non-Stationary Variance in Unemployment Rates ....... The Variance in State Unemployment Rates: 1961-1978 ..... Correlogram of the Variance's Autocorrelation Function Net Variance--Personal Income ................ Net Variance--Tran5fer Payments ............... Net Variance--Constant Terms ................ Net Variance--Property Income ................ Net Variance--Wages ..................... Net Variance--Educational Attainment ............ Net Variance--Teenage Labor Force .............. Net Variance--Non-White Labor Force ............. Net Variance--AGNP/PGNP ................... Net Variance--Residuals ................... Hypothetical Frequency Distributions of the Employment Rate Contributions of Personal Income ...... Net Variance--Personal Income ................ Net Variance-~Transfer Payments ............... Net Variance-~Constant Terms ................ Net Variance--Property Income ................ Net Variance--Wages ..................... Net Variance--Educationa1 Attainment ............ Net Variance--Teenage Labor Force .............. 25 25 25 91 92 93 94 95 95 96 95 95 96 97 137 138 140 141 142 5-8. Net Variance--Non-White Labor Force ............ 5-9. Net Variance--AGNP/PGNP .................. 5-10. Net Variance--Residuals .................. xi 142 142 142 CHAPTER 1 INTRODUCTION Macroeconomists traditionally center attention on the aggregate rate of unemployment as a measure Of labor market performance. In the past twenty years the U.S. rate of unemployment achieved a maximum of 8.5 percent in 1975 and a minimum of 3.7 percent in 1969. Focusing sole attention on this particular statistic, however, ignores very wide disparities in unemployment experience across geographic areas. For example, decomposing the U.S. labor market by state in 1975 reveals unemployment rates as high as Michigan's 12.5 percent and as low as North Dakota's 3.6 percent. An entire distribution of state unemployment rates exists between these upper and lower limits. In any given year, therefore, one observes a dispersion of area unemployment rates about the national rate of unemployment. Over time this dispersion varies considerably. From a policy standpoint the dispersion in unemployment rates is of interest for several reasons. A well-known hypothesis holds that a ceteris paribus increase in the sectoral dispersion of unemployment rates leads to an increase in the rate of change in the wage level. Since the rate of change in the wage level is a prime determinant of the level of inflation, an increase in the dispersion of unemployment rates should ultimately lead to an increase in inflation. to I? fisca In a related sense, if areas differ substantially with respect to their individual unemployment rate experience, then expansionary fiscal or monetary policy may induce wage levels to increase in low unemployment rate areas before causing a decline in unemployment rates in high unemployment rate areas. Thus a policy objective of full employment is attainable only at the expense of a high rate of inflation. Furthermore, the dispersion in unemployment rates is traditionally identified as one measure of how well the labor market performs its resource allocation function. If the dispersion of unemployment rates increases over time, then high unemployment rates become more concen- trated in some areas, leading to the conclusion that the economy's level of structural unemployment is rising. In this study I examine three main areas. First, I analyze various measures Of unemployment rate dispersion for the eighteen year period, 1961-1978, in order to identify time trends and systematic f1uCtuationsithhe dispersion. Second, I specify and estimate a formal model of the determinants of the dispersion in state unemployment rates to further the general understanding of and to provide policy makers with a guide to what factors are most responsible for change in the dispersion over time. Third, I analyze the underlying pattern of states comprising the unemployment rate distribution to distinguish regional patterns and structural change in the distribution over time. ChapterI] focuses attention on the behavior of the dispersion of state unemployment rates from 1961 to 1978. Results presented in this chapter contradict previous research suggesting that the unemployment rate dispersion experienced a substantial increase in the mid-19605. LITE NC' 3 .Or 7‘ u u h pi A .h ‘1 u t lU $ u ul ‘1 - fury n! as 54 I El ‘5 r. ink I.‘ | AER ‘4.- ..9 l! .,.',I _ ll ‘5“ 1‘ D b‘ 1 VA. . v c 0 TD \ In \I a \J' S Ru 5 AI 5 S Furthermore, Chapter'IIshows empirically that the dispersion Of state unemployment rates is a stationary time series. Contrary to other work, this finding implies that the U.S. economy demonstrates no tendency toward greater and greater levels of structural unemployment over time. Chapters III through V provide a model of the determinants of the geographic dispersion of unemployment rates. Combining the neo- classical theories Of utility and profit maximization, Chapter III supplies the theoretical specification of the model. This chapter develops a two-step procedure whereby the individual state unemployment rates are specified as functions of a set of state-specific demand- supply shift variables. These equations are then substituted into the measure of unemployment rate dispersion--the statistical variance in state unemployment rates--showing it to be a function of cross-equation variances and covariances in the explanatory variables. I then analyze these variances and covariances to distinguish the level of importance of each of the explanatory variables in determining the dispersion of state unemployment rates. Chapter IV carries out the first step of the above procedure by using least squares regression analysis to estimate the state unemploy- ment rate equations. 'Hueestimated regression coefficients, in turn, are analyzed for regional patterns. Not surprisingly, I find that variables reflecting demand conditions in the product market (specifically, state personal income and state transfer payments) exert a pronounced effect on state unemployment rates in the industrial Northeast, but exert little effect on relatively less industrialized areas such as states in the South and in the West North Central regions. Implementation of the second step of the model reveals a hierarchy of effects attributable to the explanatory variables. The primary determinants of the dispersion in unemployment rates are differing sensitivities to changes in product market demand conditions and differing levels of structural and frictional unemployment across states. Cross-state differences in factor costs and educational attainment are of somewhat secondary importance in determining the dispersion. Cross-state differences in demographic variables such as age and race exert very little influence on the overall dispersion. Chapter V reports the results of a re-estimation of the state unemployment rate equations in a two-stage least-squares framework, taking into account the simultaneity that presumably exists between transfer payments and unemployment rates. Though the range of the estimated coefficients expands somewhat, the essential results of the variance-covariance analysis remain qualitatively unaltered. The conclusions drawn in Chapter IV, therefore, are robust. Chapter VI concentrates on the underlying elements of the distribution--the individual state unemployment rates. The analysis in this chapter yields several important results. Regional patterns in the distribution are identified: states of the West North Central region maintain the lowest unemployment rates throughout the period of study while states in the Pacific region suffer the highest unemployment rates. Furthermore, the results of this chapter show that the states demonstrate a substantial tendency to shift positions within the rank distribution of state unemployment rates over the business cycle. In addition, Chapter VI indicates that a major structural Change in the distribution of state unemployment rates occurred in the 19705. Specifically, states of the Northeast and East North Central regions, while relatively low unemployment rate states during the 19605, became relatively high unemployment rate states in the 19705. Conversely, Southern states, while relatively high unemployment rate states during the 19605, became relatively low unemployment rate states in the 19705. Chapter VII reports the study's conclusions and policy implications. The fundamental contributions of this dissertation lie both in its research methods and in its conclusions. This study uses state rather than regional data, providing a closer approximation to true geographic labor markets. Chapter II shows that use of regional data led other researchers to inapprOpriate conclusions regarding changes in the level of the dispersion. In addition, this study utilizes various analytic techniques and empirical measures in examining the behavior of the dispersion in state unemployment rates over time. Chapter II reveals that direction of movement in the dispersion is completely invariant to one's choice of functional form for the dispersion and to the particular test procedure employed. Furthermore, Chapter VI implements tests which determine the extent of structural change in the rank distribution of state unemployment rates over time. This chapter indicates that much rank shifting among the statestakespflace both over the business cycle and in the long run. Most importantly, this work develops a new mOdel through which the determinants Of the dispersion in unemployment rates may be analyzed. Neoclassical theories of profit and utility maximization are integrated in a two-step procedure, allowing one to decompose the dispersion into component parts. Empirical estimation of the model leads overwhelmingly to the conclusion that the dupersion is primarily a function of geographic differences in the shength and structure of product demand. The ; relevance of OfeCO-noric ; SECular yam latter Sectlc Introduce “eh conclusions 0 CHAPTER II THE DISPERSION OF STATE UNEMPLOYMENT RATES, 1961-1978 2.1. Introduction The purpose of this chapter is twofold. It first establishes the relevance of the geographic dispersion in unemployment ratesikn~purposes of economic policy. The remainder of the chapter examines cyclic and secular variation in the dispersion during the last twenty years. The latter sections review previous empirical findings and, more importantly, introduce new analyses that lead to results that directly contradict conclusions drawn in other work. 2.2. The Relevance of the Geographic Dispersion of UhempTOyment for POTicy Knowledge of the determinants of the dispersion of unemployment is useful from a policy standpoint. A well-known hypothesis, originating with Lipsey, states that a ceteris paribus increase in the sectoral dispersion of unemployment leads to an increase in the rate of change in the wage level.1 G.C. Archibald provides the general mathematical conditions which must be met to Obtain this result.2 Using state data to estimate a macro-Phillips relationship, Archibald finds the impact of the dispersion on the rate of wage inflation to be quite sizable and statistically significant. One as follows. change in rl therefore, 1' various .ri Cr econo'y COOS ”ne’PIOFED‘. la'DOr Parke: 1'-“.crease in in the high lO'w’ rate sec causes the r t0 fall, but ”‘99 in th “Aversion , One can summarize the intuitive reasoning behind this hypothesis as follows. Change in the macro-wage level is an aggregation of wage change in micro-markets in the economy. A macro-Phillips relationship, therefore, is an aggregation over similar relationships existing in the various micro-markets. For conceptual simplicity, suppose a two-sector economy consisting of a high unemployment rate sector and a low unemployment rate sector. If wage rates adjust more rapidly in tight labor markets than in loose labor markets, then a ceteris paribus increase in the dispersion (i.e., an increase in the unemployment rate in the high rate sector, and a decrease in the unemployment rate in the low rate sector such that the macro-unemployment rate is left unchanged) causes the rate of wage increase in the high unemployment rate sector to fall, but to decline less than the increase in the rate of wage change in the low unemployment rate sector.3 Thus, an inCrease in dispersion augments the overall rate of wage inflation. Another reason advanced for concern with the dispersion-~and, by implication, its determinants--is that if areas differ substantially with respect to their individual unemployment experience, then general expansionary fiscal or monetary policy might induce wage levels to increase in low unemployment areas prior to any decline in unemployment 4 Thus the policy objective (e.g., rates in high unemployment rate areas. full employment) is attainable only at the expense of a high rate of inflation. It is reasonable to presume that, at any randomly selected point in time, excess demand characterizes labor markets in some areas while excess supply characterizes labor markets in other areas.5 An expansionary policy measure adds to the level of demand in all regions in the economy. The additional demand created in tight labor markets, however, has no effect on the local unemployment rate in these areas. The added demand in loose labor market areas, on the other hand, elicits a decline in unemployment rate levels in these areas, with little or no effect on price levels. Policy measures focused on loose labor market areas alone are therefore likely to effect a larger decline in the average rate of unemployment for a smaller overall increase in the average price level. The dispersion of unemployment is also important because it serves as a measure of how well the labor market performs its resource allocation function. In order to see why,consider the following example. Once again assume a two-sector economy. Assume also that this economy is in an initial state of full employment, where, in this context, full employment signifies the existence of zero excess demand for labor in both sectors. Hence each sector is at its frictional lower-bound unemployment rate-~an unemployment rate purely determined by worker and firm search. Some dispersion necessarily exists in these unemployment rates since information is likely to diffuse at different rates in the two sectors and since no assumption is made here of firm or worker homogeneity across sectors. Suppose, now, that an exogenous decline in the demand for labor occurs in the relatively high unemployment rate sector. This decline causes an increase in involuntary unemployment in this sector (through layoffs, firings, etc.), and hence raises the overall dispersion of unemployment in the economy. Assuming competitive forces are at work, the additional unemployment in the affected sector should create down- 1O ward pressure on this sector's relative wages. The newly unemployed are unable to find work at their old wage, and employed workers notice their wages declining relative to wages of workers in the low unemploy- ment rate sector. Given factor mobility, workers leave the initially affected sector and look for work in the unaffected sector. In this manner the additional unemployment experienced in the high unemployment rate sector diffuses throughout the economy. Eventually, through the operation Of the economy's inherent equilibrating forces, wages rates once again equalize and the initial dispersion of unemployment--as determined by the distribution of frictional unemployment--returns. The equilibrating forces in the economy may be weak, however. Workers may choose not to leave the initially affected sector for a variety of reasons. Explicit and implicit contracts between workers and firms in the affected area may prevent wages from falling enough in this sector to induce any significant emigration. In addition, ties with family and friends within the affected area may be strong enough to inhibit at least some of the out-migration which economic theory predicts. It may be the case, therefore, that the dispersion in unemployment rates does not adjust rapidly back to what might be identified as its optimal level, or that level of dispersion consistent with zero excess demand in all geographic markets. One may infer, then, that the labor market is not performing its allocative function as efficiently as might be hoped. net-te netnan‘ They aT labor I “3183 *. AV ad‘s Jr. ‘.' l L") I. / 11 2.3. Previous Empirical Evidence In the "structural” versus "insufficient aggregate demand" debate of the early 19605, the structuralists held that the allocative mechanism of the U.S. labor market had indeed become less efficient. They argued that, because of growing structural imperfections in the labor market, area unemployment rates had become more dispersed over time.6 The bulk of the empirical evidence, however, presented by Edward F. Denison,7 Otto Eckstein,8 9 and Lowell Gallaway, among others, served to refute the structuralist hypothesis as a credible description of reality in the labor market and suggested thatruachange in the geographic dispersion had taken place. By 1965, the controversy was seemingly laid to rest. In 1975 Andrew Sum and Thomas Rush presented new empirical evidence indicating that the geographic dispersion Of unemployment rates increased radically from relatively low levels in the early 1960s to a much higher level from 1965 to 1973 (which is the last year of their sample period)-10 Table 2-1 summarizes their results. Table 2-1. Average Coefficients of Variation for 1961-1964 and 1965-1973. Avg. Coefficient of Variation 4 Region Data 9 Region Data CV"61-'64 . .097 .156 CV..65_.73 .227 .221 Source: A.M. Sum and T.P. Rush, "The Geographic Structure of Unemployment Rates," Monthly Labor Review, 3/75, p. 4 and p. 5. As t coefficient the Bureau 0 the standard average rate and 12 As their primary gauge of dispersion, Sum and Rush use the coefficient of variation measured over regional aggregates defined by 1] The coefficient of variation equals the Bureau of Labor Statistics. the standard deviation in regional unemployment rates divided by the average rate of unemployment: —- 2 fiaitwit ‘ “t) (2.1) CVt(u) = __ “t where i indexes region i; ait is the proportion Of U.S. labor force residing in region i in year t; and U, is the labor force weighted average unemploy- ment rate in year t. The coefficient of variation allegedly purges fluctuations in the dispersion resulting from purely cyclical effects.12 The results reported in Table 2-1 suggest an alarming increase in the geographic dispersion of unemployment of over 134 percent using 4-region data and of almost 42 percent using the more disaggregate 9-region data. In both cases, a t-test for equality of means indicates that one cannot reject the hypothesis that the means of the two periods differ.13 These results imply that in the middle 19605 unemployment became more concentrated in some labor markets and that equilibrating market forces did not act to redistribute this excess unemployment during the eight year period, 1965-1973. A noteworthy shortcoming of the Sum and Rush study, however, is its reliance on data measured over very large regional aggregates. cos;ri APZFDX 13 Theoretically, one desires data collected over true geographic labor markets.14 Given great disparities in population, institutional, and industrial characteristics across states, individuals in different states are likely to respond differently to marginal changes in economic variables, on average. Findings at the regional level reflect only an average of what is occurring in the individual states that comprise the region. The Census regions, therefore, are likely to approximate true geographic labor markets quite poorly. This study assumes that states approximate geographic labor markets much more closely than regions. All empirical work to follow uses state data as its basis of measurement.]5’16 2.4. Analysis of the Dispersion in State Unemployment Rates--The Coefficient of Variation Given the inadequacy of regional data in analyzing the dispersion in unemployment rates, I repeat the Sum and Rush calculations here using state data. In this way the robustness Of their conclusions can be tested. Moreover, if a large increase in dispersion does occur in 1965, the extended sample period of this study (1961-1978) allows a test Of whether or not the labor market re-adjusts the dispersion to its relatively low pre-1965 levels in the post-1973 years. Table 2-2 lists the variance, standard deviation, labor force weighted average, and coefficient Of variation of unemployment rates for the years 1961 through 1978. These statistics are computed using unemployment rate data collected on the fifty states.17 Table 2-3 summarizes the results on the state coefficients of variation so that comparison may be made with Table 2-1. ozcu two Sign is tl Ye - 14 The state coefficients of variation make less clear the occurrence of any change in unemployment rate dispersion between the two periods. A test for equality of means yields a t-statistic significant at the 95% level of confidence.18 One's initial reaction is therefore to reject the hypothesis that the means of the two periods are the same. The increase in average dispersion implied in Table 2-3, however, is less than 5 percent. This increase is substantially less than the percentage increase in average dispersion implied for either four or nine region data (134 percent and 42 percent, respectively). Moreover, reference to Table 2-2 reveals that the true outliers are the dispersions Of 1963 and 1964. The average coefficient of variation for 1961 and 1962 is .252. Therefore, no long-term change in the coefficient of variation is implied, merely a short-term deviation. Such short-term deviations are perfectly consistent with the notion of an adjusting labor market. Though the coefficient of variation presumably provides a measure Of dispersion free from cyclic variation, no guarantee exists that it actually accomplishes this task. A proportionate increase in the standard deviation of unemployment rates owing to a decline in aggregate demand may not necessarily be matched by an exactly propor— tionate increase in the unemployment rate. Using coefficients of variation defined over 4 and 9 region data, Sum and Rush indeed find that this measure of dispersion is not invariant to the level of 19 Their results indicate that the coefficient of aggregate demand. variation become smaller as the unemployment rate increases, other things equal. If the state coefficient of variation is not invariant to cyclic s ‘1‘ d‘v 'P‘Ul ‘ Ea / // 15 Table 2-2: 'Variance, Standard Deviation, Labor Force Weighted Average, and Coefficient of Variation in State Unemployment Rates: 1961-1978. t 02(0) 0(u) O- o/U 1961 3.441 1.855 7.334 .253 1962 2.323 1.524 6.070 .251 1963 1.917 1.384 5.845 .237 1964 1.608 1.268 5.332 .238 1965 1.589 1.260 4.654 .271 1966 1.115 1.056 3.925 .269 1967 1.123 1.060 4.043 .262 1968 0.909 0.953 3.881 .246 1969 0.845 0.919 3.737 .246 1970 1.587 1.260 5.051 .249 1971 2.330 1.527 6.051 .252 1972 2.036 1.427 5.529 .258 1973 1.644 1.282 4.897 .262 1974 1.885 1.373 5.662 .243 1975 3.676 1.917 8.532 .225 1976 3.203 1.790 7.674 .233 1977 2.140 1.463 6.987 .209 1978 1.354 1.163 6.010 .193 Table 2-3: Average Coefficients Of Variation for 1961-1964 and 1965—1973 (state data). Avg. Coefficient of Variation 50 States CV..61-'64 .245 CV. I65_I73 .257 16 conditions, then some Of the difference in its average for the 1961- 1964 and 1965-1973 periods may be attributable to differences in aggregate demand across periods rather than to secular variation. The estimated regression equations of Table 2-4 account for the possibility that the coefficient of variation is not invariant to movements in the aggregate unemployment rate. All equations contain a constant term, the national unemployment rate (to proxy for aggregate demand), and either a continuous time trend (which allows for a smooth increase or decrease in the coefficient of variation over time), a dummy variable for the 1961-1964 period (which allows for an abrupt shift in the coefficient of variation in 1965), or both a time trend and a time dummy. OLS estimation yields unacceptably small Durbin- Watson statistics in this case; therefore, given the tendency of OLS to overstate significance levels under first order positive serial correlation, Table 2-4 presents coefficient estimates obtained by the Cochrane-Orcutt Iterative Procedure. The estimated unemployment rate coefficient is quite small and is statistically insignificant in all nine equations Of Table 2-4. Contrary to the results Of Sum and Rush, the state coefficients Of variation are invariant to the level of aggregate demand throughtout the sample period. As noted above, one desires this property in the measure of dispersion. The time trend is statistically insignificant in equations (1), (3), (4), and (6), indicating no upward drift in dispersion during the thirteen year period, 1961-1973. This finding contradicts the assertions of both the structuralists and of Sum and Rush, who contend 17 Table 2-4. Regression Results: State Coefficients of Variation ‘- Independent Variables Time Aggregate U.S. Time Time 2 Period Constant Unemployment Rate Trend Dummy R D.W. (1) 1961-1973 0.268 -0.00455 0.000981 -- .245 1.629 (~0.901) (0.736) (2) 1961-1973 0.259 -0.000773 -- -0.0356 .717 1.546 (-0.231) (-4.667) (3) 1961-1973 0.232 -0.00144 0.00224 -0.0359 .727 1.662 (-0.393) (0.670) (-4.519) (4) 1961,1962. 0.230 -0.000251 0.00217 -- .577 1.571 1965-1973 (—0.069) (1.007) (5) 1961,1962, 0.249 0.000928 -- -0.00533 .516 1.331 1965-1973 ( 0.256) (-0.301) (6) 1961,1962. 0.189 -0.000436 0.00528 0.0316 .626 2.153 1965-1973 (-0.120) (1.337) (0.829) (7) 1961—1978 ‘ 0.304 -0.00246 -0.00447 -- .639 1.532 (-0.651) (-1.639) (8) 1961-1978 0.186 -0.00252 -- -0.0383 .763 1.480 (-0.935) (-3.275) (9) 1961-1978 0.308 -0.00135 -0.00517 -0.0385 .798 1.539 441:0.450) (:2.760), 41:3.204) Notes: Dependent variable is the state coefficient of variation. The trend variable takes a value of l in 1962, 2 in 1962, and so The time dunnw'takes a value of 1 for the years 1961-1964 in equation (2) and the years 1961-1962 in equation (4). Its value is 0 otherwise. (4) t-Statistics are in parentheses. (5) Because of the high degree of serial correlation found in the original OLS equations, all nine equations are estimated by the Cochrane-Orcutt Iterative Technique. AAA w N —‘ vvv 18 that geographic unemployment rates become more dispersed with the passage of of time. Equations (2) and (3) of Table 2-4, on the other hand, both suggest that an upward shift in dispersion took place in 1965. The negative and highly significant coefficient Of the dummy variable in these two equations implies that the dispersion of unemployment rates was somewhat lower during the 1961-1964 period than during the 1965- 1973 period. Equation (2) of Table 2-4 implies an estimated constant of .223 for the early 19605, 14 percent less than that implied for the rest of the period, and equation (3) implies an estimated constant of .196 for the early 19605, 15 percent less than that implied for the rest of the period (.232). As suggested earlier, however, the coefficients of variation for 1963 and 1964 appear to represent simple short-term deviations from a long-term average. Equations (5) and (6) exclude these suspect years from the sample. Not surprisingly, the estimated coefficient of the dummy variable associated with 1961 and 1962 is statistically insignifi- cant. Equations (5) and (6), therefore, confirm that, though a short- term downward deviation in dispersion took place in 1963 and 1964, no long run shift in dispersion occurred in the 19605. While determining the precise cause of the deviation in the coefficient of variation in 1963 and 1964 is, at best, difficult, analysis of the State unemployment rate data for this period does yield some insight. Chapter VI below shows that the industrialized Northern states dominated the lower tail of the state unemployment rate distribu- tion, where state unemployment rates are less than the aggregate 19 unemployment rate, during the 19605. Table 2-5, however, reveals that these states--particularly the Northeastern states--were very slow to recover from the 1961 recession. Moving from 1962 to 1963, the aggregate unemployment rate fell 4.9 percent, but unemployment rates of only four of the eleven Northern states in the lower tail of the distri- bution declined at all. Since the average decline in unemployment rates in these lower tail states does not nearly match the percentage decline in the overall unemployment rate (2.0 percent versus 4.9 percent), the lower tail of the distribution swings inward towards the mean unemployment rate, implying a decline in the spread of the distribution.20 Moving from 1963 to 1964, the situation changes somewhat. Unemployment rates of all of the states listed in Table 2-5 decline from their 1963 levels, in 1964, and six of the eleven states experience percentage declines greater than the U.S. average. The average decline in unemployment rate in these eleven states is slightly less than that of the aggregate rate (7.3 percent versus 8.6 percent). In 1964, therefore, unemployment rates of the major states in the lower tail Of the distribution fell at approximately the same rate as the mean of the entire distribution, and, in turn, the coefficient of variation remained at its 1963 level. Table 2-5 further shows that, as the economy heated up in the mid- 19605, unemployment rates of states in the North began to fall at a proportionately faster pace than the economy's average unemployment rate. Comparing 1965 with 1964, ten of the eleven Northern states in the lower tail of the distribution experienced larger percentage declines in their unemployment rates than did the economy as a whole. Thus the 20 Table 2-5. Unemployment Rates of Eleven Northern States: 1962-1965. % Decline in Unemployment Unemployment Rate Rate from Preceding Year Area* 1962 1963 1964 1965 1963 1964 1965 U.S. 6.1 5.8 5.3 4.7 4.9 8.6 11.3 New England Connecticut 5.4 5.2 5.0 4.2 3.7 3 8 16.0 Massachusetts 4.9 5.2 5.1 4.4 - 6.1 1.9 13.7 New Hampshire 4.9 5.7 5.0 3.6 -l6.3 12.3 28.0 Rhode Island 4.8 5.1 4.6 3.6 - 6.3 9.8 21.7 Vermont 5.8 6.4 5.8 4.6 -10.3 9 4 20.7 Mid-Atlantic New Jersey 4.9 5.1 4.8 .1 - 4 l 5. 14 6 New York 5.7 .9 5.6 5.0 - 3 5.1 10.7 East North Central Illinois 5.0 4.7 4.0 3.5 6.0 14.9 12.5 Indiana 4.7 4.2 3.8 3.0 10.6 9.5 21.1 Michigan 6.3 5.0 4.4 3.5 20.6 12.0 20.5 Wisconsin 3.4 3.4 3.2 2.8 0.0 5.9 12.5 Labor Force Weighted, Average Rates of Decline for the Eleven Northern States 2.0 7.8 14.2 * Maine,Pennsylvania, and Ohio are excluded from the table since they were in the upper half of the unempyoyment rate distribution during this period. lower tail of the unemployment rate distribution actually shifts out in 1965, and the 14 percent increase in the coefficient of variation in this year clearly reflects this shift. One may therefore attribute the downward deviation in dispersion in 1963 and 1964 to the sluggish recovery from the 1961 recession of many of the Northern states. These states comprised the major portion of the lower tail of the unemployment rate distribution during this period. 21 Chapters IV and VI show that these Northern states are particularly sensitive to fluctuations in the level of aggregate demand. As the economy expanded in the mid-19605, the Northern states more than compensated for their weak performance early in the decade, and the coefficient of variation returned to its average level. Thus, whether one makes a rough comparison of sub-sample average coefficients of variation or conducts the more sophisticated regression analysis, the conclusion is the same: the dispersion in state unemploy- ment rates, measured by the coefficient of variation, remains relatively stable during the 1961-1973 period. Though the dispersion is quite stable from 1961 to 1973, Table 2-2 reveals a continuous decline in the coefficient of variation from 1973 through 1978--the years following the Sum and Rush study. The average coefficient of variation is .252 from 1961 to 1974, but only .215 from 1975 to 1978. Moreover, equation (9) of Table 2-4 yields a negative and statistically significant trend term, suggesting that the dispersion in unemployment rates declines continuously over the full eighteen-year period, 1961-1978, other things equal. Unfortunately, this decline in the coefficient Of variation for the later years of the sample cannot be interpreted as evidence that unemployment becomes more uniformly distributed on a geographic basis, or that large, geographic pockets of unemployment are less prevalent in the second half of the 19705. This decline in the coefficient of variation for the later years merely serves to highlight a methodological flaw involved in use Of the coefficient Of variation as a measure of structural/frictional dispersion. The methodological flaw 22 lies in assuming that a given unemployment rate imparts identical information about the strength of aggregate demand over all time periods. During the last twenty years, labor force participation rates of married females and of teenagers have increased.substantially.21 Average unemployment rates of these two groups are higher than that of prime-age males. The increase in share of the labor force by married females and by teenagers, therefore, implies an upward shift in the overall average unemployment rate, independent of the level of aggregate demand. At the same time, coverage Of the unemployment insurance laws has increased considerably with time. Unemployment insurance benefits reduce incentives to the unemployed to return to work and may induce individuals from high unemployment rate groups to enter the labor force.22 Holding the level of aggregate demand constant, both effects imply a higher average unemployment rate over time. Given these changes in the U.S. economy, the consensus holds that the non-accelerating inflation rate of unemployment underwent an increase during the period of this study. Holding constant for aggregate demand, the average rate of unemployment observed at time t is less than that observed at time t + s. Equivalently, holding constant for unemploy- ment rates, the relative strength of aggregate demand at time t is less than that observed at time t + 5. Though average U.S. unemployment rates in 1971 and 1978 are approximately identical at 6 percent, labor market conditions during the two years differ greatly. In 1971 the U.S. economy experienced a recession while in 1978 the economy enjoyed an expansion. The marked disparities in variances and standard deviations for the two years (as 23 shown in Table 2-2) reflect these cyclic differences. Thus the coefficient of variation does not standardize the dispersion for cyclic conditions throughout the entire sample period. The results of this section lead to two conclusions. First. the state coefficients of variation during the 1961-1978 period demonstrate little systematic time variation. This observation is directly opposite the results of Sum and Rush, whose results imply a large increase in unemployment rate dispersion in 1965. Their rather startling conclusion, therefore, appears to be an artifact of the highly aggregate data which they use. Indeed, their own results support this assertion. Table 2-1 indicates a substantial decline in the percentage increase in the coefficient of variation that they find when they base their results on 9-region rather than 4-region data. (Recall that 4- region data implies a 134 percent increase in 1965 while 9-region data implies only a 42 percent increase in 1965.) The second conclusion to be drawn from this section relates to the post-1973 period. Given the methodological problems involved with use of the coefficient of variation, little can be said concerning the behavior of the dispersion from 1974 through 1978. The following section suggests methods, however, which avoid the problems associated with use of the coefficient of variation and allow one to make judgments regarding the behavior of the dispersion over the entire time period. 24 2.5. The Behavior of Alternative Measures of Unemployment Rate Dispersion: Variance and Relative Inter-Quartile Range Time series analysis is one method which is an analytically appealing approach to testing for change in the structural/frictional dispersion in unemployment rates. If the pure structural/frictional dispersion in unemployment rates is rising, then the mean value of the variance in unemployment rates should increase over time as in Figure 2-1. One should find that the mean of the series is time dependent and, therefore, that the series itself is non-stationary. Observations drawn at time t and at time t + 5, representing identical points in the business cycle, should reveal a greater value of 02(u) for the later year, if the level of structural/frictional dispersion in unemployment rates is truly increasing. Figure 2-2 plots the variance in state unemployment rates. Table 2-6 lists the values of the sample autocorrelation function of the variance.23 Figure 2-3 is the correlogram corresponding to the sample autocorrelation function of Table 2-6. Figure 2-2 leads one to conclude that no perceptible upward trend exists in the variance over time. The series appears to be stationary, indicating that no change in the structural/frictional dispersion of unemployment takes place. Corroborating this conclusion, the sample autocorrelation function is initially large (p1 = .53), but drops off for lags of more than one period. Such behavior indicates a high degree of correlation in neighboring years, but little correlation between years well separated in time. The sample autocorrelation functions of non-stationary time-series, on the other hand, tend to 25 52m) 5--..-- -- + b--——- Figure 2-1. A Non-Stationary Variance in Unemployment Rates 51 52 573 54 55 55 57 55 59 7O 71 72 73 74 75 75 77 75 t Figure 2-2. The Variance in State Unemployment Rates: 1961-1978 Figure 2-3. Correlogram of the Variance's Autocorrelation Function 26 Table 2-6. Sample Autocorrelation Function of Variance in State Unemployment Rates: 1961-1978 Lag Period k pk 1 0.527 2 0.081 3 -0.041 4 0.073 5 —0.100 6 -O.323 7 -0.459 8 -0.381 9 -O.198 10 -0.047 11 -0.056 12 -0.042 13 0.062 14 0.286 15 0.174 16 0.008 ._.I ‘4 I O .075 27 remain large and positive as the number of periods lagged increases.24 As a further check of the time-series evidence reported on the variance of state unemployment rates in this section, a regression analysis similar to that presented in the previous section is conducted. As noted in footnote 12 and as can be seen in Figure 2—2, the variance is dependent on the level of aggregate demand. Notably, the variance tends to be much larger when aggregate demand is relatively weak. In the regression equations that follow the average U.S. unemployment rate proxies for aggregate demand in order to control for this cyclic dependence. Once one takes cyclic effects into account, the variance's behavior over time can be analyzed. The regression analysis includes a time trend to capture any smooth increase in dispersion which might have occurred over time. In addition, the regression equations make use of a dummy variable, defined over the 1961-1964 period, to determine if an upward shift in the variance took place in 1965. The relevant sample period for all equations extends from 1961 through 1978. Table 2-7 reports the results. Not surprisingly, all six equations of Table 2-7 yield a positive and highly significant regression coefficient for the average unemploy- ment rate. The regressions strongly confirm the intuition of footnote 12, indicating that an increase in the average unemployment rate causes a subsequent increase in the variance of state unemployment rates. Holding constant for cyclic variation, one can examine the behavior of the variance in state unemployment rates over time. Equation 283 .ouuc ucosao_aew:= mmucm>u ogu m. a .omwzgmguo o wee .wua—uenmp menu» as» so» — ya mapo> a moxou we “my a .om_zgwguo c was $2 eee $2 28» 9: Le _ co 2:: e 85.3 C .E e5 E 25:38 5 .3 -.~V mee_u.=ee e. 53.:eeeee a new .eee.-_ee_ memes 5;» Lee _ c5 ee_a> a “use“ .2 Amy .uuo .gnma vcouom on» c— N .manom on» we goo» awe?» oz» cw — we ospo> n muse» opna.uo> econ» ugh Rev .mmmogucogun cw use mu.um_uoum-a any .mmcmacm ammo. acucvvco an voguevumm m— Amy cowuonco m—vsz .maavccumu o>vuuemuv uuauco-ocoe;uou u:.m: voguevumm use Amv-Apv m:o_au=au “NV .muuug unease—gems: macaw c, mu:u.cu> my o—aa_co> acovcunmvcu A—v "mmuoz Amwe._ . Aoee.m v wee—-mem_ MN». as». -- -- wee.e -- emm.o e_P._- Nem_.pee_ Aev Ae_m.o-v ._m_.~.v wee—-mee_ emo.~ .me. -- -- .Nm.~- -- eme.e wom.~- Nee_._ee_ “my Am_m.eVAmme.o-v Aaee.~-v AFNm._-V Amee.e v pmm._ Nee. mme.e ”we.e- eem.e- Nme.e- eee.e Fe_.F- weep-_em. Aev nee—.m-v .e~m.m-. Aewm.~pv me~._ ewe. -- -- eme.o- eeo.o- mee.o ewe..- m~e_-_ea~ Anv Aee~.~-v Ammm.m_v emm._ mom. -- -- eem.o. -- eme.e mmm.~- e~e_-_ee_ ANS AeNe._-v A__N.c_v m_m._ ewe. -- -- -- eme.e- ~me.¢ op~._- wee_-_eo_ A.V .:.e Ne Ne.= Ne Fe eeeee some seeese_eeee= .emeeu ee.eea we.» mete .m.= .mse mo—am_cm> acmucammvc_ .mmumz acosxopasocs macaw :. mono—Le> "mu—:mwz covmmogaoz .uum open» 29 (l) of Table 2-7 utilizes a continuous time trend as the relevant time regressor. The estimated value of the coefficient is negative but statistically insignificant at conventional levels. This result nevertheless admits the possibility that the variance in state unemployment rates actually declines over the time period. The point estimate certainly implies that no increase in dispersion takes place over time. Equation (2) of Table 2-7 replaces the time trend with a time dummy, Tl. This variable takes a value of l for the years 1961-1964 and 0 otherwise. The associated regression coefficient is negative and statistically significant at the 99 percent level of confidence. One obtains a result here similar to that obtained in the previous section dealing with the coefficient of variation. Both measures of dispersion appear to experience an upward shift in 1965. Equations (5) and (6) drop observations for 1963 and 1964 from the regression sample, and they redefine Tl as 1 in 1961 and 1962, and 0 otherwise. Equation (5) uses the Cochrane-Orcutt Iterative technique, and equation (6) employs ordinary least squares. Equation (5) obtains a very large but highly insignificant negative coefficient for T1. Though the point estimate is in the appropriate direction for consistency with the upward shift in dispersion hypothesis, one cannot distinguish this estimate from zero with any reasonable degree of certainty. The OLS equation, on the other hand, yields a positive coefficient for the time dummy, significant at the 90 percent level of confidence (this t-value, of course, is most likely overstated given the apparent serial correlation). Other things equal, this result implies 30 that the dispersion of unemployment rates is greater in 1961 and 1962 than during 1965-1978. Serial correlation causes inconsistency in OLS estimates but not bias. Hence the estimated coefficients associated with T1 in equations (5) and (6) are both unbiased estimates of the true parameter. Equation (6), however, uses more information since the Cochrane- Orcutt procedure ignores the first Observation of the sample, 1961, in estimating 8T1“ Given the statistical insignificance of the two estimates(6T] of (5) is definitely insignificant, and ET, Of (5) is most likely insignificant) and given that a positive estimate is Obtained in equation (6), one must again conclude that the unemployment rate dispersions of 1963 and 1964 represent downward deviations from the long term level of overall dispersion and that no fundamental structural change in the level of dispersion occurs in 1965. Equation (3) Of Table 2-7 presents a third specification, including both the time trend and the time dummy of the previous equations. 8T1 is negative and statistically significant, but, as demonstrated above, this outcome is due to inclusion of 1963 and 1964 in the sample. More importantly, one finds the estimated coefficient of the time trend to be negative and highly significant in this equation. Other things equal, this finding suggests that the dispersion in state unemployment rates actually declines over the sample period. This result, however, is neither supported by the regression evidence on the coefficient of variation, which yields a trend coefficient of virtually zero, nor by the sample autocorrelation function of the variance, which indicates that the variance is a stationary time series. Hence, it may be more appropriate to say that the statistically significant and negative trend 31 coefficient provides very strong evidence that state unemployment rate dispersion is non-increasing over the sample period. Finally, the close Of the previous section articulates reservations concerning the change in the relationship between a given average unemployment rate and the overall level of aggregate demand that this unemployment rate implies. Equation (4) provides a test of whether or not this altered relationship causes any change in the degree Of association between the variance in unemployment rates and the average unemployment rate. As in equation (3) the specification includes both a dummy term for the 1961-1964 period and a trend term. In addition, the specification utilizes a dummy term, T2, equal to l for the years 1974-1978 and 0 otherwise, and an interaction term between the unemployment rate and 12. The interaction term allows for the possibility that the relationship between the variance and the mean unemployment rate is different from 1974 on. Given the increase in the degree of overall market tightness that a given unemployment rate implies in the later years of the sample period, one expects an increase in the unemployment rate to induce a relatively smaller increase in variance during the 1974-1978 period than during the rest of the sample. The results reported in equation (4) of Table 2-7 do not bear this reasoning out, however. The coefficient of the interaction term is statistically insignificant and is not in the hypothesized direction. In addition, though inclusion of the interaction term slightly reduces the coefficient of the trend term (in absolute value) from its level in equation (3), the trend remains statistically significant. The finding that a downward time trend in the variance exists is, therefore, robust, 32 and this finding further bolsters the conclusion that the dispersion in state unemployment rates is non-increasing over time. The regressionanalystsof the variance in state unemployment rates strongly argrees with the findings presented relating to the coefficient Of variation. In all cases, one finds no evidence indicat- ing that an increase in state unemployment rate dispersion occurs over time. Indeed, the regression results pertaining to the variance suggest that the dispersion may actually decline slightly with time. The results presented thus far are therefore quite consistent with the conception of an economy which adjusts relatively rapidly to disequili- brium conditions across geographic labor markets. Concomitantly, these results totally disagree with any notion of a labor market wherein unemployment rates become increasingly dispersed geographically and where no adjusting flows in factors of production occur across sectors. A singular result issues from the analysis thus far: the dispersion in state unemployment rates does not increase secularly over time. Nevertheless, this result may be an artifact of the functional form used to measure the dispersion. The coefficient Of variation and variance differ only by a variable factor of proportionality. In order to minimize the probability of a Type II error, a third measure of dispersion, the relative inter-quartile range, is considered here. The relative inter-quartile range is defined as follows: RIQR = “75%,t' “25%,t “50%.t where uj% t is the unemployment rate of the state located at the jth percentile of the state unemployment rate distribution in year t; 33 and ”25%,t < ”50%,t < ”75%,t Since one measures the inter-quartile range relative to the median unemployment rate, it is likely to possess a cyclic invariance property similar to that Of the coefficient of variation. Table 2-8 reports the values of this measure attained over the sample. Table 2-8. Relative Inter-Quartile Range: 1961-1978. t RIQR t RIQR 1961 .353 1970 .316 1962 .333 1971 .291 1963 .315 1972 .412 1964 .333 1973 .393 1965 .367 1974 .433 1966 .368 1975 .325 1967 .354 1976 .338 1968 .368 1977 .363 1969 .370 1978 .307 As in the case of both the coefficient Of variation and the variance, one can estimate regressions of the relative inter-quartile range that separate variation in the measure over time from cyclic variation. If state data is to corroborate the Sum and Rush findings, either a positive time trend or a positive shift in the dispersion measure must be evident in the regressions. The independent variables used in the analysis are a constant, the average U.S. unemployment rate, a time trend, and a time dummy for the 1961-1964 period. Table 2-9 contains the results. Similar to the coefficient of variation, Table 2-9 reveals that the relative inter-quartile range is invariant to cyclic swings in aggregate demand. In all four Of the regression equations the estimated coefficient associated with the average unemployment rate is very small (in absolute terms) significant. and is never statistically Table 2-9. Regression Results: Relative Inter-Quartile Range. Independent Variables Avg. U.S. Unemployment Time Time 2 Time Period Constant Rate Trend Dummy R D.W. (1) 1961-1973 0.386 -0.00912 0.00175 -- .172 1.680 (-0.933) (0.654) (2) 1961-1973 0.390 -0.00654 -- -0.0166 .167 1.667 (-0.532) (-0.606) (3) 1961-1973 0.385 -0.00785 0.00124 -0.00652 .173 1.687 (-0.569) (0.266) (-0.l37) (4) 1961-1978 0.395 -0.0102 0.00153 -- .138 1.618 (-1.498) ( .875) (5) 1961-1978 0.396 -0.00700 -- -0.0193 .142 1.651 (-l.064) (-0.916) (6) 1961-1978 0.395 -0.00818 0.000608 -0.0130 .144 1.637 (-0.852) (0.175) (-0.311) Notes: ( ( ( ( 1) Equations are estimated by ordinary least squares. 2) Dependent variable is the relative inter-quartile range. 3) The time dummy takes a value of l for theyear 1961-1964 and 0 otherwise. 4) t- tatistics are in parentheses. 777% T3 35 Table 2-9 also confirms the evidence presented above concerning movement in the dispersion Of unemployment rates over time. Equations (1), (3), (4), and (6) use a continuous time trend as a regressor. In all cases, the estimated coefficient corresponding to the time trend is virtually zero and is never statistically significant. NO secular increase in dispersion is apparent, therefore, either during Sum and Rush's sample period, 1961-1973, or during the longer sample period of this study, 1961—1978. Equations (2), (3), (5), and (6) of Table 2-9 employ a dummy variable corresponding to the 1961-1964 period as a time regressor. The estimated coefficient corresponding to this variable is statistically insignificant in all equations. Recall that for both the coefficient of variation and the variance one finds a negative and statistically significant coefficient for this variable (indicating an upward shift in dispersion in 1965). Removing observations for 1963 and 1964 drove the coefficient to statistical insignificance in both cases. Given the insignificance of the estimated coefficient associated with the time dummy in Table 2-9, on the other hand, the dispersion, when measured by the relative inter-quartile range, shows no tendency in 1963 and 1964 to be less than the long term level of dispersion. Both this and the immediately preceding section carefully examine several measures of state unemployment rate dispersion for evidence of secular increase over time. All measures of dispersion are subjected to a regression analysis that holds constant for swings in aggregate demand and allows one to determine variation over time in the respective dispersion measure. In addition, a time-series analysis of 36 the variance in state unemployment rates is conducted that allows one to determine whether or not this series is stationary (i.e., whether or not the mean value of the variance is non-time dependent). Finally, the study makes a comparison of mean values in the coefficient of variation across sub-sample periods. All test evidence presented in Sections 2.4 and 2.5 leads to overwhelming rejection of the hypothesis that a secular increase in dispersion occurred during the eighteen year sample period. One finds no decline in the efficiency with which the U.S. labor market performs its resource allocation function during the 1961-1978 period. 2.6. Conclusion From a policy standpoint the geographic dispersion of unemploy- ment rates is of interest for three reasons. First, an increase in the dispersion leads to an increase in the rate of change in the wage level and, therefore, to an increase in the rate of inflation. Second, a narrower dispersion in unemployment rates facilitates implementation of general expansionary fiscal or monetary policy. Third, the level of dispersion in unemployment rates is one indicator of how well the labor market performs its resource allocation function. For each of these reasons, knowledge of movements in the dispersion, and of the determi- nants of the dispersion, is of concern. This chapter considers movements in the level of the dispersion while the chapters to follow consider the determinants of the dispersion. Though various analytic methods and empirical measures are utilized in examining the behavior of the dispersion in state unemploy- 37 ment rates over time, a singular result nevertheless recurs throughout. Holding constant for the level of aggregate demand, the dispersion in unemployment rates exhibits no secular increase over the eighteen year sample period of this study. The dispersion of unemployment rates is a stationary time-series. The theoretically pleasing inference directly follows that, though geographic pockets of unemployment may form at any given point in time, the price system and migration act relatively quickly to redistribute the unemployed geographically and return the economy to what one might term its natural level of dispersion. 38 NOTES 1. Lipsey (1960), pp. 19-23. 2. Archibald (1969), pp. 126-128. Archibald's proof requires neither that the micro-Phillips relationships be identical nor that they be convex, which is a substantial improvement over Lipsey's initial hypothesis requiring that both conditions be met. 3. A tight labor market is defined here as one in which the quantity of labor demanded exceeds the quantity Of labor supplied. The only sort of unemployment in such a market is that related to optimal firm and worker search. 0n the other hand, a loose labor market is defined as one in which the quantity of labor supplied exceeds the quantity of labor demanded. Such a market is characterized not only by frictional unemployment, but also by other forms of unemployment such as involuntary unemployment and structural unemployment. Involuntary unemployment exists when not every unemployed worker who desires a job can obtain one at the going wage. Structural unemployment occurs when jobs are available, but workers with the requisite skills necessary to fill those jobs are not. The proposition advanced in the text, that wages adjust more rapidly in tight labor markets than in loose labor markets, follows if, for example, explicit and implicit contracts in the economy result in wage rigidities in the downward direction. 4. Sum and Rush (1975), p. 3. 5. The definition of a labor market characterized by excess supply is synonymous with the definition of a loose labor market supplied in footnote 3. Similarly, a labor market characterized by excess demand is identical to the tight labor market of footnote 3. 6. See Killingsworth, in U.S. Senate (1964), pp. 194-219. Also see Solow (1964). 7. See Eckstein in Ross (1964). 8. Eckstein. 9. See Gallaway (1963). 10. Sum and Rush, pp. 4-6. 11. The nine U.S. regions are defined as follows: New England--Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, and Connecticut. 39 Mid-Atlantic States-~New Jersey, New York, and Pennsylvania. East North Central States--Illinois, Indiana, Michigan, Ohio, and Wisconsin. West North Central States--Iowa, Kansas, Minnesota, Missouri, Nebraska, North Dakota, South Dakota. South Atlantic States--Delaware, Florida, Georgia, Maryland, North Carolina, South Carolina, Virginia, West Virginia. East South Central States--Alabama, Kentucky, Mississippi, Tennessee. West South Central States--Arkansas, Louisiana, Oklahoma, Texas. Mountain States--Montana, Idaho, Wyoming, Colorado, New Mexcio, Arizona, Utah, Nevada. Pacific States--A1aska, California, Hawaii, Oregon, Washington. BLS 4 region data are comprised as follows: Northeast--New England States and Mid-Atlantic States. North Central--East North Central and West North Central States. South--South Atlantic, East South Central, and West South Central States. West--Mountain and Pacific States. 12. More conventional measures of dispersion such as the variance or standard deviation tend to move cyclically, being greater when aggregate demand is weak than when it is strong. This cyclical movement occurs because unemployment rates are bounded from below by zero. Of course, an upper bound of 100 exists, but this constraint is never remotely binding. As the economy expands in an upswing, unemploy- ment rates, in an increasingly larger number of states, accumulate around some lower limit. This accumulation induces a decline in variance, which is clearly an artifact of the increased aggregate demand. 0n the other hand, as the economy contracts, the average rate of unemploy- ment moves away from its lower bound. Individual state unemployment rates which make up the distribution are freer to vary about the average given the aggregate unemployment rate's increased distance from zero. Because the effective constraint on the distribution becomes much less binding in a contraction, the variance in unemployment rates is much larger. A measure of dispersion that controls for this sort of fluctuation would allow one to guage the dispersion in unemployment rates owing to frictional and structural elements in the economy. If one had such a measure, and it registered much smaller at time t than at time t + s, 40 then one could conclude that due to growing structural imperfections in the economy geographic unemployment rates had become more dispersed over time. Sum and Rush propose that the coefficient of variation controls for cyclic fluctuation in the dispersion. As the standard deviation in unemployment rates (i.e., the numerator of the coefficient of variation) declines in an expansion, so tOO does the average rate of unemployment (i.e., the denominator of the coefficient of variation), essentially leaving the coefficient of variation itself unchanged. In a contraction, the reverse occurs. The claim is that by comparing the coefficient of variation at different points in time one is able to compare measures of dispersion purged of cyclic elements. 13. The computed t statistics are significant at the .01 level in both cases. 14. Following the U.S. Department Of Labor, let a true geographical labor market be defined as an economically integrated geographical unit within which workers may readily change jobs without Changing place of residence. See Area Trends in Employment and Unemployment, August-September 1975, p. 13. 15. Archibald notes that a dispersion computed on state data serves as a good proxy for the dispersion of excess demand over true, geographic labor markets. See Archibald (1969), p. 127. Brechling uses state data in his study of how the Phillips relation is affected by unemployment dispersion. See Brechling (1973). 16. It is true, of course, that one could find even closer approximations to geographic labor markets by using SMSA data. For the purposes of this research, however, state data is more useful and informative. Unemployment data on the fifty states cover the entire U.S. population. SMSA unemployment data only cover individuals living in SMSAs. For this reason an increase in the SMSA dispersion of unemployment does not necessarily imply an increase in the dispersion of unemployment for the country as a whole. Conclusions drawn from results using SMSA data might over- or underestimate true unemployment dispersion. Indeed, the Sum and Rush study clearly reveals this problem. Not only do Sum and Rush compute dispersions for the Census four and nine regions, but also for 28 SMSAs. They find that the SMSA dispersions are neither of the same magnitude nor necessarily move in the same direction as the regional dispersions. 17. These computations utilize three series of state unemployment rates. Series 1 is drawn from the Manpower Report of the President, 1970 and 1974 and runs from 1957 through 1972. Series 2 is taken from the Manpower Report of the President, 1977, and runs from 1970 through 1974. Series 3 is drawn from the Employment and Training Report of the President, 1978 and 1979, and runs from 1973 through71978. Series 1 and Series 2 are spliced together to form a fourth series which is then spliced with Series 3 to obtain the unemployment rate series actually 41 used (running from 1957 through 1978). Series 3 is presumably the best series of unemployment data available since these estimates are drawn from the Current Population Survey. Series 1 and Series 2 are partially based on insured unemployment data and on estimating procedures using national average patterns and relationships taken from the decennial census. For an excellent discussion Of state unemployment data, see Goldstein (1978). 18' Ho‘ CV'51-'54 ‘ CV'55-'73 ”a‘ V'51-'54 = CV'55-'73 TI I ' ‘57-! I and t z 55- 73 51- 54 2 2 M/(8)s '55-'73 + (3)S n51--54 (1/9 + 1/4) (9 + 4 - 2) 19. In a regression of the coefficient of variation (4-region) on a constant, the unemployment rate, and a time trend, Sum and Rush Obtain an estimated coefficient for the unemployment rate that is negative and significant at the 99% level of confidence. See Sum and Rush, p. 6. 20. The unemployment rates of the other 14 states in the lower half of the unemployment rate distribution declined at a labor force weighted average rate of 4.2 percent in 1963. The eleven Northern states discussed in the text account for 68 percent Of the total labor force of all states in the lower tail of the distribution; therefore, the overall average rate of decline in unemployment rates for all lower half states is heavily skewed (2.7 percent) toward that found for the eleven Northern states (2.0 percent). 21. See Hamermesh (1980), p. 2. 22. Hamermesh, pp. 15-17. 23. The sample autocorrelation function is: T—k __ __ 2 (yt ' y) (yt+k " .11) pk = t-l T —-2 2 (7t - y) t=l is the variance in state unemployment rates in where y ygar t; and k indexes the number of years lagged. 42 24. Pindyck and Rubinfield (1976), p. 441. CHAPTER III THE DISPERSION MODEL 3.1. Introduction With the importance of the geographic dispersion in unemployment rates as an indicator of overall labor market performance now established, this chapter provides the theoretical specification of a model Of dispersion. The factors that determine the dispersion in a given year and how these factors interact to cause the dispersion to change over time are of central interest. Integrating neoclassical profit and utility maximization theory, I first develop a state unemployment rate equation. The extension of this specification to each state in the Union yields a fifty-equation system of state unemployment rates. I show how these equations can be substituted into the relevant measure of dispersion to decompose it into component parts attributable to the individual explanatory variables. Chapter III concludes by considering a two-sector, two-variable model, in order to provide insight to the properties entailed in the full fifty-state model of dispersion. 3.2. Specification of the State Unemployment Rate Function For the purpose of generality the model which follows uses the weighted variance in state unemployment rates as its measure of l dispersion. The weighted variance is: 43 where ot(u) is the weighted variance in state unemployment rates in year t; ait is the proportion of the U.S. labor force residing in state i, in year t; Uit is the unemployment rate of state i in year t; U£ is the labor force weighted average unemployment rate in year t (i.e., ut = 2 “it ”it)‘ i=1 Equation (3.1) indicates that as the spread from the mean in state unemployment rates become wide, the overall dispersion becomes greater, and vice versa. Yet equation (3.1) gives no indication of what factors determine the dispersion. These factors, of course, must depend on what variables determine the various state unemployment rates themselves. The modeling of the dispersion in state unemployment rates thus involves a two-step procedure. The first step requires that one functionally specify the individual state unemployment rates. The following identity characterizes the unemployment rate in state i: (3.2) u. _ LFi/Pi ' Ei/Pi _ 1 E./P. ‘ Z LF./P. = ‘ 1 ' l l LFi/Pi where u. is the unemployment rate of state i; LF. is total labor force of state i; E. is total employment in state i; P. is total population of state i. 45 Hence, the interaction of factors affecting both labor supply (LFi/Pi) and labor demand (Ei/Pi) determines the unemployment rate of a particular state. Consider state labor force participation, LFi/Pi' For the individual one can specify a utility function with income and leisure as arguments.2 Assuming that the individual maximizes utility subject to a budget constraint, one can further derive a labor supply function with wages and non-labor income as arguments. An individual is more likely to participate given an increase in the wage rate and is less likely to participate given an increase in non-labor income. Respectively, these represent the standard substitution and income effects of neoclassical theory.3 Aggregating over all individuals in the labor market, one can then write a state labor force participation equation with both the average wage rate and non-labor income as arguments. The working-age population in a given state is a heterogenous group Of people. On average, different groups of individuals differ with respect to their relative attachment to the labor force. Utility functions for individuals in the various groups should differ, therefore, wages and non-labor income held constant. One must add demographic variables to the specification in order to take this work-force heterogeneity into account. Two groups with less than average labor force participation rates are youths and non-whites. A variety of factors such as commitment to schooling, job shopping, and pursuit of other non work- related activities may account for the weak labor force attachment of 46 the former group. Discrimination, indolence bred and fostered by ghetto culture and an oppressive welfare system, and relatively more attractive Opportunities outside of the conventionally defined labor market may account for the lower participation rates of non-whites. These issues are, of course, far beyond the scope of this research.4 For the purposes at hand suffice it to say that the greater the proportion of individuals from either group--teenagers or non-whites-- relative to a state's total working—age population, the lower should the state's overall labor force participation be. Females comprise a third group in the working-age population possessing a labor force participation rate less than that of prime-age white males. They are excluded from the model specification on practical grounds, however. The form of the demographic variables included in the state's labor force participation function is: percentage of state working age population belonging to the demographic group under consideration. This proportion varies somewhat over time in the case of non-whites and teenagers. Non-whites made up 25.7 percent Of Georgia's working age population in 1960, but only 20.5 percent of its working age population in 1978. Teenagers (i.e., 16-19 year-olds) made up 8.7 percent of Michigan's working age population in 1960, but they accounted for 11.3 percent of the state's working age population in 1978. At any given point in time and in any given state, on the other hand, females comprise approximately 50 percent of the working age population. This figure varies little over time. Hence, a collinearity problem exists in any regression equation containing both a constant term and a variable taking into account the proportion of state working 47 age population that is female. At best, since such a variable fluctuates so little, the associated regression coefficient would not explain much of the variation in the dependent variable. At worst, if the female demographic variable does not fluctuate at all over time, a situation of perfect multicollinearity results, and estimation of the related regression equation is not possible. Just as the proportion of working-age females to working-age population varies little over time, in a given state, it also varies little at a single point in time, across states. Non-whites comprised 32.6 percent of Mississippi's working-age population in 1970, but, in the same year, they accounted for only 0.4 percent of Vermont's working- age population. Teenagers made up 13.5 percent of Utah's working-age population in 1970, but only 9.2 percent of Florida's working-age population in the same year. Females, however, account for approximately 50 percent of the working-age population in all states in any given year. This cross-sectional distinction is of great relevance in executing the second step of the model. In this step, cross-equation variances and covariances, which are functions of the independent variables and their respective regression coefficients (the regression coefficients are obtained from regressions of state unemployment rates on a set of explanatory variables), are analyzed. Since the ratio Of working-age females to the working-age population is roughly equal across states, this variable, relative to the other independent variables of the model (which all vary widely across the states), would account for comparatively little of the variance in state unemployment rates. Thus, even if one could obtain an estimated coefficient for the 48 ratio of working-age females to working-age population for each state, the added explanatory power this variable would give to the model is quite small. Because of these considerations, the model excludes the percentage of females from the state labor force participation specification. One can further distinguish the working-age population in a fourth way-~by educational attainment. Schooling increases one's access to the more interesting and challenging jobs and, concomitantly, to jobs in the primary work force where long term commitment on the part of employees is required. Since the two require a similar sort of discipline, a positive correlation between one's taste for schooling and one's taste for work may also exist. The greater the educational attainment level in a particular state, therefore, the greater should be the overall level of labor force participation, other things equal. In addition to the foregoing demographic factors, it is well known that aggregate demand conditions in the general economy affect the level of labor force particiaption. This supposition relates to the discouraged worker hypothesis, which essentially holds that, as aggregate demand slackens, some unemployed workers become totally frustrated in their search for employment and exit the labor market.5 Others, who would have entered the labor force had the economic climate been more favorable, choose to remain out of the labor force devoting time to non-market activities. In expansions, one observes reverse behavior. Given the increased availability of jobs and the higher probability of employment, workers flow into the labor force at a relatively greater pace as economic conditions improve. In general, 49 then, the stronger is aggregate demand, the greater should state labor force participation be. The actual labor supply specification to follow distinguishes between economic conditions within the state itself and economic conditions in the national economy. Certainly, it is possible for the economy of a particular state to be depressed while that of the nation prospers, and vice versa. Given a state's industrial mix, a change in national economic conditions may have a different impact on the state's labor supply response than a change in state economic conditions. One can write the state labor force participation rate as a log linear function Of the above supply-shift variables: (3 3) LFi/Pi = f, (Xi); i = 1, . . ., 50 where Xi is the vector of supply-shift variables associated with state i. The employment to population ratio, Ei/Pi’ in equation (3.2) can be derived in much the same manner as equation (3.3). Assuming that firms seek to maximize profits subject to factor costs, a given firm's demand for labor depends on the wage rate and on the demand for its output. Aggregating over all firms, the Ei/Pi function takes the average state wage and proxy variables for aggregate demand as argu— ments.6 Again, the actual specification distinguishes between state- specific and natiOnal economic conditions since some firms produce primarily for national markets while others produce primarily for local markets. A marginal increase in the wage induces firms to substitute other productive factors for labor in the production process, which 50 causes total employment to decline. An increase in demand for output, on the other hand, raises the demand for all factors of production (assuming that none are inferior), thus raising labor demand and total employment. Hourly wage costs are not the only cost that a firm incurs in employing a worker, however.7 Costs independent of total employee hours, but dependent on the stock of employees, also exist. Examples are recruitment costs, training costs, fringe benefits, and various other indirect costs of labor. Given the firm-specific quit rate, the individual firm must forego some amount of its resources to finance the hiring and training of new workers. Presumably, then, the greater the turnover rate of the work force, the greater is this fixed cost of labor faced by the firm. Firms seek to hire workers whose voluntary turnover rates are low in order to minimize this cost. Since the firm does not know a priori what the voluntary turnover rate of a particular prospective employee is--this information is itself too costly to obtain--the firm attempts to make judgments on the basis of the individual's background characteristics such as age, race, and education.8 Turnover rates are higher among the young, non-whites, and less educated (training costs may be higher for this last group of individuals also).9 The greater the proportion of any of these groups to the overall state population, therefore, the lower should Ei/Pi be, other things equal. 2 To recapitulate, state labor demand (i.e., Ei/Pi) depends on the average level of wages in the state, on demand conditions in the product market, and on the demographic mix of the labor force in terms of the 51 age, race, and skill composition of the state's population. One can write the employment rate as a log linear function of these variables as follows: (3.4) Ei/Pi = 91.01.); i =1, . . ., 50 where Y, is the vector of demand-shift variables associated with state i. Given equations (3.3) and (3.4), equation (3.2) can be rewritten as: (3.5)U151-m. 1 In putting the model into estimable form, the supply and demand equations, f1 and gi, are specified over an identical set of explanatory variables, Z1, 50 that, given the log linear form of both fi and 9,, equation (3.5) can be written as: (3.5) u]. 51 - h]. (21.) Taking natural logarithms on both sides of (3.6) yields a dependent variable that is non-linear in the parameters of the explanatory variables. Rather than estimate equation (3.6), an equation using the employment rate, Ei/LFi’ as the dependent variable is used instead: (3.7) ei = Ei/LFi = hi (Zi) = 1 - 01. Taking logs of both sides of equation (3.7) provides a dependent variable that is linear in the parameters of the explanatory variables. The parameter estimates obtained from equation (3.7) affect the unemploy- 52 ment rate in the Opposite manner in which they affect the employment rate. Since the employment rate is a linear transformation of the unemployment rate, variances in the state values of the two must be identical, and variances in their log values differ monotonically. With the exception of the wage, there are no a priori expecta- tions about the signs of the estimated parameters in equation (3.7). An increase in demand in the product market increases labor demand, hence increasing E1. An improvement in the general economic climate, on the other hand, also draws more individuals into the labor force (the reverse discouraged worker effect), thus increasing LFi. Whether or not the employment rate, e1, increases or decreases depends on whether labor demand or labor supply is more responsive to a marginal change in product market conditions. Similar ambiguity results for marginal changes in any of the demographic variables. An increase in educational attainment should increase both employment and labor force participation; therefore, theeffect on the employment rate itself cannot be predicted a priori. An increase in either non-white or teenage labor force should cause both the numerator and denominator of the state's employment rate to decline. The direction of the effect on the employment rate depends, once again, on whether labor demand or labor supply is more responsive to a change in the given explanatory variable. The one variable for which there is an a priori sign expectation is the wage rate. An increase in the wage should cause employment to fall and should cause labor force to increase, inducing an overall decline in the state's employment rate. The estimated regression coefficients, in general, represent net effects. Individual supply and demand effects are not identified. 53 Chapter IV presents regression results drawn from estimating an equation of the form of (3.7) for each state. An implicit assumption is made that the structure of labor demand and supply differs across areas. A marginal change in one of the explanatory variables should affect state i's employment rate differently than it affects state j's employment rate. Other research ignores this issue. Authors typically pool area data and estimate single employment rate or unemployment rate equations, and then explain cross-area differences in empyoyment rates and unemployment rates in terms of cross-area differences in the 10 The regression results levels of the independent variables themselves. Of the following chapter show quite clearly that a wide diversity exists in both the strength and direction with which a marginal change in a given explanatory variable affects employment rates, indicating, in turn, that the relative responsiveness of labor supply and demand to the various explanatory variables differs across states. Cross-state differences in employment rates, therefore, depend both on cross-state differences in the explanatory variables and on differences in the impacts with which changes in these variables affect employment rates. 3.3. A Two-Sector Model Of Employment Rate Dispersion As noted at the outset of this chapter, modelling the geographic dispersion in employment rates (and unemployment rates) is a two-step procedure. The methodology involves first estimating an employment rate equation for each state. Then, in order to decompose the variance in employment rates for a given year, the appropriate values of the independent variables for each state for the year in question are 54 reinserted into the estimated employment rate equations (along with the residual terms for the particular year). Substituting these equations for the respective employment rates in the variance, one is able to decompose the variance in employment rates into the cross- equation variances and covariances attributable to the independent variables and to the residual term. In order to gain an intuitive grasp of the properties entailed in the full fifty state model, consider the following two-sector, two-variable model. Suppose that there are two sectors in the economy (i.e., two labor markets). Further, suppose that the estimated employment rate equations for the two sectors, in year t, are: (3.8) e1t = blx1t + c1 th (3.9) :6 X + 2t C2Z eZt 2 2t where eit is sector i's employment rate in year t; Xit’ zit are the explanatory variables of sector i in year t; bi’ Ci are sector i's estimated regression coefficients. For expositional simplicity, the residuals here are assumed equal to zero. In year t the dispersion in sectoral employment rates measured by the variance is: (3.10) 0 Note that: E- II °l X + 0I N 55 Substituting equations (3.8) and (3.9) into (3.10): 2 _ — —2 (3.11) o (et) — 01((01 Xlt - bXt) + (c1 th - th)) — ——2 + a2((b2 X2t - Xt) + (C2 ZZt - CZt)) _ —2 —2 ‘ Z O'ii;(bi xlt ' Xt) +2 O'it(cizii: ' CZt) + 22 a1 b. xit - Xt) (C.Z. - CZ t( 1 1 it t) 2 c 2 o (bXt) + o th) + 20 (bXt, th). According to the last line of (3.11), the variance (or dispersion) in sectoral employment rates is equal to the sum of the variances (or dispersions) in the employment rate contributions of the two explanatory variables plus twice the covariance Of the employment rate contributions Of the two variables. The variance terms on the right hand side of the last line of (3.11) are interpretable in a straightforward manner. By definition these two terms are necessarily positive and must, therefore, have a dispersion increasing effect. Intuitively, they signify that the wider the difference across sectors in the employment rate contribution of a given variable, the greater must the dispersion in employment rates be, other things equal. One of these variance terms in isolation--for example, 02(bxt)--indicates what the dispersion in employment rates would be if the employment rate contributions of the other variable were equal across sectors (i.e., clz1t = CZZZt). Similar intuition holds for 02(c2t) vis-a-vis variable X. The variance terms, therefore, represent the pure effects of cross—sector differences in the employment rate contributions of each of the variables on the dispersion. 56 While the variance terms are necessarily positive, there is no sign restriction on the covariance term, o(bXt, th), in equation (3.11). The covariance reflects the interaction of the two variables in determining the employment rate in each particular sector. If o(bXt, CZ is negative, then bXt tends to dampen the employment rate ‘.'> contribution of Z in the sector for which th is relatively large (i.e., relative to Cl in the other sector); and, bXt tends to add to the employment rate effect of Z in the sector for which th is relatively small. The covariance term thus takes into account the fact that employment rate contributions of individual variables do differ across sectors. While the variance terms in (3.11) allow for the pure effects of each of the variables, the covariance term captures the interaction effects of the variables in determining employment rate dispersion. A negative covariance between the employment rate contributions of the two 11 variables, therefore, exerts a dispersion decreasing effect. Equation (3.11) can be rewritten in the following manner: (3.12) 52(e = [02(5xt) + o(bXt,th)] + [52(57 ) + o(bXt,th)] t) “t = UNV (bXt) + ONV (th) where ONV (bXt) is defined as the net variance in the employment rate contributions Of variable X; CZ is defined as the net variance in the CW ( t) employment rate contributions of variable 2. 57 A given net variance, then, is equal to the variance Of employment rate contributions in a particular variable plus the covariance in employ- ment rate contributions of both variables. The following chapter employs the net variances as summary statistics to indicate whether or not cross-sector differences in the employment rate contributions of a particular explanatory variable increase or decrease the overall dispersion in employment rates, on net. The component terms of the individual net variances in equation (3.12) indicate that the employment rate contributions of a particular variable influence the dispersion in employment rates in two countervailing directions (assuming that 0(bXt, th) is negative). 0n the one hand, the variance component of a given net variance (i.e., 02(bXt) or 52(th)) has the dispersion increasing effect already noted. It indicates what the dispersion would be if employment rate contributions in the other variable were equal across sectors. The covariance component of a given net variance, on the other hand, hasaidamping effect on the employment rate contributions of the other variable. This component of the net variance has a dispersion decreasing effect. Whichever component dominates, variance or covariance, determines whether or not cross-sector differences in the particular variable in question increase or decrease the dispersion in employment rates, on net. 2i One may gain further insight to the properties Of 0 et) by rewriting equation (3.11) as follows: (3.13) 52(e I M Q I—‘l A 0' X I X t)‘. it 11 M Q -J ('I' A U' a—l x -l fi I X ('I' v A I'D —I (*5 I ‘P | fl V + ° M Q .10 ‘.’- A n .6. N “C Cr I O N CI" v 58 = o(bXt, et) + o(th, et) According to (3.13), the variance in state employment rates is the sum of the covariances of the employment rate with the employment rate contribution of each of the explanatory variables respectively, (Note that each of the covariances in the last line of (3.13) is equal to the corresponding net variance in (3.12), e.g., o(bXt, et) = oNv(bXt),) If o(bXt, et) is positive, then the relatively high employment rate sector has a relatively large employment rate contribution in variable X, and the low employment rate sector has a relatively small employment rate contribution in variable X. If, on the other hand, o(bXt, et) is negative, then the relatively high employment rate sector has a relatively small employment rate contribution in variable X, and the low employment rate sector has a relatively large employment rate contribu- tion in X. The factors which cause the dispersion in employment rates to change from year to year are also of interest. Consider the total derivative of equation (3.11): 2 -' *" ... (3.14) do (et) (51.xit - bXt)(bidXit) + [(§ n,t(c1.zit - th) = {2 E O'it "'(bidxit)+ § ait(bixit ' bxt)(cidzit)]} + {2 E ait(cizit - Ejt)(cidzit) + [(E ait(ciZit - E71)(bldxit) + ... l l + E alt(blxlt ' Xt) (CIdZIt)]} + {Z a (b X - 77-)2 do- + a (c Z CZ )2da + it i it t 1t 1 1 it t it 59 ' + 220'ii:(bixit ' Xt) "' ' (Cizit ’ €72) do‘it Accordingly, sources of change in dispersion are the explanatory variables, X and Z, and the labor force weights, a1 (structural relationships are assumed stationary). Even in this highly simplified version of the model, changes in employment rate dispersion over time result from complex, multi-dimensional causes. For example, whether cross-sector changes in variable X increase or decrease employment rate dispersion in a given year depends on: how X1 changes relative to X2; how Z1 and Z2 change relative to X1 and X2; the signs and magnitudes Of b1, b2, c], and c2; and variability in the labor force weights. In the fifty-state, nine-variable model to follow, the degree of complexity increases exponentially. Nevertheless, the results do indicate rather easily identifiable and intuitively reasonable patterns in the net variances of the explanatory variables. 3.4. The Full Model of Employment Rate Dispersion The principles and properties Of the foregoing two-sector, two- variable model carry over directly to the full, fifty—state model of employment rate dispersion. The variance in state employment rates in a given year is the sum of the net variances of the explanatory variables and the net variance in the residual terms: (3.15) 02(e = z ONV(bJXJ) + oNV (Gt) where j indexes the set of explanatory variables; 60 GNV(bJX%) is the net variance in employment rate contri- butions, across all fifty states, in variable Xj; GNV(9t) is the net variance, across all fifty states, in the regression residuals of year t. Any given net variance in equation (3.15) is equal to the variance in the employment rate contributions of the variable in question plus each of the covariances between the variable's employment rate contributions and those of the other explanatory variables plus the covariance Of the variable's employment rate contributions with the residual terms. R For example, the net variance of kat is: t) + 2 C(bkxk, bjxi) + o(kat, G Ji‘k If the net variance in bkxt is positive, then variable X (3.16) ONV(bkxT) = 02(ka t) k is a net contributor to the dispersion in employment rates. Cross-state k cause wide differences in the employment rate contributions of X enough differences in employment rates to outweigh any dispersion decreasing negative covariance terms embodied in ONV(bkxt)' Given equation (3.13), a positive net variance then indicates that, on average, deviations from the mean in state employment rates vary positively with deviations from the mean in the employment rate contributions of the variable in question. Thus high employment rate states tend to be k states for which the employment rate contribution of X , for example, is relatively large. 0n the other hand, if oNv(ka:) is negative, then k cross-state differences in X do not cause wide enough differences in 61 state employment rates to outweigh the dispersion decreasing, negative, covariance components of the net variance. Therefore (given (3.13)), high employment rate states tend to be states for whiCh the employment rate contribution of the variable in question is relatively small (i.e., has a negative mean deviation from the average employment rate contribution, kak); and low employment rate states are those for which the employment rate contribution of the variable in question is relatively large. 3.5. Conclusion This chapter establishes the theoretical underpinnings of the model Of employment rate dispersion. Modelling the dispersion is a two-step procedure. The determinants of individual state employment rates are first specified. These include factor costs, non-labor income, demand conditions in the product market, and the demographic mix of the labor force. Upon estimating the functional relationships for the individual states, one can decompose the variance in state employment rates, for any given year, into the component parts attributable to each of the explanatory variables and to the residual terms. This second step involves reinserting the appropriate values of the explanatory variables for the year in question into the estimated structural relationships and then taking the cross-equation variances and covariances in the variables and residuals. Through analysis of these cross-equation variances and covariances one is able to determine which variables exert the greatest relative influence on the dispersion in employment rates. 62 NOTES 1. The weighted variance in the natural logarithms of state unemployment rates is also used. 2. The usual approach is adopted here in defining leisure as all time spent in non-market activities. 3. In case the text is not totally clear on this point, it must be stressed that what is being discussed here is simply the participation decision and not hours of work. In the case of the hours of work decision, an increase in the wage is likely to involve both substitution and income effects. When the choice is with respect to participation only, an increased wage involves solely a substitution effect. 4. The interested reader should see: Bowen and Finegan (1969), Chapters 3, 4, 12, 13, and 14; Rees (1979), Chapter 1; Piore in Piore (1979), pp. 11-12; and Doeringer and Piore (1971). 5. Note that this is a net effect. For, as aggregate demand weakens, some workers are drawn into the labor force to supplement family income. The empirical evidence indicates that the discouraged worker effect dominates this added worker effect; hence, the discussion in the text focuses solely on the former. See: Mincer in Gordon and Gordon (1966), and Fleisher and Rhodes (1979). 6. The cost of capital is excluded from the specification for lack of an adequate index on this variable at the state level. Clark and Freeman have also shown that when micro constraints on the aggregate production function are relaxed, the elasticity of aggregate employment with respect to a change in the cost of capital is very small (approximately .06). See Clark and Freeman (1977). 7. See Rosen (1969), Nadiri and Rosen (1967), and Thurow in Piore (1979), pp. 17-32. 8. Sex is excluded from the analysis due to the difficulties articulated in the labor supply section. 9. See Perry (1972) and Hall (1972). 10. See Metcalf (1975) and Browne (1978). 11. If o(bXt, th) is positive, then the covariance term reinforces the dispersion increasing effect of the variance terms. CHAPTER IV EMPIRICAL ESTIMATION OF THE DISPERSION MODEL 4.1. Introduction Chapter IV presents the results Obtained in estimating the model specified in Chapter III. This chapter analyzes the factors which determine the dispersion in state employment rates in a given year and which cause it to change over time. Section 4.2 describes the data set that makes the model operational. Section 4.3 discusses and interprets the parameter estimates Obtained in estimating the state employment rate equations. Section 4.4 relates various regional patterns found in the estimated regression coefficients. And Section 4.5 analyzes the empirical results of the full fifty-state dispersion model and discusses the relative impacts of cross-state variation in each of the explanatory variables upon the overall dispersion in state employment rates. Though some regional patterns are apparent, wide variation exists, in general, in the estimated regression coefficients correspond- ing to each of the explanatory variables. The regression results presented below show that differences across areas in sensitivity to fluctuations of demand in the product market and that differences across areas in structural and frictional unemployment play principal roles in determining the dispersion in a given year. Factors that play secondary roles, on the other hand, are area differences in wage costs 63 64 and in human capital accumulation. Differences among states in the age and racial mix of the labor force have a negligible impact on the overall dispersion in state employment rates. 4.2. The Data Set The sample period of the state employment rate equations extends from 1958 through 1978.1 All monetary variables enter the equations in real terms (1967 dollars). A variety of sources yield the individual time series of the explanatory variables. Appendix A contains a detailed listing of data sources. The employment rate equations use gross average hourly earnings of production workers in manufacturing to proxy for state wage levels. Various May issues of Employment and Earnings contain these annual averages. A more comprehensive index would take into account the wages of all workers; however, such an index is not available. Total rent, interest, and dividend income in each of the states (hereafter referred to as state property income) and total transfer payments in each state are used as proxy variables for non-labor income. The Regional Division of the Bureau of Economic Analysis (U.S. Depart- ment of Commerce) provided both series. The data reflect the classificational, definitional, and statistical revisions introduced in the national personal income series in 1976. The transfer payment variable includes all major programs such as: Old Age, Disability, and health insurance; educational and training assistance payments; unemployment insurance benefits; and income maintenance payments. Both property income and transfer payments capture income effects that are likely to differ across income groups. On the one 65 hand, low income individuals and individuals marginally attached to the work force typically receive transfer payments.2 High income individuals, on the other hand, who, presumably, are firmly attached to the work force (if they are in it at all), typically receive property income. Since both variables move cyclically, they also are likely to explain some Of the variation in labor demand. The U.S. Census of Population, 1950, 1960, and 1970, and the Geographic Profile of Employment and Unemployment, published annually since 1971, provide the age and race data for each of the state employment rate equations. The actual variables used are the percentage of the state working age population that is 16-19 years Of age and the percentage of the state working age population that is non-white. Unfortunately, a missing observation problem characterizes these time series. Prior to publication of the Geographic Profile, no observations on either variable existed for intercensal years. Observations for 1958, 1959, and 1961 through 1969 are created by linearly interpolating the census data of 1950, 1960, and 1970. With the publication of the first Geographic Profile in 1971, state age and race data became available on an annual basis. Even with the emergence of the Geographic Profilg_in 1971, however, the missing Observation problem did not end for many states. Since the sample size of the Current Population Survey (upon which the Geographic Profile is based) was initially not large enough to guarantee an adequate degree of statistical reliability for many states, the Geographic Profiles of 1971 and 1972 contain detailed population data for only the ten largest states. With the expansion of the sample in the mid-19705, the 1974 edition contains data for twenty- 66 five states, and the 1975 edition contains data for twenty-six states. With the further expansion of the Current Population Survey in the later 19705, all editions from 1976 and on contain a complete set of observa- tions on age and race for all fifty states. Hence, for some years in the 19705, one must interpolate age and race data for a number of states. In interpolating the data the implicit assumption is that these large population aggregates vary mainly along a trend and, therefore, that interpolation provides reasonable intercensal estimates.3 In order to take educational attainment into account, the empirical model below uses the percentage of state population, twenty- five years and older, who hold at least a high school diploma. A missing observation problem. however, also confounds these data. Observations on this variable are available from the U.S. Census for 1950, 1960, and 1970 but for none of the intervening years. The Survey of Income and Education, presented in the Current Population Reports, Series P-60, #110-113, provides estimates of educational attainment, by state, for 1976. Hence, actual Observations for all fifty states exist for 1960, 1970, and 1976. Linear interpolation yields estimates for 1957-1959, 1961-1969, and 1971-1975. Extrapolation of the yearly growth rate in each state's level Of educational attainment during the 1970-1976 period provides estimates of educational attainment for 1977 and 1978. The implicit assumption, here, is that the true Observations for the intercensal years do not exhibit much variation and that they are characterized primarily by an upward time trend. The model uses personal income in each state to take into account product market demand conditions. Personal income is composed of: wages 67 and salaries; other labor income; proprietor's income; rent, interest, and dividend income; and transfer payments. The Bureau of Economic Analysis provided these data. Finally, to take into account demand conditions in the national economy, I construct a GNP variable. I divide actual GNP by potential GNP for each year of the sample and enter the resulting quotient into the state employment rate equations. The Economic Roport Of the President provides the relevant series. The GNP variable is the only variable in the model which does not vary cross-sectionally. 4.3. The Regression Results Using the foregoing set Of explanatory variables I estimate the following employment rate equation for each state: (4 l) e, = A1 + b1iWi + bZiTPi + 531 PRPi + b4ini + 5515A, AGNP , . _ where ei is the employment rate in state i; A. is a state specific constant; W1 is gross average hourly earnings of production workers in manufacturing; TP. is transfer payments in state i; PRP. is property income in state i; NW. is the proportion of state i's working age population that is non-white; EA. is the proportion of state i's population, 25 years and older, with at least a high school diploma; 68 Ti is the proportion of state i's working age population that is 16-19 years of age; AGNP is actual GNP; PGNP is potential GNP; PI, is personal income in state i; v. is a stochastic disturbance term specific to state i; and, all variables are entered in logarithmic form. Table 4-1 lists the estimated regression coefficients and indicates levels of statistical significance. Equation (4-1) fits Pennsylvania 2 of .990, and it fits North Dakota worst, with an R2 of best, with an R .608. The unweighted average R2 for the fifty states is .913. Several comments regarding the signs of the estimated coefficients are in order. Consider first the personal income and GNP variables used to control for demand conditions in the product market. The coefficients associated with both variables are positive in a majority of the regression equations (forty-six in the case of personal income and forty- one in the case of AGNP/PGNP). As postulated in Chapter III, an increase in either personal income or AGNP/PGNP should lead to an increase in total state employment since the demand for labor is a derived demand dependent on commodity demand. Increases in these variables also imply improving economic conditions, however, causing more workers to be drawn into the labor force through reverse operation of the discouraged worker effect. Increases in either variable, therefore, lead to increases in both the numerator and denominator of the state employment rate specified in equation (3.7). The large number 69 Table 4-1. Regression Results: State Employment Rates STATE CONST. WAGES TRAN.PAY PRP INC. NON-WHITE £0.4TT. TEENS 55%; PERS.1NC. 82 0.8. Alabama 1.815 -.041 .019 .076' .008 -.189 -.079 .290" .073 .889 2.063 Alaska 5.156"' -.024 .013 .O91" -.179"' -.449"‘ .157"' -.057 -.021 .906 2.600 Arizona 2.139"' -.126' -.141"' -.047 -.033 -.065 .012 .378"' .297"' .936 1.719 Arkansas 3.823"' .132 -.044 -.033' -.056 -.077 -.063 .319" .125' .885 2.826 California 1.583' -.384"' -.021 -.049 .008 -.261" .052 .342" .239" .920 2.114 Colorado 3.491"' -.l95"' -.006 -.055 .045' -.073 -.021 .250"‘ .125"' .787 2.767 CannecticUt 0.876"' -.230‘ -l65"' .013 -.043 .270"' -.O72' -.035 .267 .928 1.287 Delaware 3.111" o.034 -.108"‘ -.0001 -.002 .082 .036 .201" .145" .969 1.587 Florida 3.251'" -.029 -.146'“ .079 -.059 .091 .068 .394‘” .101 .961 2.395 Georgia 1.506' -.053 -.153"' -.O36 -.088" -.021 .025 -.121 .316"‘ .977 2.952 Na-aii 3.553" .350'“ -.097“ .119'" -.054 -.449" o.138"' -.248" .118 .950 3.363 Idaho 4.908"° -.014 -.049"‘ -.094"‘ -.016 .276"' -.010 .210"‘ .062"‘ .941 2.328 IllinOIS 2.026 .103 -.045 .023 -.018 -.125' -.005 .102 .141' .920 2.197 Indiana 5.460"' .168' -.lO4" .020 -.006 .098 .045' .274' .008 .935 2.073 Iowa 3.693"' -.053 .023 .039" -.004 -.158' .009 .165"' .012 .891 1.732 Kansas 4.019"' -.078 ..018 .037' -.091"‘ .048 -.051" .319"' .013 .856 1.995 Kentucky 1.687 -.067 -.077" .009 -.056' -.068 -.040 .119 .210" .916 1.654 L00151808 1.453 -.103 -.074' .034 .037 -.044 -.071 .094 .184‘ .814 1.455 Maine 2.927" -.034 -.033 .036 .015" -.003 -.104 .420"' .085 .931 1.992 Naryland 2.900"' -.235"' - 012 .056 -.054 .079 -.080 .282 .043 .937 1.813 Massachusetts -7.218"' -.712"' -.254"‘ -.2l4"' .033" .095‘ .010 -.147' .933"‘ .970 1.664 Nichigan 6.322"' .036"‘ -.193"' -.031 .143' .104 .099 .065 .071 .959 1.978 Minnesota 1.291' .080 .008 .198"‘ .003 -.357"‘ -.081"' .129‘ .020 .914 2.290 Mississippi 1.837 -.193" -.066 -.055 .028 .129 .213 .244' .188" .920 3.198 Nissauri 1.418"' -.O77 -.073" .012 .102 -.093 -.036 .093 .203' .930 2.119 Montana 5.l45"' -.091" o.035' -.006 .040‘ .116‘ .006 .206"‘ -.010 .923 2.178 Nebrasxa 4.151"' -.022 .036" -.00006 -.025"‘ -.097" .003 .131"' .007 .918 2.603 Nevada 3.714"' .098' -.165' ..048" -.033 .972' -.148"‘ .043 .050 .839 1.241 New Hampshire -0.048 -.196" -.064 .018 .0005 -.258' .029 .227' .307"' .963 3.081 New Jersey -0.327 -.036 -.236"' -.181"' .097 .166' -.032 -.164' .548"' .973 1.864 New Mexico 2.667"' -.075 -.085 -.l90"' .161 .082 .003 .326"' .305"‘ .828 1.723 New York -5.918"' -.522"' -.253"' -.231"' .053 .373"' -.116 -.024 .831"' .953 2.248 North Carolina 2.609" .096 -.201"‘ .0006 -.049' .172"' .040 -.115' .235"‘ .968 2.477 North Dakota 4.717"' -.110" -.032 .007 .049 .024 .069‘ .075 .005 .608 1.664 Ohio 2.960“ .104‘ -.l70"' -.078' .184"‘ .128' -.014 .028 .249“‘ .951 2.266 Oklahoma 2.721"' -.120' -.013 -.027' .045" -.111' -.O49" .333"' .143"' .950 2.393 Oregon 0.637 .002 -.110'" .109' -.056“ -.262‘ -.019 .008 .224” .950 1.270 Pennsylvania 0.004 .139" -.U95"' .023 .143'” -.172"' .140“‘ .052 .249'“ .990 1.751 Rhode Island 4.239"‘ .493"' -.157"' -.O90‘ .043“ .057 -.204 -.081 .227 .944 2.619 South Carolina 1.391' -.090 -.mm -.144'" .079 -.046 -.242‘ .197 .366'“ .898 1.880 south Dakota 4.007"' -.055" .061"' .011 -.164"‘ -.l29"‘ .073"' .098"‘ -.009 .852 2.407 Tennessee 3.764"' -.015 .033 .131' .114 -.031 .116 .582‘ -.133 .912 1.851 Texas 1.857°" -.237“' .009 -.013 .065"‘ -.145" -.010 .273" .142"' .951 1.996 Utah 3.797"' -.007 .008 -.032 -.082" .001 -.059" .198"' .068 .794 1.881 Vermont 0.509 -.438" -.015 -.036‘ -.007 -.106 .158" .478"' .260“' .944 2.225 Virginia 2.819“' .047 .011 .050‘ .080‘ -.204" .006 .119‘ .041 .947 1.888 Washington 1.776"‘ -.270"' -.l60"' .044 .043"' 103 -.063" .168“ .223"‘ .955 1.814 Nest Virginia 0.717. -.198" -.097"' .079" -.004 .151' .130“ .286"‘ .160" .982 2.327 Wisconsin 3.466"' .090‘ -.069"‘ -.059" -.034 -.040 .065 .052 .160"‘ .952 2.813 Nyoning 4.662"' .009 -.053' -.046 .004 .275 .013 .125‘ .028 .744 1.128 Note: 1.) All variables are entered in logarithmic ions. 2.) ' indicates that ltl 1 1 ; ' ° 64 " indicates that ltl 11.5; ” ' 55 '“ indicates that It] :2; ‘.' ‘ 119 70 of positive coefficients obtained for these two variables indicates that the labor demand effect dominates the labor supply effect in most cases. State employment is more responsive to improvements in economic conditions than the state labor force, resulting in a positive net employment rate effect for personal income and for %%%%3 on average. Signs of the estimated coefficients for both the non-white labor force variable and the teenage labor force variable are virtually evenly split between positive and negative. The non-white labor force variable has twenty-six positive signs, and the teenage labor force variable has twenty-five positive signs. According to Chapter III, increases in either variable affect both the numerator and the denominator of the employment rate negatively. Total state employment should decline because firms perceive members of both groups as having higher voluntary turnover rates and, therefore, higher fixed costs of labor. At the same time, state labor force should decline because of the relatively less desirable employment opportunities available to non-whites and because of the relatively greater amount of time devoted to human capital accumulation by teenagers. The even split in signs for both variables indicates that neither the employment effect nor the labor force effect dominates. The coefficient signs of the educational attainment variable are also virtually evenly split, with twenty-three being positive and twenty-seven negative. Chapter III asserts that an increase in this variable increases both the numerator and the denominator of the (Employment rate. Firms should prefer more educated workers, other things sequal, since the productivity of these workers is presumably greater and 71 their training costs are lower. At the same time, however, if incre- ments to education increase worker attachment to the labor force, then more workers will join the labor force. The even split in signs indicates no tendency for either effect to dominate across states. The employment rate equation includes transfer payments and property income to capture labor supply effects resulting from changes in income received from non-labor sources. If leisure is a normal good, an increase in an individual's income from a non-labor source induces that person to consume more leisure and reduce work effort. This effect results since the individual gains a greater command over all resources with no change in the terms of trade between leisure and other goods. An increase in non-labor income should induce individuals at the margin to reduce their supply of labor to zero; therefore, the denominator of the employment ratio, state labor force, declines given an increase in non-labor income. 'Hueemployment rate, in turn, should rise. The expected sign of the coefficient for both transfer payments and property income is therefore positive. The mixed signs obtained for these two variables in Table 4-1 (indeed, there are forty negative transfer payment coefficients) indicate more is involved here than a simple income effect. Consider transfer payments. Transfer payments are income payments to individuals for which no services are rendered. The sub- programs that make up the very general transfer payment category, however, are not at all homogeneous. As noted earlier, the major ‘transfer payment programs are: Old Age, Disability, and health 'insurance; unemployment insurance benefits; educational and training 72 assistance payments; and income maintenance payments.4 The labor supply effects of any one of these programs are likely to differ substantially from those of the others. On the one hand, programs such as Old Age Insurance, Disability Insurance, and educational aid undoubtedly have the hypothesized negative effect on state labor force. Substantial evidence exists suggesting that the anti-work bias of the OASI program has increased over time as the earnings replacement ratio has increased from approximately 28% of final earnings in 1966 to 40% of final earnings in 1976.5 Other evidence suggests that workers with few marketable skills, whether severely impaired or not, have a greater incentive to seek disability compensation. Since such workers are likely to have low market wages, the level of support offered by the Disability Insurance program provides an attractive alternative to work (especially if the job opportunities available to these individuals are confined to the secondary labor market).6 Disability Insurance, therefore, induces workers to exit the labor force and thus raises the overall employment ratio. Similarly, educational assistance payments reduce both out of pocket costs and the opportunity cost of attending school. Such incentives,in turn, induce younger individuals to either exit the labor force or not enter it at all. Hence, the overall employment rate should rise as the overall level of educational assistance payments increases. An additional characteristic of programs such as Old Age and [Disability Insurance and educational aid is that they do not simply 73 induce a random sample of workers to exit the labor force. These programs, rather, induce workers with an above average incidence 0f unemployment (i.e., the old, non-whites, and the young) to leave the labor force.7 This exodus shifts the composition of the labor force toward individuals with lower average unemployment, causing the overall rate of unemployment to fall and, concomitantly, causing the overall rate of employment to increase. While the aforementioned programs cause state labor force to decline and, therefore, the employment rate to increase, other transfer programs exist which are likely to account for an increase in labor force and which consequently cause the employment rate to decline. Transfer programs carrying work registration requirements are food stamps, aid to families with dependent children, and unemployment insurance benefits. In order to receive the benefits of these programs, one must register with the state's employment security agency as being in the labor force and willing to accept a job if offered. If individuals who receive such benefits have a higher average incidence of unemployment, then these programs also exert a compositional effect. Such transfer programs, by bringing individuals who possess a higher probability of becoming unemployed into the labor force, raise the overall unemployment rate and, in turn, lower the overall employment rate. Unemployment insurance benefits lower the overall employment ‘rate in a third way to the extent that they induce workers who receive ‘them to remain unemployed for longer periods of time than they might (otherwise. Since continued receipt of benefits is conditioned upon 74 continued unemployment, durations of unemployment spells should lengthen. Unemployment insurance benefits, therefore, provide workers a financial incentive to remain unemployed, which, in turn, lowers the employment rate.8 Further evidence exists suggesting that some transfer payments (specifically, unemployment insurance benefits) affect the demand side of the employment ratio. It has been argued that since the tax which finances unemployment insurance is not fully experience rated, employment fluctuations increase. This effect occurs because the marginal tax cost to employers of an additional layoff, past a certain cutoff point, falls to zero if the tax is not fully experience rated.9 Movements in transfer payments also inherently involve a cyclic component. Periods in which transfer payments rise more rapidly than average are generally periods of weak aggregate demand. As demand conditions in the product market deteriorate, firms reduce vacancies by eliminating positions rather than filling them and by laying off workers, causing employment (and therefore the employment rate) to fall. In this sense movements in transfer payments may also serve as proxy for changing conditions in the product market. It is clear, then, that transfer payments embody more than the simple non-labor income of economic theory. The result is that the signs of the coefficients associated with this variable may be either positive or negative. As shown in Table 4-1, forty of the transfer payment coefficients are negative, reflecting the powerful influences of Ianemployment insurance benefits and also reflecting transfer payments' V‘ole as proxy for demand conditions in the product market. 75 The signs of the property income coefficients are evenly split between positive and negative. Chapter III suggests that an increment to an individual's property income results in a pure income effect. One expects, in turn, that an increase in a state's total property income should induce a decline in that state's labor force and, therefore, an increase in the state's employment ratio. It is conceivable, however, that increases in property income affect state employment (or state labor demand) positively. Rising rent, interest, and dividend income mark more favorable business conditionsikn~firms, causing vacancies and hiring to increase. Thus variations in a state's property income may also proxy for changes in conditions in its product market. Both the negative supply effect and the positive demand effect of an increase in property income would account for the twenty-five positive property income coefficients found in Table 4-1. Operation of either effect, alone or in concert, should increase the employment rate. The foregoing considerations, however, do not explain the twenty-five negative property income coefficients in Table 4-1. One may account for these latter coefficients by considering what effect an increase in property income has on the overall composition of the labor force. As with an increase in transfer payments, an increase in property income, other things equal, is not likely to induce a random sample of workers to leave the labor force through operation of the income effect. Individuals who receive rent, interest, and dividend income are generally older, upper income individuals with a below iaverage incidence of unemployment. An increase in property income is 76 therefore likely to shift the composition of the labor force toward individuals with higher average unemployment. This shift, in turn, causes the overall unemployment rate to increase and, therefore, the employment rate to decline. The sign of the estimated property income coefficient for a given state thus depends on the relative strengths of the compositional and labor demand effects at work. ‘ Table 4-1 reveals thirty-five of the state wage coefficients to be negative but fifteen to be positive. Chapter III hypothesizes the signs of the wage coefficients to be negative; therefore, one must reconcile the contradictory empirical results with the theoretical prediction. The most plausible explanation of the positive coefficients derives from the nature of the particular variable selected to proxy for state wages. Recall that this variable is gross average hourly earnings of production workers in manufacturing. With the usual assumptions regarding profit maximization by firms and utility maximiza- tion by workers, a marginal increase in the variable should reduce employer demand for production workers and increase the supply of production workers, thus lowering the overall employment rate of state production workers. But what are the implications of an increase in the wage variable for the entire state employment rate, i.e., the employment rate of all workers in the state? If wages of other types of labor do not move in unison with wages of production workers in manufacturing (there is, of course, no reason that they should in the short run), a change in relative wage ratios occurs. 77 On the demand side an increase in the relative wages of production workers not only leads to a decline in the demand for services of this particular factor but also leads to substitution of other factors in the production process such as white collar labor, workers from the secondary ‘0 The result is that demand for labor market, and capital equipment. these alternative factors increases (assuming them to be substitutes for production workers rather than complements). Factor substitution thus mitigates, to some extent, the employment effect of a marginal increase in the wage variable. The exact amount of the offset depends on the relevant substitution elasticities which presumably differ across states given varying industrial mix and institutional characteris- tics. At the same time, an increase in the wages of production workers in manufacturing is not likely to alter only the supply of labor of production workers. The wages of these workers also enter the utility functions of at least some workers outside of manufacturing. If one examines the problem from a family utility maximization viewpoint and makes some simplifying but plausible assumptions, then the result follows directly that an increase in the wages of production workers in manufacturing has an ambiguous effect on state labor force, rather than the positive effect suggested in Chapter III. Assume first that the production worker in manufacturing is typically the family's primary income earner and is typically a prime age male. Further, assume that second and third income earners in the family unit, such as working \uives and teenagers, take jobs other than as production workers in Inanufacturing. For these latter workers the wages of production workers 78 in manufacturing enter the individual utility function as non-labor income, an increase of which causes a decline in labor supply. increase in the value of the husband's market time makes the wife's non-market time more valuable. An increase in the value of the father's market time makes non-market alternatives such as additional schooling or greater concentration on schooling more attractive to younger members of the family unit. An increase in the wages of production workers in manufacturing may, therefore, lead some members of the population to reduce the amount of labor they supply (and, in some cases, to leave the labor force). A second supply side issue to be considered here is the compara- tive attachment to the labor force of production workers in manufacturing relative to that of other workers. If production workers in manufacturing are typically prime-age males, then an increase in their wage rate is likely to induce few members of this group into the labor force since these individuals are strongly attached to the labor force to begin with. An increase in non-labor income from the viewpoint of second and third earners in the family unit, on the other hand, may cause a large reduction in labor supply given the relatively weaker labor force attachment of individuals who constitute these groups. As a corollary to the foregoing argument, a compositional effect also exists which must receive due consideration. Females and teenagers have higher average unemployment rates than prime age males. If an increase in the wages of production workers induces individuals 'from the two former groups to leave the labor force, then the overall (:omposition of the labor force shifts toward groups with lower average 79 unemployment rates, resulting in a higher average employment rate. Thus an increase in production worker wages positively influences the overall employment rate through this latter channel. Whether or not an estimated wage coefficient is positive depends on a number of factors: elasticities of factor substitution; labor supply elasticities of second and third earners in the family unit; and average unemployment rates of these latter groups in the state in question. Each of these factors exerts an offsetting influence on the primary adjustments in state employment and labor force induced by a marginal change in the wage variable. Whichever set of opposing effects that dominates determines the sign of the wage coefficient.12 This section analyzes the regression results from the fifty- state employment rate model. The results indicate a wide diversity in both the strength and direction with which marginal changes in the independent variables affect employment rates across states. The principal findings are: 1. State personal income and AGNP/PGNP, which are designated as proxies for demand conditions in the product market, primarily affect the employment rate positively; 2. Age, race, and education variables, which take into account state demographic mix, are approximately evenly split between exerting upward or downward pressure on state employment rates; 3. State transfer payments and state property income, which are designated as proxies for non-labor income, affect state employment rates counter to theoretical expectations in many cases. However, when individual features of some of the transfer programs involved and 80 compositional factors are taken into account, the contradictory signs are reconciled and, indeed, make good economic sense; 4. Gross average hourly earnings of production workers in manufacturing, used to proxy for state wages, exhibit in a majority of cases (35 of 50) the expected negative effect on the state employment rate. The other fifteen cases in which positive signs are obtained are attributed to countervailing labor supply and demand effects occurring in other sectors of the state economy. 4.4. Regional Patterns in the Regression Coefficients Since Table 4-1 lists the individual regression coefficients in alphabetical order, regional patterns in the coefficients are not readily apparent. In order to remedy this situation, Table 4-2 presents results from regional t-tests for equality of means for each of the explanatory variables. For a given variable the specific test involves taking the regional mean of the state regression coefficients in a single Census sub-region (using the 9-region classification) and then comparing this mean with the mean regression coefficient of all states not belong- ing to this particular region. If the absolute value of the computed t-statistic is greater than some critical value, then one must infer that it is highly improbable that the regional mean coefficient and the sample mean coefficient differ simply because of chance. Table 4-2 reveals that, in many cases, the regional averages do not differ significantly from the sample averages, indicating that the individual state regression coefficients, which comprise the regional means, are randomly distributed in the entire sample. Some notable 81 Table 4-2. weighted Regional t-Statistics Assoc1ated with the OLS Coefficients AGNP REGIM COhSl. URGES TRAN. PM PRP. INC. MN-Iilll [0.411. KENS FCNT‘ PERS. INC. Ne- England -J.IOb"' -2.835"' -2.331°' o1.780' -0.876 1.329 -0.957 -2.195" 3.108"' (Cl. Hi. HA. NH. 81. V1) Hid Atlantic -3.688"‘ -0.971 -2.563" -2.842"' 1.553 1.959‘ —0 541 -1.999" 3.712"‘ (NJ. NY, PA) East North Central 2.118" 3.036"' ~0.577 0.181 1.296 0.444 0.900 -0.623 -1.l70 (IL. IN. MI. DH. 81) Nest North Central 1.110 0.815 2.667°" 2.664"' ~0.96l -1.909° -1.014 0.214 -2.081" (14. KS. MN. 80. NE. ND. 50) Scoth Atlantic 1.076 0.803 -O.228 1.570 -2.542" 0.580 0.061 0.080 -1.037 (0t. 04. FLA, H0, NC. SC, VA. NV) Cast South Central 0.692 0.337 1.925' 1.838' -0.154 -0.503 1.026 2.367" -1.597 (Al, KY, HS. 1N) Uest Sputh Central 0.494 -0.482 2.044" 0.483 0.303 -1.171 -0.831 1.476 -0.883 (48K. LA. 0k. 11) NOuntain 1.941' 0.162 1.203 -0.941 -0.790 1.190 -0.726 1.909' -1.200 (AZ. C0. 10. 81. NV. NI. UT. NY) Pacific 0.217 -2.096" 1.358 0.323 -1.033 -2.881"' 0.779 l.972°‘ -0.238 (AK. CA, NA, 00, HA) Note 1.) 7 r t ' 8‘ - 8 (n‘ - 1) Si 9 (SO-hi - 1) s? 1 1 ‘5 (a. (50-n‘1) where 8‘ - 3. 13 813' 1' states in region i 8 - I ak Qt. k - all states but states in region i if) 2 _ t T 2 s‘ E o‘J (bi) - a.) 5 I I °h (8k ‘ 612 If) a is average labor force in state j 13 divided by average labor force in region is o is average labor force in state k divided by average labor force in U.S. (based on all states but those in region 1). 2.) ' indicates significant at .10 level. " indicates significant at .05 level. "' indicates significant at .01 level. 82 exceptions exist, however. In particular, the regression coefficients obtained for the Mid-Atlantic region differ significantly from the sample mean for six of the nine variables. Most interesting is the t-statistic associated with personal income, which indicates that the sensitivity of state employment rates in the Mid-Atlantic region to marginal changes in personal income is much greater than that in other regions. Recall that personal income proxies for demand conditions in the product market. Employment rates in the Mid-Atlantic region, then, are strongly dependent on conditions in the product market. This result is consistent with the hypothesis advanced in the regional economics literature that regions producing goods with high income elasticities of demand (such as durable goods) experience unstable employment behavior relative to regions producing goods with low income elasticities of demand (e.g., food, services, etc.).13 Of the nine regions, the Mid- Atlantic region ranks third in percentage of total non-agricultural employment devoted to durable goods production.M The large personal income coefficients for states in this region no doubt reflect the strong dependence on cyclically sensitive manufacturing industries, particularly durable goods industries. Consumers are able to postpone purchases of these sorts of goods in economic downturns, implying greater variation in product demand in these states and, therefore, greater variation in employment rates. Both the New England states and the Nest North Central states also possess statistically significant t-statistics in the personal income variable. The test statistic for the New England region is positive and likely reflects similarities in the economies of the states 83 which make up this region to those of states comprising the Mid-Atlantic region. (Recall from footnote 14 that this region ranks directly behind the Mid-Atlantic region in terms of employment in durable goods industries.) The t-statistic associated with the personal income coefficients of the West North Central states is negative and significant, on the other hand, indicating that employment rates in this region are relatively unresponsive to changes in personal income. Since food demand is income inelastic, the relatively greater concentration on agricultural production in the Nest North Central region insulates the state economies in this region from the vagaries of the business cycle. Fluctuations in personal income, therefore, have little effect on state employment rates here. Table 4-2 shows that the transfer payment coefficients also exhibit some degree of regional variation. For this variable the t-statistic of both the Mid—Atlantic and New England regions is negative and highly significant, implying that a marginal increase in transfer payments has a substantially deleterious effect on employment rates of states in the Northeast. The tendency for both regions to have large, negative transfer payment coefficients reflects a confluence of two factors. First, as noted above, industry in both regions is heavily concentrated in the production of cyclically sensitive durable goods. Layoffs in economic downturns should be relatively greater here, necessitating relatively larger expenditures on unemployment insurance benefits which increase the duration of unemployment spells. Second, there are a number of large, urbanized, central cities present in the 84 overall region with considerable populations of indigenous poor. The composition of transfer payments in both regions is therefore tilted toward programs such as aid to families with dependent children, food stamps, and unemployment insurance benefits, which bring individuals from groups with high average unemployment rates into the labor force. These factors combine to cause the very negative transfer payment coefficients associated with the states in the region. The t-statistic associated with the transfer payment coefficients of the West North Central region, on the other hand, is positive and highly significant, reflecting both the low cyclic sensitivity in the area, determined by the industrial base, and the tilt in the composition of transfer payments in this region toward programs which induce individuals to leave the labor force (e.g., Old Age Insurance). Table 4-2 further reveals negative and significant t-statistics associated with the constant terms of the New England and Mid-Atlantic regions and positive and significant t-statistics for the constants of both the East North Central and Mountain states. If one adopts the interpretation that the regression constants serve as rough, but nevertheless good, indicators of structural and frictional unemployment in the individual states, then one must infer that structural/frictional unemployment is well above the average in the Northeast and is well below the average in the Mountain and East North Central states.15 Untestable explanations of this regional variation are: differing degrees of search efficiency in the job/worker matching process, varying degrees of regional labor market segmentation, and variation in the number of declining versus expanding industries across regions. 85 Table 4-2 also indicates regional variation in the coefficients of some of the other variables of the model. Wage coefficients of the East North Central region are well above average, but are well below average in the New England area. Property income coefficients are significantly greater than average among the West North Central and East South Central states, but significantly less than average among the New England and Mid-Atlantic states. Coefficients of the non-white labor force variable are well below average in the South Atlantic states. Educational attainment coefficients are relatively large in the Mid-Atlantic states, but well below average in the Pacific and West North Central states. Coefficients of the GNP variable are significantly greater than average in the states of the East South Central, Pacific, and Mountain regions, but significantly less than average in the New England and Mid-Atlantic states. And one finds no regional variation in the coefficients of the teenage labor force variable. In general, the regression results indicate that states in certain well-defined areas respond similarly to marginal changes in particular economic variables. States in the Mid-Atlantic region demonstrate the greatest cohesiveness in this respect, with the null hypothesis that the regional mean equals the mean of the other forty- seven states rejected for six of the nine variables. Given the regional industrial mix, the findings of this section confirm what one might expect to be the case. State employment rates in the heavily industrialized Northeast are very sensitive to fluctuations in product demand (proxied for by personal income and transfer payments). The employment rates of the agricultural states of the Midwest, on the 86 other hand, do not seem to be susceptible at all to cyclic fluctuation. As indicated in Tables 4-1 and 4-2 personal income and transfer payment coefficients for states in this region of the country are near zero in both cases. The following section shows how these regional patterns in the coefficients have interacted to affect change in the overall dispersion of state employment rates. I ‘.‘Ahuw I DAMP J‘s; 4.5. Empirical Results from the Full Dispersion Model This section analyzes the results of the full, fifty-state, nine-variable model. The impacts that cross-state variation in each independent variable exert on the dispersion in employment rates, and how these impacts change over time, are discussed and interpreted. The principal findings are: 1. Cross-state variation in personal income has a substantial dispersion narrowing effect, particularly in the 19705; 2. Cross-state differences in transfer payments, in property income, in the constants (structural/frictional unemployment) and, to a lesser degree, in the wage rate, have a dispersion increasing effect throughout most of the sample period; 3. Cross-state variation in educational attainment exerts a relatively small.dispersion-increasing effect during the 19605 and a small dispersion-decreasing effect during the 19705; 4. Cross-state differences in the other two demographic variables (non-white and teenage labor force), in the GNP variable, and in the residual terms exert very little influence on the dispersion. 87 Given the estimated employment rate equations contained in Table 4-1, one can model the determinants of the geographic dispersion in employment rates (and unemployment rates). Recall from Chapter III that the net variance in the employment rate contributions of a particu- lar variable (say X1) in a given year is: (4.2) oNV(b'x;) = 02(b' xi) + '7' o(b' x), b3 xi) + o(b' xl,3t) j 1 = o(b' x), et) where b1 is the vector of estimated state regression coefficients for variable i; x; is the vector of values for the 50 states of explanatory variable i in year t; Ct is the vector of residuals for the fifty state regression equations in year t; and et is the vector of state employment rates in year t. If the net variance is positive, then differences across states in the variable in question act to increase the dispersion in employment rates in the year under consideration. By equation (3.13), a given net variance equals the covariance between the employment rate contributions of the variable being considered (i.e., bixi) and the state employment rates. A positive net variance, therefore, implies that states with relatively high employment rates tend to have greater than average employment rate contributions in Xi, while states with relatively low employment rates have less than average employment rate contributions in X1. If the net variance of a particular variable is less than zero, 88 then differences across states in this variable act to decrease the dispersion in employment rates. In this case states with relatively high employment rates tend to have less than average employment rate contributions in Xi while states with relatively low employment rates have greater than average employment rate contributions in X1. Table 4-3 presents the variance in log employment rates for each year from 1961 through 1978. As noted earlier employment rate dispersion is greatest in years of economic slack, e.g., 1961 and 1975, and least in years of strong aggregate demand, e.g., 1968 and 1969. Table 4-3. Variance of Log Employment Rates:* 1961-1978 t 02(e) t 02(e) 1961 .4033 1970 .1782 1962 .2664 1971 .2664 1963 .2169 1972 .2297 1964 .1798 1973 .1830 1965 .1763 1974 .2123 1966 .1218 1975 .4380 1967 .1230 1976 .3750 1968 .0992 1977 .2467 1969 .0918 1978 .1526 * All variances are multiplied by 103. Table 4-4 decomposes the yearly variances in Table 4-3 into the respective net variances attributable to the independent variables and to the residual terms. Figures 4-1 through 4-lO depict these net variances in graphical form. The remainder of this section considers the behavior of each variable's net variance over time. 89 Personal Income Table 4-4 and Figure 4-1 indicate that cross-state variation in pesonal income exerts the greatest influence on the dispersion in state employment rates, that its influence is dispersion decreasing, and that this dispersion decreasing effect becomes more powerful over time. Except for 1961, 1962, and 1970, states with relatively high employment rates tend to be states for which the employment rate contribution of personal income is less than average. States with relatively low employment rates tend to be those for which personal income's contribu- tion to the employment rate is above average. But why is the net variance corresponding to this variable negative? Furthermore, what factors cause this net variance to become more negative over time? These questions can be answered jointly. Appendix Table B-1 shows that from 1961 through 1978 the variance in the employment rate contributions of personal income declined 9.3 percent. Recall that the variance is that component of the net variance which is necessarily positive and, therefore, adds to the overall dispersion in employment rates. As noted in Chapter III the variance term reflects what the total variance in employment rates would be if all other employment rate contributions for each of the other variables were held equal across states. The variance in the employment rate contributions of personal income declines relative to other terms in the net variance which can be either dispersion increasing or decreasing (i.e., PI-PI, ijJ)). 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Npmo. om¢m.o mmem. mm—o.— ppmm.o oom— scoo. cmvm.e_i wooo.i coo—. i pace.p mpco. i m~eo.v ~cpm.p i swmm.p moon.m momp moooo. mmnm.epi m—po. momm. i show. seam. i FmF~.n momp. mace.p mmmm.a «cap osoo.i pooo.m i memo. Napo. i ——oo.p ccmm. i sump. i m—ee. i mean. —~m0.c moa— upoo. m-~.m memo. mmmm. u mmpc.p mwso. i mmew.ei mopw. i mpmo. i mmvm. i mom— Nmmo. pmnp.mp mmvo. .msm.—i mmmo. one—.pi mwmw.mi pmmm.~ mmwo. i nmnm.oi poa— 3552. 5.32... Age}... 2.3;. 8.3;. 3.3:... 25.3? ates... 33.3,... $2... a «sew» Fmauvmoz mg» use mmpnopca> acmucmamv=~ mgu yo mco_u:n_cucou mama acosxopaEm as» we mmucuwgo> umz .eie o—noh 60‘ 50i 40‘ 30‘ 20‘ 10‘ 5 1 b 91 -5. -10« -151 -20. -30‘ -50 a -60 1 -70 4 ~80‘ I’ 61 62 . 64 65 66 Figure 4-1. Else—70 71 72 73 Net Variance--Personal Income 74 75 76 77 92 NV 301- 2041 4—‘ 10” .—, 5.. [-— E W _50 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 -100 -15‘[ -20.. -4017 Figure 4-2. Net Variance-—Transfer Payments 93 40 .. 20 0 15 0 rj ‘7 *— 61‘ 63764 65 66 67 68 69 70|7172 73 74 75 76 77 78 L._..l . -5i’ . 40*» -15 0 -20.. ~40" Figure 4-3. Net'VarianceQ-Constant Terms 30 " 20 0 150 10 .1 5 0 94 1_, r— l 61 -54» -10 'P ~15¢ -204L -30.. 62 7'63 64 65 66 67 68 69 70 71 72 73 Figure 494. Net Variance--Pronerty Income 74 '75 75 77 78 95 '“Nwéw -1 ' 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 Figure 4-5. Net Variance-~Nages 61 62 63 64 65 66 67 68 69 7O Figure 4-6. Net Variance--Educational Attainment 96 °Nv 241. ‘ldk -1“ 63 64 65 66 67 68 69 7O 71 72 73 74 75 76 77 78 _2.. Figure 4-7. Net Variance--Teenage Labor Force NV 2 l -1 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 t Figure 4-8. Net Variance--Non-White Labor Force NV -14 61 62 63 64 65 66 67 68 69 7O 71 72 73 74 75 76 77 78 Figure 4-9. Net Variance--AGNP/PGNP NV 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 I Figure 4-10. Net Variance--Residuals 97 on in the sample period, causing the net variance in personal income contributions to be negative throughout (excluding 1970). The personal income variable's offset effect vis-a-vis other variables becomes greater than its own dispersion increasing effect as a direct result of the relative decline in the variance of the employment rate contributions of personal income. In order to understand the precipitous decline in the variance (and, therefore, the net variance) of personal income contributions, consider the following. Recall that Table 4-1 shows that virtually all of the personal income coefficients are positive. Personal income tends to grow for all states over time.16 The mean employment rate PI contribution in this variable, b .PI , therefore, shifts outward over time. Figure 4-11 pictures hypothetical frequency distributions for the employment rate contributions in personal income at time t and at time t + i. f(b'PI) Figure 4-11. Hypothetical Frequency Distributions of the Employment Rate Contributions of Personal Income 98 Since bPI-PI is positive and growing in virtually all states and since the variance in the frequency distribution declines with time (as in Figure 4-ll), it is clear that terms in the lower half of the distribution catch up with terms in the upper half. Employment rate contributions in personal income have tended to equalize over time, accounting, consequently, for the decline in their variance (and net variance). The explanation of this phenomenon is apparent when one considers the rank ordering of the personal income coefficients given in Table 4-5. In the upper half of the distribution one finds many of the heavily industrialized states of the Northeast and North Central regions (recall the discussion in Section 4.4). Present here are five of the six New England states (Connecticut, Massachusetts, New Hampshire, Rhode Island, and Vermont), all three Mid-Atlantic states (New Jersey, New York, and Pennsylvania), and two of the five East North Central states (Ohio and Wisconsin). Table 4-6 shows that, with the exception of New Hampshire, all of these states experienced below average growth in real personal income during the period studied. States in the lower half of Table 4-5, however, tend to be the fast growing states of the South and Southwest. Present here are Texas, Nevada, Idaho, Utah, Maryland, Virginia, Arkansas, Alabama, Florida, and Hawaii. As Table 4-6 shows, all of these states experienced above average growth in real personal income during the period studied. The Spearman rank correlation coefficient, used here to compare a state's rank in the personal income coefficient distribution with its rank in the distribution of personal income growth rates, is -.201 and is 99 Table 4-5. Rank Order of State Personal Income Coefficients Rank State Coefficient Rank State Coefficient 1 Massachusetts .933 26 Texas .142 2 New York .831 27 Illinois .141 3 New Jersey .548 28 Arkansas .125 4 South Carolina .366 29 Colorado .125 5 Georgia .316 30 Hawaii .118 6 New Hampshire .307 31 Florida .101 7 New Mexico .305 32 Maine .085 8 Arizona .297 33 Alabama .073 9 Connecticut .267 34 Michigan .071 10 Vermont .260 35 Utah .068 11 Ohio .249 36 Idaho .062 12 Pennsylvania .249 37 Nevada .050 13 California .239 38 Maryland .043 14 North Carolina .235 39 Virginia .041 15 Rhode Island .227 40 Wyoming .028 16 Oregon .224 41 Minnesota .020 17 Washington .223 42 Kansas .013 18 Kentucky .210 43 Iowa .012 19 Missouri .203 44 Indiana .008 20 Mississippi .188 45 Nebraska .007 21 Louisiana .184 46 North Dakota .005 22 West Virginia .160 47 South Dakota -.009 23 Wisconsin .160 48 Montana -.010 24 Delaware .145 49 Alaska -.021 25 Oklahoma .143 50 Tennessee -.133 100 Table 4-6. Percentage Growth in Real Personal Income by State: 1961-1978 % Change in % Change in Personal Income: Personal Income: Rank State 1961-1978 Rank State 1961-1978 1 Nevada 224.8 26 Kentucky 108.7 2 Alaska 217.2 27 New Mexico 108.1 3 Florida 192.3 28 California 100.7 4 Arizona 183.7 29 Michigan 97.3 5 Texas 142.7 30 Vermont 96.8 6 South Carolina 141.9 31 Minnesota 96.3 7 Arkansas 135.8 32 West Virgina 88.9 8 Georgia 135.1 33 Montana 87.8 9 Colorado 134.7 34 Iowa 86.0 10 Virginia 129.0 35 Nebraska 85.0 11 North Dakota 127.1 36 Indiana 84.6 12 Oregon 127.0 37 Wisconsin 82.9 13 North Carolina 124.9 38 Kansas 80.8 14 Hawaii 124.8 39 Delaware 79.1 15 Tennessee 120.8 40 Maine 76.0 16 Louisiana 120.8 41 Missouri 75.5 17 Idaho 120.6 42 South Dakota 71.6 18 Wyoming 120.2 43 New Jersey 71.0 19 Mississippi 119.8 44 Connecticut 68.7 20 Maryland 116.4 45 Ohio 68.4 21 New Hampshire 116.2 46 Illinois 67.9 22 Oklahoma 115.3 47 Rhode Island 67.3 23 Alabama 113.4 48 Pennsylvania 60.7 24 Utah 112.8 49 Massachusetts 60.2 25 Washington 112.0 50 New York 41.0 101 statistically significant at the .10 level.17 An inverse relationship exists, therefore, between a state's rank in the former distribution and its rank in the latter. This relationship implies that the employment PI i lower half of the coefficient distribution grow faster than the rate contributions of personal income (i.e., b -PIi) of states in the employment rate contributions of personal income of states in the upper half ofiflmecoefficient distribution. Hence the variance in the personal income variable's employment rate contributions (02(bPI-PI)) necessarily declines. This decline, in turn, causes the net variance of personal income to become more negative over time. Though the net variance declines sharply over the time period, it does not do so in a monotonic fashion. The specific reasons causing personal income'snet variance to rise or fall in a given year can only be determined by decomposing the net variance into its component variance and covariance terms and comparing these across years. Appendix Table B-1 provides this decomposition. (Tables B-2 through B-lO decompose the net variances of each of the other explanatory variables.) A year-by-year and variable-by-variable analysis at this detailed level is beyond the scope of this research. A very general comment can be made regarding the variations in personal income's net variance, however. Much of the fluctuation appears to be cyclic in nature. In years of recovery (e.g., 1972 and 1976) large declines in the net variance occUr because of relatively large declines in the variance of the employment rate contributions in personal income. The inference to be drawn here is that cyclically insensitive states (i.e., states in the lower half of the personal income coefficient distribution) recover 102 rapidly from recessions and register relatively large initial increases in personal income. Cyclically sensitive states (i.e., states in the upper half of the personal income coefficient distribution) recover more sluggishly and experience relatively small increases in personal income initially. The result is a large decline in the variance of personal income contributions in recovery years and relatively smaller declines in this variance in other years (as the economies of cyclically sensitive states also revive). Personal income's net variance also declines rather sharply in recession years. This decline occurs because the negative covariance between the contributions to employment rates of personal income and transfer payments becomes even more negative when the economy contracts, thus causing personal income's net variance to decline (become more negative). In recession years, transfer payments increase relatively which in turn expands mean deviations in the employment rate contributions of this variable. The result is that, in recession years, the offset effect of personal income with respect to the employment rate contribu- tions of transfer payments becomes much greater. The dispersion decreasing influence of personal income, therefore, increases in recession years because of the expansion across states in transfer payments. The results of this section lead to the principal conclusion that cross-state differences in demand conditions in the product market, as proxied by personal income, are a key determinant of the overall dispersion in state employment rates. Table 4-4 and Figures 4-1 through 4-lO show the effect of this variable on the overall variance of 103 employment rates to be greater than all others (in an absolute sense). Moreover, as the employment rate contributions of personal income become more equal over time, the dispersion-decreasing effect of personal income grows to be quite large. Increasingly, states with high employment rates are those whose employment rates are relatively insensitive to changes in personal income, and states with low employment rates are those whose employment rates are relatively sensi- tive to changes in personal income. The implications for policy are clear. One way to reduce the dispersion would be to promote economic growth in those low employment rate states that are relatively sensitive to fluctuations in personal income and to allow other states simply to respond to market forces. (Of course, not all low employment rate states are sensitive to changes in personal income.) Transfer Payments Figure 4-2 depicts the net variance in the employment rate contributions of transfer payments over the time period. This net variance is differentially greater in recession years such as 1961, 1971, and 1975 and is indeed a major contributor to the peaks in overall dispersion experienced in these years (see Figure 3-2). Hence cross- state differences in transfer payments exert a dispersion increasing influence particularly in recession years and particularly in the 1970s. As noted in Section 4.4, employment rates of certain states are very sensitive to increases in transfer payments. Principal among this group are the three Mid-Atlantic states, three of the six New 104 England states (Connecticut, Massachusetts, and Rhode Island), and four of the five East North Central states (Indiana, Michigan, Ohio, and Wisconsin). When demand conditions in the product market slacken, transfer payments (particularly in the aforementioned states) increase. States sensitive to fluctuations in transfer payments experience declines in employment rates, and states not sensitive to fluctuation in transfer payments (i.e., blp 330) undergo little change in respective employment rates. In years of economic slack, then, as transfer payments increase across states, the variance in the employment rate contributions of transfer payments, 02(bTP~TP), increases differentially. In turn, the overall dispersion of employment rates necessarily increases. Table 4-7 lists the variance in the contributions of transfer payments, along with the percentage change in this variance, on a year- by-year basis. This variance experiences its greatest percentage increases in 1971 and 1975, and it actually declines in some of the non- recession years (i.e., 1972-1973 and 1976-1978). This fluctuation accounts for the tendency of transfer payments' net variance to peak in certain years. The noticeable upward trend in this net variance, throughout the 1970s, still lacks adequate explanation, however. The underlying cause of much of the increase in the net variance of transfer payments relates to the equalization of personal income's employment rate contributions diScussed in the previous section. The covariance between the employment rate contributions of transfer payments and personal TP P PI. TP income (note that o(b -TP, b I-PI) = o(b PI, b -TP)) is negative. Hence, cross-state differences in transfer payments offset the employment 105 rate effects of personal income and, therefore, diminish the dispersion increasing influence of personal income (i.e., of 02(bPI'PI)). As the employment rate contributions of personal income became more equal over time, however, the offsetting effect exerted by transfer payments on the contributions of personal income necessarily ebbed. In turn, the covariance between the employment rate contributions of transfer payments and personal income becomes less negative in the 19705. Since this covariance is a major component of the net variance corresponding to transfer payments, its increase causes the net variance of transfer payments to rise in the 1970s. Appendix Table B-2 clearly shows the increase in the covariance of the employment rate contributions of these two variables. To the extent that variations in transfer payments proxy well for variations in aggregate demand, the results of this section again underscore the great influence which demand conditions in the product market exert on the dispersion of employment rates. Furthermore, though indistinguishable from this demand side, cyclic effect, the results also highlight the great impact of transfer programs that do much to increase a state's labor force but do little to increase its level of employ- ment (thus causing a decline in the employment rate). Programs that have this effect are unemployment insurance, aid to families with 18 Because of differences across dependent children, and food stamps. states in the mix of transfer programs, the effect of a marginal increase in transfer payments differs widely across areas with consequent impact on the overall dispersion. The following chapter attempts to separate these two influences, i.e., demand side versus supply side, by re- 106 Table 4-7. Variance in Employment Rate Contributions of Transfer Payments t 02(bTP.Tp) % Change in 02(bTP'TP) 1961 3.8849 ' ' 1962 3.8769 '0-2‘ 1963 3.8850 0-2‘ 1964 3.8858 0-02 1965 3.8953 0-24 1966 3.9140 0°48 1967 3.9525 0-98 1968 3.9831 0-77 1969 3.9914 0-21 1970 4.0259 0-85 1971 4.0740 ‘-19 1972 4.0693 '°°'2 1973 4.0556 '0-34 1974 4.0686 0-32 1975 4.1274 1°45 1976 4.1208 '0-‘6 1977 4.0988 '0-53 1978 4.0743 '0-50 estimating the model in a two-stageleast-squaresframework and taking into account the simultaneity which presumably exists between transfer payments and employment rates. 107 Constants Figure 4-3 and Table 4-4 reveal that a third key determinant of the dispersion in state employment rates is cross-state variation in the estimated constant terms. As noted earlier, others have interpreted constants used in this context as rough approximations of structural/ frictional levels of area unemployment or employment rates. Given the relative size of the net variance of the constant terms, states differ substantially in this regard. These differences have a dispersion increasing effect. States with high employment rates tend to have relatively small levels of structural/frictional unemployment, and states with low employment rates tend to have relatively high levels of structural/frictional unemployment. The data do not identify the precise causes of these differences (i.e., skill mismatches, differential rates of information diffusion, or differential patterns of economic growth or decline). Figure 4-3 also indicates a somewhat variable upward trend in the net variance of the constants. The dispersion increasing influence of the constant terms, therefore, grows with time. Primarily responsible for this upward trend is the relationship of the state constants to the employment rate contributions of personal income. Their covariance is negative. But Table B-3 shows that the covariance between the constants and the employment rate contributions of personal income becomes substantiallyless negative during the time period studied. As is the case with transfer payments, the equalization of the employment rate contributions of personal income over time implies a reduction in the amount by which a given constant offsets a given contribution of personal 108 income. Components of the constants' net variance that are dispersion increasing (e.g., 02(6)) therefore gain in relative stature over time. Also noteworthy in Table B-3 is the decline in the variance of the constants. Since the constant terms are as their name implies, constant, the decline in variance results purely from a change in the labor force weights. Table 4-8 lists the top ten and bottom ten states by relative size of the constant coefficient. Table 4-8 also lists the associated state labor force weights at both the period's outset, 1961, and end, 1978. Table 4-8 shows that the top ten states experience no overall change in the proportion of U.S. labor force residing within their boundaries. The bottom states, however, register a decline of 12.8 percent. Hence, shifts of population toward the middle of the constant terms' distribution induce the decline in the variance of the constants. States with relatively small constants receive less weight in the calculation of the variance over time. lable 4-8. Ten Largest and Ten Smallest Constant Coefficients with Associated Labor Force Weights Wei hts Wei hts Rank State Constant 1961 1978 Rank State Constant 1961 1978 1 Michigan 6.32 .042 .042 41 Minnesota 1.29 .019 .020 2 Indiana 5.46 .026 .026 42 Connecticut 0.88 .015 .015 3 Alaska 5.16 .001 .002 43 West Virginia 0.72 .008 .007 4 Montana 5.15 .004 .004 44 Oregon 0.64 .010 .012 5 Idaho 4.91 .004 .004 45 Vermont 0.51 .002 .002 6 North Dakota 4.72 .003 .003 46 Pennsylvania 0.004 .063 .052 7 Wyoming 4.66 .002 .002 47 New Hampshire -0.05 .004 .004 8 Rhode Island 4.24 .005 .004 48 New Jersey -0.33 .036 .034 9 Nebraska 4.15 .008 .008 49 New York -5.92 .101 .078 10 Kansas 4.02 .012 .012 50 Massachusetts -7.32 .031 .028 TOTAL .107 .107 .289 .252 109 The decline in the variance of the constants is not great enough to nullify the larger increase in the covariance between the employment rate contributions of personal income and the constants. By the end of the period cross-state differences in the constants, therefore, exert a much greater dispersion increasing influence than they do early in the period. Property Income Figure 4-4 and Table 4-4 show that cross—state differences in property income have a relatively sizable dispersion increasing effect throughout most of the sample period. This result again points up the importance of cross-area differences in product market demand conditions given the cyclic dependence of property income noted in the previous chapter. The net variance corresponding to property income increases with time. As is the case with both transfer payments and the constants, the relationship between property income and personal income, in the model, accounts for this upward trend. The covariance between the employment rate contributions of the two variables is negative and relatively large in absolute value (see Appendix Table B-4). As the employment rate contributions of personal income become more equal over time, however, the offsetting effect of the employment rate contributions of property income declines. The relative importance of the dispersion augmenting components of property income's net variance, in turn, increases. 110 Wages Table 4-4 and Figure 4-5 indicate that cross-state variation in wages has a positive impact on the dispersion in state employment rates throughout virtually the entire time period. High employment rate states tend to display above average employment rate contributions in wages, and low employment rate states tend to possess less than average employment rate contributions in wages. Though the net variance in wages remains relatively constant over time, it does appear to diminish slightly in recession years. Reference to Appendix Table B-5 shows that the variance in wage contributions in 1970, 1974, and 1975 actually declines, accounting to some extent for the overall decline in the net variance of the employment rate contributions of wages in these years. Comparison of the net variance corresponding to wages with the net variances of the four variables already considered shows the influence of wages on the dispersion in state employment rates to be of second order importance. Table 4-9 lists ratios of the net variance in wages to the net variances of each of these other variables for 1978. The other four net variances clearly dwarf the net variance of the wage rates, indicating that the former are much more important than the latter in exerting influence on the dispersion. Factor costs, therefore, as measured by the state wage variable, are not a principal determinant of state employment rate dispersion. Of course, this is not to say that wages play no part at all in determining the dispersion, for clearly they do to some extent. It does mean, however,that the roles played by the geographic structure of product market demand, by overall 111 cyclic conditions, and by structural/frictional considerations are of much greater importance than that played by wages.19 Table 4-9. Ratio of the Net Variance in Employment Rate Effects of Wages to the Net Variance in Employment Rate Effects of Personal Income, Transfer Payments, Constants, and Property Income for 1978. W 1 1 oNV(b oN)/0Nv(b -X ) N PI _ oNV(b oN)/0Nv(b ~PI) - -.028 W TP _ oNV(b -N)/ONV(b sTP) - .087 N C _ oNV(b ~N)/0Nv(b ) - .066 N PRP _ 0NV(b ~W)/oNv(b -PRP)- .090 Educational Attainment As do cross-state differences in wage rates, cross-state differences in educational attainment also exert a very modest influence on the dispersion in state employment rates. Figure 4-6 and Table 4-4, however, show that state differences in educational attainment increase the dispersion during the 1960s, but decrease the dispersion during the 19705. Appendix Table B-6 reveals that the relationship of educational attainment to personal income is principally responsible for the decline in net variance which takes place. The covariance between the employment rate contributions of these two variables is positive. The employment 112 rate contribution of educational attainment in a given state, therefore, tends to reinforce the employment rate effect of personal income. Over time this covariance declines due to the equalization in the employment rate contributions of personal income. (The rate of decline is much greater in the 1970s at an annual average rate of .63 percent per year compared with .16 percent per year in the 1960s.) The decline in this large, positive component of educational attainment's net variance allows other negative components to gain relatively, eventually causing the sign change in 1971. Though this sign change occurs, it is of little consequence for the overall dispersion. Comparison with the net variances in personal income, transfer payments, the constants, and property income shows that cross-state differences in human capital accumulation (proxied by educational attainment) are much less important in determining the dispersion in employment rates than are the other four explanatory variables. Age and Racial Mix Table 4-4 and Figures 4-7 and 4-8 indicate that the other two demographic variables employed in the study, teenage and non-white labor force, have relatively little impact on the dispersion in state employment rates. The employment rate contributions of these variables are therefore randomly distributed with respect to state employment rates. One is as likely to find a high employment rate state with an above-average employment rate contribution in either of these variables as one is to find a high employment rate state with a below average 113 employment rate contribution in either variable (since oNV(bT-T) = T NW NW, o(b ~T,e)‘*0“o(b 'NW, e) = o b NW)). On the basis of these 11v( results one must reject the hypothesis outlined in Chapter III that geographic differences in the racial or age composition of the labor force affect the dispersion in state employment rates. The dispersion in employment rates remains invariant to these demographic variables though at least one identifiably large demographic fluctuation occurs during the time period. Early in the period of study, individuals belonging to the baby boom generation began to come of working age. According to the U.S. Census Bureau, the baby boom began in 1946. In this year the U.S. birthrate increased sharply and continued at a higher rate through the mid-19505, after which it declined.20 Individuals from this age cohort began to reach age 16 in 1962, which resulted in increasing ratios of 16-19 year-olds relative to the rest of the working-age population from 1962 through the mid- l970s. Because of the decline in the birth rate that occurred in the mid to latter 19505, state ratios of working age teenagers to the rest of the working age population began to decline in the mid-19705. Since the coefficients of the teenage labor force variable are evenly split between positive and negative, the across the board increase of this variable should cause the variance of the employment rate contributions in teenage labor force to increase. Appendix Table B-7 reveals an increase in variance from 1962 to 1975. After 1975, 02(bT-T) declined as the teenage labor force, in general, declined. Figure 4-7 and Table 4-4 clearly show, however, that this demographic change has little effect on the net variance in the employment rate contributions of 114 teenage labor force, and, therefore, little effect on the overall dispersion in state employment rates. Though the dispersion model indicates that state differences in age and race composition have little effect on the dispersion of state employment rates, this finding does not preclude these variables from playing important roles in the determination of employment rates in particular states. Further, though teenage labor force increases greatly during the period of study, the dispersion of employment rates registers little change because of this demographic shift. AGNP/PGNP and Residual Terms Table 4-4 and Figures 4-9 and 4-10 show that the amount of the variance in employment rates attributable to the GNP variable and to the residual terms is negligible in all years. The specification includes éggg-to capture effects which aggregate demand conditions in the national economy exert on employment rates in individual states. Most likely, this variable exercises so little influence on the dispersion in employment rates because variation in employment rate contributions of %%%g depends totally on variation in the estimated coefficients of é%%%c The variable itself is identical across states in a given year. The miniscule net variance corresponding to the residual terms, on the other hand, may be attributed both to the general random- ness in these terms across states and to the overall goodness of fit obtained in the regression equations reflected by the high R2 values. 115 4.6. Conclusion This chapter presents and analyzes the results from an empirical estimation of the dispersion model outlined in Chapter III. The time period studied spans twenty-one years, 1958 through 1978. The explanatory variables of the model take into account factor costs, demand conditions in the product market, non-labor sources of income, and several demographic characteristics. For any given explanatory variable, the regression results indicate that the estimated coefficients differ greatly across states. This finding supports the hypothesis that, because of area differences in population, industrial, and institutional characteristics, underlying labor demand and labor supply relationships must vary across states. In addition, though the estimated coefficients themselves are quite diverse, one does find some regional patterns in the coefficients. Particularly interesting is the result that employment rates of Northeastern states are very sensitive to fluctuations in variables proxying for demand conditions in the product market while the employment rates of farm belt states, on the other hand, are quite insensitive to fluctuations in such variables. The results of the full dispersion model lead to several important conclusions. The absolute size and strength of the net variances in personal income, transfer payments, and property income indicate that the geographic structure of demand is of preeminent importance in determining the dispersion of state employment rates. Personal income and property income reflect economic growth conditions in a given state, and transfer payments, to a large extent, proxy for cyclic variation in product demand. 116 The fact that regional differences in product demand and differences in sensitivity to changes in product demand play such large roles in determining overall dispersion is not at all surprising. After all, the demand for labor is derived from demand conditions in the product market. Malinvaud argues that rationing in the product market and labor market is so tightly interdependent that, in order to study policies which would diminish involuntary unemployment, one is justified in concentrating attention exclusively on the formation of demand in the goods market.21 As shown earlier, cyclic variation in product demand (primarily through fluctuations in the net variance of transfer payment contributions) gives the time plot of the dispersion in employment rates its wave-like shape (see Figure 3-2). Given the results, the implications for policy are clear: one possible channel through which the dispersion in employment rates might be controlled is through use of regional stabilization policy.22 This chapter also shows that geographic differences in structural/ frictional unemployment, as measured by differences in the estimated constants, are quite influential in determining the dispersion in state employment rates. Frictional unemployment has been defined as the product of full employment values of the inflows to unemployment (such as, layoffs, quits, discharges, and labor force entrances) and the average job hunting interval.23 Structural unemployment refers to unemployment attributable to mismatches between workers and jobs. Factors determining structural unemployment relate to such diverse causes as lack of mobility in the labor force, sluggish adjustment in worker reservation wages to objective market conditions, and shortfalls in 117 worker skills appropriate for the available job vacancies. Given differences in population and industry on a geographic basis, no reason exists to believe (or expect) that any of the factors that determine structural and frictional unemployment are identical across areas. The results from the dispersion model confirm that these factors do, indeed, differ quite substantially across states. Policy makers might therefore attempt to reduce the dispersion by seeking to lower structural/ frictional unemployment in areas where the model indicates that high levels of this type of unemployment prevail (either instead of or in addition to a regional stabilization policy). llmemodel further reveals that cross-state differences in wage rates and in educational attainment both play rather modest roles in determining the dispersion in state employment rates. Factor costs and human capital accumulation, while somewhat responsible for differences in state employment rates, clearly play secondary roles when compared with factors related to overall demand conditions and with factors related to structural and frictional elements in the economy. Finally, geographic variation in the age and racial mix of the state labor forces explains a negligible amount of the variance in state employment rates. This is not to say that these variables do not play an important part in determining state employment rates in some cases. Only that, when taken as a whole, the contributions to state employment rates of these two variables are randomly distributed with respect to employment rates. The novelty of the research presented in this chapter lies in the methodology used to study employment rate dispersion. Neo-classical 118 theories of profit and utility maximization are integrated in a two- step procedure that breaks yearly dispersions down into component parts. Within this framework the various results noted above follow directly with accompanying implications for policy. 119 NOTES 1. With the following exceptions: Alaska and Hawaii, for which wage data are not available until 1961; and Alabama, Delaware, Georgia, Kentucky, Louisiana, Mississippi, New York, North Carolina, Oklahoma, South Dakota, Vermont, West Virginia, and Wyoming, for which unemployment rate data are not available until after 1960. 2. Unemployment insurance benefits may be the exception to the rule. These accounted for only 3.2% of total transfer payments disbursed in 1969 (a year of relatively strong aggregate demand), however, and 6.6% of total transfer payments in 1975 (a year of relatively weak aggregate demand). Source: Unemployment Insurance Statistics, March 1970 issue, Table 6, and July/August 1976 issue, Table 6. 3. See Kmenta (1971), pp. 336-345. 4. Local Area Personal Income, 1973-1978, p. xviii. 5. See Munnell (1977), p. 64, and Hamermesh in Burgess and Kingston (1978), p. 98. 6. See Parsons (1980), and Hamermesh (1980), p. 20. 7. See Hamermesh (1980), p. 20. 8. See Hamermesh in Burgess and Kingston, p. 100. 9. See Feldstein (1976), and Baily (1977). 10. See Hamermesh and Grant (1979). ) 11. See Mincer in Lewis (1962), and Ashenfelter and Heckman (1974 . 12. Some of the coefficients may have turned out positive because of the randomness in the estimation process itself. That is, the particular time sample chosen may be unlucky in that it yields an estimated coefficient which is not near the true parameter. 13. Cho 6nd McDougall (1978). 14. In terms of percentage of total non-agricultural employment devoted to durable goods production, the 9 Census regions rank as follows: 120 % of Total Non-Agricultural Employment Devoted to Durable Rank 329122. Goods Production 1 East North Central 23.8 2 East South Central 15.3 3 Mid-Atlantic 14.2 4 New England 13.7 5 Pacific 13.7 6 West North Central 12.4 7 West South Central 10.4 8 South Atlantic 9.8 9 Mountain 8.4 *These percentages are based on 1972 data (a year reasonably close to sample mid-point, for which good data are available). Source: Employment and Earnings, States and Areas, 1939-78 (1979). 15. Others who have estimated regional unemployment rate equations have suggested that the constant term does serve as a reasonable indicator (but not an exact predictor) of the structural/ frictional level of unemployment in an area. The usual interpretation is that the greater is the estimated constant, the greater is the level of structural/frictional unemployment in the area under consideration. In the case of the employment rate equations of this study, the reverse interpretation follows. The larger the estimated constant, the lower the level of structural/frictional unemployment in the state, and vice versa. See Hyclak and Lynch (1980), Fearn (1975), and Brechling (1967). However, since the constant in any linear regression equation is merely a statistical construct used to obtain a straight line which fits the observed data to the greatest degree, this interpretation should be made with caution. 16. There are some exceptions. Illinois, Indiana, Michigan, New York, Ohio, and Pennsylvania all experienced declines in real personal income in 1974 and 1975. In general, however, personal income increases over time for all states. 17. The Spearman rank correlation coefficient measures the degree of association between two ranked series. It can be written as: 2 r- :1- 5 n(n2-l) 121 where X, is the rank of observation i of series x; yi is the rank of observation i of series y; n is the number of observations. for n >10, rS is distributed as t, such that: t = r / n - 2 s 2 ‘\ 1 - r S See Siegel (1956), pp. 199-215. 18. Appendix Tables 0-1 and D-2 list, by state, the percentage of total transfer payments paid as unemployment insurance benefits in 1969 and in 1975, respectively. These two years represent widely differing cyclic experience. The percentages in Tables D-1 and D-2 are ranked from smallest to largest values. Thus, Vermont, for which unemployment insurance benefits account for 0.7% of total transfer payments in 1969, receives a rank of l in that year. On the other hand, Alaska, for which unemployment insurance benefits account for 11.8% of total transfer payments in 1969, receives a rank of 50 in that year. In order to test for a relationship between the transfer payment regression coefficients and the share of unemployment insurance benefits in total state transfer payments, Spearman rank correlation coefficients are constructed. Using Table 4-1, the transfer payment regression coefficients are first ranked from highest to lowest. Thus, South Dakota's transfer payment regression coefficient of .061 receives a rank of 1, while Massachusetts' transfer payment regression coefficient of -.254 receives a rank of 50. The hypothesis implied in the test is that the greater the share of particular transfer programs which increase a given state's labor force, but do little to increase its level of employment (of which unemployment insurance is one such program), the more negative will the transfer payment regression coefficient of the state in question be. If this hypothesis is correct, then the computed Spearman rank correlation coefficients should be positive. The computed Spearman ranks for 1969 and 1975 are: 1969 _ - = 1975 = . = rs .535, w1th t48 4.387 Both coefficients are statistically significant at the .01 level. Thus the hypothesis is verified, and, therefore, one does find that the greater the percentage share of a given state's transfer payments paid out as unemployment insurance benefits, the more negative is the regression coefficient corresponding to that state's transfer payments. 122 19. Particularly interesting here is the similarity of these results to those which fueled the Machlup-Lester debate of three decades ago. As Machlup pointed out then, the finding that wages play a relatively smaller role in determining factor adjustments by firms in no way discredits marginal productivity theory; it only indicates that other considerations may be more important. See Machlup (1946), and Lester (1946). 20. See Current Population Reports, Population Estimates and Projections (1971). 21. Malinvaud (1977), p. 4. 22. There are procurement and grant programs currently in existence whose stated goal is to ". . . award appropriate contracts and grants to, and to execute agreements with eligible labor surplus area concerns and to encourage prime contractors to place subcontracts with concerns which will perform substantially in labor surplus areas." See Ch. l-l.802-l, Code of Federal Regulations, #41 Public Contracts and Property Management, 1978. The success of such procurement programs in lowering unemployment in distressed areas, however, is difficult to assess since prime contractors and sub—contractors are not required to be located in the area within which they have been contracted to perform their services. Hence there may be substantial leakage of funds to areas not suffering high unemployment problems. 23. Kalachek (1973), p. 84. CHAPTER V A REFORMULATION OF THE MODEL IN A TWO-STAGE LEAST-SQUARES FRAMEWORK 5.1. Introduction Chapter IV alludes to the possibility that a state's employment 1 In rate and level of transfer payments are simultaneously determined. order to illustrate this point consider the following example. Suppose the employment rate of a given state declines because of some random shock. Thus assume that some group of individuals, employed in period t, becomes unemployed in period t + 1. Some members of the newly unemployed group may shun public assistance altogether and simply search the market for other employment. But, certainly, other members of the newly unemployed group, who are covered by the unemployment insurance laws, are likely to seek and obtain unemployment insurance benefits. Still other members of the newly unemployed group, not covered by the U.I. laws, may decide to: (l) retire early and draw Old Age Insurance benefits; (2) draw Disability Insurance benefits; (3) return to school and draw educational aid; or (4) enroll in a public assistance program such as AFDC or food stamps.2 Clearly, then, the negative shock to the state's employment rate simultaneously elicits an increase in the state's level of transfer payments. 123 124 Of course, the process does not end at this point. Since the state's level of transfer payments is also an explanatory variable in the state's employment rate equation, the induced increase in transfer payments in turn affects the employment rate. In all likelihood, therefore, a given state's employment rate and its level of transfer payments are simultaneously determined. If indeed transfer payments and the error terms of the employment rate equation are correlated, then Chapter IV's ordinary least-squares estimates are biased. This chapter seeks to determine whether or not one changes the essential results of Chapter IV by taking the simultaneity between transfer payments and employment rates into account. The chapter accomplishes this goal by re-estimating the state employment rate equations of Chapter IV in a two-stage least squares (ZSLS) framework and then decomposing the resulting cross-equation variances and covariances in the explanatory variables. The ZSLS procedure reduces the bias in the estimated coefficients and thus yields closer approxima- tions to the true parameters of the model.3 This chapter shows that, though ZSLS estimation changes some of the parameter estimates, the essential conclusions of Chapter IV's variance decomposition remain the same. Product market demand exerts the greatest influence on the dispersion in employment rates; income effects and structural/frictional elements exert a somewhat smaller but nevertheless substantial influence on the dispersion; factor costs and human capital accumulation exert a rather weak second-order effect on the dispersion; and demographic mix exerts very little influence on the dispersion. In the remainder of this chapter, I discuss the ZSLS 125 results, compare these with the OLS results of the previous chapter, and relate the findings of the variance decomposition under the ZSLS regime to the findings of Section 4.5. 5.2. The Two-Stage Least-Squares Results This chapter assumes that the level of state transfer payments enters each state's employment rate equation as an endogenous right- hand side variable. State i's employment rate equation, therefore, is: _ i i (5.1) e1 — YiTPi + X B + Vi where e1 is state i's employment rate; TPi is state i's level of transfer payments; X1 is a previously defined vector of exogenous variables specific to state i; Yi is the regression coefficient corresponding to TPi; B. is a vector of regression coefficients correspond- ing to X1; and v. is a stochastic error term. Assume further that the level of state transfer payments is a function of state economic conditions in both the current and immediately preceding periods and is also a function of demographic mix in the current period. Specifically, then, state i's transfer payment equation is: 126 (5.2) TPi = at + ble. + cle +d; TP_ 1 1 1 1 —1,i + fiPI- 1,1 1,1 +g'NW1. + hiTi + 011. where PI_1 and TP_], respectively are personal income and transfer payments logged one period; NW and T, respectively, are non-white and teenage labor force; a', b', c', d', f', g', and h' are regression coefficients; and w is a stochastic error term. Equation (5.2) serves to identify the parameters of equation (5.1) and is not estimated. Table 5.1 contains the ZSLS parameter estimates. The fifty equations yield an average R2 of .892. Equation (5.1) fits West Virginia best with an R2 of .993, and Arkansas worst with an R2 of .570. In estimating the model by 2SLS one finds that levels of statistical significance in the regression coefficients decline somewhat from the levels obtained in the OLS estimation. The number of coefficients significant at the .01 level falls from 119 to 92, the number of coefficients significant at the .05 level falls from 55 to 42, and the number of coefficients significant at the .10 level falls from 64 to 54. This decline in significance is consistent with Monte Carlo research cited by Goldberger. He reports evidence showing that OLS estimation results in coefficients with minimum variance compared to coefficients 127 Table 5-1. ZSLS Regression Results: State Employment Rates State Const. Wages Tran.Pay. Prp.Inc. Non-White Ed.Att. Teens 70%; Pers.lnc. 112 Alabama 1.105"' -.031 -.081 -.006 -.049 -.103 .034 .069 .251"‘ .884 Alaska 5 O76"' ..019 v.01? .079' -.17l"‘ -.445"' .155"0 -.O63 -.008 .912 Arizona 2.549"' -.l3l' -.057 —.087 -.D65 -.268 -.058 .448' .286"' .926 Arkansas 1.377 -.ZC7 .332 -.021 .158 -.426 .045 .891' -.096 .570 California 2.948." ..482'“ .075 .m4 .016 -.390" .018 .597" .076 .925 Colorado 3.647"' -.l94' .037 -.053 .038 -.138 -.029 .296"' .091 .767 Connecticut 1.162 -.355' -.137 .035 -.093 .296" -.035 .133 .211 .938 Delaware 1 309 ,033 .004 .047 -.021 -.206 -.085 .286" .131' .957 Flor‘ca 2.733 .162 - 237 .089 -.017 .193 .054 .227 .169 .952 Georg a 1.603' -.032 -.159"' -.023 -.082' -.014 .026 ..134 .302... .977 ha-a‘i -0.356 .408‘ - 207"' .093‘ .128 -.534 -.087 -.452" .377'° .924 Idaho 4 ass--- ..019 -.043"‘ -.095°" -.016 .257"' -.014 .222"' .062" .947 Illinois 7.499'°° -.8:7° .257' .229. c.082 -.053 121 1.136' - 516 .646 Inciana 5917... .008 -.046 .027 -.104 .116 .029 .962" -.017 .951 10~a 3.329"' .026 -120“' .138"' .043 -.580"‘ - 022 .272"' -.076‘ .831 Kansas 3.965"' .043 .168 .110 —.150' - 363 - 140' 522" -.l36 60: Kentu:1y 1.442"' -.077 - 062 .032 -.063‘ - llo - 048 142 .194 909 Lo.~s-ana 1.752 -060 -.034 .087 .026 - D97 - 082 135 .096 817 Kaine 2.373. .093 .087 .178' .016" - 369 - 331' 490"‘ -.039 918 Waryland 5 463-- -.087 .310 .367' -.280 -.229 - 243- 637"' -.546 765 Massazhosetts -12 355 -.349"' -.‘16' -.3l7" .012 .260 -.010 -.541 1.372" .95? H-:r‘;an 4.628"' .163" -.148'°' .,021 .106 .052 .020 .153 .119' .976 Minnesota 0.800 .034 .083' .251... .008 - 493" - 117" .241" - 045 863 M‘ssissrcoi . 0.022 -.185° .022 .031 .198 -.095 .348' .422‘ 110 .921 "15503’1 4.327"' -.188" -.O2O ..018 ._054 .045 .107 .333‘ .041 .931 Menta"a 4.515rrr - 396°" -.028 .005 .039" .028 .018 .159“' .020 .952 Netras-a 4.037'r' -.027 .OSC" .008 -.028" - 122“ - 013 .136"' -.004 ‘5 Nevaca 4.133'°' .129“ -.219" -.093"‘ -.053‘ 1 504"‘ - 17l"‘ .024 .003 919 Ne» “8'15""! . 0.477 -.107 -.1OC' .035 .0033 - 276 . 032 .13] .351... 96‘ Ne. Jersey 1.270 .049 -.075 -.095 .216 - 182 - 121 .12 .309 958 Nev “el‘:o 3.053' - 026 9.036 -.l73"° .098 .013 - 054 .406"' .252" 821 Ne- York - 9 818 -.64S‘“ -.391"‘ .,351'“ .097 .655" - 257 o.244 1.196'“ 943 North Carol‘na 2701' .118 --?10" .012 -.049 .181' .043 -.138 .226' .968 North Dakota 3.793"° -.063 .014 .031 -.057 .003 .079- .048 -.009 .620 Ohio 2.594rr' -.045 - 109' -.064 .131. .107 -.040 .220 .215'°° .952 0' 81004 2.605"' —.083 --053 -.039' .029 - O70 . 031 .285"' 185"' 951 Oregon 0.568 .006 -.020 ,osq ..037. , 453... _ 06... .152. 2,3... 969 PennSylvan‘a 0.365 -.042 - 013 .106 .lo7°-' - 2210' lair-0 .269° 102 985 9006? Island 8.871"' .368' .141 .050 .077" - 246 033 .806' - 348 899 5052- :aro’ina 1.177 -.081 -.095 .,1440-- ,033 . oso . 255- .148 392'°' 897 Sootr Dakota 3,351... -.035 .085"' _039 ..209900 . 1740-0 .oeovoo .122"‘ - 012' 825 Tennessee 6.595 --157 .134 .085 .175" .121 .171-0 .987" - 338 92‘ Te”; 2.665... ”1990- ‘124 .013 .“3” . 28‘" _ 192 .408". 02] c1: ctar 4,078"' -.0003 -023 -.020 -.083' - 007 D70"' .210"' 040 ’35 Vermont -l.188 -.811"‘ .056 -.028 .004 - 233" 231°°' .649"' 303"° 954 11's"=a 2.786' .054 .191 .144 .266 -.581‘ - 076 .243 - 157 866 Hashington 1.318"‘ -.416"‘ -.l46" -.013 .034"' .167' -.057" .233"‘ .278"' .976 W.I1rg‘hia 4.833"' .044 -.067"' .119"' .011 .362"‘ .192"' .300"' -.l44' .993 Wisc0nsin 4.516"' -.066 -.013 -.057" -.030 -.006 .079 .259" .063 .953 WyOang 4.715"' .045‘ -.019 .013 -.002 .184‘ -.101 .154"‘ -.040 .939 Notes' (1) All variables are entered in logarithmic fonm. ° indicates that ' t l_>_l-. “ 54 0' indicates that l t .2 1.5; '.‘ 42 "‘ indicates that 1 t 12.2. "" 92 128 obtained by zsLs and ms.4 Note, in passing, that Goldberger concludes that the smaller variance of the OLS coefficients may be sufficient to compensate for their larger bias in small samples. Table 5-1 further reveals the signs of the ZSLS coefficients to be divided between positive and negative much as in Table 4-1. A substantial decline occurs, however, in the number of negative transfer ‘31 payment coefficients. One finds forty states with negative transfer payment coefficients in Table 4-1, but in Table 5-1 one finds only F; M‘*' " "- twenty-nine states with negative transfer payment coefficients. Simultaneity between transfer payments and employment rates therefore biases the OLS transfer payment coefficients downward. Simultaneity causes transfer payments to appear to have a much more negative impact on state employment rates than is actually the case. As noted in Chapter III, if transfer payments simply transfer income to individuals, then transfer payments must exert a positive influence on the employment rate through a pure income effect. Chapter IV qualifies this expectation by noting that certain transfer programs (i.e., unemployment insurance benefits, food stamps, and aid to families with dependent children) entail work registration requirements and provide incentives that induce individuals to remain in the labor force when they otherwise would not. These same programs may also induce individuals from high unemployment groups to enter the labor force when they otherwise would not. Such transfer programs, therefore, adversely affect the employment rate. Since the majority of transfer payment 129 coefficients remain negative under 2SLS, programs such as UI, AFDC, and food stamps clearly play a major role in determining the effect of trans- fer payments on the state employment rate. Table 5-2 presents weighted averages, weighted variances, and corresponding t-statistics for the coefficients of the explanatory variables obtained both by OLS and by ZSLS. The table thus allows one to compare average coefficient values for each variable obtained by the two estimating methods. Consistent with the decline in the number of negative transfer payment coefficients in Table 5-1, Table 5-2 shows Table 5-2. Weighted Averages, Variances, and t-Statistics of OLS and 2SLS Coefficients . 7? 7\' T T var'ab'e Bo1s 82s1s V(Bols) V(32sls) t Constant 1.338 1.438 9.932 22.569 -0.124 Wages -O.lO6 -0.205 0.0612 0.0913 1.793* Transfer Payments -0.099 -0.041 0.0083 0.0338 -1.999** Property Income -0.031 0.024 0.0095 0.0244 -2.lll** Non-Whites 0.035 0.031 0.0053 0.0102 0.227 Educational Attain. -0.006 -0.040 0.0389 0.1030 0.638 Teens 0.001 -0 027 0.0063 0.0164 1.314 Q§§§ 0.135 0.277 0.0297 0.1310 -2.505** Personal Income 0.254 0.188 0.0628 0.1930 0.923 _. 50 . Notes: (1) Bk = Z aiBik; k = OLS, ZSLS i=1 where “i is average labor force of state i, 1961-1978, divided by average U.S. labor force, 1961-1978. 0 ._ 5 _. A A A 2 (2) V(Bk) = §=1 ai(Blk ' Bk) 130 gols A251S 1 V(gels) + v(0251s) 50 (4) * indicates significant at .10 level; ** indicates significant at .05 level. (3) t = that transfer payment coefficients are less negative--on average--when estimated by ZSLS. Other coefficients registering statistically significant increases in average value under ZSLS are property income and éggg. Since éggg—measures aggregate demand, that this variable experiences an increase in explanatory power when one purges the cyclic component of transfer payments from the regression equation is eminently reasonable. On the other hand, Table 5-2 reveals that the average coefficient of real wages becomes more negative when one takes simultaneity between the employment rate and transfer payments into account. Given the negative sign hypothesized for real wages in Chapter III, this result is also comforting and suggests that the simultaneity problem biases the wage coefficients upward in the OLS regressions. Finally, variables experiencing no statistically significant change in average coefficient value are personal income, the three demographic variables--age, race, and education--and the constant. Thus the simultaneity between the level of transfer payments and the employment rate apparently contaminates only a subset of the regression coefficients. Besides allowing one to compare coefficient averages under the two estimating schemes, Table 5-2 also affordsauiopportunity to compare 131 the coefficient variances of each of the explanatory variables. Notably, ZSLS increases the spread in coefficients about respective means in the case of all nine regressors. This point carries important implications for the variance-covariance analysis below, and I shall return to it. Before proceeding to the next section, allow me to recapitulate the principal findings of this section. First, making state transfer 3 payments endogenous to the system reveals bias in a subset of the OLS l regression coefficients. Second, 2SLS estimation increases the cross— 5 state variance in the coefficient estimates of all nine of the explanatory variables. 5.3. Regional Patterns in the ZSLS Coefficients Judging by Section 5.2 one might draw the conclusion that re- estimating the model by ZSLS yields entirely different results from those obtained in Chapter IV. All differences between the results of Chapter IV and V, however, essentially end at this point. It is quite true that the average coefficient values of a subset of the variables obtained by ZSLS differ significantly from their OLS levels, and it is also true that ZSLS estimation widens the spread of each explanatory variable's coefficients. But aside from these differences, the similarities between the results to follow and those of Chapter IV are quite striking. In this section I compare regional patterns in the 2SLS coefficients with those of the OLS coefficients. I show that regional patterns in the OLS coefficients are also apparent in the ZSLS coefficients. 132 Table 5-3 contains the weighted regional t-statistics associated with the 2SLS coefficients. The null hypothesis holds that the average regional coefficient of a given explanatory variable equals the average sample coefficient of this variable (excluding, of course, the coeffi- cients of the states in the region in question from computation of the latter). Table 5-3 compares this hypothesis with the simple two-sided alternative. Table 5-3 reveals regional patterns in the 2SLS coefficients very similar to those of the OLS coefficients. For instance, one finds that employment rates in the New England and Mid-Atlantic states are extremely sensitive to changes in personal income, implying strong dependence on demand conditions in the product market in these two regions. Moreover, estimation by ZSLS does not alter the OLS result that employment rates of states in both the New England and Mid-Atlantic regions are more adversely affected by an increase in the level of transfer payments than state employment rates in any other region. In addition, the 2SLS constants of the New England, Mid-Atlantic, and East North Central regions all differ significantly from the corresponding population means, as they do under OLS (note that even the significance levels are the same). The constants of the New England and Mid-Atlantic states are, in general, much less than average, implying a high level of structural unemployment in the two regions. The constants of the East North Central states, on the other hand, are much greater than average, implying relatively less structural unemployment in this area than in others. 133 Table 5-3 Weighted Regional t-Statistics Assoc1ated with the ZSLS Coefficients Region Const. Wages Trans.Pay Pro Inc. Non-White £d.Att. Teens :CNP Pers.lnc. 0N1“ New inqland -3.195"' -2.333" -2 418" -1.828' -1 025 1.273 -0.983 -2 469" 2.920"' Mid-Atlantic -3.301"' - .771 -2.064" -2.387'° 1.921' 1.861' -l.378 -l.650‘ 2.807'°' East North Central l.964'° -0.049 O 646 0.755 -O 368 0.602 1.341 1.699“ -1.476 West Narth Central 0.872 1.286 1.390 1 522 -1.647' -1.981“ 0.188 0.078 -1.183 500th Atlantic 0.913 2.636"' -O.238 1.746' -1 306 0.025 o0.197 -O.977 -O.B9l East South Central 0.566 0.649 0.563 0.574 0.580 0.052 2.202" 0.907 -0.754 West South Central 0.416 0 302 1.558 0.281 0.615 -1.294 -l.706' 0 653 -0.676 "Duntain 1.333 1.142 0.262 -l.126 -0.957 0.621 -0.427 0.072 -O.4l6 Pac1f1c 0.518 -1 594 0 925 O 221 -0.373 -2.282" 0.494 1.327 -0.348 Notes: (1) t . F - 8 where B, ' 01-.) “k g 0‘3 313 ; J - states in region i E' “k at i k - all states but states in region 1 If) = Average labor force in state J divided by average labor force in region 1 . Average labor force in state k divided by average labor force in U.S. (based on all states but those in region 1). (2) ' indicates significant at .10 level; " indicates significant at .05 level; "' indicates significant at .01 level. 134 Finally, excluding the New England and Mid-Atlantic regions, one finds that average coefficient values of most regions do not differ significantly from the respective sample average. This finding is a subtler yet no less important similarity which the ZSLS and OLS results share. Analysis of regional patterns in the ZSLS coefficients reveals, therefore, remarkable similarities to regional patterns in the OLS coefficients. One must conclude that correction for simultaneity leads only to monotonic adjustment in the coefficients. Though the state coefficients of a given explanatory variable may change somewhat after adjustment for simultaneity, differences among states within the coefficient distribution are preserved. The following section shows this property to have importantramifications for the variance-covariance analysis of the state employment rates 5.4. Two-Stage Least-Squares and the Full Dispersion Model This chapter seeks to determine whether and in what way simultaneity between the employment rate and transfer payments affects the results and conclusions drawn in the variance-covariance analysis of Chapter IV. Chapter IV's analysis--based on OLS regressions--shows that cross-state differences in product market demand, in income effects relating to transfer payments and property income, and in structural/frictional elements play central roles in determining the dispersion in state employment rates over time. The analysis further shows that cross-state differences in factor costs and human capital as 135 accumulation are of somewhat second-order importance in determining the dispersion, while cross-state differences in age and race composi- tion exert very little influence over the dispersion. One would like to know, then, whether these conclusions stand on their own regardless of the change in model specification made in this chapter. Given that the coefficient averages of four of the explanatory variables--transfer payments, wages, property income, and %%%%—-change significantly when one adjusts for simultaneity, concern that the conclusions of Chapter IV may be altered is legitimate. This section shows that, in spite of the change in the average coefficient values of the aforementioned variables, decomposition of the ZSLS equations into the underlying variances and covariances reveals that the conclusions drawn in Chapter IV are robust. Table 5-4 reports the ZSLS net variances in the employment rate contributions of each of the explanatory variables and of the residual term for the 1962-1978 period.5 Figures 5-1 through 5-10 depict these net variances graphically. On comparison of Table 5-4 with Table 4-4 one finds that the absolute values of the particularly important net variances (i.e., of the constants, transfer payments, property income, and personal income) of Table 5-4 outweigh those of the comparable net variances in Table 4-4. No systematic difference between the net variances of the less important variables in the two tables, on the other hand, appears to exist. Comparison of Figures 5-1 through 5-10 and Figures 4-1 through 4-10 are somewhat more revealing than simple comparison of Tables 5-4 136 ——co.i mwmm.me i vc—o.i empo. i vmwm.Mi —e~o. i mmm~.v— woom.o— ommv.— poem.o~ oka— sN-o.i cxmo.mw 1 vmmo.i momm. 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Rama. 1 comm. i coco.—p mmm~.o mmo—.— v~_o.~— oom— ~m_o. xmo¢.oN - mooo.i momm. comm. ovmm. i mkom.w omcw.— ome~.— ~_—N.m moa— _ooo. opnv.mm . .poo. mmqo. i —mmo. exec. i ovfio.~ Nomo.v ooms. memv.o— coa— omco. mmom.m i ~o_c. moon. 1 seen. i Nomx. i Nocc.~ Kmeo.m meow. «mom.m mo¢_ ovoc.i come.m om_o. woke..- okmm. . meme. . mowe.v i _~o—.~ mwmm. i moo—.n i Noo— -.a-.a->za -a.a-ze -mnwm.--ze -.a-za -<-.a-ze -=z.a-zo --a.a-za --.a->za -s.--zo ----2a .66- Ecmp peat-mom use mo_ne_co> xco-e:6_axu 65- ea mco-:n_c-cou mum: acme»o_asm ecu we modem-68> “oz mamm .e-m upon» 137 -15.. -20<1 _30 0 _40 4h -50 4- -100 r -110. I -120. V 62 63 64 65 66 67 68 Figure 5-1. 69 7O 71 72 73 74 75 Net Variance-«Personal Income 76 77 78 50" 30‘ 204- 15a "r—r—l—l—F 10 138 62 63 64 65 66 67 Figure 5-2. 68 69 7O 71 72 73 74 Net Variance--Transfer Payments 75 76 77 78 501 40‘ 30‘ 20‘ 15. 104. 7 139 -54 -104» -15‘ -204 D 62 63 64 65 66 67 68 69 0* 71 72 73 74 Figure 5-3. Net Variance-~Constant Terms 75 76 77 78 401 30‘ 20‘ 15‘ 10‘ 140 'c-i—i— _5. -10‘ 63 64 65 66 67 Figure 5-4. 68 69 70 71 72 73 74 75 Net Variance--Property Income 76 77 78 10» 50 141 4rJ""1 L—::;============J 1 1 E:==3———J [—5 [—5 I ”"62‘63 64 65 66 67 68 69 70 7172 73 74 75 76 77 78 t -5.. l -104 Figure 5-5. Net Variance--Wages °Nv 10‘- '1 54» _ 9L Tm “ I62:63 64 65 66 67 68 69 70171 72 7417s 76 77 78 _54> 41a 1 -109 'L—7 Figure 5-6. Net Variance--Educational Attainment 142 31w 2.5.. m L_, 2 5 ’ 62 63 64 65 66 67 68» 69 7O 71 72 73 74 75 76 77 78 Figure 5-7. Net Variance--Teenage Labor Force °~v 41 " 62 63 64 65 66 67 68 69 7O 71 72 73 74 76 77 78 -2.5 . Figure 5-8. Net Variance--Non-White Labor Force 011v 10 y 62 63 64 65 66 67 68 69 7O 71 72 73 74 75 76 77 78 -1 ii 0 Figure 5-9. Net Variance--AGNP/PGNP NV 1” 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 Figure 5-10. Net Variance--Residuals 143 and 4-4. Figure for figure, the net variances of Chapter V virtually replicate the net variances of Chapter IV. The only discernible difference is the scaling factor mentioned in the preceding paragraph. The ZSLS net variances in the employment rate contributions of the constants, of transfer payments, of property income, and of personal income are somewhat larger in absolute value than their OLS counterparts. The shapes of the figures, however, do not essentially differ from those of Chapter IV. Given that cross-state differences in personal income are dispersion decreasing while cross-state differences in the constants, transfer payments, and property income are dispersion increasing, the increases in absolute net variances cancel out.6 Most importantly, Figures 5-1 through 5-10 show that the hierarchical structure of net variances--established by the OLS results of Chapter IV--remains unaltered by the ZSLS equations. Hence, one clearly sees from both the figures and Table 5-4 that the net variance of personal income is much greater than all other net variances. Net variances in the employment rate contributions of the constants, of transfer payments, and of property income are relatively similar in size, and stand next in the hierarchy. Net variances in the employment rate contributions of educational attainment and of wage rates are relatively small in absolute value, while net variances in the employ- ment rate contributions of the model's demographic variables are negligible. Two questions remain. First, given the change in average estimated coefficient of four of the explanatory variables, why are the results of the variance-covariance analyses of Chapters IV and V so 144 strikingly similar? Second, why are the absolute values of the net variances in the employment rate contributions of the constants, transfer payments, property income, and personal income relatively larger under ZSLS than under OLS? The answer to the first question relates to the discussion of Section 5.3. Section 5.3 shows that, despite any change in the actual coefficients themselves caused by ZSLS estimation, regional patterns in the coefficient distributions remain the same. Hence, whether one h u.- estimates the state equations by OLS or ZSLS, the New England and Mid- 9 Atlantic states are extremely sensitive to changes in personal income while the West North Central states are not. Similarly, a marginal increase in transfer payments causes employment rates to fall substantially in the New England and Mid-Atlantic states relative to states in the rest of the country. Therefore, though ZSLS estimation induces an absolute shift in some of the coefficients, the relative relationships among the states within the various coefficient distributions essentially are preserved. Thus deviations about means--the essence of the net variance method-~change little. One finds, in turn, little change in the hierarchi- cal structure that exists among the net variances whether the estimation procedure implicit in the underlying regression equations is OLS or ZSLS. The second question above asks why the four major net variances of the model (constants, transfer payments, property income, and personal income) increase in absolute value when one estimates the state regressions by ZSLS. 'Hueanswer to this question relates to a result in Section 5.2. The regression results of that section show that estimation of the state employment rate equations by 2SLS increases the variance in 145 the state coefficients of the individual explanatory variables over that obtained by OLS estimation. Recall that the net variance of a given variable, X, is: (5.3) oNV(bX) = ; 61(bix, - bX)(e1 - e). 1 Since 02( 2(b) , since the coefficient distribution of b is, b)Zsls > 0 01s in general, preserved under ZSLS, and since neither the X1 nor the ei change whether estimation is by OLS or by ZSLS, it logically follows that: bX) bX) ONV( ZSLS > °Nv( OLS. Further, since the net variance in the employment rate contributions of personal income under 2SLS becomes more negative, while the relatively smaller net variances of the employment rate contributions of the constants, of transfer payments, and of property income become more positive, these changes cancel each other out. This section shows that the conclusions drawn from the dispersion model in Chapter IV remain unaltered when one takes the likely simulta- neity between transfer payments and state employment rates into account. Taking simultaneity into account should, of course, alter some coefficients in the model. But if the bias is general across all states, there is no reason that relative relationships between state coefficients should change. As shown in the text, the net variances of the dispersion model depend on these latter relative relationships. 146 5.5. Conclusion This chapter presents results from a re-estimation of the dispersion model taking into account possible simultaneity between a state's level of transfer payments and its employment rate. The results show that: 1. There apparently is simultaneous equations bias involved since the average values of several of the coefficients experience a statistically significant change when estimation is by 2SLS; 5:: am; 2. Regional patterns in the ZSLS regression coefficients are similar to those found in the OLS coefficients; and 3. Analysis of the 2SLS cross-equation variances and covariances leads one to precisely the same conclusions regarding the determinants of the employment rate dispersion as drawn in the OLS model of Chapter IV. The above findings are noteworthy for the following reasons. In any econometric analysis the researcher faces the problem of determining which variables are endogenous and which variables are exogenous to the model. Factors such as theoretical considerations, data availability, sample size, and cost govern this selection process. The research presented here specifies an employment rate function for each state. Initially, assuming all other variables aside from employment rates to be exogenous, I estimate a fifty equation model, conduct the variance-covariance analysis, and draw a set of conclusions from the results. It is, of course, somewhat unrealistic to assume that employment rates are exogenously determined. If one desired very precise point estimates of the parameters of the employment rate functions, one would have to expand one's sample size, make all variables relevant to the 147 employment rate functions endogenous, and further make all variables relevant in determining the variables on the right hand side of the employment rate functions endogenous. Because of the selection criteria mentioned in the preceding paragraph, construction of such a large-scale econometric model is far beyond the scope of this research. Chapter V's work seeks a middle ground between total exogeneity and total endogeneity in the right hand side variables. It is assumed without proof that transfer payments are more highly correlated with the error terms of the employment rate equations than any of the other explanatory variables, and this variable is made endogenous to the model. Since this major change in model specification leaves the conclusions drawn from the OLS model completely unshaken, it seems safe to say that further modifications in the model would also have no effect on the conclusions drawn regarding the relative importance of each of the dispersion's determinants. 148 NOTES 1. Of course, wages, personal income, and property income may also vary simultaneously with a state's employment rate. Construction of a full-scale model of the U.S. economy, however, is beyond the scope of this research. Given the direct link between the unemployment rate (hence the employment rate) and some components of transfer payments-- particularly, unemployment insurance benefits--I believe the simultaneity between these two variables to be of greatest importance. Therefore, I take only this relationship into account in re-estimating the model. 2. All four of these options are contingent on eligibility. 3. Since the sample for any given state is small (18 f_n f 21), the fact that ZSLS estimates are consistent and asymptotically efficient is of no consequence. The small sample properties of the 2SLS procedure are unknown. Goldberger does cite Monte Carlo evidence, however, showing that the bias found in ZSLS estimates tends to be smaller than that found in OLS estimates. See Goldberger (1964), pp. 359-360. 4. See Goldberger, pp. 359-60. 5. Note that 1961 is excluded since the transfer payment equation included several lagged variables. This necessitated using 1962 as the initial year of the sample so that 1961 could be used as the initial year for the lagged variables. 6. Whether one estimates the model by OLS or by 2SLS the amount of dispersion to be explained remains constant. Therefore, it is not very surprising that the increase in absolute net variances cancels out overall. -a,-.._An.e - u: bk CHAPTER VI A DYNAMIC ANALYSIS OF THE DISTRIBUTION OF STATE UNEMPLOYMENT RATES 6.1. Introduction The preceding chapters show that unemployment rates differ by state because labor supply and labor demand relationships differ across states and because the underlying variables that determine state unemployment rates also differ by state. One may view the question of the existence of the dispersion from a somewhat different perspective. That is, one should always expect to find some dispersion in state unemployment rates for two fundamental reasons. Choosing any point in time, some state labor markets are likely to be characterized by excess supply, while others are likely to be characterized by excess demand.1 Hicks noted long ago that the labor market is rarely in equilibrium and that the labor market is an imperfect market in which the equalizing 2 Thus given the various degrees of forces are rather slow to act. disequilibrium found across state labor markets, it is unlikely that one should ever find a degenerate distribution of state unemployment rates. In addition, even if one could locate a time period in which the economy's vector of prices, wages, and interest rates adjusts such that all labor markets are in equilibrium--where unemployment in each 149 150 state labor market is frictional and any worker who desires a job can obtain one at the going rate-~one would still observe a non-degenerate distribution of state unemployment rates because frictional unemployment rates differ geographically. Kalachek defines frictional unemployment to be ". . . the product of full employment values of the inflows to unemployment (from layoffs, quits, discharges, and labor force entrances) and the average job hunting interval."3 Given differences across states in population mix, industrial mix, and institutional characteristics, neither the full employment inflows to unemployment nor average search time are likely to be equal across states. Hence frictional unemployment rates differ by state yielding a dispersion of unemployment rates even if all state labor markets are in equilibrium. With the existence of a distribution in state unemployment rates well established, this chapter further considers the properties of this distribution. Up to this point little mention is made of two other important characteristics of the distribution: the mean (or measure of central tendency) of the distribution; and, the underlying dynamic of the individual random variables (i.e., the state unemployment rates) that comprise the distribution. Other work in the literature 4 deals extensively with the mean. The principal finding is that this 5 Researchers in this area parameter has drifted upward over time. typically attribute the rising overall rate of unemployment to such factors as the increasing labor force participation rates of females and teenagers; the growing school attendance of teenagers (implying greater frequency of unemployment spells and more job search by this group); and the ever-widening coverage of the unemployment insurance laws over the 151 last twenty years. Given the great deal of attention paid to the mean unemployment rate in other research, this study gives little further consideration to this topic. This chapter concerns itself with the latter characteristic of the distribution noted above, i.e., the underlying dynamic of the individual random variables comprising the distribution. Given the stability of the variance in the state unemployment rates (in the cyclic sense), one should like to know whether or not it is also true that the rank order of individual state unemployment rates remains relatively constant over time. In other words, one should like to know whether or not the underlying structure of the distribution is stable in some sense. In separate studies analyzing British regional data (sample period 1952-1963) both G.C. Archibald and F. Brechling find that the 6 In rank ordering of regional unemployment rates is relatively stable. light of this finding Archibald draws the conclusion that regional policy measures had not been particularly successful in eliminating regional imbalances.7 Given the relative stability in the British distribution, one should like to know whether or not the same structural stability holds true, at least to some proximate degree, when one decomposes the U.S. labor market by state. As one might guess from the results of Chapter IV, the answer to this question is somewhat ambiguous. It is shown below that some states do indeed maintain their relative position in the distribution. On the other hand, other states move either up or down substantially in the distribution over time. 152 That some states do demonstrate a proclivity to change positions in the unemployment rate distribution is eminently reasonable from a theoretical standpoint. Over time, tastes, expectations, and relative prices of goods, factors, and resources all tend to change. Ultimately, demand for labor in some areas rises and in other areas falls. Unemployment rates in areas of the former type decline-~assuming they are not initially at their frictional lower bounds--and in areas of the latter type increase--assuming that these markets do not adjust instantaneously. As this process unfolds, the relative rank ordering of state unemployment rates may very well change. It appears, therefore, that the stability in the rank order of the distribution considered by Archibald and Brechling is an artifact of the relatively short time period that they considered. The remainder of this chapter presents an explicit analysis of the distribution of state unemployment rates. Section 6.2 identifies those states which have continually registered the lowest unemployment rates, and it identifies those states which have continually registered the highest unemployment rates. Section 6.3 tests for whether or not the rank ordering of states in the unemployment rate distribution changes over time. This section employs regression analysis both to determine the degree to which the underlying pattern of states comprising the distribution of unemployment rates changes over the business cycle and to assess the extent to which this pattern has changed in the long run . 153 6.2. The Rank Distribution of State Unemployment Rates As important as an understanding of the factors which determine the distribution in state unemployment rates is, one would be remiss if one omitted an explicit analysis of the underlying elements of this distribution and the positions these elements occupy within the distri- bution. This section examines the rank order of the various states over the eighteen year sample period. Of specific interest is how the states have fared on average in terms of overall rank. In addition, one should like to know what regional patterns are identifiable within the distribution of unemployment rates. Dynamic considerations are taken up in the next section. Table 6-1 contains a complete listing of the rank order of states, in terms of unemployment rates, for each year from 1961 through 1978. Thus since Nebraska had the lowest unemployment rate of all fifty states in 1970, it is assigned a rank of 1 for that year. Since Washington had the highest unemployment rate that year, it receives a rank of 50. The average ranks range from Nebraska's low of 1.5 to New Mexico's high of 45.61. In order to facilitate an understanding of these data in terms of their regional implications, one can group the state rank averages by Census region (9-region classification). One can then compute weighted regional rank averages and standard deviations for each region. Table 6-2 presents these weighted averages and standard deviations. Comparison of the average regional ranks in Table 6-2 reveals thatstates in the West North Central region have the lowest unemployment rates over the eighteen year sample period. The highest overall :‘ T:T“.‘:““.“.‘1 "I I: ‘__ 154 Table 6-1. State Unemployment Rate Rankings; 1961-1978 51318 '61 '62 '63 '64 '65 '66 '67 ‘68 '69 '70 '71 '72 '73 ‘74 '75 '76 '77 '78 R Alabanu 44 4O 44 4O 38 44 41 45 41 40 36 34 26 44 27 24 34 35 3.56 914151 34 45 43 42 45 49 49 49 47 45 47 48 47 47 12 32 49 50 44.17 Arizona 2 37 37 44 46 4O 2 38 32 35 27 25 32 39 49 47 4O 31 38,17 Arkansas 33 40 30 33 39 41 36 35 36 2 28 24 21 23 36 28 25 36 32 72 California 40 41 45 48 49 46 46 46 46 46 48 44 46 43 41 42 41 44 45.44 Colorado 18 29 33 2 31 37 34 33 35 29 10 9 17 7 14 13 20 20 23.61 Connecticut 28 21 19 19 20 17 18 31 33 38 49 49 42 31 32 44 27 16 30 44 Delaware 24 24 13 17 ll 20 27 24 26 33 31 27 33 37 40 37 44 47 29 39 florlda 43 42 38 20 18 16 12 21 17 16 20 11 22 32 46 39 42 38 28.28 Georgia 36 31 24 21 21 24 24 22 14 11 5 12 11 24 27 33 26 22 22 22 Hawaii 9 26 32 25 25 32 37 25 24 28 38 46 48 48 23 48 33 48 33.89 Idaho 16 19 22 22 17 25 32 34 27 30 23 28 29 20 9 10 15 23 22 94 Illinois l9 17 12 ll 8 ll 13 12 15 17 15 21 18 ll 18 22 21 32 16.89 Indiana 2 11 8 7 4 4 10 11 5 26 24 13 23 25 28 17 14 24 15.89 Iowa 3 3 1 1 1 l 2 2 2 3 3 2 2 1 4 4 4 9 2.67 Kansas 5 5 6 5 9 5 6 5 10 25 22 7 4 4 6 6 5 2 7.94 Kentucky 37 34 25 28 26 30 28 37 34 22 16 16 10 12 20 7 6 17 23.17 LOuisiana 47 49 46 43 43 43 43 47 48 47 44 39 44 40 21 25 28 43 41.89 Maine 18 35 39 38 29 31 21 28 37 36 42 40 38 34 44 38 45 33 36.67 H“Hand 23 27 23 18 23 14 14 16 16 9 17 33 19 18 15 26 19 21 20.17 Massachusetts 12 16 20 26 24 26 22 23 20 27 32 38 43 41 48 45 39 34 30.16 Michigan 46 32 15 13 10 13 29 29 25 43 43 43 39 50 50 43 43 41 34.50 Minnesota 7 7 7 9 7 6 5 6 4 11 8 14 27 8 8 14 10 5 9.44 Mississippi 41 38 40 39 32 35 39 39 38 31 21 15 12 13 24 23 35 45 31.83 Missouri 10 10 9 6 6 10 8 9 9 4 18 17 13 17 16 19 16 14 12.06 Montana 11 6 5 8 12 15 15 13 29 14 12 22 31 26 10 18 23 29 17.22 Nebraska 1 1 2 2 2 2 1 1 1 1 1 1 1 2 3 1 3 1 1.50 Nevada 26 18 21 37 47 47 47 43 39 39 4O 42 40 46 39 40 29 11 36.94 New Hamoshire 20 14 27 23 13 3 4 3 11 18 3O 35 25 28 33 21 17 6 18.89 New Jersey 13 15 16 16 19 19 19 19 21 19 25 3O 37 33 43 50 50 46 28.00 New Mexico 39 43 47 49 48 48 48 48 49 49 46 45 49 49 42 41 38 27 45.61 New York 25 23 28 32 33 39 33 26 28 21 39 41 36 35 37 49 48 49 35.39 NOrth Carolina 35 36 31 34 34 28 30 3O 22 23 11 4 7 14 29 20 18 10 23.78 North Dakota 27 20 17 27 35 38 31 32 3O 15 13 19 8 6 1 3 7 12 19.61 Ohio 45 44 34 29 27 22 26 2O 23 34 33 29 24 19 34 30 24 18 29.33 Okalahoma 8 8 10 10 14 12 9 10 7 6 6 8 S 10 19 8 9 8 9.56 Oregon 29 28 26 31 36 42 41 40 44 43 41 37 4O 45 45 46 36 30 36.44 Pennsylvania 48 47 48 41 30 21 20 17 13 12 26 31 3O 21 25 31 37 42 30.72 Rhode Island 15 12 18 15 15 8 7 7 6 7 14 23 28 27 47 34 46 39 20.89 500th Carolina 42 39 42 45 44 45 45 44 42 41 34 26 20 30 31 27 32 25 37.06 500th Dakota 2 2 3 3 6 9 3 4 3 2 2 3 3 3 2 2 1 3 3.11 Tennessee 49 46 49 47 41 36 44 42 43 42 37 20 14 22 26 16 22 28 35.39 Texas 31 33 41 35 37 29 16 14 18 20 19 18 15 9 7 11 11 13 21.61 Utah 6 9 13 3O 40 33 38 41 4O 37 29 32 34 29 13 12 12 7 25.94 Vermont 22 25 35 36 28 23 23 18 12 24 35 36 35 36 35 35 3O 26 29.28 Virginia 14 13 ll 12 16 16 17 15 19 5 4 5 9 15 11 15 13 19 13.22 Washington 30 22 36 46 42 34 35 36 45 50 50 50 50 42 38 36 47 40 41.33 West Virginia 50 50 50 50 50 50 50 50 50 48 45 47 45 39 30 29 31 37 45.33 Wisconsin 4 4 4 4 3 7 11 8 8 8 9 10 16 16 17 9 8 15 9.22 Wyom1ng 17 30 29 14 22 29 25 27 31 13 7 6 6 5 5 5 2 4 15.89 Note: 8‘ is the average rank for state 1 over the eighteen year period. 155 Tab1e 6—2. Weighted Regiona1 Averages and Standard Deviations of State Unemp1oyment Rate Ranks (1961-1978). Average State Rank Standard Deviation Region in Region* of Region's State Ranks** New EngTand 29.52 4.21 Mid-At1antic 32.46 3.04 East North Centra1 22.91 8.79 West North Centra1 8.15 4.45 South At1antic 24.80 7.94 East South Centra1 32.61 5.81 West South Centra1 24.52 9.64 Mountain 29.28 9.13 Pacific 43.82 3.22 * ” The weighted average regiona1 state rank is computed as fo11ows: k1 .— U- = Z a.. R.- 1 j=1 TJ 13 __ 18 where Rij = 1/18 2_ Rijt; t-1 R.. is the unemp1oyment rate rank of state j be1onging to region i in year t; k. is the number of states in region i; ”i” is the average 1abor force of state j in region i 3 (1961-1978) divided by the average 1abor force of region i. ** ~The regiona1 standard deviations are ca1cu1ated as fo110ws: 156 unemp1oyment rates, on the other hand, characterize the Pacific states. SurprisingTy, the East North Centra1 region ranks second in terms of average rank during the period, behind on1y the West North Centra1 division. This is surprising in that the East North Central region has the greatest concentration of non-agricuTturaT emp10yment devoted to the manufacture of durab1e goods (see footnote 14, Chapter IV). Given that consumers are most easi1y ab1e to postpone purchase of durab1e goods unti1 economic recovery takes place, durab1e goods industries are particu1ar1y susceptible to high unemp1oyment in recessions. In turn, this makes states where such industries are concentrated prone to high unemp1oyment rates. Two factors appear to account for the East North Centra1 region's 10w average rank. Though overa11 aggregate demand was weak throughout much of the 1970$--accounting for relativeTy high unemp1oyment rates in Michigan and Ohio in these years--aggregate demand was quite strong during much of the 19605--offsetting the effect of the 19705 (particu1ar1y in Michigan [see Tab1e 6-1]). In addition, Tab1e 6-1 revea1s that unemp10yment rate rankings in 111inois, Indiana, and Wisconsin remain low throughout the entire period. This fact suggests that the economies of these three states are somewhat more akin to the cyc1ica11y insensitive agricuIturaT economies of the states of the West North Centra1 region.8 Tab1e 6-3 reports the resu1ts of pairwise Mann-Whitney U-tests conducted to determine statisticale significant differences in the samp1es of regiona1 mean ranks. Appendix E contains a comprehensive exp1anation of the properties of the Mann-Whitney test. Since the 157 number of mean rank observations corresponding to any region is sma11-- the Mid-At1antic region has on1y three such observations, while the South At1antic and Mountain regions have on1y eight such observations-— one cannot invoke the Centra1 Limit Theorem and use the t-test to determine regiona1 differences in unemp1oyment rate rank. Moreover, it wou1d be presumptuous to simp1y assume that the mean state ranks of a given region are norma11y distributed. Again, one must ru1e out use of the t-test. The distribution-free Mann-Whitney test, therefore, is the appropriate procedure. Since the Mann-Whitney test is a non- parametric procedure, the nu11 hypothesis imp1icit in Tab1e 6-3 is that the respective samp1es of the average state ranks obtained for region i and region j derive from the same popu1ation. (Here one to app1y a t-test the nu11 hypothesis wou1d state that the average of the mean state ranks is equa1.) Tab1e 6-3 reports resu1ts from an app1ication of the sma11- samp1e Mann-Whitney test. Note that actua1 significance 1eve15 are not reported. Instead, asterisks (or Tack thereof) indicate the 1eve1 of significance of regiona1 differences. A positive sign in the tab1e signifies that the U statistic associated with the sum of the ranks of region i (where i indexes the rows of the tab1e) is greater than that of region j (where j indexes the cqumns of the table). In 1ight of the discussion in Appendix E this means that the average state ranks of region i tend to be 1ess than those of region j. ConverseTy, a negative sign indicates the U statistic of region i is 1ess than that of region 3, implying that average state unemp10yment rates of region i tend to be greater than those of region j. 158 Tab1e 6-3. Pairwise Mann-Whitney Test Resu1ts Comparing Regiona1 Average Unemp10yment Rate Ranks (1961-1978) Region NE MAS ENC NNC SAS ESC NSC MTN PAC NE + _ -*** _ + + 0 +*** MAS _ _*** - + - _ +** ENC _** + +* + + +*** WNC +*** +*** +** +*** +*** SAS + _ + +** ESC - - +* NSC + +* MTN +* PAC Notes: (1) A + sign indicates that Uiz-Uj’ where (”i + 1) U1 = "i - nj +————§———. - R1; (”j + 1) i indexes row region i; j indexes cqumn region j; and, Rk is the sum of ranks assigned to region k, k = i, j. A - sign indicates that U13_Uj. (2) *** indicates statistica1 significance at the .01 1eve1. ** indicates statistica1 significance at the .05 1eve1. * indicates statistica1 significance at the .10 1eve1. In order to c1arify the above discussion consider that ce11 of Tab1e 6-3 in which the East North Centra1 region is the re1evant row region, and the West North Centra1 region is the re1evant coTumn 159 region. A negative sign is obtained, therefore: U < U ENC NNC' This, in turn, implies (see E.1) : (NENC 7' 1) (NWNC '1' I) 7N + -R (NENC.N + N we 2 ENC WNC z ENC WNC where Nk is the number of observations corresponding to region k (k = 5 for ENC, and k = 7 for HNC); and, Rk is the sum of the assigned ranks corresponding to states in region k in the pooled, ordered sample. Since terms other than the Rk values virtua11y cancel, the negative sign obtained for this particular cell indicates that RHNC< RENC. Thus when the values of the two samples are combined and ranked by order of magnitude, the average ranks of states in the West North Central region tend to be located relatively lower in the unemployment rate distribut- tion. Given the double asterisk in the call, one cannot accept the hypothesis that the two regions are alike in their unemployment rate experience during the eighteen year sample period, and one must conclude that average unemployment rates in the West North Central region are much 1ower than those in the East North Central region. Full examination of the test results in Table 6-3 reveals no statistically significant differences in average state unemployment rate ranks between any of the regions save the West North Central and 160 the Pacific.9 For these two areas the Mann-Whitney tests indicate wide disparities in rank when compared with each of the other seven regions and when compared with each other. On the one hand, average ranks of states in the West North Central region tend to be much less than those associated with states of any other region while, on the other hand, average ranks of states in the Pacific division are much greater than average ranks of states in all other areas. In terms of the regression model of Chapter IV the low unemploy- ment rates of the West North Central states derive from the relatively low frictional/structural unemployment in the region (as evidenced by the constant terms; see Tables 4-1 and 4-2) and, concomitantly, from the pervasive insensitivity to the vagaries of the business cycle exhibited by states in the region (as evidenced by the near zero personal income and transfer payment coefficients of states here). The West North Central region's industrial mix determines its low degree of frictional/structural unemployment and its high degree of cyclic insensitivity to a large extent. The West North Central region leads all regions in terms of IO Turnover among farm workers is low since agricultural employment. many are either self-employed or work on the family farm. One neither lays oneself off nor fires one's relatives. In addition, farming is an industry not likely to be adversely affected in a cyclic downturn. One may forego the purchase of a new automobile in the short run, but one is not likely to be able to forego purchase of one's next meal for a comparable period. The small percentage of total employment involved in the manufacture of durable goods in the West North Central region also 161 contributes to this area's relative cyclic insensitivity. Of the nine regions, the West North Central ranks sixth in this category (see footnote 14, Chapter IV) at 12.47 percent. As noted earlier durable goods industries are very sensitive to cyclic fluctuation. The lower the concentration of such industry within a region, the less sensitive is the region to swings in the business cycle. In sharp contrast to the states of the West North Central region, Table 6-3 indicates that the unemployment rate ranks of Pacific states are much greater than those of states in all other regions. Recall that Table 4-1 reveals small estimated constant terms for California, Oregon, and Washington implying a relatively greater degree of frictional and structural unemployment in these states. Contributing to the Pacific region's high degree of frictional and structural unemployment are such factors as a relatively large amount of in-migration to the area, greater seasonality in the area's industrial base (e.g., migrant farming), and the youthful composition of the area's labor force.11 California, Oregon, and Washington are also somewhat sensitive to cyclic fluctuation as indicated by their above average personal income coefficients and by the above average (in absolute value) transfer payment coefficients of Oregon and Washington. Such cyclic sensitivity leads to a higher average unemployment rate over time and, therefore, to a higher average unemployment rate rank for Pacific states. Though the Pacific division ranks fifth in percentage of total employment involved in the manufacture of durable goods (footnote 14, Chapter IV), examination of the three-state sub-region of California, Oregon, and Washington reveals a much greater degree of concentration 162 in durable goods production. On average, the percentage of total employment involved in durable goods production in this three-state sub-region is 14.25 percent (with California at 14%, Oregon at 17.3%, and Washington at 13.7%).12 This average places the sub-region third in terms of percentage of employment in durable goods industries, directly behind the East South Central region and ahead of the New England and Mid-Atlantic states. It is therefore not at all surprising that California, Oregon, and Washington in addition to having a large amount of frictional/structural unemployment are also quite sensitive to swings in the business cycle. Aside from the foregoing regional considerations one also would like to know what states in particular are most prone to either very high or very low unemployment rates. Table 6-4 lists the ten states with the most appearances in the highest quintile of the rank distribu- tion (i.e., ranks 41 through 50) and the ten states with the most appearances in the lowest quintile of the rank distribution (i.e., ranks 1 through 10). Consider first the states on the left hand side of Table 6-4-—the low unemployment rate states. Present in this category are six of the seven West North Central states discussed above. Present also are two East North Central states--Indiana and Wisconsin--and one state each from the West South Central and Mountain regions,respective1y-- Oklahoma and Wyoming. It is argued above that Indiana and Wisconsin tend to have such low unemployment rates because their economies are more akin to the agricultural economies of the West North Central region and are less like the economies of their relatively more industrialized 163 neighbors--Michigan and Ohio. One can advance a similar argument for Oklahoma. Oklahoma is much more a Plains state than a member of the Table 6-4. States Most Prone to Very Low or Very High Unemployment Rates 10 States with Most Appearances in 10 States with Most Appearances the Lowermost Quintile of the Rank in the Uppermost Quintile of the Unemployment Rate Distribution Rank Unemployment Rate Distribu- tion State No. of Appearances State No. of Appearances we Nebraska 18 California 16 1 South Dakota 18 Alaska 15 1 Iowa 18 New Mexico 15 3- Kansas 16 Louisiana 13 Minnesota 14 West Virginia 13 Oklahoma 13 South Carolina 9 Wisconsin 12 Tennessee 9 Missouri 9 Alabama 8 Wyoming 8 Michigan 8 Indiana 5 Oregon 7 South (which was chronically depressed in the 19605--see below.) As for Wyoming, reference to Table 4-1 reveals a relatively large constant term, suggesting low frictional/structural unemployment in this state. Moreover, Wyoming's relatively small personal income coefficient suggests that the state's employment rate is not very sensitive to swings in the business cycle. In large part this latter result must be due to the negligible amount of durable goods production that takes place in the state.13 Of the ten states with the most appearances in the highest quintile of the rank distribution, there are three Pacific states-- California, Alaska, and Oregon; five Southern states--Louisiana, West Virginia, South Carolina, Tennessee, and Alabama; and one state 164 each from the East North Central and Mountain regions, respectively-- Michigan and New Mexico. The Pacific region is discussed in detail above. Regarding the five Southern states, reference to Table 6-1 shows that most of their appearances in the uppermost quintile occur during the 19605. Given the economic and industrial growth which has taken place in the South, it is not surprising that high unemployment rates in these five states disappear in the 19705. Table 4-6 shows that growth in personal income over the eighteen year sample period is greater than the median for four of the five states under consideration; West Virginia is the exception. Attracted by relatively low wage costs, little unionization, and a favorable climate, capital has flowed into the region thus increasing the demand for labor and creating new jobs. Gellner notes sigzable growth in the South's non-durab1e goods industries, such as textiles and food processing, and in industries in the South's service producing sector.14 As noted above, these industries tend to be relatively insulated from swings in the business cycle. Michigan's experience, on the other hand, is much different from that of the aforementioned Southern or Pacific states. While unemployment rates are chronically high in the Pacific states, and high during the 19605 in the five Southern states, Michigan's unemployment rate tends to be extremely high (i.e., in the top quintile of the rank distribution) in years of weak aggregate demand. This cyclic sensitivity is, of course, explicable in terms of the large proportion of employment devoted to durable goods production, in general, and to production of 15 automobiles, specifically, in the state. When demand for autos declines in a cyclic downturn, so too does firm demand for labor. The result is 165 a large-scale increase in layoffs and involuntary unemployment, both of which vanish once economic conditions improve. Like the three Pacific states, New Mexico's unemployment rate is chronically high, falling outside the uppermost rank quintile in only 1961, 1977, and 1978. Given the long-term nature of the unemploy- ment problem here, one is tempted to label it a structural problem. At the same time, however, such long-term high unemployment may simply .-‘9 be indicative of a very high frictional or natural rate of unemployment _- w A (defined as the product of full employment values of the inflows to 1' °““ unemployment and the average job hunting interval). Given New Mexico's lack of manufacturing base,16 the average job hunting interval may be quite long. This section conducts an essentially static analysis of the rank distribution of state unemployment rates, first examining the data to determine how individual regions fare with respect to their unemploy- ment rate experience and then identifying states prone to either exceptionally high or exceptionally low unemployment rates. Little consideration, however, is yet given to certain dynamic characteristics of the rank distribution. For example, though Michigan is a high unemployment rate state, it seems to be so only in years of weak aggre— gate demand. Though exceptionally high unemployment rates also plague Tennessee, this is true only until 1971, after which Tennessee's average unemployment rate rank is slightly below twenty-third. At least in some cases, therefore, a state or region's position in the rank distribution of unemployment rates is not randomly associated with time. The following section addresses questions concerning the dynamic behavior 166 of the rank distribution to determine whether or not behavior similar to that of Michigan or Tennessee is observable over a wide range of states. 6.3. Dynamic Change in the Distribution of State Unemployment Rates The preceding section shows the states and regions of the country prone either to very high unemployment rates or to very low unemployment rates during the 1961-1978 period. But little is yet said concerning variation in the underlying pattern of states in the distribu- tion of state unemployment rates over time. Given that the variance of this distribution is stationary (see Chapter 11), one might reasonably ask whether or not the pattern of states within the distribution is invariant with respect to time. Is it the case, then, that West Virginia always has one of the highest unemployment rates in the nation, while Nebraska always has one of the lowest? If it is not the case, then an equally important question is why is it not the case? Given the ubiquitous flux in the economy's vector of prices and tastes, the economist's initial reaction would be to dismiss out of hand the possibility of a stable, underlying configuration of states in the distribution of state unemployment rates. The rise of new industries in some areas and the decline of old industries in other areas should most certainly lead to an ever-changing pattern in the state unemploy- ment rate distribution. But, as noted earlier, Archibald and Brechling do find a rather remarkable stability in the unemployment rate distribution of British regions over time. Moreover, though not directly 167 comparable to the geographic distribution, the demographic distribution of unemployment rates in the United States also remains quite stable. White prime-age males have the lowest unemployment rates, females have somewhat higher unemployment rates, non-whites have unemployment rates that are higher than those of both of the aforementioned groups, and teenagers possess the highest unemployment rates of all. Given the underlying stability in the British regional and U.S. demographic distributions, it is legitimate to ask whether or not the underlying pattern of state unemployment rates in the U.S. distribution is stable over time. If the state distribution is not stable, one should like to know whether or not the changes which have occurred are simply random events, or if, rather, the distribution has changed in some fundamentally systematic way. In a dynamic setting, economists distinguish between two senses of time-~the short run and the long run. This distinction is quite useful for the purposes at hand. More specifically, both the cyclic (short run) behavior of the distribution and the secular (long run) behavior of the distribution, over the 1961-1978 period, are of para- mount interest. The cyclic behavior of the distribution is relevant because of the empirical results of Chapters 11, IV, and V. Chapter II shows that the variance in state unemployment rates is inversely proportional to the strength of aggregate demand. Chapters IV and V reveal that some states are more cyclically sensitive than others. Given these factors, it seems likely that the underlying structure of the unemployment rate distribution also changes over the course of the business cycle. For, 168 if an increase in aggregate demand is spread equally over two sets of states, and one set of states is more cyclically sensitive than the other set, then a shift in the pattern of unemployment rate ranks is likely to ensue. The secular behavior of the unemployment rate distribution is equally important. Given continual changes in factor and product prices, changes in tastes, and expansion and decline across industries, it is not likely that the underlying configuration of states in the unemployment rate distribution has remained constant over time. One should like to identify the type and degree of long-run change which has taken place and to distinguish random from systematic change in the distribution. Popular accounts in the media herald the rise of the Sunbelt and decline of the Frostbelt in the 19705. This section's analysis allows one to determine the impact that this phenomenon has had on the underlying pattern of states in the unemployment rate distribution. In order to provide a theoretical framework for the subsequent analysis, consider the following: a given state's rank in the unemploy- ment rate distribution depends not only on its own unemployment rate, but also on the unemployment rates of the other forty-nine states. Therefore, state i's rank is: (6.1) R1. = f1. (01. . . .. U50) As noted in Chapter III, a state's unemployment rate is a non-linear function of variables measuring wages, non-labor income, demographic mix, and product market conditions. Using the data set of Chapter IV, one could ostensibly write the rank of state i as a function of some 169 450 variables. Since one has only eighteen rank observations for any state, however, a rank function specified over 450 variables is not estimable. One must, therefore, adopt a more practical approach. In general, the explanatory variables either vary cyclically-- e.g., transfer payments, personal income, property income, and %%%%—- or vary monotonically--e.g., educational attainment, and, to a lesser degree, teenage and non-white labor force. In order to proxy for variables of the former type, the state rank equations that follow utilize the aggregate unemployment rate. In order to proxy for 1‘ ’AA I* i_ variables of the latter type--variables which increase monotonically-- the state rank equations include a continuous time trend. The time trend takes a value of 1 in 1961, 2 in 1962, and so on. In addition, the state rank specification includes a dummy variable taking a value of l for the years 1970-1978 and 0 otherwise. This variable accounts for the possibility that a fundamental shift in the configuration of states underlying the distribution of unemployment rates took place in the 19705 because of the flight of capital and labor from the Frostbelt to the Sunbelt, as hypothesized in other work.'7 The rank of the unemployment rate of state i, then, is: (6.2) Ri = fi(U, t, 119705); i = l, . . ., 50 where U'is the national unemployment rate; t is a continuous time trend; T is equal to l for 1970-1978 and 0 19705 otherwise. In order to simplify estimation, assume that equation (6.2) is linear, hence: 170 (6.3) R1 = A1 + bi U + Cit + diT19705 + e1 where A1, b ci, and di are regression parameters specific i! to state i; and ei is a stochastic error term. Table 6.5 contains the OLS regression results obtained in 2 estimating equation (6.3) for each of the fifty states. With an R of .958, equation (6.3) fits West Virginia best. Time factors and cyclic conditions explain virtually all of the variation in West Virginia's unemployment rate rank. With an R2 of only .134, equation (6.3) fits Maryland worst. Thus time factors and cyclic conditions explain relatively little of the variation in this state's unemployment rate rank. For the set of fifty equations, the unweighted average R2 is .604. The regression equations allow one to separate cyclic behavior in the state ranks from long-run secular change. Consider first the cyclic behavior of the rank distribution of state unemployment rates. Holding constant for all other factors, the equations of Table 6-5 allow one to measure the impact of an increase in the national unemployment rate (decline in aggregate demand) on the rank of a state's own unemployment rate. If the effect of such an increase is statistically different from zero, then variation in the strength of aggregate demand affects the standing in the rank distribution of the particular state in question. A statistically significant and positive coefficient indicates that a decline in aggregate demand causes the unemployment rate of the state in question to rise relative to the unemployment rates of other 171 Table 6-5. Regression Results: State Unemployment Rate Ranks Independent Variables State Constant U' T197Os t R2 D.W. New England Connecticut 36.58*** -l.533 26.437** -1.212 .489 1.424 ( 3.320) (- 8.49) ( 2.898) ( .815) Maine 23.638*** 2.223(* 6.417 -O.364 .529 2.427 ( 4.160) ( 2.392) ( 1.366) (- .867) Massachusetts 11.534 0.781 6.510 1.116** .800 .719 ( 1.750) ( .727) ( 1.192) ( 2.289) New Hampshire 10.941 2.246 23.897*** -1.803** .614 1.623 ( 1.230) ( 1.539) ( 3.239) (-2.737) Rhode Island -30.389 6.256*** -9.266 2.l36*** .856 1.349 (-4.260) ( 5.344) (-l.566) ( 4.042) Vermont 21.453** 1.406 12.792* -O.758 .457 .823 ( 2.866) ( 1.146) ( 2.063) (-1.369) Mid-Atlantic New Jersey -11.377** 3.130*** -8.293** 2.647*** .946 1.590 (-2.770) ( 4.645) (-2.435) ( 8.703) New York 14.117* 1.369 -7.702 1.747*** .623 1.286 ( 1.913) ( 1.132) (-1.260) ( 3.199) Pennsylvania 5.791 5.950*** ~4.221 -0.752 .464 .819 ( .485) ( 3.042) (- .427) (- .851) East North Central Illinois 3.472 1.378 -0.440 0.556 .455 1.219 ( .599) ( 1.451) (- .091) ( 1.297) Indiana 6.207 1.184 16.621*** -0.621 .689 1.695 ( .963) ( 1.121) ( 3.114) (-1.302) Michigan 10.893 2.795 19.001* -0.251 .672 .849 ( 1.015) ( 1.589) ( 2.137) (- .316) Ohio 22.354*** 3.403*** 9.588** -1.860*** .860 1.794 ( 5.546) ( 5.151) ( 2.871) (-6.237) Wisconsin 5.271 -0.414 1.822 0.536* .610 1.436 ' ( 1.344) (- .644) ( .561) ( 1.846) Table 6-5 (Cont'd.). 172 Independent Variables State Constant U T19705 t D.W. West North Central Iowa - 2.292 0.532 - 1.461 0.284* .442 1.183 (- 1.155) ( 1.636) (- .889) ( 1.933) Kansas 21.214*** - 1.809 15.875** - 1.197** .379 1.037 ( 3.189) (-1.659) ( 2.880) (-2.431) Minnesota 13.700 - 0.879 11.530** - 0.575 .359 2.094 ( 2.333) ( .914) ( 2.370) (-1.324) Missouri 0.447 1.211* 1.040 0.415 .624 2.366 ( .114) ( 1.879) ( .319) ( 1.426) Nebraska - 0.153 0.247 - 0.868 0.073 .210 2.144 (- .175) ( 1.725) (- 1.198) ( 1.136) North Dakota 47.146 - 3.546*** -12.983** - 0.187 .852 1.553 ( 7.585) ( 3.480) (- 2.521) (- .406) South Dakota 6.621*** - O.608* - 1.304 0.059 .379 1.702 ( 3.337) ( 1.869) (- .793) ( .401) East South Central Alabama 55.368*** - 1.750 - 0.778 - 0.775 .590 2.426 ( 8.281) (-1.597) (- .140) (-1.566) Kentucky 34.713*** - 0.276 -12.435** - 0.468 .771 1.661 ( 5.180) ( .251) (- 2.239) (- .944) Mississippi 22.585** 1.958 -26.071*** 1.111 .550 .975 ( 2.318) ( 1.226) (- 3.229) ( 1.541) Tennessee 50.167*** 0.066 - 7.481 - 1.277* .741 1.242 ( 5.923) ( .048) (- 1.066) (-2.038) West South Central Arkansas 30.437*** 0.640 -12.674** 0.452 .484 2.064 ( 5.047) ( .648) (- 2.536) ( 1.014) Louisiana 71.909*** - 3.912*** 8.932* - 1.397*** .738 1.113 ( 12.478) (-4.l42) ( 1.871) (-3.275) Oklahoma 1.658 1.237* - 6.122* 0.392 .275 1.708 ( 0.431) ( 1.960) (- 1.919) ( 1.378) be 173 Table 6-5 (Cont'd.). Independent Variables - 2 State Constant U T1970$ t R D.W. Texas 36.562*** 0.297 2.734 - 1.963*** .755 .919 ( 5.025) ( .249) ( .454) (- 3.647) South-At1antic Delaware 5.858 1.487 0.631 1.483*** .813 .473 ( .962) ( 1.493) ( .125) ( 3.298) Florida -23.813*** 8.905*** -15.553** 0.937 .764 .699 (- 2.885) ( 6.582) (-2.274) ( 1.535) Georgia - 6.893 5.279*** -20.386*** 0.943* .690 .328 (- 1.083) ( 5.061) (-3.866) ( 2.003) Maryland 12.982* 1.523 0.598 - 0.247 .134 .144 ( 1.769) ( 1.267) ( .098) (- .455) North Carolina 14.940** 3.385*** -19.120*** - 0.137 .792 .080 ( 2.276) ( 3.146) (~3.516) (- .282) South Carolina 47.244*** -0.483 - 9.822* - 0.346 .733 .575 7.997) (- .498) (-2.007) (- .791) Virginia 5.094 0.652 -16.533*** 1.287*** .757 .054 ( 1.633) ( 1.276) (-6.397) ( 5.576) West Virginia 74.161*** -3.383*** 6.516*** - 1.463*** .958 .633 ( 33.892) (-9.432) ( 3.594) (- 9.035) Mountain Arizona 21.283** 2.476* -14.831** 1.010 .315 .309 ( 2.732) ( 1.940) (-2.298) ( 1.753) Colorado 39.006*** -2.259* -17.250** 0.560 .725 .212 ( 5.375) (-1.900) (-2.869) ( 1.044) Idaho 52.014*** -5.207*** 7.845* - 0.461 .781 .641 ( 11.211) (-6.847) ( 2.041) (- 1.343) Montana 19.900** -2.73l** - 0.064 1.274** .647 .758 ( 2.944) (~2.466) (- .011) ( 2.547) Nevada 51.959*** -3.478 0.931 0.295 .169 .875 ( 3.806) (-1.554) ( .082) ( .292) Table 6-5 (Cont'd.). 174 Independent Variables ** ~indicates significant at .05 level. * ‘indicates significant at .10 level. - 2 State Constant U T1970$ t R D.W. New Mexico 63.742*** -2.608** 7.241 -0.839* .469 .829 (10.984) (-2.742) ( 1.506) (-1.955) Utah 75.333*** -9.087*** 10.515 -0.438 .736 1.177 ( 8.197) (-6.033) ( 1.381) (- .644) Wyoming 34.422*** -1.748* -15.259*** -0.165 .853 1.883 ( 5.969) (-1.849) (-3.193) (- .389) Pacific Alaska 75.139*** -5.887*** 6.562 -0.209 .592 1.522 ( 9.144) (~4.371) ( .964) (- .344) California 54.006*** -l.618*** 2.055 -0.145 .556 1.650 (21.543) (-3.937) ( .989) (- .783) Hawaii 38.987*** -3.262* 12.021 0.674 .577 2.073 ( 3.849) (-1.965) ( 1.432) ( .899) Oregon 40.062*** -1.598 1.556 0.623 .351 .791 ( 8.528) (-1.345) ( .259) ( 1.162) Washington 54.404*** -3.325** 15.749** -0.324 .560 2.022 ( 7.500) (-2.797) ( 2.620) (- .604) Notes: (1) Sample period is 1961-1978. (2) Dependent variable is state unemployment rate rank. (3) *** ~indicates significant at .01 level. 175 Table 6-6. States with Statistically Significant Regression Coefficients in the Aggregate Unemployment Rate. State Coefficient State Coefficient Florida 8.905 Utah -9.087 Rhode Island 6.256 Alaska -5.887 Pennsylvania 5.950 Idaho ~5.207 Georgia 5.279 Louisiana -3.912 Ohio 3.403 North Dakota -3.546 North Carolina 3.385 West Virginia -3.383 New Jersey 3.130 Washington -3.325 Arizona 2.476 Hawaii -3.262 Maine 2.223 Montana -2.731 Oklahoma 1.237 New Mexico -2.608 Missouri 1.211 Colorado -2.259 Wyoming -l.748 California -l.618 South Dakota -0.608 states. A statistically significant and negative coefficient, on the other hand, implies that a decline in aggregate demand causes the unemployment rate of the state under consideration to decline relative to the unemployment rates of other states (though, of course, no absolute decline is implied). Table 6-6 lists all states with statistically significant regression coefficients in the aggregate unemployment rate variable from Table 6-5. The left side of Table 6—6 lists the eleven states for which an increase in the aggregate unemployment rate elicits an increase in rank. These states are primarily located in the far eastern portion of the U.S. with eight of the eleven states belonging to the New England, Mid- Atlantic, East North Central, and South Atlantic regions. The eleven states on the left side of Table 6-6 are more cyclically sensitive than 176 the majority of states. A decline in aggregate demand evokes more than a proportionate increase in the unemployment rates of these states causing each state to shift rightward in the unemployment rate distribu- tion. The converse occurs when aggregate demand increases. Of these eleven states, Florida appears to be most sensitive of all to fluctuation in aggregate demand. A one unit increase in the national unemployment rate induces nearly a nine unit increase in Florida's unemployment rate rank. The right side of Table 6-6 lists the fourteen states for which an increase in the aggregate unemployment rate causes a decline in unemployment rate rank. Here, too, there is a strong regional bias with ten of the fourteen states located in the far western portion of the U.S. (in the Mountain and Pacific regions). These fourteen states are the least cyclically sensitive of all U.S. states. A decline in aggregate demand induces a less than proprtionate decline in the unemployment rates of these states, causing each state to shift leftward in the unemployment rate distribution. When the economy expands, the reverse occurs. The unemployment rates of states that are more cyclically sensitive decline to a relatively greater extent than the unemployment rates of the fourteen states listed on the right side of Table 6-6. The unemployment rate ranks of the latter, therefore, rise as the economy expands. Of these fourteen states, Utah's rank is the most sensitive to variation in aggregate demand. A one unit increase in the aggregate unemployment rate elicits more than a nine unit decline in Utah's rank. At this point, one might reasonably ask what makes these twenty- five states so special? Why should a given state be more cyclically 177 sensitive or less cyclically sensitive than the large majority of states? Using spectral analysis, Cho and McDougall find that regions with a large concentration of employment in durable goods, and in manufacturing industries in general, are most sensitive to the vagaries of the business cycle.18 Comparison of the industrial mix of the states in question with the industrial mix of the U.S. as a whole is, therefore, a logical path of analysis. J Table 6-7 reports the results of a regression analysis conducted by the author to determine the degree of cyclic sensitivity of the major industry groups in the U.S. The general form of the regression equation is: (5'4) Uit = A1 + biUt T Cit " git where ”it is the unemployment rate of industry i in year t; Ut t is a continuous time trend; is the aggregate unemployment rate in year t; Sit is a stochastic error term. In estimating this equation unemployment rate data from Table A-24 of The Employment and Training Report of the President, 1979, are used. The aggregate unemployment rate proxies for aggregate demand, and the time trend accounts for secular change in industry unemployment rates. The regression results of Table 6-7 indicate that the construction industry is by far the most cyclically sensitive industry in the U.S. An increase in the aggregate unemployment rate clearly causes a propor- tionately greater increase in this industry's unemployment rate relative 178 Table 6-7. Regression Resu1ts: Cyclic Sensitivity of Major Industry Groups (1958-1978). Major Industry Regression Coefficient of 2 Group National Unemployment Rate R D.W. Construction 2.457 .964 1.842 (21.641) Durable Goods 1.699 .875 0.998 (11.211) Non-Durable Goods 1.207 .963 2.016 (20.996) Mining 1.148 .908 1.206 ( 7.315) Agriculture 1.109 .781 1.233 ( 7.976) Wholesale and 0.981 .978 1.582 Retail Trade (26.761) Transportation and 0.885 .959 1.397 Public Utilities (20.201) Services 0.757 .952 1.177 (18.196) Finance, Insurance, 0.446 .917 1.457 and Real Estate (11.443) Government 0.424 .941 1.283 (11.473) Notes: (1) Dependent variable in each equation is the unemployment rate of the industry under consideration. (2) Also included in each equation, but not reported, are a constant term and a time trend. (3) The t-statistics are contained in the parentheses. §3¥¥EEEfi 179 to all other industry unemployment rates. In a recession, firms are less likely to have new plants built, and families are less likely to buy new houses--a house is the ultimate consumer durab1e. In light of Cho and McDougall's results, it is not surprising that durable goods industries rank second in terms of cyclic sensitivity, while non-durable goods industries rank third. Weighting by labor force, Table 6-8 lists the average proportion of area income accounted for by the construction, durable goods, and non- durable goods industries in the U.S., in the eleven states whose ranks are positively affected by an increase in the aggregate unemployment rate, and in the fourteen states whose ranks are negatively affected by an increase in the aggregate unemployment rate.19 Table 6-8 shows that the states whose ranks are positively affected by the aggregate unemployment rate have an above average concentration of the construction industry and have very large concentra- tions of durable and non-durable goods industries. The durable and non- durable goods industries, respectively, account for 18 percent and 22 percent more income in these eleven states than on average in the U.S. The lower portioncH’Table 6-8 reveals an antithetical pattern in the industrial mix of the fourteen states whose ranks decline given an increase in the aggregate unemployment rate. The proportion of income derived from durable goods industries in these states is 15 percent lower than the U.S. average while the proportion of income derived from non-durable goods industries is more than 33 percent less than the U.S. average. The proportion of income derived from construction is slightly greater than the U.S. average. 180 Table 6-8. Percentage Share of Area Income by Industry % Share of Area % Share of Area % Share of Area Income Provided Income Provided Income Provided Area by Construction by Durable Goods by Non-Durable Goods U.S. 6.5 14.7 9.9 Eleven states with positive and statistically significant unemployment rate coefficients 6.8 17.3 12.1 Fourteen states with negative and statis- tically significant unemployment rate coefficients 6.7 12.5 6.6 Note: Percentages are based on 1972 data. Though isolating specific causes accounting for the propensity of a given state to be either more or less cyclically sensitive than the majority of states is difficult, the analysis of this section is consistent with the proposition that industrial mix plays an important role in determining a state's sensitivity to fluctuations in aggregate demand. Those states which move rightward in the unemployment rate distribution as the economy slips into recession also tend to be states whose economies are dominated by cyclically sensitive manufacturing industries. For these states, an increase in the aggregate unemployment rate induces a relatively greater increase in the state's unemployment rate causing the state's standing in the unemployment rate distribution to deteriorate. 181 Conversely, those states which move leftward in the unemployment rate distribution as the economy slips into recession tend to have particu1ar1y low concentrations of the major industry groups that are cyclically sensitive. Rather, industry in these states tends to be concentrated in the government, service, and agricultural sectors. A decline in aggregate demand, therefore, causes unemployment rates in these states to rise proportionately less than in the majority of states. The analysis of this section further shows that rank shifting among the states is quite extensive over the course of the business cycle. The unemployment rate ranks of twenty-five states, in all, experience a statistically significant change as aggregate demand varies. Even in the short run, therefore, the underlying configuration of states is not stable. Turning attention now to long-run considerations and, therefore, holding aggregate demand constant, what does the regression analysis of Table 6-5 tell of changes in the underlying pattern of states in the unemployment rate distribution over time? Since the rank regressions contain both a dummy variable for the 19705 and a continuous time trend, one can distinguish abrupt shifts in rank occurring in the 19705 from long-term secular increases or decreases in rank occurring over the entire sample period. In order to determine how much a given state's rank changes on average over time, however, one must combine the two time variables. Holding constant for aggregate demand, the average 182 difference in a state's rank between the 19705 and the 19605 is: (6.5) DIFFi = (13.5 c1 + d1) - (4.5 Ci) = 9ci + di where 61 is the estimated trend coefficient for state 1'; A and d1 is the estimated dummy coefficient for state i. Excluding the U term, 13.5 61 + 8i is the average rank of state i during the 19705, and 4.5 81 is the average rank of state i during the 19605. Assuming that 81 and 81 are normally distributed, with mean vector (c1, di) and covariance matrix 2 = Po: oc d1 i i’ i o o2 ’ 1. Ci ’di d1. DIFFiis normally distributed with mean 9c, + di and variance (9)2 oi 2 1 . d .20 Given estimates of the mean and variance, one 1’ i can further compute the statistical significance of the average difference + 0d +18'o i in rank between the two periods for each state. Table 6-9 lists the average shift in rank from the 19605 to the 19705 for each state. The table arrays these figures from largest increase in rank to largest decrease in rank, and it includes the corresponding t-statistics. Table 6-9 indicates that Hawaii experiences the greatest increase in unemployment rate rank in the 19705 and that North Carolina experiences the sharpest overall decline. Only thirteen states register no change whatsoever in average rank over the two decades. 131the long run, therefore, a considerable amount of rank shifting takes place among the states. 183 Table 6-10 classifies by region the direction and statistical significance of the changes documented in Table 6-9 in order to illuminate underlying regional patterns in the regression results. Table 6-10 indicates that Northern states (i.e., states from the New England, Mid-Atlantic, and East North Central regions) account for more than half of the states that bear a statistically significant increase in unemployment rate rank in the 19705. Moreover, the average change in rank (weighted by relative state labor force) of these eleven Northern states, at 10.67, is 34 percent greater than the average change in rank of the other nine, non-Northern states (their average shift is 7.93 units). Only three Northern states--Maine Ohio, and Pennsylvania--do not experience an upward shift in rank in the 19705. Twelve of the seventeen states whose ranks fell in the 1970s are from the South. The average decline in rank of these twelve Southern states is 12.78 units, which is 33 percent greater than the average decline in rank of the other five non-Southern states (their average decline is 9.62). Delaware is the only Southern state that experienced an increase in rank, on average, in the 19705. A very clear regional pattern of change in state ranks thus emerges from this analysis. Ranks of states in the industrialized Northern portion of the country increased in the 19705, and they increased at a proportionately greater rate than ranks of other states whose unemployment rates also increased relatively in the 19705. At the same time, ranks of states in the less developed South declined from levels attained in the 19605, and they declined at a substantially greater rate than ranks of other non-Southern states whose unemployment rates also declined re1ative1y in the 19705. 184 Table 6-9. Average Change in State Ranks from the 19605 to the 19705 Avg. Shift in b Rank State Rank from '605 to '705a t-Statistic (1) Hawaii 18.09 4.163***C (2) Michigan 16.74 3.637*** (3) Massachusetts 16.55 5.856*** (4) New Jersey 15.53 3.808*** (5) Connecticut 15.529 3.289*** (6) Delaware 13.98 5.365*** (7) Washington 12.83 4.124*** (8) Montana 11.40 3.932*** (9) Indiana 11.03 3.992*** (10) Rhode Island 9.96 3.252*** (11) New York 8.02 2.534** (12) New Hampshire 7.67 2.009* (13) Oregon 7.16 2.304** (14) Wisconsin 6.65 3.954*** (15) Utah 6.57 1.667 (16) Minnesota 6.35 2.521** (17) Vermont 5.97 1.860* (18) Kansas 5.10 1.788* (19) Missouri 4.77 2.828** (20) Alaska 4.68 1.328 (21) Illinois 4.56 1.837* (22) Idaho 3.70 1.857* (23) Nevada 3.59 0.613 (24) Maine 3.14 1.291 (25) Iowa 1.09 1.281 (26) California 0.75 0.698 (27) Nebraska - 0.21 - 0.231 (28) New Mexico - 0.31 - 0.125 (29) South Dakota - 0.77 - 0.905 (30) Maryland - 1.63 - 0.516 (31) Oklahoma - 2.59 - 1.569 (32) Louisiana - 3.64 - 1.473 (33) Virginia - 4.95 - 3.700*** (34) Arizona - 5.74 - 1.718 (35) West Virginia - 6.65 - 7.086*** (36) Florida - 7.12 - 2.011** (37) Ohio - 7.15 - 4.136*** (38) Alabama - 7.75 - 2.702** (39) Arkansas 8.60 - 3.325*** (40) Pennsylvania -10.99 - 2.147* (41) Georgia -11.90 - 4.360*** (42) Colorado -12.21 - 3.923*** (43) South Carolina -12.96 - 5.115*** (44) North Dakota -l4.67 - 5.503*** (45) Texas -14.93 - 4.784*** (46) Mississippi -16.07 - 3.845*** 185 Table 6-9 (Cont'd.) Avg. Shift in Rank Rank State from '605 to '705 t-StatistiC' (47) Kentucky -]6,65 -5.793*** (48) Wyoming -16,75 -6.772*** (49) Tennessee -18.97 -5.222*** (50) North Carolina -20.35 -7.228*** Notes (a) The figures in this column are computed by taking 981 + 3i for each state, where 31 is the estimated trend coefficient and 3, is the estimated dummy coefficient. The underlying variance implicit in this t-statistic is (9)2 0% + OE + 18 08 a i di 1’ 1 *** indicates significance at .01 level. ** indicates significance at .05 level. * indicates significance at .10 level. .FH.--_,1. 186 Table 6-10. Regiona1 Classification of State Rank Changes from 19605 to 19705 States which Experience States which States which a Significant Increase Experience Experience a in Rank in the 19705 No Signifi- Significant Region cant Change Decline in Rank in 19705 Northeast New England 5 1 0 1 Mid-Atlantic 2 0 1 North Central East North Central 4 o 1 i” West North Central 3 3 1 South South-Atlantic 1 1 6 East South Central 0 0 4 West South Central 0 2 2 West Mountain 2 4 2 Pacific 3 2 0 Extending the analysis to cover a longer time period does not essentially change the regional patterns identified above. Table 6-9 and 6-10 compare changes in state rank from the middle of the 19605 to the middle of the 19705. Holding constant for aggregate demand, Tables 6-11 and 6-12 compare changes in state rank from 1961 to 1978. Follow- ing the earlier discussion, the change in a given state's unemployment rate rank from 1961 to 1978 is: (1881. + 31.) - (81.) 178, + 8, (6.6) DIFF; 187 The variance of this linear combination is (17)2 o? + o? + 34 o, A . c. . c.,d. Table 6-11 lists the total shift in rank, by order 6f maghitude, fdr 1 each state. Table 6—12 classifies these shifts by region and by level of statistical significance. Over the entire period New Jersey experiences the greatest increase in unemployment rate rank, and Texas experiences the largest decline. Since a number of states possess one positive time coefficient and one negative time coefficient, fewer states--twenty-seven--experience a statistically significant change in rank over the entire period than do from the middle of the 19605 to the middle of the 19705. Seven of the fifteen states whose ranks are significantly greater in 1978 than in 1961 are from the North (i.e., from the New England, Mid-Atlantic, or East North Central regions). Notably, the unemployment rate ranks of three New England states--Connecticut, New Hampshire, and Vermont--whose ranks, on average, are significantly greater in the 19705 than in the 19605, do not differ at the end of the period from levels attained at the period's outset. Increases in rank are therefore primarily concentrated in the Mid-Atlantic and East North Central portions of the country over the full sample period. Of the fifteen states whose ranks are significantly greater in 1978 than in 1961, the seven Northern states bear the most sizable increases. The average increase in rank (weighted by relative state labor force) of the Northern states is 20.04 units, which is more than double the average increase--9.22 units-- of the other eight non- Northern states. Table 6-12 further indicates that Southern states comprise the majority of states whose ranks are significantly lower in 1978 than in 188 Table 6-11. Shifts in State Rank from 1961 to 1978 Total Shift in Rank t-Statistic b West Virginia Kentucky Rank State from 1961 to 1978a (1) New Jersey 36.71 (2) Rhode Island 27.05 (3) Delaware 25.84 (4) Massachusetts 25.48 (5) Hawaii 23.48 (6) New York 22.00 (7) Montana 21.59 (8) Michigan 14.73 (9) Oregon 12.15 (10) Wisconsin 10.93 (11) Washington 10.24 (12) Illinois 9.01 (13) Missouri 8.09 (14) Indiana 6.06 (15) Nevada 5.95 (16) Connecticut 5.83 (17) Virginia 5.35 (18) Iowa 3.37 (19) Utah 3.07 (20) Alaska 3.01 (21) Arizona 2.34 (22) Minnesota 1.75 (23) Oklahoma 0.54 (24) Nebraska 0.381 (25) Florida 0.376 (26) Maine 0.23 (27) Idaho 0.01 (28) Vermont - 0.09 (29) South Dakota - 0.30 (30) California - 0.41 (31) Maryland - 3.60 (32) Georgia - 4.35 (33) Kansas — 4.47 (34) Arkansas - 4.99 (35) New Hampshire - 6.75 (36) New Mexico - 7.02 (37) Mississippi - 7.18 (38) Colorado - 7.73 (39) Alabama -13.95 (40) Louisiana -14.82 (41) South Carolina -15.70 (42) North Dakota -16.16 (43) Pennsylvania -17.01 (44) Wyoming -l8.08 (45) -18. (46) I N O on SD 12.864***c «DNDNWWWWdddd—‘OOOOOOOOOOOOOOONNOO—‘NNN-fi-N—‘h-filwwmm I _a .456*** .127*** .570*** .339*** .294*** .602*** .977* .415** .015*** .034* .240** .963** .355 .628 .673 .471** .446** .481 .528 .433 .429 .203 .626 .066 .058 .001 .017 .220 .236 .707 .985 .968 .192 .093 .743 .062 .534 .005** .704*** .828*** .745*** .053* .516*** o 08 *** .383*** 189 Table 6-11 (Cont'd.) Total Shift in Rank Rank State from 1961 to 1978 t-Statistic (47) North Carolina -21.45 -4.707*** (48) Ohio -22.03 -7.874*** (49) Tennessee -29.l9 -4.g55*** (50) Texas -30.64 '6.066*** Notes: (a) (b) (C) These figures are derived by assuming aggregate demand constant across periods and computing 17Ci + 31, where 81 is the estimated trend coefficient for state i and 31 is the estimated dummy coefficient for state i. The variance implicit in these t-statistics is (l7)2 0% i O 0.)“) + 34 0A A . i Ci’di *** indicates significance at the .01 level. ** indicates significance at the .05 level. * indicates significance at the .10 level. + 190 Table 6-12. Regiona1 Classification of State Rank Changes from 1961 to 1978 States Experiencing Number of Number of States a Significant In- States which which Experience crease in Rank from Experience No a Significant Region 1961 to 1978 Significant Decline in Rank Change from 1961 to 1978 Northeast New England 2 4 O Mid-At1antic 2 O 1 North Central East North Central 3 1 1 West North Central 2 4 1 South South-At1antic 2 3 3 East South Central 0 l 3 West South Central 0 2 2 West Mountain 1 6 1 Pacific 3 2 O 1961. Three South Atlantic states--Florida, Georgia, and Virginia-- however, whose ranks, on average, are significantly lower in the 19705 than in the 1960s, experience no significant decline in rank over the entire sample period. Indeed, because of its very positive trend coefficient, Virginia's rank is approximately five points greater in 1978 than in 1961. Secular declines in rank, therefore, are primarily concentrated in the East South Central region (Alabama, Kentucky, and Tennessee) over the entire eighteen-year period. F“ TE 191 Of the twelve states whose ranks are significantly lower in 1978 than in 1961, the eight Southern states enjoy the greatest average reductions. The ranks of the Southern states fall 23.6 units, on average, while ranks of the other four non-Southern states decline 19.32 points (a 22 percent difference). Whether one compares average differences in rank between the 19705 and 19605 or compares differences in rank over the entire period, one must draw the same basic conclusion: unemployment rates of states in the South have declined re1ative1y, while those of the industrialized Northern states have risen re1ative1y. Thus the distribution of state unemployment rates undergoes a fundamental transformation in terms of its underlying regiona1 composition during the 1961-1978 period. Northern states, on the one hand, tend to lie in the lower tail of the unemployment rate distribution during the 19605. Southern states, on the other hand, tend to be located in the middle of and in the upper tail of this distribution during the same period. As time passes this situation reverses itself. Southern states decline in rank, while Northern states concomitantly rise in rank. The underlying pattern of states in the unemployment rate distribution, therefore, is not at all stable during the 1961-1978 period. But why does this change in the configuration of states in the distribution take place? Chapters 111 through V, to a large extent, already answer this question. Chapter IV explicitly shows that personal income grows at a much faster rate in Southern than in Northern states during the period (see Table 4-6). Since nearly all of the regression coefficients associated with personal income are positive, the larger 192 growth rates in personal income of states in the South imply that employment rates grow at a differentially greater rate here than in the North when other factors are held constant. Chapter IV's results additionally indicate that a marginal increase in transfer payments lowers employment rates in most states. Northern states, however, appear to be much more sensitive to changes in transfer payments than other states. Since transfer payment levels increase in all states during the period studied, the more negative Northern coefficients dictate that employment rates in the North decline at a faster rate than employment rates in the South when other factors are held constant. In a more fundamental, economic sense, the results of this section and of Chapter IV reflect a large scale geographic change in what Hicks labelled ". . . the ultimate determinants of economic activity--those things which we have to take as the final data of 2] Changes in taste, relative prices, technology, economic enquiry." natural environment, and efficiency in the factors of production combine to determine the shifts in the rank distribution of unemployment rates that take place during the 1961-1978 period. Economic growth is clearly not distributed uniformly on a geographic basis. Over time, old industries decline in the North while new ones arise and grow in the South. Production in the North is concentrated in such major durable goods industries as machinery and electrical equipment in New England, primary metals in the Mid-Atlantic states, and motor vehicles in the East North Central region. These industries--particu1arly autos and steel--are commonly cited as victims of entrenched inefficiencies and foreign trade competition. 193 With its industry concentrated in the non-durab1e goods and in the service producing sectors, the Southern economy has grown re1ative1y in the 19705. Lower energy costs and a relatively cheaper and unorganized labor force have attracted new firms to this region, creating jobs in the South and destroying jobs in the North. The change in the underlying configuration of states in the unemployment rate distribution, therefore, can be attributed to the working out of this process of industrial expansion in the South and economic decline in the North. 6.4. Conclusion This chapter examines the underlying pattern of states in the unemployment rate distribution over time. Several noteworthy resu1ts issue from the analysis. First, it is shown that states in the West North Central region experience the lowest unemployment rates and that states in the Pacific region experience the highest unemployment rates throughout the 1961-1978 period. This situation is invariant with respect to time. States in these two regions respectively remain at the lower and upper ends of the unemployment rate distribution throughout the period. The results of this chapter additionally indicate that the underlying configuration of states in the unemployment rate distribution is quite susceptible to short-run variation because of swings in the business cycle. The unemployment rate ranks of twenty-five states experience a statistically significant change given a change in the strength of aggregate demand. 194 Finally, this chapter shows that the underlying pattern of states in the unemployment rate distribution undergoes a great deal of secular or long-run change during the period studied. Holding aggregate demand constant, the analysis of the preceding section shows that thirty-seven of the fifty states experience a statistically significant change in unemployment rate rank in the 1970s from average levels achieved in the 19605. From an economic perspective the results of this chapter are quite pleasing. The great flux in the underlying pattern of states in the unemployment rate distribution indicates an open economy where resources and factors of production are quite mobile across states. One finds neither the stability in the British distribution noted by Archibald and Brechling, nor the invariant relationships among the unemployment rates of the various demographic groups in the U.S. As patterns of demand and economic growth have changed, so too has the underlying configuration of states in the unemployment rate distribution. The pronounced leftward shift of southern and southwestern states in the distribution and the concomitant rightward shift of northern and northeastern states during the 1961-1978 period clearly demonstrate the powerful effect of such forces. One must conclude from the results of this chapter that the distribution of state unemployment rates-- though its variance is stationary--is subject to continual change in the pattern of states underlying it. 195 NOTES 1. Excess demand in a labor market is defined here to mean that the only unemployment which exists in the labor market in question is that associated with optimal job search, i.e., frictional unemploy- ment. In such a market, all individuals who desire work can obtain it at the going market wage. 0n the other hand, excess supply in the labor market implies here that not every worker who desires a job can obtain one at the going market wage. This latter definition takes into account frictional, structural, and involuntary unemployment. 2. See Hicks (1964), p. 18 and p. 76. 3. Kalachek, p. 84. 4. For example, see Perry (1970), Perry (1980), and Hall (1975). 5. A one-tail t-test pitting the null hypothesis that the mean U.S. unemployment rate observed during the 19605 (1961 through 1969) is equal to that observed during the 1970s (1970 through 1978) against the alternative that the latter is greater than the former rejects the null hypothesis with a better than 95% degree of confidence (estimated t = 2.215). 6. See Archibald (1967), and Brechling (1967). 7. Archibald, p. 23. 8. Indeed, in 1970 the percentage of civilian labor force in agricultural production and services is greater in Illinois (2.31%), Indiana (3.01%), and Wisconsin (5.87%), than in either Michigan (1.47%) or Ohio (1.71%). Source: Characteristics of the Population, 1970 Census of Population, Vol.1, parts 15, 16, 24, 37, and 51. 9. There is one exception in that a statistically significant difference at the .10 level is also found to exist between the East North Central and East South Central regions. The positive sign in the associated table cell indicates that average unemployment rates in the East North Central region tend to be lower than those of states in the East South Central region. 10. In terms of percentage of total U.S. farm employment in 1970, the nine Census regions rank as follows: 196 Rank Region % of U.S. Farm Employment 1 West North Central 20.2 2 East North Central 17.0 3 South Atlantic 15.9 4 West South Central 13.7 5 East South Central 11.7 6 Pacific 9.3 7 Mountain 5.4 8 Mid-At1antic 5.2 9 New England 1.6 Source: Statistical Abstract of the United States, 1971. 11. See Gellner (1974), p. 17. 12. This is a weighted average where the individual state weight, as in footnote 14 of Chapter IV, is equal to the labor force in that particular state divided by total labor force in the region considered. Source: Employment and Earnings, States and Areas, 1939-78, 1979. 13. Employment in durable goods industries accounted for only 2.8% of total non-agricultural employment in Wyoming in 1972. Source: Employment and Earnings, States and Areas, 1939-1978. 14. See Gellner, p. 18. 15. In 1972, 28.1% of all non-agricultural employment in Michigan was devoted to the production of durable goods. Moreover, durable goods industries provided for 35% of Michigan's personal income in this year, half of which was accounted for by the motor vehicles and equipment industry. Sources: Employment and Earnings, States and Areas, 1939-1978 and unpublished data provided by the Bureau of'Economic Analys1s, U.S. Department of Commerce. 16. In 1972, only 8% of New Mexico's total non-agricultural employment was located in manufacturing industries (4.7% of the state's employment was in durable goods production in this year). Source: Employment and Earnings, States and Areas, 1939-78. 17. See Gellner, also see Browne (1978). 18. Cho and McDougall, p. 70. 19. The industry income data are from 1972, a year of relatively strong aggregate demand and a year reasonably close to the mid-point of the sample. These data are unpublished, and were provided by the Bureau of Economic Analysis, U.S. Department of Commerce. 197 20. According to Theil, if a vector x is multinormally distributed, with mean vectoriland covariance matrix 2, then any linear combination a'x has a univariate normal distribution, with mean a'u and variance a'ZIa. See Theil (1971), p. 79. 21. See Hicks, p. 18. CHAPTER VII CONCLUSIONS This dissertation develops and estimates a model of the determinants of the geographic dispersion of unemployment rates, taking into account wages, non-labor income, demographic mix, and product market demand conditions. In addition, the behavior of the dispersion over time is analyzed, and short-run and long-run changes in the distri- bution of state unemployment rates are examined. The principal findings of this study are: 1. Product market demand conditions and sensitivity of state unemployment rates to changes in product market demand conditions play a predominant role in determining the dispersion of unemployment rates. Cross-state variation in frictional/structural levels of unemployment rates is also a major determinant of the dispersion. Wages and educational attainment play secondary roles in determining the dispersion. And cross-state differences in age and racial mix have a negligible impact on the dispersion of unemployment rates. 2. Employing a number of empirical measures and analytic techniques, this study finds no secular increase in the dispersion of state unemployment rates over time. This result directly contradicts the findings and assertions of others who have studied this topic. 3. Though the variance in state unemployment rates is a stationary time-series, the underlying configuration of state unemployment 198 199 rates is neither stable over the business cycle nor in the long-run. This finding indicates that the U.S. economy responds to an ever- changing vector of tastes, technologies, and relative factor and product prices. In examining the geographic dispersion of unemployment rates, this study incorporates a number of novel approaches that distinguish it from previous work. First, the empirical analyses herein employ state data, which are more appropriate from a theoretical standpoint, rather than regiona1 data. Second, regression analysis allows identification and separation of secular trends from cyclic variation in the dispersion, and it also facilitates in the study of both short run and long-run change in the distribution of state unemployment rates. Most importantly, this research provides a set of state unemployment rate equations, consistent with utility and profit maximization, and uses this system to develop a model of unemployment rate dispersion. Net variance analysis, which may be of use to future studies employing cross-section and time-series data, issues from this model. The empirical application of the model yields estimates of underlying parameters that should be taken into account by policy makers in any effort aimed at altering the level of dispersion in unemployment rates. The results of this study lead to several important though contradictory policy conclusions. First, if policy makers wish to lower the dispersion in unemployment rates, one promising approach appears to be through a regionally discriminatory stabilization policy. Policy makers could seek to raise the level of demand in the product markets of those high unemployment rate states whose unemployment rates 200 are particularly sensitive to changes in product market demand conditions. This objective might be accomplished through such measures as improved targeting of federal procurement programs, favorable tax treatment for investment carried out in the specified areas, or favorable tax treatment for individuals living in high unemployment rate areas. A second promising approach through which the dispersion in unemployment rates might be decreased would be to reduce levels of frictional and structural unemployment in those high unemployment rate states whose levels of frictional and structural unemployment are large relative to such levels in other states. Policy makers might achieve this aim by improving the flow of information in targeted states (which would also improve job/worker matches), by making receipt of unemploy- ment insurance benefits less attractive to workers and thus lowering reservation wages, by reducing critical skill vacancies through sub- sidized worker-training programs, and by reducing institutional barriers such as licensing and discrimination. Nevertheless, though measures are suggested here through which the dispersion in unemployment rates might be lowered, the results of Chapters II and VI indicate that policy makers must consider very carefully the wisdom of tampering with the dispersion in unemployment rates. Variation in the dispersion-~at least over the last twenty years-- is clearly cyclic in nature. No upward trend in the dispersion of state unemployment rates exists. Thus unemployment is not becoming more concentrated in certain areas over time. Migration and the price system act to redistribute unemployment geographically in a reasonably 201 short period of time. When stabilization policy is followed, an inherent risk of incurring an unacceptable level of inflation is present since the rate of unemployment at which prices remain constant in any given area is unknown. Moreover, past applications of manpower policy, aimed at lowering frictional and structural unemployment, have fallen somewhat short of their proposed objectives. The findings of this study show that the dispersion in state unemployment rates remains constant, on average, over the last twenty years and, therefore, that one may upset an equilibrium relationship in attempting to further lower the dispersion. Future research remains to be done in two main areas. First, empirical work on this topic should be recast using smaller geographic units than states. A state comprises numerous smaller geographic labor markets. From a theoretical viewpoint, these smaller labor markets are the appropriate units of study. But states are the smallest geographic units for which adequate time-series are currently available and which, when combined, cover the entire U.S. population. It is doubtful, however, that the conclusions of a study using smaller units would differ markedly from the conclusions of this study: the price system and migration act very well in re-distributing disequilibrium unemployment on a geographic basis. Second, future research should consider the optimal level of dispersion in unemployment rates. This level is clearly not zero-- implying a degenerate distribution--since areas differ in terms of purely frictional unemployment rates. The optimal dispersion of unemployment rates, rather, is that level of dispersion consistent with 202 a rate of unemployment in each labor market at which the rate of change in the level of wage inflation is zero. Future research in this area should therefore attempt to determine the non-accelerating inflation rates of unemployment in each individual labor market and incorporate these in a larger study of the geographic dispersion in unemployment rates. APPENDIX A DATA SOURCES .AL 203 APPENDIX A DATA SOURCES Variable Source Unemployment 1957-1962: Manpower Report of the President, (Wishington, D.C.: U.S. Government Printing Office, 1970). Table 0-4. 1963-1972: Manpower Report of the President, 1974. Table D-4. 1970-1974: Manpower Report of the President, 1977. Table D-4. 1973-1978: Employment and Training Report of the President,’1979. Gross Average Hourly 1958-1978: Various May Issues of Employment and Earning , Earnings of Production Workers in Manufacturing % of Working Age Population 1950 and that is Non-White 1960 ' 1970: 1971, 1972, 1974-1978: % of Working Age Population 1950 and that is 16-19 years of Age 1960 1970: 1971, 1972, 1974-1978: U.S. Department of Labor,’Bureau of Labor Statistics. The various state volumes of the 1960 0.5. Census. Tables 95 and 96. The various state volumes of the 1970 U.S. Census. Tables 19 and 20. From the various Geographic Profiles of Emplpyment and Unemploymentlfor those specific years. Bureau of Labor Statistics Report Nos.: 402, 421, 452, 481, 504, 539, 571. State Volumes of 1960 U.S. Census. Tables 95 and 96. State Volumes of 1970 U.S. Census. Tables 19 and 20. Geographic Profiles of Employment and Unemployment. 204 % of Population, 25 years 1950 and 1960: State Volumes of 1960 U.S. Census, Table 103. and older holding at least a high school diploma 1970: State Volumes of 1970 U.S. Census, Table 51. 1976: From the Survey of Income and Education in the Current Population Report, Series P-60, NOS. ' g a Transfer Payments 1958-1978: Data provided by the Bureau of Economic Analysis, U.S. Department of Commerce. This data is partially available in Surve of Current Business, August 1979, Part 11, Table 3. Rent, Interest and Dividend 1958-1978: Data provided by the Bureau of Economic Analysis, U.S. Department of Commerce. This data is partially available in the Surve of Current Business, August 1979, Part II, Table 3. Personal Income 1958-1978: Data provided by the Bureau of Economic Analysis, U.S. Department of Commerce. This data is also fully available in the Surve of Current Business, August 1979, Part II, TaBTe l. Actual and Potential GNP 1958-1978: Economic Repprt of the President, (Washington, —01C.: U.S. Government Printing Office, 1979), Table 6, p. 54. Consumer Price Index 1958-1978: Ibid. Table 8-49, p. 239. APPENDIX B Decomposition of Net Variances to Component Variances and Covariances 205 APPENDIX B Table 8-1. Annual Variance and Covariances in the [uploylent Rate Contributions of Personal Income 1 2m) 0(PI. Const) em. Hg) 0(PI. 19) am. mi 0(PI, m) o(P1. u) gun. I) 6(P1.%;) am. 9) 1961 39.397 -19.020 -1.054 -9.610 -12.096 0.104 2.664 -0.414 0.034 0.009 1962 39.275 -18.922 -1.067 -9.565 -12.084 0.106 2.660 o0.418 0.021 -0.0007 1963 39.112 -18 816 -1.080 -9.537 -12.062 0.110 2.653 -0.419 0.019 0.013 1964 39.028 -18.731 -1.096 -9.587 -12.057 0.112 2.650 -0.421 0.011 -0.004 1965 38.935 -18.646 -1.106 ~9.485 -12.050 0.117 2.647 -0.424 -0.0006 -0.002 1966 38.846 -18.563 -1 112 o9.478 -12.026 0.119 2.644 -0.426 ~0.013 -0.009 1967 38.755 -18.489 -1.124 -9.492 -11.991 0.122 2.640 —0.428 -0.007 0.004 1968 38.677 -18 407 -1.138 -9 505 -11.962 0.124 2.636 -0.428 -0.012 0.011 1969 38.524 .18.314 -1.138 -9.476 -11.911 0.126 2.630 o0.430 o0.006 -0.011 1970 38 369 -18.223 -1.l38 -9.470 -11.872 0.128 2.624 -0.431 0.017 0.002 1971 38.329 -18.176 o1.166 -9.519 -11.857 0.126 2.649 -0.431 0.020 0.002 1972 37.716 -17.819 -1.175 -9 403 -11 672 0.128 2.608 -0.425 0.008 o0.004 1973 37.214 .17.559 -l.154 ~9.279 -ll.520 0.125 2.558 -0.415 -0.004 0.003 1974 36.948 -17 471 -1.116 -9.215 -11.457 0.123 2.547 -0.412 0.022 0.00002 1975 36.900 -17.463 -1.104 -9.268 ~11.430 0.132 2.559 o0.410 0.047 -0.003 1976 36.571 .17.295 -1.107 -9.201 -ll.338 0.130 2.547 -0.400 0.032 -0.016 1977 36.082 -l7.034 -1.100 ~9.085 -11.199 0.129 2.515 -0.395 0.021 0.007 1978 35 737 -16.854 -1.085 -8.982 -ll.109 0.139 2.484 -0.391 0.016 0.009 206 APPENDIX B Table 8-2. Annual Variance and Covariances in the [Inlay-ent Rate Contributions of Transfer Pay-ents t 32119) oilP, Const) am. “9) am. PM «or. m) am. :41 am. i) am. 43%) 0111’. m am. 6) 1961 3.885 3.731 0.102 3.060 -0.056 -l.162 0.070 -0.013 -9.610 -0.003 1962 3.877 3.698 0.101 3.050 -0.057 -1.166 0.070 -0.008 ~9.565 -0.0004 1963 3.885 3.675 0.101 3.046 -0.058 -l.173 0.070 -0.007 -9.537 -0.003 1964 3.886 3.648 0.102 3.042 -0.059 -1.179 0.070 -0.004 -9.507 0.003 1965 3.895 3.622 0.101 3.039 -0.060 -1.186 0.071 0.0002 o9.485 0.001 1966 3.914 3.604 0.100 3.037 -0.062 -l.194 0.071 0.005 -9.478 0.003 1967 3.953 3.597 0.101 3.037 -0.063 -1.205 0.071 0.003 -9.492 -0.003 1968 3.983 3.587 0.100 3.039 -0.064 ~1.215 0.071 0.005 -9.505 -0.003 1969 3.991 3.564 0.100 3.027 -0.065 -1.221 0.072 0.002 o9.476 0.003 1970 4.026 3.550 0 101 3.027 -0.066 -1.230 0.072 .0.007 -9.470 ~0.001 1971 4.074 3.562 0.103 3.039 -0.065 -1.250 0.072 -0.008 -9.519 -0.002 1972 4.069 3.486 0.101 3.001 o0.066 -l.250 0.070 -0.003 o9.403 0.003 1973 4.056 3.423 0.097 2.955 -0.064 -l.246 0.067 0.002 -9.279 -0.001 1974 4.069 3.401 0.091 2.930 -0.063 -l.257 0.068 -0.009 -9.215 -0.001 1975 4.127 3.431 0.088 2.938 -0.064 o1.276 0.068 -0.019 o9.268 0.003 1976 4.121 3.397 0.084 2.915 -0.063 -1.281 0.065 -0.013 o9.201 0 004 1977 4.099 3.337 0.078 2.879 o0.063 -1.279 0.064 -0.009 ~9.085 -0.002 1978 4.074 3.289 0.073 2.846 -0.066 -1.278 0.063 -0.006 -8.982 -0.003 Table 8-3. Annual Variance and Covariances in the Constants 207 APPENDIX B t 02(Const) olConst. I91 a1Const. TP) o(Const. P891 oiConst. NU) 0(Const, £41 6(Const. 1) e(Const. :EEE) a1t0nst. PI) o(c6nst. 9) 1961 10 530 0 597 3.731 4.988 -0.023 o0.992 0.203 -0.014 -19.020 -0.004 1962 10 465 0.604 3.698 4.967 -0.024 -0.986 0.205 -0.008 -18.922 0.0009 1963 10.402 0.611 3.675 4.946 -0.025 o0.979 0.206 -0.008 ~18.816 -0.006 1964 10.341 0.620 3.648 4.927 -0.025 -0.972 0.207 -o.005 -18.731 0.0003 1965 10.282 0.625 3.622 4.908 -0.026 -0 966 0.209 0.0002 o18.646 -0.00005 1966 10.225 0 628 3.604 4.883 -0.027 ~0.960 0.210 0.005 -18.563 0.004 1967 10.174 0.634 3.597 4.856 -0.028 -0.954 0.211 0.003 -18.489 -o.ooo4 1968 10.116 0.643 3.587 4. 27 -0 028 -0 947 0.211 0.005 .18.407 -0.005 1969 10.063 0.643 3.564 4.796 -0.028 -0.941 0.213 0.002 -18.314 0.004 1970 10.012 0.642 3.550 4.771 -0.029 -0.935 0.214 -0.007 -18.223 -0.001 1971 9.975 0.658 3.563 4.756 -0.030 -0.944 0 214 -0.oos -18.176 0.0003 1972 9.778 0.664 3.486 4.644 -0.029 -0.918 0.211 -0.003 -17.819 0.0009 1973 9.646 0.653 3 423 4. 2 -0.028 o0.890 0.206 0.002 -17.559 ~0.001 1974 9.610 0.633 3.401 4.554 -0.027 -0.888 0.205 -o.oo9 -17.471 0.002 1975 9.606 0.627 3.431 4.552 -0.031 -0.895 0.206 -0.019 -17.463 -0.0005 1976 9.518 0.631 3.397 4.502 -0.031 -0.887 0.202 -0.013 -17.295 0.008 1977 9.379 0.628 3.337 4.425 -0.030 -0.870 0.200 -0.008 -17.034 -0.004 1978 9.283 0 620 3.289 4.375 -0.034 -0.852 0.198 -0.006 -l6.854 -0.004 APPENDIX 8 208 Table 8-4. Annual Variance and Covariances in Employment Rate Contributions of Property lnco-e t 0219110) 9(PRP, Const) c(PRP, 119) “one, TP) new, in) ate”, :4) um, i) 6(949, gag) 0(PRP, P1) 6(PRP. Q) 1961 4.694 4.988 0.310 3.060 -0.075 -1.009 0.135 -0.010 -12.096 -0.003 1962 4.706 4.967 0.313 3.050 -0.076 -1.011 0.136 -0.006 42.004 0.00007 1963 4.716 4.946 0.318 3.046 -0.078 -l.012 0.136 o0.006 -12.062 ~0.004 1964 4.728 4.927 0.323 3.042 -0.080 -1.015 0.137 -0.003 -12.057 0.002 1965 4.741 4.908 0.326 3.039 -0.(B? -l.017 0.138 0.0002 -12.050 0.001 1966 4.742 4.883 0.327 3.037 -0.CB3 -1.018 0.138 0.004 ~12.026 0.003 1967 4.735 4.856 0.330 3.037 -0.085 -1.017 0.138 0.002 -11.991 -0.002 1968 4.729 4.827 0.334 3.039 -0.086 -1.017 0.138 0.003 -11.962 -0.004 1969 4.715 4.796 0.333 3 027 -0.087 -l.015 0.138 0.002 -11.911 0.004 1970 4.711 4.771 0.333 3.027 -0.088 1.015 0.138 -0.005 -11.872 -0.0004 1971 4.710 4.756 0.341 3.039 -0.087 -1.025 0.137 -0.006 -11.857 -0.002 1972 4.664 4.644 0.343 3.001 -0.(B9 -1.015 0.136 -0.002 -1l.672 0.0009 1973 4.633 4.562 0.337 2.955 -0.089 -1.002 0.134 0.001 -11.520 o0.0007 1974 4.619 4.554 0.327 2.930 -0.090 -0.998 0.132 -0.007 -11.457 -0.002 1975 4.610 4.552 0.324 2.938 -0.094 -1.002 0.131 -0.014 -11.430 0.002 1976 4.591 4.502 0.325 2.915 -0.094 -l.002 0.127 o0.009 o11.338 0.005 1977 4.560 4.425 0.323 2.879 -0.093 -0.995 0.125 -0.006 -11 199 ~0.002 1978 4 548 4.375 0.319 2.846 -0.097 -0.987 0.125 -0.005 -11.109 o0.004 209 APPENDIX 8 Table 8-5. Annual Variance and Covariances in the Employment Rate Contributions of the Wage Rates t 02(89) 0(W9.Const1 nilg. 1P) 0(89,PRP) “149, N) n(lg,£A) 0(149. T) “149.5%? o(lg.PI) “09.9) 1961 0.062 0.597 0.102 0.310 0.008 0.038 o0.014 0.00009 -1.054 -0.0002 1962 0.064 0 604 0.101 0.313 0.008 -0.037 0.014 0.00006 -1.067 0.00007 1963 0.066 0.611 0.101 0.318 0.008 -0.037 0.014 0.00006 -1.078 0.0004 1964 0.068 0.620 0.102 0.323 0.008 -0.038 0.015 0.00004 -1.096 0.00004 1965 0.070 0 625 0.101 0.326 0.008 -0.038 0 015 -0.00002 -1.106 0.00009 1966 0.071 0.628 0.100 0.327 0.008 -0.037 0.015 o0.00005 -1.111 0.0003 1967 0.073 0.634 0.101 0.330 0.008 -C.037 0.015 -0.00003 -1.123 --0.00001 1968 0.075 0.643 0.100 0.333 0.008 -0.037 0.016 ~0.00005 -1.137 -0.0003 1969 0.075 0.643 0.100 0.333 0.008 -0.037 0.016 -0.00002 -1.138 0.0001 1970 0.075 0.642 0.101 0.333 0.008 0.037 0.016 0.00007 -1.138 0.00004 1971 0.078 0.658 0.103 0.341 0.008 -0 039 0.016 0.00008 o1.l65 0.0002 1972 0.082 0.664 0.101 0.343 0.009 -0.039 0.017 0.00003 -I.175 o0.0003 1973 0.081 0.653 0.097 0.337 0.009 -0.037 0 016 -0.00002 -1.154 -0.00003 1974 0.076 0.633 0.091 0.327 0.009 -0.035 0 016 0.0001 -1.116 0.0002 1975 0.076 0.627 0.088 0.324 0.008 -0.034 0.016 0.0002 -1.104 -0.0001 1976 0.078 0 631 0.084 0.325 0.008 ~0.033 0.016 0.0002 -1.107 0.0006 1977 0.080 0.628 0.078 0.323 0.008 -0.032 0.016 0.0001 -1.100 -0.0002 1978 0 080 0.620 0.073 0.319 0.008 -0.03O 0.015 0 0001 -1.100 -0.0002 210 APPENDIX 8 Table 8-6. Annual Variance and Covariances in the Employ-eat Rate Contributions of Educational Attainment t 92(24) 0(EA, Cons!) 0(EA. lg) 6(EA. TP) o(EA, PRP) 6(EA, 4H) o(EA. T) o(EA, $1 o(EA, PI) o(EA. 1}) 1961 0.563 -0.992 0.038 -1.162 -1009 -0.012 -0.042 0.003 2.664 0.0009 1962 0.570 -0.986 -0.037 -1.166 -1.011 0.013 -0.043 0.002 2.660 -0.0002 1963 0.578 0.979 -0.037 -1.173 -1.012 0.013 o0.043 0.002 2.653 0.0007 1964 0.585 -O.972 -0.038 o1.179 -1.015 0.013 -0.044 0.001 2.650 -0.w06 1965 0.592 -0.966 -0.038 -1.186 -l.017 0.014 -0.045 -0.0m 2.647 -0.00002 1966 0.599 -0.960 -0.037 -1.l94 o1.018 0.014 o0.045 -0.001 2.644 .0001 1967 0.606 -0.954 -0.037 o1.205 -1.017 0.014 -0.046 -0.W7 2.640 0.” 1968 0.612 -O.947 -0.037 -1.215 -1.017 0.015 -0.046 -0.001 2.636 0.0000 1969 0.619 -0.941 -0.037 -1.221 -1.015 0.015 -0.047 -0.M6 2.630 -0.001 1970 0.625 -0.935 -0.037 -1.230 -1.015 0.015 -0.047 0.002 2.624 0M7 1971 0.638 -0.944 -0.039 -1.250 -1.025 0.015 -0.047 0.002 2.649 0.0005 1972 0.643 -O.918 -0.039 -1.250 -l.015 0.016 -0.047 0.0001 2.608 -o.001 1973 0.648 -O.89O -0.037 -1.246 4.002 0.015 -0.046 -0.0004 2.558 0.0007 1974 0.659 -O.888 -0.035 ol.257 -0.998 0.015 o0.047 0.002 2.547 0.“ 1975 0.670 -O.895 -0.034 -1.276 -1.002 0.016 -0.048 0.005 2.559 00009 1976 0.680 -0.887 -0.033 -1.281 4.002 0.016 -0.047 0.003 2.547 -0001 1977 0.684 -O.87O ~0.032 o1.279 --0.995 0.016 -0.047 0.002 2.515 0.0007 1978 0.688 -O.852 -0.030 -1.278 ~0.987 0.017 -0.046 0.002 2.484 0.0009 211 APPENDIX 8 Table 8-7. Annual Variance and Covariances in the Employ-ent Rate Contributions of the Teenage Labor Force t 3(1) on, Const) «1.99) on. m 011."!7’) 0(1. nu) 0(1, :4) 0(7. :3; 0(T, 01) 0(1. 1) 1961 0 032 0.202 0.014 0.070 0.135 0.003 o0.042 -0.0004 -O.414 -0.0001 1962 0.032 0.205 0.014 0.070 0.136 0.003 -0.043 -0.0002 -0.418 0.0001 1963 0.033 0.206 0.014 0.070 0.136 0.003 -0.043 -0.0002 -0.419 -0.0001 1964 0.033 0.207 0.015 0.070 0.137 0 003 -0.044 -0.0001 «0.421 o0.00008 1965 0.034 0.209 0.015 0.071 0.138 0.003 -0.045 0.000007 -0.424 -0.0001 1966 0.034 0.210 0.015 0.071 0.138 0.003 -0.045 0.0001 -0.426 0.0001 1967 0.034 0.211 0 015 0.071 0.138 0.003 -0.046 0.00008 -0.428 0.00009 1968 0.035 0.211 0.016 0.071 0.138 0.003 -0.046 0.0001 o0.428 0.00009 1969 0.035 0.213 0.016 0.072 0.138 0.003 -0.047 0.00007 o0.450 0.0001 1970 0.036 0.214 0.016 0.072 0.138 0.003 -0.047 -0.0002 -0.431 o0.00007 1971 0.035 0.214 0 016 0.072 0.137 0.003 ~0.047 o0.0003 o0.431 -0.00008 1972 0.035 O 211 0.017 0.070 O 136 0.003 -0.047 -0.00009 -0.425 0.0002 1973 0 035 0 206 0.016 0.067 0.134 0.003 -0.046 0.00005 -0 415 -0.0002 1974 0.035 0.205 0.016 0.068 0.132 0.003 -0.047 -0.0003 -0.412 -0.00003 1975 0.035 0.2 0.016 0.068 0.131 0.003 -0.048 0.0006 -0.410 -0.0003 1976 0.034 0.202 0 016 0.065 0.127 0.003 -0.047 -0.0004 -O.400 0.0004 1977 0.034 0.200 0 016 0.064 0.125 0.003 ~0.047 -0.0003 0.395 -0.0002 1978 0.033 0.198 0.016 0.063 0.125 0.003 o0.046 .o,oooz 0.391 -0.00007 212 APPENDIX 8 Table 8-8. Annual Variance and Covariances in the EnolorIent Rate Contributions of the Non-White Labor Farce t 92““) 0(74'. COOS!) 0"“. H9) o(~. TV) (Hm, PR9) 0(NU. [I1 (Km, T) 0(W, %) ed”, 91) (WW, V) 1961 0.026 -0.023 0.008 -0.056 -0.075 0.012 0.003 0.0001 0.104 0.000005 1962 0.026 -0.024 0.008 -0.057 -0.076 0.013 0.003 0.00009 0.106 0.00006 1963 0.027 -0.025 0.008 -0.058 -0.078 0.013 0.003 0.111009 0.110 0.000003 1964 0.027 -0.025 0.008 -0.059 -0000 0.013 0.003 D.WOOS 0.112 0111003 1965 0.027 -0.026 0.008 -0.060 -0.082 0.014 0.003 -0.000003 0.117 0.00004 1°66 0.028 -0.027 0.008 -0.062 0.1113 0.014 0.003 -0.00006 0.119 0.00004 1967 0.028 -0.028 0.008 -0.063 -0.085 0.014 0.003 -0.00004 0.122 0.00005 1968 0.028 -0.o28 0.008 o0.064 -0.CB6 0.015 0.003 -0.00006 0.124 0.00003 1969 0.028 -0.028 0.008 -0.065 -0.087 0.015 0.003 00000: 0.126 0.0001 1970 0.028 -0.029 0.008 -0.066 -0.088 0.015 0.003 0.0001 0.128 -0.0001 1971 0.028 -0,030 0.008 -0.065 -0.007 0.015 0.003 0.0001 0.126 0411007 1972 0.028 -0.029 0.009 -0.066 .0089 0.016 0.003 0.00004 0.128 -0.00007 1973 0.029 -0.028 0.009 -0.064 -0.089 0.015 0.003 -0.00002 0.125 0.00001 1974 0.030 -0.027 0.009 -0.063 -0.090 0.015 0.003 0.0001 0.123 0.00009 1975 0.029 -0.031 0.008 -0.m4 -0.094 0.016 0.003 0.0003 0.132 0.00003 1976 0.029 -0.031 0.008 -0.063 -0.094 0.016 0.003 00102 0.130 0000004 1977 0 029 -0.030 0.009 -0.063 -0.093 0.016 0.003 0.0001 0.129 -0.00009 1978 0.030 -0.034 0.008 -0.066 -0.097 0.017 0.003 0.0001 0.139 0.00005 231 51 APPENDIX B Table 8-9. Annual Variance and Covariances in the Employment Rate Contributions of AGNP/PGNP ' 312%,?) (11%;. Const) c1933; we) «31%;. W) 01931;. PM «93%;. ~10 01%;. m “$.11 49.5. m 1.1%. J) 1961 0.00009 -0.014 0.00009 -0.013 -0.010 01001 0.003 -0.0004 0.034 0.00001 1962 0.00003 -0.008 0.00006 -0.008 .0006 0.00009 0.002 -0.0(IJ2 0.021 D.WZ 1963 0.00003 -0.008 0.00006 -0.007 -0.006 0.00009 0.00? -0.0002 0.019 mm 1964 0.00001 -0.005 0.00004 -0.004 -0.003 0.00005 0.001 .0.0001 0.011 o0.000003 1965 0.00000003 0.0002 -0.000002 0.0002 0.11302 -0.000003 -0.00006 0.000007 -0.0006 0.00000002 1966 0.00001 0.005 -0.00005 0.005 0.004 0.00006 -0.001 0.0(I11 o0.013 D.WOOOZ 1967 0.000004 0.003 -0.00003 0.003 0.002 -0.00004 -0.0007 0.00000 -0.007 -0.w00006 1968 0.00001 0.005 -0.00005 0.005 0.003 -O.CA')006 -0.001 ~0.0001 -0.012 -0.000005 1969 0.0(A1003 0.002 ~0.00002 0.002 0.002 -0.(X)OO3 -O.m06 0.00007 -0.006 0.00000? 1970 0.00002 -0.007 0.00007 -0.007 -0.005 0.0001 0.002 -o.oooz 0.017 -0.000002 1971 0.00003 -0.008 0.00008 -0.008 -0.006 0.0001 0.002 -0.0003 0.020 0.000005 1972 0.000005 -0.003 0.00003 -0.003 -0.002 0117004 0.0007 -0.0(X709 D.WO 0000004 1973 0.000001 0.002 -0.00002 0.00? 0.001 -0.(A1002 -0.0004 0.00005 -0.004 -0.000001 1974 0.00004 -0.009 0.0001 -0.009 -0.007 0.0001 0.002 -0.0003 0.022 0.00W06 1975 0-0002 -0.019 0.0002 -0.019 -0.014 0 0003 D.WS o0.0(X)6 0.047 0.000007 1976 0.00009 -0.013 0.0002 -0.013 -0.009 0.0002 0.003 -0.0004 0.032 -0.00002 1977 0.00004 -0.008 0.0001 -0.009 -0.006 0.0001 0.002 -0.0003 0.021 0.000007 1978 0.0000? -0.006 0.0001 -0.006 -0.005 0.0001 0.002 -0.0002 0.016 0.000003 214 IPPENDI X B 1.01: 0-10. Rnnual Variance and Covariances 1n the flesidun Terms z 92m 0(11. Const) 016.119) 01;.19) 0(17, pm on}. nu) 0(6, m on. 1) on}. 933;) on}, m 1961 0.00001 -0.00d -0.0002 -0.003 .0003 0.000005 0.0009 -0.0001 0.00001 0.009 1962 0.000005 0.00007 -0.0007 0.0004 0.00007 0.00006 -0.0002 0.0001 0.000002 -0.0007 1963 0.00001 -0.006 -0.0004 -0.003 -0.004 0.000003 0.0007 -0.0001 0.000004 0.013 1964 0.000008 0.0003 -0.0000£ o0.003 0.002 -0.00003 -0.0006 o0.00008 -0.000003 -0.004 1965 0.000008 -0.00005 0.00009 0.001 0.001 -0.00004 -0.00002 0.0001 0.00000002 -0.002 1966 0.000007 0.00! 0.0003 0.003 0.003 0.00006 -0.001 0.0001 0.000002 -0.009 1967 0.000009 -0.0004 -0.00001 -0.003 -0.002 0.00005 0.0006 0.00009 o0.0®00% 0.004 1968 0.000008 -0.005 -0.0003 -0.003 -0.004 0.00003 0.0008 -0.00009 ~0.000005 0.011 1969 0.000009 0.00! 0.0002 0.003 0.004 -0.0001 -0.001 0.0001 0.000002 -0.011 1970 0.00001 -0.001 -0.00004 -0.001 -0.0004 -0.0001 0.0007 .o_ooom ~0.000002 0.002 1971 0.00001 0.0003 0.0002 ~0.002 ~0.002 0.00007 0.0005 -0.00006 0.000005 0.002 1972 0.00001 0.0009 -0.0003 0.003 0.0009 -0.00007 -0.001 0.0002 -0.000004 -0.004 1973 0.00001 -0.001 -0.000003 -0.001 -0.0007 0.00001 0.0007 -0.0002 -0.000001 0.003 1974 0.00001 0.002 0.0002 -0.001 -0.002 0.00009 0.0008 -0.00003 0.000006 0.00002 1975 0.00001 -0.0005 -0.0001 0.003 0.002 0.00003 -0.0009 -0.00003 -0.000007 -0.003 1976 0.00002 0.008 0.0006 0.00! 0.005 -0.00000£ -0.001 0.000! o0.00002 -0.016 1977 0.000007 -0.004 -0.0002 -0002 -0.002 -0.00009 0.0007 -0.0002 0.000007 0.007 1978 0.00001 -0.004 -0.0002 -0.003 -0.00l 0.00005 0.0009 -0.00007 0.000003 0.009 APPENDIX C Tota1 U.S. Transfer Payments: 1961-1978 Tota1 U.S. Transfer Payments (mi1ions of do11ars): 215 APPENDIX C 1961-1978 Year Transfer Payments % Change in Transfer Payments 1961 36626 ---- 1962 37274 1.77 1963 39082 4.85 1964 40291 3.09 1965 42766 6.14 1966 45954 7.45 1967 52595 14.45 1968 57505 9.34 1969 60576 5.34 1970 68685 13.39 1971 77585 12.96 1972 83080 7.08 1973 89321 7.51 1974 95346 6.75 1975 110525 15.92 1976 113690 2.86 1977 114603 0.80 1978 114599 -0.003 Source: Unpub1ished data provided by Bureau of Economic Ana1ysis (U.S. Department of Commerce). APPENDIX 0 Percentage of State Transfer Payments Paid as Unemp1oyment Insurance Benefits: 1969 and 1975 216 Tab1e D-1. % of State Transfer Payments Paid as Unemp1oyment Insurance Benefits in 1969 Z of Tran. Pay 1 of Tran. Pay Rank State Paid as U18 Rank State Paid as UIB 1 Virginia 0.7 26 Montana 2.4 2 F1orida 0.8 27 Mary1and 2.5 3 Texas 0.986 28 I11inois 2.575 4 CoIorado 0.995 29 Missouri 2.590 5 New Hampshire 1.19 30 Pennsy1vania 2.8 6 Georgia 1.25 31 Tennessee 2.9 7 0k1ahoma 1.32 32 Vermont 3.01575 8 Nebraska 1.34 33 Wisconsin 3.01583 9 Arizona 1.38 34 Idaho 3.4 10 Mississippi 1.40 35 Maine 3.457 11 Hyoming 1.835 36 Hawaii 3.511 12 Indiana 1.837 37 Utah 3.6 13 Ohio 1.893 38 Oregon 3.8 14 Iowa 1.901 39 New York 4.092 15 South Dakota 1.921 40 Louisiana 4.098 16 Nest Virginia 1.947 41 Washington 4.27 17 North Caro1ina 1.955 42 Michigan 4.30 18 Minnesota 1.989 43 De1aware 4.32 19 A1abama 2.02 44 Massachusetts 4.5 20 New Mexico 2.05 45 Rhode Is1and 5.0 21 Arkansas 2.1078 46 Ca1ifornia 5. 22 Kansas 2.1082 47 Nevada 5.5 23 North Dakota 2.109 48 New Jersey 6.706 24 Kentucky 2.2 49 Connecticut 6.717 25 South CaroIina 2.3 50 A1aska 11.8 Source: U.S. Department of Labor. Emp1oyment, and Training Administration, Unemp1oyment Insurance Statistics, March 1970, Tab1e 6; and unpubTished Hata proViHed by the Bureau of Economic Ana1ysis (U.S. Department of Commerce). 217 Tab1e D-2. % of State Transfer Payments Paid as Unemp1oyment Insurance Benefits in 1975 x of Tran. Pay 1 of Tran. Pay Rank State Paid as 018 Rank State Paid as 018 1 South Dakota 2.0 26 Washington 6.0 2 Texas 2.2 27 Minnesota 6.1 3 North Dakota 2.6 28 Georgia 6.2 4 Wyoming 2.7 29 Tennessee 6.3 5 Oklahoma 3.0 30 Ca1ifornia 6.5 6 New Mexico 3.1 31 Hawaii 6.7 7 Mississippi 3.4 32 Indiana 6.8 8 Kansas 3.5 33 Oregon 6.857 9 West Virginia 3.56 34 New York 6.876 10 Virginia 3.61 35 New Hampshire 7.0 11 F1orida 3.72 36 Vermont 7.3 12 Co1orado 3.75 37 I11inois 7.4 13 Louisiana 4.1 38 Ohio 7.5 14 Nebraska 4.36 39 Wisconsin 7.7 15 Montana 4.44 40 South Caro1ina 7.9 16 Iowa 4.5 41 North CaroIina 8.1 17 Idaho 4.6 42 Massachusetts 8.2 18 Kentucky 5.2 43 Pennsy1vania 8.8 19 Arkansas 5.279 44 Rhode Is1and 8.9 20 Utah 5.290 45 Nevada 9.5 21 A1abama 5.299 46 New Jersey 9.999 22 Maine 5.6 47 A1aska 10.003 23 Mary1and 5.7 48 Michigan 10.69 24 Missouri 5.813 49 De1aware 10.71 25 Arizona 5.847 50 Connecticut 11.5 Source: U.S. Department of Labor, Emp1oyment. and Training Administration, Unemp1gyment Insurance Statistics, Ju1y/August 1976, Tab1e 6: and unpub1ished data proviaed by the Bureau of Economic AnaIysis (U.S. Department of Comerce). APPENDIX E THE MANN-WHITNEY U TEST 218 APPENDIX E THE MANN-WHITNEY U TEST Chapter VI focuses attention on the rank distribution of state unemp1oyment rates. Section 6.2 asks how much individua1 regions differ in terms of average state unemp1oyment rate ranks. One's initia1 reaction might be to test the nu11 hypothesis by app1ying a t-test for equa1ity of means. But the t-test is inappropriate in this situation because one neither has enough rank observations to invoke the Centra1 Limit Theorem, nor can one be certain that the sma11 samp1e distribution of the ranks is norma1. Thus Chapter VI emp10ys the Mann-Whitney U statistic, a non-parametric or distribution-free procedure, to test the nu11 hypothesis. This appendix provides a se1f-contained description of the Mann-Whitney test to supp1ement the materia1 in Chapter VI. The Mann-Whitney test is one of the most powerfu1 of the avai1ab1e nonparametric tests (see Siege1, p. 116). It attains approximate1y 95% of the power of the t-test when the re1evant observations actua11y are distributed norma11y. Since the unemp1oyment rate ranks are most 1ike1y not distributed norma11y (i.e., by state and across years), it is 1ike1y that the Mann-Whitney test is more powerfu1 than the t-test. Un1ike the t-test, which compares the means of two distributions, the Mann-Whitney statistic tests whether or not two samp1es come from identica1 popu1ations. In order to i11ustrate this concept, suppose one has two samp1es of observations respectiver named A and B. Let there be nA observations in samp1e A, and nB observations in samp1e 8. 219 The Mann-Whitney test statistic is obtained by ordering a11 nA + nB observations according to their magnitude and then taking the sum of the ranks of either one of the sub-samp1es (the choice of sub-samp1e is arbitrary). For examp1e, if A is chosen as the samp1e of interest, then the re1evant Mann-Whitney U statistic is: n (n + 1) _ A A (E.1) UA - "A ° nB + 2 " R A where RA is the sum of the ranks assigned to the observations of A in the poo1ed, ordered samp1e. Very 1arge or very sma11 va1ues of U imp1y a separation of the ordered A and B observations and therefore provide evidence indicating a difference between the popu1ation distributions of A and B. If UA is 1arge, then RA is necessari1y sma11 imp1ying that va1ues of A are found predominantIy in the Iower ha1f of the pooIed, ordered samp1e. Converse1y, if UA is sma11, va1ues of A are re1ative1y 1arge. The probabi1ities required for ca1cu1ating the significance 1eve1, a, for samp1es where either nA or nB is 1ess than or equa1 to eight can be found by consu1ting a mathematica1 statistics book (for examp1e, see Siege1 or Mendenha11 and Scheaffer). In order to i11ustrate the foregoing an examp1e from Tab1e 6-3 is provided. As in Tab1e 6-3, suppose one wishes to test whether or not average state ranks--measured over the 1961-1978 period--differ significant1y between two regions. Let the two regions under considera- tion be the West North Centra1 (WNC) and the East South Centra1 (ESC) regions. Then, from Tab1e 6-1: 220 ESC: 38.56 (AL) 23.17 (KY) 31.83 (MS) 35.39 (TN) NNC: 2.67 (IA) 7.94 (KS) 9.44 (MN) 12.06 (NO) 1.50 (NE) 19.61 (ND) 3.11 (50) where state abbreviations are in parentheses with the mean ranks to which they correspond. The East South Centra1 region has four states and therefore four average ranks, whi1e the West North Centra1 region has seven states and therefore seven average ranks. Arranging these va1ues joint1y and in increasing order of magnitude, one obtains: 1.50 2.67 3.11 7.94 9.44 12.06 19.61 23.17 31.83 35.39 §§;§§_ where the average rank va1ues of the East South Centra1 region are under1ined. Assigning the observations in the poo1ed ordered samp1e the ranks 1, 2, . . ., 11, the va10es of the East South Centra1 region occupy ranks 8, 9, 10, and 11. Therefore, the U statistic for the East South Centra1 region is: 4-5 (4 7) + (-§-) - (8 + 9 + 10 + 11) 38 - 38 = O. U ESC Since this is the sma11 samp1e case, probabi1ity tab1es corresponding to the Mann-Whitney test must be consu1ted. One finds that: P {0E5C = 0 1 nESC = 4, "ch = 7} = .0030 The probabi1ity that one wou1d obtain a va1ue of u equa1 to zero when both samp1es are drawn from the same popu1ation, therefore, is 221 1ess than one percent. One must conc1ude that the two samp1es are drawn from different popuIations. Further, since the U statistic corresponding to the East South Centra1 region is so sma11, the U statistic corresponding to the West North Centra1 region must be quite 1arge. Unemp1oyment rates of West North Centra1 states, therefore, are significant1y 1ess than those of the East South Centra1 states during the 1961-1978 period. BIBLIOGRAPHY 222 BIBLIOGRAPHY Archiba1d, G.C. "Regiona1 Mu1tip1ier Effects in the U.K." Oxford Economic Papers, 19, No. 1, (1967), pp. 22-45. . "The Phi11ips Curve and the Distribution of Unemp1oyment." American Economic Review, 59, No. 2, (1969), pp. 124-134. Ashenfe1ter, Or1ey and James Heckman. "The Estimation of Income and Substitution Effects in a Mode1 of Fami1y Labor Supp1y." Econometrica, 42, No. 1, (1974), pp. 73-85. Bai1y, Martin. "On the Theory of Layoffs and Unemp10yment." Econometrica, 45, No. 5, (1977), pp. 1043-1063. Bowen, Hi11iam and Thomas Finegan. The Economics of Labor Force Participa- tion. Princeton: Princeton University Press, 1969. Brech1ing, Frank. "Trends and Cyc1es in British Regiona1 Unemp1oyment." Oxford Economic Papers, 19, No. 1, (1967), pp. 1-21. . "Wage Inf1ation and the Structure of Regiona1 Unemp1oyment." Journa1 of Money, Credit, and Banking, 5, No. 1, Part 2, (1973), pp. 355-384. Browne, Lynn. "Regiona1 Unemp1oyment Rates--Why Are They so Different?" New Eng1and Economic Review, No. 4, (1978), pp. 5-26. Cho, Dong and Gera1d McDouga11. "Regiona1 Cyc1ica1 Patterns and Structure, 1954-1975." Economic Geography, 54, No. 1, (1978), pp. 66-74. C1ark, Kim and Richard Freeman. "Time Series Mode1s of the E1asticity of Demand for Labor in Manufacturing." Harvard Discussion Papers, No. 575, Harvard Institute of Economic Research, 1977. Doeringer, Peter and Michae1 Piore. Interna1 Labor Markets and Manpower Ana1ysis. Lexington: O.C. Heath and Co., 1971. Eckstein, Otto. "Aggregate Demand and the Current Unemp1oyment Prob1em." In Unem31oyment and the American Economy. Ed. Arthur Ross. New York: John Ni1ey and Sons, Inc., 1964. Fearn, Robert. "Cyc1ica1, Seasona1, and Structura1 Factors in Area Unemp1oyment Rates." Industria1 and Labor Re1ations Review, 28, No. 3, (1975), pp. 424-431. 223 Fe1dstein, Martin. "Temporary Layoffs in the Theory of Unemp1oyment." Journa1 of Po1itica1 Economy, 84, No. 5, (1976), pp. 937-959. F1eisher, Be1ton and George Rhodes. "Individua1 Labor Force Decisions and Unemp1oyment in Loca1 Labor Markets." Review of Economics and Statistics, 61, No. 4, (1979), pp. 629-634. Ga11away, Lowe11. "Labor Mobi1ity, Resource A110cation, and Structura1 Unemp10yment." American Economic Review, 53, No. 4, (1963), pp. 694-716. Ge11ner, Christopher. "Regiona1 Differences in Emp10yment and Unemp1oyment, 1957-72." Monthly Labor Review, 97, No. 3, (1974), pp. 15-24. Go1dberger, Arthur. Econometric Theory. New York: John Wi1ey and Sons, 1964. Go1dstein, H. State and Loca1 Labor Force Statistics. Washington, O.C.: Nationa1 Counci1 on Emp10yment and Unemp1oyment, 1978. Ha11, Robert. "Turnover in the Labor Force." Brookings Papers on Economic Activity, No. 3, (1972), pp. 709-757. . "The Rigidity of Wages and the Persistence of Unemp1oyment." Brookings Papers on Economic Activity, No. 2, (1975), pp. 301-331. Hamermesh, Danie1 and James Grant. "Econometric Studies of Labor- Labor Substitution and Their Imp1ications for PoIicy." Ihg_ Journa1 of Human Resources, 14, No. 4, (1979), pp. 518-542. Hamermesh, Danie1. "Income Maintenance and F011 Emp10yment." In High Emp10yment: Prob1ems and So1utions. Eds.Pau1 Burgess and Jerry Kingston. Phoenix: U.S. Department of Labor, Emp10yment and Training Administration, 1978, pp. 95-107. . "Transfers, Taxes, and the NAIRU." NBER Working Paper, No. 548, Nationa1 Bureau of Economic Research, September 1980. Hicks, John. Theory of Wages. London: MacMi11an Pub1ishing, 1964. Hyc1ak, Thomas and Gera1d Lynch. "An EmpiricaI Ana1ysis of State Unemp1oyment Rates in the 19705." Journa1 of Regiona1 Science, 20, No. 3, 1980. PP. 377-386. Ka1achek, Edward. Labor Markets and Unemp10yment. Be1mont, CA: Wadsworth, 1973. Ki11ingsworth, Char1es. "Automation, Jobs, and Manpower." In Exp1oring the Manpower Revo1ution. U.S. Senate, Committee on Labor and Pub1ic We1fare, Subcommittee on Emp10yment and Manpower, 88th Congress, 2nd Session, Washington, O.C.: U.S. Government Printing Office, 1964. 224 Kmenta, Jan. E1ements of Econometrics. New York: MacMi11an, 1971. Lester, Richard. "Shortcomings of Margina1 Ana1ysis for Wage Emp10yment Prob1ems." American Economic Review, 36, No. 1, (1946), pp. 63-80. Lipsey, Richard. "The Re1ation between Unemp1oyment and the Rate of Change of Money Wage Rates in the United Kingdom, 1862-1957: A Further Ana1ysis." Economica, 27, No. 105, (1960), pp. 1-31. Mach1up, Fritz. "Margina1 Ana1ysis and Empirica1 Research." American Economic Review, 36, No. 4, (1946), pp. 519-554. Ma1invaud, Edmond. The Theory of Unemp1oyment Reconsidered. Oxford: Basi1 B1ackwe11 and Mott Ltd, 1977. Mendenha11, Wi11iam and Richard L. Scheaffer. MathematicaI Statistics with App1ications. North Scituate, MA: Duxbury Press, 1973. Metca1f, David. "Urban Unemp1oyment in Eng1and." Economic Journa1, 85, No. 339, (1975), pp. 578-589. Mincer, Jacob. "Labor Force Participation and Unemp1oyment: A Review of Recent Evidence." In Protperity and Unemp10yment. Eds. R.A. Gordon and M.S. Gordon. New York: John Wi1ey and Sons, 1966. pp. 73-112. "Labor Force Participation of Married Women." In Aspects of Labor Economics. Ed. Gregg Lewis, Universities-Nationa1 Bureau Conference Series, No. 14, Princeton: Arno Press, 1962, pp. 63-97. Munne11, A1icia. The Future of Socia1 Security. Washington, O.C.: Brookings Institutibn, 1977. Nadiri, M-1. and Sherwin Rosen. A Disegui1ibrium Mode1 of the Demand for Factors of Production. New York: Nationa1 Bureau of Economic Research, 1967. Office of the Federa1 Register. Code of Federa1 Regu1ationst_#41 Pub1ic Contracts and Property Management. Washington, O.C.: Nationa1 Archives and Records Service, GeneraI Services Administration, 1978. Parsons, Dona1d. "RaciaI Trends in Ma1e Labor Force Participation." American Economic Review, 70, No. 5, (1980), pp. 911-920. Perry, George. "Changing Labor Markets and Inf1ation." Brookipgs Papers on Economic Activity, No. 3, (1970), pp. 411-441. . "Inf1ation in Theory and Practice." Brookings Papers on Economic Activity, No. 1, (1980), pp. 207-241. 225 . "Unemp1oyment F1ows in the U.S. Labor Market." Brookings Papers on Economic Activity, No. 2, (1972), pp. 245-278. Pindyck, Robert and Danie1 Rubinfie1d. Econometric Mode1s and Economic Forecasts. New York: McGraw-Hi11 Book Co., 1976. Piore, Michae1. "Unemp1oyment and Inf1ation: An A1ternative View." In Unemp10yment and Inf1ation: Institutiona1ist and Structura1ist Views. Ed. Michae1 Piore. White P1ains, NY: M.E. Sharpe, Inc., 1979. Rees, A1bert. The Economics of Work and Pay, 2nd. ed. New York: Harper and Row, 1979. Rosen, Sherwin. "On the Interindustry Wage and Hours Structure." Journa1 of Po1itica1 Economy, 77, No. 2, (1969), pp. 249-273. Siege1, Sidney. Nonparametric Statistics for the BehavioraI Sciences. New York: McGraw-Hi11, 1956. So1ow, Robert. The Nature and Sources of Unemp1oyment in the United States. Stockh01m: A1mqvist and WiCkseIT: 1964. Sum, Andrew and Thomas Rush. "The Geographic Structure of Unemp1oyment Rates." Monthly Labor Review, 98, No. 3, (1975), pp. 3-9. Thei1, Henri. PrincipIes of Econometrics. New York: John Wi1ey and Sons, 1971. Thurow, Lester. "A Job Competition Mode1." In Unemp1oyment and Inf1ation: Institutiona1ist and Structura1ist Views. Ed. Michae1 Piore. White P1ains, NY: M.E. Sharpe, 1979. U.S. Bureau of the Census. U.S. Census of PopuIation: 1950, V01. II. Characteristics of the Popu1ation, Parts 2-50. Washington, O.C.: U.S. Government Printing Office,71952. . U.S. Census of Popu1ation: 1960, V01. 1. Characteristics of the Popu1ation, Parts 2-52. Washington, O.C.: U.S. Government Printing Office, 1963. . Census of Popu1ation: 1970, V01. 1. Characteristics of the PppuIation, Parts 2-52. Washington, O.C.: U.S. Government Printing Office, 1973. U.S. Counci1 of Economic Advisers. Economic Report of the President. Washington, O.C.: U.S. Government Printing Office, 1979. U.S. Department of Commerce. Loca1 Area PersonaI Income, 1973-1978, V01. 1. Washington, O.C.: U.S. Government Printing Office, 1980. U.S. Department of Commerce. Survey of Current Business, V01. 59, No. 8, Part II. Washington, O.C.: U.S. Government Printing Office, 1979. 226 U.S. Department of Commerce, Bureau of the Census. Current PopuIation Reports, Series P-60, Nos. 110-113. Washington, O.C.: U.S. Government Printing Office, 1978. . Current P0pu1ation Reports, Popu1ation Estimates and Projections, Series P-25, No. 465. Washington, O.C.: U.S. Government Printing Office, 1971. Statistica1 Abstract of the United States, 1971. Washington, O.C.: U.S. Government Printing Office, 1971. U.S. Department of Labor. Area Trends in Emp10yment and UnempIQyment, Apgust-September 1975. Washington, O.C.: U.S. Government Printing Office,1975. Emp10yment and Training Repprt of the President. Washington, O.C.: U.S. Government Printing Office, 1977, 1978, and 1979. . Manpower Report of the President. Washington, O.C.: U.S. Government Printing Office, 1970 and 1974. . Unemp1pyment Insurance Statistics. Washington, O.C.: U.S. Government Printing Office, March 1970 and Ju1y/August 1976. U.S. Department of Labor, Bureau of Labor Statistics. Emplpyment and Earnings, States and Areas, 1939-1978. Bu11etin 1370-T3. Washington, O.C.: U.S. Government Printing Office, 1979. . Geographic Profi1e of Emp10yment and Unemp1oyment, Nos. 402, 421, 452, 481, 504, 539, 571. Washington, O.C.: U.S. Government Printing Office, 1971-1978. 0097 4 H H l I Y III N H "II n H l l 3 1 I .1111 1111