REAPPRAISAL* robert j. saunders:

Transcription

1 FABRICANTS DETERMINATION AFTER TWENTY YEARS: A CRITICAL REAPPRAISAL* by roy w. bahl?c robert j. saunders: Interstate differences per capita expenditures have been attributed to variations : (a) the quality and scope public services; (b) the demographic, economic, and social structure state populations; (c) historical traditions regardg the distribution and scope governmental operations, and to (d) a random component. Although some synthesis these alternatives, which are not mutually exclusive, no doubt explas terstate expenditure differences, data limitations have led to repeated empirical tests the relationship between the characteristics impiled (b) above and levels per capita state and local expenditures. These analyses (all which have employed a multivariate regression technique) have revealed that substantial portions the variations may be explaed by a number readily dentifiable factors. At the local level, Brazer, Hawley, and Scott and Feder have applied lear regression models to variations per capita city government expenditures and have isolated several "determants" municipal spendg levels. (x) Solomon Fabricant attempted to expla state-to-state per capita spendg differentials by usg the same technique on aggregated current outlays for all state and local governments. (2) In analyzg 1942 expenditure data, Fabricant examed per capita come, per cent population livg urban areas, and population density. He was able to expla 72 per cent terstate variations the level total expenditures, and from 29 to 85 per cent for various functional, classes. More recently, Fisher(3) has expanded Fabricantes model to clude additional demographic, economic, and socio-political variables, while Sacks and Harris(4) have concluded that federal and state aid are major determants terstate expenditure variations. *Paper presented at the Seventy-Eighth Annual Meetg tion, New York, December the American Economic Associa **Assistant Pressors Economics, West Virgia University. The authors are debted to Pressors William H. Miernyk and James H. Thompson for their comments on prelimary drafts this paper and to Mart B. Solomon, Jr. the University Kentucky Computg er. 1. Harvey Brazer, City Expenditures the United States, Occasional Paper 66 (New York: National Bureau Economic Research, 1959). Amos H. Hawley "Metro politan Population and Municipal Government Expenditures ral Cities,"" Journal Social Issues, VII (1951). Stanley Scott and Edward Feder, Factors Associated with Variations Municipal Expenditure Levels, (Berkeley, California: Bureau Public Admistration, Feb., 1957). 2. Solomon Fabricant, The Trend Government Activity the United States sce (New York: National Bureau Economic Research, 1952). 3. Glenn W. Fisher, "Determants State and Local Government Expenditures: A Prelimary Analysis"' National Tax Journal, XIV (December, 1961), pp Glenn ' W. ' " * Fisher, Interstate Variation State and Local Government Expenditure, National Tax Journal, XVII (March, 1964), pp Seymour Sacks and Robert Harris "The Determants State and Local Govern ment Expenditures and Intergovernmental Flows Funds,** National Tax Journal XVII (March, 1964), pp Sage Publications Inc. is collaboratg with JSTOR to digitize, preserve, and extend access to The American Economist

2 Interpretation the results these analyses raises at least two major questions. The first relates to the relatively small amount attention which has been paid to the problem multicollearity. Interpretation the fdgs the studies mentioned has been based largely on the statistical significance regression coefficients which have been taken to imply the importance de pendent variables. But while statistical ference fers a method ascerta g significance, it fers no correspondg method for determg importance when there is a high degree terdependence among dependent variables. If two dependent variables are highly terrelated (collear) their standard errors tend to be large,(5) and a simple t test may lead to the conclusion that one or the other their coefficients is not significantly different from zero. This can happen for one two reasons : (a) it is actually not related to the dependent variable and thus not important, or (b) it is closely related to the dependent variable but collearity has caused its standard error to blow up. Consequently, only after a detailed consideration the tercorrelations among the depen dent variables can an attempt be made to fer the true importance any explanatory factors. Where there is substantial correlation among dependent variables, measures separate effect such as partial correlation, elasticity, and beta coefficients have little meang when terpreted out context. The second major question concerns the possible scope terpretation previous statistical analyses. In most cases, lear regressions have been applied to cross-section data validly leadg to descriptions differences per capita state and local expenditures, but contributg little to an understandg changes these expenditures. SCOPE AND METHODOLOGY The general objectives this paper are twold: (a) to consider the effects multicollearity on the terpretation earlier fdgs, and (b) to attempt an terpretation the present fdgs both a static and a temporal context. Operationally, the analysis is carried out on three levels: (a) three multi variate regressions on a cross section 1942 per capita state and local expendi tures with up to ne dependent variables; (b) similar cross-sectional analyses per capita expenditures on 1962 data with up to 12 dependent variables, and (c) regressions on changes per capita expenditures between 1942 and A comparison the static models 1942 and 1962 should dicate the extent to which the same or a similar set variables expla terstate differ ences through time. Sacks and Harris, usg such a method, found that the predictive value Fabricants three origal variables had decled between 1942, 1957, and However, their explanation for this decle is con sistent with the fdgs the present analysis. THE VAEIABLES This study, as was true Fabricants, is primarily concerned with per capita expenditures for current operation. Consequently, per capita state and local operatg expenditures will be used as the dependent variable throughout the analysis. 5. J. Johnston, Econometric Methods (New York: McGraw-Hill Book Co., Inc., 1963), p

3 Fabricantes three "standard*' variables? per capita come, population density, and per cent poulation urban? are analyzed usg both 1940 and 1960 data. The method measurg the latter two these variables is open to some question. Population density cities has been found to be significantly related to the level per capita municipal expenditures. However, Fabricants form the variable (state population as a per cent state land area) does not give a valid comparison terstate urban density differentials and there fore its meang is uncerta. The comparability between 1940 and 1960 the per cent urban variable is also subject to question sce the census defition urban population changed durg this period. Because the old defition was used by Fabricant, it will be retaed the present study. capita federal grants to states is cluded the analysis to exame the Sacks-Harris hypothesis that tergovernmental flows funds significantly affect the level per capita governmental expenditures. It is further hypo thesized that the magnitude terstate differentials per capita expenditures may be approximated by the magnitude federal grants relative to revenues received from ternal sources. Thus, given the level general revenue, the higher the level federal grants the higher will be the level per capita spendg. Spangler has suggested that there is a direct relationship between rate population growth and per capita state and local expenditures because what he terms "...the disruptive effects expansion."(6) His significance tests are not conclusive evidence, however, sce the per cent crease population between 1950 and 1960 is correlated significantly with both per capita come and per cent population urban Further, Spangler 's thesis is con sistently refuted by empirical analyses at the local level. (7) Nevertheless, to measure the effect population growth rate on expenditure levels, the per cent crease population over the previous decade and the degree urbanization are used both the 1942 and 1962 models. Fally, the per cent labor force employed agriculture and the per cent employed manufacturg represent general measures socio-economic differences among states. Additional variables employed the 1962 analysis are the per cent families with comes greater than $10,000 ; the per cent families with comes less than $3,000, and the Advisory Committee on Intergovernmental Relations dex the yield a representative tax system. (8) Fisher found differentials the come distribution to be significantly associated with terstate spendg differences. However, the high correlation between come distribution and come level variables may have obscured the true direct effect on government expenditures his analysis. In analyzg the importance the Advisory Committee's suggested measure fiscal capacity, Fisher found it to be generally more important the case education and highway expenditures than the case other functions more typical municipalities. INTERSTATE DIFFERENCES IN PER CAPITA TOTAL CURRENT EXPENDITURES? 1942 Fabricant, explag over 70 per cent the variation per capita current expenditures, concluded that come was the most important the three dependent variables while "... urbanization is by itself a mor factor, much less important than come and not more important than density. "(9) 6. Richard Spangler, "The Effect Population Growth Upon State and Local Govern ment Expenditures'' National Tax Journal XVI (June, 1963), pp Brazer, op. cit., p. 29, Scott and Feder, op. cit., p Advisory Commission on Intergovernmental Relations, Measures State and Local Fiscal Capacity and Tax Effort (Washgton, D.C., 1962). 9. Fabricant, op. cit., p

4 TABLE 1 REGRESSION EQUATIONS'* OF PER CAPITA CURRENT EXPENDITURES ON SELECTED INDEPENDENT VARIABLES: 1942 Population Capita Ratio Determation Number Term Income Density Urban Federal Grants Federal Grants Coefficient to General Revenue A ('.0178) (!oi32) (!l516) NI NI ? B.6035 (.0218) (.0192) (.3134) NI NI C.6593 (.0108) (.0097) (.1050) (.3256) NI D (.0233) (.0210) (.3234) (2.0154) NI E NI NI (.0652) (.3964) (.5911) a. Standard errors regression coefficients appear parenthesis below each coefficient. Beta coefficients appear below the standard errors.?? b. All coefficients determation are adjusted for sample size.

5 This conclusion was based on the significance the regression coefficients (see Table 1, equation A) and the relative size elasticity coefficients. An exama tion 1942 data reveals the three standard variables to be highly tercorrelated (see Appendix Table A) with the lowest degree association between come and = density (r.53) and the highest between come and urbanization (r =.80). Thus it is not surprisg that Fabricant did not fd urbanization to be a significant explanatory variable. This lack statistical significance, however, does not necessarily imply a lack importance. In fact, zero order correlation coefficients dicate that both come and urbanization are more closely related to expenditures than is density. (10) Fabricant contends that any fluence the urbanization variable is primarily due to its close association with come and that its direct fluence on expenditures is relatively small. (n) He appears to be referrg to the relative magnitudes the net regression coefficients when he states that: "At a given level come (and density), even fairly pronounced differences degree urbanization are associated with only slight differences per capita expendi tures.'^12) This conclusion may not be justified on two counts. First, the highly terdependent nature the explanatory variables makes it impossible to hold any two dependent variables constant while examg the third. Even if come and density could be held constant, the above net regression coefficient for urbanization would not describe the isolated effect relative urbanization on expenditures because it is computed under conditions where all three explanatory factors vary simultaneously. Secondly, it is open to question on a priori grounds. In states with relatively homogenous levels come and density, there appears to be no reason to assume that per capita expenditure levels will not be responsive to terstate differentials the degree urbanization. While the isolated effect urbanization on expenditures cannot be tested? empirically because it is impossible to abstract from the terrelations with come and density? it is possible to reduce the variability the come and density factors. By group g 15 high come-high density states, (13) the coefficient variation for come is reduced from 32.7 per cent (for 48 states) to 15.7 per cent, and that for density from per cent to 84.1 per cent. (14) When the three standard variables are regressed on per capita expenditures the 15 states, urbanization is found to be statistically significant while the regression coefficients neither come nor density differ significantly from zero. A comparison the beta coefficients (15) the 15-state and 48-state models (see Table 1) implies a greater relative importance the urbanization variable when it is examed the more homogeneous come? density context. The conclusion that at given levels come and density, the degree urbanization exerts only a mor direct fluence on expenditure levels is, there fore, not supported by these results. 10. The simple correlation coefficients between per capita expenditures and the de pendent variables are as follows: capita Income (r =.83), Population Density (r? -.23), cent Urban (r =.62). 11. Fabricant, op. cit., p. 128, ff. 12. Fabricant, op. cit., pp California, Connecticut, Illois, Indiana, Delaware, New Hampshire, New Jersey, New York, Massachusetts, Maryland, Michigan, Ohio, Pennsylvania, Ehode Island, Wiscons. 14. In the contuous form, the coefficient variation is the standard deviation ex pressed as a per cent the mean. 15. The beta or standardized regression coefficient is subject to all the limitations a net regression coefficient when multicollearity is present. 31

6 The Effects Federal Aid Eecent empirical analyses have focused on the relationship between the level per capita expenditures and the level federal grants to states. When used as an dependent variable, per capita federal aid has, without exception, signi ficantly creased the per cent variation explaed. Equation C Table 1 shows that, by troducg federal aid to Fabri cantes origal three-variable model, the amount variation explaed is creased by almost 13 per cent and all four dependent variables are " signifi cant. Aga, urbanization is apparently more than...a mor factor, much less important than come and not more important than density.''(16) In fact, as shown equation C, Table 1, a comparison beta coefficients implies that urbanization is approximately the same importance as federal aid and come, and greater importance than density. One possible explanation for the change relative importance the come and density variables is their asso ciation with per capita grants. Previous studies have shown that federal aid is significantly related to levels come and density, and not correlated signifi cantly with urbanization. Consequently, some the importance come and density the origal three-variable models may be attributable to the omission the federal grants variable. (17) When the 15 high come-high density states are examed separately, the addition the federal grants variable creases explaed variation only slightly. As the three variable case for the 15 states, urbanization is the only significant explanatory factor. The Effect Additional Independent Variables(ls) Fisher attempted to expla a greater percentage 1960 expenditure variations by expandg the number explanatory variables. In the present study, the number dependent variables is creased to demonstrate proxy relationships between the origal four variables and other social, economic, and demographic factors. When all ne variables are cluded the model, only three? federal grants to states, the ratio federal grants to total general? revenues, and urbanization are statistically significant. When examed alone, these three explanatory factors account for approximately 88 per cent the variation state and local expenditures, or 16 per cent more than was explaed by Fabricants three-variable model. Of the variation explaed, 92 per cent may be attributed to per capita federal aid and the ratio federal grants to total general revenue. Although these two variables are highly tercorrelated (r =.74), equation E Table 1 shows that given the level federal grants, the ratio federal grants to total revenues is versely related to the level per capita expenditures. This implies that states which have relatively equal levels general revenue, those which contribute smaller propor tions to total revenue from ternal sources spend significantly higher amounts per capita. 16. Fabricant, op. cit., p See James A. Maxwell, "The Equalizg Effect Federal Grants'", Journal Fance, Vol. IX, May, 1954, p. 209, and M. A. Haskell, "Federal Grants and the Income Density Effect"", National Tax Journal, March, 1962, p In addition to the come, density, urbanization, and federal aid variables, the ratio federal grants to total general revenue, per cent crease population between 1930 and 1940, per cent crease per cent urban , per cent employed agriculture, 1940, and per cent employed manufacturg, 1940, were added to the model. 32

7 to General Revenue Number Density Urban b Term Federal Income Grants Determation (.9157) E (.2126) NI.8113 NC (.6527) (2.2737) F NI NI NI a Population Capita Ratio Coefficient TABLE 2 REGRESSION EQUATIONS'1 OF CAPITA PER CURRENT EXPENDITURES SELECTED INDEPENDENT VARIABLES: 1962 a. Stondard errors regression coefficients appear parenthesis below each coefficient. Beta coefficients appear below standard errors. C (.0113) B (.0230).7766 (.0875) (.1491) NI D (.0226) (.6638) (.8526) (.6102) NI NI (.0407) (.0268) (.0346) (.0120) (.0973) (.0265) A gg All determation b. coefficients adjusted for are sample size.

8 The data presented Appendix Table A suggest two non-mutually ex clusive explanations the importance the urbanization variable: (1) it reflects a proxy relationship between per cent population livg urban areas and other socio-economic and demographic variables. States havg greater proportions the population livg urban areas tend to have higher per capita comes, higher population densities, smaller proportions the labor force employed agriculture and greater proportions employed manufactur g. (2) It possibly reflects a direct relationship between urbanization and the level per capita expenditures. When the 15 high come-high density states are considered, the simple correlation coefficient between urbanization and come is reduced from.80 to.51 and the simple correlation coefficient between expenditures and urbanization (r =.54) is higher than between expenditures and any other dependent variable. INTERSTATE DIFFERENCES IN PER CAPITA TOTAL CURRENT EXPENDITURES? 1962 Fisher and Sacks and Harris have attempted to re-evaluate the importance Fabricante determants by analyzg data for more recent years. Fisher examed 1957 and 1960 data while Sacks and Harris analyzed 1960 data. Both studies concluded that the variables which contributed significantly to the regressions 1942 are generally the same as those which were significant for 1957 and The results the present study are agreement with the above that the magnitudes and signs the regression coefficients are similar to those the 1942 model (see equation A, Table 2).(19) When the 15 high come-high density states are separated, the coefficient variation for come is reduced from 20.7 per cent (for 48 states) to 11.7 per cent. The results the present three-variable regressions are similar to those the 1942 analysis 15 states that urbanization becomes an important explanatory factor, but differ that come and density are also significant. In fact, the relative size the beta coefficients equation B, Table 2 implies that the variables are approximately equal importance. The Effects Federal Aid?1962 To the extent that per capita expenditures for different functions are fluenced by the same factors, the tercorrelations among expenditure categories will be higher or lower. That is, if the determants per capita highway expenditures are also the determants per capita education outlays, then highway and education expenditures would themselves be highly correlated. Table 3 reveals that the terrelations between the expenditure categories de cled between 1942 and 1962, which dicates that the same set variables does not account for as much the terstate variations all functions the later years. 19. However, the present study, as Fabricante origal analysis, the dependent variable form used is per capita current expenditures while both Fisher and Sacks and Harris used per capita total general expenditures. 34

9 TABLE 3 COMPARISON OF INTERCORRELATIONS AMONG SELECTED PER CAPITA EXPENDITURE CATEGORIES: 1942 and 1962(a) Local Schools Highways Police and Fire (.92) (.63) (.68) Total Current Local Schools _ Highways (.53) (.51) (.13) (a)the simple correlation coefficient for 1942 is shown parenthesis above the correspondg 1962 coefficient. Sacks and Harris, attemptg to expla the marked decle the pro portion variations expenditures that can be explaed by the three basic factors, cited the creasg importance tergovernmental flows funds. (20) By troducg per capita federal aid the 1962 model, explaed variation is creased from.46 to.56; however, as shown Table 4, the addition the same variable the 1942 model creased explaed variation from.72 to.86. Given the importance federal aid 1942, Sacks and Harris's hypothesized explanation for the declg importance the three basic variables seems untenable. TABLE 4 A COMPAEISON OF MULTIPLE DETERMINATION COEFFICIENTS FOR 48 STATES AND 15 STATES: 1942 and 1962 Fabricant Fabricant 3 Variable 3 Variable states 15 states 48 states 15 states Model Model and Capita Federal Aid All Variables (a).8874 n.c n.c. (a) Ne dependent variables for 1942 and 12 for Equation C Table 2 shows that when four dependent variables (the three basic factors and per capita federal grants) are regressed on 1962 expen ditures, only come and federal aid are found to be significant. When federal aid was troduced to the 1942 model, the importance the come variable decled markedly whereas the troduction federal aid to the 1962 model was accompanied by no such substantial decle the importance come. (21) 20. Sacks and Harris, op. cit., p See Equation C, Table 1 and Equation C, Table 2. 35

10 This result is consistent with recent empirical analyses which have shown a defite trend toward the greater equalizg effects federal grants. (22) In 1942 the level federal aid was positively related to the level come, but the distribution grants among the states has sce altered markedly favor the poorer states. Consequently, 1962, no significant correlation is observed between per capita federal aid and per capita come. The Effect Additional Independent Variables (2S) When all 12 dependent variables are regressed on per capita operatg expenditures, only per capita federal aid to states and federal aid as a per cent general revenue are found to be significant. The clusion only these two variables the model results an explaed variation approximately 81 per cent (see equation E, Table 2). When only 15 high come-high density states are considered, the same two explanatory factors result a coefficient determation.77 (see equation F, Table 2). Table 5 shows that these high come states receive relatively lower amounts federal aid per capita, and tend to fance a greater proportion expenditures from ternal sources. TABLE 5 A COMPARISON OF THE LEVELS OF SELECTED INDEPENDENT VARIABLES: 48 STATES AND 15 SELECTED STATES Average Ratio Average Capita Federal Aid to Capita Federal Aid General Revenue Income 48 States $ % $ States $ % $2509 The implicit relationship between the above two variables and per capita expenditures was found to be as follows : where F = per capita Federal grants to states I = general revenues from ternal sources I + F = total general revenue E = per capita current general expenditures This relationship is significant that it suggests a difference the relative effect federal aid on high come as opposed to low come states. It follows from equation (1) that an crement per capita federal aid to a state which raises, on the average, a relatively large proportion revenues from ternal sources (a high come state) will result a higher level expenditures than 22. Maxwell, op. cit., and Haskell, op. cit. 23. In addition to the ne variables the 1942 analysis, the 1962 cross section cludes per cent families with come under $3000, per cent fam?ies with comes over $10,000, and the dex the yield a representative tax system. 36

11 will an equal jection federal aid to a low come state. Consequently, matchg requirements federal grants would absorb larger proportions state-local tax revenues poor than rich states. Total expenditures the poor states would not crease by as large an amount sce order to fance services eligible for federal aid, state legislatures may tend to divert state money from services not eligible for federal aid.(24) THE TEMPORAL PATTERN OF INTERSTATE VARIATIONS One possible method vestigatg the temporal pattern state and local per capita expenditures is to compare the results static analyses. For example, Sacks and Harris found that the three basic variables could expla a smaller amount expenditure variations 1960 than While static cross-sectional analysis? such as those Fabricant, Fisher, and Sacks-Harris? may go far toward identifyg the determants differences expenditure levels, one may fer little from them about the determants changes expenditure levels. In the short run, it may well be that a knowledge the factors which are associated with movements per capita expenditures has the greatest utility for fancial planners and admistrators. (25) One approach to statistically analyzg the pattern movements per capita expenditures volves regressg changes the dependent variables on changes per capita expenditures^26) D?termants Changes Capita Expenditures Approximately 24 per cent the variation changes per capita expen ditures (between 1942 and 1962) can be explaed by 1940 to 1960 changes the three basic variables. Only changes per capita come are found to be statistically significant. When changes eight dependent variables (27) are regressed on changes per capita expenditures, the only two explanatory factors which at any time prove to be significant are changes per capita come and changes per capita federal aid. These two variables expla 35 per cent the variation the dependent variable or 97 per cent the amount explaed by all eight dependent variables. (28) This fdg is consistent with the results the 1962 cross-sectional analyses which federal aid and come were the only significant explanatory factors the four-variable model. 24. Maxwell, op. cit., p See Roy W. Bahl and Robert J. tf Saunders, Determants Changes State and Local Government Expenditures", National Tax Journal, XVIII, March, 1965, pp. 26. The lear regression equation will be the form Y = a-f-biax1-f-b2ax2-{-.. -f-... bnaxn. A regression coefficient should be terpreted as the change ex penditures which is accompanied by a one unit change the dependent variable. In the one year cross-section model, a regression coefficient is terpreted as the difference expenditures which results from a one unit difference the variable. dependent 27. In addition to changes the three basic factors and federal grants, the variables are dependent change the ratio federal grants to general revenue, ; change per cent employed agriculture, ; change per cent employed manufacturg, , and per cent crease population, The regression equation is Y = a -f.051 Xx -j-,436x2 where X1 is the change per capita come and X2 is the change per capita federal aid. The beta co efficients were.433 and.365 respectively, which this case gives a good dication relative importance sce the relationship between the two variables was almost zero (r =.031). 37

12 The ability the model to expla a greater proportion terstate variations changes per capita expenditures may be due to the length the terval considered. Recent fdgs suggest that the variation explaed may be creased considerably by usg a shorter time span.(29) A Coparison 1903, 1942 and 1962 Models Fabricant hypothesized that the 1942 relationships among his basic variables would be relatively the same if computed usg 1903 data.(30) Sce he found per capita come to be the most important the explanatory variables 1942, he concluded that the chief cause risg per capita expenditures durg the period was risg come. However, as was shown above, Fabricant 's failure to clude federal aid as an dependent variable may have exaggerated the importance come (see equations C and A, Table 1). In fact, the four-variable model the present analysis produces a more accurate estimate the average level 1903 per capita expenditures than does Fabricants three-variable model. Fabricant overestimated mean 1903 expenditures by $4.94 while the four-variable model underestimated 1903 expenditures by only $3.62. Because adequate data are not available, the average amount federal aid 1903 was assumed to be zero. Usg the same two 1942 models to predict 1962 expenditures, it may be seen from Table 6 that the clusion federal aid results a substantially better estimate. This aga supports the fdg that the omission federal aid Fabricante 1942 model tended to distort the relative importance the dependent variables. A COMPARISON OF THE ESTIMATES OF 1962 PER CAPITA EXPENDITURES OBTAINED BY FABRICANTS 1942 THREE VARIABLE MODEL AND THE 1942 FOUR-VARIABLE MODEL OF THE PRESENT STUDY 3-Variable Model 4-Variable Model Actual $ $ Estimated Difference CONCLUSIONS The present study dicates that Fabricants conclusions regardg the determants terstate variations per capita expenditures may be ques tioned on two counts: (1) his failure to adequately consider tercorrelations among the dependent variables led him to underestimate the importance urbanization, and (2) his failure to clude federal aid led him to overestimate the relative importance per capita come. Sacks and Harris concluded that the decle the importance the three basic variables between 1942 and 1960 may be attributed to the creasg importance tergovernmental flows funds. The results the present study, which show that per capita federal aid was approximately the same relative importance 1962 as 1942, appear to refute this hypothesis. In regard to the temporal pattern per capita expenditures, it was found that changes come and changes federal grants were positively associated with changes expenditures. 29. See Bahl and Saunders, op. cit., p Fabricant, p

13 APPENDIX TABLE A ZERO ORDER CORRELATION COEFFICIENTS'1 BETWEEN ALL POSSIBLE COMBINATIONS OF INDEPENDENT VARIABLES, 1942: FOR 48 STATES AND FOR 15 HIGH INCOME-HIGH DENSITY STATES Capita Density Urban Income Population nue Eatio Increase Labor Force Labor Force crease Federal Population, Employed Employed Grants Agriculture Manufactur- Urban, General g Capita Federal Grants to States Capita Income Population Density Urban Ratio Federal Grants to General Revenue Increase Population, Labor Force Employed Agriculture Labor Force Employed Manufacturg (-.0441) (-.3891) (.4618).5285 (-.2683) (.5072).7983 (.8211).7088 (.7195).7352 (-.2877) (-.5006) (-.6494) (.6505).2180 (.2663) (-.4962) (-.3280) (.3543).1175 (.1698) (-.5929) (-.7371) (-.7836) (.4261).4823 (.2926) (-.3542) (-.0009).4995 (.5961).7107 (.3402).6493 (-.2296) (-.6586) (-.5168) (-.2213).2038 (-.1553).5319 (.0054) (-.1859) (.1559).6017 (-.1785) (.4237).7232 (-.2906) CO to a. The simple correlation coefficient for 15 states is shown parenthesis above the correspondg 48 state coefficient

14 APPENDIX TABLE B ZERO ORDER CORRELATION COEFFICIENTS'1 BETWEEN ALL POSSIBLE COMBINATIONS OF INDEPENDENT VARIABLES, 1962: FOR 48 STATES AND FOR 15 HIGH INCOME-HIGH DENSITY STATES Capita Population Yield a Federal Grants Income Density Urban Representative Ratio Tax System to General Revenue Capita Federal Grants (-.0115).0720 (-.3750) (.3626) (.6084).6194 Capita Income (.2509).4460 (.0757).1773 (.2846).4281 (-.5253) Population Density (.6442).0967 (-.2440).2406 (-.2894) Urban (.2628) (-.0178) Yield a Representitive Tax System (-.2501) Ratio Federal General Revenue Grants to Increase Population, Families with Incomes less than $3,000 Families with Incomes greater than $10,000 Labor Force Employed Agriculture Labor Force Employed Manufacturg a. The simple correlation coefficient for 15 states is shown parenthesis above the corres pondg 48 state coefficient, 40

15 (TABLE B Contued) In Increase Families Families Labor Force Labor Force crease Population with Incomes with Incomes Employed Employed Urban, Under $3,000 Over $10,000 Agriculture Manufacturg (-.4531).2679 (-.0246) (-.0233).0552 (.1978).1793 (-.3092) (.1943).2081 (.5432).4401 (-.6495) (.8549).9268 (-.2792) (-.3742) (-.2339) (-.5222) (.1474).4585 (-.6489) (.2857).6230 (-.0197) (-.4550).4990 (-.3826) (-.0165).2414 (-.4838) (.1812) (.5936).6456 (.1866).1307 (-.1122) (.4155).4851 (-.0708) (-.5346).3247 (.3384).1943 (.0169) (.2525).4872 (0.5227) (.0435).4349 (.1841) (.1597).3202 (.2028) (.6407).5333 (.1452) (-.5346) (.3402).2233 (-.6837) (.5680).5380 (-.0577) (-.1996).3899 (-.1925) (-.4895).2824 (-.0774) (-.2374) (.0103).2915 (-.0234)