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Jurisdictional homogeneity and the Tiebout hypothesis
JOURNAL
OF URBAN
ECONOMJCS
Jurisdictional
10,227-
239 (198 1)
Homogeneity Hypothesis
and the Tiebout
RANDALL W. EBERTS Department of Economtcs,Unrversq
of Oregon,
Eugene, Oregon 97403
AND TIMOTHY J. GRONBERG Texas A & M Unwersity, College Station, Texas 77843 Received April 24, 1980; Revised July 10, 1980 In this paper, an alternative to the caprtalizatroonapproach to testing the Trebout model is presented. The Tiebout foot votmg mechanism suggests that households will sort and stratify into (approximately) homogeneouslocal public goods jurisdictions. At a point in time, the efficiency of the sort will be positively related to the number of existing jurisdictions. Using a measure of homogeneity introduced by Theil, the relationship between stratification (homogeneity within Jurisdiction) and number of jurisdictions is tested. For a sample of school districts within 33 SMSAs, the Tiebout stratification hypothesis is confirmed. I. INTRODUCTION
Since its inception in 1956, Tiebout’s [ 181theory of a marketplace in local public goods has provided the foundation for numerous theoretical and empirical models of public sector allocation. Much of the theoretical attention has focused upon the normative efficiency properties of the Tiebout migration allocation mechanism (see, for example, Buchanan and Goetz [5] and Hamilton [9]). The empirical work, pioneered by Oates [ 141, has centered upon an investigation of the capitalization of net public goods benefits into property values. Significant capitalization findings have been viewed as supporting the relevance of the Tiebout model as a positive theory of household behavior. At both the theoretical and the empirical level, the extant Tiebout literature emphasizes the importance of local public sector variables in determining the properties of market clearing housing (land) prices. This emphasis upon the characteristics of equilibrium prices within the Tiebout setting has served to obscure a second conjecture in the original Tiebout paper. As an outcome of the local public goods allocation process, Tiebout suggeststhat communities will consist of (approximately) homogeneous public goods demand groups. This result, which has been derived more formally by Epple et al. [7], follows from the market properties of the 227 0094-l 190/8 l/050227- 13$02.00/0 Copyn&t 0 198 I by Acadermc Press. fnc Au n&s of reproduction m any form reserved
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Tiebout process. In a perfect Tiebout world, consumers face a posted market price for local public goods. Consumers determine their optimal public (and private) goods bundle at the prevailing price(s), and shop in the marketplace in communities in an effort to match that bundle. Consumers with identical demands will, therefore, locate within the same community. If tastes are relatively constant across income classesand the income elasticity of demand for public goods is nonzero, then homogeneous grouping by public goods demand implies homogeneous grouping by income. Thus, a second hypothesis derived from the Tiebout model is that public goods jurisdictions will stratify the population by income class. In this paper we attempt to assessthe validity of the Tiebout stratification hypothesis. Our approach utilizes Theil’s [17] entropy measure of income inequality in quantifying the concept of homogeneity. Given a division of population into independent groups, the Theil measure allows for the decomposition of population inequality (heterogeneity) into a weighted sum of inequality within and between the groups. Treating an SMSA as a population and school districts as independent groupings of that population, we decompose total SMSA inequality into the sum of between and within school district inequality. Using a sample of 33 SMSAs, we generate a series of observations on the degree of heterogeneity (stratification) within school districts. We then treat the ratio of within district heterogeneity to total heterogeneity as a dependent variable in a single equation regression model. Our attention is focused upon the coefficient of the number of school districts within the SMSA.’ A positive relationship between the number of public goods jurisdictions and the degree of stratification (homogeneity) is suggestedby the Tiebout model. For our sample, the empirical evidence supports the stratification hypothesis. ‘Hamilton ef al. [I I] have also tested the stratification hypothesis by examining the relationship between income inequality and number of school districts. Our study is differentiated from theirs in two significant ways. First, we utilize the Theil inequality measure rather than the Gini coefficient measure employed by Hamilton er al. The Theil decomposability property, in turn, allows us to obtain a smgle measure of jurisdictional homogeneity for each SMSA. We feel that this provides a better statistical framework for testing the stratification hypothesis than the Hamilton et al. approach which involved sampling among the Gini values of individual jurisdictions. Secondly, our data set is defined over school districts rather than over census tracts. In a second related study, Pack and Pack [ 151have investigated the relationship between income heterogeneity (as measured by the coefficient of variation in income), demand heterogeneity, and Lindahl pricing for local public services.They argue that the observed degree of income heterogeneity among communities m their sample requires that Tiebout’s stratification hypothesis be rejected. Our study can be vrewed as a response to their suggestion that “more complicated versions of the model, for example, suggesting that actual observations are a snapshot of a system moving towards equilibrium could reconcile our evidence with the theory” (Pack and Pack [15, p. 3571)
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Section II provides a sketch of the Tiebout model. Particular emphasis is placed upon differentiating between the capitalization and the stratification processes. Section III presents our empirical methodology, including a discussion of the properties of the Theil inequality measure. In Section IV the regression results for our sample are listed and discussed, and conclusions are drawn. II. THE TWO TIEBOUT HYPOTHESES Consider an economy divided into M spatially separated labor markets. Assume that there is perfect migration of labor within each market and zero migration across markets. The equilibrium distribution of wageswithin each market is determined by the demand and supply conditions internal to that market. Given the distribution of population across markets, the distribution of skills within each market, the leisure-labor preferences of individual workers, the spatial distribution of workers and firms and the derived demand curves for labor (by skill category), an equilibrium distribution of wages will emerge for each labor market area. Assume that each labor market is itself divided into G contiguous political jurisdictions. The emergence of these political units is motivated by the desire for collective provision of certain types of goods and services (e.g., those possessing the joint characteristics of economies in consumption and nonexclusion). Each jurisdiction or community is assumed to provide a uniform quantity of a single local public good. The publicly provided commodity is local in the sense that there are no interjurisdictional spillover benefits. We assume further that the public good is congestable in the sensethat the cost of providing a given level of the good is dependent upon the level of population in the community. The provision of the public good by each local fist is financed through a proportional tax on the value of residential property. Under this type of financing arrangement, the Lindahl share price of the public good to any citizen is determined by the percentage of the community housing stock which he owns. The level of the public good within each community is determined by a majority voting process, with the equilibrium outcome reflecting the preferences of the median voter. Under the assumptions of preference homogeneity and a positive income elasticity of demand for housing, each community public goods offering can be written as a function of the median share price (which is the share price of the median income household), median income, and the prices of private goods, including housing. It is assumed that all nonhousing private goods are available at uniform prices throughout the economy. The price of housing, however, may vary due to capitalization effects. As argued in Hamilton [lo] and developed more rigorously in Brueckner [3], perfect migration within a labor-housing market implies the equaliza-
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tions of utilities, in equilibrium, across the communities of that market by income class. The bid rent (constant utility) offered by identical income households for identical sites in different fiscal environments, i.e., different tax-price-public goods combinations, will vary according to the potential consumer surplus associated with each local public goods offering. The equilibrium market rent profile across communities will, due to perfect mobility, leave identical consumers on the same individual bid rent curve. Thus, the redistribution of real income (utility) affected through the local public sector is precluded by migration. This is the essenceof the concept of capitalization of net fiscal benefits into property values. If the migratory process leads to compensating variations in housing prices, then sites in income homogeneous and nonhomogeneous communities are rendered equally desirable in locational equilibrium. If utilities to high income individuals are the same in both homogeneous and nonhomogeneous communities, is there an economic motivation for the formation of homogeneousjurisdictions? In other words, do the Hamilton and Brueckner results refute the Tiebout hypothesis concerning metropolitan fragmentation and segregation according to public goods demand (by income class in our model)? We would argue that the capitalization type models deal with a different analytical problem than the segregation hypothesis. The capitalization literature attempts to characterize the set of housing prices which will support an allocation of households among a fixed set of public goods locations. If identical consumers are allocated to different locations, the value of their indirect utility functions must be the same when evaluated at the equilibrium prices and the given public goods-tax parameters. The equilibrium prices sort households among communities such that the resulting allocation is individually incentive compatible (i.e., no individual has an incentive to relocate). These models thus serve to formalize Tiebout’s notion of a “foot voting” equilibrium. The tendency of the urban system towards homogeneous public goods jurisdictions, however, is a dynamic theory of group formation. The static equilibrium Tiebout models do raise an important point in considering the dynamics of the system. They serve to indicate that stratification is not the direct result of the desire of individuals to avoid redistribution per se. Rather, two plausible alternative rationales exist to explain why the population will tend to coalesce into stratified political units. Both explanations are motivated by the realization that capitalization equilibrium is a Nash concept. First, a partitioning of the population into heterogeneous communities may be supported by a set of prices in a Nash sense,but the resulting equilibrium may not prove to be group incentive compatible.2 As “The long-run equihbrium stratification by adjacent income classesdeveloped in Epple et al. [7] is consistent with our analysis. Within their analytical framework, with partitioning treated as endogenous in the long run, exhaustion of potential gains from trade yields a stratified solution.
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developed in papers by McGuire [13] and Ellickson [6], the globally Pareto efficient provision of congestable public goods in an economy with heterogeneous tastes and/or endowments requires that the population stratifies into homogeneous consumption clubs.3 In terms of the static model outlined above, the equilibrium level of utility under the stratified partitioning of the population is potentially greater for both high- and low-income individuals than that which obtains relative to a mixed partitioning. Therefore, gains from trade exist in moving from heterogeneous to homogeneous local public goods jurisdictions. During the evolutionary process of metropolitan fragmentation, developers and/or politicians will be in a position to exploit these potential gains through institutional arrangements (e.g., zoning) leading to income stratification. Second, households participate in two markets in local public goods. They vote with their feet relative to a fixed vector of offerings, and they vote with the ballot box within their present community to consider changing one element of that vector. Within a heterogeneous community, given the prevailing set of tax prices, the majority voting choice of G will reflect the optimizing choice of the median income household. The remaining community members will find themselves consuming a nonoptimal quantity of the local public good. In order to avoid frustration through the public choice decision process, there will exist a tendency for individuals with similar public goods demand curves to combine into collective units. Successin appropriating gains from stratification should be reflected in greater jurisdictional fragmentation of a given labor market area. If Tiebout’s hypothesis concerning the existence of a local public goods stratification process holds, then we would expect, ceteris paribus, a positive correlation between the number of public goods jurisdictions and jurisdictional homogeneity. In the next section we propose a methodology for testing this hypothesized relationship between income homogeneity and jurisdictional fragmentation. III. TESTING THE STRATIFICATION
HYPOTHESIS
Returning to our original labor market scenario, we pose the following question: Does the number of public goods jurisdictions within a given labor market prove to be a significant variable in explaining the variance in jurisdictional income homogeneity across labor markets? As developed in Section II, the Tiebout stratification hypothesis suggestsa positive correlation between homogeneity and degree of fragmentation.4 ‘These results rest upon the assumption of sufficient numbers of each consumer type for efficient group formation. The Epple ef al. [7] heterogeneous(but stratified) long-run solution follows from the alternative assumption of insufficient numbers for the achievement of perfect homogeneity. 40bviously, m the limrt a one-to-one correspondence between Jurisdictions and consumers yields homogeneity. This limiting property is irrelevant for our purposes.
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However, it may be the case that the number of jurisdictions when entered in the model with the population of the labor market serves as a proxy for the average population of the jurisdictions. Thus the positive correlation observed between the homogeneity measure and the number of jurisdictions may not be entirely due to the Tiebout hypothesis. For a host of reasons unrelated to the Tiebout hypothesis, individuals tend to live near others of their own income level. Given the distribution of incomes within the local labor market, as the population of a typical jurisdiction increases,a greater number of the segregated income groups will be included in the jurisdiction which increases the level of heterogeneity. Fortunately, the two effects can be disentangled by including in the linear model of income stratification a variable which measures the average population size of jurisdictions within the local labor markets.5 Thus, in order to test the Tiebout stratification hypothesis, the homogeneity measure is regressedagainst the number of jurisdictions, the average population size of jurisdictions plus selected socioeconomic variables designed to hold constant the economic, geographic, and demographic characteristics across the labor markets. The empirical specification of the model requires three transitional definitions. We define labor market boundaries to be coterminous with SMSA boundaries. To the extent that within SMSA mobility exceedsacross SMSA mobility, this assumption is validated. Within each SMSA we define school districts as the relevant public goods jurisdiction. Obviously there exists a vector of local public goods offerings in each labor market, with different geographical boundaries associated with the various elements of that vector. Consistent with the bulk of the Tiebout empirical literature, we assume that educational services represent the dominant public goods factor in locational decisions. Finally, we define jurisdictional homogeneity in terms of Theil’s [ 171entropy measure.The Theil measure of income inequality proves to be particularly useful in testing the stratification hypothesis due to its decomposability properties, which we discuss briefly below. The degree to which the Tiebout mechanism precipitates a rational sorting of individuals can be measured by the relationship between the distribution of income within a community and the distribution between communities. It follows that a perfect Tiebout world is one in which there is perfect homogeneity within each community6 and the inequality of the 5We are indebted to the referee for suggesting this possibility. Including both the number of jurisdictions and the average population of the jurisdictions may create a problem of multicollinearity. However, the simple correlanon between the two variables IS not statistically significant, which partially allays some of the fears. ‘The Tiebout analysis actually suggests sorting by public goods demand, which is a function of both income and preferences. That income itself is an important determinant of local public goods demand is well established. (See Bergstrom and Goodman [I]. Borcherding and Deacon
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SMSA is totally accounted for by the inequality between communities. It is, therefore, crucial to any analysis of the relationship between the number of jurisdictions and the level of within community inequality that the inequality measure be decomposed exclusively into within and between set components. A recent article by Bourguignon [I9741 demonstrates that Theil’s entropy measure of inequality is the only inequality measure that can be decomposed satisfactorily into the appropriate components of within and between community inequality measures.’ The Theil measure defines inequality in the following manner:
where N: G: y: Yg: Ng: s,:
Number of individual families in the SMSA; number of communities or jurisdictions in the SMSA; individual i ‘s share of the total income in SMSA; community g’s share of SMSA income; number of families in community g; set of families in community g.
The Theil inequality measure expresses the total inequality of a population as the sum of the between community inequality (the first term on the right in Eq. (l)), and the within community inequality (the second term on the right). The between set inequality relates community g’s actual share of the total SMSA income to its share if all income were divided equally among all communities. When income is distributed equally, that is when community g’s income share equals its population share, the between set inequality measure equals zero. Stated slightly differently, there is a maximum of homogeneity between communities when the average income of each community is equal. The within community component compares individual i’s share of total income in community g with his share if all income in community g were distributed equally among its residents. Again, if income is distributed [2], and Gronberg [8]). We assume here that the distribution of income serves as an adequate approximation to the distribution of demand for public goods. To the extent that our socioeconomic variables fail to account for variation in tastes, however, the potentldfor biasis introduced. ‘More accurately, the Theil measure is the only satisfactory income weighted decomposable inequality measure. Bourguignon introduces a population-weighted decomposable measure in the paper which satisfies his evaluative criteria
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equally, the within set inequality measure equals zero. The relative share of each individual as compared with their aliquot share is weighted by the individual’s actual share of community g’s income. These weighted individual measures are summed over all individuals in community g to yield a within set inequality measure for each community. In turn, each within community inequality measure is weighted by the community’s share of total income and summed to yield the total within community inequality for the SMSA. Theil’s measure possessesthe following properties: (1) it is symmetric with respect to population size, (2) homogeneous of degree zero in income, and (3) additively decomposable into between and within group components. The first two conditions are intuitively straightforward. The symmetry condition reflects the anonymity rule that the personality or preferences of income earners are irrelevant to the measure of inequality. It implies that the Theil inequality measure is invariant to the replication of a given distribution. Consequently, the size of the population of the SMSA will not bias the inequality measure, holding the distribution of incomes as fixed. The income-zero homogeneous property assuresthat the inequality measure is invariant when all incomes are multiplied by the same scalar. This guarantees that any systematic relationship between population size and income levels (Hoch [ 121)will not bias the measurement of inequality. The additively decomposable characteristic permits the total inequality of a population to be divided into mutually exclusive groups. This has a considerable advantage over nondecomposable inequality measures such as the popular Gini coefficient. Pyatt [16] demonstrates that the Gini coefficient can be divided into mutually exclusive groups only if homogeneity is perfectly obtained within communities. Any heterogeneity within groups will cause the distributions of the different communities to overlap, biasing the within community inequality measure. Theil’s measure of inequality has an interesting interpretation for the Tiebout mechanism. The within group population shares can be thought of as prior probabilities of what one might believe would result if the Tiebout mechanism worked perfectly. The within group income shares are the posterior probabilities of the Tiebout event. The ratio between the two indicates the relative efficiency of the mechanism. Perfect efficiency implies that the ratio is unity, and the corresponding inequality measure is zero. IV. ESTIMATION RESULTS The analysis is performed on 34 SMSAs within seven states (California, Illinois, Iowa, Michigan, Missouri, New York, and Wisconsin). Unified school districts are chosen as the political jurisdictions for reasons mentioned earlier and also because they provide for mutually exclusive and
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coterminous delineations of the SMSAs. The number of school districts within the selected SMSAs ranges from 2 to 39 and the total number of families within the metropolitan areas varies from 16,829 to 402,765. Income distributions are calculated from 1970 Census data broken down by school districts. Incomes in each community are divided into 15 brackets with the midpoint of each interval serving as the mean. The mean income of the open-ended bracket is approximated by the mean of the Pareto distribution for this range.* The spirit of the Tiebout hypothesis of homogeneous political formation can best be captured by expressing within jurisdiction inequality as a percentage of total inequality within the SMSA. In this form, one would expect that as the number of jurisdictions increases, the percentage of total inequality accounted for by the within group component should decrease.’ So far we have considered the number of jurisdictions to be exogenous. However, through political actions individuals have actively sought to influence the number of school districts. In the past state legislatures have made a conscious effort to improve efficiency by consolidating school districts. For example, Iowa enacted a law “to encourage the reorganization of school districts into such units as are necessary, economical, and efficient.. . ” (Iowa Annoted Code, para. 275.1). Other states have passed similar legislation. The possibility of endogeneity is examined by first regressing the number of jurisdictions on dummy variables which are entered to represent the different policies and historical trends among the seven states included in the sample.lo Even though the system is recursive, we assume that the error terms in the two equations are correlated since stratification is a result of both individual and collective decisions. The predicted values of the number *The11 shows that if the midpoint of each bracket is used and the midpoint of the open interval is approximated by the Pareto distribution, the error in most casesis of the order of 1% of a nit. A nit is a term borrowed from information theory to describe the informational content of a message. The units themselves are not important but what is crucial is their relative position between perfect equality (0 nits) and perfect inequality (log N nits) where N is the number of individuals in the population. 91t should be recognized that since within and between set inequalities sum to total inequality by construction of the measure, the percentage of within and between set inequality will sum to unity. Thus, correlation between error terms across equations may exist, This normally requires the use of ZelIner’s seemingly unrelated equations technique, but since one of the two equations is redundant, ordinary least squares is appropriate and will yield consrstent. unbrased, and efficient estimates. “The following results were found to explain the number of Jurisdictions: JUR = 9.85 + 2.94 ILL - 1.86 IA + 13.81 A40 + 24.94 NY + 2.14 WN (3.25) (0.62) (0.37) (2.49) (5.31) (0.43) + 4.81 MI (1.08)
R2 = 0.60.
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of jurisdictions (along with the predicted values of average size) are entered into the homogeneity equation. Comparing the instrumental variable estimates with OLS estimates substantiates the fact that OLS estimates are biased downward and inefficient. Consequently, our comments will be confined to the results of the instrumental variable estimation. The estimates of the stratification equation are displayed in Table 1. Both the Tiebout hypothesis and the average size hypothesis are supported at acceptable confidence levels. The coefficient of the number of jurisdictions is negative and statistically significant at the 0.05 level. Thus, with an increase in alternatives, individuals will sort themselves into more homogeneous public goods jurisdictions. The coefficient of the average population TABLE I Estimates of the Income Stratification Equation Using Both Instrumental Variables and OLS Techniques* Dependent variable: Percentage of within district inequality IV** oLs**
Explanatory variables -__ Constant
Number of school districts*** Average size of school districts Number of families in SMSA Percentage of school revenues per student received from state Percentage of SMSA urbanized Percentageof nonwhite SMSA population Percentage change in number of households Percentage of SMSA population 18 years and under Total inequality of SMSA
Ill.59 (45.54) - 0.12 (5.88) o.OOQ2 (1.93) - 0.00002 (3.76) 0.09 (6.64)
95.07 (24.49) - 0.05 (1.W 0.0003 (8.91) - 0.00003 (8.18) 0.05 (3.36)
- 0.01 (0.65) - 0.24 (5.91) 003 (6.43) - 0.27 (5 73) - 0.16 (2.31)
003 (1.42) - 037 (6.28) - 0.01 (1 53) - 0.02 (0.37) 0.08 (1.03)
SSE (corrected for 24.94 Heteroscedasticity) 23.75 19092 173.49 SEE (uncorrected) ~-_____ ‘Heteroscedasticity corrected by wetghting by the estimated residuals. **Values in parentheses are f statistics. ***See Footnote 10 for the estimates of the Jurisdiction regression.
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size of jurisdictions is positive and statistically significant at the 0.05 level. The positive coefficient suggeststhat given a level of income inequality for the total SMSA, an increase in the population of a single jurisdiction will be associated with an increase in the percentage of the inequality contained within the jurisdiction. This reflects the fact that jurisdictions with larger populations can encompassa greater range of income levels. Therefore, even though individuals consciously sort themselves into homogeneous groups, the degree of homogeneity depends upon the population of the school districts. In addition to the effect of state reorganization policies on the sorting decisions of individuals, the amount of state funding of local school districts may also distort individual decisions. A major reason for state funding is to reduce the fiscal disparity. SMSAs in states with generous funding would be expected to be less stratified since the advantages and disadvantages of compensatory mixing is attenuated. The percentage of per capita revenue for local public education received from state funds is entered to measure the impact of intergovernmental grants upon the Tiebout mechanism. The coefficient of the state aid variable is positive and statistically significant at the 0.01 level which indicates that SMSAs with higher than average state aid will not stratify according to income levels to the extent they would otherwise. The estimates of selected socioeconomic variables are also worth noting. The impact of increasing the percentage of nonwhites in the population upon the degree of income stratification is ambiguous. If nonwhites, either due to personal preferences of locating near individuals with similar cultural and economic backgrounds or due to forced segregation, tend to cluster independently of their income characteristics, then one would expect a positive relationship between within group inequality and percentage nonwhite. If the income distribution of nonwhites is more equal than that of whites, then stratification by race may ameliorate income stratification, leading to an expected negative coefficient on the nonwhite variable. For our sample, a negative relationship is confirmed at the 0.01 significance level. The percentage of school age children, 18 years and under, in an SMSA is entered to reflect the preferences of families for educational services. The sign of the coefficient indicates that educational considerations are important in the choice of local public goods. The results also show a statistically significant positive relationship between the level of total inequality and the ratio of within to total inequality. One might expect that since an increase in total inequality causesa greater disparity within the population of relative tax burdens of families and their preferences of local public goods, there would be a greater incentive for families to stratify.
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CONCLUSION There are really two Tiebout hypotheses. One is the net benefit capitalization effect of the market clearing process for a given public good partitioning of the population. The other is the homogeneity of income within jurisdictions which emergesas a result of the dynamic sorting or partitioning process. Previous tests of the first hypothesis have produced conflicting results as well as various interpretations of what is actually causing the capitalization effect. By employing a little-used though powerful decomposable measure of inequality, we have been able to test empirically the relationship between jurisdiction homogeneity and the number of jurisdictions. The results of our sample indicate that an increase in the number of local jurisdictions promotes within community homogeneity thus confirming the second Tiebout hypothesis. ACKNOWLEDGMENTS The authors wish to thank Ray Battalio, Gerry Goldstein, Mark Pauly, and an anonymous referee for helpful comments on an earlier draft of this paper.
REFERENCES I. T. Bergstrom and R. Goodman, Private demands for public goods, Amer. Econ. Reo., 290-296, (June 1973). 2. T. E. Borcherding and R. B. Deacon, The demand for the services of non-federal government, Amer. &on. Rev., 891-902 (December 1972). 3. Jan K. Brueckner, Property values, local public expenditure and economic efficiency, J. Pubhc Econ., 2,223-245 (April 1979). 4. Francois Bourguignon, Decomposable income inequality measures, Econometrrcu,47, No. 4, 901-920 (July 1979). 5. J. M. Buchanan and C. J. Goetz, Efficiency limits of fiscal mobility, J. Publrc Econ., 1, 25-44 (February 1972). 6. Bryan Ellickson, The politics and economics of decentralization, J. Urban Econ., 4, 13% 149 (April 1977). 7. D. Epple, A. Zelenitz, and M. Visscher, A search for testable implications of the Ttebout hypothesis, J. Pubbc Econ., 86, No. 3, 405-425 (June 1978) 8. T. J. Gronberg, The interaction of markets in housing and local public goods: A simultaneous equations approach, Southern Econ. J., 445-459 (October 1979). 9. Bruce W. Hamilton, Zoning and property taxation in a system of local governments, Urban Studtes, 12, 205-21 I (June 1975). IO. Bruce W. Hamilton, Capitalization of intranuisdictional differences m local tax prices, Amer. Econ. Rev., 66, No. 5, 743-753 (December 1976). Il. B. Hamilton, E. Mills, and D. Puryear, The Tiebout hypothesis and residential income segregation, m “Fiscal Zoning and Land Use Controls” (Edwin S. Mills and Wallace E. Oates, Eds.), Heath, Lexington, Mass., 1975. 12. Irving Hoch, Income and city size, Urban Studtes, 9, 299-328 (October 1972). 13. M. McGuire, Group segregation and optimal Jurisdictions, J. Pol Econ., 82, No I, Il2- 132 (January/February 1974)
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14. Wallace E. Oates, The effects of property taxes and local public spending on property values: An empirical study of tax capitalization and the Tiebout hypothesis, J. Pal. &on., 77, No. 6,957-971 (November/December 1969). IS. H. Pack and J. Pack, Metropolitan fragmentation and local public expenditure, Nat. Tax J., 31, 349-362 (December 1978). 16. G. Pyatt, On the interpretation and disaggregation of Gini Coefficients, Econ. J., 86, 243-255 (June 1976). 17. H. Theil, “Economics and Information Theory,” Amencan Elsevier, New York, NorthHolland, Amsterdam, 1967. 18. Charles M. Tiebout, A pure theory of local expenditure, J. Pol. .&on., 64, No. 5, 416-424 (October 1956).
OF URBAN
ECONOMJCS
Jurisdictional
10,227-
239 (198 1)
Homogeneity Hypothesis
and the Tiebout
RANDALL W. EBERTS Department of Economtcs,Unrversq
of Oregon,
Eugene, Oregon 97403
AND TIMOTHY J. GRONBERG Texas A & M Unwersity, College Station, Texas 77843 Received April 24, 1980; Revised July 10, 1980 In this paper, an alternative to the caprtalizatroonapproach to testing the Trebout model is presented. The Tiebout foot votmg mechanism suggests that households will sort and stratify into (approximately) homogeneouslocal public goods jurisdictions. At a point in time, the efficiency of the sort will be positively related to the number of existing jurisdictions. Using a measure of homogeneity introduced by Theil, the relationship between stratification (homogeneity within Jurisdiction) and number of jurisdictions is tested. For a sample of school districts within 33 SMSAs, the Tiebout stratification hypothesis is confirmed. I. INTRODUCTION
Since its inception in 1956, Tiebout’s [ 181theory of a marketplace in local public goods has provided the foundation for numerous theoretical and empirical models of public sector allocation. Much of the theoretical attention has focused upon the normative efficiency properties of the Tiebout migration allocation mechanism (see, for example, Buchanan and Goetz [5] and Hamilton [9]). The empirical work, pioneered by Oates [ 141, has centered upon an investigation of the capitalization of net public goods benefits into property values. Significant capitalization findings have been viewed as supporting the relevance of the Tiebout model as a positive theory of household behavior. At both the theoretical and the empirical level, the extant Tiebout literature emphasizes the importance of local public sector variables in determining the properties of market clearing housing (land) prices. This emphasis upon the characteristics of equilibrium prices within the Tiebout setting has served to obscure a second conjecture in the original Tiebout paper. As an outcome of the local public goods allocation process, Tiebout suggeststhat communities will consist of (approximately) homogeneous public goods demand groups. This result, which has been derived more formally by Epple et al. [7], follows from the market properties of the 227 0094-l 190/8 l/050227- 13$02.00/0 Copyn&t 0 198 I by Acadermc Press. fnc Au n&s of reproduction m any form reserved
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Tiebout process. In a perfect Tiebout world, consumers face a posted market price for local public goods. Consumers determine their optimal public (and private) goods bundle at the prevailing price(s), and shop in the marketplace in communities in an effort to match that bundle. Consumers with identical demands will, therefore, locate within the same community. If tastes are relatively constant across income classesand the income elasticity of demand for public goods is nonzero, then homogeneous grouping by public goods demand implies homogeneous grouping by income. Thus, a second hypothesis derived from the Tiebout model is that public goods jurisdictions will stratify the population by income class. In this paper we attempt to assessthe validity of the Tiebout stratification hypothesis. Our approach utilizes Theil’s [17] entropy measure of income inequality in quantifying the concept of homogeneity. Given a division of population into independent groups, the Theil measure allows for the decomposition of population inequality (heterogeneity) into a weighted sum of inequality within and between the groups. Treating an SMSA as a population and school districts as independent groupings of that population, we decompose total SMSA inequality into the sum of between and within school district inequality. Using a sample of 33 SMSAs, we generate a series of observations on the degree of heterogeneity (stratification) within school districts. We then treat the ratio of within district heterogeneity to total heterogeneity as a dependent variable in a single equation regression model. Our attention is focused upon the coefficient of the number of school districts within the SMSA.’ A positive relationship between the number of public goods jurisdictions and the degree of stratification (homogeneity) is suggestedby the Tiebout model. For our sample, the empirical evidence supports the stratification hypothesis. ‘Hamilton ef al. [I I] have also tested the stratification hypothesis by examining the relationship between income inequality and number of school districts. Our study is differentiated from theirs in two significant ways. First, we utilize the Theil inequality measure rather than the Gini coefficient measure employed by Hamilton er al. The Theil decomposability property, in turn, allows us to obtain a smgle measure of jurisdictional homogeneity for each SMSA. We feel that this provides a better statistical framework for testing the stratification hypothesis than the Hamilton et al. approach which involved sampling among the Gini values of individual jurisdictions. Secondly, our data set is defined over school districts rather than over census tracts. In a second related study, Pack and Pack [ 151have investigated the relationship between income heterogeneity (as measured by the coefficient of variation in income), demand heterogeneity, and Lindahl pricing for local public services.They argue that the observed degree of income heterogeneity among communities m their sample requires that Tiebout’s stratification hypothesis be rejected. Our study can be vrewed as a response to their suggestion that “more complicated versions of the model, for example, suggesting that actual observations are a snapshot of a system moving towards equilibrium could reconcile our evidence with the theory” (Pack and Pack [15, p. 3571)
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Section II provides a sketch of the Tiebout model. Particular emphasis is placed upon differentiating between the capitalization and the stratification processes. Section III presents our empirical methodology, including a discussion of the properties of the Theil inequality measure. In Section IV the regression results for our sample are listed and discussed, and conclusions are drawn. II. THE TWO TIEBOUT HYPOTHESES Consider an economy divided into M spatially separated labor markets. Assume that there is perfect migration of labor within each market and zero migration across markets. The equilibrium distribution of wageswithin each market is determined by the demand and supply conditions internal to that market. Given the distribution of population across markets, the distribution of skills within each market, the leisure-labor preferences of individual workers, the spatial distribution of workers and firms and the derived demand curves for labor (by skill category), an equilibrium distribution of wages will emerge for each labor market area. Assume that each labor market is itself divided into G contiguous political jurisdictions. The emergence of these political units is motivated by the desire for collective provision of certain types of goods and services (e.g., those possessing the joint characteristics of economies in consumption and nonexclusion). Each jurisdiction or community is assumed to provide a uniform quantity of a single local public good. The publicly provided commodity is local in the sense that there are no interjurisdictional spillover benefits. We assume further that the public good is congestable in the sensethat the cost of providing a given level of the good is dependent upon the level of population in the community. The provision of the public good by each local fist is financed through a proportional tax on the value of residential property. Under this type of financing arrangement, the Lindahl share price of the public good to any citizen is determined by the percentage of the community housing stock which he owns. The level of the public good within each community is determined by a majority voting process, with the equilibrium outcome reflecting the preferences of the median voter. Under the assumptions of preference homogeneity and a positive income elasticity of demand for housing, each community public goods offering can be written as a function of the median share price (which is the share price of the median income household), median income, and the prices of private goods, including housing. It is assumed that all nonhousing private goods are available at uniform prices throughout the economy. The price of housing, however, may vary due to capitalization effects. As argued in Hamilton [lo] and developed more rigorously in Brueckner [3], perfect migration within a labor-housing market implies the equaliza-
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tions of utilities, in equilibrium, across the communities of that market by income class. The bid rent (constant utility) offered by identical income households for identical sites in different fiscal environments, i.e., different tax-price-public goods combinations, will vary according to the potential consumer surplus associated with each local public goods offering. The equilibrium market rent profile across communities will, due to perfect mobility, leave identical consumers on the same individual bid rent curve. Thus, the redistribution of real income (utility) affected through the local public sector is precluded by migration. This is the essenceof the concept of capitalization of net fiscal benefits into property values. If the migratory process leads to compensating variations in housing prices, then sites in income homogeneous and nonhomogeneous communities are rendered equally desirable in locational equilibrium. If utilities to high income individuals are the same in both homogeneous and nonhomogeneous communities, is there an economic motivation for the formation of homogeneousjurisdictions? In other words, do the Hamilton and Brueckner results refute the Tiebout hypothesis concerning metropolitan fragmentation and segregation according to public goods demand (by income class in our model)? We would argue that the capitalization type models deal with a different analytical problem than the segregation hypothesis. The capitalization literature attempts to characterize the set of housing prices which will support an allocation of households among a fixed set of public goods locations. If identical consumers are allocated to different locations, the value of their indirect utility functions must be the same when evaluated at the equilibrium prices and the given public goods-tax parameters. The equilibrium prices sort households among communities such that the resulting allocation is individually incentive compatible (i.e., no individual has an incentive to relocate). These models thus serve to formalize Tiebout’s notion of a “foot voting” equilibrium. The tendency of the urban system towards homogeneous public goods jurisdictions, however, is a dynamic theory of group formation. The static equilibrium Tiebout models do raise an important point in considering the dynamics of the system. They serve to indicate that stratification is not the direct result of the desire of individuals to avoid redistribution per se. Rather, two plausible alternative rationales exist to explain why the population will tend to coalesce into stratified political units. Both explanations are motivated by the realization that capitalization equilibrium is a Nash concept. First, a partitioning of the population into heterogeneous communities may be supported by a set of prices in a Nash sense,but the resulting equilibrium may not prove to be group incentive compatible.2 As “The long-run equihbrium stratification by adjacent income classesdeveloped in Epple et al. [7] is consistent with our analysis. Within their analytical framework, with partitioning treated as endogenous in the long run, exhaustion of potential gains from trade yields a stratified solution.
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developed in papers by McGuire [13] and Ellickson [6], the globally Pareto efficient provision of congestable public goods in an economy with heterogeneous tastes and/or endowments requires that the population stratifies into homogeneous consumption clubs.3 In terms of the static model outlined above, the equilibrium level of utility under the stratified partitioning of the population is potentially greater for both high- and low-income individuals than that which obtains relative to a mixed partitioning. Therefore, gains from trade exist in moving from heterogeneous to homogeneous local public goods jurisdictions. During the evolutionary process of metropolitan fragmentation, developers and/or politicians will be in a position to exploit these potential gains through institutional arrangements (e.g., zoning) leading to income stratification. Second, households participate in two markets in local public goods. They vote with their feet relative to a fixed vector of offerings, and they vote with the ballot box within their present community to consider changing one element of that vector. Within a heterogeneous community, given the prevailing set of tax prices, the majority voting choice of G will reflect the optimizing choice of the median income household. The remaining community members will find themselves consuming a nonoptimal quantity of the local public good. In order to avoid frustration through the public choice decision process, there will exist a tendency for individuals with similar public goods demand curves to combine into collective units. Successin appropriating gains from stratification should be reflected in greater jurisdictional fragmentation of a given labor market area. If Tiebout’s hypothesis concerning the existence of a local public goods stratification process holds, then we would expect, ceteris paribus, a positive correlation between the number of public goods jurisdictions and jurisdictional homogeneity. In the next section we propose a methodology for testing this hypothesized relationship between income homogeneity and jurisdictional fragmentation. III. TESTING THE STRATIFICATION
HYPOTHESIS
Returning to our original labor market scenario, we pose the following question: Does the number of public goods jurisdictions within a given labor market prove to be a significant variable in explaining the variance in jurisdictional income homogeneity across labor markets? As developed in Section II, the Tiebout stratification hypothesis suggestsa positive correlation between homogeneity and degree of fragmentation.4 ‘These results rest upon the assumption of sufficient numbers of each consumer type for efficient group formation. The Epple ef al. [7] heterogeneous(but stratified) long-run solution follows from the alternative assumption of insufficient numbers for the achievement of perfect homogeneity. 40bviously, m the limrt a one-to-one correspondence between Jurisdictions and consumers yields homogeneity. This limiting property is irrelevant for our purposes.
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However, it may be the case that the number of jurisdictions when entered in the model with the population of the labor market serves as a proxy for the average population of the jurisdictions. Thus the positive correlation observed between the homogeneity measure and the number of jurisdictions may not be entirely due to the Tiebout hypothesis. For a host of reasons unrelated to the Tiebout hypothesis, individuals tend to live near others of their own income level. Given the distribution of incomes within the local labor market, as the population of a typical jurisdiction increases,a greater number of the segregated income groups will be included in the jurisdiction which increases the level of heterogeneity. Fortunately, the two effects can be disentangled by including in the linear model of income stratification a variable which measures the average population size of jurisdictions within the local labor markets.5 Thus, in order to test the Tiebout stratification hypothesis, the homogeneity measure is regressedagainst the number of jurisdictions, the average population size of jurisdictions plus selected socioeconomic variables designed to hold constant the economic, geographic, and demographic characteristics across the labor markets. The empirical specification of the model requires three transitional definitions. We define labor market boundaries to be coterminous with SMSA boundaries. To the extent that within SMSA mobility exceedsacross SMSA mobility, this assumption is validated. Within each SMSA we define school districts as the relevant public goods jurisdiction. Obviously there exists a vector of local public goods offerings in each labor market, with different geographical boundaries associated with the various elements of that vector. Consistent with the bulk of the Tiebout empirical literature, we assume that educational services represent the dominant public goods factor in locational decisions. Finally, we define jurisdictional homogeneity in terms of Theil’s [ 171entropy measure.The Theil measure of income inequality proves to be particularly useful in testing the stratification hypothesis due to its decomposability properties, which we discuss briefly below. The degree to which the Tiebout mechanism precipitates a rational sorting of individuals can be measured by the relationship between the distribution of income within a community and the distribution between communities. It follows that a perfect Tiebout world is one in which there is perfect homogeneity within each community6 and the inequality of the 5We are indebted to the referee for suggesting this possibility. Including both the number of jurisdictions and the average population of the jurisdictions may create a problem of multicollinearity. However, the simple correlanon between the two variables IS not statistically significant, which partially allays some of the fears. ‘The Tiebout analysis actually suggests sorting by public goods demand, which is a function of both income and preferences. That income itself is an important determinant of local public goods demand is well established. (See Bergstrom and Goodman [I]. Borcherding and Deacon
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SMSA is totally accounted for by the inequality between communities. It is, therefore, crucial to any analysis of the relationship between the number of jurisdictions and the level of within community inequality that the inequality measure be decomposed exclusively into within and between set components. A recent article by Bourguignon [I9741 demonstrates that Theil’s entropy measure of inequality is the only inequality measure that can be decomposed satisfactorily into the appropriate components of within and between community inequality measures.’ The Theil measure defines inequality in the following manner:
where N: G: y: Yg: Ng: s,:
Number of individual families in the SMSA; number of communities or jurisdictions in the SMSA; individual i ‘s share of the total income in SMSA; community g’s share of SMSA income; number of families in community g; set of families in community g.
The Theil inequality measure expresses the total inequality of a population as the sum of the between community inequality (the first term on the right in Eq. (l)), and the within community inequality (the second term on the right). The between set inequality relates community g’s actual share of the total SMSA income to its share if all income were divided equally among all communities. When income is distributed equally, that is when community g’s income share equals its population share, the between set inequality measure equals zero. Stated slightly differently, there is a maximum of homogeneity between communities when the average income of each community is equal. The within community component compares individual i’s share of total income in community g with his share if all income in community g were distributed equally among its residents. Again, if income is distributed [2], and Gronberg [8]). We assume here that the distribution of income serves as an adequate approximation to the distribution of demand for public goods. To the extent that our socioeconomic variables fail to account for variation in tastes, however, the potentldfor biasis introduced. ‘More accurately, the Theil measure is the only satisfactory income weighted decomposable inequality measure. Bourguignon introduces a population-weighted decomposable measure in the paper which satisfies his evaluative criteria
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equally, the within set inequality measure equals zero. The relative share of each individual as compared with their aliquot share is weighted by the individual’s actual share of community g’s income. These weighted individual measures are summed over all individuals in community g to yield a within set inequality measure for each community. In turn, each within community inequality measure is weighted by the community’s share of total income and summed to yield the total within community inequality for the SMSA. Theil’s measure possessesthe following properties: (1) it is symmetric with respect to population size, (2) homogeneous of degree zero in income, and (3) additively decomposable into between and within group components. The first two conditions are intuitively straightforward. The symmetry condition reflects the anonymity rule that the personality or preferences of income earners are irrelevant to the measure of inequality. It implies that the Theil inequality measure is invariant to the replication of a given distribution. Consequently, the size of the population of the SMSA will not bias the inequality measure, holding the distribution of incomes as fixed. The income-zero homogeneous property assuresthat the inequality measure is invariant when all incomes are multiplied by the same scalar. This guarantees that any systematic relationship between population size and income levels (Hoch [ 121)will not bias the measurement of inequality. The additively decomposable characteristic permits the total inequality of a population to be divided into mutually exclusive groups. This has a considerable advantage over nondecomposable inequality measures such as the popular Gini coefficient. Pyatt [16] demonstrates that the Gini coefficient can be divided into mutually exclusive groups only if homogeneity is perfectly obtained within communities. Any heterogeneity within groups will cause the distributions of the different communities to overlap, biasing the within community inequality measure. Theil’s measure of inequality has an interesting interpretation for the Tiebout mechanism. The within group population shares can be thought of as prior probabilities of what one might believe would result if the Tiebout mechanism worked perfectly. The within group income shares are the posterior probabilities of the Tiebout event. The ratio between the two indicates the relative efficiency of the mechanism. Perfect efficiency implies that the ratio is unity, and the corresponding inequality measure is zero. IV. ESTIMATION RESULTS The analysis is performed on 34 SMSAs within seven states (California, Illinois, Iowa, Michigan, Missouri, New York, and Wisconsin). Unified school districts are chosen as the political jurisdictions for reasons mentioned earlier and also because they provide for mutually exclusive and
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coterminous delineations of the SMSAs. The number of school districts within the selected SMSAs ranges from 2 to 39 and the total number of families within the metropolitan areas varies from 16,829 to 402,765. Income distributions are calculated from 1970 Census data broken down by school districts. Incomes in each community are divided into 15 brackets with the midpoint of each interval serving as the mean. The mean income of the open-ended bracket is approximated by the mean of the Pareto distribution for this range.* The spirit of the Tiebout hypothesis of homogeneous political formation can best be captured by expressing within jurisdiction inequality as a percentage of total inequality within the SMSA. In this form, one would expect that as the number of jurisdictions increases, the percentage of total inequality accounted for by the within group component should decrease.’ So far we have considered the number of jurisdictions to be exogenous. However, through political actions individuals have actively sought to influence the number of school districts. In the past state legislatures have made a conscious effort to improve efficiency by consolidating school districts. For example, Iowa enacted a law “to encourage the reorganization of school districts into such units as are necessary, economical, and efficient.. . ” (Iowa Annoted Code, para. 275.1). Other states have passed similar legislation. The possibility of endogeneity is examined by first regressing the number of jurisdictions on dummy variables which are entered to represent the different policies and historical trends among the seven states included in the sample.lo Even though the system is recursive, we assume that the error terms in the two equations are correlated since stratification is a result of both individual and collective decisions. The predicted values of the number *The11 shows that if the midpoint of each bracket is used and the midpoint of the open interval is approximated by the Pareto distribution, the error in most casesis of the order of 1% of a nit. A nit is a term borrowed from information theory to describe the informational content of a message. The units themselves are not important but what is crucial is their relative position between perfect equality (0 nits) and perfect inequality (log N nits) where N is the number of individuals in the population. 91t should be recognized that since within and between set inequalities sum to total inequality by construction of the measure, the percentage of within and between set inequality will sum to unity. Thus, correlation between error terms across equations may exist, This normally requires the use of ZelIner’s seemingly unrelated equations technique, but since one of the two equations is redundant, ordinary least squares is appropriate and will yield consrstent. unbrased, and efficient estimates. “The following results were found to explain the number of Jurisdictions: JUR = 9.85 + 2.94 ILL - 1.86 IA + 13.81 A40 + 24.94 NY + 2.14 WN (3.25) (0.62) (0.37) (2.49) (5.31) (0.43) + 4.81 MI (1.08)
R2 = 0.60.
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of jurisdictions (along with the predicted values of average size) are entered into the homogeneity equation. Comparing the instrumental variable estimates with OLS estimates substantiates the fact that OLS estimates are biased downward and inefficient. Consequently, our comments will be confined to the results of the instrumental variable estimation. The estimates of the stratification equation are displayed in Table 1. Both the Tiebout hypothesis and the average size hypothesis are supported at acceptable confidence levels. The coefficient of the number of jurisdictions is negative and statistically significant at the 0.05 level. Thus, with an increase in alternatives, individuals will sort themselves into more homogeneous public goods jurisdictions. The coefficient of the average population TABLE I Estimates of the Income Stratification Equation Using Both Instrumental Variables and OLS Techniques* Dependent variable: Percentage of within district inequality IV** oLs**
Explanatory variables -__ Constant
Number of school districts*** Average size of school districts Number of families in SMSA Percentage of school revenues per student received from state Percentage of SMSA urbanized Percentageof nonwhite SMSA population Percentage change in number of households Percentage of SMSA population 18 years and under Total inequality of SMSA
Ill.59 (45.54) - 0.12 (5.88) o.OOQ2 (1.93) - 0.00002 (3.76) 0.09 (6.64)
95.07 (24.49) - 0.05 (1.W 0.0003 (8.91) - 0.00003 (8.18) 0.05 (3.36)
- 0.01 (0.65) - 0.24 (5.91) 003 (6.43) - 0.27 (5 73) - 0.16 (2.31)
003 (1.42) - 037 (6.28) - 0.01 (1 53) - 0.02 (0.37) 0.08 (1.03)
SSE (corrected for 24.94 Heteroscedasticity) 23.75 19092 173.49 SEE (uncorrected) ~-_____ ‘Heteroscedasticity corrected by wetghting by the estimated residuals. **Values in parentheses are f statistics. ***See Footnote 10 for the estimates of the Jurisdiction regression.
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size of jurisdictions is positive and statistically significant at the 0.05 level. The positive coefficient suggeststhat given a level of income inequality for the total SMSA, an increase in the population of a single jurisdiction will be associated with an increase in the percentage of the inequality contained within the jurisdiction. This reflects the fact that jurisdictions with larger populations can encompassa greater range of income levels. Therefore, even though individuals consciously sort themselves into homogeneous groups, the degree of homogeneity depends upon the population of the school districts. In addition to the effect of state reorganization policies on the sorting decisions of individuals, the amount of state funding of local school districts may also distort individual decisions. A major reason for state funding is to reduce the fiscal disparity. SMSAs in states with generous funding would be expected to be less stratified since the advantages and disadvantages of compensatory mixing is attenuated. The percentage of per capita revenue for local public education received from state funds is entered to measure the impact of intergovernmental grants upon the Tiebout mechanism. The coefficient of the state aid variable is positive and statistically significant at the 0.01 level which indicates that SMSAs with higher than average state aid will not stratify according to income levels to the extent they would otherwise. The estimates of selected socioeconomic variables are also worth noting. The impact of increasing the percentage of nonwhites in the population upon the degree of income stratification is ambiguous. If nonwhites, either due to personal preferences of locating near individuals with similar cultural and economic backgrounds or due to forced segregation, tend to cluster independently of their income characteristics, then one would expect a positive relationship between within group inequality and percentage nonwhite. If the income distribution of nonwhites is more equal than that of whites, then stratification by race may ameliorate income stratification, leading to an expected negative coefficient on the nonwhite variable. For our sample, a negative relationship is confirmed at the 0.01 significance level. The percentage of school age children, 18 years and under, in an SMSA is entered to reflect the preferences of families for educational services. The sign of the coefficient indicates that educational considerations are important in the choice of local public goods. The results also show a statistically significant positive relationship between the level of total inequality and the ratio of within to total inequality. One might expect that since an increase in total inequality causesa greater disparity within the population of relative tax burdens of families and their preferences of local public goods, there would be a greater incentive for families to stratify.
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CONCLUSION There are really two Tiebout hypotheses. One is the net benefit capitalization effect of the market clearing process for a given public good partitioning of the population. The other is the homogeneity of income within jurisdictions which emergesas a result of the dynamic sorting or partitioning process. Previous tests of the first hypothesis have produced conflicting results as well as various interpretations of what is actually causing the capitalization effect. By employing a little-used though powerful decomposable measure of inequality, we have been able to test empirically the relationship between jurisdiction homogeneity and the number of jurisdictions. The results of our sample indicate that an increase in the number of local jurisdictions promotes within community homogeneity thus confirming the second Tiebout hypothesis. ACKNOWLEDGMENTS The authors wish to thank Ray Battalio, Gerry Goldstein, Mark Pauly, and an anonymous referee for helpful comments on an earlier draft of this paper.
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14. Wallace E. Oates, The effects of property taxes and local public spending on property values: An empirical study of tax capitalization and the Tiebout hypothesis, J. Pal. &on., 77, No. 6,957-971 (November/December 1969). IS. H. Pack and J. Pack, Metropolitan fragmentation and local public expenditure, Nat. Tax J., 31, 349-362 (December 1978). 16. G. Pyatt, On the interpretation and disaggregation of Gini Coefficients, Econ. J., 86, 243-255 (June 1976). 17. H. Theil, “Economics and Information Theory,” Amencan Elsevier, New York, NorthHolland, Amsterdam, 1967. 18. Charles M. Tiebout, A pure theory of local expenditure, J. Pol. .&on., 64, No. 5, 416-424 (October 1956).