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1 A Search for Testable Implications of the Tiebout Hypothesis Author(s): Dennis Epple, Allan Zelenitz, Michael Visscher Source: The Journal of Political Economy, Vol. 86, No. 3 (Jun., 1978), pp Published by: The University of Chicago Press Stable URL: Accessed: 01/02/ :10 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. The University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to The Journal of Political Economy.

2 A Search for Testable Implications of the Tiebout Hypothesis Dennis Epple Carnegie-Mellon University Allan Zelenitz University of Pittsburgh Michael Visscher Ohio State University This paper derives an econometrically meaningful test of the Tiebout hypothesis and demonstrates that previous tests are inappropriate. The implications generated by two closely related models of voter-determined local fiscal variables and individual resident housing choices are compared. We demonstrate that when the Tiebout mechanism operates without interference, housing quantity and location choices are Pareto efficient, while they are not when frictions interfere with its operation. We show that the appropriate test requires joint estimation of a set of structural equations determining housing purchases and locational choices utilizing data for both median and nonmedian voters across metropolitan area jurisdictions. I. Introduction The last 8 years have produced a number of empirical studies designed in part to verify the validity or operation of the Tiebout hypothesis. The test procedure of these studies has almost invariably been through an assessment of the relation between local fiscal variables and the value or We wish to acknowledge helpful suggestions received from Bruce Hamilton, Judy Lave, Jack Ochs, Tom Romer, Katherine Schipper, members of the University of Chicago Urban Economics Workshop, and members of the Carnegie-Mellon University Public Choice Group. [Journal of Political Economsy, 1978, vol. 86, no. 3] (? 1978 by The University of Chicago /78/ $

3 406 JOURNAL OF POLITICAL ECONOMY amount of median family housing. The assumption, explicit or implicit, underlying these tests is that such relationships are implications of the Tiebout hypothesis. The purpose of this paper is to demonstrate that this assumption is not necessarily correct and that tests based on it do not produce econometrically meaningful tests of the Tiebout hypothesis. In his path-breaking study, Oates (1969) reasoned that the Tiebout hypothesis is based on the notion that individuals are aware of the available local fiscal environments and that they are willing to bid up the entry fee (i.e., housing prices) in those localities with lower tax rates for a given level of public services or those with a larger bundle of services for a given tax rate. Thus, he argued, if the Tiebout hypothesis is correct, local governmental tax and spending levels should significantly affect housing prices. Although some objected to his data, variables, or econometric techniques (see Oates 1973; Pollakowski 1973; Gustely 1976), the major objection was to his specification of the econometric tests and to his interpretation of the test results (see Edel and Sclar 1974; Hamilton 1975b, 1976). The specification controversy is whether, and to what extent, housing values (and/or rents) are affected by local property taxes and expenditures. Edel and Sclar (1974) and especially Hamilton (1 975a, 1976) have pointed out that in a fully adjusted Tiebout equilibrium local property taxes are pure benefit taxes, that is, they are regarded by individuals as the price of the local government services. Therefore, neither expenditures nor taxes should have any relation to the taxed commodity's (housing's) market price. Their econometric prediction in support of the Tiebout hypothesis is just the opposite of Oates's. Indeed, their criticism of Oates is that he was testing not for the presence but for the absence of a Tiebout mechanism. They further argued that whenever a correlation exists between housing prices and fiscal variables the system of local governments is not in full Tiebout equilibrium. As an alternative to testing for the "capitalization" of fiscal variables into local housing values, Hamilton has argued that the more local communities are like those described by Tiebout the less effect will fiscal variables have upon the quantity of housing chosen by individuals. We believe that this disagreement over the appropriate procedure for testing the Tiebout hypothesis arises for the following reasons: 1. While the maintained hypothesis is Tiebout's, the alternative hypothesis is not explicitly stated. Thus, it is not clear what one should find if the Tiebout hypothesis is incorrect. If there is not a perfect balancing between taxes and public benefits in each community, what then are the means of discerning this imbalance? The usual test is some assessment of the capitalization of taxes and/or benefits into housing values, prices, or rentals. But it is not clear why both benefits and taxes should be capitalized, or, as Hamilton (1975b) argued, only taxes. In fact, it is not clear why any capitalization should occur at all.

4 IMPLICATIONS OF THE TIEBOUT HYPOTHESIS The reason for this ambiguity is that the econometric equations purporting to test the hypothesis have not been derived from a formal model. Instead, specifications of the econometric equations have been based upon intuitive arguments about the consequences of the Tiebout mechanism. What is required is an explicit model which can generate testable hypotheses. 3. The implications of the factors which prevent full achievement of a Tiebout equilibrium are not clear. Implicit assumptions about the elasticity of supply of land and the effects of unique locational attributes (such as accessibility to places of employment) of individual jurisdictions have not been fully articulated. As a consequence, the question of the validity of the Tiebout hypothesis has been confused with the question of the incidence of the local property tax. In the following sections two closely related comparison models of local government finances and housing choice are specified. Our goal is not to model the complexity of the urban environment or of government decision making. Nor is our goal to explain or give a full exposition of what Tiebout "really" said or meant. Rather, our goal is to examine the circumstances under which an econometric test can be formulated which will distinguish between a metropolitan area composed of communities like those described by Tiebout and one which is composed of communities without those features. However, our interpretation of Tiebout (1956) is inherent in our analysis. The Tiebout hypothesis is an ingenious theory designed to explain how sets of locally provided public goods could be determined in a Pareto-efficient manner through a mechanism of individual self-interest. Essentially, Tiebout maintained that, given an infinite spectrum of localities offering (balanced-budget) bundles of public goods and taxes, individuals optimize via locational choices. We believe that the two essential features of the Tiebout hypothesis are the following: (1) rationality-that each individual will choose his best perceived opportunity in selecting a place to live based upon fiscal as well as housing variables (i.e., people truly will "vote with their feet"); and (2) that through the mechanism of individual selection of residence, deadweight loss arising from local taxes is reduced and under certain conditions is completely absent. Our contention is that any test of the Tiebout hypothesis must concentrate on the latter feature. At question is not the simple presence or absence of the suggested rational behavior; it is a fundamental tenet of neoclassical theory that people promote their own interests when able to do so. Instead, the questions are whether and to what extent the mechanism of rational locational choice can reduce the deadweight loss of taxation, and whether the degree to which that reduction is achieved can be distinguished by examination of fiscal and housing variables. By specifying different economies of scale in the production of govern-

5 408 JOURNAL OF POLITICAL ECONOMY ment services, we generate two comparison models. One of the modelsthat of the Tiebout community-contains what we believe to be the essential Tiebout result, the absence of an excess burden associated with individual choices of fiscal variables, the taxed commodity (housing), or any other commodity; it is a Pareto-efficient result. The alternative model that of the heterogeneous community-is one in which an excess burden obtains. In addition to demonstrating that the pure Tiebout result and an understandable alternative can be obtained from simple theoretical models, we ask how the presence or differential in excess burden could exhibit itself in the relation between fiscal and housing variables. Our goal again is to discern whether and how two such representative models could be econometrically distinguished. WVe show that such models and, by inference, the analogous real-world communities are not distinguishable by the econometric tests employed to date. II. The Tiebout Mechanism and an Alternative In this section we investigate taxation, government-spending, and housingpurchase decisions in two types of jurisdictions. Conceptually, we are thinking of a metropolitan area (or its suburban portion) composed of communities of one type or the other. Ultimately, we are seeking a way of discovering which type of community exists. We assume that taxation and spending decisions in each of these jurisdictions satisfy the preferences of the median individual.' We also assume that individuals' preferences and incomes and the factor-supply functions for the metropolitan area are invariant with the type of community. The models of the jurisdictions will be made to differ according to whether scale economies in the production of government services are assumed to be absent or present. All other differences between the models are derivative of the difference in the scale-economies assumption. In our model of the Tiebout community we will assume constant returns to scale in the provision of local government services. Alternatively, in our model of the heterogeneous communities we will assume that scale economies are present, in that a minimumsize community must be established to provide the public service. While Tiebout (1956, p. 419) assumed U-shaped cost curves, we find this simple dichotomy both acceptable and revealing for our needs. In particular, this artificial but simple dichotomy is sufficient to have one model, that of the Tiebout community, generate the pure Tiebout result with regard to the absence of deadweight loss, and one model, that of the heterogeneous ' One of the difficulties in analyzing problems involving collective decisions is the lack of a well-developed model of the decision-making process. While median voter theory provides a convenient framework for analysis, work on alternative and perhaps more realistic models is under way (see Romer and Rosenthal [1976]).

6 IMPLICATIONS OF THE TIEBOUT HYPOTHESIS 409 community, which does not. We demonstrate that this crucial difference between the two models is exhibited in the form of the resulting housingdemand equations. We then consider whether the alternative models lead to sets of equations which are econometrically distinguishable. A. The Tiebout Community We assume that all individuals in the Tiebout community have the same utility function, U(G, H, B), over government services, G; housing, H; and the numeraire bundle, B. In addition, all individuals have the same income, L All factors including land are assumed to be in perfectly elastic supply to the community, so that housing produced from land and nonland factors is available at a constant price, PH. Local expenditures are assumed to be financed entirely from a residential property tax applied at the same rate, t, to both land and improvements. Thus the property tax does not distort the choice of housingfactor inputs. The single governmental good is consumed at the same level by all residents of the community. However, it is a local rather than a pure public good; the cost of supplying an additional individual is PGG, where PG is the unit cost of the good, assumed to be constant. The budget constraint for the individual is then: I = PHH(l + t)?b. (1) where the price of the numeraire bundle is unity. The governmental budget constraint is: tnphh = NPGG, (2) where N is the community population. Following Hamilton (1975a), we assume that the local government can establish restrictions, such as zoning, to effectively regulate the minimum amount of housing individuals must purchase to be allowed as community members. Thus each individual votes not only for his preferred tax rate and spending level, but also for the minimum housing purchase, knowing that whatever restriction is adopted will be applied uniformly to all. Only tax and spending combinations satisfying the budget constraint are placed on the ballot. Given the above assumptions, the individual voting decision is determined by maximization of the following Lagrangian expression with respect to G, H, B, t,,2, and?2: h = U(G, H, B) + AIl(NtPHH - NPGG) + 2I - PHH(l + t) - B]. (3) Deriving the first-order conditions, substituting for Al in terms of )2, and solving the government budget constraint for t and substituting into

7 4IO JOURNAL OF POLITICAL ECONOMY the private budget constraint, the first-order conditions can be rewritten as: UG = '2PG) (4a) UH = '2PHH (4b) UB = )L22 (4c) I=PHH +PGG + B. (4d) t PGG (4e) PHH As Tiebout asserted, conditions (4a)-(4d), determining the choice of the public and private goods, are identical to the conditions one would obtain if all goods were purchased on the private market. Condition (4e) gives the tax rate implied by this choice of goods. Equations (4a)-(4d) can be solved to obtain the demand functions for housing, government services, and other goods. These functions (omitting that for the numeraire, since it is not of interest) are: H = H(PH, PG, I), (5a) G = G(PH, PG, I). (5b) Equations (4e) and (5) determine the tax rate, housing purchases, and government services in a Tiebout community. We now derive the corresponding set of equations for a non-tiebout community and contrast them with those derived above. B. Heterogeneous Communities As an alternative to the Tiebout model, we assume that there are economies of scale in the production of government services-specifically, that the unit cost of government services expressed as a function of the number of individuals served is L-shaped. Thus heterogeneity arises if the minimum size of the community required by this cost function is larger than the smallest group of homogeneous individuals. We thus assume that all individuals have the same tastes in the heterogeneous community but differ in income due to the necessity of a minimum-size community. As in the Tiebout community, the preferences of the median individual determine the tax rate, the level of government services per capita, and zoning restrictions that effectively fix the minimum housing purchase required for an individual to enter the community.2 First we describe an equilibrium allocation of households in the alter- 2 Where multidimensional decisions are required, we will assume that such decisions are made serially, so that single peakedness of preferences can be assured for each dimension of choice.

8 IMPLICATIONS OF THE TIEBOUT HYPOTHESIS 411 native model and then consider the choice problem of the median voter in each community. We assume, as we did implicitly in the pure Tiebout model, that mobility is costless, that all individuals have perfect information, and that households locate on a "featureless plain." It is clear that there will be incentives, as in the Tiebout model, for individuals with high incomes and like preferences for public services to group together in a single jurisdiction and establish requirements that restrict entry by lower-income individuals. The size of a jurisdiction is determined in part by the type of cost curve assumed, that is, by the minimum size needed to realize the economies of scale. In fact, if the minimum viable size were small enough, this model would reduce to the constant-returnsto-scale model presented in Section IIA. In that model the absence of economies of scale assures the Tiebout result, because each individual may form his own community if he cannot find others just like himself. This homogeneity implies analytic equivalence between public and private goods. Whenever homogeneity is prevented by economies of scale, communities with multiple income classes will be formed, and there can be no equivalence of public and private goods. What are the properties of a long-run equilibrium allocation of individuals among such heterogeneous communities; that is, what structure of communities would emerge when no individual has any further incentive to relocate? (We are not addressing the more difficult question of how any community actually emerges; i.e., we are not describing or analyzing the dynamics of community formation.) The most easily understood equilibrium structure of communities is that which arises when groups in order of decreasing income form communities of minimum size. If S' is the minimum number of households required to form a viable community, then the N wealthiest households can form a community of minimum size. The desire to exclude the (IN + 1)st household is a consequence of the fact that that household would have lower income but would consume the same amount of government services as each other household while contributing less in taxes. To assure that the community does not grow beyond the minimum size, the minimum housing purchase can be set large enough so that the Nth household (the household with lowest income) will just be indifferent between remaining in the high-income jurisdiction or moving to its next best alternative. If the Nth household is just indifferent, then all lower-income households will prefer to live elsewhere, if, as assumed here, households have the same preference function. The next suburb can form with the wealthiest N households among those remaining. Again, the minimum housing-purchase requirement can be just large enough to make the least wealthy household indifferent between that suburb and its next best alternative. The allocation of the remaining households is now obvious. As one moves from right to left

9 412 JOURNAL OF POLITICAL ECONOMY along the metropolitan income distribution, each N households adjacent in wealth form a suburb. Since, by assumption, each household in a suburb must pay the same tax rate and consume the same quantity of the local public good, poor communities cannot make special concessions to wealthier individuals from other suburbs, "bribing" them to move. Thus in equilibrium there is no incentive for any household to move. Wealthier suburbs may have higher per capita government services financed by a tax rate which could quite possibly be the same or even lower than the tax rate in poorer suburbs. Still, lower-income households will not move because the minimum housing-purchase constraint in the wealthy suburbs is set high enough to make such a move unattractive.3 More generally, an equilibrium is a set of communities each of which must have N or more residents. Some and perhaps all of these communities will be heterogeneous if there are fewer communities than there are types of individuals. Each community consists of a spectrum of individuals with adjacent incomes on the ranking of individuals by income. Individuals with incomes smaller than the lowest income in each community will be dissuaded from moving by minimum housing standards set high enough to make the move unattractive. Individuals within a community in voting for housing standards will trade off the desire to minimize community size with the desire not to bind their own housing choices. (Lower standards admit poorer residents that consume the average government expenditure while contributing less than the average amount of tax revenue; higher housing standards apply to residents as well as potential residents, and it is likely that effective standards will require some residents to distort their housing choices.) To recapitulate: although people with similar demands for housing group together in both Tiebout and heterogeneous communities, the segregation of citizens by housing size is complete only in the pure Tiebout suburb. Each suburb in the alternative model achieves or exceeds the minimum necessary size to obtain scale economies in the distribution of government services but blocks immigration by poorer citizens by imposing a minimum housing-purchase constraint. Since all individuals in the heterogeneous community have the same utility function and differ only in their incomes, the median voter will 3The following three assumptions are sufficient but not necessary to assure that a zoning constraint will segregate individuals in a metropolitan area into income classes. (1) Housing is a normal or superior good, and desired housing purchases increase without bound as income increases without bound. (2) An arbitrarily chosen individual, if housing purchases are unconstrained, would prefer a wealthy community to a poor community at the tax-rate and government-spending levels chosen by the median in each community. (3) The marginal utility of income to an individual subjected to a housing constraint in a wealthy community is greater than the marginal utility of income to that same individual living in a poor community. Details are available upon request.

10 IMPLICATIONS OF THE TIEBOUT HYPOTHESIS 413 then be the individual with median income, Ik. By analogy with (3), the objective function for the median voter in a representative community is: N h = U(G, Hk, Bk) + Ilk(tPH Z Hi- NPGG) i= 1 (6) + 42k[k - PHHk(l + t) - Bk]. The first constraint is the government-budget constraint, but individuals are now permitted to buy differing quantities of housing. The median voter is assumed to make his choices, treating the housing purchases of all other voters as fixed.4 Community size is N > N. The first-order conditions with respect to Ask and )2k yield the constraints in (6). The remaining conditions determining the tax rate, government-spending level, and purchases of housing and other goods for the median individual are: Oh - = UG - 2IkNPG =O (7a) 8G Solving (7d) for ilk ak - = UHk +,l ktph - X2kPH( 1 t) = 0, (7b) OHk k ah _ = UBk - ~22 = 0 ( 7c) Oh N - = IkEH Hi - 42kPHHk = 0. (7d) at in terms of )2k and substituting into (7b) yields UHk / N ftph Z Hi - = X2k Pu1 + X2k 1 tphhk The second term in parentheses on the right-hand side is the median individual's tax contribution. This contribution will be negligible relative to the total tax revenue of the community, given by the first term in the parentheses, and the individual can safely ignore it. To make the contrast between the current model and the one preceding as sharp as 4 The nonmedian voter takes G and t as fixed and chooses Hi and Bi to maximize his utility subject only to his private budget constraint. This does not result in asymmetric treatment of the median and nonmedian voters. When the tax contribution of the median voter is a small proportion of total tax revenue-the assumption adopted below-the first-order conditions for median and nonmedian voters for H and B have the same form.

11 414 JOURNAL OF POLITICAL ECONOMY possible, we will further assume that the housing purchased by the median voter equals the mean: N E Hi Hk H = = i=1 With the above two assumptions, the first-order conditions for (6) can be rewritten as: UG = A2kPG, (8a) UHk = A2kPH(l + t), (8b) UBk = A22k (8c) A = PHHk + PGG + Bk, (8d) PGG PJJH. PH k As before, equations (8a)-(8d) can be solved for the demand functions for housing and government services: Hk = (8e) Hk(PH5, t PG1 Ik)i (9a) G = G(PH, t, PG 'k) (9b) Equations (8e) and (9) determine the tax rate, housing purchases of the median voter, and government services in a heterogeneous community. The final equilibrium condition is that the minimum housing-purchase constraint be set high enough that the lowest-income individual is just indifferent between staying in the community and moving to the community inhabited by the next-lower income group. Comparison of equations (5) and (9) indicates the effect of the Tiebout mechanism on the median voter. In the heterogeneous community, the property tax causes a deadweight loss in the purchase of housing and government services because housing-purchase decisions are based upon the gross of tax price of housing. In the Tiebout community, this loss is eliminated; housing purchases are based upon net of tax prices as efficiency requires. Since (9a) gives the form of the housing-demand function for all voters in the heterogeneous community, the efficiency loss in housing purchases applies to all residents. There is also redistribution in the heterogeneous communities since all households consume the same level of government services but have differing tax bills. No such redistribution occurs in the Tiebout community. C. Econometric Implications Suppose that data for a series of communities were available, and one wished to test whether the Tiebout model or the heterogeneous-community model were appropriate. Since we have assumed that housing and govern-

12 IMPLICATIONS OF THE TIEBOUT HYPOTHESIS 415 ment services are in perfectly elastic supply to all communities, we may take the prices of these goods to be unity and measure housing and government services in dollar terms. We will further assume that data for the median individual in each community are to be used for the test. Finally, assume that the functions in (5) and (9) are approximately log linear. Then the alternative econometric specifications of the two models for j = 1,..., J communities are: Tiebout community: heterogeneous community: log Hj = ao + a, log Ij + clj, (loa) log G1 = bo + b1 log Ij + (2j, (lob) log ti = log G1 - log Hj + c3j; (loc) log Hj = go + ai log I, + X2 log tj + P'1Ij (pa) log Gj = /3 + J31 log Ij + f2 log tj + P2j, logti (llb) = logg1 - loghj + P3j. (llc) Note that the elasticities in the two models are not necessarily the same. By comparing equations (1 Oa) and (1 Ia), it is obvious that the difference in the housing equations is the appearance of the tax rate in the housing equation for the heterogeneous community. Seemingly, a natural test would be to regress the quantity of housing purchased against income and the tax rate with all variables expressed in logarithmic form. A significant coefficient on the tax-rate variable in the equation would serve as evidence for rejection of the Tiebout model. Upon further reflection, however, it becomes apparent that the above test is not operational. The difficulty arises from the simultaneity in the determination of the three endogenous variables: log tp, log Hj, and log Gj. The problem is not merely that log tj is correlated with the error in (11 a); the coefficient on log t1 is not identified. Using only median-voter data, the model in ( 11) is empirically indistinguishable from the model in (10). The identification problem can be partially solved by using data for several communities for both median and nonmedian individuals.5 A semi-reduced-form equation determining housing purchases for both median and nonmedian voters in either the Tiebout or heterogeneous community can be written as follows: Hi = Hi[Gik, PH( + tik)p, Ii] (12) For residents of a Tiebout community, i = k, p = 0, and (12) is obtained from conditions (4b)-(4d). For the median voter in a heterogeneous We wish to thank Dennis Carlton, who emphasized that data for nonmedian individuals might be useful in overcoming the identification problem.

13 4I6 JOURNAL OF POLITICAL ECONOMY community, i = k, p = 1, and (12) is obtained from conditions (8b), (8c), and the private budget constraint as expressed in (6); equation (12) could also be derived by solving (9b) for PG and substituting the result into (9a). Each nonmedian voter takes Gik and tik as fixed and chooses Hi and Bi to maximize utility subject to his private budget constraint. (The Giik and tik are, of course, the same for all i in a given community.) The form of the objective function is similar to that given in (6) without the first constraint. The form given in (12) follows directly from maximization of this objective function. If equation (12) for each individual is log linear and PG = = 1, (12) may be written in either of the following equivalent forms: log Hi = 70 + y1 log Ii + y2p log (1 + tik) + 73 log Gik + qi, (13a) log Hi = TYo + Yi log Ii + 72P log (1 + tik) + 73 log tikhk + qi. (13b) Equation (13b) is merely (13a) with Gik eliminated by use of the government-budget constraint. In these equations 72 is the price elasticity of housing demand. If the coefficient y2p were not significantly different from zero, this would imply either a zero housing-price elasticity, a Tiebout community, or both. This ambiguity arises because there is no independent variation in PH by which Y2 might be separately identified. In Section IV we present a model which does give rise to systematic variation in PH but at the expense of adding considerably to the complexity of the estimation problem. Two further caveats should be noted in attempting to utilize equation (13) or its extensions to be presented in Section IV. First, an appropriate test depends upon the form of the utility function specified. This point can be illustrated by example. Equation (13) was derived under the assumption that equation (12) is log linear. However, if, for instance, the utility function for each individual were Cobb Douglas, U = H2BPGYI it is a simple exercise to demonstrate that equation (13) would take the form: log Hi = log I -log (1 + tik) + ( + tik)] + 1,- (13 ) Although the critical test again is whether p is zero (Tiebout) or one (heterogeneous), in this Cobb Douglas example the test no longer focuses upon the coefficient of log (1 + t). Since the appropriate test does depend upon the specified utility function, the econometric implications of the utility function chosen must be known prior to the estimation process. Second, the zero-one dichotomous test of p's value depends upon the implicit assumption that the underlying first-order conditions-in particular, equations (4b) and (8b) do obtain as equalities for the sampled households. However, if due to the minimum housing-size constraint some households consume more housing than they would if unconstrained,

14 IMPLICATIONS OF THE TIEBOUT HYPOTHESIS 417 these first-order conditions would become inequalities. For example, in the presence of a housing constraint the marginal utility of housing might fall in the range 22PH < UH < X2PH(l + t). To maintain the equality UH = A2PH(1 + t)p, the parameter p would then take on a value on the unit interval. It is conceivable for relatively low-income individuals in a community that the marginal utility of housing is sufficiently low that UH < A2PH, and the value of p required to maintain the above equality would then be negative. In applying the test, both constrained and unconstrained individuals might be included in the sample. One might nonetheless proceed with the test suggested previously treating the estimated value of p as a weighting of the values for constrained and unconstrained individuals. An estimated value of p in the interval (0, 1] would indicate a heterogeneous community. A nonpositive value would be ambiguous and require further investigation. However, this procedure entails a specification error since the value of p differs among individuals in the sample and may give rise to biases in estimates of all parameters in the model. An approach which can conceptually handle this problem is to include an equation determining the zoning constraint and to utilize switching-regression procedures to distinguish between constrained and unconstrained observations. III. Testing for Capitalization of Fiscal Variables into Housing Values An alternative procedure for identifying the appropriate model is to test for differential effects of taxes on housing prices rather than housing quantities. However, we will argue below that this procedure is nonoperational. A. Perfectly Elastic Supply Testing for capitalization of differential tax rates and/or government spending levels into housing or land values is clearly inappropriate in the foregoing model. We assumed at the outset that all factors used in housing production were in perfectly elastic supply; thus, housing is in perfectly elastic supply, and the property tax must necessarily be shifted forward. The price of' housing net of the tax is then the same across jurisdictions in both the Tiebout and the alternative model. Consequently, the models are not distinguishable with regard to housing prices when the supplies of production factors are perfectly elastic. The question, then, is whether implications generated from more general (and more realistic) models can be used to distinguish Tiebout from non-tiebout communities. Specifically, we will analyze models in which the supply of these factors, and especially land, is not infinitely elastic for the entire metropolitan area.

15 4I8 B. Inelastic Supply JOURNAL OF POLITICAL ECONOMY We will now argue that elasticity of housing supply has nothing to do with the lack of capitalization into the price of property. Consider the extreme case, that is, that land suitable for housing in the metropolitan area is in fixed supply. The price of housing services then would be entirely demand determined. Pure Ricardian rent would accrue to the owners of land in amounts just sufficient to ration the available land among competing claimants. In equilibrium, the marginal unit of land must offer value to its owner equal to its value in any alternative use. The price (net of rents to preferred locations if any exist) that the land commands must be equal to that of all other land suitable for housing on the featureless plain. In equilibrium, the price of land, and hence of housing, would vary across communities only if certain parcels were to offer a greater return, in some form, to their holders than could be obtained by holding different parcels-that is, rents would accrue to the inframarginal units of a land "type" in short supply. But what land types are in short supply? According to our assumption, land suitable for housing is in fixed supply; hence, it would receive a rent, and its price compared to nonurban land would be higher. Similarly, if some land were closer to a desirable location, say a central business district (CBD), it too would receive a higher rent, so that land and housing prices would vary according to CBD accessibility. Finally, would land and housing prices vary by fiscal locality? If the world conformed to the pure Tiebout model, the return to (or price of) housing must be that due to the housing services provided and would be unrelated to the property taxes which are imposed as payment for the locality's governmental services since such taxes are pure benefit taxes. Thus, the net of tax housing price would be the same across Tiebout communities. Yet essentially the same result with regard to housing prices accords in a world of heterogeneous communities. Any resident of any such community will choose the most preferred locale in balancing his worldly desires against the prices which must be paid for them. Since we are not assuming that individuals are forever bound to their communities or that governmental boundaries are immutably fixed, there is no rationale for offering or paying a higher price for housing, net of taxes, in one community than in another. Consider two adjacent heterogeneous communities with different levels of income and governmental services. Suppose that the price of housing net of taxes in the higher-mean-income community is higher than that in the lower. Land from the latter would then be bid away from its present owners and substituted for land previously held in the former community, since it is demonstrably to the advantage of the wealthier individuals to do so. As long as the higher-income individuals are free to bid for land-

16 IMPLICATIONS OF THE TIEBOUT HYPOTHESIS 419 and thus reformulate community boundaries by annexation of land previously in the low-income suburb into the high-income suburb the price of the land itself (i.e., net of tax) will be the same regardless of the taxes imposed or fiscal packages provided by the communities. Alternatively, the price of housing net of taxes might be higher in the lower-mean-income community. If this possibility should arise, there would then be an incentive for residents of the lower-income suburb to bid land away from the higher-income community, annexing it to their own community. As long as a price differential net of tax existed, there would always be this incentive toward equalization. Furthermore, the gross income of individuals would be immaterial in their bidding process, as long as land could be transferred among communities-that is, given that an unimpeded market for land exists, there will be but one marketclearing equilibrium price. Should the amount of land in the higherincome suburb desired by the lower-income individuals be less than that prescribed by the minimum housing-size constraint and thus seemingly prevent the market for land from operating efficiently, there would still be every incentive for a wealthier profit maximizer to perform the function of an arbitrageur or intermediary, purchasing land in the low-cost suburb and subdividing it for higher prices in the other suburb. The assumption above is that the long-run jurisdictional boundaries are not given. Obviously this assumption of movable boundaries plays a crucial role in the foregoing analysis.6 Finally, an objection to the above conclusion might be that the minimum housing size is in itself a distinguishing characteristic of a community's land and thus should earn a rent that gets incorporated into the price of the land. If this objection were valid, then the net of tax land prices would vary across communities, the determining factor of variation being the housing-size constraint. However, this argument is fallacious, since it is the organization of the community itself and not the land occupied which is the distinguishing factor. This distinguishing factor is really no more than the assertion that there are income differentials, and it is to the advantage of higher-income individuals to form exclusive groups in order to prevent redistribution of their wealth to poorer individuals. IV. The Role of Accessibility The purpose of this section is to show that accessibility, and price-accessibility functions, have econometric implications not.found in the model of 6 It may be possible by a selection of alternative assumptions to demonstrate that other models incorporating different degrees of the Tiebout hypothesis could be distinguished. However, our task above was to demonstrate that reasonably constructed models could not be so distinguished, and in this we have been successful. Investigation of the effect which a fixed-boundaries assumption would have is contemplated.

17 420 JOURNAL OF POLITICAL ECONOMY Section II. For illustrative purposes we assume, as in the models of Muth (1969) and Mills (1972), that residents of the metropolitan area must regularly travel to and from a centrally located place of employment. Accessibility to the central business district then becomes a choice variable for the individual. A. The Tiebout Model The budget constraint for the individual is now: I = PHH(l + t) + B + Tu, (14) where u is distance from the central business district and T is a constant per-mile travel cost.7 The governmental budget constraint is: tn(u)phh = N(u)PGG, (15) where N(u) is the number of identical individuals, possibly no more than one, located at distance u. All identical individuals residing at distance u will be defined to constitute a Tiebout community. Thus our Tiebout communities are analogous to households occupying no finite area in the standard calculus models of urban communities. The median voter determines, as before, the tax-rate and governmentspending level, the community-housing constraint, and his purchases of the numeraire commodity. In addition, the individual chooses distance from the central business district. Government goods and the numeraire commodity are assumed to be available at constant unit costs independent of distance from the central business district. Housing prices must rise as one approaches the central business district, for otherwise all individuals would locate at the center. Thus PH = PH(u), and each individual will be assumed to take this housing price-distance function as exogenous. Equilibrium conditions for determining PH(u) will be presented below. The individual voting decision is determined by maximization of the following Lagrangian: h = U(G, H, B) + Al[tPH(u)H -PGG] (16) + '22[' -P.(u)H(l + t) - B - Tu]. By deriving the first-order conditions and performing simple algebraic manipulations similar to those in Section IIA, the equations determining 7 It is easily imagined that T may be a function of other variables, especially I. But admitting that possibility appears to offer no additional insights nor overturn any results derived; therefore we will maintain the constant T assumption.

18 IMPLICATIONS OF THE TIEBOUT HYPOTHESIS 42 1 tax rate, housing services, government services, and the distance, u, from the central business district of a Tiebout community can be shown to be H = H[PH(u), PG, I- Tu], (17a) G = G[PH(u), PG5 I- Tu], (17b) u = p-1 ( T) (17c) PGG (I 7d) PH(u)H There will, of course, be a large number of income groups in most metropolitan areas, and each income group may have a different value of travel time T. The first-order conditions will hold for each income group. In addition, by the same argument utilized in Section III, equilibrium will require that PH(u) be the same on either side of the "boundary" separating any two Tiebout communities. Since a Tiebout community is located at each distance u, this is equivalent to asserting that the PH(u) function is not only monotonic but continuous across boundaries. The remaining conditions determining equilibrium are set forth in Mills (1972, chap. 5). Housing may be assumed to be produced from land and nonland factors via a neoclassical production function. The choice of inputs is determined by the first-order conditions for profit maximization subject to the production-function constraint. In addition, housing demand must equal housing supply at each location, and the cumulative amount of housing in all communities in the metropolitan area must be sufficient to house the total population. The demand for land in housing production at each location must equal the supply of land at each location, and the rental rate on land at the boundary of the metropolitan area must equal the rental rate on the surrounding agricultural land. The conditions enumerated above combined with the first-order conditions are sufficient to determine, inter alia, the housing price-distance function, the amount of housing, government services, and the tax rate at each location. B. Heterogeneous Communities The median voter in the heterogeneous community now chooses his own location within the community, the allocation of his income, and the taxrate and government-spending level. The Lagrangian for the choice problem is: h = U(G, Hk, Bk) +,Zlk(tV - NPGG) + 2k[k - PH(uk)Hk(l + t) - Bk - TUkJI (18)

19 422 JOURNAL OF POLITICAL ECONOMY where N > N and V is the value of housing in the community. Housing value is found by integrating over the area, A, of the community: V = fa PH(a)H(a)da. As before, the price of housing function PH(u) is taken as exogenous by the median individual. Of course, the function PH(u) in equilibrium need not be the same in the metropolitan area with heterogeneous communities as in the metropolitan area with homogeneous communities. Again utilizing first-order conditions for (18) and performing suitable substitutions and approximations similar to those in Section IIB, the demand functions for housing and government services and the functions determining distance selected and the tax rate at each distance can be shown to be of the following form :8 Hk = Hk[PH(Uk), t, PG, Ik TUk]I (19a) Gk = Gk[PH(Uk), t, PGIk - TUk] (1 9b) =k t)]' (I19c) NPGG V [ k.l + 0 ](1 C (I9d) As before, the minimum-purchase constraint on housing must be set large enough to make the lowest-income individual indifferent between staying in the community and moving to the community housing the nextlower income group. By comparing (17) with (19) it is seen that the tax affects the quantity of housing purchased and the distance selected in the metropolitan area composed of heterogeneous communities but not in that composed of Tiebout communities. C. Econometric Implications As noted, the tax rate enters the demand and distance functions for heterogeneous communities but not the analogous Tiebout-communities' functions. However, an investigation of (19) indicates that the parameter on t cannot, in general, be identified using only median voter data or without imposing particular functional forms or restrictions. As was seen in Section IJC, use can be made of both nonmedian and median individual data to reduce the identification problem. The impact of this section is that specifying functional forms, in particular for the price-distance function and the utility function, can in principle permit the two models to be distinguished, since variation in the price of housing allows identification of both the price elasticity of housing demand and the tax parameter p. As an illustration, consider equations (20), which in semireduced form 8 Detailed derivations are available from the authors upon request.

20 IMPLICATIONS OF THE TIEBOUT HYPOTHESIS 423 provide the solution to the optimization problem for heterogeneouscommunity members, both median and nonmedian, as well as Tieboutcommunity members: Hi = Hi[Gij, PH(ui) (1 + ti1), I, - Tuil] (20a) ui = [HP~ l + ttp.l (20b) where subscript j refers to the community inhabited by individual i. This equation is analogous to equation (12) and can be similarly derived. Various particular specifications for the demand and price-distance functions have been investigated to assess the feasibility of estimating (20).9 The important parameter to be estimated for purposes of this discussion is p. If p = 0, the model conforms to Tiebout; if p = 1, the tax variable affects the housing and distance choices, and the model conforms to the heterogeneous-communities model. For certain functional specifications it is readily verifiable that the resulting simultaneous equations are highly nonlinear but are likely to allow identification of p. Although estimation of the resulting equations may be difficult, it is not an intractable task given standard nonlinear techniques. The major obstacle to following such a procedure is the absence of readily available data on perperson government expenditures, effective tax rates, etc. for samples of individuals within numerous metropolitan communities. A remaining possibility is a test based on a comparison of housing prices across jurisdictions. In the Tiebout model, equilibrium requires that the price of housing net of the tax be equal on either side of the boundary between any two jurisdictions, since with distance fixed, the price of housing is determined solely by the value of housing services provided. To deduce the appropriate condition in the heterogeneous-community model, it is necessary to determine whether differential tax rates or governmentspending levels across jurisdictions can be capitalized into land rents. The potential for such capitalization is limited by the differential between the rent earned by land in use in a given suburb relative to the next best alternative use of that land. Suppose land on one side of a boundary between two suburbs earns a higher rent than that on the other side of the boundary. With a competitive housing industry, this gives rise to differential prices for housing. Individuals paying the higher price for housing would have an incentive to purchase housing on the opposite side of the boundary and annex it to their own suburb. Thus the mechanism, utilizing movable boundaries, described in Section IIIB for equalization of housing prices and rents across boundaries, operates in the current model as well. In equilibrium, therefore, the price of housing net of taxes must be the same on either side of the boundary between two hetero- 9 Details available upon request.

21 424 JOURNAL OF POLITICAL ECONOMY geneous communities. Since the equilibrium condition acrossjurisdictional boundaries is the same in the Tiebout- and the heterogeneous-community models, it is obvious that a test based on comparison of housing prices in different suburbs cannot identify which is the correct model. V. Summary and Conclusions We have investigated the implications of two alternative models of the provision of local public goods. In both models consumer-voters have perfect information and jurisdictional boundaries can be costlessly redrawn. Differences between the models arise because economies of scale in the provision of local public goods are assumed to be present in one model but not in the other. To investigate the role of differing assumptions about the supply of land, we considered three cases: land in perfectly elastic supply and costless mobility, land in fixed supply and costless mobility, and land in perfectly elastic supply and transportation costs proportional to the distance from a central business district. The result in each of these cases was that the two models differed in the efficiency of allocation of housing and government services. In none of the three cases, however, were the differences discernible by econometric analysis based on the equilibrium conditions of the alternative models. While these results are surprising, they indicate clearly why ambiguities and contradictions have arisen in past attempts to empirically test the Tiebout hypothesis by a test of tax capitalization. We find that jointly estimating the set of structural equations determining housing purchases and locational choice can potentially distinguish between the models. While the test appears feasible, the data requirements are stringent and the estimating equations are necessarily nonlinear. Under the assumptions of our model, we are led to conclude that to date no meaningful test of the Tiebout hypothesis has been conducted. References Edel, Matthew, and Sclar, Elliott. "Taxes, Spending, and Property Values: Supply Adjustment in a Tiebout-Oates Model." J.P.E. 82, no. 5 (September/ October 1974): Gustely, Richard D. "Local Taxes, Expenditures and Urban Housing: A Reassessment of the Evidence." Southern Econ. J. 42 (April 1976): Hamilton, Bruce W. "Property Taxes and the Tiebout Hypothesis: Some Empirical Evidence." In Fiscal Zoning and Land Use Controls, edited by Edwin S. Mills and Wallace E. Oates. Lexington, Mass: Heath, (a). "Zoning and Property Taxation in a System of Local Governments." Urban Studies 12 (June 1975): (b) "The Effects of Property Taxes and Local Public Spending on Property Values: A Theoretical Comment." J.P.E. 84, no. 3 (June 1976):

22 IMPLICATIONS OF THE TIEBOUT HYPOTHESIS 425 Mills, Edwin S. Urban Economics. Glenview, Ill.: Scott, Foresman, Muth, Richard F. Cities and Housing: The Spatial Pattern of Urban Residential Land Use. Chicago: Univ. Chicago Press, Oates, Wallace E. "The Effects of Property Taxes and Local Public Spending on Property Values: An Empirical Study of Tax Capitalization and the Tiebout Hypothesis." J.P.E. 77, no. 6 (November/December 1969): "The Effects of Property Taxes and Local Public Spending on Property Values: A Reply and Yet Further Results." J.P.E. 81, no. 4 (July/August 1973): Pollakowski, Henry 0. "The Effects of Property Taxes and Local Public Spending on Property Values: A Comment and Further Results." J.P.E. 81, no. 4 (July/ August 1973): Romer, T., and Rosenthal, H. "Bureaucrats vs. Voters: On the Political Economy of Resource Allocation by Direct Democracy." GSIA Working Paper no , Carnegie-Mellon Univ., October Tiebout, Charles M. "A Pure Theory of Local Expenditure." J.P.E. 64, no. 5 (October 1956):