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Leviathan, local government expenditures, and capitalization
Regional Science and Urban Economics 29 (1999) 155–171
Leviathan, local government expenditures, and capitalization William H. Hoyt* Department of Economics, Gatton College of Business and Economics, University of Kentucky, Lexington, KY 40506 -0034, USA Received 15 October 1996; received in revised form 20 April 1998; accepted 23 May 1998
Abstract A number of recent studies have found a positive relationship between local government expenditures and the concentration of local governments, offering support for the contention of Brennan and Buchanan [Brennan, G., Buchanan, J., 1980. The Power to Tax: Analytical Foundations of a Fiscal Constitution. Cambridge University Press, Cambridge] that Leviathan governments are limited by competition among localities. I develop an alternative explanation. Expenditures are greater in large cities because the costs of inefficiency to residents are lower there. While tax increases in small cities are fully capitalized into property values, they are not for large cities. Because residents of large cities do not bear the full burden of inefficiently high taxes they have less incentive to limit government inefficiency. 1999 Elsevier Science B.V. All rights reserved. Keywords: Capitalization; Leviathan; Local Governments; Decentralization; Taxation JEL classification: H7; R51; H71
1. Introduction In their 1980 treatise on taxation and Leviathan governments, Geoffrey Brennan and James Buchanan argue that decentralization of government decision making should reduce government expenditures by reducing the monopoly power of *Tel.: 1606-257-2518; fax: 1606-323-1920; e-mail: [email protected] 0166-0462 / 99 / $ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S0166-0462( 98 )00027-1
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governments. Decentralization of government decision making enables individuals to ‘‘vote with their feet’’. The greater mobility of both people and taxable resources that results from greater decentralization should reduce the government’s ability to spend more than its residents’ desire. A literature has developed following Brennan and Buchanan that has empirically examined the relationship between the decentralization of government activity and government expenditures. These studies have sought evidence of a relationship between the decentralization of government activities and government expenditures. Oates (1985) was the first of these studies. Using data from the 1977 Census of Governments, Oates examined the relationship between state and local tax receipts as a fraction of income (government size) and (a) the state share of state and local expenditures and (b) the number of local governmental units in the state. Oates argued that if the Leviathan model was correct, there should be a positive relationship between the state share of expenditures and government size and a negative relationship between the number of local governmental units and government size. He found no statistically significant evidence indicating that these relationships existed. Other empirical studies examine this question using different data and empirical specifications. The results of this empirical literature are mixed with the study by Forbes and Zampelli (1989) finding no evidence supporting the Leviathan model, while Nelson (1987); Zax (1989); Bell (1988) and Eberts and Gronberg (1990) did. Fewer theoretical studies have examined the effects of decentralization on governmental expenditures. Epple and Zelenitz (1981) develop a model that formalizes Brennan and Buchanan’s conjecture.1 In their model, local governments choose tax and government service policies to maximize surplus, the difference between tax revenue and the (minimum) cost of providing government expenditures. Epple and Zelenitz demonstrate a negative relationship between government expenditures and the number of competing localities. Hoyt (1995) argues that other models of local governments would also predict a negative relationship between government expenditures and the number of competing localities. When governments maximize residents’ utility, Hoyt (1991) shows that a negative relationship between the number of competing localities and government expenditures exists because of tax competition (Wilson, 1985, 1986) while Hoyt (1992) demonstrates that larger cities will set higher tax rates. Hoyt (1995) demonstrates that if governments are Leviathans and their expenditures are constrained by competition among local governments then local property tax rates must equal to or exceed the revenue-maximizing tax rate. Using data on Massachusetts and Minnesota local government expenditures and tax rates, Hoyt 1 Bell (1989) develops a model of Leviathan governments in a model similar to Epple and Zelenitz (1981). He includes jurisdictional spillovers, however, and focuses on the optimal number of jurisdictions given the tradeoff between minimizing spillovers and constraining Leviathan governments.
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(1995) finds no evidence that local property tax rates exceed or are equal to the revenue-maximizing rate. In this paper, a model of Leviathan governments is developed that reconciles the finding (at least in some studies) that competition among governments lowers expenditures with the finding in Hoyt (1995) that governments are not setting revenue-maximizing tax rates as expected if Leviathan governments are constrained by competition among governments. An alternative explanation for a negative relationship between government expenditures and the extent of decentralization in which local governments are constrained by political considerations is that the costs of excess government expenditures is lower for residents of cities having a large share of the population of the metropolis. This is because the decrease in property values as a result of a tax increase is smaller in larger cities. In larger cities tax increases are not fully capitalized into property values. Since monitoring and restraining government inefficiency is a cost to the residents, given the lower costs of inefficient expenditures, residents of larger cities have less incentive to spend resources to control government spending. In addition, the fewer the localities (and therefore the larger the share each city has of the metropolis population), the less incentive residents have to engage in efforts to control government spending. Section 2 provides a brief review of the literature on public sector costs and inefficiency. Section 3 outlines the model of property value determination; Section 4 develops a simple model of the political determination of tax and service levels in the city and demonstrates the relationship between city size and the government policies; and Section 5 concludes.
2. A review of the literature on the costs and politics of public services Brennan and Buchanan’s discussion of Leviathan governments and the decentralization of government activities, is perhaps best summarized in the following passage: Total government intrusion in the economy should be smaller, ceteris paribus, the greater the extent to which taxes and expenditures are decentralized, the more homogenous are the separate units, the smaller the localities, and the lower the net locational rents. (Brennan and Buchanan, 1980, p. 185) This prediction seems to rely on a parallel between the effects of increasing competition in private markets and among governments. If increasing the number of producers in the private market reduces prices, then increasing the number of governmental units providing the government service should reduce government
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expenditures if governments maximize revenue. This constraint is the ‘‘Tiebout mechanism,’’ the mobility of residents and taxable resources among localities. Brennan and Buchanan note the importance of net locational rents on the extent of government intrusion. Epple and Zelenitz (1981) examine decentralization within the context of a model in which net locational rents exist because of limited land in the metropolis. Epple and Zelenitz have governments choose property tax rates and service levels to maximize surplus, the difference between tax revenue and the cost of producing the government services. While these governments face no political constraints, they are unable to control the movements of capital and residents among cities. Even as the number of cities becomes large, bureaucrats are able to extract positive surplus. This is possible because of positive locational net land rents. Bureaucrats, through taxation, are able to transfer land rents from landowners to themselves. Lower land rents ensure that some citizens still reside in the city. While surplus never disappears, Epple and Zelenitz show that as the number of jurisdictions increases surplus and taxes are reduced. Numerous studies have provided at least some evidence of the existence and potential magnitude of this surplus by comparing the costs of services provided in both the public and private sectors. Studies have compared the costs of public and private provision of waste collection (Hirsch, 1965 and Savas, 1977); electrical production (Spann, 1977 and DeAlessi, 1974); fire protection (Ahlbrandt, 1973) and school bus service (McQuire and Van Cott, 1984) among other services. Borcherding et al. (1983) has a comprehensive listing of studies for the United States and the Federal Republic of Germany prior to 1983. While not all these studies indicate public provision is more costly than private, a majority do. These studies were primarily conducted in the 1960’s and 1970’s. In the late 1970’s and the 1980’s, several theoretical studies have argued that the extent of government inefficiency suggested in these early studies is overstated. Wittman (1989) argues that the principal-agent and informational problems that enable bureaucrats to obtain rents are not as extensive as earlier studies imply. Wittman notes that while voters are certainly not perfectly informed about political markets, voters can obtain information on candidates by seeking the advice of individuals or organizations with similar preferences.2 Wittman also argues that the impact of biased information provided by government agencies is also overstated since voters, given the source, should rationally expect this information to be biased. Borcherding et al. (1988) provides a theoretical framework based on the concept of vertical integration for evaluating the decision of whether to publicly-produce a service or to have the government privately contract the service out. He argues that both public and private production have their unique sources of inefficiency, with
2
Wittman (1989) gives the example of hunters reading the literature of the National Rifle Association rather than an organization attempting to ban guns to determine which candidate to support.
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private production leading to ‘‘chiseling costs’’ because of the difficulties in measuring outputs and enforcing contracts. Because of these costs in some cases it might be more efficient to publicly produce the service. Borcherding et al. (1988) also argues that public sector monitoring is more complicated than earlier studies suggest because politicians are by no means homogeneous, having very different objective functions and representing very different political constituencies. While Borcherding et al. (1988) briefly discusses ‘‘Tiebout’’ constraints on government inefficiency, the emphasis of both Borcherding et al. (1988) and Wittman (1989) is on the constraints imposed by ‘‘political’’ markets. Romer and Rosenthal (1982) finds that political constraints, the reversion level of expenditures on referenda in Oregon public school districts, influenced the level of school district expenditures. Another study, Hoyt (1990), presents an empirical test of whether the mobility of capital and residents constrains government expenditures using data on properties and local government policies from the Milwaukee MSA. The results of this study found no evidence suggesting that the Tiebout mechanism influenced government service provision. While numerous empirical studies suggests surplus may be substantial for some public services, there is both theoretical and empirical evidence that suggests that political institutions influence local government expenditures. The influence of political constraints is a departure from the ‘‘no-politics’’ frameworks of Brennan and Buchanan (1980) and Epple and Zelenitz (1981) that generate a relationship between surplus and the extent that government is decentralized. In the next two sections, I develop a political model in which the number (and size) of local governments does affect government expenditures.
3. Capitalization and city size In this section a model of property value determination in which both capital and residents are mobile among localities within the market (metropolitan area) is developed. This model is then used to examine the impact of local tax rates and government expenditures on property values with a particular emphasis on how these impacts vary with the size of the locality. The impact of local government policies on property values is examined because in Section 4 it is assumed that residents will desire the mix of government policies that maximize the value of their property (land). This objective is consistent with a ‘‘Tiebout’’ world where residents can costlessly move among a large number of localities (cities) that offer a variety of tax / public service combinations.3 3
Property value maximization has been the government objective in numerous studies of local tax and public service determination including Yinger (1982); Henderson (1985) and Hoyt (1991), (1993).
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3.1. The model The model is similar to those of Epple and Zelenitz (1981); Henderson (1985) and Hoyt (1992). Each one of J cities in a large metropolitan area provides a government service to its residents and taxes housing in the city to finance the government service. While the metropolis has a fixed population, the J cities differ in populations. Differences in the populations can be attributable to both different land areas and government policies among the cities. Because capital is mobile across the cities, as the price of housing in a city changes both its housing supply and population change. While city population is endogenously determined, the land area of each city is exogenously determined and does not change. Following the standard assumptions of Tiebout models, residents can costlessly move among all cities in the metropolis. For simplicity, I assume that these residents have identical tastes and incomes. The utility of the resident is given by function, U(x, h, g) 5 x 1 Uh (h) 1 Ug ( g) where x, h, and g are a private good, housing, and the public service.4 The indirect utility function is f ( y, p 1 t, g) where y is income, p is the net price of a unit of housing, and t is the property tax rate. Income includes the implicit rent from property owned by the resident. The public service is actually a publicly-provided private good with one unit per resident being produced by one unit of capital.5 One unit of capital also produces one unit of the private good. As capital is mobile across cities, competition ensures the price of the private good is unity in all cities as is the cost of the public service per resident. Housing is produced using both capital and land. The net price of housing, p, is equal to k 1 rl, where k and l are capital and land per unit of housing and r is net land rent.
3.2. Equilibrium conditions Because residents have identical incomes and tastes they must receive the same level of utility in all cities. The equilibrium utility level, U *, and housing prices are endogenously determined and depend upon government policies and housing market conditions throughout the metropolis. For each city j,
f ( y, pj 1 tj , g j ) 5 U *, j 5 1, . . . ,J. 4
(1)
The separable form of the utility function is chosen to simplify the analysis of the price gradients by eliminating income effects that arise from changes in property values. For a discussion of incorporating income effects into the price gradients see Henderson (1994). 5 The results found here are qualitatively the same if g is not a pure private good but instead a pure public good (for residents of the city) or a congestible public good. I thank a referee for suggesting this point.
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Equilibrium also requires that the housing market clear in both the metropolis and in each of the cities. In each city, the product of the population (n j ), housing per resident (h j ), and land per unit of housing (l j ) must equal the supply of land in the city (Lj ), n j l j h j 5 Lj , j 5 1, . . . ,J.
(2)
Finally, the sum of the populations of the cities must equal the population of the metropolis,
O n 5 N, J
j
(3)
j51
where N is the population of the metropolis. Using (1)-(3) the equilibrium level of utility can be solved as function of the metropolis population and the land areas and government policies in each of the cities. Then we represent U * by U * 5 U *(N, ] L, t], g) 5 U *(n 2 n j , L2j , t2j , g2j ), j 5 1, . . . ,J, ] ] ] ]
(4)
where L, ] t], and g] represent vectors of the land area, tax rates, and service levels in each of the cities. Utility is decreasing in population and the tax rate of any city and increasing in the land area and service level of any city. Because utility is equal in all cities, (4) also describes the utility level for a single city or a subset of the cities (U *(N-n j , L-j , t-j , g-j )) where L ]-j , t]-j , and ]g-j refer to vectors representing ] ] ] the land areas, tax rates, and government service levels of all cities except for city j. Fig. 1 depicts the equilibrium price of housing and populations for a metropolis consisting of two cities (1 and 2).6 Equilibrium requires that the demand for housing equal the supply of housing in both cities and the households in both cities receive the same level of utility. In Fig. 1, the supply of housing sites in city 1 (the number of households that can live in city 1) depends on the price of housing in city 1 and is given by N s1 ( p1 , t1 , g1 ). Since the demand for housing sites in city 1 equals the total population less the number of households living in city 2, the housing demand in city 1 depends on p2 . In addition, the equal utility condition requires that f ( y, p2 1t2 , g2 )5 f ( y, p1 1t1 , g1 ), yielding another relationship between prices in the two cities. Then using this relationship we can express the demand for housing in city 1 as a function of p1 , N d1 ( p1 , t1 , g1 ). The price of housing in and population of city 1 and are determined by the intersection of N d1 ( p1 , t1 , g1 ) and N s1 ( p1 , t1 , g1 ) with the price of housing in city 2 being p 2* . 6
I am grateful to Jon Sonstelie for suggesting a graphical interpretation of equilibrium and the comparative statics in this model.
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Fig. 1. Equilibrium in the housing market.
3.3. The effects of taxation and public services on population and prices To find the effect of an increase in the tax rate in city j on housing prices, we must consider its effect on both the utility level in the metropolis and equilibrium in the housing market. Then differentiating (1), (2), and (4) and solving for (dpj / dtj ) yields
S D
U *N 1 ≠l j ] ]] dpj a h j lj ≠pj ] 5 2 1 1 ]]]]]]]]] , 0, j 5 1, . . . ,J, dtj 1 U *n 1 ≠l j 1 ≠h j ]1] ] ]1] ] n j a h j l j ≠pj h j ≠pj
F
S
DG
(5)
where a is the marginal utility of income and U *N , denotes ≠U * / ≠N ,0. Inspection of (5) indicates that dpj / dtj is a function of the population of city j. Then differentiating (5) with respect to the n j gives
S D
F G
1 U N* 1 ≠l j dpj ]2 ] ]] ] dtj n j a h j l j ≠pj d ]] 5 ]]]]]]]]]2 . 0, j 5 1, . . . ,J, dn j 1 U n* 1 ≠l j 1 ≠h j ]1] ] ]1] ] n j a h j l j ≠pj h j ≠pj
F
S
DG
(6)
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As the population of the city increases relative to the rest of the metropolis, the magnitude of its price change decreases. This decrease occurs because a larger city has more influence on the metropolitan utility level, thereby passing on the effect of its tax increase to other cities. A city’s influence on the utility level depends on the number of residents who leave the city when the tax rate increases. The more who migrate, the greater the reduction in utility. For a small city, the tax increase is fully capitalized into housing prices with dpj / dtj 5-1. Full capitalization occurs because its population change has almost no impact on the population of the rest of the metropolis. The same approach can be taken to determine the effects of a change in a city’s service level on its housing prices. Totally differentiating (1), (2), and (4) and solving for dpj / dg j yields Ug j dpj ] 5 ]]]]]]]]]] . 0, j 5 1, . . . ,J. dg j 1 ≠l j 1 ≠h j a h j 1 U N* nj ] ] 1 ] ] l j ≠pj h j ≠pj
F
S
DG
(7)
Differentiating (7) with respect to n j gives
F G
S
D
dpj 1 ≠l j 1 ≠h j d ] U *n ] ] 1 ] ] Ug j dg j l j ≠pj h j ≠pj ]]] 5 2 ]]]]]]]]]]2 , 0, j 5 1, . . . ,J. dn j 1 ≠l j 1 ≠h j a hj 1 U *N n j ] ] 1 ] ] l j ≠pj h j ≠pj
F
S
DG
(8)
Again, the magnitude of the price change decreases with city size because the migration of residents into a small city will not have as much influence on the population of the rest of the metropolis and, therefore, the utility level. In Fig. 2 we graphically depict the impacts of a tax increase for a small city (Fig. 2a) and a large city (Fig. 2b). Differences in city size relative to size of the rest of the metropolis (city 2) are reflected in the elasticity of demand for housing in the city. Fig. 2a depicts the impact of a tax increase from t 01 to t 19 for a city that is small relative to the metropolis and therefore has an almost perfectly elastic demand for housing. The tax increase will increase the supply of sites (each household buys less housing) as well as the demand as a function of p1 as an increase in t1 means that for any given p2 , p1 must decrease. The tax increase leads to a reduction in p1 almost equal to the tax increase with almost no impact on housing prices in the rest of the metropolis. In Fig. 2b the same tax increase for a larger city has a small impact on its housing prices because some of the tax increase is ‘‘passed on’’ to residents of other cities in the metropolis through increased housing prices there ( p 29 ). Finally, because the objective of residents is land value maximization, note that since p5rl 1k,
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Fig. 2. Impact of property tax on housing prices.
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dr j 1 dpj dr j 1 dpj ] 5 ] ] and ] 5 ] ], j 5 1, . . . ,J. dtj l j dtj dtj l j dtj
(9)
4. Government policies, political pressure, and city size Epple and Zelenitz (1981) demonstrates that even with the costless mobility of capital and residents among a large number of localities, surpluses can be obtained by bureaucrats if not constrained politically. The greater the surplus received by the bureaucrats, the lower property values in the city. This suggests that it may be worthwhile for property owners to undertake some measures to constrain the government policies chosen by bureaucrats. In this section, a model in which bureaucrats (politicians) maximize surplus is developed. Unlike Epple and Zelenitz (1981), the politician faces a ‘‘political’’ constraint-the efforts of residents to defeat politicians whose policies reduce their property values. Residents’ efforts to constrain politicians (by reducing the probability of the politician being reelected) are chosen considering both the benefits of these efforts, increased property values, and the cost of the effort. Because the impact of taxes and services on property values varies with the size of the city, so do the efforts of the residents and therefore the tax and services as well.
4.1. The politicians’ objectives Following Becker (1983) and Hoyt and Toma (1989), I assume that politicians (or bureaucrats) respond to the efforts of residents in the city (lobbying and voting). Politicians may have the incentive to minimize the surplus received by bureaucrats and themselves, by lowering tax rates and increasing public services, because these policies will increase the probability of their reelection. Let the benefits received by politicians obtain be a function of expected surplus (ES) obtained from holding office
O b S P s(t T
ES(t, g, e) 5 n(t ph 2 g) 1
t 51
t
t
k 51
t 21
D
, gt 21 , e t 21 )9 n t (tt pt h t 2 gt ), (10)
where b is the discount factor ( b ,1) and T is the time until the politician would like to retire. The probability of being reelected is given by s(t, g, e)-reelection depends on the current policies and the efforts against the incumbent (e), with ≠s / ≠t ,0, ≠s / ≠g.0, and ≠s / ≠e,0.7 Thus the incumbent’s reelection depends 7
I assume that voters perceive the current policy as the best predictor of future policy and therefore the probability of reelection depends on current policy.
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upon his current policies and the level of effort in a campaign against him. This effort includes campaign expenditures, voting for alternative candidates, and unfavorable publicity. The politician, when choosing current government policies, must consider how these policies affect the efforts of residents to defeat him in the next election. For each level of effort, there are the associated expected surplus maximizing tax and public service policies, t (e) and g(e). As shown in Appendix A, the politician will reduce the tax rate when effort increases, dt / de,0, and decrease the service level, dg / de.0. Further, assume that d 2t / d 2 e.0 and d 2 g / de 2 ,0, the effects of effort by the residents on the politicians’ choice of policies decrease with the level of effort. Given the effects of effort on the probability of reelection, the politician will set a lower tax rate and higher service level than he would if the policies he chose had no impact on his reelection.
4.2. The residents’ objectives Residents will choose their effort against current politicians to decrease current (and expected) property tax rates and increase public service levels. Essentially, the residents are modeled as Stackelburg leaders. Residents, if they believe that a politician is not doing a satisfactory job, will spend money trying to elect a politician who will provide higher service levels and lower taxes (a politician with a lower discount rate and longer time horizon). The politician then views this as a credible threat and chooses his policies accordingly. As briefly discussed in Section 3, because residents are mobile and there is assumed to be a large number of cities offering different tax / service mixes, residents obtain their desired service / tax mix by choosing where to live–not by changing the mix of services in any city. Instead, as shown by Sonstelie and Portney (1978), residents will choose public services and taxes in the city where they own property (and reside) to maximize the value of that property (land).8 In the context of our model, residents will choose effort to maximize net land rent less the cost of this effort, Maximize V(e) 5 r(t (e), g(e))l] 2 e, e
(11)
where l] is the amount of land owned by a representative resident. Then the optimal effort is given by 8 For cities that are large enough to affect the level of utility in metropolis, residents of that city may consider how changes in the city’s policies will affect the general level of utility. If these changes are also considered then the residents would not simply choose the policy that maximizes land rent. The change in the general utility level, however, is likely to be secondary to any change in income residents may receive from a change in land rent they receive.
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F
G
≠r dg ≠r dt ] ] 1 ] ] l 5 1, ≠g de ≠t de ]
167
(12)
or, substituting price changes for the rent changes,
F
G
≠p dg ≠p dt ] ] 1 ] ] h 5 1. ≠g de ≠t de
(129)
Residents equate the marginal benefit of effort, the increase in property value from decreases in tax rates and increases in service levels, with its cost. The benefits of efforts by the residents depend on the changes in property values a government policy change brings. From (6) and (8), the change in housing prices arising from policy changes depends on the size of the city. To find how the efforts of the residents depend on the size of their city, (129) is totally differentiated with respect to n and e to give
3F
G
F G
dp dp d ] dt d ] dg dg dt ] ]]] ]]] ] 1 de dn de dn de ] 5 2 ]]]]]]]]] , 0. dn [d 2V/ de 2 ]
4
(13)
By (6) and (8), the numerator is negative and by the second order condition the denominator must also be negative, making de / dn,0. In larger cities, residents have less incentive to put effort into the political process because the cost of ‘‘bad’’ local politics is not as costly as it is in small cities. This is because of the incomplete capitalization of government policies into property values. Part of the cost of a tax increase in a large city is passed on to the rest of the metropolis in the form of higher property values-an externality ignored by the residents of the large city. An increase in the tax rate in a small city is more costly because it will result in a greater decrease in property values. An increase in the service level in a small city is also more beneficial because it will result in a greater increase in property values. Because a decrease in the tax rate and increase in the service level bring greater changes in property values in the small city, greater effort to achieve these policy changes will occur there. If effort levels are higher in smaller cities then tax rates will be lower and service levels higher. With identical cities, the more cities in the metropolis the smaller the share of the metropolis population each city has. Then the more cities, the greater the extent of capitalization and the more costly are tax increases and service decreases. With many cities in a metropolis tax rates should be lower and public service levels should be higher because residents have a greater incentive to exert effort to limit governments. Fig. 3 depicts the optimal efforts by residents in a small city (city 1) and a large city (city 2). The optimal effort for the small city is given by e 1* where dr 1 / de 1 51. However, at this level of effort for the large city dr 2 / de 2 ,dr 1 / de 1 5
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Fig. 3. Optimal effort and city size.
1 because decreases in tax rates and increases in public service levels bring small increases in property values in larger cities, so this level of effort is not optimal for the larger city. Instead, it will choose a lower level of effort, e 2* , where dr 2 / de 2 51.
5. Conclusion In this paper I develop a simple model that predicts that local government expenditures, and waste (surplus) should be greater in larger cities and in metropolitan areas that have fewer localities supplying public services. However, unlike Brennan and Buchanan (1980) and Epple and Zelenitz (1981) this prediction is not made in a framework without politics. Instead, the size (population) of a city, in relationship to that of the metropolis, influences the cost of inefficiency. This relationship exists because in larger cities the ‘‘cost’’ of higher taxes or lower quality services is lower because of incomplete capitalization. The larger a city or, alternatively, the fewer the number of cities, the smaller the decreases in property value for any given tax increase. Thus the benefit of increased efficiency and lower taxes, the increase in property values in the city, is
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smaller in larger cities. Thus residents of larger cities have less incentive to spend resources limiting government inefficiency. In equilibrium, then, we expect less monitoring and higher tax rates in larger cities and in metropolitan areas with fewer, larger cities.
Acknowledgements The author would like to thank seminar participants at the University of Maryland, George Mason University, and the 1993 Annual Meeting of the Southern Economics Association for their comments and suggestions. I am especially grateful to the editor and an anonymous referee of this journal, Wallace Oates, Jon Sonstelie, and Sally Wallace for their comments and suggestions.
Appendix A Let St represent the surplus in period t. Then the policies that maximize expected surplus must satisfy ≠s O S P s(t , g , e )D ] 5 0. ≠t
(A.1)
≠s O S P s(t , g , e )D ] 5 0. ≠g
(A.2)
T ≠ES ≠S ]] 5 ]0 1 b t St ≠t ≠t t 51
t
0
k51
k
k
k
0
and T ≠ES ≠S ]] 5 ]0 1 b t St ≠g ≠g t 51
t
0
k51
k
k
k
0
Assume that ≠ 2 s / ≠t ≠e,0, that an increase in lobbying effort increases the marginal reduction in the probability of being reelected due to a tax increase. Analogously, assume that ≠ 2 s / ≠g≠e.0, an increase in effort will increase the marginal increase in the probability of being reelected due to a service increase. Totally differentiating (A.1) with respect to t and e gives
FO
P
G
t ≠ 2s t ]] b s S( t , g , e ) d t 51 k 51 k k k dt ≠t ≠e ] 5 2 ]]]]]]]]]]] , 0. 2 de ≠ ES ]] ≠t 2 T
Differentiating (A.2) with respect to g and e gives
(A.3)
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FO
P
G
≠ 2s ]] t 51 b s k 51 S(tk , gk , e k )d ≠g≠e dg ] 5 2 ]]]]]]]]]]] , 0. de ≠ 2 ES ]] ≠g 2 T
t
t
(A.4)
References Ahlbrandt, R., 1973. Efficiency in the provision of fire services. Public Choice 16, 1–16. Becker, G.S., 1983. A theory of competition among pressure groups for political influence. The Quarterly Journal of Economics 98, 371–400. Bell, C.R., 1988. The assignment of fiscal responsibility in a federal state: an empirical assessment. National Tax Journal 61, 191–208. Bell, C.R., 1989. Between anarchy and leviathan: a note on the design of federal states. Journal of Public Economics 39, 207–222. Borcherding, T.E., Pommerchne, W.W., Schneider, F., 1983. Comparing the efficiency of private and public production: the evidence from five countries. Journal of Economics 10, 127–156. Borcherding, T.E., Pommerchne, W.W., Schneider, F., 1988. Some revisionist thoughts on the theory of public bureaucracy. European Journal of Political Economy 4, 47–64. Brennan, G., Buchanan, J., 1980. The Power to Tax: Analytical Foundations of a Fiscal Constitution. Cambridge University Press, Cambridge. DeAlessi, L., 1974. An economic analysis of government ownership and regulation: theory and the evidence from the electric power industry. Public Choice 19, 1–42. Eberts, R.W., Gronberg, T.J., 1990. Structure, conduct, and performance in the public sector. National Tax Journal 63, 165–173. Epple, D., Zelenitz, A., 1981. The implications of competition among jurisdictions: does Tiebout need politics?. Journal of Political Economy 89, 1197–1217. Forbes, K.F., Zampelli, E.M., 1989. Is leviathan a mythical beast? American Economic Review 79, 568–576. Henderson, J.V., 1985. The Tiebout model: bring back the entrepreneurs. Journal of Political Economy 93 (2), 248–264. Henderson, J.V., 1994. Will homeowners impose property taxes? Regional Science and Urban Economics 25 (2), 153–181. Hirsch, W., 1965. Cost functions of and urban government service. Refuse Collection Review of Economics and Statistics 47, 87–92. Hoyt, W.H., 1990. Local government inefficiency and the Tiebout hypothesis: does competition among municipalities limit local government inefficiency? Southern Economic Journal 57, 481–496. Hoyt, W.H., 1991. Property taxation, Nash equilibrium, and market power. Journal of Urban Economics 30, 123–131. Hoyt, W.H., 1992. Market power of large cities and policy differences in metropolitan areas. Regional Science and Urban Economics 22, 539–558. Hoyt, W.H., 1993. Tax competition, Nash equilibria, and residential mobility. Journal of Urban Economics 34, 358–379. Hoyt, W.H., 1995. Leviathan and local tax policies: do local governments maximize revenue. Working Paper E-185-95, Center for Business and Economic Research, University of Kentucky. Hoyt, W.H., Toma, E.F., 1989. State mandates and interest group lobbying. Journal of Public Economics 38, 199–213. McQuire, R.A., Van Cott, T.N., 1984. Public vs. private activity: a new look at school bus transportation. Public Choice 43, 25–44.
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Nelson, M.A., 1987. Searching for leviathan: comment and extension. American Economic Review 77, 198–204. Oates, W.E., 1985. Searching for leviathan: an empirical study. American Economic Review 75, 748–757. Romer, T., Rosenthal, H., 1982. Median voters or budget maximizers: evidence from school expenditure referenda. Economic Inquiry 20, 556–577. Savas, E.S., 1977. Policy analysis for local government: public vs private refuse collection. Policy Analysis 3, 49–74. Sonstelie, J.C., Portney, P.R., 1978. Profit maximizing communities and the theory of local public expenditures. Journal of Urban Economics 5, 263–277. Spann, R.M., 1977. Public versus private provision of government services. In: Borcherding, T.E. (Ed.), Budgets and Bureaucrats: The Sources of Government Growth. Duke University, pp. 71–89. Wilson, J.D., 1985. Optimal property taxation in the presence of interregional capital mobility. Journal of Urban Economics 17, 73–89. Wilson, J.D., 1986. A theory of interregional tax competition. Journal of Urban Economics 19, 296–315. Wittman, D., 1989. Why democracies produce efficient results. Journal of Political Economy 97, 1395–1424. Yinger, J., 1982. Capitalization and the theory of local public finance. Journal of Political Economy 90, 917–943. Zax, J.S., 1989. Is there a leviathan in your neighborhood? American Economic Review 79, 560–567.
Leviathan, local government expenditures, and capitalization William H. Hoyt* Department of Economics, Gatton College of Business and Economics, University of Kentucky, Lexington, KY 40506 -0034, USA Received 15 October 1996; received in revised form 20 April 1998; accepted 23 May 1998
Abstract A number of recent studies have found a positive relationship between local government expenditures and the concentration of local governments, offering support for the contention of Brennan and Buchanan [Brennan, G., Buchanan, J., 1980. The Power to Tax: Analytical Foundations of a Fiscal Constitution. Cambridge University Press, Cambridge] that Leviathan governments are limited by competition among localities. I develop an alternative explanation. Expenditures are greater in large cities because the costs of inefficiency to residents are lower there. While tax increases in small cities are fully capitalized into property values, they are not for large cities. Because residents of large cities do not bear the full burden of inefficiently high taxes they have less incentive to limit government inefficiency. 1999 Elsevier Science B.V. All rights reserved. Keywords: Capitalization; Leviathan; Local Governments; Decentralization; Taxation JEL classification: H7; R51; H71
1. Introduction In their 1980 treatise on taxation and Leviathan governments, Geoffrey Brennan and James Buchanan argue that decentralization of government decision making should reduce government expenditures by reducing the monopoly power of *Tel.: 1606-257-2518; fax: 1606-323-1920; e-mail: [email protected] 0166-0462 / 99 / $ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S0166-0462( 98 )00027-1
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governments. Decentralization of government decision making enables individuals to ‘‘vote with their feet’’. The greater mobility of both people and taxable resources that results from greater decentralization should reduce the government’s ability to spend more than its residents’ desire. A literature has developed following Brennan and Buchanan that has empirically examined the relationship between the decentralization of government activity and government expenditures. These studies have sought evidence of a relationship between the decentralization of government activities and government expenditures. Oates (1985) was the first of these studies. Using data from the 1977 Census of Governments, Oates examined the relationship between state and local tax receipts as a fraction of income (government size) and (a) the state share of state and local expenditures and (b) the number of local governmental units in the state. Oates argued that if the Leviathan model was correct, there should be a positive relationship between the state share of expenditures and government size and a negative relationship between the number of local governmental units and government size. He found no statistically significant evidence indicating that these relationships existed. Other empirical studies examine this question using different data and empirical specifications. The results of this empirical literature are mixed with the study by Forbes and Zampelli (1989) finding no evidence supporting the Leviathan model, while Nelson (1987); Zax (1989); Bell (1988) and Eberts and Gronberg (1990) did. Fewer theoretical studies have examined the effects of decentralization on governmental expenditures. Epple and Zelenitz (1981) develop a model that formalizes Brennan and Buchanan’s conjecture.1 In their model, local governments choose tax and government service policies to maximize surplus, the difference between tax revenue and the (minimum) cost of providing government expenditures. Epple and Zelenitz demonstrate a negative relationship between government expenditures and the number of competing localities. Hoyt (1995) argues that other models of local governments would also predict a negative relationship between government expenditures and the number of competing localities. When governments maximize residents’ utility, Hoyt (1991) shows that a negative relationship between the number of competing localities and government expenditures exists because of tax competition (Wilson, 1985, 1986) while Hoyt (1992) demonstrates that larger cities will set higher tax rates. Hoyt (1995) demonstrates that if governments are Leviathans and their expenditures are constrained by competition among local governments then local property tax rates must equal to or exceed the revenue-maximizing tax rate. Using data on Massachusetts and Minnesota local government expenditures and tax rates, Hoyt 1 Bell (1989) develops a model of Leviathan governments in a model similar to Epple and Zelenitz (1981). He includes jurisdictional spillovers, however, and focuses on the optimal number of jurisdictions given the tradeoff between minimizing spillovers and constraining Leviathan governments.
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(1995) finds no evidence that local property tax rates exceed or are equal to the revenue-maximizing rate. In this paper, a model of Leviathan governments is developed that reconciles the finding (at least in some studies) that competition among governments lowers expenditures with the finding in Hoyt (1995) that governments are not setting revenue-maximizing tax rates as expected if Leviathan governments are constrained by competition among governments. An alternative explanation for a negative relationship between government expenditures and the extent of decentralization in which local governments are constrained by political considerations is that the costs of excess government expenditures is lower for residents of cities having a large share of the population of the metropolis. This is because the decrease in property values as a result of a tax increase is smaller in larger cities. In larger cities tax increases are not fully capitalized into property values. Since monitoring and restraining government inefficiency is a cost to the residents, given the lower costs of inefficient expenditures, residents of larger cities have less incentive to spend resources to control government spending. In addition, the fewer the localities (and therefore the larger the share each city has of the metropolis population), the less incentive residents have to engage in efforts to control government spending. Section 2 provides a brief review of the literature on public sector costs and inefficiency. Section 3 outlines the model of property value determination; Section 4 develops a simple model of the political determination of tax and service levels in the city and demonstrates the relationship between city size and the government policies; and Section 5 concludes.
2. A review of the literature on the costs and politics of public services Brennan and Buchanan’s discussion of Leviathan governments and the decentralization of government activities, is perhaps best summarized in the following passage: Total government intrusion in the economy should be smaller, ceteris paribus, the greater the extent to which taxes and expenditures are decentralized, the more homogenous are the separate units, the smaller the localities, and the lower the net locational rents. (Brennan and Buchanan, 1980, p. 185) This prediction seems to rely on a parallel between the effects of increasing competition in private markets and among governments. If increasing the number of producers in the private market reduces prices, then increasing the number of governmental units providing the government service should reduce government
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expenditures if governments maximize revenue. This constraint is the ‘‘Tiebout mechanism,’’ the mobility of residents and taxable resources among localities. Brennan and Buchanan note the importance of net locational rents on the extent of government intrusion. Epple and Zelenitz (1981) examine decentralization within the context of a model in which net locational rents exist because of limited land in the metropolis. Epple and Zelenitz have governments choose property tax rates and service levels to maximize surplus, the difference between tax revenue and the cost of producing the government services. While these governments face no political constraints, they are unable to control the movements of capital and residents among cities. Even as the number of cities becomes large, bureaucrats are able to extract positive surplus. This is possible because of positive locational net land rents. Bureaucrats, through taxation, are able to transfer land rents from landowners to themselves. Lower land rents ensure that some citizens still reside in the city. While surplus never disappears, Epple and Zelenitz show that as the number of jurisdictions increases surplus and taxes are reduced. Numerous studies have provided at least some evidence of the existence and potential magnitude of this surplus by comparing the costs of services provided in both the public and private sectors. Studies have compared the costs of public and private provision of waste collection (Hirsch, 1965 and Savas, 1977); electrical production (Spann, 1977 and DeAlessi, 1974); fire protection (Ahlbrandt, 1973) and school bus service (McQuire and Van Cott, 1984) among other services. Borcherding et al. (1983) has a comprehensive listing of studies for the United States and the Federal Republic of Germany prior to 1983. While not all these studies indicate public provision is more costly than private, a majority do. These studies were primarily conducted in the 1960’s and 1970’s. In the late 1970’s and the 1980’s, several theoretical studies have argued that the extent of government inefficiency suggested in these early studies is overstated. Wittman (1989) argues that the principal-agent and informational problems that enable bureaucrats to obtain rents are not as extensive as earlier studies imply. Wittman notes that while voters are certainly not perfectly informed about political markets, voters can obtain information on candidates by seeking the advice of individuals or organizations with similar preferences.2 Wittman also argues that the impact of biased information provided by government agencies is also overstated since voters, given the source, should rationally expect this information to be biased. Borcherding et al. (1988) provides a theoretical framework based on the concept of vertical integration for evaluating the decision of whether to publicly-produce a service or to have the government privately contract the service out. He argues that both public and private production have their unique sources of inefficiency, with
2
Wittman (1989) gives the example of hunters reading the literature of the National Rifle Association rather than an organization attempting to ban guns to determine which candidate to support.
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private production leading to ‘‘chiseling costs’’ because of the difficulties in measuring outputs and enforcing contracts. Because of these costs in some cases it might be more efficient to publicly produce the service. Borcherding et al. (1988) also argues that public sector monitoring is more complicated than earlier studies suggest because politicians are by no means homogeneous, having very different objective functions and representing very different political constituencies. While Borcherding et al. (1988) briefly discusses ‘‘Tiebout’’ constraints on government inefficiency, the emphasis of both Borcherding et al. (1988) and Wittman (1989) is on the constraints imposed by ‘‘political’’ markets. Romer and Rosenthal (1982) finds that political constraints, the reversion level of expenditures on referenda in Oregon public school districts, influenced the level of school district expenditures. Another study, Hoyt (1990), presents an empirical test of whether the mobility of capital and residents constrains government expenditures using data on properties and local government policies from the Milwaukee MSA. The results of this study found no evidence suggesting that the Tiebout mechanism influenced government service provision. While numerous empirical studies suggests surplus may be substantial for some public services, there is both theoretical and empirical evidence that suggests that political institutions influence local government expenditures. The influence of political constraints is a departure from the ‘‘no-politics’’ frameworks of Brennan and Buchanan (1980) and Epple and Zelenitz (1981) that generate a relationship between surplus and the extent that government is decentralized. In the next two sections, I develop a political model in which the number (and size) of local governments does affect government expenditures.
3. Capitalization and city size In this section a model of property value determination in which both capital and residents are mobile among localities within the market (metropolitan area) is developed. This model is then used to examine the impact of local tax rates and government expenditures on property values with a particular emphasis on how these impacts vary with the size of the locality. The impact of local government policies on property values is examined because in Section 4 it is assumed that residents will desire the mix of government policies that maximize the value of their property (land). This objective is consistent with a ‘‘Tiebout’’ world where residents can costlessly move among a large number of localities (cities) that offer a variety of tax / public service combinations.3 3
Property value maximization has been the government objective in numerous studies of local tax and public service determination including Yinger (1982); Henderson (1985) and Hoyt (1991), (1993).
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3.1. The model The model is similar to those of Epple and Zelenitz (1981); Henderson (1985) and Hoyt (1992). Each one of J cities in a large metropolitan area provides a government service to its residents and taxes housing in the city to finance the government service. While the metropolis has a fixed population, the J cities differ in populations. Differences in the populations can be attributable to both different land areas and government policies among the cities. Because capital is mobile across the cities, as the price of housing in a city changes both its housing supply and population change. While city population is endogenously determined, the land area of each city is exogenously determined and does not change. Following the standard assumptions of Tiebout models, residents can costlessly move among all cities in the metropolis. For simplicity, I assume that these residents have identical tastes and incomes. The utility of the resident is given by function, U(x, h, g) 5 x 1 Uh (h) 1 Ug ( g) where x, h, and g are a private good, housing, and the public service.4 The indirect utility function is f ( y, p 1 t, g) where y is income, p is the net price of a unit of housing, and t is the property tax rate. Income includes the implicit rent from property owned by the resident. The public service is actually a publicly-provided private good with one unit per resident being produced by one unit of capital.5 One unit of capital also produces one unit of the private good. As capital is mobile across cities, competition ensures the price of the private good is unity in all cities as is the cost of the public service per resident. Housing is produced using both capital and land. The net price of housing, p, is equal to k 1 rl, where k and l are capital and land per unit of housing and r is net land rent.
3.2. Equilibrium conditions Because residents have identical incomes and tastes they must receive the same level of utility in all cities. The equilibrium utility level, U *, and housing prices are endogenously determined and depend upon government policies and housing market conditions throughout the metropolis. For each city j,
f ( y, pj 1 tj , g j ) 5 U *, j 5 1, . . . ,J. 4
(1)
The separable form of the utility function is chosen to simplify the analysis of the price gradients by eliminating income effects that arise from changes in property values. For a discussion of incorporating income effects into the price gradients see Henderson (1994). 5 The results found here are qualitatively the same if g is not a pure private good but instead a pure public good (for residents of the city) or a congestible public good. I thank a referee for suggesting this point.
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Equilibrium also requires that the housing market clear in both the metropolis and in each of the cities. In each city, the product of the population (n j ), housing per resident (h j ), and land per unit of housing (l j ) must equal the supply of land in the city (Lj ), n j l j h j 5 Lj , j 5 1, . . . ,J.
(2)
Finally, the sum of the populations of the cities must equal the population of the metropolis,
O n 5 N, J
j
(3)
j51
where N is the population of the metropolis. Using (1)-(3) the equilibrium level of utility can be solved as function of the metropolis population and the land areas and government policies in each of the cities. Then we represent U * by U * 5 U *(N, ] L, t], g) 5 U *(n 2 n j , L2j , t2j , g2j ), j 5 1, . . . ,J, ] ] ] ]
(4)
where L, ] t], and g] represent vectors of the land area, tax rates, and service levels in each of the cities. Utility is decreasing in population and the tax rate of any city and increasing in the land area and service level of any city. Because utility is equal in all cities, (4) also describes the utility level for a single city or a subset of the cities (U *(N-n j , L-j , t-j , g-j )) where L ]-j , t]-j , and ]g-j refer to vectors representing ] ] ] the land areas, tax rates, and government service levels of all cities except for city j. Fig. 1 depicts the equilibrium price of housing and populations for a metropolis consisting of two cities (1 and 2).6 Equilibrium requires that the demand for housing equal the supply of housing in both cities and the households in both cities receive the same level of utility. In Fig. 1, the supply of housing sites in city 1 (the number of households that can live in city 1) depends on the price of housing in city 1 and is given by N s1 ( p1 , t1 , g1 ). Since the demand for housing sites in city 1 equals the total population less the number of households living in city 2, the housing demand in city 1 depends on p2 . In addition, the equal utility condition requires that f ( y, p2 1t2 , g2 )5 f ( y, p1 1t1 , g1 ), yielding another relationship between prices in the two cities. Then using this relationship we can express the demand for housing in city 1 as a function of p1 , N d1 ( p1 , t1 , g1 ). The price of housing in and population of city 1 and are determined by the intersection of N d1 ( p1 , t1 , g1 ) and N s1 ( p1 , t1 , g1 ) with the price of housing in city 2 being p 2* . 6
I am grateful to Jon Sonstelie for suggesting a graphical interpretation of equilibrium and the comparative statics in this model.
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Fig. 1. Equilibrium in the housing market.
3.3. The effects of taxation and public services on population and prices To find the effect of an increase in the tax rate in city j on housing prices, we must consider its effect on both the utility level in the metropolis and equilibrium in the housing market. Then differentiating (1), (2), and (4) and solving for (dpj / dtj ) yields
S D
U *N 1 ≠l j ] ]] dpj a h j lj ≠pj ] 5 2 1 1 ]]]]]]]]] , 0, j 5 1, . . . ,J, dtj 1 U *n 1 ≠l j 1 ≠h j ]1] ] ]1] ] n j a h j l j ≠pj h j ≠pj
F
S
DG
(5)
where a is the marginal utility of income and U *N , denotes ≠U * / ≠N ,0. Inspection of (5) indicates that dpj / dtj is a function of the population of city j. Then differentiating (5) with respect to the n j gives
S D
F G
1 U N* 1 ≠l j dpj ]2 ] ]] ] dtj n j a h j l j ≠pj d ]] 5 ]]]]]]]]]2 . 0, j 5 1, . . . ,J, dn j 1 U n* 1 ≠l j 1 ≠h j ]1] ] ]1] ] n j a h j l j ≠pj h j ≠pj
F
S
DG
(6)
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163
As the population of the city increases relative to the rest of the metropolis, the magnitude of its price change decreases. This decrease occurs because a larger city has more influence on the metropolitan utility level, thereby passing on the effect of its tax increase to other cities. A city’s influence on the utility level depends on the number of residents who leave the city when the tax rate increases. The more who migrate, the greater the reduction in utility. For a small city, the tax increase is fully capitalized into housing prices with dpj / dtj 5-1. Full capitalization occurs because its population change has almost no impact on the population of the rest of the metropolis. The same approach can be taken to determine the effects of a change in a city’s service level on its housing prices. Totally differentiating (1), (2), and (4) and solving for dpj / dg j yields Ug j dpj ] 5 ]]]]]]]]]] . 0, j 5 1, . . . ,J. dg j 1 ≠l j 1 ≠h j a h j 1 U N* nj ] ] 1 ] ] l j ≠pj h j ≠pj
F
S
DG
(7)
Differentiating (7) with respect to n j gives
F G
S
D
dpj 1 ≠l j 1 ≠h j d ] U *n ] ] 1 ] ] Ug j dg j l j ≠pj h j ≠pj ]]] 5 2 ]]]]]]]]]]2 , 0, j 5 1, . . . ,J. dn j 1 ≠l j 1 ≠h j a hj 1 U *N n j ] ] 1 ] ] l j ≠pj h j ≠pj
F
S
DG
(8)
Again, the magnitude of the price change decreases with city size because the migration of residents into a small city will not have as much influence on the population of the rest of the metropolis and, therefore, the utility level. In Fig. 2 we graphically depict the impacts of a tax increase for a small city (Fig. 2a) and a large city (Fig. 2b). Differences in city size relative to size of the rest of the metropolis (city 2) are reflected in the elasticity of demand for housing in the city. Fig. 2a depicts the impact of a tax increase from t 01 to t 19 for a city that is small relative to the metropolis and therefore has an almost perfectly elastic demand for housing. The tax increase will increase the supply of sites (each household buys less housing) as well as the demand as a function of p1 as an increase in t1 means that for any given p2 , p1 must decrease. The tax increase leads to a reduction in p1 almost equal to the tax increase with almost no impact on housing prices in the rest of the metropolis. In Fig. 2b the same tax increase for a larger city has a small impact on its housing prices because some of the tax increase is ‘‘passed on’’ to residents of other cities in the metropolis through increased housing prices there ( p 29 ). Finally, because the objective of residents is land value maximization, note that since p5rl 1k,
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Fig. 2. Impact of property tax on housing prices.
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165
dr j 1 dpj dr j 1 dpj ] 5 ] ] and ] 5 ] ], j 5 1, . . . ,J. dtj l j dtj dtj l j dtj
(9)
4. Government policies, political pressure, and city size Epple and Zelenitz (1981) demonstrates that even with the costless mobility of capital and residents among a large number of localities, surpluses can be obtained by bureaucrats if not constrained politically. The greater the surplus received by the bureaucrats, the lower property values in the city. This suggests that it may be worthwhile for property owners to undertake some measures to constrain the government policies chosen by bureaucrats. In this section, a model in which bureaucrats (politicians) maximize surplus is developed. Unlike Epple and Zelenitz (1981), the politician faces a ‘‘political’’ constraint-the efforts of residents to defeat politicians whose policies reduce their property values. Residents’ efforts to constrain politicians (by reducing the probability of the politician being reelected) are chosen considering both the benefits of these efforts, increased property values, and the cost of the effort. Because the impact of taxes and services on property values varies with the size of the city, so do the efforts of the residents and therefore the tax and services as well.
4.1. The politicians’ objectives Following Becker (1983) and Hoyt and Toma (1989), I assume that politicians (or bureaucrats) respond to the efforts of residents in the city (lobbying and voting). Politicians may have the incentive to minimize the surplus received by bureaucrats and themselves, by lowering tax rates and increasing public services, because these policies will increase the probability of their reelection. Let the benefits received by politicians obtain be a function of expected surplus (ES) obtained from holding office
O b S P s(t T
ES(t, g, e) 5 n(t ph 2 g) 1
t 51
t
t
k 51
t 21
D
, gt 21 , e t 21 )9 n t (tt pt h t 2 gt ), (10)
where b is the discount factor ( b ,1) and T is the time until the politician would like to retire. The probability of being reelected is given by s(t, g, e)-reelection depends on the current policies and the efforts against the incumbent (e), with ≠s / ≠t ,0, ≠s / ≠g.0, and ≠s / ≠e,0.7 Thus the incumbent’s reelection depends 7
I assume that voters perceive the current policy as the best predictor of future policy and therefore the probability of reelection depends on current policy.
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upon his current policies and the level of effort in a campaign against him. This effort includes campaign expenditures, voting for alternative candidates, and unfavorable publicity. The politician, when choosing current government policies, must consider how these policies affect the efforts of residents to defeat him in the next election. For each level of effort, there are the associated expected surplus maximizing tax and public service policies, t (e) and g(e). As shown in Appendix A, the politician will reduce the tax rate when effort increases, dt / de,0, and decrease the service level, dg / de.0. Further, assume that d 2t / d 2 e.0 and d 2 g / de 2 ,0, the effects of effort by the residents on the politicians’ choice of policies decrease with the level of effort. Given the effects of effort on the probability of reelection, the politician will set a lower tax rate and higher service level than he would if the policies he chose had no impact on his reelection.
4.2. The residents’ objectives Residents will choose their effort against current politicians to decrease current (and expected) property tax rates and increase public service levels. Essentially, the residents are modeled as Stackelburg leaders. Residents, if they believe that a politician is not doing a satisfactory job, will spend money trying to elect a politician who will provide higher service levels and lower taxes (a politician with a lower discount rate and longer time horizon). The politician then views this as a credible threat and chooses his policies accordingly. As briefly discussed in Section 3, because residents are mobile and there is assumed to be a large number of cities offering different tax / service mixes, residents obtain their desired service / tax mix by choosing where to live–not by changing the mix of services in any city. Instead, as shown by Sonstelie and Portney (1978), residents will choose public services and taxes in the city where they own property (and reside) to maximize the value of that property (land).8 In the context of our model, residents will choose effort to maximize net land rent less the cost of this effort, Maximize V(e) 5 r(t (e), g(e))l] 2 e, e
(11)
where l] is the amount of land owned by a representative resident. Then the optimal effort is given by 8 For cities that are large enough to affect the level of utility in metropolis, residents of that city may consider how changes in the city’s policies will affect the general level of utility. If these changes are also considered then the residents would not simply choose the policy that maximizes land rent. The change in the general utility level, however, is likely to be secondary to any change in income residents may receive from a change in land rent they receive.
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F
G
≠r dg ≠r dt ] ] 1 ] ] l 5 1, ≠g de ≠t de ]
167
(12)
or, substituting price changes for the rent changes,
F
G
≠p dg ≠p dt ] ] 1 ] ] h 5 1. ≠g de ≠t de
(129)
Residents equate the marginal benefit of effort, the increase in property value from decreases in tax rates and increases in service levels, with its cost. The benefits of efforts by the residents depend on the changes in property values a government policy change brings. From (6) and (8), the change in housing prices arising from policy changes depends on the size of the city. To find how the efforts of the residents depend on the size of their city, (129) is totally differentiated with respect to n and e to give
3F
G
F G
dp dp d ] dt d ] dg dg dt ] ]]] ]]] ] 1 de dn de dn de ] 5 2 ]]]]]]]]] , 0. dn [d 2V/ de 2 ]
4
(13)
By (6) and (8), the numerator is negative and by the second order condition the denominator must also be negative, making de / dn,0. In larger cities, residents have less incentive to put effort into the political process because the cost of ‘‘bad’’ local politics is not as costly as it is in small cities. This is because of the incomplete capitalization of government policies into property values. Part of the cost of a tax increase in a large city is passed on to the rest of the metropolis in the form of higher property values-an externality ignored by the residents of the large city. An increase in the tax rate in a small city is more costly because it will result in a greater decrease in property values. An increase in the service level in a small city is also more beneficial because it will result in a greater increase in property values. Because a decrease in the tax rate and increase in the service level bring greater changes in property values in the small city, greater effort to achieve these policy changes will occur there. If effort levels are higher in smaller cities then tax rates will be lower and service levels higher. With identical cities, the more cities in the metropolis the smaller the share of the metropolis population each city has. Then the more cities, the greater the extent of capitalization and the more costly are tax increases and service decreases. With many cities in a metropolis tax rates should be lower and public service levels should be higher because residents have a greater incentive to exert effort to limit governments. Fig. 3 depicts the optimal efforts by residents in a small city (city 1) and a large city (city 2). The optimal effort for the small city is given by e 1* where dr 1 / de 1 51. However, at this level of effort for the large city dr 2 / de 2 ,dr 1 / de 1 5
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Fig. 3. Optimal effort and city size.
1 because decreases in tax rates and increases in public service levels bring small increases in property values in larger cities, so this level of effort is not optimal for the larger city. Instead, it will choose a lower level of effort, e 2* , where dr 2 / de 2 51.
5. Conclusion In this paper I develop a simple model that predicts that local government expenditures, and waste (surplus) should be greater in larger cities and in metropolitan areas that have fewer localities supplying public services. However, unlike Brennan and Buchanan (1980) and Epple and Zelenitz (1981) this prediction is not made in a framework without politics. Instead, the size (population) of a city, in relationship to that of the metropolis, influences the cost of inefficiency. This relationship exists because in larger cities the ‘‘cost’’ of higher taxes or lower quality services is lower because of incomplete capitalization. The larger a city or, alternatively, the fewer the number of cities, the smaller the decreases in property value for any given tax increase. Thus the benefit of increased efficiency and lower taxes, the increase in property values in the city, is
W.H. Hoyt / Regional Science and Urban Economics 29 (1999) 155 – 171
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smaller in larger cities. Thus residents of larger cities have less incentive to spend resources limiting government inefficiency. In equilibrium, then, we expect less monitoring and higher tax rates in larger cities and in metropolitan areas with fewer, larger cities.
Acknowledgements The author would like to thank seminar participants at the University of Maryland, George Mason University, and the 1993 Annual Meeting of the Southern Economics Association for their comments and suggestions. I am especially grateful to the editor and an anonymous referee of this journal, Wallace Oates, Jon Sonstelie, and Sally Wallace for their comments and suggestions.
Appendix A Let St represent the surplus in period t. Then the policies that maximize expected surplus must satisfy ≠s O S P s(t , g , e )D ] 5 0. ≠t
(A.1)
≠s O S P s(t , g , e )D ] 5 0. ≠g
(A.2)
T ≠ES ≠S ]] 5 ]0 1 b t St ≠t ≠t t 51
t
0
k51
k
k
k
0
and T ≠ES ≠S ]] 5 ]0 1 b t St ≠g ≠g t 51
t
0
k51
k
k
k
0
Assume that ≠ 2 s / ≠t ≠e,0, that an increase in lobbying effort increases the marginal reduction in the probability of being reelected due to a tax increase. Analogously, assume that ≠ 2 s / ≠g≠e.0, an increase in effort will increase the marginal increase in the probability of being reelected due to a service increase. Totally differentiating (A.1) with respect to t and e gives
FO
P
G
t ≠ 2s t ]] b s S( t , g , e ) d t 51 k 51 k k k dt ≠t ≠e ] 5 2 ]]]]]]]]]]] , 0. 2 de ≠ ES ]] ≠t 2 T
Differentiating (A.2) with respect to g and e gives
(A.3)
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FO
P
G
≠ 2s ]] t 51 b s k 51 S(tk , gk , e k )d ≠g≠e dg ] 5 2 ]]]]]]]]]]] , 0. de ≠ 2 ES ]] ≠g 2 T
t
t
(A.4)
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