The median voter according to GARP.

1. Introduction

The median voter hypothesis is the proposition that local governments behave "as if" they maximize the utility of the median income voter in the jurisdiction. Although an important tool in public economic analysis, there has been no conclusive direct test of the maximization hypothesis to date. Revealed preference theory shows that any finite set of price and quantity observations satisfying the generalized axiom of revealed preference (GARP) can be rationalized by the constrained maximization of an increasing, continuous, concave utility function (Afriat 1967, 1973; Varian 1982). This paper adapts the revealed preference method to the public goods problem in order to test municipal spending data for consistency under GARP, thereby providing the first direct test of whether or not the local governments behave "as if" they maximize median voter utility.

The median voter hypothesis represents a simple tool that is the most widely used characterization of local government behavior. Given its prominence in the literature, it is not surprising that the hypothesis itself has become the subject of scrutiny. The framework assumes direct or representative democracy without strategic behavior, in which competition among politicians ensures that the public sector bureaucracy responds efficiently to voters' desires. Public sector decision making reduces to an "as if" constrained maximization problem, a simplified picture of the outcome of collective action. Still, much of the empirical testing literature is motivated by concerns over whether the model is too simplistic. Nonetheless, it can be argued that, given its depiction as an "as if" outcome, the median voter hypothesis should be judged not by its descriptive accuracy of the public sector decision process but instead by how well it explains observed local fiscal choices.

On this basis, the existing empirical evidence, although mixed, reveals a surprising amount of indirect support for the framework. One approach taken in the literature is to evaluate the median voter hypothesis by testing the predictive power of regression equations with median income and tax price terms for explaining state or local fiscal behavior. In this line of the literature, Inman (1978) and Deno and Mehay (1987) find that variables not associated with the median income voter do not add any significant explanatory power over and above the median voter regression model of local government spending for school districts and municipalities, respectively. Similarly, Holcombe (1980) determines that school district spending in Michigan follows the Bowen equilibrium predicted by the median voter hypothesis. McEachern (1978) concludes that state debt levels tend to follow those predicted by the median voter regression model and appear to be unaffected by whether debt issue decisions are made by direct democracy referenda or by elected representatives. Gramlich and Rubinfeld (1982) similarly find support for the "as if" median voter framework for county government spending in Michigan using individual voter survey data. On the other hand, Romer and Rosenthal (1982) show that Oregon school district spending follows neither the simple median voter hypothesis nor an alternative expanded model with bureaucratic agenda control.

Another line of literature tests the median voter hypothesis using econometric specification tests, evaluating the statistical performance of regression models with median income and tax price variables relative to ad hoc alternative spending models. Pommerehne and Frey (1976), Pommerehne (1978), Turnbull and Djoundourian (1994), and Turnbull and Mitias (1998) take this approach to show that median voter specifications tend to dominate the ad hoc alternatives for both Swiss and U.S. municipalities, even for multidimensional collective action decisions, but not for the higher level county and state governments in the U.S.

This paper takes a different approach to testing the median voter hypothesis. All of the above studies rely on parametric econometric methods. As such, they are really joint tests of both the underlying hypothesis and the specific algebraic forms used in the regression equations. Further, aside from using median income or tax price variables identified with the median voter, the econometric models typically do not incorporate all of the parametric restrictions of the median voter hypothesis (e.g., income-intergovernmental aids symmetry). Thus, it is not always clear if a particular study is testing the median voter hypothesis or some modification allowing for bureaucratic discretion, taxpayer fiscal illusion, or other mediating features. In contrast, this paper uses the nonparametric revealed preference theory to directly test the simplest form of the "as if" median voter utility maximization hypothesis without assuming a particular algebraic representation of preferences.

The discussion is organized as follows. Section 2 explains the revealed preference axioms used in the study and explains how the test procedure is adapted to the public goods problem. Section 3 tests the pooled sample of medium-size cities in five Great Lakes states. The results show numerous weak axiom and transitivity violations, thereby soundly rejecting the median voter hypothesis for the pooled sample. But this simply may mean that the assumption of homogeneous tastes and other factors does not hold across the broad multistate region covered by the pooled sample. Therefore, to see if pooling matters, we partition the data by state and then conduct the revealed preference tests on each separate state sample. These tests show unambiguous support for the median voter hypothesis in two states, strong support in one state, and rejection of the hypothesis in two states.

Section 4 looks more closely at the institutional features that might help explain the GARP violations in the data. In this section, we partition each state sample by the municipal government management structure, whether run by elected mayor-council or professional city managers. Tests of each data subset reveal that the conclusions are sensitive to these institutional factors; cities that are managed by professional managers who are hired by elected councils tend to support the median voter hypothesis, while cities that are managed directly by the elected mayor-council government tend to reject the hypothesis. Further tests also reveal, however, that once we control for population density, even the mayor-council form of city management supports the median voter hypothesis.

Section 5 contains our concluding remarks.

2. Testing the Median Voter Hypothesis Using GARP

The Revealed Preference Axioms

Let x = [y g] and p = [1 t] denote the median voter's consumption vector and price vector, respectively. Private consumption spending is y and the voter's consumption of the publicly provided service is g. The price of private consumption is normalized to one and the median voter's tax price of additional g is t.

The revealed preference relation is defined over consumption bundles in the usual fashion. Direct revealed preference is denoted R, while direct strict revealed preference is denoted P. For direct revealed preference, if [x.sup.i] is chosen by the voter facing prices [p.sup.i], then [x.sup.i] is directly revealed preferred to [x.sup.j], or [x.sup.i]R[x.sup.j], when [p.sup.i][x.sup.i] [greater than or equal to] [p.sup.i][x.sup.j]. For direct strict revealed preference, [x.sup.i]P[x.sup.j] when [p.sup.i][x.sup.i] [greater than] [p.sup.i][x.sup.j].

Under the weak axiom of revealed preference (WARP), if [x.sup.i]R[x.sup.j], then not [x.sup.j]P[x.sup.i], or the asymmetric relation,

[p.sup.i] [x.sup.i] [greater than or equal to] [p.sup.i][x.sup.j] [implies] [p.sup.j][x.sup.j] [less than] [p.sup.j][x.sup.i] (1)

We introduce the notion of indirect revealed preference V as the transitive closure of the direct relation R: If there exists some sequence [x.sup.i], [x.sup.k], . . ., [x.sup.i], [x.sup.j] such that [x.sup.i]R[x.sup.k], [x.sup.k]R[x.sup.r], . . ., [x.sup.l]R[x.sup.j] then [x.sup.i]V[x.sup.j]. Under the generalized axiom of revealed preference (GARP), [x.sup.i]V[x.sup.j] implies not [x.sup.j]P[x.sup.i], or

[p.sup.i][x.sup.i] [greater than or equal to] [p.sup.i][x.sup.k], [p.sup.k][x.sup.k] [greater than or equal to] [p.sup.k][x.sup.r], . . . [p.sup.i][x.sup.i] [greater than or equal to] [p.sup.i][x.sup.j] [implies] [p.sup.j][x.sup.j] [less than or equal to] [p.sup.j][x.sup.i]. (2)

Varian (1982) extends Afriat's (1967, 1976) results to show that if any finite number of {p, x} observations satisfy GARP in the form of Inequalities 2, then the data set can be rationalized by a continuous, increasing, concave utility function. In our context, if the public spending data satisfy GARP, then they can be regarded "as if" they were generated by the constrained maximization of a well-behaved utility function. Thus, in principle, testing the median voter hypothesis reduces to the task of testing the municipal spending data to see whether or not they satisfy Inequalities 1 and 2. To make the GARP test procedure operational in the public spending environment, we must first specify the median voter's price and consumption vectors, p and x, in terms of the observed public spending data. We consider this issue next.

The Price and Consumption Vectors in Terms of Observable Quantities

There are two related problems peculiar to public services that the median voter model must address. First, the total service level being provided to the jurisdiction is not directly observable; and second, the publicly provided service may exhibit an unknown degree of publicness or consumption congestion. Publicly provided goods are usually measured as expenditures, which takes care of the first problem. To deal with the second problem, we follow Borcherding and Deacon (1972) and Bergstrom and Goodman (1973) and a large subsequent literature and assume that the individual voter's consumption g is a function of the service provided to the jurisdiction, G, and the jurisdiction population n such that

g = G[n.sup.-[Pi]], (3)

where [Pi] is the congestion parameter. This approach admittedly sidesteps consumption distribution issues raised by Denzau and Mackay (1976), Hamilton (1983), Blecha (1987), and others, but this is still a reasonable place to begin. Equation 3 represents a popular specification in the literature and turns out to be easy to work with in the revealed preference environment.

Following the usual characterization, with lump-sum intergovernmental aid receipts A, the jurisdiction requires total tax revenues G - A to balance its budget. The voter's share of the local tax base (assumed to be the property tax share) is s, so that the tax bill is s(G - A). With income m and private consumption spending y, the voter's budget constraint is m = s(G - A) + y, which leaves

y = m + sA - sG. (4)

Finally, in order to specify the median voter's tax price of the public good, substitute G = g[n.sup.[Pi]] from Equation 3 into the voter's tax bill to get s([n.sup.[Pi]]g - A). Differentiating, the marginal tax price facing the median voter is therefore t = s[n.sup.[Pi]].

Pulling these results together, for our application, the price and consumption vectors are

p = [1 s[n.sup.[Pi]]] (5)

x = [m + s(A - G) G[n.sup.-[Pi]]], (6)

where px = m + sA. Following convention, assume that the congestion parameter is constant across all jurisdictions. In this application, WARP is Inequality 1 with Equations 5 and 6, or

[m.sub.i] + [s.sub.i][A.sub.i] [greater than or equal to] [m.sub.j] + [s.sub.j][A.sub.j] - [s.sub.j][G.sub.j] + [s.sub.i][[n.sub.i].sup.[Pi]] [[n.sub.j].sup.-[Pi]] [G.sub.j] [implies] [m.sub.j] + [s.sup.j][A.sup.j] [less than] [m.sub.i] + [s.sub.i][A.sub.i] - [s.sub.i][G.sub.i] + [s.sub.j][[n.sub.j].sup.[Pi]] [[n.sub.i].sup.-[Pi]] [G.sub.i], (7)

while the transitive closure implies the GARP Inequalities 2, here expressed as

[Mathematical Expression Omitted]. (8)

Notice that, once [Pi] is known, all prices and quantities in Inequalities 7 and 8 are expressed in terms of observable variables: median income, tax share, total city spending, intergovernmental aids receipts, and population. Of course, [Pi] is not known a priori; we can nonetheless calculate this parameter in the process of conducting the GARP tests below.

To summarize, Equations 5 and 6 allow us to use GARP to test the median voter hypothesis. The next section tests the observed city government spending patterns for compliance with Inequalities 7 and 8. If the data satisfy GARP, then they satisfy the "as if" median voter utility maximization hypothesis; if the data violate GARP, then they reject the "as if" hypothesis.

[TABULAR DATA FOR TABLE 1 OMITTED]

3. Utility Maximization Test Results

The data set comprises the 141 municipal governments with populations between 20,000 and 150,000 from the five Great Lakes states, Illinois, Indiana, Michigan, Ohio, and Wisconsin, for 1980. By drawing the data from contiguous states, we hope to minimize major interregional variation in climate, culture, etc., factors that might otherwise affect public spending patterns. This is particularly important for our tests of the pooled data because the nonparametric testing procedure does not allow us to conveniently introduce direct controls for many of these factors on city spending patterns. The total property tax base data are collected from Moody's Municipal and Government Manual and all other variables are from the 1983 City-County Data Book.

The variables used in the construction of Equations 5 and 6 are defined as typically found in the empirical literature. G is municipal general expenditures, m is the median household income, A is city intergovernmental aid receipts from higher level governments, n is jurisdiction population, and s is the median property tax share, calculated as the median value single-family house divided by the total property tax base.

We test the data for their consistency with GARP using a version of Varian's (1982) algorithm adapted to the SAS environment. Since the congestion parameter [Pi] is unobservable, we calculate it during the GARP testing procedure. We begin by constructing p and x vectors conditional on a given [Pi] value and then subject the set of constructed vectors to the GARP test. For each sample reported in Table 1, this process is repeated individually for each of the 101 constructed data sets for [Pi] values in increments of 0.01 over the interval 0.00 [less than or equal to] [Pi] [less than or equal to] 1.00. We then choose the [Pi] value from this series of tests that minimizes the total number of cities involved in violations of the Inequalities 7 and 8; these are the [Pi] values reported in Table 1.

Table 1 reports the GARP test results and congestion parameter estimates for the pooled data and for each separate state in the sample. The GARP-violation minimizing congestion parameter value (or values) [Pi] is reported in the third column. In a sample of N cities, there are N(N - 1)/2 violations of WARP possible and at least [N.sup.3] violations of transitivity possible. The fourth column presents the number of GARP violations that are possible in each case; this represents a lower bound on the number of potential violations and is offered as a reference point. The fifth column in Table 1 reports the total number of observed GARP violations for each sample. The numbers of cities that are involved in these violations are reported in the last column of the table.(1)

The congestion parameter estimates are similar to those typically found in the parametric econometric literature. For the samples with the least number of GARP violations (Illinois, Indiana, Michigan, and Ohio), the congestion parameter estimates generally fall between about 0.40-0.50. Only Indiana lends support to either purely public or uncongested ([Pi] = 0.0) and perfectly congested ([Pi] = 1.0) interpretations of the publicly supplied services.

The GARP test results are summarized in the last two columns in Table 1, particularly the last column relative to the number of cities in the sample. The pooled sample of cities in all five states clearly rejects GARP, hence the median voter hypothesis. This result contradicts much of the existing econometric evidence (Pommerehne and Frey 1976; McEachern 1978; Pommerehne 1978; Holcombe 1980; Gramlich and Rubinfeld 1982; Deno and Mehay 1987; Turnbull and Djoundourian 1994). This difference in outcomes may be driven to some extent by factors for which we have not controlled in the nonparametric tests.

In order to sort out the effects of some of these factors that may vary across states, we sort the entire sample by individual states, recalculating the congestion parameter estimates and the GARP tests, as reported in Table 1. Two states, Illinois and Indiana, reveal zero GARP violations. The medium-size municipalities in these states exhibit spending behavior that can be rationalized as if they maximize the utility of the median income voters; these states provide unambiguous and strong support for the median voter hypothesis.

Ohio exhibits 2 GARP violations that involve only 2 of the 39 cities. Strictly speaking, even a single GARP violation leads to the rejection of the utility maximization hypothesis. Nonetheless, the subsample of 37 cities out of 39 total cities generates no GARP violations, which shows some support for the hypothesis.

The Michigan and Wisconsin samples also show GARP violations. Unlike Ohio, though, the numbers of cities involved in the violations are relatively large, with 18% and 42% for Michigan and Wisconsin, respectively. Thus, even though the total number of GARP violations observed for each of these two states is small relative to the number of violations possible, the test clearly rejects GARP, hence the median voter hypothesis.

On balance, our evidence concerning the median voter hypothesis is mixed, which should not be surprising given the simplicity of the utility maximization hypothesis tested thus far. We have only controlled for the effects of consumption congestion in a rudimentary fashion and have ignored other factors that reflect differences in median voter tastes as well as institutional features of local governments that might affect how they operate. Further analysis of Michigan, Ohio, and Wisconsin is needed in order to see if we can sort out some of the factors that might be driving the observed GARP violations.

4. Institutional Effects on the Median Voter Hypothesis

This section addresses how institutional factors and other exogenous features affect government performance, thereby affecting the relevance of the median voter hypothesis for government behavior. Two factors that can be readily identified in the literature are the management structure of the local governments and the degree of urbanization. Consider the effects of each factor in turn.

Government Management Structure Effects

There are primarily two forms of management structure observed in our sample of municipal governments. In the mayor-council management structure, the management oversight activities are performed by the elected mayor. In the city manager management structure, the public bureaucracy is managed by a professional city manager, who is in turn employed by and responsible to the elected city council. On one hand, it is likely that the city manager form of government is generally better able to reduce costs, largely because professional management training and experience leaves the manager in a better position to organize efficient production and to bargain with public sector employees for wages, benefits, task assignments, and other work rules. The empirical evidence regarding the effects of professional city management on costs and expenditures, however, is mixed (Booms 1966; Ehrenberg 1980; Edwards and Edwards 1982; Deno and Mehay 1987; Hayes and Chang 1990).

On the other hand, because city managers are hired by the elected city councils, the city manager form of government introduces an additional principal-agent relationship with attendant agency problems. Therefore, even if the elected politicians are wholly responsive to voter's interests, unless an incentives mechanism can be constructed to bring the manager's behavior into line with voters' interests, the professional manager may drive a greater wedge between the level of public services provided and the level most desired by the median voter.

Thus, there are reasons to believe that cities being run by professional city managers might behave differently than those run directly by elected officials. We have no a priori expectation about how the two forms of government management will reflect upon the median voter hypothesis. If agency problems dominate, then even if the professional manager can provide the public services more efficiently, the outcome may diverge from that most preferred by voters. If the efficiency gains from professional management are sufficiently large, then even though the public manager introduces agency costs, the former may outweigh the latter with the end result of bringing the public sector activities more in line with what voters most prefer.

Booms (1966) finds that professionally managed governments tend to spend less than their counterparts with elected management. In contrast, Deno and Mehay (1987) find no discernible difference in spending behavior between the two types of management structures.(2) Although both studies present evidence regarding how the city management structure affects total spending, neither generates any direct evidence about how close either form of government comes to meeting voter demands. This section provides some direct evidence.

As reported in Table 1, Indiana and Illinois reveal no difference between city council and professional city manager governments; both forms support the median voter hypothesis. In this sense, these states yield results similar to Deno and Mehay's (1987) econometric results. The other three states, however, require additional scrutiny.

In order to see if the management structure affects whether or not the spending behavior follows the median voter hypothesis for the Michigan, Ohio, and Wisconsin municipalities, we [TABULAR DATA FOR TABLE 2 OMITTED] partition the sample of cities in each state by their management structure and then test each subsample for GARP violations.(3) Table 2 reports the results.

Comparing the city manager with the mayor-council results reported in the table, we see unambiguous support for the median voter hypothesis for city manager governments in both Ohio and Wisconsin. There is at best only weak support for the hypothesis for the mayor-council governments in all three states. The mayor-council governments in Wisconsin unambiguously reject the median voter hypothesis, with 43% of the cities involved in at least one WARP or transitivity violation. Taken together, these results appear to be more consistent with Booms (1966) than with Deno and Mehay (1987). The professional city manager governments in these states tend to behave as if they maximize the utility of the median income voter, while the elected council managed governments do not. At face value, these results support the notion that professional city management brings public spending behavior closer to meeting voter demands. The gains from professionally managing the resource mix in production and dealing with public sector unions appear to outweigh any efficiency losses arising from the principle-agent relationship between the elected officials and the managers.

Urbanization Effects

So why do elected mayor-council managed cities not behave consistently with the interests of the median voter in Michigan, Ohio, and Wisconsin? In order to shed additional light on this question, we further stratify the subsamples exhibiting GARP violations by the degree of urbanization, as measured by relative population densities. We sort the data in each subsample by density, partition the samples into higher and lower density halves, and then apply the GARP tests separately to each split sample.

Interestingly, all municipalities unambiguously support the median voter hypothesis once the city manager and mayor - council subsamples are further stratified by population density. For the cities managed by elected councils in particular, these results imply that the GARP rejections found earlier arise solely because the mayor-council governments in higher population density cities behave "as if" they are maximizing a different utility function than mayor-council governments in lower population density cities. Interpreted in this way, the results reported in Table 2 are largely consistent with the Tiebout (1956) hypothesis that voters sort themselves among jurisdictions to find those locales with private and public consumption opportunities closest to their most preferred outcomes. Consumers who choose to live in more densely settled municipal jurisdictions have different tastes than those who choose to live in less densely settled jurisdictions.

5. Concluding Remarks

According to established results drawn from demand theory, if the spending data are found to be consistent with GARP, then they can be rationalized by the maximization of a well-behaved utility function (Afriat 1967, 1973; Varian 1982). This paper applies the GARP empirical methodology in order to ascertain whether or not the observed local spending behaviors are "as if" the city governments maximize the utility of the median income voter in the jurisdiction.

We tested spending data from medium-size municipal governments in the five Great Lakes states. The initial results reject the median voter hypothesis for the pooled sample. Testing the data state-by-state, though, reveals unambiguous support for the median voter hypothesis in two states, strong support in one state, and outright rejection of the hypothesis in the other two states.

A closer look at the effects of the management structure and population density on the GARP test results shows that professionally managed cities tend to support the median voter hypothesis, while cities that are managed directly by the elected officials tend to reject the hypothesis. Nonetheless, further tests revealed that, once we control for jurisdiction population density, even the mayor - council form of city management supports the median voter hypothesis.

In summary, the revealed preference-based tests of the median voter hypothesis are sensitive to the degree of aggregation in the sample, institutional factors like the public sector management structure, and population density. Several studies have offered econometric evidence supporting median voter government behavior models with median income, tax share, intergovernmental aid receipts, population, and population density as common explanatory variables in their regression equations (Pommerehne and Frey 1976; Inman 1978; McEachern 1978; Pommerehne 1978; Holcombe 1980; Gramlich and Rubinfeld 1982; Deno and Mehay 1987; Turnbull and Djoundourian 1994). Similarly, this paper finds that the data are consistent with GARP. Applying Afriat's theorem, the municipal spending data can be rationalized by the maximization of a well-behaved utility function subject to the budget constraint of the median income household in each jurisdiction; the medium-size municipal governments in the sample behave "as if" they maximize median voter utility once we control for the state-specific effects, management structure, and population density.

1 Gross (1991) shows that the size of the violation in terms of normalized expenditures is not an accurate indicator of how far off the data is from satisfying the maximization of a single utility function. Therefore, we rely solely on the number of violations and the number of cities involved in the violations as the test decision criteria.

2 Hayes and Chang (1990) find that neither city management form clearly dominates the other in terms of cost-minimizing behavior, a result roughly consistent with Deno and Mehay (1987).

3 Each of the tests for the partitioned subsamples in Table 2 is based on the congestion parameters calculated for the respective entire state samples.

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