Tiebout Competition, Yardstick Competition, and Tax Instrument Choice: Evidence from Ohio School Districts Joshua C. Hall* Assistant Professor of Economics Department of Economics and Management Beloit College 700 College Street Beloit, WI 53511 [email protected] Justin M. Ross Assistant Professor of Public Finance and Economics School of Public & Environmental Affairs Indiana University, Bloomington 1315 East Tenth Street Bloomington, IN 47405 [email protected] Abstract Previous research has shown that Tiebout-style fiscal competition among local governments reduces the likelihood of adopting income taxes. This literature has not yet considered the impact of yardstick competition on tax instrument choice. This paper employs spatial econometrics to test for yardstick competition in the decision to adopt an income tax. The results, based on Ohio school district data, indicate that school districts are more likely to adopt an income tax if their neighbors have already done so. While a negative correlation of Tiebout competition on district income tax adoption persists, controlling for spatial dependence reduces the statistical significance of the effect.

Keywords: interjurisdictional competition; tax structure; education finance JEL code: H71

*

The authors would like to thank Nigel Ashford, Peter Boettke, David Brasington, Stratford Douglas, Richard Hornbeck, Peter Leeson, Santiago Pinto, Todd Nesbit, John Spry, Russell Sobel, and Mehmet Tosun for helpful comments, suggestions, and assistance. Special thanks are also due to John Spry for sharing his data. Hall would like to thank the Institute for Humane Studies, West Virginia University, and the Social Philosophy and Policy Center for financial support.

Tiebout Competition, Yardstick Competition, and Tax Instrument Choice: Evidence from Ohio School Districts

1

INTRODUCTION

In his seminal 1956 paper, Charles Tiebout suggested that the mobility of households between local governments could approximate a competitive market setting if the number of local communities was sufficiently large (Goodspeed 1998). Tiebout‟s goal was to show how preferences for local public goods could be revealed in a world without politics (Fischel 2001). The Tiebout model is also the underpinning of the conventional wisdom among public finance economists that local governments do face strong competitive pressures from mobile households (Mieskowski and Zodrow 1989). Thus, „voting with your feet‟ is commonly viewed as being analogous to voting with your pocketbook in conventional market settings, so much that voting at the ballot box is often viewed as inconsequential to the level and quality of goods provided by local governments. This idea has motivated empirical research on horizontal competition among governments and has been found to improve efficiency in a variety of settings.1 This „Tiebout-style‟ fiscal competition among local governments is often thought to limit the ability of local governments to levy non-benefit taxes, i.e., taxes where the level of benefits is not commensurate with level of taxation (Oates 1999).2 For instance, the mobility of households might prevent local governments from engaging in redistribution if upper income households can move to a nearby community with less redistribution. In this manner, fiscal competition among local governments could also affect the tax structure they adopt. Given the widely-held view in public finance that

1

governments should diversify their tax base for the purpose of revenue stability, existence of mobility constraints on tax instrument choice could have important policy implications. The interest of this paper will focus on residency-based school district income taxes, for which Spry (2005) found fiscal competition to be a limiting factor in their adoption. In the tax competition literature, however, there exists another form of competition: yardstick competition. Formalized by Besley and Case (1995), yardstick competition suggests that voters in one locality utilize information from surrounding localities in making their decisions. Though theoretically the effect of yardstick competition on income tax adoption is ambiguous, as voters can respond positively or negatively to the adoption of an income tax in nearby school districts, the model does imply spatial clustering of policy choices as multiple localities observe their neighbor and react to this information. This motivates the implementation of spatial econometrics, where the adoption of a school district income tax can be modeled as a function of adoption by its neighbors.3 Research by Fiva and Rattsø (2007) on yardstick competition and tax instrument choice has similarly employed this empirical approach and uncovered evidence of spatial dependence. In the presence of spatial dependence, non-spatial estimates can be biased, inconsistent, or both (Anselin 1988). Thus, a finding of spatial autocorrelation casts doubt on the estimates of coefficients on the remaining regressors, including measures of interjurisdictional competition.4 Brasington (2007) demonstrates that failing to account for spatial dependence among local governments can lead to an upward bias in empirical estimates of interjurisdictional competition. This result is important because the statistical

2

and economic significance of fiscal competition measures could disappear or amplify once spatial dependence among local governments is properly taken into account. Using data from a cross-section of Ohio school districts, this paper demonstrates that yardstick competition matters in the choice of whether or not to adopt a residencybased income tax.5 In addition, it is demonstrated that a failure to account for spatial dependence in tax instrument choice biases the estimates on the effect of fiscal competition. While there is still a negative relationship between the degree of interjurisdictional choice and income tax adoption, once spatial dependence is taken into account, the statistical significance of fiscal competition disappears. Section 2 presents an overview of the institutional setting and the data. Section 3 provides a first look at possible yardstick competition in the data. Section 4 discusses the empirical approach adopted to meet the two goals of this paper. Section 5 follows with the empirical results, and section 6 concludes.

2

DATA

To investigate the relative role of fiscal and yardstick competition in the determination of local government tax structure, a cross-section of Ohio school districts for the 1996-1997 school year is employed. Ohio is one of only two states that allow school districts to adopt both property and income taxes. Thus, the data set presents a unique opportunity to study the impact of yardstick and interjurisdictional competition on local government tax structure. While Ohio school districts are required to raise revenue through property taxation, in 1989 the state government gave school districts the option of also levying a residency-based income tax (Busch, Stewart, and Taub 1999). During the first year, 17

3

school districts received voter approval to tax income, and by the 1996-97 school year 119 of the 611 school districts in the state employed the income tax option. The dependent variable for the analysis is a binary variable equaling one if a school district utilized an income tax during the 1996-97 school year, and zero otherwise. Following Spry (2005), the extent of fiscal competition is measured as the number of other school district centroids that are within a ten mile radius of a district‟s centroid. This variable can be thought of as representing the „cost‟ of voting with one‟s feet. As the number of nearby districts increases, the cost of finding a nearby district to move to decreases, and reduces the ability of districts to extract revenue from high-income taxpayers. Thus, the hypothesized relationship between the number of districts within 10 miles and the use of the income tax is negative.6 The distance in this specification seems to be a reasonable proxy as it is about three-fifths of the average size of an Ohio county, but is somewhat arbitrary. To check for robustness, the empirical results will include alternative specifications and variables intended to capture the effect of fiscal competition. To facilitate a direct comparison of estimated parameter coefficients, the same explanatory variables used in Spry (2005) are employed in this analysis. Of primary importance in modeling the choice of tax structure is the ability to export the tax burden onto non-residents, since they cannot vote in district elections. As the income tax is residency-based, the entire statutory burden of the tax falls on district residents. In contrast, to some extent the burden of the property tax can be exported onto non-resident landowners and consumers. For example, Norstrand (1980) and Sjoquist (1981) find that local governments are more likely to use the property tax when it is viewed as being

4

exported onto non-residents. Similarly, Ross (2010) finds that local property assessors have higher assessment-to-sale price ratios for commercial property than for residential property. Therefore, the percentage of taxable business properties (commercial, industrial, or public utility) is included to measure the ability of a community to export the property tax burden. The greater the percentage of taxable business property within a school district, the lower the probability should be that it would internalize the school spending burden by adopting an income tax. The percentage of taxable property with a mineral classification is included with similar intuition and expectations regarding its sign. The percentage of taxable property that is in agricultural use is included to account for the fact that farmers are generally property-rich but income-poor, and thus would likely favor an income tax over a property tax of a similar amount.7 In analyzing voter behavior in over 1,200 Ohio school district elections, Shock (2004-2005) finds that the percentage of agricultural property strongly predicts the passage of an income tax. A positive relationship is also expected between the percentage of a school district‟s residents that are renters and the school district income tax rate. This is motivated by what is known as „renter illusion,‟ the perception that renters do not pay property taxes (Oates 2005). If homeowners view renters as being akin to free-riders who dodge property taxes, they might perceive the local income tax as a mechanism to recapture them.8 Shock (2004-2005) finds this relationship in his study of voting behavior, but Spry (2005) finds no statistically significant relationship. There is a large literature showing the effect of the elderly on school spending (Button 1992; Poterba 1997; Berkman and Plutzer, 2004; Brunner and Baldson 2004).

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There are two primary reasons to think that elderly voters would be in favor of an income tax. First, elderly homeowners are likely to see their tax burden fall when the income tax is used, because senior citizens tend to have lower incomes and higher property values. Second, elderly homeowners are more likely than the average homeowner to own their home outright. Thus, their property tax payments are lump-sum payments made separately to the county auditor‟s office instead of being collected with their mortgage payment and being held in escrow. The fiscal illusion created by paying property taxes together with the mortgage is reduced for many elderly taxpayers, and therefore, they may be more anti-property tax than would otherwise be explained by the first reason. From the perspective of the median voter, the likelihood of an income tax being utilized is expected to decline as the share of the income tax increases to the median voter. The income tax share for the median voter is calculated by multiplying one thousand times the median adjusted gross income in a school district divided by the total adjusted gross income in the school district. The higher the income tax share to the median voter, the less likely it is that a school district will utilize the income tax. The median voter pays property taxes as well, so their property tax share is likely to influence the adoption of an income tax. The property tax share is calculated as the median price of owner-occupied housing in the school district times the residential assessment ratio, divided by total property taxable value in the district.9 As the median voter property tax share increases, use of the income tax is expected to increase. Also included in the design matrix is the percentage of district residents that live in a rural area, and a binary variable equaling one if the school district is located inside a local government that also levies a local income tax.10 Rural residency is thought to be

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positively correlated with the adoption of a school district income tax beyond being involved in agriculture, though we are unaware of any theoretical reason given in the literature. Perhaps non-farmer rural voters tend to identify with the interests of their neighbors engaged in agriculture, or they tend to have more property than income. The „city tax‟ binary variable is thought to measure competition among local governments for the income tax base. Spry (2005) makes the case that the expected relationship is negative because use of the income tax by local cities would crowd out attempts by the school district to adopt the tax. Spry finds, however, that the relationship between the city tax and the school district tax is positive. This finding is not inconsistent with yardstick competition in that voters observing an income tax in use at the municipal level have information on its merits, and become more likely to adopt it. The data come from three sources. Demographic variables on school district residents were obtained from the National Center for Education Statistics (1994) „School District Data Book.‟11 That publication tabulates school district information for all U.S. school districts from answers on the 1990 Census long form. Data on assessed valuation by property type and school district income tax information comes from various publications of the Ohio Department of Taxation (2007) and the Ohio Department of Education (2007).12 The number of school districts within 10 miles was calculated by Spry (2005) using Geographic Information System maps from the U.S. Census Bureau. Data on the median home value and median income in a school district, used to calculate the property and income tax share variables, were obtained from the Ohio Department of Education (2007). Table 1 presents summary statistics for the variables.

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3

FOLLOW THY NEIGHBOR: A FIRST LOOK

Figure 1 shows a map of Ohio school districts. The grey districts are those that were using the school district income tax to raise revenue during the 1996-1997 school year. As noted in Spry (2005), the school district income tax appears to be clustered primarily in rural areas with less interjursidictional competition. This would appear to be consistent with the income tax being adopted in locations where there is a greater cost to „voting with your feet.‟ A good example of this would be in Mercer County, which is in the western part of the state along the Indiana border. The first district in the area to adopt an income tax was the Coldwater school district in 1990, one year after the state granted the power to school districts. One determining factor for their adoption was likely the property tax share paid by the median voter, which the previous literature has found to be directly correlated with the adoption of an income tax. The property tax share facing the median homeowner in Coldwater was 0.71, two standard deviations above the state mean. In 1991, neighboring Fort Recovery joined them in adopting the income tax (property tax share 0.45). Two other neighboring districts with property tax shares of 0.36 and 0.09 joined them in 1996. By 1997, four of the six school districts in the county had adopted a school district income tax. Figure 2 graphically presents this adoption process by year for Mercer County, with the number of districts in the county presented on the y-axis. The figure shows that as time progresses from 1989, the number of districts in the county using an income tax to raise revenue goes from zero to four. Figures 3-5 present a similar graphical analysis of income tax adoption over time for three additional counties where the income tax is

8

prevalent, and reveals a similar pattern. Figure 5, for example, shows Miami County (near Cincinnati) starting with zero districts using the income tax in 1989 and having one district adopt an income tax per year until 1994. Note that yardstick competition is clearly not the only factor leading to the adoption of an income tax. If it were, then the income tax would eventually be adopted by all school districts in Ohio. The factors that are negatively related to income tax adoption, such as the ability to export part of the tax burden through the taxation of business property, limits the geographic spread of income tax usage. In Miami County, for example, the remaining districts that have not adopted the income tax since 1996 have either a very high income tax share, have a lot of taxable business property, or both. The pattern of school district income tax adoption in Figure 1 presents a picture consistent with spatial dependence. The time-series presentation in Figures 2-5 provides evidence of yardstick competition in the adoption of the income tax, as the usage of the income tax seems to spread geographically within each county over time. While not proof of yardstick competition in the use of the income tax, these cases are suggestive of such a relationship. At the same time, they are not incompatible with there being a negative relationship between fiscal competition and income tax adoption. To further isolate statistically the importance of yardstick and fiscal competition in the adoption of an income tax, the remainder of the paper discusses and presents an economic analysis isolating these effects.

4

EMPIRICAL APPROACH

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The traditional approach to testing the effect of interjurisdictional competition on income tax adoption is to employ a standard probit model of the form: J

SDITi    WITHIN 10i    j Z ij   i

(1)

j 1

where SDITi is the binary variable identifying if school district i levied a school district income tax during the 1996-97 school year; WITHIN10i is the number of school districts within ten miles of school district i; and Zi is a j-dimension vector of the remaining explanatory variables representing other demographic and financial variables at the school district level. The coefficient of primary interest is  , because it measures the effect of Tiebout competition on the tax structure adopted by school districts. This is the approach adopted by Spry (2005). If there is no spatial dependence among school districts, the estimation of equation (1) by log-likelihood is appropriate. However, if the likelihood of a school district adopting an income tax is also a function of whether one‟s neighbors have adopted the tax, then the results of the standard probit analysis can be biased, inconsistent, or both (Anselin 1988). The geographic pattern of income tax adoption visible in Figure 1 is consistent with there being spatial dependence in the dependent variable. Brasington (2007) has found that the failure to control for spatial dependence among school districts in education production functions leads to estimates of the effect of interjurisdictional competition on outcomes being overstated. More generally, failure to take into account actual spatial dependence could potentially bias all parameter estimates and void subsequent hypothesis testing. Therefore, the empirical approach described here not only detects yardstick competition among local school districts, but

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also corrects for potential bias and erroneous findings of significance resulting from uncorrected spatial dependence. This paper addresses this potential problem by using two different models of spatial dependence. The first model is what is commonly referred to as a spatial probit lag model or spatial autoregressive probit model (SARP).13 A general overview of the SARP model can be found in LeSage (1999), but the basic idea can be obtained by analogy to an autoregressive (AR) model in time-series analysis. Just as an AR model includes lags over time to reflect the fact that a dependent variable might be influenced by its own value in previous periods, the SARP model includes lags over geographic space. In the context of school districts, one spatial lag from district i would encompass all contiguous neighbors, with each subsequent lag enveloping the neighbors of district i’s neighbors. The equation for the SARP model is very similar to the traditional probit model with one exception: J

SDITi      W  SDIT   WITHIN 10 i    j Z ij   i .

(2)

j 1

The primary difference between the traditional probit model and the SARP mode is the

 W  SDIT term. The spatial weight matrix, W, is a symmetric matrix that summarizes the spatial configuration of Ohio school districts on a map.14 The number of school districts in Ohio, in this case, 608, determines the number of rows and columns in the matrix.15 For each school district in the sample, the matrix specifies that district‟s geographic neighbors based on first-degree contiguity, while maintaining zeroes along the diagonal to avoid identifying an observation as a neighbor to itself.16 For example, if the school district in row one had only two geographic neighbors, its neighbors would 11

receive positive weights in their respective columns. All other columns for row one are given zeros as they represent the district itself or non-contiguous neighbors. Before being employed in regression analysis, the weight matrix is standardized so that each row equals unity with each contiguous neighbor receiving equal weight. For the school district represented in row one with two contiguous neighbors, each neighbor would have a weight of 0.5. A district with three neighbors would each receive a weight of 0.33, and so on. If ρ, the coefficient on the spatial weight matrix, is statistically different from zero there is evidence of spatial dependence in the dependent variable. The estimate of spatial dependence can be thought of as a school district‟s reaction function to the use of the school district income tax in nearby districts (Brueckner and Saavedra 2001). Following Fiva and Rattsø (2007), a value of ρ statistically different from zero is taken as evidence that yardstick competition matters in the choice of the income tax by school districts. The Bayesian approach to estimating the SARP model is conventionally employed to deal with two practical issues. First, maximum likelihood approaches to estimating spatial probit models take a notoriously large amount of time to compute, especially compared to the Bayesian approach. Beron and Vijverberg (2004) reported that it took several hours to estimate such a model with 49 observations, whereas Pace and LeSage (2009) report that a sample of 1,000 achieved convergence with a Bayesian Markov Chain Monte Carlo approach in 586 seconds. Second, heteroscedasticity introduced by the non-spherical variance-covariance matrix is created by the SARP. In a survey of different methods of dealing with heteroskedasticity in discrete dependent variable spatial models, Fleming (2004) concludes that the Bayesian approach pioneered

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by LeSage (2000) is the superior approach to dealing with this problem. The advantage of the Bayesian approach is that it allows for heteroskedastic error terms that it does not lead to inconsistent parameters. An excellent overview of the Bayesian SARP model can be found in Fiva and Rattsø (2007). The Bayesian SARP method developed by Pace and LeSage (2009) is a Markov Chain Monte Carlo (MCMC) method using a Gibbs sampling process, which is repeated a large number off times to obtain conditional distributions for the model parameters. The Gibbs sampler requires a large number of draws to derive conditional distributions for all the parameters. According to convergence diagnostics, the MCMC process converges after roughly 950 draws with the first fifteen discarded in order for the sampler to reach a steady-state. The results here are all based on 1,000 draws with the first fifty excluded.17 Relying on a finding that ρ is non-zero and statistically significant in the SARP model as evidence of yardstick competition can be problematic, since the SARP model assumes that the variance-covariance matrix of the error term is not spatially dependent.18 This is often not the case since unobserved, and therefore omitted, variables often follow spatial patterns in cross-section data. In other words, spatially dependent omitted variable bias could result in a biased estimate of ρ and the other regression coefficients. Spatial dependence in the error term is readily incorporated into models with continuous dependent variables, but these approaches have not been developed for limited dependent variable spatial models (Fiva and Rattsø 2007). It is the case, however, that spatial dependence in the error term can be nested into the spatial Durbin model by including the spatial lags of the other explanatory variables. In vector form, the generic spatial Durbin model can be expressed as

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y    Wy  X  WX    .

(3)

Pace and LeSage (2010) demonstrate that estimates of β and γ in the spatial Durbin model are not affected by the magnitude of spatial dependence in the omitted variables, and that there is no asymptotic bias in ρ. They conclude that the ability of the spatial Durbin model to deal with this omitted variable bias provides a strong econometric motivation for its use. This paper employs the Bayesian probit version of the model, called the spatial Durbin probit (SDP) model, which takes the following form: SDIT      W  SDIT  X  WX    .

(4)

For notational convenience, the independent variables in equation (2) are subsumed into design matrix X in equation (4). The WX term is the product of all independent variables multiplied with the spatial weight matrix. The γ coefficients thus pick up the extent to which the demographic variables of nearby districts influence the decision to adopt an income tax in the original school district. This approach significantly reduces bias in cross-section results by eliminating spatially dependent omitted variable bias (Pace, Barry, and Sirmans 1998; Brasington and Hite 2005; Pace and LeSage 2010).19 In the presence of spatial dependence in the error term, this will be the appropriate specification.20

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EMPIRICAL RESULTS

The first objective of the empirical analysis is to test for yardstick competition among school districts in adopting an income tax. Recall that if the spatial lag coefficient, ρ, is statistically different from zero then this will be taken as evidence of yardstick competition. If yardstick competition is observed, then it is also likely that the estimated

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coefficients from traditional probit analyses of tax instrument choice are biased. Thus the second goal of the empirical analysis is to see, conditional on there being spatial dependence, how the conclusions on fiscal competition and tax instrument choice differ between spatial and non-spatial models. Table 2 presents the results of these benchmark regressions against SARP and SDP. The non-spatial probit estimates replicate the results of Spry (2005) and are generally consistent with prior expectations.21 As with traditional probit estimation, the coefficients in Table 2 are difficult to interpret, and require relating the variable of interest to the calculation of the probability curve‟s slope, while holding all other variables constant. Since the magnitude of the slope is dependent, not just on the correlation coefficients, but the level at which the other variables are held constant, the conventional approach is to evaluate them at their means and at zero for dummy variables. These marginal effects can then be calculated as the change in the predicted probability that a school district has adopted an income tax, holding all other variables constant at their respective means. The spatial lag term in the SARP model has an estimated coefficient of 0.53 and is significantly different than zero at the one percent level, indicating the presence of yardstick competition. One of the consequences of this finding is that a change in the explanatory variable will have an indirect effect, which occurs through the spatial interdependence among observations.22 If spatial dependence was not important, then the direct and total marginal effects listed in table 2 would be the same. The total and direct marginal effect for all spatial models presented in this paper take this „spatial multiplier effect‟ into account using the approach from LeSage and Pace (2009, 293-5). In much the same way the money multiplier creates more than a dollar whenever a new dollar

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enters the banking system, the spatial multiplier has the ability to augment the effect of changing magnitudes in the explanatory variables. Unfortunately, since the spatial lag term ρ is the coefficient of an unobserved latent variable, the marginal effects of neighboring districts‟ use of an income tax on the probability of the home district adopting an income tax cannot be calculated (Rincke 2006). To contrast the marginal effect interpretations in table 2, the non-spatial probit model estimates a -0.019 marginal effect for the fiscal competition variable, Within10. The interpretation of this estimate is that if we were to observe two school districts that were identical in all ways except that one had one additional school district within 10 miles, the predicted probability regarding if the school district would have adopted the school district income tax would fall by -1.9 percent. However, the SARP model estimates that the direct impact of one district increase is to reduce its probability by -5.3 percent.23 Though the direct impact is the most analogous to the non-spatial probit marginal effect, note that some of this -5.3 percent estimate is generated through the spatial process. Intuitively, as the original district‟s neighbors become less likely to adopt the school district income tax through the spatial lag term, they themselves become even less likely to adopt the tax because they are their neighbor‟s neighbor. To the extent these impacts circle back to the originating observation, they are accounted for in this 5.3 percent estimate. However, the subsequent spatial spillover impacts from yardstick competition on neighboring observations, and accumulate to an additional -5.8 percent (0.111+0.053 = -.058) that is spread across all other observations. Thus the total marginal effect of -0.111 represents the sum of the reduced probabilities across all school districts

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of adopting the income tax, for the case when the school district has one more competing school district within ten miles. Table 2 demonstrates that the total marginal effect is more than double that of the direct marginal effect for all of the independent variables except for the fiscal competition variable. This suggests that in the SARP specification, yardstick competition plays a considerable role in understanding the social consequences of changes in the independent variables. Note also that the statistical significance changes in the direct marginal effects of several variables across the SARP and non-spatial probit models. Despite gains in magnitude, both fiscal competition (Within 10) and the percentage of taxable property that have a mineral classification lose their statistical significance, while the median income tax share variable gains statistical significance at the ten percent level. Finally, there are several magnitude changes among the statistically significant variables between the probit and SARP model‟s direct marginal effects. For additional interpretation, the marginal effect of a one standard deviation change in each continuous independent variable is also calculated and provided in appendix table 1. Finally, table 2 also presents the results from the SDP model, which extends the control variables to include spatial lags of the independent variables. While this specification is more draining on degrees of freedom, recall that this specification is helpful in applied work, because it clears spatially dependent omitted variable bias in the independent variables and provides asymptotically unbiased estimates of ρ (Pace and LeSage 2010). The spatial lag of the percentage of property that is agricultural is significant at the five percent level providing strong evidence of spatial dependence. Most importantly, however, the spatially lagged dependent variable is still positive and

17

statistically significant at the one percent level, suggesting that the finding of yardstick competition in the SARP regression was not the result of spatially dependent omitted variable bias. Again, for interpretive purposes, the parameter estimates of the SDP model must be ignored, and the direct effects have to be calculated. Like the SARP model, the direct marginal effects in the SDP are most analogous to the marginal effects of the non-spatial probit model, and like the SARP specification, they account for spatial shocks in a school district that circles back to them after passing through neighbors. However, in the SDP, these changes in independent variables have an additional pathway through their corresponding spatial lag. The total marginal effect includes both the direct effect on the area itself and the cumulative change in predicted probabilities for all other observations, and interpretation is the same as with the SARP model. Marginal effects for a standard deviation change in the SDP model are also included in appendix table 1. The SDP results have a smaller spatial dependence parameter in ρ than does SAR, likely due to the clearing of spatially dependent omitted variable bias. In general, the SDP model direct impact estimates are pretty similar to the SARP estimates. The main variable of interest for this paper, fiscal competition (Within10), is virtually unchanged. The percentage of taxable property from agriculture loses statistical significance and shrinks in magnitude from 2.30 to 1.47. Both of these magnitudes in the spatial models are larger than the statistically significant non-spatial probit estimates. The median income tax share variable gains some statistical significance in the direct marginal effect, albeit at a slightly reduced magnitude.

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There are more changes in the total marginal effects going to the SDP model from SARP, including with the income tax share. Even though the direct effect is larger in SARP, the indirect effects spilling over onto other school districts create a larger and statistically significant total marginal effect. Similarly, the direct effect of having a city income tax increases the predicted probability of school district income tax adoption by 46.6 percent, smaller than the 57.5 percent estimate in SAR. However, the aggregated change in predicted probability impacts on all other school districts by adding another 93.7 percentage points for a total impact of 140.3 percent.24 If policymakers are interested in advancing school district income tax adoption, then this finding regarding the city tax should be of interest. The finding that fiscal competition is no longer statistically significant once spatial dependence is taken into account might be a function of how the degree of interjurisdictional competition is defined. In addition to the number of school districts within ten miles, Spry (2005) also estimates the number of districts within 12 and 15 miles. Another definition of fiscal competition frequently used in the literature is a Herfindahl index of market concentration (see, for example, Borland and Howsen (1996) or Hoxby (2001)). Here the Herfindahl index takes the form of: J

HERF  1   S 2jm

(4)

j 1

where s jm is equal to district j‟s share of school enrollment in county m. Using this formulation, a „monopoly‟ county will have a value of zero and as „perfectly competitive‟ county would approach zero in the limit.

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Using the same specification employed in table 2, table 3 presents an abridged reporting of the marginal effects for the alternative fiscal competition measures when estimated with the non-spatial probit, SARP, and SDP models. Unabridged results are available upon request from the authors. As can be seen in table 3, changing the definition of fiscal competition does not change the results. Under all three fiscal competition definitions, the non-spatial probit model reports a five percent level of statistical significance that is wiped out once spatial dependence is taken into account. In the case of the within 12 and within 15 miles measures, the marginal effect is smaller compared to the ten mile measure as well. This is to be expected given the usual assumption that further away districts would be weaker substitutes. Thus, the evidence presented in this paper suggests that fiscal competition does not play a large role in the tax structure of local school districts.25 In addition, the spatial lag term is statistically significant in all three specifications, with spatial lag estimates ranging from 0.426 to 0.538, providing further evidence to support the finding that yardstick competition plays an influential role in the decision of school districts to adopt an income tax.

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CONCLUSION

This paper finds evidence of yardstick competition in the choice of Ohio school districts to adopt an income tax. The parameter on the spatial lag term estimating the degree of yardstick competition varied from 0.426 to 0.538 across the appropriate specifications. These findings suggest that the probability of passing an income tax is higher in school districts whose neighbors already utilize the income tax.

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Previous research has found a negative relationship between Tiebout-style fiscal competition and the use of an income tax by Ohio school districts. However, once spatial dependence is taken into account this statistical significance disappears. Furthermore, spatial dependence can demonstrate to policy makers which variables have considerable spillover impacts on other observations through yardstick competition. These findings are consistent those presented in Brasington (2007), which demonstrated that interjurisdictional effects are biased when spatial dependence is omitted. Researchers examining the effect of interjurisdictional competition on various outcomes need to account for spatial dependence among governments in order to avoid having biased, inefficient, and inconsistent parameter estimates.

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REFERENCES Anselin, Luc. 1988. Spatial Econometrics: Methods and Models. Dordrecht: Kluwer Academic Publishers. Anselin, Luc. 2002. Under the Hood: Issues in the Specification and Interpretation of Spatial Regression Models. Agricultural Economics 27(3): 247-67. Berkman, Michael B., and Eric Plutzer. 2004. Grey Peril or Loyal Support? The Effects of the Elderly on Educational Expenditures. Social Science Quarterly 85(5): 1178-92. Belsley, David A., Edwin Kuh, and Roy E. Welsch. 1980. Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: Wiley. Besley, Timothy, and Anne C. Case. 1995. Incumbent Behavior: Vote Seeking, Tax Setting and Yardstick Competition. American Economic Review 85(1): 25-45. Beron, Kurt J., and Wim P.M. Vijverberg. 2004. Probit in a Spatial Context: A Monte Carlo Analysis. In Advances in Spatial Econometrics, Luc Anselin, Raymond J.G.M. Florax, and Sergio J. Rey, eds., 169-195. Berlin: Springer Verlag. Borland, Melvin V., and Roy M. Howsen. 1996. Competition, Expenditures and Student Performance in Mathematics: A Comment on Couch et al. Public Choice 87(3-4): 395-400. Brasington, David M. 2007. Public and Private School Competition: The Spatial Education Production Function. In Time and Space in Economics, T. Asada and T. Ishikawa, eds., 175-203. Tokyo: Springer. Brasington, David M., and Diane Hite. 2005. Demand for Environmental Quality: A Spatial Hedonic Analysis. Regional Science and Urban Economics 35(1): 57-82 Brennan, Geoffrey, and James M. Buchanan. 1980. The Power to Tax: Analytical Foundations of a Fiscal Constitution. Cambridge: Cambridge University Press. Brunner, Eric, and Ed Balsdon. 2004. Intergenerational Conflict and the Political Economy of School Spending. Journal of Urban Economics 56(2): 369-88. Busch, Ronald J., Douglas O. Stewart, and Allan J. Taub. 1999. Ohio‟s City-School District Income Tax: A Tale of Two Cities. Journal of Education Finance 24(3): 339-52. Button, James W. 1992. A Sign of Generational Conflict: The Impact of Florida‟s Aging Voters on Local School and Tax Referenda. Social Science Quarterly 73(4): 78697. 22

Brueckner, Jan, and Luz A. Saavedra. 2001. Do Local Governments Engage in Strategic Property-Tax Competition? National Tax Journal 54(2): 203-29. Cox, Michael E., and Justin M. Ross. 2010. Robustness and Vulnerability of Community Irrigation Systems: The Case of the Taos Valley Acequias. Workshop in Political Theory and Policy Analysis Working Paper, Bloomington, IN. Fischel, William A. 2001. Homevoters, Municipal Corporate Governance, and the Benefit View of the Property Tax. National Tax Journal 54(1): 157-74. Fiva, Jon H., and Jørn Rattsø. 2007. Local Choice of Property Taxation: Evidence from Norway. Public Choice 132(3-4): 457-70. Fleming, M. 2004. Techniques for Estimating Spatially Dependent Discrete Choice Models. In Advances in Spatial Econometrics: Methodology, Tools and Applications, L. Anselin, R. J. G. M. Florax, and S. J. Rey, eds., 145-68. Berlin: Springer-Verlag. Goodspeed, Timothy J. 1998. Tax Competition, Benefit Taxes, and Fiscal Federalism. National Tax Journal 51(3): 579-86. Hall, Joshua C. 2006. Fiscal Competition and Tax Instrument Choice: The Role of Income Inequality. Economics Bulletin 8(12): 1-8. Hall, Joshua C. and Justin M. Ross. 2010. Municipality-School Border Congruency and the Coordination of Inputs to Education: Evidence Ohio School Public Financing and Class Size. Indiana University School of Public & Environmental Affairs Working Paper, Bloomington, IN. Hoxby, Caroline M. 2000. Does Competition Among Public Schools Benefit Students and Taxpayers? American Economic Review 90(5):1209-38. King, Kerry A. 2005. The Impacts of School Choice on Regional Economic Growth. The Review of Regional Studies 35(3): 356-68. LeSage, James. P. 1997. Regression Analysis of Spatial Data. Journal of Regional Analysis and Policy 27(2): 83-94. LeSage, James P. 1999. Spatial Econometrics. In The Web Book of Regional Science (www.rri.wvu.edu/regscweb.htm), Scott Loveridge, ed. Morgantown, WV: Regional Research Institute, West Virginia University. LeSage, James P. and R. Kelly Pace. 2009. Introduction to Spatial Econometrics. Boca Raton, FL: Taylor & Francis Group.

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Mieszkowski, P., and G. Zodrow. 1989. Taxation and the Tiebout Model: The Differential Effects of Head Taxes, Taxes on Land Rents, and Property Taxes. Journal of Economic Literature 27(3): 1098-146. Mukherjee, Bumba, and David A. Singer. 2008. Monetary Institutions, Partisanship, and Inflation Targeting. International Organization 62(Spring): 323-358. Mur, Jesus, and Ana Angulo. 2005. A Closer Look at the Spatial Durbin Model. ERSA conference papers ersa05p392, European Regional Science Association. National Center for Education Statistics. 1994. School District Data Book. Washington, DC: National Center for Education Statistics. Norstrand, Rolf. 1980. The Choice between Income Tax and Land Tax in Danish Municipalities. Public Finance 35(3): 412-24. Oates, Wallace E. 1999. An Essay on Fiscal Federalism. Journal of Economic Literature 37(3): 1120-49. Oates, Wallace E. 2005. Property Taxation and Local Public Spending: The Renter Effect. Journal of Urban Economics 57(3): 419-31. Ohio Department of Education. 2007. District Profile Report (formerly Cupp Report) [electronic file]. Columbus, OH: Ohio Department of Education. Ohio Department of Taxation. 2007. Tax Data Series: School District Data [electronic file]. Columbus, OH: Ohio Department of Taxation. Pace, R. Kelley, and James P. LeSage. 2010. Omitted Variable Biases of OLS and Spatial Lag Models. In Progress in Spatial Analysis: Methods and Applications, Antonio Páez, Julie Le Gallo, Ron N. Buliung and Sandy Dall‟Erba, eds.,17-28. Berlin: Springer. Pace, R. Kelley., Ronald Barry, and C. F. Sirmans. 1998. Spatial Statistics and Real Estate. Journal of Real Estate Finance and Economics 17(1): 5-13. Poterba, James M. 1997. Demographic Structure and the Political Economy of Public Education. Journal of Policy Analysis and Management 16(1): 48-66. Rincke, Johannes. 2006. Policy Innovation in Local Jurisdictions: Testing for Neighborhood Influence in School Choice Policies. Public Choice 129(1-2): 189200. Ross, Justin M. 2010. Assessor Incentives and Property Assessment. Forthcoming in Southern Economic Journal.

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Schneider, Mark. 1986. Fragmentation and the Growth of Local Government. Public Choice 48(3): 255-64. Shock, David R. 2004-2005. Voting Behavior in School District Tax Elections: An Analysis of Property and Income Tax Options. Journal of Economics and Politics 17(1): 1-15. Sjoquist, David. 1981. A Median Voter Analysis of Variations in the Use of Property Taxes among Local Governments. Public Choice 36(2): 273-85. Sobel, Russell, and Kerry King. 2008. Does School Choice Increase the Rate of Youth Entrepreneurship? Economics of Education Review 27(4): 429-38. Sobel, Russell, and Andrea Dean. 2008. Has Wal-Mart Buried Mom and Pop? The Impact of Wal-Mart on Self-Employment and Small Establishments in the United States. Economic Inquiry 46(4): 676-95. Spry, John A. 2005. The Effects of Fiscal Competition on Local Property and Income Tax Reliance. Topics in Economic Analysis and Policy 5(1): 1-19. Stansel, Dean A. 2006. Interjurisdictional Competition and Local Government Spending in U.S. Metropolitan Areas. Public Finance Review 34(2): 173-94. Staley, Samuel R., and John P. Blair. 1995. Institutions, Quality Competition and Public Service Provision: The Case of Public Education. Constitutional Political Economy 6(1): 21-33. Tiebout, Charles. 1956. A Pure Theory of Local Expenditures. Journal of Political Economy. 64: 416-24. Zax, Jeffrey. 1989. “Is There A Leviathan In Your Neighborhood?” American Economic Review 79(3): 560-67.

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Figure 1: Ohio School Districts with an Income Tax, 1997

Note: Districts in gray are those using the school district income tax during the 1996-97 school year.

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Figure 2: Income Tax Use in Mercer County, 1989-1997 6

Number of School Districts

5

4

3

2

1

0 1989

1990

1991

1992

27

1993

1994

1995

1996

1997

Figure 3: Income Tax Use in Darke County, 1989-1997 9 8

Number of School Districts

7 6 5 4 3 2 1 0 1989

1990

1991

1992

28

1993

1994

1995

1996

1997

Figure 4: Income Tax Use in Miami County, 1989-1997 9

Number of School Districts

8 7 6 5 4 3 2 1 0 1989

1990

1991

1992

29

1993

1994

1995

1996

1997

Figure 5: Income Tax Use in Putnam County, 1989-1997 9 8

Number of School Districts

7 6 5 4 3 2 1 0 1989

1990

1991

1992

1993

1994

1995

1996

1997

Table 1: Summary Statistics Variable

Mean

Min

Max

Standard Deviation

0.20 4.21 0.36 0.00 0.11 0.24 0.23 0.40 0.24 0.54 0.64

0 0 0.050 0 0 0.051 0 0.004 0 0 0

1 19 0.88 0.04 0.47 1 0.45 41.67 2.54 1 1

0.397 3.536 0.146 0.005 0.107 0.099 0.055 1.746 0.233 0.413 0.481

School District Income Tax Number of Districts Within 10 Miles Business Property % Mineral Property % Agricultural Property % Renters % Elderly % Income Tax Share Property Tax Share Rural % City Tax

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Table 2: Fiscal Competition and Tax Instrument Choice: Model Comparisons Dependent variable: Binary Variable Equaling 1 if Taxing Income Non-Spatial Probit Variable

Parameter Estimates

SAR Probit Model

Marginal Effect

Constant

-0.711 (0.561) Within 10 -0.093 (0.034) Property Tax Share 1.264 (0.574) Income Tax Share -0.333 (0.258) % Renters -0.010 (1.111) City Tax Dummy 0.598 (0.162) % Senior Citizens -1.249 (1.463) % of Agricultural Property 2.901 (1.014) % of Mineral Property -53.264 (18.310) % of Business Property -1.818 (0.694) % of Rural Residents 0.273 (0.327) Spatial Lag Term ρ

*** ***

***

*** *** ***

-0.019 (0.007) 0.265 (0.129) -0.070 (0.053) -0.002 (0.225) 0.126 (0.029) -0.262 (0.310) 0.609 (0.226) -11.175 (3.892) -0.382 (0.144) 0.057 (0.069)

*** ***

***

*** *** ***

Parameter Estimates -0.304 (0.636) -0.049 (0.036) 1.527 (0.611) -0.578 (0.315) 0.359 (1.077) 0.535 (0.172) -1.117 (1.621) 2.148 (1.120) -21.498 (16.832) -2.158 (0.842) 0.265 (0.361) 0.538 (0.097)

Lag W10 Lag Property Tax Price Lag Income Tax Price Lag Renters Lag City Tax Lag Senior Citizens Lag % Agriculture Lag % Mineral Lag % Business Lag Rural Number of Observations Psuedo R-squared

607 0.23

Direct Marginal Effect

Total Marginal Effect

Spatial Durbin Probit Model Parameter Estimates

-0.503 (1.127) -0.053 -0.111 -0.067 (0.038) (0.089) (0.065) ** 1.637 ** 3.429 ** 1.320 (0.648) (1.534) (0.617) * -0.621 * -1.315 -0.460 (0.341) (0.860) (0.243) 0.387 0.850 1.000 (1.161) (2.597) (1.208) *** 0.575 *** 1.227 ** 0.416 (0.189) (0.550) (0.180) -1.203 -2.602 0.150 (1.761) (4.233) (1.976) * 2.304 * 4.845 * 1.004 (1.211) (2.930) (1.299) -22.904 -46.052 -5.935 (17.906) (37.398) (24.816) ** -2.329 ** -5.089 * -2.657 (0.945) (2.857) (0.918) 0.286 0.625 0.477 (0.391) (0.919) (0.397) *** 0.426 (0.132) 0.063 (0.089) 0.237 (1.015) -0.437 (0.537) -1.670 (2.328) 0.360 (0.378) -5.192 (3.352) 4.715 (2.424) -31.321 (34.047) 1.848 (1.522) -0.065 (0.793)

607 0.77

Direct Marginal Effect

-0.064 (0.062) ** 1.392 (0.632) * -0.517 (0.248) 0.902 (1.211) ** 0.466 (0.184) -0.353 (1.999) 1.473 (1.296) -8.883 (24.005) *** -2.595 (0.918) 0.497 (0.408) ***

** **

**

***

Total Marginal Effect

-0.008 (0.114) 2.757 (2.011) -1.590 * (0.947) -1.017 (4.559) 1.403 * (0.763) -9.617 (6.964) 10.330 ** (4.784) -65.364 (50.671) -1.426 (2.757) 0.828 (1.655)

*

607 0.65

* indicates significance at the 10% level, ** at 5% level and *** at the 1% level. The numbers in parentheses for non-spatial probit are standard errors, rest are posterior standard deviations. Marginal effects calculated at the means for continuous variables and zero for City Tax.

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Table 3: Fiscal Competition and Tax Instrument Choice: Robustness Checks on SDP Model Dependent variable: Binary Variable Equaling 1 if Taxing Income Within 12

Within 15

Herfindahl Index

Direct Marginal Effect

Total Marginal Effect

Direct Marginal Effect

Total Marginal Effect

Direct Marginal Effect

Total Marginal Effect

Non-Spatial Probit, equation (1)

-0.0131 ** (0.006)

N.A.

-0.0092 ** (0.004)

N.A.

-0.2396 ** (0.104)

N.A.

SARP Model, equation (2)

-0.012 (0.059)

-0.004 (0.101)

-0.0095 (0.040)

-0.0064 (0.067)

-0.639 (0.645)

-3.052 (2.930)

SDP Model, equation (4)

-0.012 (0.059)

-0.004 (0.101)

-0.010 (0.040)

-0.006 (0.067)

-0.639 (0.645)

-3.052 (2.930)

Model

* indicates significance at the 10% level, ** at 5% level and *** at the 1% level. The numbers in parentheses for non-spatial probit are standard errors, rest are posterior standard deviations. Marginal effects calculated at the mean for the continuous variables and zero for the 'City tax.'

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Appendix Table 1: Marginal Effects of Standard Deviation Change NonSpatial Probit Variable Within 10 Property Tax Share Income Tax Share % Renters % Senior Citizens % of Agricultural Property % of Mineral Property % of Business Property % of Rural Residents

SARP Model

SDP Model

ME

DME

TME

DME

TME

-0.069 0.062 -0.007 0.000 -0.028 0.000 -1.632 -0.158 0.027

-0.187 0.381 -0.061 0.021 -0.129 0.012 -3.344 -0.962 0.138

-0.392 0.799 -0.130 0.047 -0.278 0.024 -6.724 -2.102 0.301

-0.228 0.324 -0.051 0.050 0.097 -0.002 0.215 -3.669 -1.248

-0.029 0.642 -0.157 -0.056 -0.109 -0.048 1.508 -26.995 -0.686

Estimates are the marginal effect of a standard deviation change centered around the mean for the estimates reported in Table 2. Abbreviations are for marginal effect (ME), direct marginal effect (DME), and total marginal effect (TME).

33

Endnotes 1

In education, there is a large literature showing a positive relationship between the degree of interjurisdictional competition among school districts and school efficiency. See, for example, the work of Staley and Blair (1995) and Hoxby (2001). Building off the work of Brennan and Buchanan (1980) on constraining Leviathan, Stansel (2006) finds slower government growth in more competitive areas. His work is consistent with previous findings of Schneider (1986) and Zax (1989). 2 The terms fiscal competition, interjurisdictional competition, and „voting with your feet‟ are all used interchangeably because all describe the notion that the ability exit to nearby districts creates competitive pressure. Yardstick competition is different in that the competitive process occurs through „voice‟, i.e., politics. 3 Some recent examples of the use of spatial econometrics to applied public policy topics include Brueckner and Saavedra (2001), King (2005), Sobel and Dean (2008), and Cox and Ross (2010). 4 Interjurisdictional fiscal and yardstick competition, while sounding similar, are both theoretically and empirically distinct. Interjurisdictional competition is about the degree of jurisdictional choice in an area whereas yardstick competition is about the choices made by nearby governments, regardless of their number. 5 This institutional context was chosen so as to be directly comparable with past research that finds a significant negative relationship between fiscal competition and tax instruments choice (Spry 2005). 6 Another measure of interjurisdictional competition that is frequently used is a Herfindahl index measuring the local government‟s share of the total city or MSA government in terms of population or land area. Hall (2006) confirms Spry‟s (2005) finding that Tiebout mobility matters using a similar data set but measuring the degree of interjurisdictional competition using a Herfindahl index. Hall (2006) also introduces the role of income inequality, which is not addressed here so as to be as directly comparable to Spry (2005) as possible. 7 The excluded classification of property that is excluded to prevent singularity is the percentage of property that is residential. 8 Even when not in the majority, homeowners are frequently the most dominant political voice in local elections (Fischel 2001). 9 In Ohio, the assessment ratio on real property is 35 percent. Homes are appraised every six years in Ohio at full market value, thus 35 percent of the full market value of a home represents its taxable value. 10 The borders of school districts and municipal governments in Ohio are not contiguous, thus this measure is imprecise because it only reflects if a portion of school district residents have to pay a municipal income tax. Fortunately, this non-congruity has not been found to influence various public finance and school outcome measures in Ohio school districts relative to congruent districts (see Hall and Ross, 2010). Unfortunately, the data do not exist to calculate a more precise figure for this variable. 11 The original school district data book came on 44 CD-ROMs from the National Center for Education Statistics. The National Bureau of Economic Research has purchased and made available a more user-friendly version of the data at: www.nber.org/sddb/.

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12

A full description of the publications used to calculate the fiscal variables can be found in Spry (2005, Table 1), but this data appears to now be exclusively available online at: www.tax.ohio.gov/divisions/tax_analysis/tax_data_series/school_district_data/publicatio ns_tds_school.stm. 13 This is sometimes called a „spatial latent variable approach.‟ See, for example, Fiva and Rattsø (2007) or Rincke (2006). 14 LeSage (1997) provides a good overview of the construction of weight matrixes. 15 While Ohio had 611 school districts during the 1996-97 school year, three districts had to be excluded from the analysis because of missing or censored data. 16 There are many other possible weight matrixes. First degree contiguity is the most popular. See, for example, Mukherjee and Singer (2008) and Sobel and King (2008). 17 As a check on the MCMC diagnostics, the baseline model specifications in Table 2 were run with 5,000, 10,000, and 20,000 draws and the parameter estimates were basically unchanged. 18 It should be noted that this paper continues using the term „statistical significance‟ when moving from the non-spatial probit estimates to the spatial Bayesian estimates for the purpose of readability, even though this term is not technically correct in Bayesian inference. Bayesian‟s still usually report results as being „significant from zero‟ by similar standards, and report „credibility intervals‟ that are fairly analogous to confidence intervals. 19 Non-spatially dependent omitted variable bias is still possible, but since the explanatory variable are the same for the original district as well as the neighbors, most omitted variable bias is likely to be spatially dependent. 20 There exists a model specifically to correct for spatial error only, the SEM model. Mur and Angulo (2005) show that the SDP model accomplishes the same thing as a SEM model with the advantage that it sorts out individual effects in the disturbance term through the use of the spatially lagged independent variables. The SEM model is more frequently used in the literature; this is primarily because the SDP model is prone to multicollinearity. Fortunately, influential observation diagnostics developed by Belsley, Kuhn, and Welsch (1980) suggest that multicollinearity is not a problem. 21 The slight differences that do exist are likely the result of two missing observations that result from missing data. 22 See Beron and Vijverberg (2004, 174-175) for further explanation of the interpretation of probit parameters in the spatial context. 23 The direct and total marginal effects in spatial models are averages. Any given observation‟s marginal effect would be determined by their spatial relationship to others, which is likely unique. Therefore, these marginal effects are calculated for each observation for the purpose of reporting the mean of those values. 24 Again, this result does not suggest that the indirect effect for other schools is 93.7 percent, but rather that 93.7 percent is distributed among the other observations in the sample. 25 In unreported regressions available from the authors, a weight matrix used by Brasington (2007) that measures a school district‟s five nearest neighbors is utilized. The findings are qualitatively similar using this alternative weighting matrix.

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