HOW MUCH MORE IS A GOOD SCHOOL DISTRICT WORTH? WILLIAM T. BOGART * & BRIAN A. CROMWELL **

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1 HOW MUCH MORE IS A GOOD SCHOOL DISTRICT WORTH? HOW MUCH MORE IS A GOOD SCHOOL DISTRICT WORTH? WILLIAM T. BOGART * & BRIAN A. CROMWELL ** Abstract This paper infers the value of public schools from sale prices of houses in neighborhoods in which public services are delivered by overlapping jurisdictions to isolate the effects of the public school from other local government services. We use information about houses that sold between 1976 and 1994 to decompose the difference in mean house value into a part due to differences in observable characteristics and an unobservable part due to differences in public services. We infer differences across jurisdictions in the value of local public schools under a variety of assumptions about the degree of tax and service capitalization. INTRODUCTION How much is your local public school worth? How much is your municipal government worth? These questions have been at the heart of the vast literature on the capitalization of taxes and public services into house values. * Department of Economics and The Center for Regional Economic Issues, Weatherhead School of Management, Case Western Reserve University, Cleveland, OH ** Deloitte & Touche, Washington, D.C Because local governments typically provide a variety of public services, it is difficult to identify the separate influence of, say, the public schools and the police department. This paper uses three examples of overlapping jurisdictions in Cuyahoga County, Ohio, to demonstrate how a standard decomposition technique can be used to infer the difference in the net-of-tax value of the distinct public services provided by two jurisdictions. Most public school districts in Ohio are coterminous with municipalities. However, there are situations in which part of a city belongs to one school district and the remainder of the city belongs to another school district. This situation makes it possible to perform an experiment whose intuition is as follows. Take a house in one school district and move it across the border to the other district. It receives the same municipal services, pays the same municipal taxes, and has the same physical characteristics as it did before. The only difference is in the school taxes owed and the public school services received. If the house value is different in the two school districts, then this reflects a difference in the net-of-tax benefits received from the respective 215

2 NATIONAL TAX JOURNAL VOL. L NO. 2 local public schools. We implement this experiment econometrically using data on sales of owner-occupied housing in the cities of Cleveland, Cleveland Heights, and Garfield Heights. We then use observed differences in taxes to estimate the differences in the value of the public school districts under a variety of assumptions about the degree of tax and service capitalization. ESTIMATION STRATEGY We use the overlap of jurisdictions providing different public services to identify the impact of the public sector on house values. To our knowledge, the only other paper to use a similar approach to this question is Richardson and Thalheimer (1981). They consider the case of Fayette County, Kentucky, in which there are two taxing districts: the city of Lexington and the county. They argue that there is no appreciable difference in service quality between the city and the county and, therefore, that any price difference is attributable to the effect of differential taxes. Their estimation technique is to include a dummy variable for the city in a hedonic regression including physical and neighborhood characteristics of houses that sold in 1973 and The study has several problems, as discussed in Yinger et al. (1988). The first problem is that the estimation approach cannot distinguish between the effect of taxes and any other omitted characteristic that varies systematically across the two districts. The second problem is that there do seem to be some service differences across the districts that are not completely accounted for. The third problem is one of sample selection bias, since Richardson and Thalheimer omit observations from the older part of the city without any justification in terms of the housing market or the provision of public services. The fourth problem also involves sample selection, since the location of a property in the city or the county depends on whether the city has chosen to annex the area. A shortcoming that is not discussed by Yinger et al. is that the dummy variable approach does not control for differences in the way that characteristics of houses are priced in the two taxing districts. In other words, the dummy variable approach does not control for possible interaction between local public services and housing characteristics. The decomposition approach we adopt explicitly accounts for this possibility. Our study also does not suffer from the simultaneity bias that Yinger et al. identify as the fourth problem in the Richardson and Thalheimer study (high property value areas may be likely targets for annexation by the city). In our case, the school district boundaries have not changed for at least 40 years. Before detailing the econometric approach we use, let us recapitulate the intuition behind our method. Consider two identical houses across the street from each other but in different school districts. They have the same physical characteristics and the same neighborhood characteristics. The only differences between them are the school taxes they owe and the quality of the school district they belong to. Any difference in the selling price of the two houses must, therefore, result from the differences in the school districts. In our case, we will compare houses in the Buckeye Shaker neighborhood of the city of Cleveland and houses in the cities of Cleveland Heights and Garfield Heights on this basis. There are two problems with our approach. First, like Richardson and Thalheimer (1981), we are subject to criticism for any omitted variables that vary systematically across districts. 216

3 HOW MUCH MORE IS A GOOD SCHOOL DISTRICT WORTH? However, this bias is attenuated because we are studying much smaller and more coherent areas than they did. Our area of study is the statistical planning area (SPA), a geographic designation used by the cities and the county as the basis for providing public services. The SPAs we study range from three to six census tracts in area. Second is the dual problem of selection bias and unobservable heterogeneity due to the fact that people choose in which local jurisdiction they wish to live. 1 Our econometric approach is a familiar one based on Oaxaca s (1973) decomposition of male-female wage differentials into a component based on differences in observable characteristics and a residual component based on unobservable characteristics. In his work, the residual component was assumed to reflect discrimination in the labor market. In our case, we will decompose the difference in average house value across jurisdictions into a component based on differences in observable characteristics of the houses and a residual component. This residual we ascribe to net-of-tax differences in the value of public services across districts. 2 The 1 value of a house is assumed to be a function of the physical characteristics of the house, the characteristics of the neighborhood in which the house is located, 1 and the characteristics of the public school district within which the house is located. This is the so-called hedonic price approach familiar from most studies of housing markets. We possess detailed information on the physical characteristics of the house and some proxies for the qualities of the neighborhood, but we do not have good measures of school district quality. Hence, our approach is to infer the value of the services provided by the local public school district. If the quality of the public schools is not orthogonal to the other characteristics of the house and the neighborhood, then the estimated coefficients on the observed variables will be affected by the omission of direct measures of the public schools. For example, the value of an additional bedroom could depend on the number of children a family has, and a bedroom in a high quality school district might be more highly valued by a family with children than a bedroom in a low quality school district. This problem exacerbates the well-known problems in inferring structural conditions of the housing market from what are essentially reduced-form regressions. See Epple (1987) 2 for a detailed discussion of this issue. This is not a problem for our analysis, however, because our only concern 2 is to completely remove the effect of observable characteristics. In other words, a reduced form interpretation of the coefficients is all that we desire. Formally, let V i and V j represent the sales price of a house in jurisdiction i and jurisdiction j, respectively. (This formulation follows Oaxaca, 1973.) Let X i and X j represent the observed characteristics of the house and the neighborhood. We estimate the following regressions using ordinary least squares (OLS). Note that the same set of right-hand-side variables is used in each of the two regressions: 1 ln (V i ) = X i β i + e i ln (V j ) = X j β j + e j. If we let V i and V j represent the geometric means of V i and V j, X i and X j the means of X i and X j, and β i and β j the estimates of β i and β j, then, from the 217

4 NATIONAL TAX JOURNAL VOL. L NO. 2 properties of OLS estimation, it must be the case that ln (V i ) = X i β i and ln (V j ) = X j β j. Now consider the following decomposition of the difference between ln (V i ) and ln (V j ). Let X be defined to equal X i X j and β be defined to equal β j β i. Then, we can write the following equation: 2 ln (V i ) ln (V j ) = X i β i X j β j = Xβ j βx i = Xβ i βx j. Equation 2 shows two alternative ways of expressing the idea that the difference in the mean house value across jurisdictions has two parts: first, a part due to differences in observable characteristics ( Xβ j or Xβ i ); and, second, a residual part that we attribute to differences in local public services ( βx i or βx j ). As Oaxaca (1973) points out, the reason that there are two alternatives is a variant of the familiar index number problem. Thus, we estimate the decomposition in both ways to establish a range of alternative estimates. In terms of the thought experiment, the index number problem arises because you can move the house in either direction across the school district boundary. In the thought experiment described earlier, the two houses being compared were physically identical. The decomposition procedure econometrically implements this assumption by controlling for the differences in the average physical characteristics of the houses in different jurisdictions ( X j or X i ). The procedure described above yields an estimate of the differential value of public services cum taxes. A related question is whether the difference in taxes between jurisdictions is completely offset by service differences ( you get what you pay for ). If the net-of-tax value of services is identical across jurisdictions, then ln (V i ) ln (V j ) = Xβ j = Xβ i. The answer to this question clearly depends both on whether taxes and public services are completely capitalized into the value of housing and on whether there are other unobserved factors explaining the house value differences. Let α represent a parameter accounting for both the degree of capitalization and the degree to which price differences across jurisdictions arise from differences in the quality of public services, 0 α 1. We expect that the rate at which tax differences and service differences will be capitalized will differ, because the monetary value of the service differences (not necessarily equal to the level of spending on services) will depend upon household demand and because the property taxes are deductible from the federal income tax. We account for this difference by using a capitalization parameter for taxes denoted ψ and equal to 0.7α, based on the idea that the marginal buyer is an itemizer and that a 30 percent marginal tax rate is a reasonable approximation for the tax rates prevailing in the period Let i represent the real discount rate, S the difference in the value of services across jurisdictions, T the difference in the taxes owed across jurisdictions, and v the difference in house values across jurisdictions due solely to the differences in taxes and public services. Then, we can write 3 3 v = (α S ψ T)/i or S = (i/α) v + (ψ/α) T. 218

5 HOW MUCH MORE IS A GOOD SCHOOL DISTRICT WORTH? Because v and T are observable, we can 3 estimate S for different values of i and α. This allows us to compare S and T. As was the case with the change in value across jurisdictions, we only want to calculate the change in taxes net of any differences in the physical and neighborhood characteristics of the house. The property taxes associated with a property can be written as T = ta, where t is the tax rate (millage) and A is the assessed value of the house. Both the millage and the assessed value change if a house moves from one jurisdiction to another. Accounting for these changes leads to the following expression for T: 4 T = t A + ta. All of the variables on the right-hand side of equation 4 are observable, so that we can calculate T. In Ohio, A is defined to equal 35 percent of the market value of the house V. Therefore, A = 0.35 V. Because we wish to focus on the changes in assessed value holding physical characteristics constant, v (defined earlier) is the correct measure of the change in value to use in calculating the change in assessed value in equation 4, that is, A = 0.35 v. An immediate question is, Why not include taxes as an independent variable in the hedonic regression? This approach, common to the capitalization literature, is conceptually different than what we are trying to accomplish. If we include taxes on the right-hand side, then it is important to include spending as well, because school taxes and school spending are correlated. But we should also include direct measures of school quality in that case, because spending is not perfectly correlated with school district quality. If we do this, then we should also pool all of the cities to take advantage of cross-sectional variation as well as time-series variation in the data. Having done all of this, we arrive back at a standard capitalization regression. If we had good measures of school spending and especially school quality, then we would be interested in this approach, if only as a comparison with the decomposition method we use. Our technique has the advantage of not requiring school quality data to be implemented. Of course, understanding why a school district is relatively good or bad is an important question in its own right. This paper only answers the question of how much the housing market values the districts, leaving for future work the question of what specific features the market finds attractive. Strictly speaking, our approach only identifies the value that the marginal person places on the relative services. There may be consumer surplus for inframarginal people that should be valued in finding the full benefit of local government services. DATA DESCRIPTION We focus on three separate areas, where the school district boundaries do not coincide with municipal boundaries. The first area is the Buckeye Shaker SPA in the city of Cleveland, part of which is in the Cleveland school district with the remainder in the Shaker Heights school district. A SPA is designated for use by the city and the county for public service provision and planning purposes. The Buckeye Shaker SPA includes three census tracts. The second area is the northern Cleveland Heights SPA, part of which is in the East Cleveland school district with the remainder in the Cleveland Heights University Heights school district. This SPA contains six 219

6 NATIONAL TAX JOURNAL VOL. L NO. 2 census tracts. The third area is the northern Garfield Heights SPA, part of which is in the Cleveland school district with the remainder in the Garfield Heights school district. This SPA contains five census tracts. Cleveland Heights, East Cleveland, Garfield Heights, and Shaker Heights border the city of Cleveland, and the Buckeye Shaker neighborhood of Cleveland borders the city of Shaker Heights. Table 1 shows the school property tax millage (applied to an assessed value defined as 35 percent of market value). 4 There is some perceived quality variation in the various districts, especially in the case of Cleveland and Shaker Heights. Shaker Heights is considered one of the best public school districts in the country, while the Cleveland public schools have struggled with a variety of severe problems. 5 Cleveland Heights is also perceived to be part of a higher quality school system than East Cleveland, and Garfield Heights is perceived to be a higher quality school system than Cleveland. 6 Our data consist of all arms-length sales of one-family owner-occupied houses in the three statistical planning areas described above for the years We possess detailed information on the physical characteristics of each house. We also calculated the average lot size in the census tract as a measure of the unobservable qualities of the neighborhood in which the house is located. Our data also included information on whether there was moderate to heavy traffic on the street where the house was located, another indicator of the type of neighborhood. The means and standard deviations of the continuous variables and the means and number of nonzero observations of the dummy variables are listed in Tables 2A 2C. 7 We use only a subset of a possible 87 physical characteristics of the house (see Bogart and Cromwell (1994) for a complete list of characteristics) due to a lack of degrees of freedom in some TABLE 1 SCHOOL NET PROPERTY TAX RATES ($ PER $1,000 ASSESSED VALUE) Year Cleveland Cleveland Heights East Cleveland Garfield Heights Shaker Heights Average tax rate Source: Cuyahoga County Auditor. 220

7 HOW MUCH MORE IS A GOOD SCHOOL DISTRICT WORTH? TABLE 2A SUMMARY STATISTICS: CLEVELAND (BUCKEYE SHAKER SPA) Variable Cleveland Schools Shaker Heights Schools Ln (SalesPrice) (constant 1987 $) Mean lot size in census tract (divided by 1,000) Moderate/heavy traffic on street Ln (Frontage) Ln (LotSize) Ln (LivingArea) Ln (Age) Mean room size Plumbing fixtures Attached garage Finished attic Construction grade B+ Construction grade B Construction grade C Fair condition Good condition Year1976 Year1977 Year1978 Year1979 Year1980 Year1981 Year1982 Year1983 Year1984 Year1985 Year1986 Year1987 Year1988 Year1989 Year1990 Year1991 Year1992 Year1993 Year1994 Observations (0.497) (0.722) (108) (0.122) (0.238) (0.277) (0.182) (48.9) (2.323) (19) (227) (4) (21) (786) (421) (14) (191) (179) (197) (195) (129) (106) (112) (131) (143) (126) (115) (117) (115) (132) (119) (86) (78) (91) (108) 2, (0.389) (0.673) 0 (0) (0.195) (0.283) (0.348) (0.329) (40.9) (3.650) (23) (131) (29) (103) (3) (6) (66) (32) (31) (34) (25) (15) (11) (14) (17) (21) (24) (17) (13) (18) (20) (23) (19) (14) (13) (22) 384 Note: Standard errors are in parentheses for continuous variables, and the numbers of nonzero observations are in parentheses for dummy variables. cases. We tested the stability of the coefficients in the hedonic regressions by dividing the sample into two subsamples, and , and calculating an F statistic to test for the equality of the coefficients. We did not reject at the 99 percent level the null hypothesis of coefficient stability in any of the three cases, so we used all of the years of data in the analysis. One possible criticism of our approach is that unobserved differences among the neighborhoods aside from school quality differences could be driving the results. We present some evidence later in the paper to examine the extent to which this problem arises. However, note that our use of the SPA as a way of defining neighborhoods alleviates some concern with respect to public service provision. If the city and county are approaching the SPA as a unit, then we do not expect to find large differences between different parts of the SPA. The relatively small size of the SPAs (between three and six census tracts) also helps reduce this problem. Recall that Richardson and Thalheimer (1981) used an entire county as their basis for analysis, while we are 221

8 NATIONAL TAX JOURNAL VOL. L NO. 2 TABLE 2B SUMMARY STATISTICS: CLEVELAND HEIGHTS (NORTH SPA) Variable East Cleveland Schools Cleveland Heights Schools Ln (SalesPrice) (constant 1987 $) Mean lot size in census tract (divided by 1,000) Moderate/heavy traffic on street Ln (Frontage) Ln (LotSize) Ln (LivingArea) Ln (Age) Mean room size Plumbing fixtures Construction grade B+ Construction grade B Construction grade C Construction grade D Bad condition Fair condition Good condition Year1976 Year1977 Year1978 Year1979 Year1980 Year1981 Year1982 Year1983 Year1984 Year1985 Year1986 Year1987 Year1988 Year1989 Year1990 Year1991 Year1992 Year1993 Year1994 Observations (0.387) (2.295) (65) (0.246) (0.358) (0.261) (0.291) (1.623) (1.898) (105) (311) (401) (5) (75) (521) (31) (126) (110) (100) (85) (67) (42) (45) (53) (56) (46) (51) (67) (1) (70) (60) (52) (58) (68) (61) 1, (0.323) (1.390) (320) (0.228) (0.356) (0.301) (0.326) (46.0) (2.061) (597) (1,861) (567) (3) (113) (368) (1,174) (389) (408) (360) (290) (232) (159) (169) (241) (213) (245) (272) (293) (7) (251) (277) (201) (227) (210) (274) 4,731 Note: Standard errors are in parentheses for continuous variables, and the numbers of nonzero observations are in parentheses for dummy variables. focusing on only one part of a city at a time. RESULTS We estimated equation 1 for the various neighborhoods using a log-linear specification. Before implementing the decomposition, we first used an approach of pooling all of the observations within a neighborhood and estimating a standard hedonic regression, including a dummy variable indicating the school district to which the house belonged. The results of this estimation are found in Table 3. The most interesting result in Table 3 is the coefficient on the dummy variable indicating the poor school district. The coefficient is negative and statistically significant in every case. More importantly, it can be used to estimate the difference in the marginal homebuyer s valuation of the tax-service bundle provided by the two school districts. Evaluated at the means of the variables, we find that the Shaker Heights public schools provide a tax- 222

9 HOW MUCH MORE IS A GOOD SCHOOL DISTRICT WORTH? TABLE 2C SUMMARY STATISTICS: GARFIELD HEIGHTS (NORTH SPA) Variable Cleveland Schools Garfield Heights Schools Ln (SalesPrice) (constant 1987 $) Mean lot size in census tract (divided by 1,000) Moderate/heavy traffic on street Ln (Frontage) Ln (LotSize) Ln (LivingArea) Ln (Age) Mean room size Plumbing fixtures Construction grade B+ Construction grade B Construction grade C Construction grade D Bad condition Fair condition Good condition Year1976 Year1977 Year1978 Year1979 Year1980 Year1981 Year1982 Year1983 Year1984 Year1985 Year1986 Year1987 Year1988 Year1989 Year1990 Year1991 Year1992 Year1993 Year1994 Observations (0.406) (0.382) (5) (0.122) (0.301) (0.208) (0.209) (30.9) (1.265) (4) (9) (482) (11) (10) (64) (31) (33) (46) (41) (48) (43) (26) (19) (22) (29) (16) (15) (15) (1) (34) (46) (41) (24) (39) (32) (0.327) (0.550) (93) (0.174) (0.322) (0.307) (0.469) (35.9) (2.131) (1) (8) (1,312) (25) (15) (67) (51) (105) (134) (132) (112) (77) (51) (50) (67) (70) (64) (78) (94) (3) (118) (108) (113) (90) (93) (119) 1,682 Note: Standard errors are in parentheses for continuous variables, and the numbers of nonzero observations are in parentheses for dummy variables. service bundle valued at $10,905 more than the Cleveland public schools, the Cleveland Heights University Heights public schools are valued at $5,627 more than the East Cleveland public schools, and the Garfield Heights public schools are valued at $11,955 more than the Cleveland public schools. 8 The complete regression results used to perform the decomposition described above in the Estimation Strategy section are shown in Tables 4 6. An asterisk is used to indicate coefficients that are significantly different from zero at the 95 percent level. Each table presents both the regression coefficients and the percent of the difference in mean sales price attributable to that variable based on the regression Xβ i / (ln (V i ) ln (V j )), to use the notation introduced earlier. For example, the logarithm of the living area is estimated to have a coefficient of in the regression using the portion of the Buckeye Shaker neighborhood that is in the Cleveland school 223

10 NATIONAL TAX JOURNAL VOL. L NO. 2 TABLE 3 REGRESSION RESULTS: DUMMY VARIABLE FOR SCHOOLS Variable Cleveland (Buckeye-Shaker) Cleveland Heights Garfield Heights Intercept Mean tract lot size Moderate/heavy traffic Poor school district Ln (Frontage) Ln (LotSize) Ln (LivingArea) Ln (Age) Mean room size Plumbing fixtures Attached garage Finished attic Construction grade B+ Construction grade B Construction grade C Construction grade D Bad condition Fair condition Good condition Observations Adjusted R * (0.489) (0.012) 0.141* (0.042) 0.278* (0.031) 0.536* (0.075) 0.129* (0.044) 0.650* (0.046) 0.369* (0.043) 0.001* (0.0002) 0.025* (0.005) 0.159* (0.067) (0.025) (0.077) 0.098* (0.048) (0.018) 0.113* (0.023) (0.053) 2, * (0.176) 0.024* (0.002) 0.106* (0.013) 0.095* (0.009) 0.151* (0.024) 0.094* (0.015) 0.204* (0.021) 0.211* (0.014) 0.001* (0.0001) 0.022* (0.002) 0.043* (0.011) (0.008) 0.026* (0.010) 0.410* (0.088) 0.215* (0.021) 0.098* (0.011) (0.009) 5, * (0.381) 0.086* (0.013) (0.031) 0.275* (0.020) 0.148* (0.051) 0.072* (0.027) 0.228* (0.040) 0.229* (0.019) (0.0002) 0.010* (0.005) 0.358* (0.132) (0.075) 0.042* (0.020) 0.205* (0.055) 0.180* (0.064) 0.113* (0.027) (0.034) 2, Note: All regressions include year dummy variables for Poor school districts are Cleveland and East Cleveland. Dependent variable is ln (SalesPrice), where SalesPrice is in constant (1987) dollars. TABLE 4 REGRESSION RESULTS: CLEVELAND SCHOOLS VERSUS SHAKER HEIGHTS SCHOOLS Cleveland Schools Explained Percent Shaker Heights Explained Percent Variable Regression of Difference Schools Regression of Difference Intercept Mean tract lot size Moderate/heavy traffic Ln (Frontage) Ln (LotSize) Ln (LivingArea) Ln (Age) Mean room size Plumbing fixtures Attached garage Finished attic Construction grade B+ Construction grade B Construction grade C Fair condition Good condition Year dummies 3.703* (0.627) (0.013) 0.173* (0.043) 0.419* (0.089) 0.117* (0.047) 0.723* (0.051) 0.452* (0.056) (0.0002) 0.034* (0.005) 0.375* (0.102) (0.031) (0.214) 0.461* (0.101) (0.019) 0.125* (0.024) 0.551* (0.120) 2,473 observations Adjusted R 2 = * (0.894) (0.043) 0.318* (0.144) 0.285* (0.095) 0.373* (0.105) 0.108* (0.051) 0.002* (0.0004) (0.007) (0.067) 0.166* (0.040) 0.143* (0.057) (0.040) (0.158) 0.518* (0.114) (0.043) 383 observations Adjusted R 2 =

11 HOW MUCH MORE IS A GOOD SCHOOL DISTRICT WORTH? TABLE 5 REGRESSION RESULTS: CLEVELAND HEIGHTS SCHOOLS VERSUS EAST CLEVELAND SCHOOLS Cleveland Heights Explained Percent East Cleveland Explained Percent Variable Schools Regression of Difference Schools Regression of Difference Intercept Mean tract lot size Moderate/heavy traffic Ln (Frontage) Ln (LotSize) Ln (LivingArea) Ln (Age) Mean room size Plumbing fixtures Construction grade B+ Construction grade B Construction grade C Construction grade D Bad condition Fair condition Good condition Year dummies 7.891* (0.186) 0.112* (0.006) 0.118* (0.014) 0.163* (0.026) 0.079* (0.015) 0.232* (0.023) 0.200* (0.014) 0.001* (0.0001) 0.023* (0.003) 0.036* (0.012) 0.017* (0.008) 0.030* (0.012) (0.138) 0.299* (0.026) 0.130* (0.014) 0.007* (0.009) 4,712 observations Adjusted R 2 = * (0.526) 0.033* (0.006) (0.039) (0.072) 0.156* (0.047) 0.158* (0.056) 0.257* (0.045) (0.0002) 0.017* (0.007) 0.098* (0.033) (0.022) (0.023) 0.553* (0.125) (0.037) 0.050* (0.021) 0.183* (0.057) 1,217 observations Adjusted R 2 = TABLE 6 REGRESSION RESULTS: GARFIELD HEIGHTS SCHOOLS VERSUS CLEVELAND SCHOOLS Cleveland Schools Explained Percent Garfield Heights Explained Percent Variable Regression of Difference Schools Regression of Difference Intercept Mean tract lot size Moderate/heavy traffic Ln (Frontage) Ln (LotSize) Ln (LivingArea) Ln (Age) Mean room size Plumbing fixtures Construction grade B+ Construction grade B Construction grade C Construction grade D Bad condition Fair condition Good condition Year dummies 9.357* (1.480) 0.112* (0.048) (0.186) (0.158) (0.072) (0.122) 0.398* (0.105) 0.002* (0.001) (0.016) 0.470* (0.197) (0.149) (0.056) (0.139) (0.152) (0.051) (0.073) 560 observations Adjusted R 2 = * (0.368) 0.117* (0.013) (0.029) 0.126* (0.051) 0.030* (0.029) 0.243* (0.030) 0.217* (0.017) (0.0002) (0.005) (0.262) 0.238* (0.095) 0.049* (0.020) 0.223* (0.058) 0.256* (0.069) 0.160* (0.033) (0.038) 1,656 observations Adjusted R 2 =

12 NATIONAL TAX JOURNAL VOL. L NO. 2 district (column 2 of Table 4). This area has a mean log living area that is smaller than that in the part of the neighborhood in the Shaker Heights school district, as can be seen in Table 2a. The number in the third column indicates that 13.9 percent of the difference in the mean price of housing between the two neighborhoods can be attributed to the larger mean living areas in the houses in the Shaker Heights school district. From Table 4, we see that 84.0 percent of the price difference is explained using the Cleveland school regression weights, while 64.8 percent is explained using the Shaker Heights school regression weights. The remaining tables can be read in a similar fashion. From Table 5, we learn that between 49.7 and 52.5 percent of the difference in the mean value of houses in the two parts of Cleveland Heights can be explained on the basis of observable characteristics. Table 6 shows that between 1.7 percent and 41.0 percent of the difference in the mean value of houses in the two parts of Garfield Heights can be explained by observable characteristics. The negative number indicates that houses in the Cleveland school district would be expected to have a higher house value than houses in the Garfield Heights school district on the basis of observed characteristics when using the regression weights from the Cleveland school district part of the SPA. The adjusted R 2 for that regression, however, is quite low. We turn now to the decomposition (equation 2) of the difference in mean house value into a component due to observable physical characteristics and a component due to unobservable presumably public servicecharacteristics. The results are presented in Table 7. The table should be read in the following way. The first column gives the school districts being compared (for example, Shaker Heights versus Cleveland in the first row). The second column gives the mean difference in house value between the two jurisdictions in question (for example, Buckeye Shaker houses in Cleveland schools versus Buckeye Shaker houses in Shaker Heights schools in the first row). The third column gives the fraction of this difference attributable to public service differences. Because there are two alternative ways of calculating the decomposition, the third column presents a range of possibilities (bounded by the two estimates) rather than a single number. The percent of the difference in mean house value across neighborhoods not accounted for by differences in the TABLE 7 DECOMPOSITION OF HOUSE VALUE DIFFERENCES Mean House Percent of Difference Due School Districts Value Difference To Schools v Cleveland versus Shaker Heights $33, $5,303 $11,648 Cleveland Heights versus East Cleveland $9, Cleveland versus Garfield Heights $17, $10,396 $17,920 Note: Fraction of difference due to schools equals 100 percent minus the percent explained by observable differences (from Tables 5 7). $4,553 $4,

13 HOW MUCH MORE IS A GOOD SCHOOL DISTRICT WORTH? observable characteristics of the house and neighborhood varies from a low of 41.0 percent (excluding the 1.7 percent in the Cleveland school district part of Garfield Heights) to a high of 84.0 percent. This, in turn, translates into a difference in the net-of-tax value of services of between $4,553 and $17,920. The results suggest that the Shaker Heights schools provide a taxservice bundle worth between $5,303 and $11,648 more than the Cleveland schools, even though the tax rates in Shaker Heights are higher. The $10,905 estimated by the dummy variable approach in Table 3 falls into the upper part of the range estimated using the decomposition approach. The Cleveland Heights University Heights public schools provide a tax-service bundle valued from $4,553 to $4,821 more than the East Cleveland public schools. The estimated difference from Table 3 of $5,627 is outside of this range. Finally, the tax-service bundle provided by the Garfield Heights public schools is valued between $10,396 and $17,920 more than the tax-service bundle provided by the Cleveland public schools. The $11,955 difference estimated in Table 3 is in the lower part of the range estimated using the decomposition approach. The most striking finding here is that the higher tax areas are also more highly valued in every case. 9 In Table 8, we use information on the differences in school district property tax rates to estimate the difference in the value of the public school system. In other words, Table 8 provides estimates of S defined in equation 3. Because the change in property taxes depends on both the change in the value of the house due to service differences and on which jurisdiction s house value is used in calculating equation 4, the results in Table 8 give a range of possible service differences. The first number is the difference in the value of the public schools calculated using the lower value of v and T, while the second number uses the higher value. The results in Table 8 are robust to the choice of capitalization rate. The column labeled Cleveland versus Shaker Heights compares the value of the services provided by the Cleveland public schools to the services provided by the Shaker Heights public schools. If the average house from the Cleveland school district (in the Buckeye Shaker neighborhood) moved to the Shaker Heights school district, it would expect to pay between $374 and $885 per year more in property taxes. 10 However, its value would increase by between $5,303 and $11,648 as a result of unobservable differences between the school districts. This increase in value TABLE 8 ESTIMATED DIFFERENCE IN THE VALUE OF PUBLIC SCHOOL SERVICES ( S = i/α v + ψ/α T) Service Tax Cleveland versus East Cleveland versus Cleveland versus Capitalization Capitalization Shaker Heights Cleveland Heights Garfield Heights Parameter (α) Parameter (ψ) ( T = $374 $885) ( T = $71 $78) ( T = $117 $203) $702 $1,555 $559 $592 $1,283 $2, $449 $1,010 $298 $316 $695 $1, $421 $970 $186 $199 $454 $620 Note: The discount rate i is set equal to three percent for all calculations. The tax capitalization parameter equals 70 percent of the service capitalization parameter to account for the deductibility of property taxes from federal income tax. 227

14 NATIONAL TAX JOURNAL VOL. L NO. 2 implies an increase in annual net service flows ((i/α) v) of between $159 and $349 when i equals three percent and α equals one. When α = 0.25, so that only 25 percent of the difference in the net value of services is reflected in house prices, the $5,303 to $11,648 increase in value implies an increase in annual net services of between $636 and $1,398. Adding the increase in the annual service flows to the net increase in property taxes yields the result that the Shaker Heights public schools provide services that exceed the value of the Cleveland schools by between $421 and $1,555 per year, depending on the extent of capitalization and the exact amount of the change in value. In any event, the difference in the value of services implies that the higher taxes are more than compensated for by better public services. An alternative view, of course, is that the lower value of the school district services enjoyed by the residents of the Buckeye Shaker neighborhood in the Cleveland school district outweighs the benefits of the lower taxes that they owe. The comparison of the East Cleveland and Cleveland Heights University Heights school districts yields a similar conclusion. The move from the East Cleveland school district to the Cleveland Heights University Heights school district leads to an annual tax increase of between $71 and $78 (despite the lower tax rate in East Cleveland) but increases in the value of housing between $4,553 and $4,821. This, in turn, represents a difference in the annual value of the services provided by the public schools of between $186 and $592. Finally, consider the comparison between Garfield Heights and Cleveland public schools. A move within Garfield Heights from the Cleveland school district to the Garfield Heights school district will cause an increase in the average tax payment of between $117 and $203 (despite the lower tax rate in Garfield Heights) but will nevertheless increase the value of the house by between $10,396 and $17,920. These figures imply a difference in the annual value of the services provided by the schools of between $454 and $2,171, depending on the extent of capitalization. Garfield Heights versus Shaker Heights Because both Garfield Heights and Shaker Heights are compared to Cleveland, they can be compared to each other if transitivity is assumed. That is, suppose that the value of the services provided by the Cleveland public schools is the same in the Buckeye Shaker neighborhood of Cleveland as in the city of Garfield Heights. Then, the relative valuation of the Shaker Heights and Garfield Heights school districts is obtained by comparing their respective relative valuations to the Cleveland schools. The change in value due to a change in school district ( v) is larger in Garfield Heights than in Shaker Heights, as seen in Table 7. However, the tax increase resulting from a move from the Cleveland schools to the Shaker Heights schools is much larger than the tax increase resulting from a move from the Cleveland schools to the Garfield Heights schools. The conclusion from Table 8 is that, if services are completely capitalized at a discount rate of three percent, the Shaker Heights schools provide services worth more than the Garfield Heights schools. However, if the capitalization is only 50 percent (alternatively, 100 percent capitalization at a 6 percent discount rate), the two districts services are judged roughly equal. If the capitalization rate falls to 25 percent, then the 228

15 HOW MUCH MORE IS A GOOD SCHOOL DISTRICT WORTH? Garfield Heights schools are found to be of higher quality than the Shaker Heights schools. Neighborhood Effects A real concern with the approach that we take in this paper is whether we have adequately accounted for differences between neighborhoods in addition to the public schools. To investigate this question, we used our decomposition technique in a situation in which two spatially distinct and demographically different neighborhoods share a common school district. As part of a redistricting in 1987, the city of Shaker Heights added part of the Moreland neighborhood to the Mercer school district. The Moreland neighborhood, in the southwestern part of the city, bordered the city of Cleveland and was relatively low income compared to the Mercer neighborhood, in the northeastern part of Shaker Heights. (See Bogart and Cromwell (1994) for details of the redistricting.) In this division of the Mercer school district into two parts we have a natural candidate for identifying the effect of the neighborhood alone, given that the students attend the same school and the neighborhoods are both within the same city. When we performed a dummy variable regression analogous to those reported in Table 3, the variable identifying the Moreland neighborhood was not statistically significantly different from zero. The decomposition approach indicated that 92.5 percent of the difference in the mean house value was explained by observable differences, leaving 7.5 percent as a pure neighborhood effect. This is a substantial amount but less than we found in our investigation of school district variation. One reaction to this finding would be to adjust our estimated school district effects downward by the neighborhood effect found in Shaker Heights. It should be realized, however, that we have stacked the deck in favor of finding significant differences in two ways by our choice of school district to study. The first reason to expect to find large neighborhood effects is that the neighborhoods are noncontiguous and, in fact, are separated by about a mile. The neighborhoods in our analysis in this paper are all contiguous. The second reason to expect large effects is that the Moreland and Mercer neighborhoods are in different statistical planning areas within the city of Shaker Heights. Thus, we expect that any neighborhood effect within the SPAs that we studied is less than the 7.5 percent of the difference in value we find in the Mercer school district. Apartment Rents in the Buckeye Shaker Neighborhood If public services are capitalized into the value of owner-occupied housing, it is also reasonable to expect them to be reflected in the rents charged for apartments. Detailed data on apartments are not widely available. However, we were able to obtain data on apartment characteristics and rents for one of the three areas studied in this paper, the Buckeye Shaker neighborhood of Cleveland. 11 These data list several characteristics of apartment buildings, including the number of bedrooms, number of bathrooms, whether heat is included in the rent, the monthly rent, and the school district in which the apartment is located. In order to check our econometric results obtained using sales of owneroccupied housing, we performed a very simple regression. The dependent variable was the monthly rent, and the 229

16 NATIONAL TAX JOURNAL VOL. L NO. 2 explanatory variables were the characteristics listed above. 12 The results of this regression are shown in Table 9. The coefficient on the dummy variable indicating Shaker Heights schools is statistically significant at the 13 percent level. The advantage of performing the regression in levels is that the coefficient immediately translates into the rental equivalent of v, the difference in the value of the tax-service bundle. The regression indicates that location within the Shaker Heights school district is worth about $36 per month in increased rent. This translates into $432 per year. The results in Table 7 suggested that the tax-service bundle provided by the Shaker Heights public schools was worth about $8,000 (in discounted present value) more than the tax-service bundle provided by the Cleveland public schools. A capitalized amount of $8,000 with an annual difference of $432 implies a capitalized discount rate (i/α) of 5.4 percent. If i = 3 percent, then we estimate α to be approximately 56 percent. To put it differently, the simple regression results using rental data yield estimates in the middle of the range of results obtained using the decomposition procedure. While this does not prove that the decomposition results are correct, the evidence is suggestive that our results are not due to the econometric procedure. 13 TABLE 9 APARTMENT RENTS IN THE BUCKEYE SHAKER NEIGHBORHOOD Variable Coefficient (Standard Error) Intercept (68.187) Shaker Heights schools (23.311) Beds * (24.096) Baths * (56.387) Heat included in rent * (37.663) Observations 50 Adjusted R Note: Dependent variable equals monthly rent. Summary and Conclusions This paper has estimated the value of public schools and municipal public services from sale prices of houses. We used evidence from neighborhoods in which houses receive public services from overlapping jurisdictions to isolate the effects of the public school from other local government services. The neighborhoods include the following: an SPA in the city of Cleveland in which some of the houses are in the Cleveland school district and some of the houses are in the Shaker Heights school district; an SPA in the city of Garfield Heights, a part of which is in the Garfield Heights school district while the remainder is in the Cleveland school district; and an SPA in the city of Cleveland Heights, a part of which is in the East Cleveland school district while the remainder is in the Cleveland Heights University Heights school district. We estimated separate regressions for house values in each area using detailed characteristics data from 1976 to We then decomposed the difference in mean house value into a part due to differences in observable characteristics and an unobservable part due to differences in public services. Because property tax rates also vary across districts, our estimate is one of net (aftertax) benefits rather than directly of benefits. We inferred differences across jurisdictions in the value of local public schools under a variety of assumptions about the degree of tax and service capitalization. A robust finding among this group of cities is that high-quality school districts provide services valued in excess of the higher taxes that they levy. A simple regression using data on apartment rents in the Buckeye Shaker neighborhood of Cleveland yielded results comparable to those found using the decomposition technique. 230

17 HOW MUCH MORE IS A GOOD SCHOOL DISTRICT WORTH? The school districts are found to provide services whose annual value differs by between $186 and $2,171, depending on the districts being compared and the assumptions about capitalization. Given that the districts each spend on the order of $6,000 per pupil per year, these differences are quite large if we assume one pupil per household. More research is needed to identify the sources of the differences in value. In particular, the link between the level of spending, the composition of spending, and the house value is likely to be a fruitful line of inquiry. ENDNOTES Thanks to Jennifer Carr, Michael Harding, and Jennifer Redman for research assistance. Thanks to Thomas Bier of Cleveland State University for the house price and quality data. Financial assistance from a Weatherhead School of Management summer research grant is gratefully acknowledged. Seminar participants at CWRU and the University of Michigan made several valuable substantive suggestions as well as improving the title of the paper. Joel Slemrod and three anonymous reviewers also made suggestions that improved the paper. 1 See Holtz-Eakin (1986) for a discussion of this problem in the context of estimating the determinants of local government spending. 2 Schafer (1979) undertakes a similar exercise to estimate the extent to which housing price differences in various neighborhoods in Boston reflect racial discrimination. 3 Strictly speaking, equation 3 only applies to the case of infinitely lived housing. However, a straightforward adjustment (increase) to the discount rate makes this formulation equivalent to one with only a finite number of periods. See Yinger et al. (1988) for details. 4 The millage shown is referred to as the net property tax rate because it reflects the actual millage applied in calculating the property tax bill after various Ohio property tax reduction measures have been subtracted from the gross property tax rate. 5 See Bogart and Cromwell (1994) for more details on the Shaker Heights public schools. 6 See Keating (1994) for a historical description of Cleveland and its suburbs, including a discussion of the public schools. 7 Omitted dummy variables in the regressions are Year 1976, Construction Grade B-, and Normal Condition. 8 In order to investigate the robustness of the results, we also estimated a specification using levels of the variables rather than logarithms. The qualitative results are the same and the quantitative results quite similar. A levels specification yields an estimated difference between the Shaker Heights and Cleveland schools of $10,526, a difference between Cleveland Heights and East Cleveland of $4,852, and a difference between Garfield Heights and Cleveland of $10, As with the dummy variables results, these findings are qualitatively similar to an alternative specification in which all variables are expressed in levels. The difference between the Shaker Heights and Cleveland public schools using a levels specification is between $17 and $7,108; the difference between Cleveland Heights and East Cleveland is between $3,416 and $4,027; and the difference between Garfield Heights and Cleveland is between $9,215 and $18, If the homeowner itemizes deductions, then the increase in property taxes will be offset to some extent by a decrease in federal income taxes. We account for itemizing by setting the tax capitalization parameter ψ equal to 70 percent of the service capitalization parameter α. 11 Thanks to Reid Robbins of the Community Development Corporation, Friends of Shaker Square, for allowing us access to unpublished data on apartment characteristics and rents. 12 Each observation is a building/type of apartment combination. For example, a building that included both one bedroom and two bedroom apartments would generate two observations. 13 Rental households may systematically differ from owner-occupied households in the number of children, so our results should be interpreted with care. REFERENCES Bogart, William T., and Brian A Cromwell. Busing, Race, Neighborhood Schools, and House Values: Evidence from an Integrated Suburb. Economics Department Working Paper # Cleveland: Case Western Reserve University, Epple, Dennis. Hedonic Prices and Implicit Markets: Estimating Demand and Supply Functions for Differentiated Products. Journal of Political Economy 95 No. 1 (February, 1987): Holtz-Eakin, Douglas. Unobserved Tastes and the Determination of Municipal Services. National Tax Journal 39 No. 4 (December, 1986): Keating, W. Dennis. The Suburban Racial Dilemma. Philadelphia: Temple University Press,

18 NATIONAL TAX JOURNAL VOL. L NO. 2 Oaxaca, Ronald. Male-Female Wage Differentials in Urban Labor Markets. International Economic Review 14 No. 3 (October, 1973): Richardson, David H., and Richard Thalheimer. Measuring the Extent of Property Tax Capitalization for Single Family Residences. Southern Economic Journal 47 No. 3 (January, 1981): Schafer, Robert. Racial Discrimination in the Boston Housing Market. Journal of Urban Economics 6 No. 2 (April, 1979): Yinger, John, Howard S. Bloom, Axel Börsch-Supan, and Helen Ladd. Property Taxes and House Values: The Theory and Estimation of Intrajurisdictional Property Tax Capitalization. New York: Academic Press,

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