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 netoftax 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 netoftax 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 owneroccupied 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 malefemale 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 netoftax 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 socalled 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 wellknown problems in inferring structural conditions of the housing market from what are essentially reducedform 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 righthandside 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 netoftax 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 righthand 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 righthand 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 crosssectional variation as well as timeseries 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 armslength sales of onefamily owneroccupied 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 loglinear 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 taxservice 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 (BuckeyeShaker) 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 =
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