to a convergence in school district housing price premiums? Third, and perhaps ... inequities in the distribution of resources among California school districts, from a ...... the SURFER computer program to generate isopleth contours. Third, the ...
School Finance Reform and Housing Values: Evidence from the Los Angeles Metropolitan Area Eric J. Brunner Department of Economics San Diego State University James Murdoch School of Social Sciences University of Texas at Dallas Mark Thayer Department of Economics San Diego State University
Abstract Over the past 25 years California has transformed its system of public school finance from one of the least equitable in the nation to one of the most equitable. This paper examines the impact of that transformation on housing values. Specifically, we use data on residential housing sales from Los Angeles County for the years 1975, 1980, 1985, and 1990, to answer three fundamental questions related to the impact of school finance reform on housing values. First, were reform-induced changes in district resources capitalized into housing values? Second, did the equalization of resources across districts lead to a convergence in school district housing price premiums? Third, and perhaps most importantly, if so, was the convergence in school district housing price premiums the result of a leveling-up or a leveling-down of school district quality? Our results indicate that the answers to the first two questions are both yes – reform-induced changes in spending per pupil were capitalized into housing values and resource equalization has led to a convergence in housing values. Perhaps most importantly, however, our results indicate that the convergence in school district housing price premiums was the result of a leveling-down of school district quality.
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Introduction Over the last 25 years, California has transformed its system of public school finance from one of the least equitable in the nation to one of the most equitable. According to Evans, Murray, and Schwab (1997), California ranked 45th in equality of spending per pupil in 1972. By 1987, it ranked 5th in equality. The transformation began in 1971 when the California Supreme Court ruled in Serrano v. Priest, that inequities in the distribution of educational resources resulting from differences in property wealth violated the equal protection clause of the state constitution. In response to Serrano, the State Legislature substantially increased aid to low-wealth districts and established a system of revenue limits designed to control the spending of high-wealth districts. By leveling-up the spending of low-wealth districts through increases in state aid, and controlling the spending of high-wealth districts through revenue limits, the State Legislature caused district resources to converge over time. While the intent of school finance reform was to reduce inequities in the distribution of resources among California school districts, from a policy perspective it seems natural to ask: has the equalization of resources led to an equalization of public school quality? Downes (1992) attempts to answer that question by examining the relationship between expenditure equalization in California and student performance on standardized tests. Comparing test results in 1976-77, before much of the equalization in district resources had occurred, with results in 1985-86, after much of the equalization in district resources had been achieved, Downes finds no evidence that school finance reform resulted in an equalization of student performance. While the results of Downes are intriguing, we believe they do not provide a complete answer to the question we pose for several reasons. First, as Sonstelie, Brunner and Ardon (2000) note, while student achievement is certainly an important element of any measure of school quality, it is not the only element. Parents most likely value a host of other elements of their child’s education such as the richness of a school’s curriculum; the variety of its extracurricular programs in the arts, music, and athletics; the competence of its teachers; and the quality of its special education program. Second, as noted by Hanushek (1986) and others, the empirical
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evidence on the relationship between spending per pupil and student performance is mixed. The results of numerous studies suggest only a weak link between spending per pupil and student performance. As a result, the use of educational production functions to measure the impact of changes in educational resources on school quality has become increasingly controversial. In light of these facts, this paper attempts to examine the relationship between school finance reform and public school quality using a very different approach. Rather than focusing on how changes in district resources affect student performance, we focus on how changes in district resources affect the residential location choices of families and thus housing values. (1) As Dee (2000) notes, by focusing on residential location choices, rather than student outcomes, no assumptions need to be made about what a family values in terms of their child's education. If increases in spending per pupil increase the perceived quality of public education in a district, that district will become more attractive to potential residents and property values will rise. (2) Our analysis is based on a unique data set constructed by merging residential housing sales data from Los Angeles County for the years 1975, 1980, 1985, and 1990 with data on school district resources and test scores. Using that data, we attempt to answer three fundamental questions related to the impact of school finance reform on housing values. First, were reform-induced changes in district resources capitalized into housing values? Second, did the equalization of resources across districts lead to a convergence in school district housing price premiums? Third, and perhaps most importantly, if so, was the convergence in school district housing price premiums the result of low-spending districts improving faster than high-spending districts and thus catching up? Or was the convergence in housing price premiums the result of a decline in the perceived quality of high-spending districts? That is, has there been a leveling-up or a leveling-down of school district quality?
Background The 1971 ruling of the California Supreme Court in the case of Serrano v. Priest sets the context for our analysis. (3) Citing disparities in property tax wealth and spending per pupil among
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California school districts, the California Supreme Court ruled that inequities in the distribution of educational resources resulting from differences in property wealth violated the equal protection clause of the state constitution. In response, the State Legislature increased aid to low-wealth districts and established a system of revenue limits, which capped the amount of property tax revenue districts could raise. Each district’s revenue limit in 1973-74 was based on the sum of its property tax revenue and state aid in 1972-73. In subsequent years, the limits of low-wealth districts were allowed to increase at a faster rate than the limits of high-wealth districts. Furthermore, to expedite the process, low-wealth districts were allocated additional state aid. By increasing the revenues of lowspending districts through increased state aid and restricting the growth in revenues of high-spending districts through the revenue limit, the State Legislature intended to cause spending per pupil to converge over time. In 1976 the California Supreme Court ruled that the initial response to Serrano v. Priest was inadequate, partly because highwealth districts were allowed to increase their revenue limits, and thus spending per pupil, through voter-approved overrides. (4) In response, legislation was passed mandating the redistribution of property tax revenue from high-wealth to low-wealth districts. Before the new legislation was enacted, however, California voters passed Proposition 13 in June of 1978. Proposition 13 essentially turned the property tax into a state tax and thus shifted the primary responsibility of financing public education from local school districts to the state. Furthermore, since Proposition 13 prohibited local governments from passing new property taxes, the revenue limits could now be used to effectively equalize resources across districts and thus satisfy the California Supreme Court. How much equalization has occurred? In the next section, we explore the answer to that question for school districts located in Los Angeles County.
School Finance Reform and the Distribution of District Resources Our analysis is conducted using data from Los Angeles County. We selected this area because it contains a large number of diverse school districts from which families may choose. In 1990, 1.34
5
million students were enrolled in one of the 82 school districts located within this region. Of these 82 school districts, 33 were elementary districts, 7 were high school districts and 42 were unified school districts. We excluded a number of these school districts for several reasons. First, to compare educational resources across school districts, we limited our sample to districts with similar organizational structure. In particular, because high schools tend to have higher costs than elementary schools, we limited our sample to unified school districts. Second, two unified school districts were eliminated from consideration since reorganization (annexation or consolidation) prevented us from accurately identifying school district boundaries over time. (5) The size and socio-economic composition of the 40 school districts in our sample vary widely. In 1990, these districts contained 735,594 families and 1.21 million students. The largest school district, Los Angeles Unified, enrolled more than 595,000 students while the smallest school district, El Segundo, enrolled 1,970 students. Family income also varied widely across districts. In the five wealthiest districts, average family income in 1990 exceeded $90,000 while in the five poorest districts, average family income in 1990 was below $38,000. To set the context for our analysis we begin by examining the relationship between school finance reform and the distribution of resources among school districts in our sample. Figure 1 illustrates the cumulative effect of revenue limits on the growth rate of real general-purpose revenue per pupil. District revenue limits in 197475, are related to the percent change in real revenue per pupil from 1974-75 to 1989-90. All revenue figures were deflated to constant 1990 dollars using the CPI for the Los Angeles Metropolitan Area. As a point of comparison, the average growth rate of revenue per pupil for the 40 school districts in our sample was 17% over the time period. The pattern of revenue growth depicted in Figure 1 suggests that school finance reform led to a significant convergence in revenue per pupil. In the ten districts with the lowest revenue limits in 197475, revenue per pupil increased by 29% on average. In contrast, in the ten districts with the highest revenue limits in 1974-75, revenue per pupil declined by 0.6% on average. These differential growth rates produced a gradual convergence in district resources.
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Figure 1 School Finance Reform and Revenue Growth
40%
Percent Change in Real Revenue Per Pupil 1974-75 to 1989-90
30%
20%
10%
0% $2,000
$2,500
$3,000
$3,500
$4,000
$4,500
$5,000
$5,500
-10%
-20%
-30%
1974-75 Revenue Limit
How much equalization has occurred? Table 1, which gives the distribution of school district resources in 1974-75 (columns 2 through 4) and 1989-90 (columns 5 through 7), provides one answer to that question. Figures are expressed in constant 1990 dollars. The first row gives the allocation of revenue limit funding per pupil. In 1974-75, revenue limit funding per pupil was less than $2,329 in 25% of the districts in our sample. In contrast, revenue limit funding per pupil was greater than $2,775 in 25% of the school districts in our sample. The difference between the 75th and 25th percentiles of revenue limit funding per pupil was $446. By 1989-90, that difference had been reduced to only $59.
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Table 1 The Distribution of Revenue Per Pupil (1989-90 dollars) 1974-75
1989-90
Resource
25th a
75th b
75th 25th
25tha
75thb
75th 25th
Revenue Limit per Pupil
2,329
2,775
446
2,918
2,977
59
Total Revenue per Pupil
2,878
3,359
481
3,830
4,110
280
Expenditure s per Pupil
2,791
3,396
605
3,746
4,097
351
a 10 (twenty-five percent) of the unified school districts in our sample had revenue per pupil less than or equal to this number. b 10 (twenty-five percent) of the unified school districts in our sample had revenue per pupil greater than or equal to this number.
The second row, which adds other local revenue not subject to the revenue limit and categorical federal and state aid, gives the allocation of real total revenue per pupil. (6) In 1974-75, other local revenue and categorical aid accounted for only a small fraction of district revenues and thus had little effect on the distribution of resources. Specifically, adding these sources of revenue increases the difference between the 75th and 25th percentiles by only $35. (7) In 1989-90, however, these sources of revenue were much more important and had the effect of widening the difference between the 75th and 25th percentiles of total revenue per pupil by more than $200. (8) Despite this fact, the difference between the 75th and 25th percentiles of total revenue per pupil declined by 42 percent, from $481 to $280, between 1974-75 and 1989-90.
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The first two rows of Table 1 suggest that school finance reform resulted in a sharp decline in revenue inequality among school districts in our sample. However, in the eyes of parents it is spending per pupil, not revenue per pupil, which really matters. How has school finance reform affected the distribution of spending per pupil? The last row of Table 1, which gives the allocation of real current expenditures per pupil, defined as total expenditures less capital expenditures and debt repayments per pupil, provides an answer to that question. In 1974-75 the difference between the 75th and 25th percentiles of real current expenditures per pupil was $597. By 1990, however, school finance reform had reduced that difference by nearly 42 percent to $347. Taken together, Figure 1 and Table 1 suggest that school finance reform has led to a substantial reduction in resource inequality among school districts in our sample. (9) Furthermore, Figure 1 and Table 1 suggest that this reduction in resource inequality was achieved by leveling-up the spending of low-spending districts and controlling the spending of high-spending districts through revenue limits. For example, in the ten districts with the lowest revenue limits in 1974-75, real current expenditures per pupil increased by 31% on average. In contrast, among the ten districts with the highest revenue limits in 1974-75, real current expenditures per pupil increased by only 17% on average. With that in mind, we next turn to examining the impact of this resource equalization on housing values.
Empirical Specification To examine whether reform-induced changes in district resources were capitalized into housing values, we estimate the price of a house as a function of its structural characteristics, neighborhood characteristics, and school district quality, as measured by spending per pupil and average school district test scores. For home i, in school district j, in year t, the regression is
Pijt = S ijt α + N ijt β + γ 1 SCHEXPjt + γ 2 SCORE jt + µ j + η t + ε ijt ,
(1)
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where Pijt denotes the logarithm of the sale price of home i, located in school district j, in year t, S ijt is a vector of house specific structural
characteristics,
N ijt
is
a
vector
of
neighborhood
characteristics, SCHEXPjt is spending per pupil in district j in year t,
SCORE jt is the average test score of students located in district j in year t, µ j and ηt are district and year fixed effects respectively, and
ε ijt is a random disturbance term. We utilize a fixed effects specification for three noteworthy reasons. First, district fixed effects provide a means of accounting for group-wise dependence in the disturbance. Group-wise dependence is likely because spending per pupil and test scores in any given year do not vary within districts. While group-wise dependence does not bias parameter estimates, Moulton (1986) has shown that it will cause the standard errors of group invariant coefficients to be biased downwards. As a result, OLS significance levels may be substantially overstated. Second, an inherent problem with the estimation of the impact of local amenities, such as spending per pupil, on housing values is omitted variable bias. If the level of services provided by a community is correlated with some unobservable community characteristics, estimates of the impact of local public service provision on housing values will be biased. The fixed effects specification mitigates the problem of omitted variable bias since it captures permanent differences between districts with district fixed effects. It therefore allows us to control for unobservable districtspecific factors that may be correlated with spending per pupil and test scores. Third, our primary objective is to examine how reform-induced changes in spending per pupil within districts have affected housing values. This is precisely what the fixed effect specification captures. As noted by Murray, Evans, and Schwab (1998), the fixed effects model is a within-group estimator that attributes to γ 1 only withindistrict movements in spending per pupil and housing prices. As a result, our estimation procedure allows us to estimate how the price of a home changes within a district as spending per pupil changes.
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Data Our data on house prices comes from the Experian Company (formerly TRW). Each observation is the record of a specific sale of an owner-occupied single-family home sold during 1975, 1980, 1985, or 1990 in one of the 40 school districts in our sample. There are 94,223 observations. Of these observations, 43,641 are in one district, Los Angeles Unified. To examine whether our results were sensitive to the inclusion of Los Angeles Unified, we estimated equation 1 using two separate samples: (1) all observations on housing sales in Los Angeles County and (2) all observations on housing sales in Los Angeles County except for those in Los Angeles Unified. We found that our results were somewhat sensitive to the inclusion of observations from Los Angeles Unified, particularly the coefficients on neighborhood level variables. However, when we included a dummy variable for Los Angeles Unified interacted with the year fixed effects the results from the two samples were quite similar. As a consequence, in the remainder of this paper, we report only the results from the sample without Los Angeles Unified. (10) The Experian database includes complete descriptive information on every piece of property (residential, commercial, etc.) in California. The data set is continually updated and, for every property, contains the address and other locational information (census tract, etc.), a detailed list of structural attributes, and information on the two most recent sales (date, price, and terms). The data is generally available to appraisers and real estate brokers and agents on a fee for use basis. The dependent variable in our empirical analysis is the home sale price of owner-occupied single-family dwellings sold during 1975-1990. House price was deflated to constant 1990 dollars using the regional CPI housing price index for the Los Angeles Metropolitan Area. In addition, following Black (1999) we adjusted all house prices to incorporate the future stream of property tax payments. The Experian database does not include the tax on each property so we constructed an estimate of the tax payment using city and school district tax rates. Specifically, for 1975, we calculated the effective tax rate applied to each home as the sum of city and school
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district tax rates times the assessment ratio. In 1965, Assembly Bill 80 standardized the assessment process by fixing the ratio of assessed value to market value at 25% throughout the state. (11) Thus, the effective tax rate in 1975 is the sum of city and school district tax rates times 0.25. The passage of Proposition 13 in 1978 fixed the nominal property tax rate at 1% throughout the state. Furthermore, under the provisions of Proposition 13, all homes were assessed at full market value upon sale. As a result, the effective tax rate for 1980, 1985, and 1990, is 1%. However, in 1980 there was still some variation in effective tax rates across cities and school districts as a result of bond-issue servicing expenses exempted under the provisions of Proposition 13. Thus for 1980, we calculate the effective tax rate as one plus the sum of the remaining city and school district bond-issue tax rates. For 1985 and 1990 we set the effective tax rate applied to each home in our sample at 1%. The net of tax house price was then calculated as:
Pit = Vit −
Trateit Vit r
,
(2)
where Pit denotes the net of tax house price for house i in year t, Vit is the sale price of house i in year t, Trateit is the effective tax rate for house i in year t, and r is the discount rate. In making this calculation we used a discount rate of 8 percent in all years. (12) Variables describing the physical characteristics of each home include both quantity and quality measures. House size or quantity is described by square footage of living space, number of bathrooms and lot size. House quality is described by house age, the presence of a pool and/or view, the number of fireplaces, and central air conditioning. We matched each home in our sample with eight measures of neighborhood quality. Four variables describe the census tract in which each house is located. The variables are percent of the population age sixty-five or older, percent below the poverty level, time to work, and percent of the population white. These variables were constructed using tract-level data from the 1970, 1980, and 1990 Census of Population and Housing. Neighborhood characteristics for 1975 were constructed by taking the average of the 1970 and 1980 census values for each variable. Similarly, neighborhood
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characteristics for 1985 were constructed by taking the average of the 1980 and 1990 census values for each variable. In addition to the census tract variables, we utilize four other neighborhood indicators: (1) environmental quality, which is assigned to each census tract and is measured by the annual average air pollution readings for total suspended particulates; (2) crime rate, measured at the city level as the FBI index of major crimes; (3) city-level expenditures per capita on all services other than police protection; and (4) neighborhood accessibility to the beach, calculated as miles to the nearest beach. Finally, we matched each home in our sample with two measures of school district quality. The first measure is school district spending per pupil, measured as current expenditures per pupil. The second measure is student performance on standardized tests. Our measure of student performance is the combined average of sixth grade math and verbal scores on the California Student Assessment Program test. District-level test scores for 1974-75, 197980, 1984-85, and 1989-90, were obtained from the California Department of Education. Variables that depict neighborhood/community influences are matched to the housing data using common location indicators. For most variables the matching exercise is straightforward since a home is located within a specific census tract, a school district, or a city. However, the air pollution data require a multi-step procedure in order to assign a specific census tract the appropriate pollution measures. We assign air pollution to each location using the method developed by Beron, et al (1998) in their recent report to the South Coast Air Quality Management District. (13) Relevant variable definitions are presented in Table 2. Summary statistics for the years 1975, 1980, 1985, and 1990 are provided in Table 3. Several interesting observations can be gleaned from a brief inspection of the summary statistics. First, the real average home sale price increased significantly from 1975 to 1990. Second, average housing characteristics are quite similar across time although the sample of homes in 1990 seems somewhat smaller (e.g., living and land area) with fewer amenities (e.g., view, pool, fireplaces) than the 1975, 1980, or 1985 samples. Third, there was a large shift in the ethnicity of the region over the 1975 – 1990 period. The proportion of whites in the sample of census tracts has markedly declined as other ethnic groups have significantly increased.
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Table 2 Variable Definitions Variable Structural Characteristics LIVAREA LANDAREA BATH CENTAIR FIRE HOME AGE POOL VIEW Community Characteristics AGE65 BEACH BPOV WHITE TWORK TSPMU
Definition
Interior Living Space (thousands of square feet) Lot Area (thousands of square feet) Number of Bathrooms Presence of Central Air Conditioning (yes=1, no=0) Number of Fireplaces Age of Home (years) Presence of Pool (yes=1, no=0) Presence of a View (yes=1, no=0)
SCORE
Percentage in Census Tract Above 65 Years Old Distance to Nearest Beach (miles) Percentage in Census Tract Below Poverty Level Percentage in Census Tract White Time to Work (minutes) Annual Average of Total Suspended Particulates (Parts Per Million) Per Capita FBI Crime Index City-Level Expenditures per Capita (Thousands of Dollars) Current Expenditures per Pupil (Thousands of Dollars) Combined Average Sixth Grade Math and Verbal Score
PRICE
Sale Price (Dollars)
CRIME CITYEXP SCHEXP
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Table 3 Summary Statistics Variable
Mean 1975
Mean 1980
Mean 1985
Mean 1990
1.62 8.57
1.62 8.40
1.62 8.50
1.53 8.02
1.88 0.20 0.79 22.77 0.22 0.04
1.86 0.27 0.74 25.80 0.20 0.04
1.82 0.26 0.70 31.60 0.20 0.03
1.73 0.19 0.61 37.85 0.17 0.03
Community Characteristics AGE65 BEACH BPOV WHITE TWORK TSPMU CRIME CITYEXP (1000's of $'s) SCHEXP (1000's of $'s) SCORE
11.51 19.12 6.49 88.00 27.94 94.25 63.15 0.507 3.03 256
14.32 20.81 8.02 79.07 28.20 95.73 66.12 0.517 3.06 252
13.46 20.48 8.18 68.43 28.49 94.14 66.16 0.602 3.51 255
11.95 20.16 9.72 53.34 28.74 98.59 70.43 0.621 3.84 255
PRICE
154,769
174,670
179,406
249,604
Number of Observations
7,154
10,244
16,474
16,710
Structural Characteristics LIVAREA (1000's of sq. ft.) LANDAREA (1000's of sq. ft.) BATH CENTAIR FIRE HOME AGE POOL VIEW
Results Results based on the estimation of equation 1 are reported in the second and third columns of Table 4. All of the structural characteristics are of the correct sign and significant at the fivepercent level. Similarly, all of the coefficients on the neighborhood/community characteristics are of the correct sign and with the exception of AGE65 and TWORK, all of the coefficients are significant at the five-percent level. The semi-log functional form makes the parameter estimates quite amenable to interpretation since the coefficients can be interpreted as percent of the sale price
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of a home. For example, our estimates indicate that each additional square footage of living space increases the sale price of a home by 0.03% while a pool and a view add 6% and 4% respectively to the sale price of a home. Using the parameter estimates reported in Table 4, we can calculate the impact of a one-unit increase in any characteristic on the sale price of a home as:
∂P = λiP , ∂X i
(3)
where P is the sale price of a home, X i is the ith characteristic, and
λi is the parameter estimate for the ith characteristic. For example, consider a house with a sale price of $150,000, which is approximately the median sale price of homes in our sample. Using equation (3), our results indicate that each additional square footage of living space increases the price of a home by approximately $45. Similarly, a pool adds approximately $9,000 to the price of a home while a view adds $6,000. Turning to the neighborhood/community characteristics, a one-unit increase in air pollution decreases the price of a home by approximately $450. Similarly, a one-unit increase in the crime rate per capita decreases the price of a home by approximately $90.
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Table 4 Estimated Hedonic Equations Dependent Variable = Ln(Net of Property Tax Sale Price) Baseline Results Variable Structural Characteristics LIVAREA LANDAREA BATH CENTAIR FIRE HOME AGE POOL VIEW Community Characteristics AGE65 BEACH BPOV WHITE TWORK TSPMU CRIME CITYEXP SCHEXP SCORE
Coefficient
St. Error
Instrumental Variable Results Coefficient St. Error
0.30 0.004 0.06 0.06 0.05 - 0.002 0.06 0.04
0.004 0.0003 0.004 0.004 0.003 0.0001 0.005 0.01
0.30 0.004 0.06 0.06 0.06 - 0.002 0.06 0.04
0.004 0.0003 0.004 0.005 0.003 0.0001 0.004 0.01
0.0001 - 0.02 - 0.007 0.002 - 0.001 - 0.003 - 0.0006 0.03 0.04 0.002
0.0003 0.001 0.0004 0.0001 0.0006 0.0005 0.0001 0.008 0.01 0.0002
0.0001 - 0.02 - 0.007 0.002 - 0.001 - 0.003 - 0.0007 0.03 0.06 0.002
0.0003 0.001 0.0004 0.0001 0.0006 0.0004 0.0001 0.008 0.01 0.0002
Notes: Regression includes district and year fixed effects. LIVAREA and LANDAREA are reported in thousands of square feet. CITYEXP and SCHEXP are reported in thousands of dollars
Our primary concern is with the impact of changes in spending per pupil and test scores on housing values. The coefficients on both of those variables are positive and statistically significant at the onepercent level. Evaluated at the median sale price of a home in our sample, our estimates imply that a one-dollar increase in spending per pupil increases the price of a home by $6. (14) Similarly, a onepoint increase in student performance increases the price of a home by $300.
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Before we accept those estimates, however, there are two further issues to investigate. The first issue is the possible endogeniety of city-level and district-level expenditures in 1975. Prior to the passage of Proposition 13 in 1978, expenditures at the city and district level depended on the tax rates levied by school districts and cities. All else equal, a higher tax rate implied a higher level of expenditures. Thus, one might argue that the estimates reported in Table 4 suffer from simultaneity bias since expenditures in 1975 are a function of tax rates (which are included in the dependent variable). (15) In 1980, 1985, and 1990, however, simultaneity bias is no longer an issue since, as a result of proposition 13, property tax rates were fixed at one percent of assessed valuation throughout the state. To account for the possible endogeneity of spending per pupil and city expenditures per capita in 1975, we re-estimated our model using instrumental variables. Our main instrument for spending per pupil in 1974-75 is base revenue limit funding per pupil in 1974-75. As noted by Goldfinger (1994), the revenue limit formulas implemented by the State Legislature included both a base revenue limit and a revenue limit adjustment that provided additional revenues. The original 1973-74 base revenue limits were set equal to each district’s property tax revenue plus non-categorical state aid in 1972-73. Each district’s base revenue limit in 1974-75 was then set equal to its base revenue limit in 1973-74 plus an adjustment for inflation. Thus, a district's base revenue limit differs from its actual revenue limit only to the extent that revenue limit adjustments, such as voter-approved overrides, differ. Because each district’s base revenue limit is determined by the state it is exogenous and thus serves as a valid instrument. Our main instrument for city-level expenditures in 1975 is the percent of households that are renters in each city. The rationale for this instrument is rooted in the empirical literature on the demand for locally provided public goods, pioneered by Borcherding and Deacon (1972) and Bergstrom and Goodman (1973). As Bergstrom and Goodman have argued, renters may not believe that they pay the entire property tax on their housing. As a result they tend to vote for more public expenditures than homeowners with similar socioeconomic characteristics. The results of empirical studies on the demand for locally provided public goods support this argument.
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Furthermore, while the percent of households that are renters is likely to be positively correlated with city-level expenditures per capita, it is not likely to be correlated with residential property tax rates, which is necessary for a valid instrument. To form instrumental variables for spending per pupil and city-level expenditures per capita, we used a two-stage least squares approach. In forming the instrument for spending per pupil in 1975, we regressed this variable on the 1975 district-level averages of all the exogenous variables in our model, base revenue limit funding per pupil in 1974-75, and the percentage of households in each city that were renters in 1975. (16) Similarly, in forming the instrument for city-level expenditures per capita, we regressed this variable on the 1975 city-level averages of all the exogenous variables in our model, base revenue limit funding per pupil in 1974-75, and the percentage of households in each city that were renters in 1975. The coefficient estimates using those instruments are reported in the fourth column of Table 4. Controlling for simultaneity bias has little effect on the parameter estimates. In particular, the coefficients on city-level expenditures per capita and spending per pupil are not much different from those reported in the baseline specification. The coefficient on spending per pupil increases from 0.04 to 0.06 while the coefficient on city-level expenditures per capita remains unchanged. The second issue we investigate is the sensitivity of our results to outliers. Figure 1 reveals that one of the high-spending districts in 1974-75 experienced a particularly sharp decline in general purpose revenue per pupil between 1975 and 1990. Specifically, real revenue per pupil in Beverly Hills Unified declined by 25 percent. No other school district experienced a decline of more than 6 percent. In fact, only three school districts actually experienced a decline in real revenue per pupil between 1975 and 1990. Are our results sensitive to the inclusion of these school districts? To answer that question we estimated two further models based on restricted samples. First, we excluded Beverly Hills Unified from the sample. Results based on this restricted sample were nearly identical to those reported in Table 4. Second, we excluded all three districts that experienced a decline in revenue per pupil between 1975 and 1990 from the sample. Once again this had very little effect on the estimated coefficients or their standard
19
errors. Specifically, the coefficients on spending per pupil and test scores were nearly identical to the estimates reported in Table 4.
Did School Finance Reform Level-Up or LevelDown School Quality? Our results indicate that reform-induced changes in district resources were capitalized into housing values. Furthermore, that result is robust to a number of refinements to our baseline model. With that in mind, we now turn to examining whether the equalization of resources across districts led to a convergence in school district housing price premiums. To examine that issue, we employed a multi-step procedure. In the first step we obtained yearly estimates of the housing price premium for each school district by estimating separate regressions, based on the specification used in the previous section (i.e. equation 1 without year and district fixed effects), for 1975, 1980, 1985, and 1990. The primary output of those regressions is a set of coefficients on our two measures of school district quality – spending per pupil and district test scores. To form yearly estimates of the housing price premium for each school district, we multiplied the district quality measures by the estimated coefficients for those measures and then summed the two products. The result is a set of estimates of the time-dependent housing price premium attached to each school district accounting for other house and neighborhood specific influences. In the second step we examined the relationship between changes in these school district housing price premiums and the equalization of school district resources using the following specification: ^
∆ Prem jt = δ 0 + δ 1 SCHEXP75 j + η t + ε it , ^
(4)
where ∆ Prem jt denotes the change in the estimated housing price premium of district j between periods t and t-1 (i.e. between 1975 and 1980, 1980 and 1985, and 1985 and 1990), SCHEXP75 j denotes
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spending per pupil in district j in 1975, ηt are year fixed effects, and
ε jt
is a random disturbance term.
The coefficient of primary
interest is δ 1 . In section 2, we showed that school finance reform led to a significant reduction in resource inequality among school districts in our sample. Equalization was achieved by leveling-up the spending of low-spending districts through increases in state aid, and controlling the spending of high-spending districts through revenue limits. Thus, if school finance reform led to a convergence in housing values, changes in school district housing price premiums should be inversely related to spending per pupil in 1974-75. In other words, δ 1 should be negative. Generalized least squares estimates of the parameters of equation 4 are presented in the second column of Table 5. (17) The coefficient on 1975 spending per pupil is negative and statistically significant at the one-percent level suggesting that changes in school district housing price premiums over time are inversely related to spending per pupil in 1975. Thus, our results support the hypothesis that school finance reform led to a convergence in housing values. While that result is intriguing, from a policy perspective it seems natural to ask: what caused the convergence? In particular, was the convergence in school district housing price premiums the result of low-spending districts improving faster than high-spending districts and thus catching up? Or was the convergence in housing price premiums the result of a decline in the perceived quality of high-spending districts? That is, has there been a leveling-up or a leveling-down of school district quality?
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Table 5 School Finance Reform and School District Housing Price Premiums Dependent Variable = Change in District Housing Price Premium Variable
Coefficient (St. Error)
Coefficient (St. Error)
Coefficient (St. Error)
SCHEXP75
- 0.022 (0.009)
___
0.011 (0.012)
Q1
___
0.005 (0.009)
___
Q4
___
- 0.022 (0.009)
___
SCHEXP75*Q1
___
___
0.003 (0.003)
SCHEXP75*Q4
___
___
- 0.008 (0.003)
CONSTANT
0.23 (0.028)
0.16 (0.009)
0.14 (0.031)
Notes: All regressions include year fixed effects. SCHEXP75 is measured in thousands of dollars.
To answer that question, we created two new dummy variables that indicate whether a district was in the first or fourth quartile of the sample distribution of spending per pupil in 1975. The first dummy variable, Q1, takes the value of one if a school district was in the lower (first) quartile of spending per pupil in 1975 (the 10 districts with the lowest spending per pupil in 1975). The second dummy variable, Q4, takes the value of one if a school district was in the upper (fourth) quartile of spending per pupil in 1975 (the 10 highest spending districts in 1975). We then regressed the change in school district housing price premiums on those two dummy variables and a set of year fixed effects. In other words, we replaced SCHEXP75 in equation 4 with the two dummy variables and reestimated the model. The omitted group in this regression is school districts in the second and third quartiles of spending per pupil in 1975.
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The sign and magnitude of the coefficients on the two dummy variables determines whether there has been a leveling-up or a leveling-down of school district quality. If the convergence in housing price premiums was the result of low-spending districts improving faster than high-spending districts (leveling-up), lowspending districts should have experienced larger increases in their housing price premiums over time than either the omitted group or high-spending districts. As a result, the coefficient on the dummy variable for low-spending districts in 1975 should be positive and larger in magnitude than the coefficient on the dummy variable for high-spending districts in 1975. In contrast, if the convergence in housing price premiums was the result of a relative decline in the perceived quality of high-spending districts and no real improvement in the perceived quality of low-spending districts (leveling-down), the coefficient on the dummy for high-spending districts in 1975 should be negative while the coefficient on the dummy for low-spending districts should be close to zero (i.e. statistically insignificant). Results are reported in the third column of Table 5. The coefficient on the dummy for high-spending districts in 1975 is negative and statistically significant while the coefficient on the dummy for low-spending districts in 1975 is not statistically different from zero. Thus, our results suggest that the convergence in school district housing price premiums was the result of a relative decline in the perceived quality of high-spending districts and no real improvement in the perceived quality of low-spending districts. In other words, our results suggest that convergence was caused by a leveling-down of school district quality. The fourth column of Table 5 presents results based on an alternative specification used to examine whether school finance reform led to a leveling-up or a leveling-down of school district quality. Specifically, rather than replacing SCHEXP75 with the two dummy variables that indicate whether a district was in the first or fourth quartile of the sample distribution of spending per pupil in 1975, we interacted those dummy variables with SCHEXP75. We then regressed the change in the estimated school district housing price premiums on SCHEXP75 and the two interaction terms. This specification provides a means of examining whether the effect school spending has on housing values differs for those districts that began as high-spending districts and those districts that began as lowspending districts. The results reported in the fourth column of Table
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5 are qualitatively similar to the results reported in the third column. In particular, the coefficient on the interaction of SCHEXP75 with the dummy variable for high-spending districts in 1975 is negative and statistically significant while the coefficient on the interaction of SCHEXP75 with the dummy for low-spending districts in 1975 is not statistically different from zero. The coefficient on SCHEXP75 is also statistically insignificant. (18) Thus, the results reported in the fourth column provide further evidence that the convergence in school district housing price premiums was the result of a relative decline in the perceived quality of high-spending districts and no real improvement in the perceived quality of low-spending districts.
Conclusions In this paper, we attempted to answer three fundamental questions related to the impact of school finance reform on housing values. First, were reform-induced changes in district resources capitalized into housing values? Second, did the equalization of resources across districts lead to a convergence in school district housing price premiums? Third, if so, was the convergence in housing price premiums the result of a leveling-up or a leveling-down of school district quality? The results reported in Table 4 indicate that the answer the first question is yes – reform-induced changes in district resources were capitalized into housing values. Specifically, our results indicate that a one-dollar increase in spending per pupil results in approximately a six-dollar increase in the price of a home, all else equal. Furthermore, the results reported in the second column of Table 5 suggest that the answer to the second question is also yes -the equalization of district resources appears to have led to a convergence in school district housing price premiums. Specifically, we find that changes in school district housing price premiums over time are inversely related to spending per pupil in 1975. What caused that convergence? The results reported in the third and fourth columns of Table 5 suggest that the convergence in housing price premiums was the result of a decline in the perceived quality of high-spending districts and no real change in the perceived quality of low-spending districts. Thus, our results suggest the convergence in housing values was the result of a leveling-down of school district quality.
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Our finding that school finance reform in California resulted in a leveling-down rather than a leveling-up of school quality is consistent with the results of several other studies. (19) For example, using state-level data, Peltzman (1993) found a negative and statistically significant relationship between increases in a state’s share of school funding for education and student performance on the SAT. Similarly, Husted and Kenny (2000) found that state-induced spending equalization lowered state-level average SAT scores but had little effect on reducing disparities in student achievement. In a related study, Downes and Figlio (1997) examined the link between statewide tax limitations, such as Proposition 13, and student achievement. They concluded that tax limits had a negative effect on student performance. Finally, the results of Sonstelie, Brunner, and Ardon (2000) indicate that in the aftermath of school finance reform in California, student performance on a range of standardized tests declined even after adjusting for changes in student demographics. Furthermore, they find that the decline in student performance may have been worst among low-income students. In summary, our results support the conclusion reached by Jonathan Kozol, who, in his 1991 book Savage Inequalities, noted: “Today in all but 5 percent of California districts funding levels are within $300 of each other. Although in this respect, the plaintiffs [in Serrano] won the equity they sought, it is to some extent a victory of losers” (Kozol, 1991: pp. 137).
Notes 1. Numerous studies have examined the relationship between housing values and interjurisdictional differences in public school quality. In general, these studies have found that houses located in districts with higher spending per pupil and higher test scores have higher housing values, all else equal. See for example, Oates (1969), Li and Brown (1980), Sonstelie and Portney (1980), Jud and Watts (1981), Reinhard (1981), Haurin and Brasington (1996), and Black (1999). 2. Wyckoff (1995) presents a theoretical analysis of the impact of spending equalization on housing values. 3. Picus (1991) and Sonstelie, Brunner, and Ardon (2000), provide a
25
more detailed description of the evolution of California’s system of public school finance. 4. During the 1975-76 academic year, revenue limit overrides were placed on the ballot in 269 districts. Voters approved the overrides in 101 of these districts. See State Controller (1975-76). 5. The two school districts were Las Virgenes and Hacienda-La Puente. 6. Other local revenue not subject to the revenue limit includes revenue from sales, rentals, parcel taxes, and voluntary contributions. 7. In 1974-75, revenue limit funding constituted 82 percent of all revenue among school districts in our sample. In 1989-90, however, revenue limit funding constituted only 74 percent of all revenue. 8. Approximately half of the $200 dollars increase is due to the impact of other local revenue; the other half is due to the impact of categorical state aid. 9. Measuring changes in resource inequality in terms of the coefficient of variation leads to a similar conclusion. For example, between 1974-75 and 1989-90, the coefficient of variation for real revenue per pupil fell by 41 percent (from 0.17 to 0.10) while the coefficient of variation for real current expenditures fell by 38 percent (from 0.16 to 0.10). 10. There is another reason to be concerned about the inclusion of Los Angeles Unified in our sample. As Freeman (1974) and Pollakowski and Shavell (1975) note, if individual communities are large enough to affect the rent bid function, the coefficients from a hedonic regression will not provide accurate estimates of the impact of local public services on housing values. 11. Doerr (1998), Part V, Chapter 1, page 9. 12. We examined the robustness of our results to alternative values of the discount rate and found that our results were essentially unaffected by the choice of r. Furthermore, we also estimated a model in which the dependent variable was the actual sale price,
26
rather than the net of tax payment sale price, and included the effective tax rate as an independent variable. The results based on this specification were nearly identical to those obtained in the following section. Results are available upon request. 13. First, the air pollution data, obtained from monitoring stations or airport readings are aggregated into a summary statistic (e.g., annual average, median, etc.). Second, these summary data are entered into the SURFER computer program to generate isopleth contours. Third, the isopleths are utilized to create pollution levels at grid points that cover the entire study area. Fourth, each census tract is assigned the pollution level of the grid point that is closest to its centroid. Finally, each single family home in a specific census tract is assigned the same pollution value. 14. Our finding that a one-dollar increase in spending per pupil results in approximately a $6 increase in the price of a home is consistent with the findings of previous studies. For example, using a sample of homes that sold between 1993 and 1995 in Massachusetts, Black (1999) found that a one-dollar increase in spending per pupil resulted in approximately a $10 increase in the price of a home. Similarly, using a 1970 sample of homes in San Mateo County, California, Sonstelie and Portney (1980) found that one-dollar increase in spending per pupil resulted in approximately a $12.50 increase in the price of a home. 15. Recall that prior to the passage of Proposition 13, school districts could override their revenue limits by a majority vote of their electorate. As a result, districts still had some control over both spending per pupil and property tax rates. During the 1974-75 academic year, voters approved revenue limit overrides in ten of the school districts in our sample. The ability of districts to increase their tax rates through voter-approved overrides suggests that spending per pupil in 1975 may be endogenous. 16. We constructed an estimate of the percentage of households that were renters in each city in 1975 by taking the average of the 1970 and 1980 census values for this variable. 17. The dependent variable in this “second stage” regression is a linear combination of estimated regression coefficients from the first stage regressions. As a result, the disturbance term in equation 4 is
27
heteroscedastic. To account for this heteroscedasticity we used a generalized least squares procedure (see Amemiya (1978) and Borjas (1987)). Specifically, let Prem jt be the true value of the housing price premium in district j in year t. The variable Prem jt is unobserved, ^
but Prem jt is estimated in the first stage regressions as ^
^
^
Prem jt = γ 1 t SCHEXPjt + γ
2t
SCORE jt . The relationship between ^
^
Prem jt and Prem jt is given by: Prem jt = Pr em jt + ω jt , where E[ω jt ] = 0 ^
^
^
^
and Var[ω jt ] = Var[γ 1t ] SCHEXPjt2 + Var[γ 2t ]SCORE 2jt + 2 Cov(γ 1t , γ 2t ) SCHEXPjt SCORE jt . Assuming that E[ω jt ω jt −1 ] = 0 , the GLS estimation procedure amounts to weighting equation 4 by
Var[ω jt ] + Var[ω jt −1 ] .
18. For completeness, we also estimated a model that included SCHEXP75, the two interaction terms, and the two dummy variables indicating whether a district was in the first or fourth quartiles of the sample distribution of spending per pupil in 1975. Although the results based on this specification were qualitatively similar to those reported in the third and fourth columns of Table 5, none of the estimated coefficients were statistically different from zero at conventional levels. Results are available upon request. 19. Fischel (1995) provides an extensive overview of the literature on the impact of school finance reform on school quality.
References Amemiya, Takeshi. 1978. "A Note on a Random Coefficients Model." International Economic Review. 19(3): 793-796. Bergstrom, Theodore C. and Richard P. Goodman. 1973. "Private Demands for Public Goods." American Economic Review. 63: 280296. Borjas, George. 1987. "Self-Selection and the Earnings of Immigrants." American Economic Review. 77(4): 531-553.
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Moulton, Brent R. 1986. "Random Group Effects and the Precision of Regression Estimates." Journal of Econometrics. 32: 385-397. Oates, Wallace E. 1969. "The Effects of Property Taxes and Local Public Spending on Property Values: An Empirical Study of Tax Capitalization and the Tiebout Hypothesis." Journal of Political Economy. 77: 957-971. Peltzman, Sam. 1993. "The Political Economy of the Decline of American Public Education." Journal of Law and Economics. 36: 331370. Picus, Lawrence O. 1991. "Cadillacs or Chevrolets?: The Evolution of State Control over School Finance Reform in California." Journal of Education Finance. 17: 33-59. Pollakowski, Mitchel, and Steven Shavell. 1975. "The Air Pollution and Property Value Debate." Review of Economics and Statistics. 57: 100-104. Reinhard, Raymond M. 1981. "Estimating Property Tax Capitalization: A Further Comment." Journal of Political Economy. 89: 1251-1260. Rosen, Sherwin. 1974. "Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition." Journal of Political Economy. 82: 34-55. Sonstelie, Jon, Eric Brunner, and Ken Ardon. 2000. "For Better or Worse? School Finance Reform in California." Public Policy Institute of California, San Francisco. Sonstelie, Jon and Paul Portney. 1980. "Gross Rents and Market Values: An Empirical Test of the Tiebout Hypothesis." Journal of Urban Economics. 7: 103-118. State Controller. 1976. Annual Report of Financial Transactions Concerning School Districts of California, Fiscal Year 1975-76. Sacramento. Wyckoff, Paul G. 1995. "Capitalization, Equalization, and Intergovernmental Aid." Public Finance Quarterly. 23: 484-508.
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