The Myth of “Free” Public Education: Impact of School Quality on House Prices in the Fremont Unified School District,California

Abstract

Using the Fremont Unified School District in Fremont, California, as the study area, this study estimates the impact of school quality on house prices and finds that a one-standard-deviation increase in the quality of elementary, middle, and high schools significantly increases house prices—by 20 percent for an average-priced house. I urge urban planners and policy makers to explicitly recognize the impact of schools on residential segregation, to consider access to high-quality K–12 education when developing plans and policies, to collaborate with school districts to improve educational quality, and to provide incentives for the construction of affordable housing in neighborhoods with high-quality schools.

Keywords

housing real estate spatial analysis school quality house prices hedonic regression K–12 education

Introduction

A 2012 American Planning Association (APA) national survey finds that schools are among the top three priorities on which respondents want local planners to spend their time (American Planning Association 2012). Moreover, in a 2000 national survey, suburban residents identified school quality as the most important “pull” factor for locating in urban areas (Zimbabwe et al. 2012). Indeed, school quality is a prominent factor in households’ residential location choice.

The nexus between household location and variation in the quality of schools leads to the capitalization of school quality into house prices. Therefore, the impact of school quality on house prices informs households’ sorting behavior in the housing market (Bayer, Ferreira, and McMillan 2007; Black and Machin 2011). Such sorting has important policy implications. For example, it might result in racially, ethnically, and economically segregated neighborhoods (Bayer, Ferreira, and McMillan 2007) because low-income, often racial and ethnic minority, households find it difficult to rent or own a house in neighborhoods with high-quality schools. This segregation poses challenges to efforts to plan equitable communities, and succeeding in such efforts becomes more difficult when localities are not able to provide affordable housing in neighborhoods with high-quality schools. Further, the location of high-quality schools in auto-oriented neighborhoods, especially in sprawling suburbs with poor pedestrian and bike accessibility, hinders efforts to reduce vehicle miles travelled and greenhouse gas emissions. Additionally, to the extent that houses within attendance zones of high-quality schools are more expensive and are likely to appreciate at a faster rate than houses in attendance zones of low-quality schools, sorting has implications for housing affordability, access to “free” high-quality public education, and households’ ability to accumulate wealth through home ownership. Finally, when bidding on a house, potential homebuyers reveal the value they place on the bundle of public goods and services that accompany that house, including the quality of public schools (Black 1999). Accurate estimation of this value should help state and local governments and school districts allocate resources more efficiently, devise ways to fund K–12 education, and advocate for additional resources. For example, a large school-quality premium could indicate a community’s willingness to vote for a bond measure to fund schools or to support a school impact fee ordinance. Further, large premiums send a signal to policy makers to prioritize schools in resource allocation.

Using the Fremont Unified School District (FUSD) in Fremont, California, as the case study area, this article seeks to answer the following two research questions:

Controlling for other factors that affect house prices, what is the impact of school quality on house prices?

Does school quality impact the rate of increase in house prices? Specifically, do the prices of houses located in attendance zones of high-quality schools rise at a faster rate than the prices of houses located in attendance zones of lower-quality schools?

Although several studies have empirically estimated the impact of school quality on house prices (see, e.g., Bayer, Ferreira, and McMillan 2007; Black 1999; Brasington and Haurin 2006; Cellini, Ferreira, and Rothstein 2010; Fiva and Kirkeboen 2008; Fack and Grenet 2010; Leech and Campos 2003; Weimer and Wolkoff 2001), this article advances research in two ways. First, it estimates the cumulative impact of the quality of elementary, middle, and high schools, whereas existing studies focus primarily on very specific proxies of school quality, such as the test scores for a specific grade, or on one type of school, such as elementary schools.

Second, existing studies largely show a modest impact of school quality on house prices. For example, a review of the recent empirical literature shows that a one-standard-deviation increase in student test scores leads to a 1–4 percent increase in house prices (Nguyen-Hoang and Yinger 2011). However, I hypothesize that high average household incomes and a paucity of high-quality schools in the study area and the surrounding region (the San Francisco Bay Area) lead households to bid aggressively for houses in attendance zones of high-quality schools. Therefore, I expect to find that school quality significantly impacts house prices. In fact, for households in attendance zones of very high-quality public schools, a monetary impact that is equivalent in magnitude to the cost of the alternative, a private school, may be expected. This hypothesis is supported by the empirical literature, which shows that higher-income households place a higher premium on school quality than lower-income households (Ries and Somerville 2010). Indeed, this article finds that a one-standard-deviation increase in the quality of elementary, middle, and high schools leads to a $131,644 increase in a resident’s marginal willingness to pay for a house, which corresponds to 20 percent of the mean house price in Fremont of $667,690—a magnitude of impact that is likely to be experienced by other communities with high education and income levels, strong residential real estate markets, and a lack of high-quality public schools.

This article is structured as follows: First, I review the existing literature on the impact of school quality on house prices. Next, the study area and the data analyzed are described, and the basic methodology is explained. The results of the analysis are then presented, along with specification checks. Finally, I offer conclusions and posit some further implications of the study findings.

Literature Review

The literature review focuses on three important issues related to research estimating the impact of school quality on house prices: the variables used to measure school quality, the reasons why school quality affects house prices, and the magnitude of the impact of school quality on house prices.

Variables Used to Measure the Effect of School Quality on House Prices

The extant literature has used both input- and outcome-based proxies to measure the impact of school quality on house prices. Examples of input-based proxies include the student–teacher ratio (used by Brasington 1999; Grether and Mieszkowski 1974; Harrison and Rubinfeld 1978), teachers’ qualifications and salaries (Brasington 1999), and expenditure per student (utilized by Brasington 1999, 2002; Bradbury, Case, and Mayer 1995; Oates 1969; Sonstelie and Portney 1980).

Over the last two to three decades, output-based proxies, such as test scores, have gained popularity. Such a change is in line with the overall shift away from input-based “activities” and “productivity” and toward outcome-based “performance” and “results” for holding government-run institutions, including schools, accountable (Campbell and Schutz 2004).¹ However, the extant literature has primarily used very specific output-based proxies to measure the impact of school quality on house prices, such as high school graduation rates used by Brasington (1999), fourth-grade test scores employed by Black (1999), twelfth-grade test scores utilized by Davidoff and Leigh (2008), and specific elementary and secondary school examination results employed by Ries and Somerville (2010).

The use of very specific measures to represent overall school quality rests on an assumption that school quality is homogeneous across a school district (i.e., school quality is considered excellent if the fourth-grade test scores are excellent). However, several elementary, middle, and high schools of varying levels of quality may exist in a school district. Therefore, a household’s residential location choice and willingness to pay for a house are likely to be sensitive to the quality of all three types of schools and consequently could vary within one school district. Similarly, school-district-level input measures fail to capture intra-school-district variation in quality.

This study uses the Academic Performance Index (API) score of FUSD schools to measure their quality. Representing the results of testing over the entire course of a student’s education, API scores constitute a comprehensive measure of educational quality. API scores are measured for each school and for various groups of students within a school, where students are grouped based on their race/ethnicity and whether English is their native language. The results of four state-level tests, administered in grades two through twelve, are used to determine API scores (California Department of Education 2013). Importantly, API scores are commonly reported in real estate listings in California to advertise school quality. In summary, API scores, a widely known measure of school quality, are ideally suited for this study as they are used by prospective homebuyers to make residential location decisions.

Why School Quality Impacts House Prices

The extant literature proposes and tests several theories that explain why prospective homebuyers would be willing to pay a price premium for school quality. Such research notes that while bidding for houses, parents are likely to consider a school’s ability to positively influence their child’s educational and labor market outcomes and to increase their satisfaction with the learning environment at school. For example, Gibbons and Silva (2011) find that parents derive satisfaction from test scores, even though these scores are not strongly associated with children’s well-being and enjoyment at school. Heck (2000) and Loeb and Bound (1996) find that many non-school-related factors, such as students’ gender, socioeconomic background, family size, and parents’ educational level determine the extent to which school-quality indicators, such as test scores, affect student achievement and that they should be considered in assessment of the impact of school quality on student achievement. Nonetheless, several empirical studies find a positive association between school quality and education outcomes such as high school graduation rates (Dee 1998), the eligibility for admission into colleges (Yun and Moreno 2006), and admission into selective colleges (Berkowitz and Hoekstra 2011). Further, formal education is theorized to provide skills that are valued by the labor market and that, therefore, increase an individual’s earning potential (Hanushek 2002). Empirical studies find support for such theory. For example, a 10 percent reduction in the student–teacher ratio is associated with a 3 percent increase in weekly earnings (Card and Krueger 1992). Similarly, a 10 percent increase in school spending is associated with a 1–2 percent increase in future earnings (Card and Krueger 1996). Finally, even if a buyer does not care about school quality, she might still choose to pay a premium because future buyers may be reasonably expected to care about and to pay for the premium. Accordingly, elderly people and households with no children often support local schools (Hilber and Mayer 2009).

Magnitude of the Impact of School Quality on House Prices

As mentioned earlier, existing studies primarily show a modest impact of school quality on house prices, where a one-standard-deviation increase in student test scores has been found to lead to a 1–4 percent increase in house prices (Nguyen-Hoang and Yinger 2011). For example, Bayer, Ferreira, and McMillan (2007), Black (1999), and Dougherty et al. (2009) report a 2 percent increase. Clark and Herrin (2000) report a 3 percent increase. A few studies report a larger impact: Brasington and Haurin (2006) note a 7 percent increase; Kane, Riegg, and Staiger (2006) report 10 % and Downes and Zabel (2002) report a 14 percent increase.

Nguyen-Hoang and Yinger (2011) note that studies that use boundary fixed effects report a smaller impact, perhaps indicative of such studies’ greater ability to control for neighborhood characteristics. Indeed, Black (1999) reports a 5 percent increase in house prices for a one-standard-deviation increase in test scores when boundary fixed effects are not included and only a 2 percent increase after they ae factored in. Further differences in such an impact could be due to measurement inconsistencies. A few studies, such as Bayer, Ferreira, and McMillan (2007) and Downes and Zabel (2002), use self-reported house values as the dependent variable instead of the prices obtained from actual sale transactions data. The magnitude of impact does not seem to vary closely by the time period or the geographic area of the study, as illustrated by the similarity in the findings between Downes and Zabel (2002), who examine school quality impacts in the Chicago Metropolitan Statistical Area for the time period from 1987 through 1991, and Brasington and Haurin (2006) who examine seven urban areas in Ohio for the year 2000.

Study Area and Data

Study Area

The study area is the FUSD. The FUSD serves the city of Fremont, and FUSD and city boundaries are conterminous. Fremont is situated in Alameda County in the eastern part of the San Francisco Bay Area of northern California. As of 2010, the city had a population of a little more than 214,000, a median household income of approximately $100,000, a majority-Asian demographic (50.6 percent), and a homeownership rate of 62.6 percent. The city can be characterized as a medium-sized, Asian-majority, higher-income suburban community. Table 1 provides a comparison of key demographic, housing, and economic characteristics of Fremont with those of Alameda County, California, and of the United States as a whole.

Table 1.

Comparison of Selected Demographic, Economic, and Housing Characteristics.

	Fremont	Alameda County	California	United States
Demographic characteristics
Race
Percent White population	32.8	43	57.6	72.4
Percent Asian population	50.6	26.1	13	4.8
Percent African-American population	3.3	12.6	6.2	12.6
Ethnicity
Percent Hispanic or Latino population	14.8	22.5	37.6	16.3
Median age	36.8	36.6	35.2	37.2
Average household size	2.99	2.7	2.9	2.58
Housing characteristics
Percent owner-occupied housing units	62.6	53.4	55.9	65.1
Percent renter-occupied housing units	37.4	46.6	44.1	34.9
Rental vacancy rate	4.5	6.4	6.3	9.2
Homeowner vacancy rate	1.3	1.8	2.1	2.4
Median gross rent^a	$1,566	$1,289	$1,224	$902
Median value of owner-occupied housing units^a	$600,300	$493,800	$366,400	$176,700
Economic characteristic^a
Median household income	$101,535	$72,112	$61,094	$53,046

Source: US Census Bureau, 2009–2013 5-Year American Community Survey.

Source for all other data: US Census Bureau, 2010 Census.

Estimation of the impact of school quality on house prices in the San Francisco Bay Area poses methodological challenges for three reasons. First, in a large majority of cases, school district and city boundaries do not match completely. For example, the city of San Jose is served by a multitude of school districts, with many districts also serving cities other than San Jose.

Second, in several cases, a house is served by more than one school district—for example, one district for the elementary and middle schools and another for the high school. This overlap of city, school district, and school attendance zone boundaries renders it extremely difficult to parse the effect of school quality separately from the effect of city- or school-district-specific characteristics. Finally, in instances where a city is served by one school district, school quality does not differ much within the district.

Fremont is a suitable study area because it avoids all these issues. First, the entire city is served by one school district, and the district and city boundaries are conterminous, limiting the likelihood of omitted variables (OV) issues such as those described above. In addition, schools within the district vary relatively widely in quality, from the nationally renowned Mission San Jose schools (considered by the local residents to closely approximate the quality of private schools) to the schools that are merely average in quality for California.

Black (1999) highlights two categories of OVs that may be correlated with school quality. The first category includes jurisdiction-level attributes, such as property tax rates and measures of the quality of jurisdiction-level infrastructure and amenities.

Because this study is focused on a single jurisdiction, Fremont, California, jurisdiction-level OV issues are not generally relevant. OV-bias-related problems are further mitigated in this study because it includes data only for houses located in school attendance zones that are completely within the city boundary; by contrast, school attendance zones that share the city boundaries are excluded from analysis to ensure that the school boundary fixed effects for these zones do not comingle with the jurisdiction-level impacts (Bayer, Ferreira, and McMillan 2007).

The second category of OVs includes neighborhood-level characteristics that are correlated with school quality. The boundary discontinuity design method (BDDM) reduces this type of OV problem by accounting for any unobserved characteristics that are shared by houses on either side of the school attendance zone boundary (Nguyen-Hoang and Yinger 2011). The BDDM reveals the effects of a change in the school attendance zone boundary on house prices by regressing the prices of houses that are on either side of a school attendance zone boundary on the structural and locational attributes of the house and the school-quality attributes. Econometrically, the BDDM is operationalized by including school attendance zone boundary fixed effects in the regression model.

The extant literature strongly supports the use of BDDM to tease out the effect of school quality on house prices (see, e.g., Bayer, Ferreira, and McMillan 2007; Black 1999; Cellini, Ferreira, and Rothstein 2010; Fack and Grenet 2010; Fiva and Kirkeboen 2008; Leech and Campos 2003; and Weimer and Wolkoff 2001). Other econometric approaches include spatial regression models and the repeat sales approach. Indeed, Nguyen-Hoang and Yinger (2011) call for the use of a variety of approaches to check the robustness of the results.

This study optimizes the BDDM by including only houses sold within a narrow band on either side of school attendance zones. In particular, three distance bands are defined for this study—0.125-, 0.25-, and 0.375-mile bands on either side of school attendance zones. In Fremont, these three distance bands closely correspond to two-, four-, and six-block distances, respectively, and they are comparable to those employed in previous studies such as Black (1999); Kane, Riegg, and Staiger (2006); Bayer, Ferreira, and McMillan (2007); and Davidoff and Leigh (2008). Further, Nguyen-Hoang and Yinger (2011) note the need to control for neighborhood-level effects that vary across attendance zone boundaries. Existing studies have used a variety of variables to capture such effects (Bayer, Ferreira, and McMillan 2007; Black 1999; Brasington and Haurin 2006; Chiodo, Hernández-Murillo, and Owyang 2010; Kane, Riegg, and Staiger 2006; Seo and Simons 2009; Zahirovic-Herbert and Turnbull 2008). Such variables commonly include individual-level characteristics such as race/ethnicity, education level, and age, as well as household characteristics such as family structure, income, and household tenure status (i.e., ownership or rental status). The neighborhood quality variables employed by these studies are largely measured at the census-block-group or census-tract level. Such measures provide a spatial scale that is too coarse for this study given the likelihood that a census block group or a census tract might span both sides of a school attendance zone, especially is an elementary school attendance zone; therefore, for this study, I include neighborhood quality variables at the much finer census-block level.

Data

This research uses real property data to estimate the impact of public school quality on prices of single-family houses sold in the FUSD during the two-year period beginning in April 2012 and ending in March 2014.

Data on parcel and property characteristics were obtained from the Alameda County Assessor’s Office. These data include the location and use of each parcel, the size of the parcel and of the house, the number of bedrooms and bathrooms in the house, the age of the house,² the date/year of the most recent sale, and the sale price. Two steps are taken to reduce the effects of outliers and miscoded extreme values. First, the top and bottom 1 percent of the records with respect to the sale price, the size of the house, and the size of the lot are dropped. Second, records showing fewer than one bedroom and more than six bedrooms are dropped. The final full data set comprises 938 observations, and the subsets for 0.375-, 0.25-, and 0.125-mile distance bands consist of 801, 642, and 354 observations, respectively.

Next, the attendance zone boundaries of all elementary, middle, and high schools were obtained from SchoolWorks, Inc.,³ a third-party vendor that hosts the GIS data for the FUSD. These boundaries were then digitized by using ArcGIS software and appended to each parcel. Next, school quality data—the API scores for each school and other school characteristics such as the student–teacher ratio, the percentage of students receiving a free or reduced-price meal, students’ race/ethnicity, and students’ proficiency levels in subject categories such as science, social science, languages, and mathematics—were obtained from the California State Department of Education and appended to each parcel. Finally, US Census 2010 data at the block level were added to measure neighborhood quality for each parcel; these data include housing vacancy rates, the percentage of the population that rents their houses, the percentage of the population comprising various races and ethnicities, and the family structure present in the home (various types of family and nonfamily households).⁴

Further explanation of the school quality variable is required. As noted earlier, this study uses each school’s API score as a measure of its quality. API scores range from 200 to 1,000, and the California State Department of Education has set a target API score of 800 for every school. As shown in Table 2, the vast majority of the schools included in this study meet or exceed the state-mandated API target. Further, all schools except Kennedy and Washington High Schools have API scores that exceed the state-wide averages. Therefore, the study data are suitable for measuring households’ willingness to pay a housing premium for a better public school education within the context of school quality ranging from state average (in this data set closely approximated by the combination of Blacow Elementary, Walter Middle, and Kennedy High Schools) to very high quality, which is considered equivalent to private-school quality by the local residents (represented in this data set by the combination of Mission Valley Elementary, Hopkins Middle, and Mission San Jose High Schools). These highest-quality schools in the district are in the top decile (i.e., the top 10 percent) of all California public schools in quality (California Department of Education 2015). The state decile rank for each school in the study area is provided in Table 2. The study-area elementary schools range from the fifth to the tenth decile, the middle schools from the sixth to the tenth, and the high schools from the fourth to the tenth.

Table 2.

School API and Z Scores.

Elementary School	API	Decile^b	z Score	Middle School	API	Decile^b	z Score	High School	API	Decile^b	z Score	Cumulative z Score^a
Blacow	835	5	−1.14	Walters	808	6	−1.25	Kennedy	750	4	−1.16	−3.55
Brier	862	7	−0.60	Walters	808	6	−1.25	Kennedy	750	4	−1.16	−3.02
Durham	865	7	−0.55	Walters	808	6	−1.25	Kennedy	750	4	−1.16	−2.96
Grimmer	818	5	−1.47	Horner	929	10	0.77	Irvington	874	10	0.70	−0.01
Green	872	7	−0.41	Horner	929	10	0.77	Irvington	874	10	0.70	1.06
Hirsch	903	9	0.21	Horner	929	10	0.77	Irvington	874	10	0.70	1.67
Weibel	971	10	1.55	Horner	929	10	0.77	Irvington	874	10	0.70	3.02
Glenmoor	882	7	−0.21	Centerville	855	7	−0.47	Washington	790	6	−0.56	−1.24
Maloney	854	6	−0.76	Centerville	855	7	−0.47	Washington	790	6	−0.56	−1.79
Parkmont	953	10	1.19	Centerville	855	7	−0.47	Washington	790	6	−0.56	0.16
Mission Valley	968	10	1.49	Hopkins	986	10	1.72	Mission San Jose	951	10	1.86	5.07
Oliveira	888	7	−0.09	Thornton	886	8	0.05	American	831	8	0.06	0.01
Average^c	892.6				883.1				827.3
Standard deviation^c	50.6				59.9				66.5
California average	815				802				753
N^c	938

Note: API = Academic Performance Index.

The scores in Tables 2 and 3 do not match because for the regression models, the score is calculated based on the API lagged by one year, while in Table 2 the score is calculated based on the API for year 2012.

School’s state decile rank.

Data for the full data set.

My initial aim for this research was to include in the regression models the API of each of the three levels of schools. However, preliminary models showed an extremely high degree of multicollinearity among the various schools’ APIs owing to a high correlation between the quality of two (or sometimes all three) of the schools. Although several elementary schools feed into each middle school in this data set, only one middle school feeds into each high school. See Table 2 for the various combinations of elementary, middle, and high schools. To address this multicollinearity problem, I created a composite measure of the quality of the three levels of schools for each attendance zone by adding the z scores for each school-level API.⁵ As shown in Table 2, a house located in the attendance zone for Hirsch Elementary, Horner Middle, and Irvington High Schools has a cumulative z score of 1.67, which is a sum of the z scores of the elementary (0.21), middle (0.77), and high (0.70) schools. Because this measure performs better (i.e., produces a higher adjusted R-square) than any other measure of API, such as the elementary, middle, or high school API, and because it addresses the multicollinearity problem, it is used for the regression modeling.⁶

The full data set comprises 938 single-family residences located within 12 elementary, five middle, and five high school attendance zone combinations. Table 3 provides descriptive statistics for the continuous variables used in the final models. The mean house price in the full data set is $663,320 with a standard deviation of $263,096.⁷ As expected, the variable measuring school quality (Sum of API z scores) has a mean of 0, which indicates an average-quality elementary–middle–high school combination for this study area. The minimum score, –3.85, is for a house located in the combined attendance zone of Blacow Elementary, Walters Middle, and Kennedy High Schools. The maximum score, 5.2, is for a house located in the combined attendance zone of Mission Valley Elementary, Hopkins Middle, and Mission San Jose High Schools. The standard deviation is 2.7, indicating significant variability in the school quality variable (see Table 3).

Table 3.

Descriptive Statistics for the Continuous Variables Used in the Final Models.

	Full Data Set		0.375-Mile Subset		0.25-Mile Subset		0.125-Mile Subset
	Mean Minimum/Maximum	SD	Mean Minimum/Maximum	SD	Mean Minimum/Maximum	SD	Mean Minimum/Maximum	SD
Consumer price index–adjusted sale price of the house ($)	663,319.9	263,095.8	667,689.6	273,407.8	653,698.7	268,403.7	644,304.0	251,531.2
	90,621/1,65,7240.5		90,621/1,65,7240.5		90,621/1,65,7240.5		90,621.1/1,651,209.8
House size (square feet)	1,623.3796/4,102	542.6	1,610.5796/4,102	550.9	1,610.5796/4,102	550.9	1,577.8840/4,102	515.8
Lot size (square feet)	7,081.412,910/25,370	2,491.21	7,015.122,910/25,370	2,571.07	7,015.122,910/25,370	2,571.07	6,807.413,200/20,203	2,125.87
Number of bedrooms	3.42/6	0.7	3.42/6	0.7	3.42/6	0.7	3.42/6	0.6
Number of bathrooms	2.11/4.5	0.6	2.11/4.5	6.2	2.11/4.5	6.2	2.11/4.5	5.9
Age of the house (year effective)	46.30/97	12.1	46.00/97	12.5	46.00/97	12.5	47.75/93	11.1
Sum of API z scores	0.0–3.8/5.2	2.7	0.3–3.8/5.2	2.8	0.3–3.8/5.2	2.8	0.2–3.8/5.2	2.9
Percent Asian population in the census block	40.40/100	19.0	41.90/100	19.4	41.90/100	19.4	41.50/100	18.8
Percent renter population in the census block	23.20/100	17.2	23.80/100	17.2	23.80/100	17.2	24.30/92	16.8
Student–teacher ratio in the high school (one-year lag)	24.321/27.2	1.7	24.521/27.2	1.6	24.521/27.2	1.6	24.421/27.2	1.6
Student–teacher ratio in the elementary school (one-year lag)	23.415.3/28.8	3.2	23.215.3/28.8	3.1	23.215.3/28.8	3.1	23.015.3/28.8	3.0
n	938		801		642		354

Methods

This study employs the hedonic regression approach (ordinary least squares [OLS] and spatial regression) to estimate owner households’ marginal willingness to pay for the quality, Q, of elementary, middle, and high schools (Q_emh). Therefore, the main estimation equation regresses the price of a single-family house i (P_i,) on its structural (X_i) and neighborhood attributes (N) in neighborhood j (Nj); the school attributes, S_emh; the quality of schools, Q_emh; and school boundary fixed effects, θ_i. ξ_i is the error term, which is assumed to be independent of Q_emh.

P_{i} {= α}_{0} {+ X}_{i} {+ N}_{j} {+ S}_{emh} {+ Q}_{emh} {+ θ}_{i} {+ ξ}_{i}

Estimation of equation (1) using OLS regression assumes homoscedasticity, or constant variance of the error term, as shown in equation (2).

V (ξ_{i}) {= σ}^{2} for all i .

Violation of this assumption could lead to biased standard errors of the coefficients, that is, over- or underestimation of the standard errors. Such violations typically occur when the variance of the error term is a function of a vector of explanatory variables z_ij (see equation (3)). Indeed, the Breusch-Pagan test for heteroscedasticity indicates nonconstant variance of the error term for the preliminary OLS regression models estimated in this study. As a remedy, the regression models are estimated with robust standard errors clustered at the school attendance zone level because the independent variable of interest, school quality, varies at this level.⁸

σ_{i}^{2} = σ^{2} f (α_{0} + \sum_{j = 1}^{P} α_{j} z_{ij})

Further, the independence of explanatory variables is assumed in the OLS. Specifically, the error terms are assumed not to correlate with each other. The temporal nature of the data in this study (the data are spread temporally over eight quarters—Spring 2012 to Winter 2014) increases the likelihood of temporal autocorrelation, the presence of which could lead to biased standard errors and thus reduce a model’s explanatory power. Therefore, a Breusch–Godfrey test for serial correlation is conducted for each regression model.

Additionally, the spatial nature of the data raises the likelihood of two types of spatial dependence: spatial error and spatial lag dependence. Under the former, the error terms may be correlated across space, thereby violating the assumption of uncorrelated error terms in OLS. This violation results in biased coefficient estimates and often results from omitted spatial variables. For example, in this study such biased estimates could be due to the omitted neighborhood-level variables. With spatial lag dependence, the dependent variable for an observation in one location could be affected by the dependent and independent variables for observations in other locations (Sedgley, Williams, and Derrick 2008) because the sale price of a house might be influenced by the sale price and characteristics of houses sold in its vicinity. The presence of spatial lag dependence violates the assumptions of uncorrelated errors and the independence of observations, and it could lead to biased and inefficient estimates. Checking and correcting for spatial dependence is therefore necessary to address the OV problem highlighted in the literature (if spatial error dependence is found) and the underlying spatial nature of the data.

The first step in checking for spatial dependence is to create a spatial weights matrix, W, in order to weight the sale price by accounting for both the spatial and temporal proximity of the sale transactions. Using the methodology employed by Di, Ma, and Murdoch (2010), I include the four sale transactions nearest to a given house in the spatial weights calculation. The transactions are further weighted by the proximity of the sale year. Transactions in the same year are given a weight of 1; transactions two years apart, a weight of 0.5; and transactions three years apart, a weight of 0.33. Second, we employ Lagrange multiplier (LM) tests to ascertain the type of spatial dependence that the models exhibit: spatial lag, spatial error, or both (Anselin 1988). The following LM tests are used: the simple LM test is used for error dependence (LM_err) and for a missing spatially lagged dependent variable (LM_lag); the RLM_err test is used for error dependence in the presence of a missing lagged dependent variable; and the RLM_lag test is used for a missing lagged dependent variable in the presence of error dependence (Bivand and Bernat 2011). Finally, I run spatial error and spatial lag regression models on those model specifications for which the LM tests indicate the presence of spatial error or spatial lag dependence. In cases where both types of spatial dependence are identified, the model with the higher log likelihood is selected for reporting the regression results.

The spatial error model equation is estimated as follows:

{P = α}_{0} {+ X + N_{j} + S}_{emh} {+ Q}_{emh} + θ + ξ

ξ = λ W ξ + ε

where ξ is a vector of error terms that is spatially weighted by using the weights matrix, W; λ is an autoregressive parameter; and ϵ is a vector of uncorrelated error terms.

The spatial lag equation is estimated as follows:

{P = α}_{0} {+ ρ WP + X + N_{j} + S}_{emh} {+ Q}_{emh} + θ + ξ

where WP is a spatially lagged dependent variable for the weights matrix, W; and ρ is a spatial autoregressive parameter.

Figure 1 provides a graphical representation of the twenty-four regression models that are estimated in this study. I examine three groups of eight models each. The first group excludes variables capturing neighbor-hood or school characteristics, the second group includes neighborhood characteristics, and the third group contains both neighborhood and school characteristics. These eight-model groups are further divided into four pairs of models—a full data set model and three distance-band-subset models with each pair comprising one model that includes boundary fixed effects and one that does not. Simple OLS coefficients and p values, p values for robust standard errors, and White’s heteroscedasticity-consistent standard errors are reported for each model. The coefficients and p values of the spatial error or lag model are also reported if spatial dependence is detected.

Figure 1.

Model structure.

Several school-characteristic variables are statistically insignificant. Additionally, in some instances, these variables are highly collinear with each other or with the API variable. Therefore, only two such variables—the student–teacher ratio for high school and elementary school—are included in the final models.^9,10 Both variables measure the level of classroom congestion; therefore, a higher ratio should have a negative impact on house prices, ceteris paribus. However, in high-quality schools, a large student–teacher ratio might be an indicator of the high desirability of a school. Therefore, an a priori assumption about the impact of these school characteristics variables on house prices is not made. Similarly, two neighborhood-level variables—percentage of the Asian population and percentage of the renter population—are used. I hypothesize that the former will increase house prices whereas the latter will decrease house prices.¹¹ Other neighborhood-level variables, such as housing vacancy rates and households’ family structure, are statistically insignificant.

Results

Tables 4 to 6 provide estimates of the school quality coefficient (Sum of API z scores) for each of the 24 hedonic price regression models, with each table containing eight models, subdivided as previously described. Table 4 provides the results when neighborhood and school characteristics are excluded from the regression models. Table 5 provides the results when neighborhood characteristics are included, and Table 6 provides the results when both neighborhood characteristics and school characteristics are included.

Table 4.

Regression Results: Coefficient of the School Quality Variable (Sum of API z Scores) When Neighborhood and School Characteristics Are Excluded.

Boundary fixed effects included^a	Full Data Set		0.375-Mile Subset		0.25-Mile Subset		0.125-Mile Susbset
	No	Yes	No	Yes	No	Yes	No	Yes
	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6	Model 7	Model 8
OLS	$42,384	$28,951	$43,510	$48,018	$42,371	$43,551	$41,164	$40,834
p value	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
p value (Robust standard errors)	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
p value (White’s estimate)	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Spatial lag model	$38,722	−	$39,001	−	$39,350	−	−	−
p value	0.000	−	0.000	−	0.000	−	−	−
Log likelihood	−12277.96	−	−10505.43	−	−8423.34	−	−	−
Spatial error model	−	−	−	−	−	−	$40,381	−
p value	−	−	−	−	−	−	0.000	−
Log likelihood	−	−	−	−	−	−	−4620.90	−
Adjusted R²	0.796	0.845	0.800	0.851	0.791	0.840	0.786	0.853
n	938	938	801	801	642	642	354	354

Note: The variance inflation factor (VIF) is less than 10 for all the variables included in the models. All the models include quarter dummies. The bold values indicate the most robust school quality coefficient for each model.

OLS = ordinary least squares.

Only statistically significant (p value less than or equal to 0.10) school boundary dummies are included because some are statistically insignificant and highly collinear with the school quality variable (VIF greater than 10).

Table 5.

Regression Results: Coefficient of the School Quality Variable (Sum of API z Scores) When Neighborhood Characteristics Are Included.

Boundary fixed effects included^a	Full Data Set		0.375-Mile Subset		0.25-Mile Subset		0.125-Mile Susbset
	No	Yes	No	Yes	No	Yes	No	Yes
	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6	Model 7	Model 8
OLS	$35,311	$28,640	$35,207	$41,720	$34,615	$41,112	$34,275	$40,184
p value	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
p value (Robust standard errors)	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
p value (White’s estimate)	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Spatial lag model	$32,815	−	$32,132	−	$31,710	−	−	−
p value	0.000	−	0.000	−	0.000	−	−	−
Log likelihood	−12256.91	−	−10484.05	−	−8403.99	−	−	−
Spatial error model	−	−	−	−	−	−	$34,460	−
p value	−	−	−	−	−	−	0.000	−
Log likelihood	−	−	−	−	−	−	−4613.68	−
Adjusted R²	0.806	0.846	0.811	0.851	0.803	0.841	0.795	0.852
n	938	938	801	801	642	642	354	354

OLS = ordinary least squares.

Table 6.

Regression Results: Coefficient of the School Quality Variable (Sum of API z scores) When Neighborhood and School Characteristics Are Included.

Boundary fixed effects included^a	Full Data Set		0.375-Mile Subset		0.25-Mile Subset		0.125-Mile Susbset
	No	Yes	No	Yes	No	Yes	No	Yes
	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6	Model 7	Model 8
OLS	$39,826	$28,006	$42,635	$43,888	$42,470	$44,364	$45,705	$42,090
p value	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
p value (Robust standard errors)	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
p value (White’s estimate)	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Spatial lag model	$37,081	−	−	−	$39,239	−	−	−
p value	0.000	−	−	−	0.000	−	−	−
Log likelihood	−12254.31	−	−	−	−8399.14	−	−	−
Spatial error model	−	−	$42,993	−	−	−	$46,532	−
p value	−	−	0.000	−	−	−	0.000	−
Log likelihood	−	−	−10478.82	−	−	−	−4608.52	−
Adjusted R²	0.807	0.846	0.813	0.851	0.805	0.841	0.799	0.852
n	938	938	801	801	642	642	354	354

Note: The variance inflation factor (VIF) is less than 10 for all the variables included in the models, except the “Student–teacher ratio in the elementary school (one year lag)” variable in the 0.375-mile subset model. The VIF for this variable equals 10.7. However, the magnitude and sign of the coefficients for the other variables do not change when this variable is included in or excluded from a regression model. All the models include quarter dummies.

The bold values indicate the most robust school quality coefficient for each model.

OLS = ordinary least squares.

Four findings are especially noteworthy. First, a comparison of the coefficients for the school quality variable between the hedonic regressions for the full data set and those for the three (0.375-, 0.25-, and 0.125-mile) distance-band subsets indicates that the inclusion of boundary fixed effects changes the results somewhat for the full model but changes the results only slightly when the data set is constrained to narrow distance bands around attendance-zone boundaries. For example, in the full data models, a one-unit increase in the school quality variable leads to a $37,081 price increase when boundary fixed effects are excluded (see Table 6, Model 1) and to a $28,006 price increase when boundary fixed effects are included (see Table 6, Model 2). On the other hand, in the distance-band-subset models, the school quality coefficients are very similar whether boundary fixed effects are excluded or included: $42,993 and $43,888 for the 0.375-mile subset (see Table 6, Models 3 and 4), $39,239 and $44,364 for the 0.25-mile subset (see Table 6, Models 5 and 6), and $46,532 and $42,090 for the 0.125-mile subset (see Table 6, Models 7 and 8).

Second, the regression models only exhibit spatial dependence when boundary fixed effects are excluded, and the inclusion of boundary fixed effects corrects for spatial dependence. The first and second findings jointly indicate that for the distance-band-subset models, many of the unobserved neighborhood characteristics are captured equally well by the boundary fixed effects models and the spatial regression models. Third, the coefficient of the school quality variable is robust across all three of the boundary subsets, as it is $43,888, $44,364, and $42,090 for the 0.375-, 0.25-, and 0.125-mile subsets, respectively (see Table 6, Models 4, 6, and 8).

Finally, once boundary fixed effects are included, the inclusion of neighborhood and school characteristics affects the coefficient of the Sum of API z scores only marginally. For example, the coefficient for the 0.375-mile subset is reduced by only $4,130, or 9 percent—from $48,018 for the model with no controls for neighborhood or school characteristics (see Table 4, Model 4) to $43,888 for the model with a full set of controls (see Table 6, Model 4). This $4,130 decrease is within two standard errors (two times $2,806, or $5,612) of the coefficient reported in Table 6, Model 4. This finding lends further support to the use of the BDDM.

Detailed Results and Further Robustness Checks

The data allow us to consider threshold distances of 0.125, 0.25, and 0.375 miles from the closest school attendance zone boundary. However, a comparison of all of these coefficient estimates with just only those for the 0.375-mile subset shows that the qualitative nature of the findings remains unchanged across the subsets. Therefore—for the sake of brevity and for the results benefit gained from a larger data set—I hereafter focus on the results of the 0.375-mile subset.¹²

Detailed results

In Table 7, Model 1 I present the results for the 0.375-mile subset when I estimate equation (1) by using OLS without school attendance zone boundary fixed effects. Because this regression model suffers from spatial error dependence, I also estimate a spatial error model, which is reported as Model 2. Models 3 and 4 provide the results with boundary fixed effects included,¹³ where Model 3 includes neighborhood and school characteristics, and Model 4 excludes them. Because Models 3 and 4 do not suffer from spatial dependence, spatial regression models are not estimated.

Table 7.

Regression Results: 0.375-Mile Subset.

Variables	Without Boundary Fixed Effects				With Boundary Fixed Effects
	Model 1		Model 2		Model 3		Model 4
	OLS		Spatial Error Model		OLS		OLS
	Coefficient	p Value	Coefficient	p Value	Coefficient	p Value	Coefficient	p Value
	(clustered robust standard error)		(standard error)		(clustered robust standard error)		(clustered robust standard error)
	(White’s standard error)				(White’s standard error)		(White’s standard error)
Intercept	638,350		671,120		557,380		452,790
	(311560)	**	(140220)	****	(154360)	****	(65526)	****
	(145818.49)	****			135570	****
House size (square feet)	185.14		187.39		173.16		170.31
	(25.38)	****	(14.78)	****	(22.98)	****	(23.93)	****
	(23.12)	****			(22.00)	****
Lot size (square feet)	13.7		13.8		11.9		11.9
	(2.2)	****	(1.9)	****	(2.3)	****	(2.4)	****
	(2.2)	****			(1.8)	****
Number of bedrooms	−1,838.60		−1,189.30		−5,436.10		−3,580.50
	(9640.20)		(8312.60)		(8575.40)		(8250.80)
	(10003.38)				(9183.70)
Number of bathrooms	323.40		248.61		1,162.70		1,125.30
	(995.27)		(1072.50)		(924.62)		951.03
	(1218.71)				(1090.70)
Age of the house (year effective)	−2,911.40(765.04)(476.94)	** **	−2,919.30(473.29)	****	−3,516.50(651.03)(434.97)	** **	−3,676.90(660.90)	****
School quality (Sum of API z scores)	42,635(9444)(3474.75)	** **	42,993(3332.70)	****	43,888(3913.30)(3362.90)	** **	48,018(2805.90)	****
Percent Asian population in the census block	1,941.50(452.30)(314.82)	** **	1,789.00(306.10)	****	251.83(344.76)(327.48)		Not included
Percent renter population in the census block	−799.77(332.84)(231.40)	* **	−803.91(260.38)	***	−525.90(216.09)(204.26)	* **	Not included
Student–teacher ratio in the high school (one-year lag)	−16,730.00(12145)(5661.75)	***	−18,200.00(5504)	****	−10,120.00(4543.70)(5843.20)	** *	Not included
Student–teacher ratio in the elementary school (one-year lag)	265.99(7980.50)(2208.06)		526.22(2223.10)		5,803.90(3140.70)(3444.70)	* *	Not included
Adjusted R²	0.81				0.85		0.85
n	801		801		801		801

Note: The variance inflation factor (VIF) is less than 10 for all the variables included in the models, except the “Student–teacher ratio in the elementary school (one-year lag)” variable in Model 3. The VIF for this variable equals 10.7. However, the magnitude and sign of the coefficients for the other variables do not change when this variable is included in or excluded from a regression model. Dependent variable: adjusted sale price of the house. All the models include quarter dummies. OLS = ordinary least squares.

***

*Significant at p = 0.001; ***Significant at p = 0.01; **Significant at p = 0.05; *Significant at p = 0.1.

All of the models include house-level characteristics (number of bedrooms and bathrooms, size of the house and lot, and age of the house) and neighborhood characteristics (percentage of the Asian population and percentage of the renter population). The regression also includes two school-quality characteristics—the student–teacher ratio for high schools and for elementary schools.¹⁴

The signs of the statistically significant variables are largely consistent with previous research on house prices. Lot and house sizes are positively correlated with house prices, as found in Brasington and Haurin (2006); Chiodo, Hernández-Murillo, and Owyang (2010); Dougherty et al. (2009); and Zahirovic-Herbert and Turnbull (2008). The age of the house is negatively correlated with house prices, as found in Goodman and Thibodeau (1995) and Uyar and Brown (2007). Among the variables that control for neighborhood characteristics, the percentage of the Asian population in a census block is positively correlated with house prices, whereas the percentage of the renter population in a census block is negatively correlated with house prices. The impact of the school characteristics is mixed. The student–teacher ratio for the high schools reduces house prices, perhaps because of the negative impact of classroom congestion; however, the student–teacher ratio for elementary schools has a counterintuitive positive sign. Indeed, many elementary schools in the study area, especially high-quality schools, suffer from overcrowding. In several cases, students have been transferred to other, less desirable schools, such as from Parkmont Elementary School to Maloney Elementary School (FUSD 2012). I posit that the positive sign is a reflection of this phenomenon.

Comparisons of the models with boundary fixed effects (Models 3 and 4) with those without these fixed effects (Models 1 and 2) reveal three important findings. First, with an adjusted R square of 0.85, Model 4, which includes only house characteristics and boundary fixed effects, performs as well as the more fully specified models that include neighborhood and school characteristics. Second, the LM tests show no spatial dependence for Model 4. Together, these two findings indicate that boundary fixed effects are able to control for neighborhood-level characteristics quite well. Third, I find that the coefficient for the school quality variable is very robust across the four models, with values always within two standard errors of any coefficient, and with a maximum inter-model variation of 13 percent ($42,635 for Model 1 compared with $48,018 for Model 4).

Additionally, I find that the spatial regression model (Model 2) performs as well as the boundary fixed effects model (Model 3) in estimating the impact of school quality on house prices, as the coefficient for the school quality variable is $42,993 for Model 2 and $43,888 for Model 3.

The coefficients for the school quality variable for Model 3, the model that controls for the largest number of independent variables, indicates that when other factors are controlled for, a one-unit increase in the Sum of API z scores increases house prices by $43,888. This result translates into a price difference of $394,992 between houses in attendance zones of the worst-performing elementary–middle–high school combination in this data set (i.e., Blacow Elementary, Walters Middle, and Kennedy High Schools combination which has a cumulative z score of −3.8), which is state average in quality, and houses in the attendance zones of the best-performing elementary–middle–high school combination (Mission Valley Elementary, Hopkins Middle, and Mission San Jose High Schools combination which has a cumulative z score of 5.2), which is considered to have private-school quality and is in the top decile in quality rankings among all California public schools. The $394,992 difference [$43,888 × ((5.2 – (–3.8)), or $43,888 times 9] equals $1,818 increase in monthly housing costs (mortgage payments and property taxes), after federal tax deductions are accounted for.¹⁵ This greater housing cost is equivalent to (or even greater than) the average monthly private school tuition cost for one child at a typical San Francisco Bay Area private school.¹⁶ In terms of a standard deviation change in school quality, a one-standard-deviation or 3-unit increase in the school quality variable (Sum of API z scores), which could result if the API scores of elementary, middle, and high schools were to increase by one standard deviation each, would increase house prices by $131,644 (three times $43,888)—an approximately 20 percent increase in the mean house price of $667,690. This increase is much larger than the modest—1 to 4 percent—increase reported in most existing studies.¹⁷

To check whether the magnitude of the impact of school quality varies at different house price levels, I estimate nine quantile regression models—one at each decile (from 10 to 90 percent) of house prices. At least one previous study, Wada and Zahirovic-Herbert (2013), has empirically demonstrated that the magnitude of the effect of school quality increases as house prices increase. These authors attribute this exponential relationship between school quality and house prices to higher income households valuing school quality more that lower income households. However, I expect to find a linear rather than an exponential relationship in this study because house prices in the study area are quite high to begin with. Therefore, I expect that owners of even lower-priced houses highly value school quality. Figure 2 provides the coefficients of the school quality variable for each quantile regression. The coefficients range from $35,997 to $45,862; however, they are within two standard errors of each other. Hence, deviations from a linear relationship are not observed.¹⁸ Further, the quantile regression models provide evidence of the findings for Model 3. The coefficients of the school quality variable in the quantile regression models are very close to the coefficient of $43,888 in Table 7, Model 3.

Figure 2.

School quality coefficients from the quantile regression for the 0.375-mile subset.

To further test the robustness of the school quality coefficient, I run a series of regressions on a data set that included only observations from the worst- and best-performing school attendance zones that have cumulative z scores of −3.8, and 5.2, respectively. The regression results are reported in Table 8. Although the data set is fairly reduced (n = 245), the models have high adjusted R square (0.85). For Model 1, the coefficient for the Mission Valley–Hopkins–Mission San Jose attendance zone equals $378,450 after I control for the quality of the house and the time of sale. However, in this model, the boundary fixed effects capture the effect of neighborhood and school characteristics as well as school quality. Therefore, I next isolate the impact of the school quality variable after controlling for neighborhood and school characteristics. I find that the boundary fixed effects and school quality variables exhibit perfect multicollinearity; consequently, the subsequent models omit the boundary fixed effects. Thus, I re-create Model 1 in Model 2, except that the boundary fixed effects are replaced with the school quality variable. The coefficient for the school quality variable is $42,574, which translates into a $383,166 difference in house price between the two school attendance zones [$42,574 × ((5.2 – (–3.8)), or $42,574 times 9]. Next, the neighborhood characteristics are added to Model 2 and a new model, Model 3, is run. The coefficient for school quality changes very slightly to $43,023. Next, a school characteristics variable—the student–teacher ratio for the high schools—is added to Model 3.¹⁹ In the resulting model, Model 4, the coefficient for the school quality variable changes slightly to $50,643 (slightly higher than the coefficient of $43,888 from Model 3 of Table 7), which translates into a $455,787 difference in the average house price in the two school attendance zones [$50,643 × ((5.2 – (–3.8)), or $50,643 times 9]. The coefficients of the other variables are also very similar in magnitude, sign, and statistical significance to the models in Table 7.

Table 8.

Regression Results: Worst- and Best-Performing School Attendance Zones.

Variables	Model 1		Model 2		Model 3		Model 4
	Coefficient	p Value	Coefficient	p Value	Coefficient	p Value	Coefficient	p Value
	(clustered robust standard error)		(clustered robust standard error)		(clustered robust standard error)		(clustered robust standard error)
	(White’s standard error)		(White’s standard error)		(White’s standard error)		(White’s standard error)
Intercept	321,040		482,750		507,440		873,720
	(138600)	**	(145490)	***	(117700)	****	(52381)	****
	(83672)	****	(86003)	****	(123130)	****	(362330)	**
House size (square feet)	150.07		150.00		149.47		148.55
	(19.32)	****	(19.23)	****	(21.02)	****	(1.9.26)	****
	(50.78)	***	50.75)	***	(48.16)	****	(48.42)	***
Lot size (square feet)	11.6		11.6		11		11
	(0.50)	****	(0.50)	****	(0.10)	****	(0.10)	****
	(3)	****	(3)	****	(3.5)	****	(3.5)	***
Number of bedrooms	926.50		1,131.60		1,006.70		2,160.00
	(26084)		(26317)		(25357)		(25588)
	(15069)		(15051)		(14696)		(14858)
Number of bathrooms	1,367.90		1,368.80		1,398.20		1,573.00
	(425.27)		(378.13)	****	(46290)	***	(55.29)	***
	(2105.8)		(2104.5)		(2193.50)	****	(2230.9)
Age of the house (year effective)	−4,583.80		−4,586.10		−4,567.80		−4,588.80
	(218.03)	****	(199.76)	****	(238)	****	(22.94)	****
	(918.50)	****	(915.95)	****	(940.21)	****	(953.93)	****
Dummy for Mission Valley elementary school attendance zone	378,450(17279)(17282)	** **
School quality (Sum of API z scores)			42,574.00		43,023.00		50,643.00
			(1948.4)	****	(469.67)	****	(453.47)	****
			(1943.5)	****	(5496.8)	****	(10040)	****
Percent Asian population in the census block					−223.63(–461.75)		−212.40(–449.39)
					(1108.9)		(1096.4)
Percent renter population in the census block					−459.11(242.87)(359.1)	*	−392.07(202.9)(353.41)	*
Student–teacher ratio in the high school (one-year lag)							−15,942.00(2485.3)(12593)	****
Adjusted R²	0.88		0.88		0.88		0.88
n	245		245		245		245

Note: The variance inflation factor is less than 10 for all the variables included in the models. All the models include quarter dummies. Dependent variable: Adjusted Sale Price of the House. OLS = ordinary least squares.

****

Significant at p = 0.001; ***Significant at p = 0.01; **Significant at p = 0.05; *Significant at p = 0.1.

Finally, I hypothesize that to the extent that houses in attendance zones of low-quality schools appreciate at a slower rate than houses in attendance zones of high-quality schools, households in the low-quality school attendance zones will accumulate wealth through homeownership at a slower rate. To test this hypothesis, I run two regressions, one for the lowest-quality school attendance zone (Blacow Elementary, Walters Middle, and Kennedy High Schools) which has a cumulative z score of −3.8, and another for the average-quality school attendance zone (Grimmer Elementary, Horner Middle, and Irvington High Schools), which has a cumulative z score of −0.01. Average house prices in both attendance zones are very similar—$465,426 for the lowest-quality attendance zone and $468,698 for the average-quality attendance zone. When I control for house- and neighborhood-level characteristics, the coefficients of the quarter dummies show that during the study period, house price appreciation is greater in the average-quality attendance zone than in the lowest-quality attendance zone: $305,500 in the former compared with $210,466 in the latter (see Figure 3). As a percentage of the average-priced house, this level of price appreciation equals 45 and 65 percent, respectively.

Figure 3.

Coefficients of the quarter dummies for houses sold in the worst- and average-performing school attendance zones.

Conclusions and Policy Implications

A high-quality education is tied to many positive social and economic outcomes. For example, Chetty et al. (2011) find that the quality of peers in kindergarten through third grade, as measured through standardized test scores, affects future earnings. The United States strives to provide high-quality free K–12 education to all its residents, and several recent federal-level education grant programs, such as Race to the Top and Investing in Innovation, seek to enhance public school quality. To foster such efforts, we must understand that the nexus between household location and variation in school quality leads to the capitalization of school quality into house prices. Previous studies have found such capitalization effects to be modest. However, these capitalization effects are expected to be larger in regions with a robust economy, a strong residential real estate market, high income and education levels, and a paucity of high-quality public schools, such as the San Francisco Bay Area.²⁰ Indeed, my research shows that for a typical household in the study area, the impact of school quality on house prices is more than three times greater than the impact typically found in studies on other regions. In terms of monthly housing costs, this impact closely matches the cost of private education for one child. This finding has critical implications for city planning—especially at the intersection of housing, equity planning, and zoning—and for the delivery mechanism for K–12 education.

In the context of housing policy, cities find it extremely difficult to provide affordable housing in areas with high-quality schools for two primary reasons. First, the high land values in such areas translate into high development costs, which are fiscally burdensome to subsidize with the use of public funds. For example, the majority of subsidized rental housing in New York City is located in areas with relatively lower land values (Ellen and Weselcouch 2015). Second, affordable housing development proposals routinely face strong opposition from local residents, who are often fearful of the potential impacts of such developments on school quality, among other complaints (Scally 2013; Scally and Tighe 2015). Therefore, these developments are often located in areas with low-quality schools, thereby spatially concentrating low-income households. Because of the close link between educational quality and future income, this perpetuates the cycle of poverty (Currie and Duncan 2001).

Therefore, what might planners and policy makers do about the inequalities that school-quality-based residential sorting may be producing? I encourage urban planners and policy makers to explicitly recognize the effects of schools on residential segregation and to respond meaningfully—to treat access to high-quality K–12 education as they would treat access to transportation infrastructure, parks and libraries—when developing plans and policies.²¹ One example of such an opportunity to enact meaningful change is provided by the recently adopted San Francisco Bay Area regional plan—Plan Bay Area—drafted to meet state mandates to sustainably accommodate future population growth and reduce greenhouse gas emissions. Among other recommendations, Plan Bay Area encourages accommodating the majority of new population growth in attached housing (apartments, condominiums, and townhomes) in compact transit-oriented developments (TODs) (ABAG and MTC 2013). Additionally, the majority of the new population is to be accommodated in the region’s three largest cities, San Jose, San Francisco, and Oakland—cities with uneven school quality. While the plan achieves the smart-growth objective of locating residences close to transit, it unfortunately does not consider access to high-quality schools, which is a missed opportunity. This omission could even become a hurdle to the success of the plan—new residents willing to pay a premium for high-quality schools may not locate in the plan-proposed areas owing to the low quality of schools. From a social-equity perspective, to the extent that low-income households are likely to live in these TODs, the plan may perpetuate a cycle of poverty. This problem is compounded when household incomes are correlated with race and ethnicity. For example, schools in the study area are racially and ethnically segregated, with larger concentrations of Asian students in higher-quality schools. Indeed, the student population is more than 80 percent Asian for several high-quality schools in this data set, such as Mission San Jose High School, and Weibel and Mission Valley Elementary Schools. The San Francisco Bay Area cities and agencies respon-sible for implementing Plan Bay Area—the Metropolitan Transportation Commission (MTC) and the Association of Bay Area Governments (ABAG)—should act to mitigate these negative social-equity impacts. To do so, they could include school quality as one factor when selecting housing-serving transportation projects and could offer financial incentives for the provision of low-income family housing in neighborhoods with high-quality schools. For example, regional agencies could include school quality as one factor in awarding grants through their One Bay Area Grant Program and cities could provide community development funds to such neighborhoods.²²

National-level affordable housing programs, such as the Low Income Housing Tax Credit (LIHTC) program, could also provide financial incentives for the development of affordable family housing in neighborhoods with high-quality schools. Developers apply for LIHTC funding, and their proposals are reviewed based on well-defined selection criteria. Such criteria often include proximity to neighborhood amenities, such as schools.²³ States should include school quality as a key project selection criterion.²⁴

Other, nonfinancial, mitigation measures should also be explored. Such mitigation measures might include working with school districts to find ways to improve quality of education and to avoid excessively accommodating population increases in neighborhoods with low-quality schools, for example, by not rezoning or not up-zoning to high-density residential uses in such neighborhoods.

I also hope that explicit recognition of the significant impacts of school quality on residential segregation will encourage reevaluation of the delivery of K–12 education and, perhaps, lead us away from the current institutional arrangement in which K–12 education is primarily the responsibility of a local, often insular, special-purpose government—the school district—that seldom collaborates with the local government. This lack of coordination often results in school siting, expansion, and renovation decisions that are not well integrated with the local government’s land use, transportation, and zoning plans and policies (Vincent and McKoy 2013). At a minimum, the reevaluation of the current delivery mechanisms and their impacts on residents should lead to better coordination among school districts, local governments, and housing and education advocates. The Center for Cities & Schools at the University of California, Berkeley, has developed an exemplary strategy, Y-PLAN! (Youth—Plan, Learn, Act, Now!), which is designed to engage students and schools in urban planning and development projects. The Center has implemented this strategy in several Bay Area communities (Center for Cities & Schools 2014). Similarly, the University of Pennsylvania partnered with the School District of Philadelphia to build a new public school—Penn Alexander—as part of the university’s larger community development efforts in the neighboring West Philadelphia neighborhood (University of Pennsylvania Graduate School of Education 2015). In the field of housing, preliminary results from a recent demonstration project for housing choice vouchers—Chicago Regional Housing Choice Initiative (CRHCI)—show that low-income families can be successfully moved to opportunity areas with better quality schools. Funded by the US Department of Housing and Urban Development (HUD), CRHCI is a partnership of eight Chicago-region Public Housing Authorities, HUD, and two nonprofit organizations—Metropolitan Planning Council and Housing Choice Partners (Housing Choice Partners, n.d.).

Finally, this study’s findings inform and augment the existing literature on household location choice by suggesting that high-quality schools might have a greater impact on residential sorting behaviors than has been previously estimated, at least in regions with strong residential real estate markets and high education and income levels but a paucity of high-quality public schools.

Footnotes

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research for this paper was partially funded through two grants: (a) College of Social Sciences, San Jose State University (SJSU) Spring 2014 Research Grant and (b) SJSU Spring 2016 Central RSCA Infusion Program.

Notes

Author Biography

Shishir Mathur is a professor in the Department of Urban and Regional Planning at San Jose State University. His research interests include urban and real estate economics, infrastructure and development finance, international development, growth management, affordable housing policy, transportation planning, and spatial econometrics.

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