Nonlinear Hedonics and the Search for School District Quality

Since the pioneering work of Tiebout (1956), economists have recognized that the quality of public services, especially schools, influence house prices. Many empirical studies have attempted to discern the extent to which the quality of public education affects house prices. Initially, researchers estimated hedonic pricing equations (Rosen, 1974). In a simple hedonic pricing model, a house's value depends on its comparable neighborhood and school district characteristics. A house's comparable characteristics include aspects such as the number of bedrooms, square feet, etc. Neighborhood characteristics typically include the distance to the nearest major downtown area, racial composition, and median household income. Education quality may be proxied by variables such as per-pupil spending, pupil/teacher ratio, and property taxes, which are usually available at the school district level, or it may be measured directly by state or local standardized tests scores, which are usually available at the school level. In an influential study, Black (1999) argues that past research estimating hedonic pricing functions (see Rosen, 1974) may introduce an upward bias due to neighborhood quality effects that are unaccounted for in the data. Specifically, she notes that better schools may be associated with better neighborhoods, which could independently contribute to higher house prices. Black circumvents this problem by estimating a linear hedonic pricing function using data only from houses which border the school attendance zone boundaries. She rationalizes that, while test scores make a discrete jump at attendance boundaries, changes in neighborhoods are more smooth. Black's linear specification presupposes that the marginal valuation of worse-than-average schools is equal to the valuation of better-than-average schools and results in a constant premium on school quality. Moreover, if school quality is normalized (i.e., expressed in terms of deviations from the mean), the linear capitalization term implies a penalty (increasing as quality decreases) for houses in attendance zones of schools performing below average. Thus, a linear model implies there exists a substantive pecuniary penalty for a really bad school compared to just a bad school. In this paper, we formulate a simple housing search model that yields a theoretical nonlinear pricing function. The nonlinearity in our model reflects two aspects of the market for public education via housing. First, alternative schooling arrangements (e.g., private school, home schooling, magnet schools, etc) can provide home buyers with high quality education even if they choose to live in below average school districts. The existence of these options underlies our belief that an increasing penalty for below average quality school attendance zones may be theoretically unappealing. Second, if buyers have positive valuations for education, they may concentrate their efforts among the highest quality attendance zones, yielding an increasing market tightness as school quality increases. Thus, buyers may face incresed competition for the highest quality schools and a rapidly increasing premium for houses in those attendance zones. Motivated by our theoretical specification, we extend Black's analysis and examine the relationship between school quality and house prices in the St. Louis, Missouri metropolitan area. A previous study by Ridker and Henning (1967) found no evidence of education capitalization in St. Louis house prices. While their main concern was to determine the negative effect of air pollution on housing prices, they included a dummy variable which indicated residents' attitudes about the quality of the schools (above average, average, and below average). Our goal is to determine the degree of education capitalization in the St. Louis MSA. We first measure education capitalization employing Black's methodology of considering only houses near attendance zone boundaries to control for neighborhood quality. This allows us to determine the extent to which Black's results extend to the St. Louis metro area. Then, we advance Black's methodology by considering the possibility that education capitalization affects house prices nonlinearly, as indicated by our theoretical framework. Black, Sandra E. "Do Better Schools Matter? Parental Valuation of Elementary Education," Quarterly Journal of Economics, May 1999, 114(2), pp. 577-599. Ridker, Ronald G. and Henning, John A. "The Determinants of Residential Property Values with Special Reference to Air Pollution," Review of Economics and Statistics, May 1967, 49(2), pp. 246-257. Rosen, Sherwin. "Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition," Journal of Political Economy, January-February 1974, 82(1), pp. 34-55. Tiebout, Charles M. "A Pure Theory of Local Expenditures," Journal of Political Economy, October 1956, 64(5), pp. 416-424.