A Semiparametric Method for Valuing Residential Location

Abstract

This paper is motivated by automated valuation systems, which would benefit from an ability to estimate spatial variation in location value. It develops theory for the LRM, a semiparametric approach to estimating a location value surface. There are two parts to the LRM: 1) an OLS model to hold constant for interior square footage, land area, bathrooms, and other structural characteristics; and 2) a non-parametric smoother (local polynomial regression, LPR) which calculates location value as a function of latitude and longitude.

The LRM was fit to geocoded hedonic sales data for six towns in the suburbs of Boston, Massachusetts. The estimates yield substantial, significant and plausible spatial patterns in location values. Local peaks and valleys in location value identified by the LRM are close to points identified by the tax assessor, and they are shown to add to the explanatory power of an OLS model.

Out-of-sample MSE shows that the LRM with a first-degree polynomial (local linear smoothing) is somewhat better than polynomials of degree zero or degree two. The optimized LRM reduces MSE from the OLS model by about 5% while adding information on statistically significant variations in location value.

Keywords: Land values, neighborhood house values, property tax assessment, local polynomial regression, smoothing regressions, nonparametric methods, semiparametric models

JEL Classification: C4, H2, R1, R5