Estimation and Inference for Spatial Models with Heterogeneous Coefficients: An Application to U.S. House Prices

Abstract

This paper considers the estimation and inference of spatial panel data models with heterogeneous spatial lag coefficients, with and without weakly exogenous regressors, and subject to heteroskedastic errors. A quasi maximum likelihood (QML) estimation procedure is developed and the conditions for identification of the spatial coefficients are derived. The QML estimators of individual spatial coefficients, as well as their mean group estimators, are shown to be consistent and asymptotically normal. Small sample properties of the proposed estimators are investigated by Monte Carlo simulations and results are in line with the paper's key theoretical findings even for panels with moderate time dimensions and irrespective of the number of cross section units. A detailed empirical application to U.S. house price changes during the 1975-2014 period shows a significant degree of heterogeneity in spatio-temporal dynamics over the 338 Metropolitan Statistical Areas considered.

Keywords: Spatial Panel Data Models, Heterogeneous Spatial Lag Coefficients, Identification, Quasi Maximum Likelihood (QML) Estimators, Non-Gaussian Errors, House Price Changes, Metropolitan Statistical Areas

JEL Classification: C21, C23