A spatial panel data model with time varying endogenous weights matrices and common factors

Abstract

Many spatial panel data sets exhibit cross sectional and/or intertemporal dependence from spatial interactions or common factors. In an application of a spatial autoregressive model, a spatial weights matrix may be constructed from variables that may correlate with unobservables in the main equation and therefore is endogenous. Some common factors may be unobserved and correlate with included regressors in the equation. This paper presents a unified approach to model spatial panels with endogenous time varying spatial weights matrices and unobserved common factors. We show that the proposed QML estimator is consistent and asymptotically normal. As its limiting distribution may have a leading order bias, an analytical bias correction is proposed. Monte Carlo simulations demonstrate good finite sample properties of the estimators. This model is empirically applied to examine the effects of house price dynamics on reverse mortgage origination rates in the United States.