Spatial Linear Regression Models

Abstract

This chapter discusses different specifications of linear spatial econo-metric models that can be considered once the hypothesis of no spatial autocorrelation in the disturbances is violated. A general form to take into account the violation of the ideal conditions for the applicability of OLS is given by the following set of equations: l b b l < (1) (2) = + + + 1 y Wy X WX u (3.1) r e r < = + 1 u Wu (3.2) with X a matrix of non-stochastic regressors, W a weight matrix exogenously given, e e s ≈ 2. .. (0,) n n X ii d N I and b (1) , b (2) , l and r parameters to be estimated. The restrictions on the parameters l and r hold if W is row-standardized. The first equation considers the spatially lagged variable of the dependent variable y as one of the regressors and may also contain spatially lagged variables of some or all of the exogenous variables (the term WX). The second equation considers a spatial model for the sto-chastic disturbances. In principle, there is no need that the three weight matrices in Equations (3.1) and (3.2) are the same, although in practical cases it is difficult to justify a different choice. Equation (3.1) can also be written as: l b l < = + + 1 y Wy Z u (3.3)