Estimating Nonlinearities in Spatial Autoregressive Models

In spatial autoregressive models, the functional form of autocorrelation is assumed to be linear. In this paper, we propose a simple semiparametric procedure, based on Yatchew's (1998) partial linear least squares, that relaxes this restriction. Simple simulations show that this model outperforms traditional SAR estimation when nonlinearities are present. We then apply the methodology on real data to test for the spatial pattern of voting for independent candidates in US presidential elections. We find that in some counties, votes for `third candidates' are non-linearly related to votes for `third candidates' in neighboring counties, which pleads for strategic behavior.