Semiparametric Spatial Autoregressive Models with Endogenous Regressors: With an Application to Crime Data

This study considers semiparametric spatial autoregressive models that allow for endogenous regressors, as well as the heterogeneous effects of these regressors across spatial units. For the model estimation, we propose a semiparametric series generalized method of moments estimator. We establish that the proposed estimator is both consistent and asymptotically normal. As an empirical illustration, we apply the proposed model and method to Tokyo crime data in order to estimate how the existence of a neighborhood police substation (NPS) affects the household burglary rate. The results indicate that the presence of an NPS helps reduce household burglaries, and that the effects of some variables are heterogeneous with respect to residential distribution patterns. Furthermore, we show that using a model that does not adjust for the endogeneity of NPS does not allow us to observe the significant relationship between NPS and the household burglary rate. A supplementary material for this article is available online.