Estimating a spatial autoregressive model with an endogenous spatial weight matrix

The spatial autoregressive model (SAR) is a standard tool to analyze data with spatial correlation. Conventional estimation methods rely on the key assumption that the spatial weight matrix W is strictly exogenous, which is likely to be violated in empirical analyses. This paper presents the speci…cation and estimation of the SAR model with an endogenous spatial weight matrix. The outcome equation is a cross-sectional SAR model where W has a model structure on its entries. Endogeneity of W comes from the correlation between error terms in its entries and the disturbances in the SAR outcome equation. We explore three estimation methods: two-stage instrumental variable (2SIV) method, maximum likelihood estimation (MLE) approach, and general method of moments (GMM), for this model with an endogenous spatial weights matrix. We then establish the consistence of the estimators from these methods and derive their asymptotic distributions. Finite sample properties of these estimators are investigated by the Monte Carlo simulation.