Estimating a spatial autoregressive model with an endogenous spatial weight matrix

The spatial autoregressive (SAR) model is a standard tool for analyzing data with spatial correlation. Conventional estimation methods rely on the key assumption that the spatial weight matrix is strictly exogenous, which would likely be violated in some empirical applications where spatial weights are determined by economic factors. This paper presents model specification and estimation of the SAR model with an endogenous spatial weight matrix. We provide three estimation methods: two-stage instrumental variable (2SIV) method, quasi-maximum likelihood estimation (QMLE) approach, and generalized method of moments (GMM). We establish the consistency and asymptotic normality of these estimators and investigate their finite sample properties by a Monte Carlo study.