Two-Stage Least Squares Estimation of Spatial Autoregressive Models with Endogenous Regressors and Many Instruments

This paper considers the IV estimation of spatial autoregressive models with endogenous regressors in the presence of many instruments. To improve asymptotic efficiency, it may be desirable to use many valid instruments. However, finite sample properties of IV estimators can be sensitive to the number of instruments. For a spatial model with endogenous regressors, this paper derives the asymptotic distribution of the two-stage least squares (2SLS) estimator when the number of instruments grows with the sample size, and suggests a bias-correction procedure based on the leading-order many-instrument bias. The paper also gives the Nagar-type approximate mean square errors (MSEs) of the 2SLS estimator and the bias-corrected 2SLS estimator, which can be minimized to choose instruments as in Donald and Newey (2001). A limited Monte Carlo experiment is carried out to study the finite sample performance of the instrument selection procedure.