On the consistency of the LIMLÂ estimator of a spatial autoregressive model with many instruments

This paper derives the LIML estimator for a spatial autoregressive model with endogenous regressors in the presence of many instruments. The LIML estimator is consistent when the number of instruments increases at a slower rate relative to the sample size. Due to spatial correlation, the LIML estimator in general is inconsistent when the number of instruments increases at the same rate as the sample size.

► We derive the LIML estimator for an SAR model with many IVs. ► The LIML estimator is consistent if the number of IVs increases slower than n. ► The LIML estimator is inconsistent if the number of IVs increases as fast as n.