A note on 2SLS estimation of the mixed regressive spatial autoregressive model

•We consider the mixed regressive spatial autoregressive model where the spatially lag term is collinear with the regressors.•The asymptotic properties of the 2SLS estimator are derived.•The coefficients of regressors may still be consistently estimated with a regular n speed of convergence.•When the coefficient of the spatial effect is close to 1, it could be also consistently estimated.

This paper considers the mixed regressive spatial autoregressive model in an important special case where the spatially lag term is collinear with the regressors. The asymptotic properties of the two-stage least square (2SLS) estimator suggested by Kelejian and Prucha (1998) are derived under such a circumstance. Although the coefficients of the spatial effect cannot be consistently estimated, the coefficients of regressors may still be consistently estimated with a regular n speed of convergence, for example, when all instruments are irrelevant. Furthermore, when the coefficient of the spatial effect is close to 1, it could be also consistently estimated.