Empirical Likelihood for Mixed Regressive, Spatial Autoregressive Model Based on GMM

For the parameters in a mixed regressive, spatial autoregressive (MRSAR) model, it is shown, in this article, that for every generalized method of moments (GMM) estimator, there is an empirical likelihood (EL) estimator which has the same asymptotic variance as the GMM estimator. Specifically, we show that there exists an EL estimator which is asymptotically efficient as the best GMM estimator and the EL confidence region for the parameters in the MRSAR model is constructed without estimating the asymptotic variance.