Empirical likelihood and GMM for spatial models

Abstract

We link the empirical likelihood (EL) and GMM for three major spatial models: spatial autoregressive model with spatial autoregressive disturbances (SARAR model), linear regression model with spatial autoregressive errors (SE model) and spatial autoregressive model (SAR model). It is shown that for every GMM estimator (GMME), there is an empirical likelihood (EL) estimator which has the same asymptotic variance as the GMME. Specifically, we show that there exists an EL estimator which is asymptotically efficient as the best GMME proposed by Liu et al. [Liu, X. D., L. F. Lee, and C. R. Bollinger. 2010. An efficient GMM estimator of spatial autoregressive models. Journal of Econometrics 159 (2):303–19] and the EL confidence regions for the parameters in above models can be constructed without the estimation of asymptotic variances.