A More Efficient Best Spatial Three - stage Least Squares Estimator for Spatial Autoregressive Models

Lee (2003) proposed for spatial autoregressive (SAR) model the best spatial two-stage least squares estimator (BS2SLSE) as an improvement on Kelejian and Prucha (1998)’s S2SLSE. In this paper, we show that one more step iteration based on BS2SLSE gives a spatial counterpart of the three-stage least squares estimator for a system of J equations. This estimator, named BS3SLSE, is shown to be equivalent to BS2SLSE under normality and more efficient under non-normality. The proposed BS3SLSE can be interpreted as a GMM estimator where the number of moments increases with the sample size n at some slow rate. The asymptotic efficiency of BS3SLSE relative to other previously proposed estimators such as MLE (Lee, 2004) and GMME (Lee, 2007a) is also discussed. As an empirical illustration, we apply these estimation procedures to re-examining the presence of environmental “race-to-the-bottom” effect in competition for FDI across China municipal governments.