Simulation Study on Estimation Bias in Spatial Lag Model from Omitted Variable Correlated with Regressors

In this research, the omitted variable problem in a spatial autoregressive model is analyzed by simulation. We examine the performances of estimators when an omitted variable is correlated with explanatory variables. In the literature, theoretical aspects of estimating spatial autoregressive models have been discussed including the spatial error model for the spatially autocorrelated omitted variable. Regarding the ideal case of the spatial lag model, in which there is not an omitted variable correlated with regressors, there have been theoretical discussions of consistency and simulation analyses on the small sample property of the estimator. In the case of real data, some important variables may not be available and most socioeconomic variables are mutually interdependent. Consequently, the performance of estimation methods should be verified in such cases. In this research, we compared three estimation methods for the spatial lag model, namely, maximum likelihood (ML), spatial two-stage least squares (S-2SLS), and the general method of moments (GMM), by using two definitions of the root mean square error. Our simulation results show that the S-2SLS estimator is strongly affected by the omitted variable under certain conditions