Estimation of Spatial Lag Model Under Random Missing Data in the Dependent Variable. Two Stage Estimator with Imputation

Abstract

The main goal of this article is to propose estimators for the Spatial Lag Model (SLM) under missing data context. We present three alternatives estimators for the SLM based on Two Stage Least Squares estimation methodology. The estimators are eÿcient within their type and consistent under random missing data in the dependent variable. Unlike the IBG2SLS estimator presented in Wang and Lee (2013) which impute all missing data we only impute missing data in the spatial lag. Our first proposal is an alternative version of the IBG2SLS estimator, the second one is based on an approximation to the optimal instruments matrix and the third one is an alternative equivalent to the first. Thorough a Monte Carlo simulation we assess the estimators performance under finite samples. Results show a good performance for all estimators, moreover, results are quite similar to the IBG2SLS estimator suggesting that a complete imputation (as IBG2SLS does) does not add information.