Unified M-estimation of fixed-effects spatial dynamic models with short panels

It is well known that quasi maximum likelihood (QML) estimation of dynamic panel data (DPD) models with short panels depends on the assumptions on the initial values, and a wrong treatment of them will result in inconsistency and serious bias. The same issues apply to spatial DPD (SDPD) models with short panels. In this paper, a unified M-estimation method is proposed for estimating the fixed-effects SDPD models containing three major types of spatial effects, namely spatial lag, spatial error and space-time lag. The method is free from the specification of the distribution of the initial observations and robust against nonnormality of the errors. Consistency and asymptotic normality of the proposed M-estimator are established. A martingale difference representation of the underlying estimating functions is developed, which leads to an initial-condition free estimate of the variance of the M-estimators. Monte Carlo results show that the proposed methods have excellent finite sample performance.