Unified M-estimation of matrix exponential spatial dynamic panel specification

In this paper, a unified M-estimation method in Yang (2018) is extended to the matrix exponential spatial dynamic panel specification (MESDPS) with fixed effects in short panels. Similar to the STLE model which includes the spatial lag effect, the space-time effect and the spatial error effect in Yang (2018), the quasi-maximum likelihood (QML) estimation for MESDPS also has the initial condition specification problem. The initial-condition free M-estimator in this paper solves this problem and is proved to be consistent and asymptotically normal. An outer product of martingale difference (OPMD) estimator for the variance-covariance (VC) matrix of the M-estimator is also derived and proved to be consistent. The finite sample property of the M-estimator is studied through an extensive Monte Carlo study. The method is applied to US outward FDI data to show its validity.