GMM Estimation of Fixed Effects Dynamic Panel Data Models with Spatial Lag and Spatial Errors

The three-step generalized methods of moments (GMM) approach of Kapoor, Kelejian and Prucha (2007), which corrects for spatially correlated errors in static panel data models, is extended by introducing fixed effects, a spatial lag, and a one-period lag of the dependent variable as additional explanatory variables. Combining this approach with the dynamic panel-data GMM estimators of Arellano and Bond (1991) and Blundell and Bond (1998) and specifying moment conditions for various time lags, spatial lags, and sets of exogenous variables yields new spatial dynamic panel data estimators. The proposed spatially corrected GMM estimates are based on a spatial lag and a transformation correcting for the spatial error correlation. We prove their consistency and asymptotic normality for a large number of spatial units and a fixed number of time periods. Feasible spatial correction based on estimated spatial error correlation is shown to lead to estimators that are asymptotically equivalent to the infeasible estimators based on a known spatial error correlation. Monte Carlo simulations show that the root mean squared error of spatially corrected GMM estimates is generally smaller than that of corresponding spatial GMM estimates in which spatial error correlation is ignored