Semiparametric GMM estimation and variable selection in dynamic panel data models with fixed effects

Often fixed-effects dynamic panel data model assumes parametric structures and an AR(1) dynamic order. The latter assumption is mainly for convenience and not consistent with many sampling processes especially when longer panels are available. A fixed-effects dynamic partially linear additive model with a finite autoregressive lag order is considered. Based on this setup, semiparametric Generalized Method of Moments (GMM) estimators of the unknown coefficients and functions using the B(asis)-spline approximation are developed. The asymptotic properties of these estimators are established. A procedure to identify the dynamic lag order and significant exogenous variables by employing the smoothly clipped absolute deviation (SCAD) penalty is developed. It is proven that the SCAD-based GMM estimators achieve the oracle property and are selection consistent. The usefulness of proposed procedure is further illustrated in Monte Carlo studies and a real data example.