We propose the second-order least squares estimator for the autoregressive panel data models. This method requires only the specification of the first two conditional moments of the unobserved effects given the process initial observation, and does not require any other distributional assumptions. The data generating process can be either stationary or nonstationary. The proposed estimator is consistent and asymptotically normal for large N and finite T under fairly general regularity conditions. Moreover, we show that our estimator reaches an optimal semiparametric efficiency bound. Monte Carlo simulation studies show that the proposed estimator performs satisfactorily in finite sample situations compared to the usual first-differenced generalized method of moment (GMM) and the random effects pseudo maximum likelihood (PML) estimators.
This is joint work with Mustafa Salamh.