Asymptotic distributions of the quadratic GMM estimator in linear dynamic panel data models

This paper establishes asymptotic distributions of the quadratic GMM estimator of the autoregressive parameter in simple linear dynamic panel data models with fixed effects under standard minimal assumptions. The number of time periods is assumed to be small. Focusing on settings where autoregressive parameter is uniquely identified, nonstandard convergence rates and limiting distributions arise in the well-known random walk case, as well as in other previously unrecognized cases. The paper finds that the convergence rates are slow in the nonstandard cases, and the limiting distributions are a mixture of two nonnormal distributions. The findings are illustrated using Monte Carlo simulations.