Practical aspects of using quadratic moment conditions in linear dynamic panel data models

We study the estimation of the lag parameter of linear dynamic panel data models with first order dynamics based on the quadratic Ahn and Schmidt (1995) moment conditions. Our contribution is twofold: First, we show that extending the standard assumptions by mean stationarity and time series homoscedasticity and employing these assumptions in estimation restores standard asymptotics and mitigates the non-standard distributions found in the literature. Second, we propose an IV estimator based on the quadratic moment conditions that consistently identifies the true population parameter under standard assumptions. Standard asymptotics hold for the estimator when the cross section dimension is large and the time series dimension is finite. We also suggest a data-driven approach to obtain standard errors and confidence intervals that preserves the time series dependence structure in the data.