Misspecification in Dynamic Panel Data Models and Model-Free Inferences

This paper discusses the issue of model misspecification and model-free methods in dynamic panel data analysis. We primarily review existing results, but also provide several new results. When the dynamics are homogeneous, we show that several widely used estimators for panel first-order autoregressive AR(1) models converge to first-order autocorrelation, even under misspecification. Under heterogeneity, these estimators converge to the ratio of the means of the first-order autocovariances and variances. We also discuss the estimation of autocovariances, the estimation of panel AR(∞) models, and the estimation of the distribution of the heterogeneous mean and autocovariances.