Panel Data Analysis with Heterogeneous Dynamics

This paper proposes the analysis of panel data whose dynamic structure is heterogeneous across individuals. Our aim is to estimate the cross-sectional distributions and/or some distributional features of the heterogeneous mean and autocovariances. We do not assume any specific model for the dynamics. Our proposed method is easy to implement. We first compute the sample mean and autocovariances for each individual and then estimate the parameter of interest based on the empirical distributions of the estimated mean and autocovariances. The asymptotic properties of the proposed estimators are investigated using double asymptotics under which both the cross-sectional sample size (N) and the length of the time series (T) tend to infinity. We prove the functional central limit theorem for the empirical process of the proposed distribution estimator. By using the functional delta method, we also derive the asymptotic distributions of the estimators for various parameters of interest. We show that the distribution estimator exhibits a bias whose order is proportional to 1/√T. Conversely, when the parameter of interest can be written as the expectation of a smooth function of the heterogeneous mean and/or autocovariances, the bias is of order 1/T and can be corrected by the jackknife method. The results of Monte Carlo simulations show that our asymptotic results are informative regarding the finitesample properties of the estimators. They also demonstrate that the proposed jackknife bias correction is successful.