On the Effect of Nonstationary Initial Conditions in Dynamic Panel Data Models

In this paper, we consider dynamic panel data models with possibly nonstationary initial conditions. We derive the asymptotic properties of the GMM estimators with various kinds of instruments when both N and T are large, where N and T denote the dimensions of the cross section and time series. We find that when initial conditions are nonstationary and the degree of heterogeneity, which is measured by the variance ratio of individual effects to the disturbances, is large, the biases and variances of the GMM estimators become small. We demonstrate that this is because the correlation between the lagged dependent variable and instruments gets larger due to the unremoved individual effects. This implies that the instruments become strong when initial conditions are nonstationary and the degree of heterogeneity is large. For the purpose of comparison, we also derive the asymptotic properties of the within groups and the LIML estimators. Numerical studies are conducted to assess the properties of these estimators.