Inference for Unit Roots in Dynamic Panels in the Presence of Deterministic Trends

This paper proposes a similar unit root testing procedure for heterogeneous dynamic panel data, based on the score principle, assuming that the time dimension of the panel is fixed. It is shown that the limiting distribution of the test is standard normal. The similarity with regard to the initial conditions and the heterogeneity (fixed effects) of the panel is achieved by considering a parameterization of the autoregressive model which allows for a trend under both the null and the alternative hypotheses, without introducing any irrelevant variables under either. Simulation evidence suggests that the proposed tests have empirical size that is very close to the nominal 5% level and considereably more power than other panel unit root tests and the corresponding unit root tests for the single time series case. As an application of our test, we re-examine whether real dividends and stock prices follow drifting random walks. In contrast with many earlier studies, we find that both real dividends and real stock prices are stationary around a deterministic trend.