Local asymptotic power of the Im-Pesaran-Shin panel unit root test and the impact of initial observations

In this note we derive the local asymptotic power function of the standardized averaged Dickey-Fuller panel unit root statistic of Im, Pesaran and Shin (2003, Journal of Econometrics, 115, 53-74), allowing for heterogeneous deterministic intercept terms. We consider the situation where the deviation of the initial observation from the underlying intercept term in each individual time series may not be asymptotically negligible. We find that power decreases monotonically as the absolute values of the initial conditions increase in magnitude, in direct contrast to the univariate case. Finite sample simulations confirm the relevance of this result for practical applications, demonstrating that the power of the test can be very low for values of T and N typically encountered in practice.