a1 University of Melbourne
a2 University of Nottingham
a3 University of Manchester
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 magnitude of the initial conditions increases, in direct contrast to what is usually observed in 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.
The authors thank Giuseppe Cavaliere and two anonymous referees whose helpful comments greatly improved the presentation of the paper.