Abstract :
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.
