The Local Power of the IPS Test with Both Initial Conditions and Incidental Trends

This paper investigates the asymptotic local power of the the averaged t-test of Im, Pesaran and Shin (2003, IPS hereafter) in the presence of both initial explosive conditions and incidental trends. By utilizing the least squares detrending methods, it is found that the initial condition plays no role in determining the asymptotic local power of the IPS test, a result strikingly different from the finding in Harris et al. (2010), who examined the impact of the initial conditions on local power of IPS test without incidental trends. The paper also presents, via an application of the Fredholm method discussed in Nabeya and Tanaka (1990a, 1990b), the exact asymptotic local power of IPS test, thereby providing theoretical justifications for its lack of asymptotic local power in the neighborhood of unity with the order of N-1/2T-1 while attaining nontrivial power in the neighborhood of unity that shrinks at the rate N-1/4T-1. This latter finding is consistent with Moon et al. (2007) and extends their results to IPS test. It is also of practical significance to empirical researchers as the presence of incidental trends in panel unit root test setting is ubiquitous.