Panel unit root tests in the presence of a multifactor error structure

This paper extends the cross-sectionally augmented panel unit root test ( C I P S ) proposed by Pesaran (2007) to the case of a multifactor error structure, and proposes a new panel unit root test based on a simple average of cross-sectionally augmented Sargan–Bhargava statistics ( C S B ). The basic idea is to exploit information regarding the m unobserved factors that are shared by k observed time series in addition to the series under consideration. Initially, we develop the tests assuming that m 0 , the true number of factors, is known and show that the limit distribution of the tests does not depend on any nuisance parameters, so long as k ≥ m 0 − 1 . Small sample properties of the tests are investigated by Monte Carlo experiments and are shown to be satisfactory. Particularly, the proposed C I P S and C S B tests have the correct size for all combinations of the cross section ( N ) and time series ( T ) dimensions considered. The power of both tests rises with N  and T , although the C S B test performs better than the C I P S test for smaller sample sizes. The various testing procedures are illustrated with empirical applications to real interest rates and real equity prices across countries.