Unit Root Inference in Generally Trending and Cross-Correlated Fixed-T Panels

Abstract

This paper proposes a new panel unit root test based on the generalized method of moments approach for panels with a possibly small number of time periods, T, and a large number of cross-sectional units, N. In the model that we consider the deterministic trend function is essentially unrestricted and the errors obey a multi-factor structure that allows for rich forms of unobserved heterogeneity. In spite of these allowances, the GMM estimator considered is shown to be asymptotically unbiased, $\sqrt{N}$-consistent and asymptotically normal for all values of the autoregressive (AR) coefficient, ρ, including unity, making it a natural candidate for unit root inference. Results from our Monte Carlo study suggest that the asymptotic properties are borne out well in small samples. The implementation is illustrated by using a large sample of US banking institutions to test Gibrat’s Law.