This paper considers unit-root tests in large n and large T heterogeneous
panels with cross-sectional dependence generated by unobserved factors. We
reconsider the two prevalent approaches in the literature, that of Moon and
Perron (2004) and the PANIC setup proposed in Bai and Ng (2004). While these
have been considered as completely different setups, we show that, in case of
Gaussian innovations, the frameworks are asymptotically equivalent in the sense
that both experiments are locally asymptotically normal (LAN) with the same
central sequence. Using Le Cam's theory of statistical experiments we determine
the local asymptotic power envelope and derive an optimal test jointly in both
setups. We show that the popular Moon and Perron (2004) and Bai and Ng (2010)
tests only attain the power envelope in case there is no heterogeneity in the
long-run variance of the idiosyncratic components. The new test is
asymptotically uniformly most powerful irrespective of possible heterogeneity.
Moreover, it turns out that for any test, satisfying a mild regularity
condition, the size and local asymptotic power are the same under both data
generating processes. Thus, applied researchers do not need to decide on one of
the two frameworks to conduct unit root tests. Monte-Carlo simulations
corroborate our asymptotic results and document significant gains in
finite-sample power if the variances of the idiosyncratic shocks differ
substantially among the cross sectional units