Local Asymptotic Equivalence of the Bai and Ng (2004) and Moon and Perron (2004) Frameworks for Panel Unit Root Testing

TL;DR

This paper demonstrates that two major frameworks for panel unit root testing are asymptotically equivalent under Gaussian innovations, and introduces an optimal test that performs well regardless of heterogeneity in the data.

Contribution

It shows the asymptotic equivalence of Bai and Ng (2004) and Moon and Perron (2004) frameworks and develops a new, uniformly most powerful test for panel unit root testing.

Findings

Both frameworks are LAN with the same central sequence.

Existing tests only optimal under no heterogeneity.

New test outperforms existing tests with heterogeneity.

Abstract

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.