Abstract
We conduct a systematic comparison of the performance of four commonly used P value combination methods applied to panel unit root tests: the original Fisher test, the modified inverse normal method, Simes test, and the modified truncated product method (TPM). Our simulation results show that under cross‐section dependence the original Fisher test is severely oversized, but the other three tests exhibit good size properties. Simes test is powerful when the total evidence against the joint null hypothesis is concentrated in one or very few of the tests being combined, but the modified inverse normal method and the modified TPM have good performance when evidence against the joint null is spread among more than a small fraction of the panel units. These differences are further illustrated through one empirical example on testing purchasing power parity using a panel of OECD quarterly real exchange rates.
Highlights
Combining significance tests, or P values, has been a source of considerable research in statistics since Tippett 1 and Fisher 2
We conduct a systematic comparison of the performance of four commonly used P -value combination methods applied to panel unit root tests: the original Fisher test, the modified inverse normal method, Simes test, and the modified TPM
We investigate the PPP hypothesis for a panel of OECD countries and find mixed evidence
Summary
P values, has been a source of considerable research in statistics since Tippett 1 and Fisher 2. For a systematic comparison of methods for combining P values from independent tests, see the studies by Hedges and Olkin 3 and Loughin 4. Despite the burgeoning statistical literature on combining P values, these techniques have not been used much in panel unit root tests until recently. Maddala and Wu 5 and Choi 6 are among the first who attempted to test unit root in panels by combining independent P values. More recent contributions include those by Demetrescu et al 7 , Hanck 8 , and Sheng and Yang 9. Combining P values has several advantages over combination of test statistics in that i it allows different specifications, such as different
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