Working Paper: CEPR ID: DP2425
Authors: Mehmet Caner; Lutz Kilian
Abstract: Tests of the null hypothesis of stationarity against the unit root alternative play an increasingly important role in empirical work in macroeconomics and in international finance. We show that the use of conventional asymptotic critical values for stationarity tests may cause extreme size distortions, if the model under the null hypothesis is highly persistent. This fact calls into question the use of these tests in empirical work. We illustrate the practical importance of this point for tests of long-run purchasing power parity under the recent float. We show that the common practice of viewing tests of stationarity as complementary to tests of the unit root null will tend to result in contradictions and in spurious rejections of long-run PPP. While the size distortions may be overcome by the use of finite-sample critical values, the resulting tests tend to have low power under economically plausible assumptions about the half-life of deviations from PPP. Thus, the fact that stationarity is not rejected cannot be interpreted as convincing evidence in favour of mean reversion. Only in the rare case that stationarity is rejected do size-corrected tests shed light on the question of long-run PPP.
Keywords: long-run PPP; mean reversion; finite-sample critical values; real exchange rate
JEL Codes: C22; F31
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Conventional asymptotic critical values for stationarity tests (C22) | Severe size distortions (F12) |
| Severe size distortions (F12) | Over-rejection of the null hypothesis of stationarity (C22) |
| Over-rejection of the null hypothesis of stationarity (C22) | Spurious rejections of long-run purchasing power parity (PPP) (F31) |
| Using finite-sample critical values (C46) | Mitigate size distortions (F12) |
| Using finite-sample critical values (C46) | Low power in detecting true stationarity (C22) |
| Rejection of the stationarity null (C22) | Not necessarily indicate mean reversion in real exchange rates (F31) |
| Stationarity rejected after size adjustments (C22) | Provide meaningful insights into the PPP question (E65) |