Abstract
Unit root tests that are in common use today tend to over-reject the stationarity of economic ratios like the consumption-income ratio or rates like the average tax rate. The meaning of a unit root in such bounded series is not very clear. We use a mixed-frequency regression technique to develop a test for the null hypothesis that a series is stationary. The focus is on regression relationships, not so much on individual series. What is noteworthy about this moving average (MA) unit root test, denoted as z(MA) test, based on a variance-difference, is that, instead of having to deal with non-standard distributions, it takes testing back to normal distribution and offers a way to increase power without having to increase the sample size substantially. Monte Carlo simulations show minimal size distortions even when the AR root is close to unity and the test offers substantial gains in power relative to some popular tests against near-null alternatives in moderate size samples. Applying this test to log of consumption-income ratio of 21 OECD countries shows that the z(MA) test favors stationarity of 15 series, KPSS test 8 series, Johansen test 6 series and ADF test 5 series.
Highlights
Economic theory often requires ratios like consumption share of income, investment share of GDP and the average tax rate to be stationary; see, for example, King et al (1991), and references therein
M is the effective sample size and Vis the sample mea√n of Vt. (Note that the subtraction of Vis not essential in large samples.) compute z = T/2σ2 and reject the null hypothesis θ = 1 if z ≤ c where c is a left-hand critical value from the standard normal distribution.We term this as z(MA) test to differentiate it from a z(AR) test that can be obtained by extending our test procedure to the AR unit root case.We extended the test procedure to the AR unit root case, which provides a generalization to the variance-ratio test developed by Lo and MacKinlay
What is of general importance is whether a regression relationship produces stationary residuals regardless of the nature of non-stationarities of the individual series
Summary
Economic theory often requires ratios like consumption share of income, investment share of GDP and the average tax rate to be stationary; see, for example, King et al (1991), and references therein Even if these series appear to be non-stationary (Harvey, 1989), the meaning of a unit root in them is not very clear. Kim and Choi (2017) have questioned the validity of previous unit root verdicts on many time series that have ignored the problem of low power. We revisit this old problem with the objective of presenting a test for the null of stationarity of the deviations from a long-run relationship.
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