Abstract
This paper re-evaluates key past results of unit root tests, emphasizing that the use of a conventional level of significance is not in general optimal due to the test having low power. The decision-based significance levels for popular unit root tests, chosen using the line of enlightened judgement under a symmetric loss function, are found to be much higher than conventional ones. We also propose simple calibration rules for the decision-based significance levels for a range of unit root tests. At the decision-based significance levels, many time series in Nelson and Plosser’s (1982) (extended) data set are judged to be trend-stationary, including real income variables, employment variables and money stock. We also find that nearly all real exchange rates covered in Elliott and Pesavento’s (2006) study are stationary; and that most of the real interest rates covered in Rapach and Weber’s (2004) study are stationary. In addition, using a specific loss function, the U.S. nominal interest rate is found to be stationary under economically sensible values of relative loss and prior belief for the null hypothesis.
Highlights
Since the seminal study by Nelson and Plosser (1982), the presence of a unit root in economic and financial time series has been a highly controversial issue
Using the decision-based significance level and the calibration rules, we examine the extended Nelson–Plosser data set for U.S macroeconomic time series; the real exchange rates covered by Elliott and Pesavento (2006); the real interest rates studied by Rapach and Weber (2004); and the nominal interest rates used by Neely and Rapach (2008)
This paper re-evaluates the key past results of unit root testing at the decision-based significance level chosen based on the line of enlightened judgement (Leamer 1978)
Summary
Since the seminal study by Nelson and Plosser (1982), the presence of a unit root in economic and financial time series has been a highly controversial issue. The purpose of this paper is to re-evaluate key past results of unit root testing at the decision-based significance levels chosen in explicit consideration of the power and expected loss, following. It is found that the decision-based levels for popular unit root tests, such as the augmented Dickey–Fuller (Dickey and Fuller 1979; ADF) and DF–GLS tests (Elliott et al 1996) are much higher than 0.05 They are in the 0.2 to 0.4 range for the sample sizes widely used in practice, under a symmetric loss function and equal chance for the null and alternative hypotheses. We demonstrate how the calibration rules for the decision-based significance levels for the Phillips–Perron and ERS–P tests are used to determine the presence of a unit root in the U.S real GNP. Rules based on asymptotic local power for a range of popular unit root tests; Section 4 re-evaluates past key results of unit root testing; and Section 5 concludes the paper
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