Unit Roots in Economic and Financial Time Series: A Re-Evaluation at the Decision-Based Significance Levels

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.