Unit roots in economic and financial time series: A re-evaluation at the decision-based significance levels

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 (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 (2006) study are stationary; and that most of the real interest rates covered in Rapach and Weber (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.