Changes in persistence, spurious regressions and the Fisher hypothesis

Declining inflation persistence has been documented in numerous studies. When such series are analyzed in a regression framework in conjunction with other persistent time series, spurious regressions are likely to occur. We propose to use the coefficient of determination R2 as a test statistic to distinguish between spurious and genuine regressions in situations where time series possibly (but not necessarily) exhibit changes in persistence. To this end, we establish some limit theory for the R2 statistic and conduct a Monte Carlo study where we investigate its finite-sample properties. Finally, we apply the test to the Fisher equation for the U.S. and Mexico. Contrary to a rejection using cointegration techniques, the R2-based test offers strong evidence favourable to the Fisher hypothesis.