Changes in persistence, spurious regressions and the Fisher hypothesis

Declining inflation persistence has been documented in numerous studies. We show that when time series with changes in persistence are analyzed in a regression framework with other persistent time series like interest rates, spurious regressions are likely to occur. We propose the coefficient of determination R 2 as a simple test statistic to distinguish between spurious and genuine regressions in situations where time series possibly exhibit changes in persistence. We extend the analysis towards fractional (co-)integration as well. To this end, we establish the limit theory for the R 2 statistic and conduct a Monte Carlo study where we investigate its finite-sample properties. The test performs remarkably well in terms of size and power and is robust to level shifts and multiple changes in persistence. Finally, we apply the test to the Fisher equation for the United States. The newly proposed R 2 -based test offers robust evidence favourable to the Fisher hypothesis.