Can economic time series be differenced to stationarity?

This article considers a class of nonstationary varying-coefficient autoregressive models that allow stochastic variability in the autoregressive root. It is argued that such models provide a better description of the behavior of macroeconomic variables than fixed-unit-root autoregressive models because they allow more general forms of nonstationarity. We construct a test of the null hypothesis of a fixed unit root against the alternative of a randomized root with unit mean and derive its asymptotic distribution. The test is applied to several U.S. macroeconomic series generally considered to contain fixed unit roots. We find that for about half of the series the fixed-unit-root null is rejected.