Fisher’s equation for the determination of the real rate of interest is studied from a fresh econometric perspective. Some new methods of data description for nonstationary time series are introduced. The methods provide a nonparametric mechanism for modelling the spatial densities of a time series that displays random wandering characteristics, like interest rates and inflation. Hazard rate functionals are also constructed, an asymptotic theory is given and the techniques are illustrated in some empirical applications to real interest rates for the US. The paper ends by calculating Gaussian semiparametric estimates of long range dependence in US real interest rates, using a new asymptotic theory that covers the nonstationary case. The empirical results indicate that the real rate of interest in the US is (fractionally) nonstationary over 1934–1997 and over the more recent subperiods 1961–1985 and 1961–1997. Unit root nonstationarity and short memory stationarity are both strongly rejected for all these periods.
Phillips, Peter C.B., "Econometric Analysis of Fisher’s Equation" (1998). Cowles Foundation Discussion Papers. 1428.