Econometric Analysis of Fisher's Equation

A bstract . 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 United States. The paper ends by calculating semiparametric estimates of long‐range dependence in U.S. real interest rates, using a new estimation procedure called modified log periodogram regression and new asymptotics that covers the nonstationary case. The empirical results indicate that the real rate of interest in the United States 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.