Dynamics of interest and inflation rates

This paper proposes that there is a dynamic relationship between interest and inflation rates that are jointly determined due to the dual existence of Fisher and Wicksell processes. The Fisher process is the positive relationship between inflation and interest rates wherein causality runs from inflation to interest rates. By contrast, the Wicksell process is the negative relationship between the two rates with causality from interest to inflation rates. While Fisher and Wicksell theories are ex ante relationships, empirical tests employ ex post interest and inflation rate series after the full realization of both Fisher and Wicksell effects. This ex post estimation procedure has led to less than unity Fisher coefficients, known as the Fisher puzzle. We derive linkages between ex ante and ex post coefficients in the Fisher and Wicksell equations and propose methods for recovering ex ante coefficients from ex post estimated relationships. Application of these methods to U.S. data and several other advanced economies supports both Fisher and Wicksell theories of interest and inflation rates and helps to explain the Fisher puzzle.