# The Fisher Effect under Deflationary Expectations

## Try factoring in Gibson's Paradox.

BY David Glasner, Federal Trade Commission | February 8, 2011

(SSRN) In most renditions, the Fisher equation relating the nominal interest rate to the real rate and the expected rate of inflation is treated as if it followed necessarily from the axiom of rationality, any violation of the Fisher equation becoming deeply problematic or paradoxical. Of course, the Fisher equation, like the equation of exchange, is a mere tautology, but it is usually interpreted, and imparted with empirical content, in the light of the Fisherian theory of interest in which the real rate of interest reflects real, not monetary, factors, so that the real rate of interest should not, at least as a first approximation, be affected by monetary factors like a mere change in the price level (Hirshleifer 1970, pp.135- 38). Gibson’s Paradox, the observed correlation between interest rates and price levels, is paradoxical precisely because, given the Fisherian theory of interest, the Fisher equation seems to disallow it.

My objective in this paper is to explore another difficulty, less well known than Gibson’s Paradox, with the Fisher equation: the effect of deflationary expectations on nominal and real interest rates. The adjustment of nominal and real interest rates to expected deflation becomes problematic when nominal interest rates fall to the neighborhood of zero at the same time that the expected rate of deflation increases. Because the nominal rate of interest can fall no further should expected deflation increase, the question arises, how can the Fisher equation hold when the nominal rate of interest is at its lower bound and the sum of the real rate and the expected rate of deflation is less than the lower bound? Read the full paper.