Validity of the Neo-Fisherian Hypothesis
Warning: Super-Technical Material Follows
The neo-Fisherian hypothesis is as follows: If the central bank commits to peg the nominal interest rate at R, then the long-run level of inflation in the economy is increasing in R. Using finite horizon models, I show that the neo-Fisherian hypothesis is only valid if long-run inflation expectations rise at least one for one with the peg R. However, in an infinite horizon model, the neo-Fisherian hypothesis is always true. I argue that this result indicates why macroeconomists should use finite horizon models, not infinite horizon models. See this linked note and my recent NBER working paper for technical details.
In any finite horizon economy, the validity of the neo-Fisherian hypothesis depends on how sensitive long-run inflation expectations are to the specification of the interest rate peg.
Intuitively, when the peg R is high, people anticipate tight future monetary policy. The future tightness of monetary policy pushes down on current inflation. The only way to offset this effect is for long-run inflation expectations to rise sufficiently in response to the peg.
In contrast, in an infinite horizon model, the neo-Fisherian hypothesis is valid - but only because of an odd discontinuity. As the horizon length converges to infinity, the level of inflation becomes infinitely sensitive to long-run inflation expectations. This means that, for almost all specifications of long-run inflation expectations, inflation converges to infinity or negative infinity as the horizon converges to infinity. Users of infinite horizon models typically discard all of these limiting “infinity” equilibria by setting the long-run expected inflation rate to be equal to the difference between R and r*. In this way, the use of an infinite horizon - as opposed to a long but finite horizon - creates a tight implicit restriction on the dependence of long-run inflation expectations on the interest rate peg
To summarize: The validity of the neo-Fisherian hypothesis depends on an empirical question: how do long-run inflation expectations depend on the central bank's peg? This empirical question is eliminated when we use infinite horizon models - but this is a reason not to use infinite horizon models.
Rochester, NY, January 12, 2016
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