In a recent paper Do Higher Interest Rates Raise or Lower Inflation? and a follow-up post, John Cochrane delves into the “neo-Fisherian” idea that “maybe raising interest rates raises inflation” and lowering interest rates lowers inflation. He starts with a two-equation “new Keynesian” model (three if you include a policy rule). He then inputted a lower interest rate path and found that the inflation rate falls; similarly, with a higher interest rate path, inflation rises. St. Louis Fed President Jim Bullard replicated and discussed the findings in his recent Permazero speech at the Annual Cato Monetary Conference. And the results bear on the famous issue of the stability or instability of an interest peg.

This is obviously an important issue, but in my view the simplified new-Keynesian model used by John Cochrane and Jim Bullard is too abstract and artificial for the purposes at hand. The model is based on a Calvo version of staggered pricing with exponential weighting, resulting in a so-called new Keynesian Phillips curve. What would happen in a staggered price or wage setting model with a rich enough micro-structure to be estimated or calibrated with detailed micro data? And what more could you learn from that?

Some of the answers to these questions can be found by looking at existing simulations of more general and realistic staggered contract models. For example, I presented the results from a model calibrated to BLS micro data on multi-period collective bargaining contracts at a Jackson Hole Monetary conference in 1982 (with critical monetarist and Keynesian comments from Phil Cagan and Bob Gordon.) In those days, the task was to find a money growth path for the Fed to transition from high inflation to low inflation with the least disturbance to real output. The results showed–surprisingly to the commentators–that it was possible to change inflation without any effect on real output or the real interest rate.

These results can be applied easily to the neo-Fisherian debate by setting the policy interest rate equal to the unchanged real interest rate plus the (rationally) expected inflation rate. The two charts show the interest rate path and the inflation rate path in the case of a policy change announced at the date shown in the charts. The first chart assumes that all wages are set in multiyear contracts and the second assumes a more realistic mixture of wage contract lengths. The real interest rate is assumed to be 2 percent, and that number is added to the expected inflation rate to get the nominal short term interest rate as shown.

As you can see, lowering the interest rate lowers the inflation rate just as in the neo-Fisherian view of the world; of course, the simulations work in reverse in the case of an increase in the interest rate. True, the path of the interest rate is much more gradual than in John Cochrane’s calculations; it was chosen that way to take account of the structure of the wage contracts and thereby prevent real output from changing.

Nevertheless, the simulation results basically support John

Cochrane’s calculations. However, the results also point to complicating policy issues. For example, somehow money growth has to be reduced when the interest rate is cut, even if very gradually at the start; effectively the expectational effect of the change in policy then offsets any liquidity effect. The simulations also point to the need for very strong credibility and the dependence of the results on the rational expectations assumption, or at least some forward looking behavior.

The results do not resolve the interest rate peg and stability issue. In the simulations, the money supply provides an anchor and the interest rate is determined in the markets. The Fed is effectively saying that it will set the money supply path and the market will then set the interest rate according to the path. (That is how Paul Volcker usually put it during the transition, by the way). To examine the stability issue you need to look at interest rate rules to deal with shocks, whether along the transition path or in the new steady state. I continue to be of the opinion that for stability the interest rate response to inflation shocks should be greater than one.