"On Modeling the Effects of Inflation Shocks," Contributions to Macroeconomics, Vol. 2: Iss. 1, Article 3, 2002.Paper: pdf file
A popular model in the literature postulates an interest rate rule, a NAIRU price equation, and an aggregate demand equation in which aggregate demand depends on the real interest rate. In this model a positive inflation shock with the nominal interest rate held constant is explosive because it increases aggregate demand (because the real interest rate is lower), which increases inflation through the price equation, which further increases aggregate demand, and so on. In order for the model to be stable, the nominal interest rate must rise more than inflation, which means that the coefficient on inflation in the interest rate rule must be greater than one.
The results in this paper suggest, however, that an inflation shock with the nominal interest rate held constant has a negative effect on real output. There are three reasons. First, the data support the use of nominal rather than real interest rates in aggregate expenditure equations. Second, the evidence suggests that the percentage increase in nominal household wealth from a positive inflation shock is less than the percentage increase in the price level, which is contractionary because of the fall in real wealth. Third, there is evidence that wages lag prices, and so a positive inflation shock results in an initial fall in real wage rates and thus real labor income, which is contractionary. If these three features are true, they imply that a positive inflation shock has a negative effect on aggregate demand even if the nominal interest rate is held constant. Not only does the Fed not have to increase the nominal interest rate more than the increase in inflation for there to be a contraction, it does not have to increase the nominal rate at all!