Fisher's Equation and the Inflation Risk Premium in a Simple Endowment Economy

It is well known that when inflation is stochastic, Fisher's theoretical equation, according to which the nominal interest rate is the sum of the real rate and the expected inflation rate, fails to hold. Under stochastic inflation, the Fisher equation must be amended to include a compensation for inflation risk: the inflation risk premium. Consequently, this article uses a simple consumption-based asset pricing model to investigate the significance of the inflation risk premium. Given the relationship between U.S. consumption growth and inflation, we find that historical estimates of the inflation risk premium are inconsequential. This result emerges because inflation surprises and unexpected movements in consumption growth exhibit little covariation in U.S. data. Moreover, using two different preference specifications, we also show that this result is quite unrelated to the notion that the equity risk premium is generally small in consumption-based asset pricing models.