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

O ne of the more important challenges facing policymakers is that of assessing inflation expectations. Goodfriend (1997) points out that one can interpret the meaning of a given interest rate policy action primarily in terms of its impact on the real rate of interest. However, evaluating this impact requires not only that one understands the various links between the nominal rate and expected inflation but also that one can quantify these relationships. To find an approximate measure of expected inflation, one often turns to the behavior of long bond rates. Two key ideas explain why this approach might be appropriate. First, Fisher’s theory holds that the real rate of interest is just the difference between the nominal rate of interest and the public’s expected rate of inflation. Second, the long-term real rate is generally thought to exhibit very little variation.1 Alternatively, and still based on Fisher’s theory, one might use the yield spread between the ten-year Treasury note and its inflation-indexed counterpart as an estimate of expected inflation. In January 1997, the U.S. Treasury indeed began issuing ten-year inflation-indexed bonds. While economic analysts typically attempt to capture inflation expectations using Fisher’s equation, this method has its flaws. When inflation is stochastic, Fisher’s relation may not actually hold. Barro (1976), Benninga and Protopapadakis (1983), as well as Cox, Ingersoll, and Ross (1985), show that the decomposition of the nominal rate into a real rate and expected inflation should