The long-run relationship between nominal interest rates and inflation: the Fisher equation revisited.

THE PAST SEVERAL DECADES have seen numerous empirical studies of the Fisher equation. This well-known hypothesis, introduced by Irving Fisher (1930), maintains that the nominal interest rate is the sum of the constant real rate and expected decline in the purchasing power of money. Starting with

Fisher and extending to the present (for example, Mishkin 1992 and Evans and Lewis 1995), this seemingly simple and intuitive hypothesis has found limited empirical support. Typically, the estimated coefficients on expected inflation are substantially less than the hypothesized value of one, excluding tax considerations. When tax effects (see Darby 1975) are considered, the hypothesized coefficient should be in the range of 1.3 to 1.5 since agents have incentives to bid nominal interest rates to levels that allow nominal interest rate movements to mirror movements in "tax-adjusted" estimates of the future course of inflation.(1) Estimates below unity imply substantial adjustment in real interest rates in response to changes in expected inflation.

A number of papers augment the basic Fisher equation with explanations of real interest rate movements that presumably reconcile these findings. Levi and Makin (1978), Melvin (1982), and Peek and Wilcox (1983) demonstrate that Mundell-Tobin effects (the decline in the marginal product of capital due to the real balance response to inflation) may have considerable significance. However, Lucas (1980) and Fried and Howitt (1983) contend that in models characterized by super-neutrality, inflation will not affect real rates in this manner over the long run. If output is supply determined, as characterized by most long-run explanations of the macro economy, short-run adjustments such as Mundell-Tobin effects should not dominate the data.

Several recent empirical studies recognize that valid tests of the Fisher relation may require consideration of the time series properties of the data. These include papers by Rose (1988), Mishkin (1992), and Evans and Lewis (1995). Rose analyzes the time series properties of the variables that constitute the Fisher paradigm and concludes that interest rates possess a unit root in their autoregressive representation, but inflation does not. If these properties do characterize the data, a regression of interest rates on inflation is necessarily spurious (see Newbold and Davies 1978) because it attempts to link variables that maintain different orders of integration. In this case the real interest rate is a nonstationary series and the textbook representation of the Fisher relation may be rejected out of hand. Rose's conclusions must be viewed carefully since the statistical inference drawn from his tests does not account for the small sample distributions of standard unit root tests in the presence of moving average errors that may characterize U.S. inflation. Moreover, it is widely recognized that conventional univariate unit root tests have a difficult time distinguishing unit and near unit root processes and may not be able to provide a definitive test of the proposition.