Home | Business News | Browse by Publication | J | Journal of Money, Credit & Banking

The long-run fisher effect: can it be tested?

Article Excerpt
THE LONG-RUN Fisher effect hypothesis states that a permanent change to inflation will cause nominal interest rates to move one-for-one with the change in inflation, thus leaving the real interest rate unchanged (see Fisher 1930). Unfortunately, empirical support for the long-run Fisher effect has been mixed (e.g., Weber 1994, King and Watson 1997, Koustas and Serletis 1999, Rapach 2003).

Empirical studies of the long-run Fisher effect have employed variations of the Fisher and Seater (1993; FS hereafter) bivariate, vector autoregression (VAR) test of long-run monetary (super)neutrality. The key to applying the FS approach is finding inflation to be integrated of order one or larger so that a shock permanently affects inflation. This paper argues that a permanent change in inflation has not taken place; i.e., inflation is not integrated of order one or larger. Instead, inflation is a mean-reverting, long-memory, fractionally integrated process. Consequently, a reduced-form test of the long-run Fisher effect will be invalid and any inference as to whether the hypothesis holds or not will be unsubstantiated.

Fractionally integrated models not only nest unit-root behavior within them, they also possess stationary and nonstationary mean-reverting dynamics, along with long-memory and antipersistent dependencies (see Granger and Joyeux 1980). In this paper, a bivariate fractionally integrated model is estimated for the inflation and nominal interest rate series of 17 developed countries. (1) In every instance, the country's postwar inflation series follows a mean-reverting, fractionally integrated, long-memory process. These findings are robust to monthly and quarterly measures of the consumer price index and to quarterly inflation series calculated with the gross domestic price deflator.

The results for the United States are also robust to potential regime shifts associated with changes in the Federal Reserve's monetary policy. Neither the Fed's October 1979 decision to move away from interest rate smoothing nor its October 1982 decision to weight monetary aggregates less heavily in setting monetary policy affects the stationary, long-memory behavior in U.S. inflation. It follows from the fractional integration behavior of inflation that the long-run Fisher hypothesis cannot be tested over the postwar period for these 17 industrialized countries.

The remainder of the paper is organized as follows. Section 1 discusses Bae et al.'s (2005) relative order of integration conditions for testing the neutrality of money and applies them to the long-run Fisher effect hypothesis. These conditions are then tested for in Section 2 by estimating the fractional order of integration for the 17 country's inflation and nominal interest rate series. The conclusions are in Section 3 along with some implications that fractionally integrated inflation may have on monetary policy.

1. INTEGRATION CONDITIONS

Table 1 lists the five relative orders of integration between inflation and the nominal interest rate associated with testing the long-run Fisher effect with a bivariate, fractionally integrated model (see Bae et al. 2005 for the derivation of each case). The [d.sub.[pi]] in Table 1 is the order of integration for inflation, [d.sub.R] is the order of integration for the nominal interest rates, and [[gamma].sub.R[pi]] is the long-run derivative of the nominal interest rate to a change in inflation. Lastly, L is the lag operator. These five cases amount to three possible outcomes for [[gamma].sub.R[pi]] (the outcome for each case is found in the fourth column of Table 1); (i) the long-run Fisher effect can be tested by conducting the hypothesis test, [H.sub.0] : [[gamma].sub.R[pi]] = 1; (ii) the long-run Fisher effect cannot be tested given the data (neither acceptance nor rejection of the hypothesis is possible); and (iii) the long-run Fisher effect is rejected outright.

The focus of this paper is Case (i) of Table 1. Under Case (i), FS (1993) reduced-form approach to testing the long-run Fisher effect hypothesis suffers from the Lucas (1972) and Sargent (1971) critique. Letting [epsilon](t) represent an exogenous shock, Lucas' and Sargent's critique can be understood in terms of the long-run derivative:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where R(t) is the nominal interest rate at time period t, and [pi](t) is the inflation rate at time t. If the shock does not give rise to a permanent change in inflation, [partial derivative][pi](t + k)/[partial derivative][epsilon](t) [right arrow] 0, as k [right arrow] [infinity]. This causes [[gamma].sub.R[pi]] to be undefined and the long-run Fisher effect to be untestable.

In Case (ii), because 1 [less than or equal to] [d.sub.[pi]], inflation will be permanently affected by an exogenous shock. However, the effect of the shock on the nominal interest rate will not be permanent. Because [d.sub.R] < 1, the nominal interest rate follows a mean-reverting, fractionally integrated process that when perturbed will slowly return to its preshock level. Thus, in Case (ii) the long-run Fisher effect hypothesis is rejected outright.

Except for the fractional nature of the orders...