Academic journal article Seoul Journal of Economics

New Empirical Evidence for the Fisher Relation: Integration and Short-Run Instability

Academic journal article Seoul Journal of Economics

New Empirical Evidence for the Fisher Relation: Integration and Short-Run Instability

Article excerpt

(ProQuest: ... denotes formulae omitted.)

I. Introduction

The Fisher relation is a key theoretical relation that underlies many important results in economics and finance. This relation describes that the nominal interest rate has a stable one-for-one relation with the expected rate of inflation. Thus, the Fisher relation implies a constant or stable level of the "real interest rate" that is equal to the nominal interest rate minus expected inflation. Typical economic theory assumes that the real interest rate is a constant or a stationary variable fluctuating around a constant mean, as implied in the Fisher hypothesis. Although the Fisher relation looks a simple relation, the empirical analysis is somewhat complicated with mixed results. In this paper, we examine the Fisher relation and related issues for data from the U.S. and Korea based on some recently developed econometric methods.

Since Fama (1975) pioneered the empirical work on the Fisher relation, many researchers have investigated data for the Fisher relation. The hypothesis that the real interest is constant was studied by Nelson and Schwert (1977), Garbade and Wachtel (1978), Mishkin (1981, 1984), and Fama and Gibbons (1982). Correlation between the inflation rate and a nominal interest rate (Fisher effect) was studied by Nelson and Schwert (1977), as well as Fama and Gibbons (1982), Summers (1982), Huizinga and Mishkin (1986), and Mishkin (1990). An alternative approach to the empirical Fisher relation has been used by Rose (1988), Atkins (1989), Mishkin (1992), and Wallace and Warner (1993) based on the concepts of unit roots and cointegration. Nominal interest rates and inflation usually have nonstationary properties (Crowder and Hoffman 1996). In such a situation, data support the Fisher relation if the real interest rate is stationary (Mishkin 1992). Often, however, stationarity of the real interest rate is not well confirmed by U.S. data (Rose 1988; Walsh 1987).

In this paper, we examine why the existing evidence in favor of the Fisher relation is weak and mixed, especially in works based on the concepts of unit roots and cointegration. Our analysis is based on the conjecture that weakness of the evidence is due to short-run instability in the relation. We analyze this conjecture based on the following two approaches. First, we apply the partial-sample instability tests of Andrews and Kim (2006) to detect such short-run instability. Our result shows clear evidence for the existence of such short-run instability for data from the U.S. and Korea in the postwar era. Second, we examine how much the partial-sample instability affects the long-memory property of the real interest rate based on the concept of fractional integration. A higher fractional integration (longer memory) implies a higher tendency of nonstationarity. Our result indicates that short-run instability causes a substantial increase in the coefficient of fractional integration, which implies an increase in the tendency of nonstationarity.

The paper is organized as follows. Section II introduces the Fisher relation and related issues to be studied in this paper. Section III explains data used in the paper. In Section IV we analyze partial-sample instability of the Fisher relation; in Section V, the fractional integration property of the real interest rate is examined. Section VI concludes the paper.

II. The Fisher Relation and Related Issues

The Fisher relation explains how the interest rate is determined. It describes that the nominal interest rate has a stable one-for-one relation with the expected rate of inflation. In other words, the Fisher relation describes a stable level of the "real interest rate" that is equal to the nominal interest rate minus expected inflation. In terms of ex-ante variables, the relation is written as

... (1)

where πte+1 is the expected inflation from period t to period t+1; rt* and it are the ex-ante real interest rate and the nominal interest rate at time t, respectively. …

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