Cointegration tests of the Fisher Hypothesis with variable trends in the world real interest rate.

• Author: Strauss, Jack

1. Introduction

   After seventy years, the Fisher hypothesis has proven to be one of the most durable and influential theories in economics. Yet after years of debate and testing, the empirical accuracy of the proposition remains in question. The Fisher hypothesis simply states that a one point increase in inflation leads to a one point increase in the nominal interest rate leaving real interest rates unchanged. This relationship does not rule out the possibility of other variables influencing the real interest rate or variable trends in the real interest rate arising from sources other than inflation. This paper merges the literature on real interest rate parity with tests of the Fisher hypothesis to control for variable trends in the real interest rate.

   From the beginning, tests of the Fisher hypothesis yielded mixed results. Studies such as Fama [15], Carr, Pesando and Smith [7], Cargill [6], Levi and Makin [28], Peek and Wilcox [37], Hoover [24], and Mishkin [33] have supported inflation neutrality and the Fisher hypothesis. However, other studies present evidence against the hypothesis [43; 31; 32; 3; 20; 42; 8]. Beginning with Nelson and Plosser [36], evidence of variable trends in both inflation and nominal interest rates began to build. Several recent papers address this issue and use cointegration tests to explore the long-run relationship between inflation and interest rates.

   Unfortunately, the cointegration tests also yield mixed results. For example, Rose [3

   The presence of a variable trend in real interest rates offers one plausible explanation for the ambiguity of these cointegration tests. The real interest rate, which is equal in the long-run to the return on capital, can be influenced by both temporary factors (such as fiscal or monetary policy) or permanent factors (such as technological shift parameters and permanent tax rate changes). King, Plosser, Stock, and Watson [27] supply evidence from the U.S. economy that the real interest rate is related to business cycle phenomena and is nonstationary. In a multicountry study, Bosner-Neal [5] reports that monetary regime shifts influence the real interest rate and Rose [38] shows that the real interest rate is unstable in the U.S. and other OECD economies.

   In addition to evidence on the univariate properties of real interest rates, theory and empirical evidence indicate a link between real interest rates across countries. Studies such as Mishkin [31; 36], Cumby and Obstfeld [11], Cumby and Mishkin [12], Merrick and Saunders [30], Gaab, Granziol and Horner [21], Modjtahedi [34], and Dutton [13] find correlations of real rates across economies. Cumby and Mishkin for instance find that "there is strong evidence that there is a positive relationship between movements in the U.S. real interest rate and those in Europe." Using cointegration tests, Modjtahedi [34] investigates the long-run relationship between real interest rates and finds cointegration between interest rates across countries. The existence of a common variable trend in real interest rates across countries suggests a specification of the Fisher equation that includes this variable trend.

   This paper tests the Fisher hypothesis using quarterly data from Canada, France, Germany, U.K., Japan, and Italy over the period 1973-1989. Our analysis includes the U.S. real interest rate to account for variable trends in the world real interest rate. We analyze long-run relationships between inflation, nominal interest rates, and the U.S. real interest rate in each of the six countries. This paper explores these relationships using the multivariate cointegration methodology proposed by Johansen [25] and Johansen and Juselius [26]. The Johansen approach allows a test of the Fisher hypothesis in a trivariate framework and avoids drawbacks of the Engle-Granger regression methodology. Unlike the static Engle-Granger approach, the Johansen approach allows for dynamic interrelationships among variables, simple tests of restrictions, and tests for the number of cointegrating vectors.

2. A Basic Model of Interest Rates

   The Fisher hypothesis asserts that a one point rise in inflation leads to a one point rise in nominal interest rates. Tests of this assertion are complicated by the fact that innovations unrelated to inflation affect both real and nominal interest rates and that all three series appear non-stationary. We derive an empirical model based on real interest parity, which allows for tests of the Fisher hypothesis. Consider the Fisher equation for country j:

   [Mathematical Expression Omitted]

   where

   [i.sup.j] = the nominal interest rate in country j,

   [[Pi].sup.ej] = the expected inflation rate in country j, and

   [r.sup.ej] = the expected real interest rate in country j.

   Equation (1) describes a long-run relationship between domestic nominal interest rates, expected inflation and ex ante domestic real interest rates in country j. Tests of the Fisher hypothesis often proceed based on the assumption that the real interest rate is constant over time. Recently, King, Plosser, Stock, and Watson [27], Bosner-Neal [5], and Modjtahedi [34] provided evidence that the real interest rate varies over time and is non-stationary. We account for non-stationary real interest rates based on the equilibrium relationship between real interest rates across countries:

   [Mathematical Expression Omitted]

   where [r.sup.ew] denotes the expected world real interest rate.

   Equation (2) combines real interest parity with the possibility that inflation effects real interest rates. If real interest rates are equalized across countries, then [[Beta].sub.0] = 0 and [[Beta].sub.1] = 1. The parameter [[Beta].sub.0] may deviate from zero as a result of a risk premium. Likewise transaction costs or differences in tax rates across countries may cause [[Beta].sub.1] to differ from one, and in the extreme case of a closed economy [[Beta].sub.1] may equal zero. Empirical evidence supports a relationship between real interest rates across countries, but suggests that [[Beta].sub.1] lies between zero and one [10; 21; 30]. Modjtahedi [34] corroborates the existence of such a relationship, by finding evidence of cointegration among real interest rates across countries. This result of cointegrated real interest rates suggests that all permanent innovations to the countries real interest rate stem from innovations in the world real interest rate, and thus...