The Fisher Hypothesis and Inflation Persistence
Evidence From Five Major Industrial Countries

This paper presents an empirical evaluation of the strength of the Fisher effect which predicts a positive relationship between the nominal interest rate and inflation in the postwar period in the five major industrial countries, utilizing recently developed time series techniques. The results suggest that the Fisher effect is stronger in France, the United Kingdom, and the United States than in Germany and Japan. It is argued that the differences in the linkage between the interest rate and the inflation rate as between the two groups of countries are reflected in the time series properties of the inflation rates, which are, in turn, partly attributable to the different extent to which monetary authorities accommodated inflationary shocks. The empirical results have a number of implications for the long-term trend in the SDR interest rate and for the financing of the Fund’s operations.

Abstract

This paper presents an empirical evaluation of the strength of the Fisher effect which predicts a positive relationship between the nominal interest rate and inflation in the postwar period in the five major industrial countries, utilizing recently developed time series techniques. The results suggest that the Fisher effect is stronger in France, the United Kingdom, and the United States than in Germany and Japan. It is argued that the differences in the linkage between the interest rate and the inflation rate as between the two groups of countries are reflected in the time series properties of the inflation rates, which are, in turn, partly attributable to the different extent to which monetary authorities accommodated inflationary shocks. The empirical results have a number of implications for the long-term trend in the SDR interest rate and for the financing of the Fund’s operations.

I. Introduction

It is important for macroeconomic policymakers to have an understanding of causes of movements in interest rates. The Fisher neutrality hypothesis, which states that nominal interest rates rise point-for-point with anticipated inflation, leaving, ceteris paribus, ex ante real rates unaffected, provides a point of departure for any theory of interest rates. The ‘classical Fisher hypothesis’ suggested by Fisher (1930) holds, for instance, in an economy without taxes in which the demand for and supply of lending determine the equilibrium real rate of interest. The nominal market interest rate then contains an inflation premium sufficient to compensate lenders for the expected loss of purchasing power associated with inflation.

The Fisher hypothesis has been the subject of a vast literature. On the theoretical side, various explanations have been given of why nominal interest rates might fail to respond one for one with expected inflation. Mundell (1963) and Tobin (1965) suggested that nominal interest rates would exhibit a less-than-unity response to expected inflation because inflation reduces real money balances. The resulting decline in wealth leads to increased real saving demand and reduced investment demand, causing a negative effect of anticipated inflation on the real interest rate. An alternative hypothesis (Fried and Howitt (1983)) suggests that inflation reduces the real rate of return on money, which is measurable as the negative of the inflation rate. It is then reasonable to suppose that inflation also reduces the real rate of return on financial assets that are close substitutes for money.

Darby (1975) and Tanzi (1976) noted that when taxes on interest or investment income are present, nominal interest rates should rise by more-than-expected inflation if the after-tax real return is to be unaffected. As empirical tests have produced somewhat ambiguous results, explanations have been sought for why the tax effect may not be as large as would be expected from the original Darby-Tanzi hypothesis. These include the possibility of the existence of fiscal illusion (Tanzi (1980)), the effects of tax evasion, the existence of tax-exempt lenders and borrowers, and capital inflows that may accompany higher interest rates induced by some tax effect. 2/

Numerous empirical studies have tested the Fisher hypothesis, most of which used data from the United States and the United Kingdom. Many of the earlier studies relied on estimation of simple static relationships using quarterly or annual data. These studies tend to support the Fisher hypothesis for the United States for the period after the Fed-Treasury Accord in 1951 until 1979 but not for the period prior to the World War II. 3/ However, recent developments in the time series econometrics literature point to possible pitfalls of this approach. This is because misleading inferences may be derived from the so-called spurious regressions when variables are nonstationary (Granger and Newbold (1974); and Phillips (1986)). Engle and Granger (1987) introduce the concept of cointegration, which provides a tool for evaluating long-run relationships between nonstationary variables. In recent years there has been an increasing number of empirical studies applying cointegration tests to the Fisher hypothesis. 4/ In particular, Mishkin (1992) applies cointegration tests to postwar U.S. interest rates and inflation rates and concludes that inflation and interest rates in the United States were nonstationary in the period 1953-1990 but they nonetheless shared common trends and hence had a stable long-run relationship.

This paper presents an examination of the Fisher hypothesis using data from five major industrial countries, namely, France, Germany, Japan, the United Kingdom, and the United States. The paper applies cointegration tests and more recently developed techniques of testing for a serial correlation common feature among stationary time series (Engle and Kozicki (1993)), depending on the time series properties of the inflation and interest rates under consideration. 5/ This study does not aim to test explicitly any of the theoretical models mentioned above. Rather, the paper attempts to compare the estimated strength of the Fisher effect among the five countries under consideration.

The results of this paper suggest the existence of a stable long-run relationship between inflation and interest rates in France, the United Kingdom, and the United States. Much weaker evidence of the Fisher effect is obtained for Germany and Japan. One explanation offered in the paper for this result concerns different time series properties of the inflation rates in the two groups of countries, which may be related to the extent to which changes in actual inflation are incorporated into expectations of future inflation. This difference may be partly attributed to the different degrees of monetary accommodation exercised in the past by the monetary authorities in the various countries.

The paper is organized as follows. The next section reviews the main difficulties in testing the Fisher hypothesis. Section III provides a discussion of the econometric methods employed in the paper. Section IV presents the empirical evidence, and Section V assesses the results and draws some policy implications. Section VI discusses the implications for the Fund of the long-term trends in the SDR interest rate. The Fund’s income and the sharing of the Fund’s financing among member countries depend, to a considerable extent, upon the level of the SDR interest rate. The final section gives some concluding remarks.

II. A Note on the Fisher Hypothesis

It is useful to begin a discussion on the Fisher hypothesis with the following equation: 6/

it=rte+bπte(1)

where

  • it = nominal interest rate known at time t for the period between t and t+1

  • rte = the ex ante real interest rate between t and t+1

  • πte = the expected inflation rate in the above period.

The coefficient b would provide an indication of the strength of the Fisher effect and the full ‘classical’ Fisher hypothesis would require b-1. 7/

The principal empirical difficulty in testing the Fisher hypothesis is the measurement of πte and rte, as both are, strictly speaking, unobservable variables. 8/ With respect to the measurement of expected inflation, two approaches are widely applied in recent empirical studies. 9/ These are the use of survey-based measures of expected inflation and the use of future actual inflation based on the assumption of rational expectations. An advantage of survey-based measures is that they can incorporate projected values of any and all determinants of inflation that market participants might think are important. However, the issue of the “rationality” of survey-based forecasts of inflation is far from settled. 10/ The rational expectations approach (Fama (1975)) assumes that inflationary expectations of economic agents in all markets tend to be fully “rational” in the sense that they are unbiased forecasts of future inflation. It should be noted that regardless of the expectation hypothesis employed in deriving expected inflation, all the empirical studies of the Fisher hypothesis are inevitably joint tests of the Fisher hypothesis and the hypothesis that inflationary expectations, however formed, are unbiased.

The ex ante real interest rate was treated as a constant in many previous studies, so that tests of the Fisher hypothesis could be conducted by regressing the nominal interest rate against a constant and expected inflation. However, this approach has been criticized on the basis that the real interest rate changes in response to changes in factors such as the productivity of capital, the price of energy, and those related to business cycles (Tanzi (1980); Wilcox (1983)). Some studies have attempted to get around this problem by introducing variables measuring supply shocks, changes in government deficits and money supply growth, and capacity utilization rates into the estimating equations. 11/ One problem with this approach, which has not been recognized in the relevant literature, is that such regressions involve a mixture of long-run equilibrium movements and short-run dynamic adjustments, and hence make it difficult to interpret the estimated coefficients. There has been increasing recognition that the Fisher hypothesis is better interpreted as a long-run equilibrium condition (as explained below) but supply shocks (such as changes in oil prices), money supply growth, and business cycle likely affect short-term movements in real interest rates.

Because there are many factors involved, it is extremely difficult to separate empirically the effects on the nominal interest rate associated with the Fisher effect from the effects on the nominal rate associated with changes in the real interest rate, which do not result directly from changes in expected inflation (Tanzi (1993)). As Summers (1983) shows, in any reasonable short-run macroeconomic model, the rate of inflation and the short-run interest rate are determined simultaneously and there is little reason to expect any stable relationship between them. Consequently, the Fisher hypothesis is better interpreted as a long-run equilibrium condition.

The issue then is how to test whether the Fisher hypothesis represents a valid long-run equilibrium condition. Recently developed time series techniques of cointegration tests offer a tool for such a task. As will be shown, cointegration analysis provides a useful interpretation of the long-run Fisher effect, while avoiding possible pitfalls associated with the more traditional methods.

III. Estimation and Testing Methods

We follow Fama (1975) and others in assuming rational expectations so that πtet+∊t, where πt represents the actual inflation rate between t and t+1, and ϵt is the forecast error of inflation, which is assumed to be orthogonal to any information known at time t. Evaluation of the Fisher hypothesis can then be conducted by testing for a significant correlation between future actual inflation and the nominal interest rate in the following regression equation: 12/

πt=α+βit+ut(2)

Alternatively, the above equation could be interpreted as a forecast equation for future inflation.

However, estimates of Equation (2) (or other forms of equation for testing the Fisher hypothesis 13/) are subject to the spurious regression phenomenon described in Granger and Newbold (1974) and Phillips (1986). Simply put, t-ratios (based on which the statistical significance of the estimated β coefficient is evaluated) could be misleadingly high if variables in the regression are nonstationary but not cointegrated (to be explained below). However, the concept of cointegration among nonstationary time series (Engle and Granger (1987)) would allow Equation (2) to be interpreted as representing a long-run equilibrium condition between interest rates and inflation. It is important, therefore, to discuss briefly the concepts of stationarity, nonstationarity, and cointegration and how they are employed in evaluating the Fisher hypothesis.

Engle and Granger (1987) suggest that a stationary time series (i) has finite variance which does not depend on time, (ii) tends to fluctuate around the mean, and (iii) has a limited memory of its past behavior (i.e., the effects of a random innovation are only transitory). A nonstationary series, however, has (i) infinite variance, (ii) wanders widely over time, and (iii) has an infinitely long memory (i.e., an innovation will permanently affect the process). Closely related to the concept of stationarity is the debate on whether macroeconomic time series are best characterized as stationary around a deterministic trend (or mean) or nonstationary with stochastic trends. 14/ There is substantial evidence in the recent literature suggesting that many macroeconomic variables are I(1) processes whose first differences are stationary. In the present context, if inflation and nominal interest rates are best represented as I(1), as is shown to be the case for three of the five countries under consideration in the next section, shocks to these variables will likely have persistent effects. In other words, movements in these series are chronic in nature. 15/

As Engle and Granger (1987) point out, if individual time series are nonstationary, it is still possible that certain linear combinations of the time series in the system are stationary. They describe such systems as cointegrated. Evidence of cointegration would suggest that there exists a long-run stable relationship between the variables under consideration as they do not move “too far” away from one another over time. Therefore, one way to evaluate the Fisher hypothesis as a long-run equilibrium condition is to test whether the residuals in Equation (2) are stationary or not. If so, expected inflation and the nominal interest rate are said to be cointegrated, with the estimated β coefficient representing the long-run relation between the two variables. Moreover, if β is found to be not significantly different from one, Equation (2) implies that the real interest rate is stationary over time. In other words, the real rate is allowed to temporarily deviate from its steady-state value due to, say, nominal or temporary real shocks. This is obviously a much less restrictive assumption than that of a constant real rate as required in many previous studies.

In the next section, univariate time series properties of nominal interest rates and inflation rates are evaluated using unit root tests. 16/ Unit root tests were conducted by computing the most widely used augmented Dickey-Fuller (ADF, see Dickey and Fuller (1981)) statistics which test the null hypothesis of a unit root against the alternative of stationarity. For those interest rates and inflation rates which are found to be best characterized as nonstationary variables, cointegration tests were conducted using two different methods.

One method is due to Engle and Granger (1987) and has been most widely used in macroeconomic empirical studies. The approach involves two steps: first, a static regression of the model represented by Equation (2) is computed, then, an auxiliary time series dynamic regression is run to test whether the residuals from the static regression are stationary or not. 17/ The Engle-Granger two-stage approach has been criticized on grounds that such tests require that one of the two variables be designated as exogenous, and that they do not have well-defined limiting distributions, implying that the critical values are sensitive to the sample size (Hall (1989)).

An alternative approach suggested by Johansen (1988) and Johansen and Juselius (1990) is based on the well-accepted likelihood ratio principle and utilizes test statistics that have an exact limiting distribution. This approach can be used to test for cointegration among a group of two or more variables which are all treated as potentially endogenous. Under Johansen’s approach, the following vector autoregressive systems are estimated:

ΔYt=Σi=1k1Γ0iΔYti+ϵ0t(3)
Ytk=Σi=1k1Γ1iΔYti+ϵ1t(4)

where Yt is a vector of the variables under consideration and Г’s are vectors of estimated coefficients. The residual vectors ϵ0t and ϵ1t can then be used to conduct the cointegration test by computing the so-called maximal eigenvalue test statistic, which evaluates the null hypothesis that there are r cointegrating vectors: 18/

τmax=Tln(1λr+1)(5)

where λr+1 is the smallest squared canonical correlations of ϵ0t with respect to ϵ1t, and T is the number of observations.

There is no a priori reason why inflation and interest rates should be nonstationary. As shown in the next section, inflation and interest rates are stationary in two of the five countries under consideration. In these cases, a static regression of Equation (2) could provide useful information for evaluating the Fisher hypothesis, as has been done in many previous studies. However, this paper employs a more recently developed time series technique called serial correlation common feature analysis (Engle and Kozicki (1993)) to evaluate the correlation between the inflation and interest rates that are stationary. Two stationary variables, which individually exhibit serial correlation, are said to have a serial correlation common feature if there exists a linear combination of the two variables that eliminates all correlation with the past and is completely unpredictable with respect to the past information set. Analogous to cointegration which provides an indicator of comovement among nonstationary variables, the existence of a serial correlation common feature indicates comovement among stationary variables. The difference is that with interest rates and inflation rates being stationary, implying frequent mean-reverting movements, comovements between the two variables would indicate a high degree of correlation between the two variables even in the short run. One intuitive interpretation would be that inflation and interest rates comove through different phases of the business cycles. On the methodological side, as noted in Engle and Kozicki (1993), an important advantage of the serial correlation common feature analysis is that it allows for simultaneous analysis of the persistence of disturbances and comovement while ordinary least-squared (OLS) estimation of Equation (2) is static in nature.

Testing for the existence of a serial correlation common feature involves two steps. The first evaluates whether an individual series exhibits serial correlation by regressing both the inflation rate and the interest rate against a constant and lagged values of both variables. The question is whether lagged inflation and interest rates provide useful information for forecasting inflation and the interest rate in the bivariate system. The test of whether past inflation and interest rates are significant in these regressions can be conducted using a Lagrange multiplier (LM) type of statistic, which is computed as TR2 from the regression and has a limiting chi-squared distribution. 19/ The second step is to run a two-stage least squares (2SLS) estimation for Equation (2) using a constant and lagged inflation and interest rates as instruments. The existence of a serial correlation common feature can then be tested using LM-type statistics, calculated as TR2 from the regression of the residuals of the 2SLS estimation against the instrumental variables (IV). Detailed proofs and procedures can be found in Engle and Kozicki (1993).

IV. Empirical Estimates of the Fisher Equation

Consumer price inflation and the three-month interest rates that are used for the calculation of the SDR interest rate 20/ at quarterly frequencies are utilized in this study. 21/ The sample periods are first quarter of 1957 to the second quarter of 1994 for Japan, the United Kingdom, and the United States, and first quarter of 1960 to the second quarter of 1994 for France and Germany, as dictated by the availability of the interest rate data taken from the International Financial Statistics. Observations on domestic call money rates are used for France for the period first quarter of 1960 to the fourth quarter of 1969 and Japan for the first quarter of 1957 to the second quarter of 1980, as data on the three-month rates for France and Japan are available only from 1970 and 1980, respectively. Charts 1 and 2, which compare the call money rates with the three-month rates in France and Japan, respectively, indicate little differences between the two rates during the subsample periods for which both rates are available. 22/ The timing of the data is as follows: a period t interest rate observation uses the end of period t-1 nominal interest rate observation, while the inflation rate for period t is computed using the period t and period t+1 consumer price index observations (from the International Financial Statistics).

Chart 1.
Chart 1.

Call Money Rate and the Three-Month Treasury Bill Rate in France

Citation: IMF Working Papers 1995, 118; 10.5089/9781451940824.001.A001

Chart 2.
Chart 2.

Call Money Rate and the Three-Month CD Rate in Japan

Citation: IMF Working Papers 1995, 118; 10.5089/9781451940824.001.A001

To determine whether inflation and interest rates contain stochastic trends or not, Table 1 presents unit root test results using ADF test statistics. The null hypothesis that inflation and interest rates are nonstationary cannot be rejected for France, the United Kingdom, and the United States, but is rejected for Germany and Japan. Consequently, cointegration and serial correlation common feature analyses are applied to the two groups of countries, respectively.

Table 1.

Unit Root Tests for Inflation and Interest Rates

article image

Significant at the 1 percent level; lags are the ‘optimal lags’ chosen as described in Campbell and Perron (1991).

Table 2 provides OLS estimates of Equation (2) and the ADF test statistics for the stationarity of the residuals for France, the United Kingdom, and the United States. Both the Durbin-Watson statistics from the static regressions and the ADF statistics from the dynamic regressions suggest rejection of the null hypothesis of no cointegration based on the critical values of the two statistics in Engle and Granger (1987).

Table 2.

Cointegration Tests of the Fisher Hypothesis: Engle-Granger Approach

article image

Significant at the 1 percent level, α and β are OLS estimates of Equation (2) with asymptotic standard errors being given in parentheses below the estimated coefficients. DW and ADF refer to the Durbin-Watson statistics and Augmented Dickey-Fuller statistics, respectively, for testing for cointegration as defined in Engle and Granger (1987).

The Johansen’s maximal eigenvalue test statistics presented in Table 3 confirm acceptance of cointegration between inflation and interest rates for France, the United Kingdom, and the United States. The estimated coefficients of β are higher than those obtained from the OLS regressions. In addition, a likelihood ratio test does not reject the null hypothesis that β is not significantly different from one for all the three countries. In short, both the Engle-Granger and Johansen cointegration tests provide evidence for the existence of a long-run stable relationship between inflation and interest rates in the three countries. Assuming rational expectations, the estimated coefficients further suggest that nominal interest rates exhibit a near-unity response to expected inflation in the long run.

Table 3.

Cointegration Tests of the Fisher Hypothesis: Johansen Approach

article image
Notes: Critical value at the 5 percent level = 15.7 for the maximal eigenvalue test; χ2(2) = a likelihood ratio test statistic for the hypothesis that β=1 and is asymptotically distributed as chi-squared with 2 degrees of freedom.

For Germany and Japan, both the OLS estimates of Equation (2) and the results from testing for a serial correlation common feature are presented in Table 4, 23/ based on which three observations can be made. First, the OLS estimates of β for Germany and Japan and the R2 from the two regressions are much lower than those for France, the United Kingdom, and the United States presented in Table 2. Second, although the IV estimate of β for Japan is substantially higher than its corresponding OLS estimate, it is still lower than the OLS estimates for the United Kingdom and the United States and much lower than the estimates from the Johansen tests presented in Table 3. Third, the hypothesis of the existence of a serial correlation common feature between inflation and interest rates is rejected for both Japan and Germany.

Table 4.

Testing of the Fisher Hypothesis in Germany and Japan

article image
Notes: Numbers in parentheses are asymptotic standard errors; DW = Durbin-Watson statistics; χ2 (3) - the common-feature test statistic which is asymptotically distributed as chi-squared with 3 degrees of freedom; Q(12) = Ljung-Box test statistic (asymptotically distributed as chi-squared with 12 degrees of freedom) which tests for serial correlation in the residuals from the instrumental variable estimation.

In summary, the results presented in this section suggest a much weaker Fisher effect in Germany and Japan than in France, the United Kingdom, and the United States. Cointegration tests for common trends in inflation and interest rates provide support for the existence of a ‘full’ long-run Fisher effect (with near one-for-one adjustment of interest rates to inflation) in France, the United Kingdom, and the United States. For Germany and Japan, the cointegration interpretation of a ‘long-run’ relation between nominal interest rates and inflation is precluded because the variables are stationary. The serial correlation common feature analysis rejects the existence of common cycles between inflation and interest rates in the two countries.

V. Inflation Persistence, the Fisher Effect, and Monetary Policy

The results from the Fisher hypothesis tests appear to be related to the time series properties of inflation and interest rates. Unit root test results suggest that inflation rates in France, the United Kingdom, and the United States are nonstationary while those in Germany and Japan are best characterized as stationary variables. Stationarity would imply that a period of accelerating inflation would be quickly followed by a period of disinflation, resulting in frequent mean-reverting movements. Nonstationarity would, however, suggest that inflation is persistent and chronic in nature. It is intuitive to argue that when inflation is persistent, movements in actual inflation are likely to be incorporated into inflation expectations. On that basis, nominal interest rates would tend to adjust to the inflation rate over time, producing common trends between inflation and nominal interest rates.

It is beyond the scope of this paper to examine why inflation is less persistent in Germany and Japan than in the other three countries. However, from a macroeconomic policy perspective, it is often argued that inflation persistence is closely related to the degree of monetary accommodation, 24/ which is likely related to, inter alia, institutional arrangements, anti-inflation sentiment within the government, and disinflation costs. 25/ In Germany, the Bundesbank is formally independent and legally obliged to achieve and maintain price stability. As a result, it may be argued that strict restrictions on the Bank’s ability to accommodate inflationary shocks have contributed to low and less persistent inflation in Germany. In Japan, although the Bank of Japan is formally linked to the Government, the monetary authorities have demonstrated historically a high degree of anti-inflation commitment.

It is widely agreed that if nominal interest rates adjust fully to the inflation rate, leaving the real rate unchanged, monetary policy would have little effect on real income growth, at least in the long run. At first glance, therefore, the results could be taken to suggest that expansionary monetary policies could be more effective in Germany and Japan than in the other three countries. However, this is too quick a conclusion. If the strength of the Fisher effect is positively related to the persistence of inflation which is, in turn, associated with the monetary authorities’ policy stance, then, it could be argued that expansionary monetary policies will remain effective only if they are unused.

VI. Implications for the Financing of the Fund’s Operations

The Fund’s income is derived mainly from periodic charges levied on the members’ use of Fund resources. 26/ The Fund sets the rate of charge at the beginning of each financial year as a proportion of the SDR interest rate so as to recover its cost of financing (mainly remuneration on creditor positions 27/) and administrative expenses and to achieve a target amount of net income to add to its reserves. When setting the proportion of the rate of charge to the SDR interest rate, the Executive Board of the Fund considers a number of factors including the use of Fund resources and creditor positions subject to remuneration.

Movements in the SDR interest rate have particular implications for the financing of the Fund’s operation. When nominal SDR interest rates fall, the proportion of rate of charge may need to be set at higher levels relative to the SDR interest rate in order to recover the Fund’s cost of financing and administrative expenses and achieve an agreed target amount of net income. Low nominal SDR interest rates may also affect the distribution of the relative shares of members in the financing of the Fund. The lower the SDR interest rate, the larger tends to be the relative share in the cost of financing the Fund of the group of members indebted to the Fund. Conversely, when SDR interest rates are rising, the rate of charge may be set at lower levels relative to the SDR interest rate and the relative share in the cost of financing of the Fund of the group of members using the Fund’s resources would tend to decrease.

Chart 3 compares the SDR interest rate and its component interest rates in 1970:1-94:2. 28/ There appears to be a declining trend in the SDR and its component interest rates since the early 1980s, despite variations associated with the business cycle. 29/ Chart 4 shows the recent relationship between the rate of charge and the SDR interest rate.

Chart 3.
Chart 3.

SDR and its Component Interest Rates

Citation: IMF Working Papers 1995, 118; 10.5089/9781451940824.001.A001

Chart 4.
Chart 4.

The Rate of Charge and SDR Interest Rate

Citation: IMF Working Papers 1995, 118; 10.5089/9781451940824.001.A001

The empirical results presented in this paper suggest that ex ante real interest rates are stationary and that as a result, any persistent up or downward trends in nominal interest rates would be associated with trends in inflation. It is widely accepted that the monetary authorities in France, the United Kingdom and the United States have demonstrated strong anti-inflation commitment since the early 1980s, which has contributed to the declining trend in inflation in these countries. 30/ Therefore, if the monetary authorities in the five major industrial countries remain committed to controlling inflation, it is perhaps likely that there will not be any significant increase in the long-term trend component of the inflation risk premium embedded in nominal interest rates and in the SDR interest rate.

VII. Concluding Remarks

This paper has evaluated the Fisher hypothesis in the postwar period in France, Germany, Japan, the United Kingdom, and the United States. Recently developed time series techniques were applied to inflation and nominal interest rates. The results from the cointegration tests suggest that there exists a long-run stable relationship between nominal interest rates and expected inflation in France, the United Kingdom, and the United States. Estimates of the coefficient on the nominal interest rate indicate further that the nominal interest rate responds near one-for-one with expected inflation in the three economies. However, both the OLS estimates and the results from the serial correlation common feature analysis suggest that expected inflation has a much weaker (linear) relationship with the nominal interest rate in Germany and Japan.

Unit root test results indicate that inflation and nominal interest rates are more persistent in France, the United Kingdom, and the United States than in Germany and Japan. It is argued that in persistent inflation, the nominal interest rate would tend to adjust fully to expected inflation over time, producing common trends between the two variables in the long run. It is further argued that the strong anti-inflation commitment by the monetary authorities in Germany and Japan has contributed to low and less persistent inflation and hence a weaker Fisher effect. Consequently, it would seem inappropriate to infer from an historically weak Fisher effect in Germany and Japan that active use of expansionary monetary policies are more effective in these two countries than in France, the United Kingdom, and the United States.

The downward trend in inflation and in the nominal interest rates since the early 1980s has been in part a result of increased commitment by the monetary authorities in controlling inflation. If the monetary authorities in the five industrial countries maintain their anti-inflation stance, the recent low levels of the nominal interest rates and the SDR interest rate would continue, perhaps, for the rest of the decade, notwithstanding variations associated with economic fluctuations, with attendant effects on the Fund’s operational income and expense and on the distribution among its members of the cost of operating the Fund.

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1/

This paper was written when the author was in the Financial Relations Division of the Treasurer’s Department. The author is indebted to Orlando Roncesvalles for advice and encouragement, and to John Berrigan, James Blalock, Owen Evans, Michael Fitzpatrick, Inci Otker, Vito Tanzi, George Tavlas, and Ann-Margret Westin for helpful comments and/or discussions. Any remaining errors, however, are the author’s own responsibility.

2/

Tanzi (1984) provides a detailed discussion of these points.

3/

See, for example, Fama (1975), Mishkin (1981), Peek and Wilcox (1983), Summers (1983), and Tanzi (1980). The absence of a Fisher effect from 1860 to 1940 is often attributed to some form of money illusion. It is argued that before the war, agents ignored inflation in making financial calculations because the level of inflation was low.

5/

In addition to the Engle-Granger approach of testing for cointegration, which is used in Mishkin (1992) and most other previous studies of the Fisher hypothesis, I also employ an alternative method by Johansen (1988) which is known to have several advantages over the Engle-Granger approach. See Section III for more details.

6/

The strict form of the Fisher hypothesis would include an additional cross-effect term, πterte, which is assumed here to be of second order importance as in most previous studies. This does not appear an unreasonable assumption, since the countries under consideration do not have hyperinflation in the sample periods used in this paper.

7/

That is, ignoring taxes and the Mundell-Tobin effect as discussed earlier.

8/

As Tanzi (1993) notes, there are two ways to define the ex ante real interest rate. One is simply the difference between the nominal interest rate and expected inflation (however measured), which, given inflationary expectations, is observable. The other is the (counterfactual) rate of interest that, ceteris paribus, would exist if there were no inflation. It is the latter definition that is relevant in empirical studies. A regression of the nominal interest rate against expected inflation and a real interest rate defined in the first way is obviously a regression of an identity.

9/

Early studies of the Fisher hypothesis followed Fisher (1930) in regressing nominal interest rates on a distributed lag of past inflation, which was used as a proxy for the expected rate of inflation. Critics of this approach stress that backward looking models of inflationary expectations tend to produce systematic forecast errors, which economic agents might be expected to correct. Another approach was to use an auxiliary equation to estimate an expected inflation rate series and then use these estimates as an exogenous variable in OLS regressions of the Fisher equation. As Pagan (1984) demonstrates, however, the use of such two-step estimators will generally result in inconsistent estimates of the variance of the estimated coefficient on the generated regressor. That is, the asymptotic t-statistics connected with the estimated Fisher effect coefficient generally overstate the true values.

10/

For the United States, the Livingston survey on inflation supplied by the Federal Reserve Bank of Philadelphia is often used in the empirical studies. Schroeter and Smith (1986) and references therein give evidence that the Livingston survey may provide a biased estimator of expected inflation. There are few studies for other major industrial countries using survey-based inflation forecasts. For an exception, see Haldane and Pradhan (1993) who study time series behavior of real interest rates among European Monetary System member countries, using survey price expectations data from European Commission sources.

11/

See, inter alia, Peek and Wilcox (1983), Tanzi (1980), and Wilcox (1983). Tanzi (1993) presents another interesting approach of dealing with the ex ante real rate. Specifically, he regresses the difference between the U.S. six-month and 12-month Treasury bills nominal rates against a constant and the difference between six-month and 12-month expected inflation rates derived from the Livingston survey. The assumption is that the ‘real rate’ for six-month Treasury bills is not systematically different from that for 12-month Treasury bills, so that the difference between the two rates could be treated as a constant.

12/

To derive Equation (2), first, assuming rte=a+ξt with a being a constant and ξt~i.i.d(0, δ2) (a less restrictive assumption will be made for the real interest rate later in the paper). Then, combining Equation (1) and the two equations for the real interest rate and expected inflation results in Equation (2), where α=-a/b, β=-1/b, and utt/b-et.

13/

Such as an OLS regression of the nominal interest rate against a constant and expected inflation and regressions which also include other variables that may influence the real interest rate.

14/

A variable containing stochastic trends belongs to a class of integrated time series, for which stationarity can only be achieved through differencing. A time series is said to be integrated of order d, denoted I (d), if it requires differencing d times to achieve stationarity.

15/

The view that inflation is nonstationary in particular sample periods does not imply that there is no tendency to mean reversion in the policy process that generates money growth and inflation rates. As noted in Mishkin (1992), high persistent inflation generated by an accommodative monetary regime such as that in the 1970s in the United States is likely to lead to a change in the regime which would reduce the inflation rate, producing a tendency for mean reversion in the long run.

16/

A time series is said to have a unit root if it is an I(1) process.

17/

The second step is achieved by computing the following ADF regression:

Δut=φut1+Σi=1PΔuti+ϵt

where Δ is the first difference operator and ρ is selected on the basis of being sufficiently large to ensure that ∊t is a close approximation to white noise. The t-ratio statistics on Φ are the ADF statistic whose critical values are tabled in Engle and Granger (1987).

18/

Note that in this paper, the null hypothesis is that of no cointegration against the alternative of one cointegrating vector. This is because with only two variables in the system, there is at most one cointegrating relationship.

19/

TR2 represents the total number of observations times the explained variance of the regression. The purpose of this step is to test whether or not cycles (serial correlation feature) exist in individual series. If not, there is no point in going further to evaluate whether the two series share common cycles.

20/

These are the three-month Treasury bill rates for France, the United Kingdom and the United States, the three-month interbank deposit rate for Germany, and the three-month certificate of deposit rate for Japan.

21/

It is often argued that long-term bond yields are more dependent on inflationary expectations than short-term interest rates. Yet virtually all Fisher hypothesis studies have limited themselves to the relationship between short-term (particularly, three-month) interest rates and short-term inflation. This is, perhaps, due to an empirical difficulty that neither current and past inflation rates nor survey data provide a guide to future long-term inflation.

22/

Statistical tests also show that the differences between the two rates are not significantly different from zero for either country.

23/

As discussed in Section II, the serial correlation common feature analysis involves two implicit steps. Table 4 presents only the test results from the second step with inflation being the normalized variable (i.e., instrumental variable estimation of Equation (2)) for a comparison with the OLS estimates of Equation (2). Results from the first step testing for serial correlation in individual series suggest the existence of serial correlation in inflation and interest rates in both countries. Furthermore, instrumental variable estimations with interest rates as the normalized variable reject the existence of a serial correlation common feature between inflation and interest rates in either Germany or Japan. In all the IV estimations, two lagged values of inflation and interest rates were used as instrumental variables. Detailed results are available from the author upon request.

24/

After all, inflation persists only if expectations of further inflation are validated by the authorities. Alogoskoufis and Smith (1991) construct an aggregate demand-supply macroeconomic model with forward-looking price-setting firms and staggered wage setting in which inflation persistence is positively related to monetary accommodation of price shocks. Alternatively, Ball (1991) employs a time-consistent model of central bank behavior to demonstrate that temporary and exogenous macroeconomic shocks trigger temporary inflation that becomes persistent only if the monetary authorities accommodate these shocks.

25/

High disinflation costs in terms of output loss would provide incentives for accommodating inflationary shocks. Chadha, Masson, and Meredith (1992) provide empirical evidence on disinflation costs in major industrial countries. One of their conclusions is that disinflation costs are related to the credibility of the policy of disinflation. In addition, relatively low disinflation costs in Japan were also attributed to more flexible labor markets, which facilitate responsiveness of prices and wages to demand conditions.

26/

The Fund also earns a modest amount of income from its holdings of SDRs and from charges on purchases. See IMF (1993) for further details.

27/

The Fund pays remuneration to a member on the amount by which its norm for remuneration exceeds the Fund’s holdings of its currency, excluding holdings that reflect the member’s use of Fund resources. The Fund has set the rate of remuneration equal to the SDR interest rate.

28/

End-quarter values. Note also that the SDR rate became fully a combined market interest rate from August 1, 1983.

29/

Note also that in the period 1983-94, the SDR rate appears to have a strong correlation with the U.S. three-month Treasury bill rate. This is, perhaps, not surprising given that the U.S. interest rate has the highest weight (40 percent). Furthermore, the component interest rates in France and the United Kingdom generally exceed the SDR rate. This compares with the interest rate in Japan which was lower than the SDR rate and the German interest rate which was lower until 1991. The higher rate in Germany since 1991 is obviously related to the effects of the German unification.

30/

Another contributing factor would be the decline in world oil price and non-oil commodity prices. Barring major supply disruptions, it is reasonable to assume no significant upward trend in the oil price. Empirical studies also suggest that much of the decline in non-fuel commodity prices is secular in nature. See Borensztein, Khan, Reinhart, and Wickham (1994) and references therein.

The Fisher Hypothesis and Inflation Persistence: Evidence From Five Major Industrial Countries
Author: Mr. Wensheng Peng