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The Fisher Hypothesis and Inflation Persistence

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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.

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

Author/Editor:

Wensheng Peng

Publication Date:

November 1, 1995

Disclaimer: This Working Paper should not be reported as representing the views of the IMF.The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate

Summary:

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.

Series:

Working Paper No. 1995/118

Subject:

Business cycles Economic growth Financial services Inflation Inflation persistence Prices Real interest rates SDR interest rate

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

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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.

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A vast literature is devoted to the size of the response of nominal interest rates to changes in expected inflation, broadly known as the Fisher (1930) effect (see Cooray, 2003). The importance of this response stems from the fact that permanent shocks to either inflation or nominal rates should not be translated into permanent disturbances to real rates themselves. Such a case would be problematic in the context of standard models of inter-temporal asset pricing. Moreover, long-run super-neutrality of money is associated with a coefficient relating interest rates to expected inflation equal to one. A value below unity implies substantial long-run non-neutralities.

Unfortunately, there is no consensus among economists about the true size of the Fisher effect, as several problems plague the empirical estimates. First, as Darby (1975) argued, the Fisher effect estimate should be greater than one in order to compensate debt holders for a lower after-tax return, since interest income is usually taxed as ordinary income. Second, the expected inflation rate is generally unobservable and when actual realised inflation is used to proxy expected inflation, an errors-in-variables bias is introduced on the estimate of the Fisher effect. Finally and more importantly, the time series properties of both interest rates and inflation rates should be considered carefully. In the event of integrated variables, the only way to establish a theoretical Fisher relationship is via co-integration techniques. However, even when applying the appropriate co-integration methods, severe problems may arise, such as the low power of co-integration tests, structural breaks and nonlinearities in the co-integrating relationship, or the performance of co-integration estimators in small samples.

In general, there is much conflicting evidence in the literature about the Fisher effect. Numerous studies have found that the slope coefficient in a regression of inflation against nominal rates is significantly different from 1, at least over certain periods. Mishkin (1992) was one of the first to suggest that the Fisher relation should be treated within the context of a co-integrated system, as in Engle and Granger (1987), but did not derive any strong conclusions due to the large standard errors of the estimated parameters. Subsequent studies used more efficient estimation procedures and generally found support for a long-run Fisher relation in the US (see Evans and Lewis, 1995, Crowder and Hoffman, 1996, Atkins and Coe, 2002, Fahmy and Kandil, 2003). Caporale and Pittis (2004) show that the inability of the frequently employed estimators to provide efficient estimates in small samples is likely to be responsible for the over-rejection of the Fisher hypothesis. Once the estimators with the best properties are chosen, the evidence is strongly supportive of the Fisher effect in the US.

Turning to studies examining whether the Fisher relationship holds internationally, Rose (1988) examined the integration properties of nominal interest rates and inflation for 18 OECD countries. The author concluded that inflation does not appear to have a unit root, while nominal interest rates do. By contrast, Koustas and Serletis (1999) established that the Fisher effect conditions hold for a set of 10 industrialised countries, without, however, establishing a unit coefficient. With the development of panel co-integration techniques, several authors examined the international Fisher effect in a panel setting. For example, developing two new panel co-integration tests for the null of no co-integration, Westerlund (2008) showed that the null can be safely rejected for a panel of 20 OECD countries. The author provided evidence of a unit slope on inflation, thus lending support to an international Fisher effect. Moreover, Coakley et al. (2006), motivated by panel data studies on the Fisher and other economic relationships, provided insights into the impact of error cross-section dependence and persistent autocorrelation on panel regression estimates.

Another strand of the literature, developed relatively recently, takes another route and attempts to explain the failure of the Fisher effect due to either nonlinearities or structural breaks which may exist in this equilibrium relationship. Bierens (2000) and Lanne (2006) found that interest rates and inflation shared common nonlinear trends. Similar evidence was provided by Kapetanios et al. (2003) and Koustas and Lamarche (2010) who found that the process of the real interest rate exhibited asymmetric mean reversion, while stationary. Christopoulos and Leon-Ledesma (2007) showed that the co-integrating relationship between US interest rates and inflation was a nonlinear one. The authors attribute the less-than-proportional relationship found in the literature to this nonlinearity. On the other hand, Haug et al. (2011) provided evidence in favour of a linear Fisher relationship when accounting for structural breaks in the co-integration equation. However, in the majority of cases, their findings could not support the assumption that nominal interest rates and inflation move one-to-one in the long run.

In this study, we also focus on the empirical examination of the long-run Fisher effect for 19 OECD countries. Our main objective is to investigate whether the empirical failure of the Fisher effect is linked to the likely distorted small-sample performance of the co-integration estimators under time-varying dynamics. Previous studies that introduced time-varying dynamics in the analysis of co-integrated variables include Bierens and Martins (2010) and Koop et al. (2011). Both studies developed a vector error correction model which allows the co-integration relationship to evolve over time. Our approach differs since, under our data generating process (DGP), the coefficient of the co-integration equation is time invariant, while the time-varying dynamics are introduced in the process of the co-integrating error and the error that drives the regressor.

Our analysis is motivated by the potential of relevant shifts in policy conduct. Specifically, changes in monetary policy regimes are likely to be an important source of variation in the processes governing both real interest rates and inflation rates. In a similar mode, Haug et al. (2011) allowed for a time-varying co-integrating coefficient subject to breaks, probably induced by shifts in monetary policy stance. However, instead of allowing for abrupt regime changes, our error model parameters shift over time in a smooth and gradual fashion consistent with interest-rate smoothing monetary policy. Trecroci and Vassalli (2010) modelled monetary policy reaction functions with a time-varying parameter model and provided an extensive discussion on its appropriateness.

We put forward a wide class of processes, which allow for more general heterogeneity properties in the data similar to those encountered in empirical applications. Specifically, we model the co-integrating error process and the error that drives the inflation process as a vector autoregressive model with either autoregressive or random coefficients. Interestingly, this class of DGPs is likely to satisfy the conditions for the applicability of the functional central limit theorem (FCLT), thus allowing for asymptotics of integrated processes to be derived and restoring the asymptotic optimality of the common co-integration estimators (Phillips and Durlauf, 1986). The behaviour of various co-integration estimators in the presence of time-varying coefficients is then examined. By means of Monte Carlo simulations, we show that these time-varying dynamics affect the behaviour of all the co-integration estimators considered in this study, causing significant size distortions when testing the Fisher effect. Our findings suggest that among the estimators under scrutiny, the augmented autoregressive distributed lag (AADL) estimator (Pesaran and Shin, 1999) appears to be the most robust estimator to time-varying dynamics, closely followed by the fully modified least squares (FMLS) estimator (Phillips and Hansen, 1990).

As a second step in our analysis, we estimate the Fisher equation and base our statistical tests on simulated critical values instead of asymptotic ones. Taking this route, we find that the Fisher effect survives the empirical evidence irrespective of the estimator choice, with just a few exceptions. We, therefore, conjecture that a possible explanation for the scarce evidence of an international Fisher effect in the literature is the poor small-sample performance of the co-integration estimators under a DGP with time-varying coefficients. A word of caution is in order here. Our findings do not rule out the possibility of alternative specifications, such as regime switching or breaks in either the error dynamics or the co-integration parameter.

The layout of this paper is as follows: Section 2 provides a discussion of the Fisher equation and introduces the DGP for the relationship between interest rates and inflation. Next, we examine the effect of time-varying dynamics on the behaviour of various co-integration estimators. Section 3 presents the estimates of the Fisher equation obtained by various estimators and discusses the main findings of our empirical analysis. Finally, Section 4 summarises the main findings of the paper.

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The Fisher effect in the presence of time-varying coefficients

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A vast literature is devoted to the size of the response of nominal interest rates to changes in expected inflation, broadly known as the Fisher (1930) effect (see Cooray, 2003). The importance of this response stems from the fact that permanent shocks to either inflation or nominal rates should not be translated into permanent disturbances to real rates themselves.

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What Is The International Fisher Effect (IFE)?

The International Fisher Effect (IFE) elucidates that the difference in nominal interest rates reflects the currency exchange rate between two countries. Irvin Fisher introduced the theory in the 1930s. Irvin was an American economist. This theory is used for predicting spot currency variation.

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The theory claims that if a country's domestic nominal interest rate is higher than its trading pair, then the domestic currency exchange rate is likely to decline. The theory makes certain assumptions that deviate from real-world scenarios.

International Fisher Effect (IFE) Explained

The international Fisher effect elucidates that the difference in nominal interest rates reflects the exchange rate between two countries. Therefore, it is used to calculate and predict a nation's inflation rate.

Before venturing further, let us first define the nominal interest rate. In finance and economics, the term ' nominal interest rate' refers to the interest rate that is not adjusted for inflation. However, it is closely linked to inflation; the nominal interest rate also increases when inflation increases. Similarly, when deflation occurs, nominal interest rates plummet.

Banks and financial institutions use nominal interest rates to express the interest imposed example, when a bank offers car loans at 10% interest; the banker is referring to the nominal interest rate. That is, it does not consider hidden fees, inflation, and other charges.

The real interest rate, therefore, is the sum of the nominal interest rate and the projected inflation rate. For investors, the real interest rate is more important.

Formula

The international fisher effect formula is as follows.

RR nominaldenotes the nominal rate of return.

RR real denotes the real rate of return.

Calculation

Now, let us look at the international Fisher effect calculation.

Let us consider two currencies: the US dollar To Indian Rupee. Let us assume that the currency pair exchange rate for USD/INR is 81.99. In this scenario, India's nominal interest rate is 4% and the US's nominal interest rate is 5%.

To calculate the future spot rate, the current spot exchange rate is multiplied by the current foreign and domestic interest ratio.

Thus,

Expected Future Spot Rate = 81.99 (1.04/1.05)

Expected Future Spot Rate = 81.209

The future spot exchange rate of USD/INR is 81.209. So, according to Fisher's theory, due to the decline in the spot exchange rate from 81. concerning the Indian rupee will lose its future value.

Current USD investors will get a lower interest rate on it, but they will earn profits when the USD value increases (concerning the Indian Rupee).

Advantages And Disadvantages

Following are the international fisher effect advantage and disadvantages.

Investors find it useful, as it helps them determine an investment's real rate of return.

It is used as an indicator to predict future inflation (of a country). Analysts, use the change in interest rates to determine inflation rate projections.

Now, let us look at the disadvantages.

It assumes that capital has a free flow. When this does not occur, the projections deviate from real-world market conditions.

The nominal rate of return cannot be considered the most accurate indicator of exchange rates. Nevertheless, even though central banks try to control it, they've had moderate success.

Many economists believe that this method of calculating inflation lacks accuracy. But, again, the overt reliance on market rates is the limitation. Markets are volatile; they are unpredictable by definition; using market rates to predict inflation can result in false positives.

International Fisher Effect And Interest Rate Parity

The International Fisher Theory elucidates the difference in nominal interest rates between two countries. On the other hand, interest rate parity is a scenario where the forward discount At the same time, higher interest currency offsets the differential between the interest rates of two countries.

The international fisher theory claims that high-interest rates lead to high inflation. The interest rate parity claims that an investor cannot earn more by investing in a foreign country that offers higher interest on deposits and investments.

The International Fisher Theory cites the forward rate of foreign currency as the cause behind the difference in interest rates. In comparison, the interest rate parity concept defines the disparity between foreign currency spot rates.

Difference Between Fisher Effect And The International Fisher Effect

The Fisher Effect signifies the variation in nominal interest rates to indicate inflation; it does not associate the concept with currency exchange. In contrast, the International Fisher Theory connects the dissimilarity of currency exchange rates with the nominal interest rates of the two countries.

The Fisher Effect elaborates that the real rate of return is equal to the nominal rate minus inflation; IFE simply extends the concept to currency markets.

The Fisher Effect claims that monetary measures dictate real interest rates. On the other hand, IFE claims that the forward rate of foreign currency causes a difference in interest rates.

Frequently Asked Questions (FAQs)

Recommended Articles

This article has been a guide to what is International Fisher Effect. Here, we explain its formula, calculation, advantages, and relation with interest rate parity. You can learn more about it from the following articles -

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The International Fisher Effect (IFE) elucidates that the difference in nominal interest rates reflects the currency exchange rate between two countries. Irvin Fisher introduced the theory in the 1930s. Irvin was an American economist. This theory is used for predicting spot currency variation.

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Fisher Effect Definition and Relationship to Inflation

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The Fisher Effect is an economic theory created by Irving Fisher that describes the relationship between inflation and both real and nominal interest rates.

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How real is the Fisher effect? As advocated by Fisher (1930), it is possible for the real and nominal interest rates to move in opposite directions in response to a rise in expected inflation. There are two channels through which inflationary expectations may affect interest rates. These effects are often documented in macroeconomic textbooks as the liquidity and Fisher effects.

According to the liquidity effect, ¹ a rise in inflationary expectation increases the cost of holding cash balances and decreases agents' incentives for liquidity. Agents react by economizing their holdings of cash balances and increasing their demand for financial assets. Subsequently, the increased supply of loanable funds decreases the price of credit, i.e., the real interest rate.

The effect on the ex post real interest rate is one factor that determines the relation between inflation and the interest rate. Fisher (1930) emphasizes, however, the effect of inflationary expectation on financial markets and, in turn, market interest rates. While the real price of credit may decrease following a rise in inflationary expectations, traders in financial markets demand a compensation for the expected rise in inflation. That is because inflation is likely to offset part of the real return on financial assets. Consequently, an inflationary premium is added to the real price of credit to hedge against inflation. The realized rate of return is the nominal interest rate, which accounts for the real interest rate plus inflationary expectation. Fisher advocates that the increase in inflationary premium is likely to dominate the reduction in the real interest rate such that the nominal interest rate increases following a rise in inflationary expectations.

We attempt to investigate the reality of the Fisher effect in which higher nominal interest rates are associated with higher inflation. The Fisher effect is widely accepted for the period after the Fed-Treasury Accord in 1951 until October 1979 in the US. ² It was expected, however, that the level of interest rates has no ability to predict future inflation in the US after the change in the design of monetary policy in October 1979 (Barsky, 1987). ³ Towards a formal examination of the Fisher effect in the latter period, this study analyzes the relation between the interest rate and inflation using monthly data for assets of varying maturity in the 1980s and early 1990s. The ex post real interest rate is the difference between the nominal rate of interest and the ex post rate of inflation. Attempts will be made to answer questions that have repeatedly arisen in the literature. Given the negative effect of expected inflation on the real interest rate, how strong is the so-called Fisher effect in which nominal interest rates reflect changes in expected inflation? It is interesting to know how well the term structure of nominal interest rates helps predict future movements in inflation. The results will determine the relative importance of the Fisher effect and the liquidity effect to the relation between nominal interest rates and inflation for assets of varying maturity.

Recent research works on the liquidity effect include Coleman, Gilles, and Labadie (1992) and Leeper and Gordon (1992). Both studies investigate the presence of the liquidity effect using short-term interest rates. Recent research works on the validity of the Fisher effect include Evans and Lewis (1995), Fama (1990), Mishkin (1992), Soderlind, 1998, Soderlind, 2001, and Wallace and Warner (1993). Fama supports the view that the term structure of interest rates does contain some information about future movement of inflation. Using a two-step OLS cointegration methodology, Mishkin examines how changes in expected inflation are associated with changes in nominal interest rates in the short run. Wallace and Warner investigate conditions under which innovations in short-term inflation will be transmitted to long-term as well as short-term interest rates. Evans and Lewis, like Mishkin, examine cointegration between inflation and nominal interest rates in the short run, employing a different OLS cointegration methodology.

Our study contributes to the investigation of the Fisher effect by examining the relation between nominal interest rates and expected inflation for varying-maturity assets. Unlike previous investigations, the data frequency is monthly in our study. Subsequently, we vary assets' maturity consecutively and consistently with the relevant inflation rate to study their relation at varying maturity. Further, we utilize cointegration techniques to add a new dimension to the investigation of the relation between inflation and the interest rate. For this investigation, we follow the approach suggested by Johansen and Juselius (1990). ⁴ The advantage of the cointegration technique stems from its ability to detect the long-run (stable) relationship between the interest rate and inflation, except for random transitory components that wash out over time.

The Fisher effect appears more dominant on the relation between inflation and nominal interest rates. The ability of nominal interest rates to forecast future inflation increases with maturity until they move in a one-to-one relationship for assets of 5-year maturity. Thus, while the Fisher effect appears negligible for short-term interest rates, as suggested by Mishkin (1991), the inflationary premium dominates the reduction in real return as the maturity of financial assets increases.

The remainder of the investigation is organized as follows. Section 2 outlines the theoretical background for the determinants of the relation between inflation and the interest rate. Section 3 investigates the relation between the term structure of the nominal interest rate and the inflation rate. First, we investigate the relation between the slope of the yield curve and the inflationary spread over time. Second, we analyze the long-run relation between the nominal interest rate and the inflation rate using recently developed cointegration techniques. Finally, a summary and conclusion are provided in Section 4.

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The Fisher effect: new evidence and implications

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Using monthly data in the 1980s and early 1990s, our results do not support the short-run Fisher effect since short-term interest rates are associated...