The Fisher hypothesis: a multi-country analysis

This paper tests whether the Fisher hypothesis holds for a sample of 26 countries by assessing the long run relationship between nominal interest rates and inflation rates taking into consideration the short run dynamics of interest rates. The empirical evidence supports the hypothesis that there is a one-to-one relationship between the interest rate and inflation for more than half of the countries under study.     

The Fisher effect: new evidence and implications

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 with negligible changes in expected inflation. However, inflation and nominal interest rates exhibit common stochastic trends in the long run. Consequently, the correlation between nominal interest rates and inflation rates increases with maturity until they move in a one-to-one relation at long horizon. This is evident by the correlation coefficients of the Johansen test for cointegration that increase with the maturity of US government securities from 2 to 5 years.     

A note on the specification of the fisher equation under inflation uncertainty

The effect of uncertainty on the relationship between the nominal interest rate and the expected rate of inflation, the Fisher equation, is examined both theoretically and empirically. It is found that the coefficient of the expected rate of inflation is significantly below unity. Variable rates of inflation tend to effect the nominal rate of interest positively, but real yields are apparently effected only by expected inflation, but not its variance.     

Evaluating the Fisher effect in long-term cross-country averages

This article uses long-term cross-country data to examine the Fisher hypothesis that nominal interest rates respond point-for-point to changes in the expected inflation rate. The analysis employs bounded-influence estimation to limit the effects of hyperinflation countries such as Brazil and Peru. Contrary to the results in Duck (1993), the present evidence does not support a full Fisher effect. By extending the empirical model to account for cross-country differences in sovereign risk, we find evidence consistent with the idea that interest rates fail to fully adjust to inflation due to variation in the implicit liquidity premium on financial assets.     

The effects of inflation uncertainty on interest rates: a nonlinear approach

In this article, we investigate the effects of inflation variability on short-term interest rates within a nonlinear smooth transition regression framework. The test results suggest that only the conditional mean of the inflation is a nonlinear process whereas the conditional variance is time variant but linear. Using the square root of conditional variance as a proxy for inflation risk, we estimate Fisher equation augmented with inflation risk. Although the estimated Fisher equations suggest that inflation risk reduces short-term interest rates, we find that the effects of inflation risk on interest rates are regime-dependent. Particularly, we find that the negative effects of inflation variability on nominal rates are greater in low-inflationary regimes when compared to high-inflationary regimes. On the other hand, it is found that both inflation and inflation uncertainty raise the expected inflation effect.     

The inflationary bias of real uncertainty and the harmonic Fisher equation

Summary. We argue that real uncertainty itself causes long-run nominal inflation. Consider an infinite horizon cash-in-advance economy with a representative agent and real uncertainty, modeled by independent, identically distributed endowments. Suppose the central bank fixes the nominal rate of interest. We show that the equilibrium long-run rate of inflation is strictly higher, on almost every path of endowment realizations, than it would be if the endowments were constant.Indeed, we present an explicit formula for the long-run rate of inflation, based on the famous Fisher equation. The Fisher equation says the short-run rate of inflation should equal the nominal rate of interest less the real rate of interest. The long-run Fisher equation for our stochastic economy is similar, but with the rate of inflation replaced by the harmonic mean of the growth rate of money.Received: 25 February 2005, Revised: 26 May 2005, JEL Classification Numbers: C7, C73, D81, E41, E58.An earlier version of this paper “Inflationary Bias in a Simple Stochastic Economy,” as a 2001 Cowles Foundation Discussion Paper No. 1333.     

A panel analysis of the fisher effect with an unobserved I(1) world real interest rate

The Fisher effect states that inflation expectations should be reflected in nominal interest rates in a one-for-one manner to compensate for changes in the purchasing power of money. Despite its wide acceptance in theory, much of the empirical work fails to find favorable evidence. This paper examines the Fisher effect in a panel of 21 OECD countries over the period 1983–2010. Using the Panel Analysis of Non-stationarity in Idiosyncratic and Common Components (PANIC), a non-stationary common factor is detected in the real interest rate. This may reflect permanent common shifts in e.g. time preferences, risk aversion and the steady-state growth rate of technological change. We therefore control for an unobserved non-stationary common factor in estimating the Fisher equation using both the Common Correlated Effects Pooled (CCEP) and the Continuously Updated (Cup) estimation approach. The impact of inflation on the nominal interest rate is found to be insignificantly different from 1, providing support of the Fisher effect.     

Money Demand in an EU Accession Country: A VECM Study of Croatia

The paper estimates the money demand in Croatia using monthly data from 1994 to 2002. A failure of the Fisher equation is found, and adjustment to the standard money‐demand function is made to include the inflation rate as well as the nominal interest rate. In a two‐equation cointegrated system, a stable money demand shows rapid convergence back to equilibrium after shocks. This function performs better than an alternative using the exchange rate instead of the inflation rate as in the ‘pass‐through’ literature on exchange rates. The results provide a basis for inflation rate forecasting and suggest the ability to use inflation targeting goals in transition countries during the EU accession process. Finding a stable money demand also limits the scope for central bank ‘inflation bias’.     

The Fisher effect,survey data and time-varying volatility

In this paper we study the Fisher hypothesis using Livingston survey data on inflation expectations. We propose a simple model for the ex-ante real interest rate where the standard deviation of survey forecasts is used to correct for heteroskedasticity. The findings of this paper contradict earlier studies. We find supportive evidence for the Fisher hypothesis that the nominal interest rate and expected inflation move one-for-one both in the short and the long run. Our results also suggest that the change of US monetary policy does not have significant effect on the dynamics of the ex-ante real interest rate such as previous work assumes.     

On some neglected implications of the Fisher effect

Following the lead of Fama [American Economic Review 65 (1975) 269–282] and of other influential articles, such as Mishkin [Journal of Monetary Economics 30 (1992) 195–215], it has become standard to interpret the Fisher effect as the ability of short-term interest rate to predict future inflation. However, in this article we demonstrate that by restricting to zero the instantaneous response of expected inflation to an interest rate shock, one can identify a disturbance that economic agents, according to the Fisherian framework, should evaluate as transitory. An important implication of this result is that short-term nominal interest rates cannot be interpreted as predictors, at least not long-run predictors, of inflation. We illustrate this result with an empirical application to US postwar data.     

Neo‐Fisherism and inflation control

According to conventional central banking wisdom, an inflation‐targeting central bank should increase (decrease) its nominal interest rate target when inflation is above (below) its target. According to neo‐Fisherites, conventional central bankers have the sign wrong. Essentially all mainstream macroeconomic models tell us that increases in nominal interest rates increase inflation—in the short run and in the long run. This paper reviews neo‐Fisherian theory and evidence and addresses issues relating to inflation control in low real interest rate environments.     

Modifying Taylor reaction functions in the presence of the zero‐lower‐bound — Evidence for the ECB and the Fed

We propose an alternative way of estimating Taylor reaction functions if the zero‐lower bound on nominal interest rates is binding. This approach relies on tackling the real rather than the nominal interest rate. So if the nominal rate is (close to) zero central banks can influence the inflation expectations via quantitative easing. The unobservable inflation expectations are estimated with a state‐space model that additionally generates a time varying series for the equilibrium real interest rate and the potential output — both needed for estimations of Taylor reaction functions. We test our approach for the ECB and the Fed within the recent crisis. We add other explanatory variables to this modified Taylor reaction function and show that there are substantial differences between the estimated reaction coefficients in the pre‐ and crisis era for both central banks. While the central banks on both sides of the Atlantic act less inertially, put a smaller weight on the inflation gap, money growth and the risk spread, the response to asset price inflation becomes more pronounced during the crisis. However, the central banks diverge in their response to the output gap and credit growth.     

Information content of U.S. treasury inflation-indexed bonds

U.S. Treasury inflation-indexed bonds are designed to provide a stable real return before taxes. A comparison between these bonds and conventional bonds reveals that the effective real yield of U.S. Treasury inflation-indexed bonds is attractive. The econometric results suggest, however, that the real rate provided by U.S. Treasury inflation-indexed bonds is not independent of inflation, implying that the Fisher hypothesis is contradicted by the data. An implication of negative correlation between the real rate and inflation is that the time to buy U.S. Treasury inflation-indexed bonds is when inflation is low. While the yields on U.S. Treasury inflation-indexed bonds are shown to reflect inflation by a lag of about one month, nominal interest rates do not fully adjust to inflation. The author would like to thank Richard A. Cohn and Mahmoud Wahab for their advice and comments.     

市场结构反转下之费雪效应研究

本文主要目的系考量结构改变风险下,对台湾地区费雪效果之再检验。模型的使用选择ZivotandAd-rews(1992)对ADF单根检定之修正模型(简称Z&A修正模型)。该模型的优点,在于允许结构断裂点(break-point)由资料特性内生(endogenizing)决定,而非研究者主观判断。过去文献指出,检验费雪效果之结果,与选用之时间序列资料之定态与否有高度相关,因此本研究使用修正后之Z&A修正模型,更严密的检视资料分析过程之前置检验阶段,将有助于后续分析获得较精确之推论结果。Z&A修正模型发现名目利率、通货膨涨率之水平项即为定态序列,在修正冲击(shock)对序列的长期影响后,两总体变数在长期间是相当稳定的。而其进一步向量自我回归分析结果,显示台湾地区之费雪效果在此一期间并无法被支持。     

Correct cointegration tests of the long-run relationship between nominal interest and inflation

The Fisher (1930) hypothesis suggests that a long-run equilibrium relationship exists between the non-stationary series: nominal interest and expected inflation. Testing such a cointegrating relationship is complicated by the presence of the unobserved ex antereal rate of interest in residuals from the cointegrating regression. Assumptions concerning the stochastic properties of the expected real rate of interest are examined, and two proxies for the ex antereal rate are employed in multivariate cointegration tests of the Fisher hypothesis.     

Monetary deregulation and inverting the inverted fisher effect

We find evidence that deregulation allowing interest payments on checkable deposits decreased (increased) the sensitivity of the real (nominal) rate of interest to expected inflation. Our results provide further confirmation of the Inverted Fisher Effect.     

Budget deficits,short-term real interest rates and the specification of expected inflation: an empirical investigation

The purpose of this paper is to illustrate whether empirical estimates of the effects of budget deficits on short-term real interest rates are sensitive to the choice of the expected inflation variable. Survey data on expected inflation and the rational expectations method described by Mishkin (1981) are used to construct two measures of the short-term real interest rate. Results for two previous studies on this deficit-interest rate relationship are re-estimated using these measures of expected inflation and the interest rate variables. Additional results reported in this paper further indicate that empirical estimates of the interest rate effects of budget deficits are sensitive to the choice of the expected inflation variable. In addition to the choice of the inflation variable, a number of other robustness tests are included. We are able to conclude that (1) increases in budget deficits do not generally raise short-term real interest rates and (2) short-term real interest rates are not independent of the expected inflation variable.

The rate of interest is always based upon expectation, however little this may be justified by realization. Man makes his guess of the future and stakes his action upon it … Our present acts must be controlled by the future, not as it actually is, but as it appears to us through the veil of chance (Fisher, 1907, p. 213).     

Cross-Country Evidence on the Ability of the Nominal Interest Rate to Predict Inflation

This paper examines the viability of using short-term interest rates to forecast inflation as implied by the Fisher hypothesis. A major problem with this approach lies in the implicit assumptions that the real interest rate is constant and that the relationship between inflation and interest rate does not change over time. We demonstrate, using quarterly data for four OECD countries, that by relaxing these assumptions and allowing for seasonality in the inflation rate it is possible to obtain a model with a high degree of forecasting accuracy and efficiency.
JEL Classification Numbers: C22, C52, E31.     

Optimal Monetary Policy

Optimal monetary policy maximizes the welfare of a representative agent, given frictions in the economic environment. Constructing a model with two sets of frictions—costly price adjustment by imperfectly competitive firms and costly exchange of wealth for goods—we find optimal monetary policy is governed by two familiar principles. First, the average level of the nominal interest rate should be sufficiently low, as suggested by Milton Friedman, that there should be deflation on average. Yet, the Keynesian frictions imply that the optimal nominal interest rate is positive. Second, as various shocks occur to the real and monetary sectors, the price level should be largely stabilized, as suggested by Irving Fisher, albeit around a deflationary trend path. Since expected inflation is roughly constant through time, the nominal interest rate must therefore vary with the Fisherian determinants of the real interest rate. Although the monetary authority has substantial leverage over real activity in our model economy, it chooses real allocations that closely resemble those which would occur if prices were flexible. In our benchmark model, there is some tendency for the monetary authority to smooth nominal and real interest rates.     

Central Bank Behavior, the Institutional Framework, and Policy Regimes: Inflation Versus Noninflation Targeting Countries

This article estimates central bank reaction functions for 20 OECD countries. It bridges the gap between the Taylor reaction function literature and the political-economy literature. Central banks react to both inflation and the output gap. Moreover, inflation-targeting countries have been able to reduce nominal interest rate to a greater extent than have non-inflation-targeting countries. Countries with fixed exchange rates react more strongly to inflation but not at all to the output gap, unlike countries with floating rates. Political influences also seem relatively more important in fixed exchange rate countries. Central bank independence also helps reduce nominal interest rates. (JEL E58 , C31 , C32 , C53 )