IS THE REAL INTEREST RATE REALLY UNSTABLE?

If nominal interest rates have a unit root, but inflation and inflation forecast errors do not, ex-ante real interest rates are argued to have a unit root and are therefore nonstationary. I show that empirical tests for nonstationarity of real interest rates using such a deductive method can be misleading when the stationary inflation forecast errors are large relative to the variation of nominal interest rates.     

An examination of real interest rates in the United States, Canada, France, and Germany during the recent floating exchange rate period

This study reexamines the international linkage of ex-ante real interest rates using the theory of cointegrated processes. The univariate unit root tests suggest the existence of a nonstationary real interest rate in the United States, Canada, and (the former) West Germany. An ex-ante real interest rate is obtained by subtracting estimates of inflation from the nominal interest rate. The expected inflation rates are obtained by modeling changes in monthly CPI values as autoregressive moving average (ARMA) processes. A multivariate test for unit roots indicates that there are two cointegrating vectors, or one common stochastic trend, for the system of three nonstationary real interest rates. In addition, the log-likelihood ratio test fails to reject the null hypothesis that, in the long run, real interest rates in the United States are equal to those in Canada and West Germany.     

Public Information Arrival and the Fisher Effect in Emerging Markets: Evidence from Stock and Bond Markets in Turkey

We examine the impact of inflation on nominal stock returns and interest rates in Turkey's emerging economy, which has a moderately high, persistent, and volatile inflation rate. Empirical evidence indicates that Turkey's inflation increased more than nominal stock returns and interest rates, implying that real returns to investors declined during our sample period. Among the different sector indexes we study, the financials sector serves as the best hedge against expected inflation, and the Fisher effect appears to hold only for this sector. We also find that public information arrival plays an important role, especially in the stock market.     

The Long‐Run Fisher Effect: Can It Be Tested?

In this paper, I provide a plausible explanation as to why past studies have been unable to find support for the long-run Fisher effect. My argument is that exogenous shocks to the inflation rates in industrialized economies have not produced the permanent change to inflation necessary for testing the Fisher effect. Instead of finding a nonstationary, unit-root process for inflation like previous Fisher effect studies, here each country's inflation rate is found to follow a mean-reverting, fractionally integrated, long-memory process. Applying a bivariate, maximum likelihood estimator to a multivariate, fractionally integrated model of inflation and nominal interest, I find that the estimated inflation rates in 17 developed countries are highly persistent, fractionally integrated, mean-reverting processes with order of integration parameters significantly less than one. Since a permanent change to inflation has not occurred, a test of whether a permanent change to inflation affects the nominal interest rate one-for-one will be uninformative as to the truth or fallacy of the Fisher effect hypothesis.     

Dynamic linkages among real interest rates in international capital markets

Short-run and long-run dynamic linkages among weekly real interest rates for G-10 countries are examined using a variety of time-series tests. These tests give special attention to the time-series properties of nominal interest rates, ex-ante expected rates of inflation and real interest rates. Term structure information is used to recover a theoretically consistent measure of ex-ante expected inflation. In-sample and out-of-sample Granger causality tests are also examined to evaluate lead/lag relationships among real interest rates. The results provide strong support for well-integrated markets, particularly in the long run. The results imply leadership roles for the US in international asset markets.     

On interest rates,inflationary expectations and tax rates

This paper provides new evidence on the relationship between inflation and the rate of interest for the United States during the 1953–1984 period. The results indicate that contrary to most previous studies, the Fisher hypothesis is inverted, which means that it is the real rate of interest rather than the nominal rate that moves inversely to the rate of inflation. However, this is the case only during periods of relatively stable inflation rates and moderate regulatory change. Over longer periods when factors are more volatile the inverted Fisher hypothesis is rejected.     

The Term Structure of Real Rates and Expected Inflation

Changes in nominal interest rates must be due to either movements in real interest rates, expected inflation, or the inflation risk premium. We develop a term structure model with regime switches, time‐varying prices of risk, and inflation to identify these components of the nominal yield curve. We find that the unconditional real rate curve in the United States is fairly flat around 1.3%. In one real rate regime, the real term structure is steeply downward sloping. An inflation risk premium that increases with maturity fully accounts for the generally upward sloping nominal term structure.     

Fisher Hypothesis Revisited: A Fractional Cointegration Analysis

This paper investigates the validity of the Fisher hypothesis using data from thirtythree developed and developing countries. Conventional cointegration tests do not provide strong evidence for a relation between nominal interest rates and inflation. Therefore, we use fractional cointegration analysis to test the long-run relationship between the two variables. The results indicate that a long-run relation between nominal interest rates and inflation does not appear for most countries in the sample when the conventional cointegration test is employed. However, fractional cointegration between the two variables is found for a large majority of countries, implying the validity of the Fisher hypothesis. The results also indicate that the equilibrium errors display long memory.     

Inflation risk premia and the expectations hypothesis

We study the properties of the nominal and real risk premia of the term structure of interest rates. We develop and solve the bond pricing implications of a structural monetary version of a real business cycle model, with taxes and endogenous monetary policy. We show the relation of this model with the class of essentially affine models that incorporate an endogenous state-dependent market price of risk. We characterize and estimate the inflation risk premium and find that over the last 40 years the ten-year inflation risk premium has been has averaged 70 basis points. It is time-varying, ranging from 20 to 140 basis points over the business cycle and its term structure is sharply upward sloping. The inflation risk premium explains 23% (42%) of the time variation in the five (ten)-year forward risk premium and it plays an important role in help explain deviations from the expectations hypothesis of interest rates.     

Real Rates, Expected Inflation, and Inflation Risk Premia

This paper studies the term structure of real rates, expected inflation, and inflation risk premia. The analysis is based on new estimates of the real term structure derived from the prices of index-linked and nominal debt in the U.K. I find strong evidence to reject both the Fisher Hypothesis and versions of the Expectations Hypothesis for real rates. The estimates also imply the presence of time-varying inflation risk premia throughout the term structure.     

The nominal duration of TIPS bonds

This paper studies the price responsiveness (effective duration) of U.S. government issued inflation-indexed bonds, known by the acronym TIPS (Treasury Inflation-Protected Securities), to changes in nominal interest rates, real interest rates, and expected inflation. Using the TIPS pricing formula derived by Laatsch and Klein [Q. Rev. Econ. Finance 43 (2002) 405], we first confirm that TIPS bonds have zero sensitivity to changes solely in expected inflation. By changes solely in expected inflation, we mean that the real rate remains unchanged and the nominal rate changes in accordance with the established Fisher [Publ. Am. Econ. Assoc. 11 (1896)] effect. We show that the first derivative of the TIPS price is zero whenever the real rate is held constant. Thus, the first partial derivative of the TIPS bond pricing formula with respect to expected inflation is zero and the first partial derivative of the TIPS bond price with respect to nominal rates is also zero, given, in each case, that we hold the real rate constant. We then temporarily shift the analysis to zero-coupon TIPS bonds and zero-coupon ordinary Treasury bonds. We prove that the nominal duration of zero-coupon TIPS bonds equals that of zero-coupon ordinary Treasury bonds when the real rate changes but expected inflation is held constant.However, if expected inflation changes and the change in the nominal rate does not yield a constant real rate, zero-coupon TIPS prices will change and they will change by a smaller percentage than will zero-coupon ordinary Treasury bonds. We analyze TIPS responsiveness to changes in nominal rates under such conditions. We derive an approximation to effective duration that demonstrates that the effective durations of various maturity zero-coupon TIPS bonds are approximately linear functions in time to maturity of the effective duration of the one-year zero-coupon TIPS bond, ceteris paribus.Nominal effective duration of TIPS bonds is certainly of interest to fixed income portfolio managers that might have a desire to include such bonds in their portfolio. After all, the greater portion of a typical fixed income portfolio is in traditional, noninflation protected bonds whose major risk exposure is to changes in nominal rates. To properly assess the role of TIPS bonds in the portfolio, portfolio managers need information as to how TIPS bonds respond to the changes in nominal rates that are driving the price behavior of the bulk of the portfolio's assets. Prior to concluding the paper, we demonstrate how portfolio managers can calculate the nominal durations of coupon TIPS bonds using the zero-coupon duration formula we derive.     

Are Tax Effects Important in the Long-Run Fisher Relationship? Evidence from the Municipal Bond Market

Are nominal bonds appropriately discounted for taxes? Empirical estimates of the response of nominal interest rates to changes in inflation, the Fisher effect, have failed to produce a definitive answer. Four reasons have been put forward as possible explanations: (i) Tobin effects, (ii) fiscal illusion, (iii) peso problems, and (iv) different estimators. Utilizing data on taxable and tax-exempt bond interest rates and several different estimators, we find that the Fisher effect estimates are always larger for the taxable bond relative to the tax-exempt bond, suggesting that fiscal illusion and different estimators cannot account for the previous results.     

On the constancy of the international real rate of interest

This paper develops an alternative method of deriving the ex-ante real rate of interest. Given assumptions regarding capital mobility and PPP, it is shown that in equilibrium the ex-ante real rate will be equalized across countries. Using cross-sectional regression techniques, this real rate can be estimated at each moment in time. Hence, it is possible to develop a time series of estimated real rates derived from cross-sectional regressions. This estimated real rate series is then used in time-series tests of the Fisher equation for the U.S.     

Do Expected Shifts in Inflation Affect Estimates of the Long-Run Fisher Relation?

Recent empirical studies suggest that nominal interest rates and expected inflation do not move together one-for-one in the long run, a finding at odds with many theoretical models. This article shows that these results can be deceptive when the process followed by inflation shifts infrequently. We characterize the shifts in inflation by a Markov switching model. Based upon this model's forecasts, we reexamine the long-run relationship between nominal interest rates and inflation. Interestingly, we are unable to reject the hypothesis that in the long run nominal interest rates reflect expected inflation one-for-one.     

Are expectations of inflation rational? or Is variation of the expected real interest rate unpredictable?

The joint hypothesis developed and tested in this paper is that the nominal interest rate is a rational expectation of the real interest rate plus the inflation rate and that variation of the expected real interest rate is unpredictable on the basis of information used in the test. This test is applied to quarterly data on three-month United States Treasury bills of 1954 to 1973. The information used in the tests includes, besides past interest rates and inflation rates, past growth rates of the source base, the money supply, and real GNP. Some of the tests allow for a positive marginal tax rate, which changes the results little. The hypothesis is generally consistent with the data, which provides support for the proposition that predictable changes of the money supply do not affect expected real interest rates over periods as short as a quarter.     

Stock returns,inflation and interest rates in the United Kingdom

The Fisherian theory of interest asserts that a fully perceived change in inflation would be reflected in nominal interest rates and stock returns in the same direction in the long run. This paper examines the Fisherian hypothesis of asset returns using alternative techniques of linear regression, and vector error correction models to examine the nature of the relationship between stock returns and inflation in the UK. Consistent with the Fisherian hypothesis, empirical evidence in the linear regression model suggests a positive and statistically significant relationship between stock returns and inflation, which regards common stock as a good hedge against inflation. The results based on the unit root and cointegration tests indicate a long-run reliable relationship between price levels, share prices, and interest rates which could be interpreted as the long-run determinants of stock returns. The findings also suggest a bidirectional relationship between stock returns and inflation. The evidence of a significant Fisher effect is robust across model specifications.     

Disagreement about inflation and the yield curve

We show that inflation disagreement, not just expected inflation, has an impact on nominal interest rates. In contrast to expected inflation, which mainly affects the wedge between real and nominal yields, inflation disagreement affects nominal yields predominantly through its impact on the real side of the economy. We show theoretically and empirically that inflation disagreement raises real and nominal yields and their volatilities. Inflation disagreement is positively related to consumers’ cross-sectional consumption growth volatility and trading in fixed income securities. Calibrating our model to disagreement, inflation, and yields reproduces the economically significant impact of inflation disagreement on yield curves.     

Inflation Uncertainty, Real-Interest-Rate Uncertainty, and the Liquidity Premium on Government Bonds

This paper shows that the components of uncertainty about nominal interest rates, real-rate uncertainty and inflation uncertainty, have different effects on the liquidity premium. An increase in inflation uncertainty should increase the equilibrium liquidity premium because investors reduce the effect of inflation uncertainty on the riskiness of their portfolios by holding more short-term bonds. In contrast, an investor can reduce the effects of uncertainty about future ex-ante real rates on portfolio return by matching more closely the maturity dates of the bonds held with the date on which the portfolio is to be liquidated for consumption purposes. Thus, the effect of an increase in real-rate uncertainty on the equilibrium liquidity premium is ambiguous, depending on the relative magnitudes of long-term and short-term saving and the proportions of short-term and long-term bonds issued by the government.     

Pricing the term structure of inflation risk premia: Theory and evidence from TIPS

In this paper, we study inflation risk and the term structure of inflation risk premia in the United States' nominal interest rates through the Treasury Inflation Protection Securities (TIPS) with a multi-factor, modified quadratic term structure model with correlated real and inflation rates. We derive closed form solutions to the real and nominal term structures of interest rates that drastically facilitate the estimation of model parameters and improve the accuracy of the valuation of nominal rates and TIPS prices. In addition, we contribute to the literature by estimating the term structure of inflation risk premia implied from the TIPS market. The empirical evidence using data from the period of January 1998 through October 2007 indicates that the expected inflation rate, contrary to data derived from the consumer price indices, is very stable and the inflation risk premia exhibit a positive term structure.     

Money and exchange rates in the Grossman-Weiss-Rotemberg model

We analyze the impact of monetary policy on inflation, interest rates and exchange rates in a model with segmented asset markets developed by Grossman and Weiss (1983) and Rotemberg (1984, 1985). We find parameters for which real and nominal exchange rates in this model are (1) much more volatile than interest rates, inflation rates, and money growth rates, (2) highly correlated with each other, and (3) highly persistent. While this model fails to match the data in other important respects, it illustrates a potentially useful approach to modelling exchange rate behavior.