Are Expected Inflation Rates and Expected Real Rates Negatively Correlated? A Long‐Run Test of the Mundell‐Tobin Hypothesis

Some empirical evidence suggests that the expected real interest and expected inflation rates are negatively correlated. This hypothesis of negative correlation is sometimes known as the Mundell‐Tobin hypothesis. In this article we reinvestigate this negative relation from a long‐term point of view using cointegration analysis. The data on the historical interest rate on T‐bills and the inflation rate indicate that the Mundell‐Tobin hypothesis does not hold in the long run for the United States, the United Kingdom, and Canada. We also obtain similar results using the real interest rate on index‐linked gilt traded in the United Kingdom.     

Inflation,real returns and capital investment

We find evidence for the hypothesis of Mundell (1963) and Tobin (1965) that the expected real return component of interest rates is negatively related to the expected inflation component. In the Mundell-Tobin model, the variation in expected real returns is caused by the variation in expected inflation. Our evidence suggests, however, that the variation in expected real returns is more fundamentally an outcome of the capital expenditures process. Equilibrium expected real returns vary directly with capital expenditures in order to induce equilibrium allocations of resources between consumption and investment. This positive relation between expected real returns and real activity, which comes out of the real sector, combines with a negative relation between expected inflation and real activity, which is traced to the monetary sector, thus inducing the negative relation between expected inflation and expected real returns predicted by Mundell and Tobin but explained in terms of a model much different from theirs.     

Real Interest Rates and Inflation: An Ex-Ante Empirical Analysis

We develop a method of measuring ex-ante real interest rates using prices of index and nominal bonds. Employing this method and newly available data, we directly test the Fisher hypothesis that the real rate of interest is independent of inflation expectations. We find a negative correlation between ex-ante real interest rates and expected inflation. This contradicts the Fisher hypothesis but is consistent with the theories of Mundell and Tobin, Darby and Feldstein, and Stulz. We also find that nominal interest rates include an inflation risk premium that is positively related to a proxy for inflation uncertainty.     

Asset Pricing and Expected Inflation

This paper provides an equilibrium model in which expected real returns on common stocks are negatively related to expected inflation and money growth. It is shown that the fall in real wealth associated with an increase in expected inflation decreases the real rate of interest and the expected real rate of return of the market portfolio. The expected real rate of return of the market portfolio falls less, for a given increase in expected inflation, when the increase in expected inflation is caused by an increase in money growth rather than by a worsening of the investment opportunity set. The model has empirical implications for the effect of a change in expected inflation on the cross-sectional distribution of asset returns and can help to understand why assets whose return covaries positively with expected inflation may have lower expected returns. The model also agrees with explanations advanced by Fama [5] and Geske and Roll [10] for the negative relation between stock returns and inflation.     

Monetary rules and the nominal rate of interest under uncertainty

The expected real rate of return on a nominal bond is shown to be equal to the real rate of interest plus a premium for systematic purchasing power risk. The particular monetary rule employed by the central monetary authority affects the entire joint distribution of inflation and aggregate real wealth. Thus, the monetary authority is able to influence the relationship between the real and nominal interest rate not only by affecting the expected rate of inflation but also by affecting the systematic purchasing power risk of fixed nominal claims.     

The term structures of equity and interest rates

This paper proposes a dynamic risk-based model capable of jointly explaining the term structure of interest rates, returns on the aggregate market, and the risk and return characteristics of value and growth stocks. Both the term structure of interest rates and returns on value and growth stocks convey information about how the representative investor values cash flows of different maturities. We model how the representative investor perceives risks of these cash flows by specifying a parsimonious stochastic discount factor for the economy. Shocks to dividend growth, the real interest rate, and expected inflation are priced, but shocks to the price of risk are not. Given reasonable assumptions for dividends and inflation, we show that the model can simultaneously account for the behavior of aggregate stock returns, an upward-sloping yield curve, the failure of the expectations hypothesis, and the poor performance of the capital asset pricing model.     

Identifying the dynamics of real interest rates and inflation: evidence using survey data

In the context of an equilibrium asset-pricing model, the dynamicsof the instantaneous real interest rate and the instantaneousrate of expected inflation are estimated. Unlike previous models,we allow real interest rates and inflation to be mutually dependentprocesses. The model is estimated as a state-space system thatincludes observations on various maturity Treasury bills andNBER-ASA survey forecasts of inflation. Over the period 1968-1988,we find evidence that instantaneous real interest rates andexpected inflation are significantly negatively correlated.Real interest rates also display greater volatility and weakermean reversion than expected inflation.     

The optimal rate of inflation revisited

Inflation viewed as a tax on cash balances is investigated using the optimal commodity tax framework. The optimal inflation rate is shown to depend on the effect of changes in the rate of inflation on quantity demanded of ‘costly-to-produce’ goods. Even when other goods are taxed, it is not always optimal to have a positive tax on money, as Phelps and others have claimed. A zero tax or even a rate of deflation greater than the pre-tax rate of interest may be optimal.     

Information,interest rates,and the volatility of asset prices

The volatility of an asset price is modelled as a function of the volatility of an information signal, real interest rates and inflation expectations. Volatility depends on the duration of cash flows, and the degree to which cash flows are indexed to real rates and inflation. The model is applied to determine asset betas, the volatility of the futures prices of assets and the volatility of equity prices.     

The Fiscal and Monetary Linkage between Stock Returns and Inflation

Contrary to economic theory and common sense, stock returns are negatively related to both expected and unexpected inflation. We argue that this puzzling empirical phenomenon does not indicate causality. Instead, stock returns are negatively related to contemporaneous changes in expected inflation because they signal a chain of events which results in a higher rate of monetary expansion. Exogenous shocks in real output, signalled by the stock market, induce changes in tax revenue, in the deficit, in Treasury borrowing and in Federal Reserve “monetization” of the increased debt. Rational bond and stock market investors realize this will happen. They adjust prices (and interest rates) accordingly and without delay. Although expected inflation seems to have a negative effect on subsequent stock returns, this could be an empirical illusion, since a spurious causality is induced by a combination of: (a) a reversed adaptive inflation expectations model and (b) a reversed money growth/stock returns model. If the real interest rate is not a constant, using nominal interest proxies for expected inflation is dangerous, since small changes in real rates can cause large and opposite percentage changes in stock prices.     

An arbitrage model of the term structure of interest rates

A formula for the price of default-free discount bonds of all maturities is found using a Black- Scholes type of arbitrage model which is based on the assumption that a portfolio of three default-free discount bonds of distinct maturities can be managed to be a perfect substitute for any other default-free discount bond. The formula relates the price of bonds to the real rate of interest, the anticipated rate of inflation and the equilibrium prices of interest rate and inflation risks. Bond prices are shown to be the expected value of the sure nominal proceeds of the bond discounted to the present at a random discount rate. It is shown that the unbiased expectations hypothesis is in general inconsistent with this model.     

Capital asset prices versus time series models as predictors of inflation: The expected real rate of interest and market efficiency

This paper examines the robustness of one month treasury bills as predictors of inflation. The evidence is inconsistent with the joint hypothesis that (1) the expected real rate of interest was constant for one-month bills and (2) that markets are efficient with regard to the time series of inflation. When the expected real rate of interest is set equal to the conditional expectation given the time series of real rates, the results are much more consistent with the efficient markets model. In more positive terms, the failure to confirm market efficiency appears to be the result of naive estimates of the expected real rate.     

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.     

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.     

Extracting inflation expectations and inflation risk premia from the term structure: A joint model of the UK nominal and real yield curves

This paper analyses the UK interest rate term structure over the period since October 1992, when the United Kingdom adopted an explicit inflation target, using an affine term structure model estimated using both government bond yields and survey data. The model imposes no-arbitrage restrictions across nominal and real yields, which enables interest rates to be decomposed into expected real policy rates, expected inflation, real term premia and inflation risk premia. The model is used to shed light on major developments over the period, including the impact of Bank of England independence and the low real bond yield ‘conundrum’.     

Macroeconomic Implications of Term Structures of Interest Rates Under Stochastic Differential Utility with Non-Unitary EIS

This paper proposes a continuous-time term-structure model under stochastic differential utility with non-unitary elasticity of intertemporal substitution (EIS, henceforth) in a representative-agent endowment economy with mean-reverting expectations on real output growth and inflation. Using this model, we make clear structural relationships among a term structure of real and nominal interest rates, utility form and underlying economic factors (in particular, inflation expectation). Notably, we show that, if (1) the EIS is less than one, (2) the agent is comparatively more risk-averse relative to time-separable utility, (3) short-term interest rates are pro-cyclical, and (4) the rate of expected inflation is negatively correlated with the rate of real output growth and its expected rate, then a nominal yield curve can have a low instantaneous riskless rate and an upward slope.     

Real Stock Returns and Inflation

This paper develops the relation between the real rate of return on the stock market and changes in the price level using a multiperiod economy with production. The observed relation between real ex post stock returns and inflation is shown to be consistent with equilibrium in an economy with rational investors. The relation between expected real returns and expected inflation is shown to depend on the form of the economy's production function and on the form of investor preferences. When the production function exhibits stochastic constant returns to scale, the model explains the negative relation between expected real returns and expected inflation which has frequently been observed in empirical studies.     

Detecting news in aggregate accounting earnings: implications for stock market valuation

How much news is there in aggregate accounting earnings? I provide evidence that earnings changes at the stock market level are correlated with new information about not only expected future cash flows but also discount rates. A comprehensive investigation of the link to discount rates reveals that aggregate earnings changes are tied to news about all components of the expected future stock market return, i.e., the real riskless rate, expected inflation, and the expected equity risk premium. Over the sample period studied, cash flow news and discount rate news in aggregate earnings changes covary positively and have offsetting impacts on stock market prices. As a result, stock market prices appear to be insensitive to aggregate earnings changes. The findings highlight the importance of separating cash flow news from discount rate news when evaluating the information content of accounting earnings at the stock market level. Overall, my study sheds new light on the informativeness and relevance of accounting earnings for valuation at the stock market level.     

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.     

Multi-factor Affine Term Structure Model with Single Regime Shift: Real Term Structure under Zero Interest Rate

In this paper, we extend the one-factor, single regime shift, affine term structure model with time-dependent regime-shift probability to a multi-factor model. We model the nominal interest rate and the expected inflation rate, and estimate the term structure of the real interest rate in the Japanese government bond market using inflation-indexed bond data under zero interest rates. Incorporating the economic structure that the Bank of Japan terminates the zero interest rate when the expected inflation rate gets out of deflationary regime, we estimate the yield curve of the real interest rate for less than 10 years, consistent with the expectation of the market participants in the Japanese government bond market, where inflation-indexed bonds are traded for only around 10 years.