Structural breaks and the Fisher hypothesis in bond and stock markets

Abstract

We attempt to resolve the empirical puzzle in the Fisher effect that nominal stock returns are negatively related to expected inflation. We postulate that this negative relation is caused by simultaneous changes in expected inflation, ex ante real interest rates on bonds and ex ante real returns on stocks due to supply shocks. We find that ex ante real interest rates and real stock returns are not independent of the expected inflation over the structural break subperiods chosen a priori to coincide with the oil price shocks of 1973 and 1979. As an alternative procedure, we employ the Cumulative Sum (CUSUM) test, in which the timing of structural breaks is based completely on sample data without requiring a priori information. The CUSUM test identifies a structural break in 1982Q1, which coincides approximately with the Federal Open Market Committee's (FOMC) deemphasis of the monetary aggregates as intermediate targets. We show that the Fisher effect cannot be rejected after the structural break identified by the CUSUM test in either the aggregate bond or stock market. In sum, our results provide evidence that the puzzling relation of expected inflation and nominal stock returns is limited to the subperiod before the 1982Q1 break.

Notes

¹ See, e.g. Jaffe and Mandelker (1976), Firth (1979), Gultekin (1983), Cochran and DeFina (1993), Erb et al. (1995), Amihud (1996), Graham (1996), Caporale and Jung (1997), Fama and Schwert (1997), Barnes et al. (1999), Davis and Kutan (2003) and Sun and Phillips (2004). For the recent studies supporting the Fisher effect, see Madsen (2005), Luintel and Paudyal (2006) and Ryan (2006). See also Cooray (2003) for a survey of studies on the Fisher effect.

² In particular, Fama (1981) proposes that inflation proxies inversely for real activity. Accordingly, an increase in expected future output is associated with an increase in both stock prices and the demand for real money. The price level would move in an opposite direction if a change in money supply does not fully adjust to the change in money demand. Hence, the negative relation between stock returns and inflation is observed because stock prices and the price level react oppositely to changes in expected future output.

³ Pilotte (2003) documents that expected output is negatively correlated to inflation while excess returns are positively correlated to inflation, and that total stock returns are negatively correlated to inflation because a negative correlation between capital gains yield and inflation dominates a positive correlation between dividend yield and inflation.

⁴ We use the employment index instead of the unemployment index as used in the original Sims’ (1980) VAR. Sims (1980) chooses these variables based on the criteria used in Hall (1975) and Hatanaka (1975).

⁵ Except for Mishkin (1992), prior research fails to fully consider stochastic trends of actual variables in modelling ex ante variables. Nelson and Plosser (1982) document that most macro variables fail to reject the null hypothesis of a unit root.

⁶ The FOMC used a monetary aggregate (M1) as an intermediate target during 1970s to reduce inflation. It controlled the Fed funds rate over a narrow range of 1/8–1/2% in order to reach its monetary objective. The tight control of the funds rate was viewed as a cause of the severe inflation and of repeatedly missing the monetary aggregate targets. The FOMC then introduced a new operating target, nonborrowed reserves, which were closely correlated with the monetary aggregates, and allowed the funds rate to change within a 4–5% range to obtain the money growth target. During 1979–1982, however, wide swings in the funds rate and the money growth rate occurred in the process of accommodating high inflation.

⁷ GNP is available only on a quarterly basis.

⁸ Although not reported here, the KPSS test for trend stationarity provides mixed evidence on the stationarity of the six variables. However, Bierens (1997) tests nonlinear trend stationarity for the GNP deflator, the CPI and the nominal interest rate and provides evidence that these series are nonlinear trend stationary.

⁹ We performed the Likelihood Ratio (LR) test to search for the optimal quarterly lag length. The analysis showed that the likelihood ratio test statistics with a lag length of up to four quarters are significantly greater than the critical value at the 5% level.

¹⁰ Evans and Lewis (1995) estimate the ex ante real interest rate by subtracting the inflation forecasts from the 1-year forward rate on a 3-month bond.

¹¹ The observations for the first four quarters of 1959Q3 through 1960Q2 are lost due to the measurement of differenced time series with four quarterly lags for both variables.

¹² See Engle and Yoo (1987) for the critical values of the cointegration test.

¹³ Perron (1989) shows that the Great Crash causes the means of most macroeconomic variables to drop sharply, while the oil price shock causes their slopes to decline. Contrary to the previous empirical findings that most macroeconomic time series possess a unit root process (see, e.g. Nelson and Plosser, 1982), Perron (1989) finds that they are trend-stationary after incorporating the change in the intercept following the Great Crash and the change in the slope following the oil price shock.

¹⁴ The coefficient of −0.193 is derived by adding the slope coefficient of −0.480 and the first and second slope dummies of −0.090 and 0.377 in Equation 10.