Growth, Inflation, Interest Rates and Real Stock Returns
in the U.S. and Canada
William E. Shambora*
Ohio University
Chulho Jung
Ohio University
Kyongwook Choi
Ohio University
Abstract
We examine the effects of expected and unexpected inflation, real growth rates and interest rates
on real stock returns for the United States and Canada. Contrary to several classic studies, we
find no evidence that expected or unexpected inflation affects stock returns. However we find
evidence that unexpected growth shocks affect real returns.
*
Corresponding author: Economics Dept.; Ohio University; 335 Bentley Annex; Athens, OH 45701; (740) 593-
1845; shambora@ohio.edu
Growth, Inflation, Interest Rates and Real Stock Returns
in the U.S. and Canada
1. Introduction
The relationship between growth, inflation, interest rates and real stock returns has been a
topic of interest in economics for a long time. In general, economic growth and real stock
returns are expected to have a positive relationship and interest rates and real stock returns a
negative relationship. However, these relationships, particularly the relationship between
inflation and real stock returns, continue to be unresolved matters in both theoretical and
empirical literature. Under monetary neutrality, real stock returns would not be expected to
change as a result of a permanent shock to inflation. Contrarily, empirical evidence of an inverse
relationship is found in several classic papers including Nelson (1976), Fama and Schwert
(1977), and Schwert (1981). Various explanations of this phenomenon have been offered.
Modigliani and Cohn (1979) suggest that agents’ difficulty in distinguishing between real and
nominal interest rates leads to faulty discounting while Feldstein (1980) shows that taxation
related to depreciation and capital gains is affected by inflation which, in turn, affects real asset
valuation. Fama (1981) posits that the inverse relationship is the result of a negative relationship
between inflation and economic activity and a positive relationship between economic activity
and stock prices. Benderly and Zwick (1985) support Fama’s arguments. Sharpe (2002) argues
that the negative relation between equity valuations and expected inflation is the results of two
effects: a rise in expected inflation coincides with both lower expected real earnings growth and
higher required real returns.
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On the other hand, Rapach (2002) disputes the findings of an inverse relationship between
real stock prices and inflation. Using the King and Watson (1997) methodology of testing for
long-run neutrality, Rapach (2002) finds no evidence of a long-run inverse relationship in a study
involving sixteen industrialized countries. Shiller and Beltratti (1992) find little correlation
between inflation and stock returns, but do find an inverse relationship between stock returns and
interest rates. Such a relationship is supported by Campbell and Ammer (1993) among others.
We extend this literature by employing a special methodology designed to examine several
questions simultaneously: 1) Do expected and/or unexpected inflation affect real stock returns?
2) Do expected and/or unexpected growth affect real stock returns? 3) Do expected and/or
unexpected interest rates affect real stock returns? Using data for the United States and Canada,
expected inflation, expected interest rates and expected economic growth are modeled as
ARIMA time series; thus deviations from these processes represent unexpected inflation, interest
rate shocks and growth rate shocks. A set of four equations are estimated simultaneously using
full information maximum likelihood (FIML) to avoid potential statistical inconsistency
problems and to achieve more efficient estimates. By controlling for all six variables, we hope to
avoid bias due to potential missing variables.
2. Model
Real stock prices are usually thought of as reflecting the present value of expected future real
earnings. From a macroeconomic standpoint corporate profits are a direct function of economic
growth. Real stock prices then would be a function of expected future real economic growth.
Because interest rates serve as the discounting mechanism, stock returns would be expected to
2
also be a function of interest rates. If, contrary to economic theory, stock prices are directly
affected by inflation as well, then they must also be a function of inflation.
We construct an empirically testable model where real stock returns are a function of
expected and surprise economic growth, expected and unexpected inflation and expected and
unexpected interest rates. It is assumed that expectations regarding economic growth, inflation,
and interest rates are formed via knowledge of the data generating processes [DGP] for each
series. It is further assumed that these processes are ARIMA processes; thus, expected growth,
inflation and interest rates are modeled as forecasts from ARIMA models. This leads to the
following general system of equations:
n
Yt Yt eYt 0 iYt i Yt
ˆ (1)
i 1
m
Pt Pt ePt 0 i Pt i Pt
ˆ (2)
i 1
o
rt rt ert 0 i ri 1 rt
ˆ (3)
i 1
ˆ ˆ
St 0 1Yt 2eYt 3 P 4ePt 5rt 6ert St
ˆ (4)
t
where Yt is the real growth rate of economic output, Pt is the inflation rate, rt is the interest rate,
and St is the real growth rate of a stock price index. The εjt terms are disturbance terms, and ejt
terms are residuals which can be interpreted as forecast errors. The fitted values based on the
data generating processes are denoted with the hat above the symbol. Stock returns are thus
viewed as being influenced by expected and unexpected growth as well as expected and
unexpected interest rates and inflation. Under the Fisher assumption that real returns are
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independent of inflationary expectations, δ3 should equal zero and if real returns are also
independent of inflationary surprises, δ4 should also be zero.
3. Data and model estimation
Equations (1) and (2) form the basis for the models of the DGP of economic growth and
inflation while (3) is the DGP for the interest rate. ARIMA models for each series are estimated
using Box-Jenkins methodology. The appropriate number of lags for each model is selected so
that the residuals are white noise. The models are then used to produce step-ahead forecasts and
forecast error. These become the right hand side variables in Equation (4). The forecasts for
growth rate, inflation and interest rates proxy for expected growth rate, inflation and interest
rates. Forecast error, the error terms from the estimates of Equations (1) through (3), are the
proxies for unexpected growth, unexpected inflation and interest rate surprise respectively. The
dependent variables used in estimating Equation (4) are the log differences of a broad stock
market index corrected for inflation for each country.
Applying OLS to Equation (4) where the regressors are from generated data would result in
an inconsistent covariance estimator.1 To remedy this we estimate Equations (1) through (4) as a
system using full information maximum likelihood (FIML).
The data are from International Financial Statistics of IMF and OECD data CD-Rom. We use
quarterly data from the first quarter of 1975 through the first quarter of 2001. For the U.S., we
use CPI for inflation, the three-month Treasury bill rate for interest rates, and quarterly industrial
production (IP) for growth rates, respectively. For Canada, we use CPI for inflation, discount
rate for interest rates, and quarterly industrial production (IP) for growth rates, respectively.
1
See Pagan (1984).
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The best fitting ARIMA (i.e., ARI) models for the U.S. are ARIMA(12,1,0), ARIMA(7,1,0),
and ARIMA (6,0,0) for growth rate, inflation, and interest rates, respectively. The best fitting
ARIMA (i.e., ARI) models for Canada are ARIMA(4,1,0), ARIMA(4,1,0), and ARIMA (8,0,0)
for growth rate, inflation, and interest rates, respectively. 2 We estimate equations (1) – (4)
simultaneously using FIML.
Estimates for Equations (1) – (3) are enumerated in Table 1 while the estimates for Equation
(4) can be found in Table 2.
[Insert Table 1 about here]
[Insert Table 2 about here]
4. Results
Inferences from the model estimates for both the US and Canada are consistent. The only
significant coefficient in Equation (4) for both countries is that on unexpected growth. The
coefficient estimates indicate that there does not appear to be a long run relationship between
real stock returns and inflation. Additionally, we find that inflation surprise as measured by ePt
does not appear to influence real stock returns either. This supports the findings of Shiller and
Beltratti (1992) and Rapach (2002), but goes against the findings of the classic studies.
The interest rate coefficient estimates do not support the findings of Shiller and Beltratti
(1992) or Campbell and Ammer (1993). Interest rates, in their role as discounting mechanism,
2
Residuals from the estimated ARIMA models are white noise. The best fitting ARI models were chosen over
more complicated ARIMA models for parsimony and to reduce the potential complexity of estimating simultaneous
equations models with MA terms.
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would be expected to have an inverse effect on stock returns yet the coefficients on expected and
unexpected interest rates are not significant.
Coefficient estimates also suggest that expected concurrent economic growth does not appear
to impact stock returns while shocks to growth have a direct effect on stock returns. This lends
support to the idea that stock market returns are more sensitive to unexpected shocks to growth
than changes in the expected growth path of the economy. A possible explanation is that long-
run economic growth is viewed as a mean reverting process and that unexpected, temporary
shocks are initially interpreted as changes in the long-run growth. As more information enters
the market, i.e. the shock wears off, the temporary nature of the shock becomes evident and stock
returns once again reflect the expected long-term growth of the economy.
5. Summary and Conclusion
Equity returns were modeled as a function of expected and unexpected inflation as well as
expected and unexpected economic growth and interest rates. Expectations were assumed to be
formed rationally based on knowledge of the model of the data generating processes. We fit
ARIMA models to economic growth, inflation and interest rate data for the U.S. and Canada.
Then we regressed the real stock return on the model forecasts and the error terms for those three
variables. The coefficient estimates suggest that, contrary to several classic studies, real stock
prices respond neither to expected nor unexpected inflation. Additionally, stock prices do not
respond to current expected or unexpected interest rates. However, stock prices respond
positively to shocks to GDP, but do not respond to changes in short-term expected GDP.
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References
Benderly, J. and B. Zwick (1985) “Inflation, Real Balances, Output, and Real Stock Returns,”
American Economic Review, 75:5, 1115-23.
Campbell, J. Y. and J. Ammer (1993) “What moves the stock and bond markets? A variance
decomposition for long-term asset returns,” Journal of Finance, 48:1, 3-37.
Fama, E. F. (1981) “Stock returns, real activity, inflation, and money,” American Economic
Review, 71:4, 545-65.
Fama, E. F. and G. W. Schwert (1977) “Asset returns and inflation,” Journal of Financial
Economics, 5:2, 115-46.
Feldstein, M. (1980) “Inflation and the stock market,” American Economic Review, 71:4, 849-47.
King, R. G. and M. W. Watson (1997) “Testing long-run neutrality,” Federal Reserve Bank of
Richmond Economic Quarterly, 83:3, 69-101.
Modigliani, F. and R. A. Cohn (1979) “Inflation, rational valuation and the market,” Financial
Analysts Journal, 24-44.
Nelson, C. R. (1976) “Inflation and rates of return on stocks,” Journal of Finance, 31:2, 471-83.
Pagan, A. (1984) “Econometric issues in the analysis of regressions with generated regressors,”
International Economic Review, 25, 901-22.
Rapach, D. E. (2002) “The long-run relationship between inflation and real stock prices,”
Journal of Macroeconomics, 24, 331-51.
Shiller, R. J. and A. E. Beltratti (1992) “Stock prices and bond yields: Can their comovements be
explained in terms of present value models?” Journal of Monetary Economics, 30:1, 25-46.
Schwert, G. W. (1981) “The adjustment of stock prices to information about inflation,” Journal
of Finance, 36, 15-29.
Sharpe, S. (2002) “Reexamining Stock Valuation and Inflation: The Implications of Analysts’
Earnings Forecasts,” The Review of Economics and Statistics, 84:4, 632-48.
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Table 1. Coefficient Estimates: Canada and the United States, Equations (1) – (3)
Canada US
Coefficient Coefficient
(Standard Error) (Standard Error)
Equation (1) Y
Constant 0.30 0.67
(0.146)** (0.153)***
AR(1) AR(2) AR(3) 0.51 0.10 0.10 0.20 0.31 0.11
(0.10)*** (0.11) (0.11) (0.09)** (0.09)*** (0.08)
AR(4) AR(5) AR(6) -0.24 -0.18 -0.02 -0.03
(0.10)*** (0.08)*** (0.08) (0.08)
AR(7) AR(8) AR(9) 0.04 -0.31 0.16
(0.08) (0.08)*** (0.08)*
AR(10) AR(11) AR(12) 0.16 0.05 -0.40
(0.08)* (0.08) (0.08)***
Equation (2) P
Constant 0.07 0.19
(0.08) (0.12)*
AR(1) AR(2) AR(3) 0.57 0.04 0.12 0.24 0.12 0.37
(0.01)*** (0.12) (0.12) (0.11)** (0.11) (0.11)***
AR(4) AR(5) AR(6) 0.19 0.39 -0.09 -0.02
(0.10)* (0.11)*** (0.11) (0.13)
AR(7) -0.22
(0.10)**
Equation (3) r
Constant 0.45 0.37
(0.35) (0.18)**
AR(1) AR(2) AR(3) 1.23 -0.39 0.21 1.21 -0.45 0.18
(0.01)*** (0.16)*** (0.16) (0.11)*** (0.16)*** (0.16)
AR(4) AR(5) AR(6) -0.16 0.01 0.08 0.18 -0.41 0.21
(0.16) (0.16) (0.16) (0.16) (0.16)*** (0.10)**
AR(7) AR(8) -0.38 0.26
(0.16)*** (0.10)***
* Significant at 10%. ** Significant at 5%. *** Significant at 1%.
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Table 2. Coefficient Estimates: Canada and the United States, Equation (4)
Canada US
Equation (4) S
Constant 4.79 3.56
(2.54)* (3.90)
Et-1(Yt) -0.09 -0.86
(0.73) (1.89)
εYt 1.19 4.38
(0.67)* (1.22)***
Et-1(Pt) 1.38 -1.67
(1.64) (1.33)
εPt 0.99 -0.37
(1.71) (1.27)
Et-1(rt) -0.59 0.16
(0.37) (0.48)
εrt -0.40 0.80
(0.83) (1.20)
F-statistic 1.66 3.82
* Significant at 10%. ** Significant at 5%. *** Significant at 1%.
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