Inflation and real stock returns revisited.
Lin, Shu-Chin
I. INTRODUCTION
This article empirically reinvestigates the relationship between
real stock returns and inflation. According to Fisher (1930), (1) in an
efficient market, real stock returns should reflect expectations only
about real factors such as growth in output and time preference of
savers such that real stock returns and inflation should vary
independently. In other words, on average, investors are fully
compensated for erosions in purchasing power over time. However, this
so-called generalized Fisher hypothesis has received little empirical
support. While Kaul (1990), Boudoukh and Richardson (1993), Solnik and
Solnik (1997), Madsen (2005), and Ryan (2006) find positive or weakly
positive correlation between stock returns and inflation, most empirical
studies, including Nelson (1976), Fama (1981, 1983), Geske and Roll
(1983), Gultekin (1983), Kaul (1987), and Solnik (1983), uncover a
negative effect of inflation (anticipated and/or unanticipated) on (real
or nominal) stock returns. These apparent inconsistencies between the
data and the predictions of economic theory have been termed as the
stock return-inflation puzzle and cited as evidence of monetary
nonsuperneutrality or irrationality (and market inefficiency). (2)
To reconcile the seemingly conflicting contributions, Danthine and
Donaldson (1986) provide a rational expectations equilibrium model in
which a negative relation between stock returns and inflation arises
from non-monetary sources (e.g., a real output shock) and a positive
relation is driven by purely monetary sources. Stulz (1986), Marshall
(1992), and Bakshi and Chen (1996) also assert that stock returns may be
negatively correlated with inflation, especially when the source of
inflation is related to nonmonetary factors. Evidently, Hess and Lee
(1999), Khil and Lee (2000), and Lee (2003) find that while monetary
shocks drive a positive correlation, real (fiscal or real output) shocks
result in a negative correlation between stock returns and inflation.
From a different perspective, Kaul (1987, 1990) argues that the relation
between these two variables depends on both the money demand and the
money supply. Specifically, while the combination of money demand
effects with a countercyclical monetary response accentuates a negative
correlation, money demand shocks along with a procyclical monetary
response lead to a neutral or positive correlation between real stock
returns and inflation. Similar arguments can be found in Day (1984),
Kaul and Seyhun (1990), Boudoukh, Richardson, and Whitelaw (1994), and
Gallagher and Taylor (2002) and are supported by compelling empirical
evidence (see, e.g., Kim 2003; Lee 1992).
As an alternative, this article models the real stock
return-inflation relationship as intrinsically dynamic, explicitly
distinguishing between the short run and the long run. Such a
distinction is crucial, because imperfect information, rigidity, and/or
contractual obligations are more prevalent in the short run than in the
long run. In that sense, the response of real stock returns to inflation
could differ in the short run versus long run. Moreover, we assess the
long- and short-run impacts of inflation uncertainty on real stock
returns. As argued, the real costs of inflation are associated with its
uncertainty. Greater inflation uncertainty resulting from higher
inflation may lead to economic inefficiency, lower real investment, and
unemployment, thereby reducing economic growth. Thus, it is interesting
to see if there are independent effects of inflation uncertainty on real
stock returns both in the short run and in the long run.
In so doing, this article uses an innovative econometric technique
to explore the long-and short-run relationships between real stock
returns and inflation (both anticipated and unanticipated) and the
relationships with inflation uncertainty. It departs from earlier work
and complements recent evidence in at least three aspects. First, we
conduct a panel analysis on data pooled from 16 industrialized Organization for Economic Cooperation and Development (OECD) countries
for the 1957:Q1 to 2000:Q1 period. Existing studies usually build on a
time series framework for a single or a group of countries. In contrast,
this article recasts the issue into a dynamic panel framework to exploit
both the cross-section and the time series dimensions of the data.
Moreover, the dynamic panel data model allows us to control
heterogeneity across countries by the inclusion of country-specific
effects.
Second, to measure the effects of both expected and unexpected
inflation and inflation uncertainty, we employ generalized
autoregressive conditional heteroskedasticity (GARCH)-type models to
obtain expected and unexpected components of inflation and conditional
variance as a proxy for inflation uncertainty. The procedure thus allows
us to avoid problems associated with the survey data (see Kandel, Ofer,
and Sarig 1996; Woodward 1992, for the detailed discussion) as well as
the problem of using volatility (or standard error) to measure inflation
uncertainty (Fountas and Karanasos 2007). As argued, conditional
variance is better to capture inflation risk and uncertainty.
Last, and most importantly, we apply the pooled mean group (PMG)
estimator of Pesaran, Shin, and Smith (1999) to estimate short- and
long-run relationships between real stock returns and inflation.
Specifically, the estimator can be applied to either I(1) and/ or I(O)
variables and does not require the pre-testing of unit roots. (3) By
focusing on different time spans, we set the basis for an explanation of
the contradictory effects of inflation on real stock returns. This
methodology can be summarized as a panel error-correction model, where
short- and long-run effects are estimated jointly from a general
autoregressive distributed lag (ARDL) model. The PMG estimator has been
recently applied to measure the effect of exchange rate uncertainty on
investment (Byrne and Davis 2005a, 2005b), to assess the trade effect of
real effective exchange rates by Catao and Solomou (2005), to estimate
the impacts of fiscal deficits on inflation (Catao and Terrones, 2005),
and to estimate the relationship between financial development and
economic growth (Loayza and Ranciere, 2006).
Our empirical findings are summarized as follows. First, while
anticipated inflation has insignificant short-run impacts on real stock
returns, it tends to have significantly negative long-run impacts on
real stock returns. Second, regarding unanticipated inflation, we find
that a negative long-run effect coexists with a positive short-run
effect on real stock returns. Finally, inflation uncertainty is found to
have independent impacts and tends to exert a significantly negative
long-run effect but an insignificant short-run effect on real stock
returns. These findings are robust to alternative measures of expected
inflation, unexpected inflation, and inflation volatility.
The remainder of this article is organized as follows. Section II
introduces the PMG estimator proposed by Pesaran, Shin, and Smith (1999)
and elaborates alternative measures of expected and unexpected inflation
and inflation uncertainty. Section III describes the data and reports
empirical results and robustness tests. Section IV concludes the
analysis.
II. INFLATION AND REAL STOCK RETURNS
A. The Generalized Fisher Hypothesis
This section tests the generalized Fisher hypothesis, which states
that the real return on common stocks and (both expected and unexpected
components of) inflation should vary independently of each other. This
conjecture makes sense to many economists since, as claims against real
physical capital, common stocks ought to act as a hedge against
inflation. (4) This generalized hypothesis is commonly tested by a
regression of the form using time series data:
(1) [r.sub.t] = [mu] + [theta][[pi].sup.e.sub.t] +
[[epsilon].sub.t],
where [r.sub.t] is the real stock returns and [[pi].sup.e.sub.t] is
the expected inflation rate. According to the generalized Fisher
hypothesis, the real rates of return on common stocks and expected
inflation rates are independent. Thus, the coefficient [theta] should
not be significantly different from 0 if the generalized Fisher
hypothesis holds. The same logic applies for the unexpected inflation
cases.
B. The ARDL Approach
In this article, as an alternative, we assess the effect of
expected inflation on real stock return using panel econometric
techniques. In particular, Equation (1) is extended to a panel data
specification. Moreover, following conventional wisdom, we assume that
there exists a long-run relationship between real stock return
([r.sub.it]) and expected inflation rate ([[pi].sup.e.sub.it]), which
can be written as:
(2) [r.sub.it] = [[mu].sub.i] + [theta][[pi].sup.e.sub.it] +
[[epsilon].sub.it]
where [[mu].sub.i] is the fixed (country-specific) effect, i = 1,
2, ..., N is the country indicator, and t = 1, 2, ..., T is the time
index. In the time series framework, Pesaran and Shin (1998) and
Pesaran, Shin, and Smith (2001) propose the ARDL models to estimate the
long-run cointegrating relationship among variables of interest. In a
panel data specification, we follow the suggestion of Pesaran, Shin, and
Smith (1999) to nest Equation (2) in an ARDL specification to allow for
rich dynamics in the way that real stock return adjusts to changes in
the anticipated inflation and to other explanatory variables, if any.
The ARDL(p, q) model, that is, the dependent and independent variables enter the right-hand side with lags of order p and q, respectively, can
be written as:
(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where [x.sub.it], is a k x 1 vector of independent variables, which
includes only the expected inflation [[pi].sup.e.sub.it] (in some cases,
the unexpected inflation [[pi].sup.u.sub.t]), in our main application.
In addition to [[pi].sup.e.sub.it], however, we also consider the
inflation uncertainty ([h.sub.it]) as an additional explanatory variable
in our later application.
Equation (3) can be reparameterized and written as:
(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where [[ph].sub.i] = - (1 - [[summation].sup.p.sub.j=1]
[[lambda].sup.ij], [[beta].sub.i] = [[summation].sup.q.sub.j] =
[[delta].sub.ij], [[lambda].sup.*.sub.ij] = -
[[summation].sup.p.sub.m=j+1] [[lambda].sub.im], and
[[delta].sup.*.sub.ij] = - [[summation].sup.q.sub.m=j+1]
[[delta].sub.im], j = 1, 2, ..., q - 1.
By grouping the variables in levels, Equation (4) can be rewritten
as:
(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where the vector [[theta].sub.i] = -[[beta].sub.i]/[[phi].sub.i]
defines the long-run equilibrium relationship between [r.sub.it] and
[x.sub.it] as [r.sub.it] = -
([[beta]'.sub.i]/[[phi].sub.i])[x.sub.it] + [[eta].sub.it]. In
contrast, [[lambda].sup.*.sub.it] and [[delta].sup.*.sub.it] are the
short-run coefficients relating real stock returns to its determinants
[x.sub.it]. Finally, [[phi].sub.i] measures the speed of adjustment of
[r.sub.it] toward its long-run equilibrium following a given change in
[x.sub.it] and [[phi].sub.i] < 0 ensures that such a long-run
relationship exists. As a result, a significant and negative value of
[phi] can be treated as evidence in support of cointegration between
[r.sub.it] and [x.sub.it].
As argued in Catao and Solomou (2005) and Catao and Terrones
(2005), the ARDL specification in Equation (5), where all explanatory
variables enter the regression with a lag, not only mitigates
endogeneity issues but also accommodates the substantial persistence of
inflation adjustments and captures potentially rich stock return
adjustment dynamics. In addition, the model allows for heterogeneity in
the relationship between stock return and expected inflation across
countries since the various parameters in Equation (5) are not
restricted to be the same across countries. Finally, the ARDL approach
allows us to estimate an empirical model that encompasses the long- and
short-run stock return effects of expected inflation using a data field
composed of a relatively large sample of countries and quarterly
observations.
There are a few existing procedures for estimating the above model.
At one extreme, the simple pooled estimator assumes the fully
homogeneous-coefficient model in which all slope and intercept
parameters are restricted to be identical across countries. At the other
extreme, the fully heterogeneous-coefficient model imposes no
cross-country coefficients constraint and can be estimated on a
country-by-country basis. This is the so-called mean group (MG)
estimator introduced by Pesaran and Smith (1995). The approach amounts
to estimate separate ARDL regressions for each group and obtain [theta]
and [phi] as simple averages of individual group coefficient
[[theta].sub.i] and [[phi].sub.i]. In particular, Pesaran and Smith
(1995) show that the MG estimator will provide consistent estimates of
the averages of parameters interested.
In between these two extremes, the dynamic fixed-effect method
allows the intercepts to differ across groups, but it imposes
homogeneity of all slope coefficients and error variances.
Alternatively, Pesaran, Shin, and Smith (1999) propose the PMG
estimator, which restricts the long-run parameters to be identical over
the cross section, but allows the intercepts, short-run coefficients
(including the speed of adjustment), and error variances to differ
across groups on the cross section. If the long-run homogeneity
restrictions are valid, it is known that MG estimates will be
inefficient. In this case, the maximum likelihood--based PMG approach
proposed by Pesaran, Shin, and Smith (1999) will yield a more efficient
estimator. (5) As shown in Pesaran, Shin, and Smith (1999), the validity
of a cross-sectional, long-run homogeneity restriction of the form
[[theta].sub.i] = [theta], i = l, 2 , ... *, N--and hence the
suitability of the PMG estimator--can be tested by a standard
Hausman-type statistic.
In terms of the real stock-inflation relation, the PMG estimator
offers the best available compromise in the search for consistency and
efficiency. This estimator is particularly useful when the long run is
given by conditions expected to be homogeneous across countries, while
the short-run adjustment depends on country characteristics such as
monetary and fiscal adjustment mechanisms, capital market imperfections,
and relative price and wage flexibility (e.g., Loayza and Ranciere
2006). Therefore, we use the PMG method to estimate a long-run
relationship that is common across countries while allowing for
unrestricted country heterogeneity in the adjustment dynamics.
C. Measures of Expected Inflation and Inflation Uncertainty
To estimate the Fisher regression, we need a measure of expected
inflation [[pi].sup.e.sub.it]. First, we follow Gultekin (1983) to use
contemporaneous inflation rates as proxies for expected inflation. The
realized values are used under the assumption that expectations are
rational. Second, we rely on a pure autoregressive integrated moving
average (ARIMA) model to generate expected inflation and unexpected
inflation. Inflation forecasts from ARIMA regressions are used as
indicators of expected inflation, while the forecast errors are used as
the measure of unexpected inflation [[pi].sup.u.sub.it]. The model is
expressed as:
(6) [[pi].sub.t] = [[alpha].sub.0] + [p.summation over (i=1)]
[[alpha].sub.i][[pi].sub.t-i] + [q.summation over (j=1)]
[[phi].sub.j][[epsilon].sub.t-j],
where [[epsilon].sub.t-j] is a white noise process. Third, to allow
for conditional hgteroskedasticity, we assume that
[[epsilon].sub.t-j]|[[OMEGA].sub.t-1] = [h.sup.1/2.sub.t][[eta].sub.t]
and [[eta].sub.t] ~ NID (0, 1). Particularly, we consider three
alternative specifications of the conditional variance [h.sub.t] for
each country. The first one is the GARCH(1,1) process set out by
Bollerslev (1986), which can be specified as:
(7) [h.sub.t] = [a.sub.0] + [a.sub.1][h.sub.t-1] +
[b.sub.1][[epsilon].sup.2.sub.t-1].
By taking account of the asymmetric effects of negative and
positive shocks, the second specification for the conditional variance
is the exponential GARCH (EGARCH) process proposed by Nelson (1991). The
specification can be written as:
(8) In ([h.sub.t]) = [a.sub.0] + [a.sub.1]ln ([h.sub.t-1]) +
[b.sub.1][absolute value of [[epsilon].sub.t-1]/[square root of
[h.sub.t-1]]] + [c.sub.1][[epsilon].sub.t-1]/[square root of
[h.sub.t-1]]].
And the third and last model for the conditional variance is an
extension of the basic GARCH model. Engle and Lee (1999) represent the
GARCH(1,1) model as characterized by reversion to a constant mean
[bar.[mu]], that is,
(9) [h.sub.t] = [bar.[mu]] + [a.sub.1]([h.sub.t-1] - [bar.[mu]]) +
[b.sub.1]([[epsilon].sup.2.sub.t-1] - [bar.[mu]]).
In contrast, their component GARCH (CGARCH) process allowing
reversion to a time-varying mean [m.sub.t] is modeled as:
(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
By estimating Equation (6) along with Equations (7), (8), and (10),
respectively, we can obtain expected and unexpected components of
inflation. Moreover, we follow conventional applications such as
Asteriou and Price (2005) and Byrne and Davis (2005a, 2005b) to proxy
inflation uncertainty by the logarithm of the fitted (conditional)
volatility values from Equations (7), (8), and (10), respectively. The
corresponding inflation uncertainty measures are denoted as
[h.sup.g.sub.it], [h.sup.eg.sub.it], and [h.sup.cg.sub.it],
respectively. In addition to expected inflation, they are used to assess
the effect of inflation uncertainty on real stock returns.
III. DATA AND EMPIRICAL RESULTS
The generalized Fisher hypothesis is examined using quarterly data
on a panel of 16 industrialized OECD countries. These countries include
Australia, Austria, Belgium, Canada, Finland, France, Germany, Ireland,
Italy, Japan, The Netherlands, New Zealand, Norway, Spain, the United
Kingdom, and the United States. The sample period runs from 1957:Q1 to
2000:Q1, with a few exceptions. The original observations are collected
by Rapach (2002) from the International Monetary Fund's
International Financial Statistics. (6) The inflation rate is computed
by taking first differences of the natural logarithm of the consumer
price index. And the real stock return is computed as the differences of
the natural logarithm of the nominal share price index deflated by the
consumer price index. Table 1 reports basic statistics for inflation and
real stock return variables for each country. As shown, Germany has the
lowest average inflation, while Spain has the highest average inflation.
Also, Belgium has the lowest average rate of stock return, whereas
Finland has the highest average rate of stock return. Moreover, the
correlation coefficients between inflation rates and real stock returns
are negative for all countries.
A. The Effects of Expected Inflation
As a benchmark, we first test the generalized Fisher hypothesis
using realized inflation as a proxy for expected inflation via the PMG
methodology. The procedure is as follows. First, the estimates of the
long-run slope parameters are obtained jointly across countries through
a (concentrated) maximum likelihood procedure. Second, the estimation of
short-run coefficients along with the speed of adjustment,
country-specific intercepts and error variances are done on a
country-by-country basis also through maximum likelihood and using the
estimates of the long-run slope coefficients previously obtained.
Table 2 displays the results on specification tests and the
estimation of long- and short-run parameters linking real stock returns
and inflation. (7) We emphasize the results from using the PMG
estimator, considering its gains in consistency and efficiency over
other panel error-correction estimators. For comparison purposes, We
also present the results obtained with the MG estimator.
To check the existence of a long-run relationship (dynamic
stability), the coefficient on the error-correction term should be
negative and within the unit circle. As can be seen in Table 2, the
pooled error-correction coefficient estimates are significantly negative
and fall within the dynamically stable range for both PMG and MG
estimators, giving evidence of mean reversion to a nonspurious long-run
relationship and therefore stationary residuals. In addition, the
Hausman test of long-run homogeneity restriction is not rejected,
indicating that the PMG estimator is more suitable for the analysis,
relative to the MG estimator. Accordingly, the following analysis
focuses on the PMG approach.
Regarding the estimated parameters, we find that the long-run
estimate of inflation is highly significant and negative, meaning that
real stock returns are strongly and negatively linked to realized
inflation in the long run. However, the short-run coefficients on
inflation tell a different story. As explained, short-run coefficients
are not restricted to be the same across countries, so that we do not
have a single pooled estimate for each coefficient. Nevertheless, we can
still analyze the average short-run effect by considering the mean of
the corresponding coefficients across countries. As shown in Table 2,
the short-run average relationship between real stock returns and
inflation appears to be positive but insignificant. This finding is
consistent with the generalized Fisher hypothesis of zero correlation
between real stock returns and inflation. Stocks, as claims against
productive capital, can fully protect shareholders from changes in
(expected) inflation.
To check if these results are sensitive to model specification
(time trend and/or seasonal effects), Table 3 reports these robustness
tests. The estimation outcome is qualitatively similar to that in Table
2. The signs and statistical significance of both long- and short-run
coefficients remain unchanged. Moreover, the pooled error-correction
coefficients continue to be significantly negative and within the unit
circle. Furthermore, the long- and short-run effects of inflation on
real stock returns are not only qualitatively but also quantitatively
very similar to those in Table 2.
As another robustness check, we experiment with alternative
measures of expected inflation. As mentioned earlier, we extract
expected components of inflation from a simple ARIMA model and the ARIMA
model with GARCH, EGARCH, and CGARCH processes, respectively. The
corresponding results are presented in Table 4. As shown, the pooled
error-correction estimates continue to signal long-run cointegration
between real stock returns and unexpected inflation, irrespective of alternative unexpected inflation measures. Moreover, the long-run
coefficient estimates remain significantly negative, while the short-run
coefficient estimates remain insignificant, irrespective of different
measures of expected inflation.
Finally, to make sure our results are not pertaining to a specific
sample, we segregate the sample into two groups, G7 and non-G7 country
categories. The results are reported in Table 5. Specifically, Panel A
of Table 5 reports the results for G7 countries, while Panel B of Table
5 reports the results for non-G7 countries. Once again, they are
qualitatively similar to those with the full sample, confirming negative
long-run correlation but zero correlation between real stock returns and
expected inflation in the short run.
B. The Effects of Unexpected Inflation
This section examines the generalized Fisher hypothesis using
unexpected inflation. As mentioned, the unexpected inflation is measured
as the difference between the actual and the expected inflation
extracted above. Table 6 summarizes the estimation results. As can be
seen, the estimates for the pooled error-correction coefficient are
significantly negative and lie inside the unit circle, indicating the
existence of long-run relationship between real stock returns and
unexpected inflation. Moreover, the long-run coefficient estimates are
negative and highly significant, whereas the short-run coefficient
estimates are positive and strongly significant, irrespective of
alternative measures of unexpected inflation. The findings suggest that
while unexpected inflation has a positive impact on real stock returns
in the short run, it tends to affect real stock returns in a negative
way in the long run. Accordingly, the evidence of coexistence of a
positive short-run effect of unexpected inflation with a negative
long-run effect of unexpected inflation implies that stocks are a poor
hedge against unexpected inflation.
The results also hold for different subsamples as shown in Table 7,
where countries are split into G7 and non-G7 country groups. In either
country group, the pooled error-correction coefficient estimates fall
within the dynamically stable range, meaning that real stock returns and
unexpected inflation are cointegrated. Moreover, the sign and
statistical significance of all long- and short-run coefficients remain
unchanged, and the magnitude of long- and short-run coefficients is
qualitatively similar to those with full sample. The data again confirm
that stocks are a poor hedge against unexpected inflation, irrespective
of time frequency, unexpected inflation indicators, and sample size
considered.
C. The Effects of Inflation Uncertainty
This section evaluates the impacts of inflation uncertainty on real
stock returns. As suggested by Friedman (1977), an increase in inflation
variability adversely affects economic activity because it reduces the
role of prices in guiding market activity and increases the cost of
assimilating information. This negative real effect of inflation
volatility is supported by Fischer (1981) and Holland (1988), among
others. On the other hand, Berument, Ceylan, and Olgun (2007) point out
that modeling inflation volatility is necessary in that risk-averse
agents tend to consider both anticipated macroeconomic variables and
associated risk of the variables in their decision-making process. In
that sense, a real effect of inflation uncertainty is expected. For
example, based on a precautionary motive and the assumption of
risk-averse agents, Dotsey and Sarte (2000) suggest that more inflation
uncertainty raises saving and hence investment and economic growth. The
impact of inflation volatility is thus an empirical matter.
To explore whether stocks are a good hedge against variable
inflation, we need an indicator of inflation uncertainty. Since there
are different ways to model inflation uncertainty, here, as mentioned,
the inflation uncertainty is measured by conditional variance obtained
from the GARCH, EGARCH, and CGARCH processes, respectively. Table 8
reports the estimation results when both expected inflation and
inflation uncertainty measures are included as explanatory variables.
Clearly, the pooled error-correction coefficient estimates continue to
be negative and significant, suggesting a long-run equilibrium
relationship among real stock returns, expected inflation, and inflation
uncertainty. As expected, anticipated inflation measures maintain
significantly negative long-run impacts along with insignificant
short-run impacts on real stock returns in all regressions. Notably,
inflation uncertainty appears to have a negative long-run effect but an
insignificant short-run impact on real stock returns, irrespective of
alternative inflation uncertainty indicators. The evidence indicates
that both the level and the uncertainty of inflation contribute to lower
real stock returns in the long run but exert little short-run influence
on real stock returns. Moreover, the observed negative long-run effect
of inflation uncertainty agrees with the proposition of malfunctioning price mechanism due to more volatile inflation.
IV. CONCLUSIONS
In the Fisherian world, inflation is a purely monetary phenomenon
in the sense that it has no real effect on economy activities. However,
because of imperfect capital markets, inertia, and/or contractual
obligation, changes in inflation may have different influence on real
activities in the short run and long run. By recognizing this
possibility, this article estimates an encompassing empirical model of
the long-and short-run effects of inflation on real stock returns using
a sample of cross-country and time series observations. We implement the
analysis using the PMG methodology of Pesaran, Shin, and Smith (1999),
which allows for short-run heterogeneity across countries but long-run
homogeneity among sample countries.
Our empirical results are summarized as follows. First, in terms of
anticipated component of inflation, we find that the Fisher effect appears to hold at short horizons, where expected inflation has
insignificant short-run impacts on real stock returns but not at longer
horizons and where anticipated inflation is found to have negative
long-run impacts on real stock returns. Second, regarding unanticipated
inflation, we find that a negative long-run effect coexists with a
positive short-run effect. The evidence thus invalidates the Fisher
hypothesis and suggests that stocks are a poor hedge against unexpected
inflation. Third, as for inflation uncertainty similar to the expected
inflation case, we find that while inflation uncertainty has a negative
long-run effect on real stock returns, it has an insignificant short-run
effect on real stock returns. Finally, these results are found to be
robust to alternative measures of expected and unexpected inflation and
inflation uncertainty.
It is noted that this article focuses on advanced countries. It
will be interesting and vital to test the generalized Fisher hypothesis
for both developed and developing countries to gain the whole picture of
the real stock returns-inflation relation. Moreover, since inflation
exerts different long- and short-run impacts on real stock returns, it
would be important for both theoretical models and empirical studies to
explore the exact mechanisms through which inflation, both expected and
unexpected, and inflation uncertainty affect real stock returns at
different time lengths. Finally, since the financial infrastructure has
changed dramatically for the sample countries, it is important for
future study to incorporate this element into the PMG estimation to see
whether structural changes play a role in the relationship between real
stock returns and inflation. (8)
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(5.) Provided that there is a unique vector defining the long-run
relationship among variables involved, and the lag orders p and q are
suitably chosen, MG and PMG estimates of an ARDL regression yield
consistent estimates of that vector, regardless of whether the variables
involved are I(1) or I(0).
(6.) All the data used in this article can be downloaded from the
Web site of Rapach at http://pages.slu.edu/ faculty/rapachde/.
(7.) Loayza and Ranciere (2006) suggest that when the main interest
is on the long-run parameters, the lag order of the ARDL can be selected
using some consistent information criteria on a country-by-country
basis; however, when there is also interest in analyzing and comparing
the short-run parameters, it is recommended to impose a common lag
structure across countries. Thus, in this article, we use the latter
procedure and set p = q = 1, for simplicity. For robustness check, we
have also tried different orders for p and q selected by Akaike
information criterion, Schwarz Bayesian criterion, and Hannan and Quinn,
respectively. We found qualitatively and quantitatively similar results.
(8.) We thank one anonymous referee for this point.
ABBREVIATIONS
ARDL: Autoregressive Distributed Lag
ARIMA: Autoregressive Integrated Moving Average
CGARCH: Component Generalized Autoregressive Conditional
Heteroskedasticity
EGARCH: Exponential Generalized Autoregressive Conditional
Heteroskedasticity
GARCH: Generalized Autoregressive Conditional Heteroskedasticity
MG: Mean Group
OECD: Organization for Economic Cooperation and Development
PMG: Pooled Mean Group
doi: 10.1111/j.1465-7295.2009.00193.x
(1.) Originally, Fisher (1930) maintains that nominal interest
rates fully reflect available information about the future values of
inflation rates, and thus, nominal interest rates should move
one-for-one with inflation, both ex ante and ex post, under the
assumption that real interest rates are independent of movements in
inflation. Fama and Schwert (1977) argue that this Fisher hypothesis,
based on a complete dichotomy between the real and the monetary sectors
of the economy, can be generalized to stocks and other forms of assets.
(2.) Several theoretical explanations have been put forth for the
negative relationship of stock returns with inflation. For example, the
Mundell-Tobin hypothesis is based on the Pigou real wealth effect in
explaining a negative relationship between asset returns and inflation
and in supporting monetary nonneutrality. However, the money illusion
hypothesis states that stock market investors suffer from money illusion
and incorrectly discount real cash flows with nominal discount rates,
thereby causing the market's subjective expectation of the future
equity premium to deviate systematically from the rational expectations
(e.g., Asness 2000; Cohen, Polk, and Vuolteenaho 2005; Modigliani and
Cohn 1979; Sharpe 2002). In addition, the proxy hypothesis suggests that
the observed negative relationship between stock returns and inflation
is proxying for a positive relation between stock returns and real
variables and a negative relation between inflation and real activity
(e.g., Fama 1981, 1983; Geske and Roll 1983).
(3.) As long as there exists long-run relationship, whether
variables are integrated is not required for the PMG methodology.
(4.) As defined in Bodie (1976, 460), a security is an inflation
hedge if and only if its real return is independent of the rate of
inflation.
Shu-Chin Lin *
* I am grateful to M. Hashem Pesaran and David E. Rapach for making
publicly available their computer code and data used in this article,
respectively. I also thank Vincenzo Quadrini (the editor) and River
Huang for helpful suggestions and comments and Albert Suen for excellent
research assistance. Any remaining errors are my own responsibility.
Lin: Professor, Department of Economics, Tamkang University, 151
Ying-Chun Road, Tamsui 25137, Taipei County, Taiwan, Republic of China.
Phone +886-2-26215656 ext 3359, Fax +886-2-26209654, E-mail:
econscl@mail.tku.edu.tw
TABLE 1
Basic Statistics and Sample Coverage
corr
Country Name r [pi] (r, [pi])
Australia 0.5445 1.3271 -0.3035
Austria 0.3968 0.9277 -0.0516
Belgium -0.2152 1.0359 -0.2377
Canada 0.5339 1.0832 -0.2070
Finland 1.7829 1.4586 -0.4056
French 0.6694 1.3688 -0.2257
Germany 0.9859 0.8136 -0.2497
Ireland 1.1471 1.6229 -0.1212
Italy 0.2872 1.7502 -0.1028
Japan 0.9841 1.0227 -0.2725
The Netherlands 1.0647 0.9773 -0.1766
New Zealand 0.0579 1.7439 -0.2684
Norway 0.5207 1.3270 -0.2264
Spain 0.2744 2.0856 -0.1661
United Kingdom 0.8567 1.5860 -0.1137
United States 1.0598 1.0533 -0.3895
Country Name Period Observations
Australia 1957:02 to 2000:01 172
Austria 1957:02 to 1998:04 167
Belgium 1957:02 to 1996:02 157
Canada 1957:02 to 2000:01 172
Finland 1957:02 to 2000:01 172
French 1957:02 to 2000:01 172
Germany 1970:02 to 2000:01 120
Ireland 1957:02 to 2000:01 172
Italy 1957:02 to 2000:01 172
Japan 1957:02 to 2000:01 172
The Netherlands 1957:02 to 2000:01 172
New Zealand 1961:02 to 2000:01 156
Norway 1957:02 to 2000:01 172
Spain 1961:02 to 2000:01 156
United Kingdom 1958:02 to 1999:01 164
United States 1957:02 to 2000:01 172
Notes: The reported values are the means of the real stock return
(r) and inflation ([pi]). In addition, the correlation coefficients
between r and [pi] for all countries over alternative sample
periods and corresponding (quarterly) observations are also
reported.
TABLE 2
The Effect of Inflation on Real Stock Return
PMG MG
Long-run coefficient
[[pi].sub.it] -1.8405 *** (0.1843) -1.8799 *** (0.2056)
Error-correction
coefficient
[phi] -0.7564 *** (0.0231) -0.7613 *** (0.0229)
Short-run coefficients
[DELTA][[pi].sub.it] 0.0037 (0.2419) 0.1345 (0.2554)
c 2.3810 *** (0.1638) 2.4454 *** (0.3389)
Hausman Test
Long-run coefficient
[[pi].sub.it] 0.1878 (0.6647)
Error-correction
coefficient
[phi]
Short-run coefficients
[DELTA][[pi].sub.it]
c
Notes: The values in the parenthesis are the standard errors
of corresponding coefficients. For Hausman test of long run
parameter homogeneity, the value in the bracket is the
corresponding p value.
*** indicates significance at 1% level.
TABLE 3
Robustness Check
T Qs
Long-run coefficient
[[pi].sub.it] -2.1497 *** (0.2257) -2.0727 *** (0.1987)
Error-correction
coefficient
[phi] -0.7546 *** (0.0195) -0.7361 *** (0.0193)
Short-run coefficients
[DELTA][[pi].sub.it] 0.3596 (0.2738) -0.1329 (0.2328)
T -0.0569 (0.4174)
Q1 0.6800 (0.7766)
Q2 0.2583 (0.9859)
Q3 -0.2060 (0.7801)
c 2.6969 *** (0.2633) 2.3554 *** (0.6372)
T plus Qs
Long-run coefficient
[[pi].sub.it] -2.2462 *** (0.2257)
Error-correction
coefficient
[phi] -0.7397 *** (0.0200)
Short-run coefficients
[DELTA][[pi].sub.it] -0.0639 (0.2347)
T -0.0576 (0.4394)
Q1 0.6862 (0.7768)
Q2 0.2620 (0.9898)
Q3 -0.2010 (0.7802)
c 2.5531 *** (0.6746)
Notes: T denotes trend and Qs denote seasonal dummies.
The values in the parenthesis are the standard errors
of corresponding coefficients.
*** indicates significance at 1% level.
TABLE 4
Alternative Expected Inflation on Real Stock Return
ARIMA
ARIMA (a) GARCH (b)
Long-run coefficient
[[pi].sup.e.sub.it] -1.9063 *** (0.2555) -1.8290 *** (0.2611)
Error-correction
coefficient
[phi] -0.7443 *** (0.0184) -0.7437 *** (0.0191)
Short-run coefficients
[DELTA][[pi].sup.e.
sub.it] 0.7154 (0.8088) -0.2265 (0.7557)
c 2.4293 *** (0.1403) 2.2899 *** (0.1266)
ARIMA
EGARCH (b) CGARCH (b)
Long-run coefficient
[[pi].sup.e.sub.it] -1.8156 *** (0.2551) -1.9146 *** (0.2606)
Error-correction
coefficient
[phi] -0.7468 *** (0.0195) -0.7472 *** (0.0194)
Short-run coefficients
[DELTA][[pi].sup.e.
sub.it] -0.1156 (0.7716) -0.3025 (0.6777)
c 2.3078 *** (0.1274) 2.3699 *** (0.1348)
Notes: The values in the parenthesis are the standard errors of
corresponding coefficients.
(a) The fitted value of inflation ([[pi].sup.e.sub.it]) from a pure
ARIMA model as in Equation (6) for each country.
(b) The fitted value of inflation ([[pi].sup.e.sub.it]) from an
ARIMA model with alternative conditional heteroskedasticity
specifications as in Equations (7), (8), and (l U), respectively.
*** indicates significance at 1% level.
TABLE 5
Subsample Results--Expected Inflation on Real Stock Return
ARIMA
ARIMA GARCH
Panel A: G7 countries
Long-run coefficient
[[pi].sup.e.sub.it] -1.6812 *** (0.3764) -1.5573 *** (0.3970)
Error-correction
coefficient
[phi] -0.7429 *** (0.0240) -0.7422 *** (0.0239)
Short-run coefficients
[DELTA][[pi].sup.e.
sub.it] -0.3598 (0.7431) -0.6735 (0.9021)
C 2.1542 *** (0.0684) 1.9613 *** (0.0494)
Panel B: non-G7 countries
Long-run coefficient
[[pi].sup.e.sub.it] -2.1012 *** (0.3470) -2.0429 *** (0.3459)
Error-correction
coefficient
[phi] -0.7460 *** (0.0280) -0.7456 *** (0.0294)
Short-run coefficients
[DELTA][[pi].sup.e.
sub.it] 1.5536 (1.2955) 0.1239 (1.1859)
c 2.6918 *** (0.2692) 2.5852 *** (0.2456)
ARIMA
EGARCH CGARCH
Panel A: G7 countries
Long-run coefficient
[[pi].sup.e.sub.it] -1.4028 *** (0.3688) -1.5484 *** (0.3810)
Error-correction
coefficient
[phi] -0.7418 *** (0.0239) -0.7428 *** (0.0238)
Short-run coefficients
[DELTA][[pi].sup.e.
sub.it] -0.5332 (0.8409) -0.6632 (0.9189)
C 1.8857 *** (0.0552) 1.9617 *** (0.0562)
Panel B: non-G7 countries
Long-run coefficient
[[pi].sup.e.sub.it] -2.1970 *** (0.3506) -2.2399 *** (0.3555)
Error-correction
coefficient
[phi] -0.7527 *** (0.0303) -0.7521 *** (0.0301)
Short-run coefficients
[DELTA][[pi].sup.e.
sub.it] 0.2308 (1.2491) -0.0005 (1.0135)
c 2.7442 *** (0.2643) 2.7781 *** (0.2729
Notes: The G7 countries are Canada, France, Germany, Italy, Japan,
United Kingdom, and United States. The non G7 countries include
Australia, Austria, Belgium, Finland, Ireland, The Netherlands, New
Zealand, Norway, and Spain. The values in the parenthesis are the
standard errors of corresponding coefficients.
*** indicates significance at 1% level.
TABLE 6
The Effects of Unexpected Inflation on Real Stock Return
ARIMA
ARIMA GARCH
Long-run coefficient
[[pi].sup.u.sub.it] -2.5082 *** (0.4046) -2.6229 *** (0.3823)
Error-correction
coefficient
[phi] -0.7257 *** (0.0179) -0.7286 *** (0.0177)
Short-run coefficients
[DELTA][[pi].sup.u.
sub.it] 0.6815 *** (0.2220) 0.7061 *** (0.2188)
c 0.5540 *** (0.0924) 0.6447 *** (0.1023)
ARIMA
EGARCH CGARCH
Long-run coefficient
[[pi].sup.u.sub.it] -2.5752 *** (0.3896) -2.6533 *** (0.3973)
Error-correction
coefficient
[phi] -0.7258 *** (0.0183) -0.7280 *** (0.0177)
Short-run coefficients
[DELTA][[pi].sup.u.
sub.it] 0.7083 *** (0.2242) 0.7482 *** (0.2114)
c 0.6145 *** (0.0900) 0.6600 *** (0.1022)
Notes: The values in the parenthesis are the standard errors
of corresponding coefficients.
*** indicates significance at 1% level.
TABLE 7
Subsample Results--Unexpected Inflation on Real Stock Return
ARIMA
ARIMA GARCH
Panel A: G7 countries
Long-run coefficient
[[pi].sup.u.sub.it] -2.5162 *** (0.6845) -2.7490 *** (0.6124)
Error-correction
coefficient
[phi] -0.7230 *** (0.0258) -0.7270 *** (0.0257)
Short-run coefficients
[DELTA][[pi].sup.u.
sub.it] 0.9255 ** (0.4031) 0.9032 ** (0.4192)
c 0.6174 *** (0.0905) 0.7485 *** (0.0889)
Panel B: non-G7 countries
Long-run coefficient
[[pi].sup.u.sub.it] -2.5041 *** (0.5017) -2.5438 *** (0.4898)
Error-correction
coefficient
[phi] -0.7278 *** (0.0261) -0.7298 *** (0.0257)
Short-run coefficients
[DELTA][[pi].sup.u.
sub.it] 0.4926 ** (0.2438) 0.5598 ** (0.2320)
c 0.5047 *** (0.1517) 0.5663 *** (0.1689)
ARIMA
EGARCH CGARCH
Panel A: G7 countries
Long-run coefficient
[[pi].sup.u.sub.it] -2.7003 *** (0.6310) -2.9373 *** (0.6655)
Error-correction
coefficient
[phi] -0.7236 *** (0.0272) -0.7264 *** (0.0263)
Short-run coefficients
[DELTA][[pi].sup.u.
sub.it] 0.9224 ** (0.4331) 0.9680 ** (0.412)
c 0.6442 *** (0.0897) 0.7429 *** (0.0979)
Panel B: non-G7 countries
Long-run coefficient
[[pi].sup.u.sub.it] -2.5004 *** (0.4957) -2.4984 *** (0.4956)
Error-correction
coefficient
[phi] -0.7275 *** (0.0263) -0.7292 *** (0.0254)
Short-run coefficients
[DELTA][[pi].sup.u.
sub.it] 0.5500 ** (0.2322) 0.6015 *** (0.2215)
c 0.5896 *** (0.1491) 0.5984 *** (0.1680)
Notes. The G7 countries are Canada, France, Germany, Italy, Japan,
United Kingdom, and United States. The non G7 countries include
Australia, Austria, Belgium, Finland, Ireland, The Netherlands, New
Zealand, Norway, and Spain. The values in the parenthesis are the
standard errors of corresponding coefficients.
*** and ** indicate significance at 1% and 5% levels.
TABLE 8
The Effect of Inflation Uncertainty
ARIMA
GARCH EGARCH
Long-run coefficients
[[pi].sup.e.sub.it] -1.6872 *** (0.2934) -1.1020 *** (0.3312)
[h.sup.g.sub.it] -0.2919 (0.3164)
-1.1948 *** (0.3510)
[h.sup.cg.sub.it]
Error-correction
coefficient
[phi] -0.7440 *** (0.0192) -0.7508 *** (0.0193)
Short-run coefficients
[DELTA][[pi].sup.e.
sub.it] -0.2033 (0.7480) -0.5196 (0.7107)
[DELTA][h.sup.g.
sub.it] -0.3659 (0.6442)
[DELTA][h.sup.eg.
sub.it] 0.4025 (1.0679)
[DELTA][h.sup.cg.
sub.it]
c 1.9457 *** (0.1310) 0.7608 *** (0.1807)
ARIMA
CGARCH
Long-run coefficients
[[pi].sup.e.sub.it] -1.6661 *** (0.2872)
[h.sup.g.sub.it]
[h.sup.cg.sub.it] -0.6100 *** (0.2931)
Error-correction
coefficient
[phi] -0.7482 *** (0.0199)
Short-run coefficients
[DELTA][[pi].sup.e.
sub.it] -0.3993 (0.6604)
[DELTA][h.sup.g.
sub.it]
[DELTA][h.sup.eg.
sub.it]
[DELTA][h.sup.cg.
sub.it] 1.7715 (1.1036)
c 1.7203 *** (0.1611)
Notes: The values in the parenthesis are the standard errors
of corresponding coefficients.
*** indicates significance at 1% level.