\documentclass{article}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%TCIDATA{OutputFilter=LATEX.DLL}
%TCIDATA{Version=4.00.0.2312}
%TCIDATA{Created=Wednesday, July 24, 2002 21:41:33}
%TCIDATA{LastRevised=Wednesday, July 24, 2002 21:52:52}
%TCIDATA{}
%TCIDATA{}
%TCIDATA{CSTFile=40 LaTeX article.cst}
\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{criterion}[theorem]{Criterion}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summary}
\newenvironment{proof}[1][Proof]{\noindent\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
\input{tcilatex}
\begin{document}
\parskip=.07in \textit{Introduction}
Why are the correlations of stock market returns between, say, the U.S. and
U.K. higher than between the U.S. and Japan, but lower than between the U.S.
and Canada? Is the level of stock markets correlations too high to be
justified by the (lower) level of correlations between countries' economic
fundamentals, such as output or consumption? Does the level of stock markets
correlations tell us anything about the degree of international financial
market integration? In this paper, we will use an equilibrium model linking
stock markets correlations to countries output correlations to shed some
light on these three puzzling questions.
The first question really asks whether stock markets correlations across
countries can be explained by economic fundamentals. Two main types of
answers can be found in the literature. First, several researchers have
examined empirically the determinants of international stock markets
correlations (among the more recent investigations, see Longin and Solnik
(1995), Erb, Harvey and Viskanta (1994), Stulz and Karolyi (1996) and Ang
and Bekaert (1999)). However, without an underlying economic model, it is
not possible to understand why and how these determinants are relevant in
explaining correlations.\footnote{
For another underlying economic model, see Bansal and Lundblad (2000).}
Second, Hamao, Masulis and Ng (1990) and the many papers that followed this
work study the spillover of information from one economy to another. While
these studies are important in tracing the type of information that causes
common movement in expected returns and volatility, they do not give us a
starting point. That is, they do not tell us why stock markets correlations
are different across countries in the first place. Proposing a theoretical
explanation of the differences in the observed level of international stock
markets correlations is the first goal of our paper.
The second question we address is motivated by Shiller (1981)'s findings.
Shiller (1981) shows with a simple pricing model that in the United States
''stock prices are too volatile to be justified by subsequent changes in
dividends''. This is confirmed by Campbell (1996) for a number of other
countries. The ''excess volatility'' puzzle is commonly ascribed to an
''excessive'' degree of volatility of the pricing kernel, where
''excessive'' is understood relative to the observed degree of volatility of
consumption. In an integrated world capital market, the same pricing kernel
is applicable to all securities. If the kernel is excessively volatile, this
should translate into an equally excessive degree of correlation of world
equity returns. That is, equity correlations should be too high to be
justified by subsequent changes in national consumptions or outputs.
Discovering whether there exists or does not exist an ''excess-correlation
puzzle'' is the second goal of our paper.
Finally, we would like to infer form stock markets correlations the degree
of international financial market integration. But can one directly use
stock markets correlations as a measure of market integration? For instance,
if one finds that correlations have been rising, one is tempted to conclude
that financial markets are in the process of gradual integration.\footnote{%
Bekaert and Harvey (1995) link correlation with the degree of market
integration.\ Freimann (1998) offers an alternative, entirely statistical
procedure based on randomization of industrial sector returns, to compare
country correlations to what they would have been under integration.}
Indeed, we shall demonstrate in the context of our particular model that,
other things equal, over the relevant parameter range, correlations of stock
returns are larger in an integrated market than they would be in a segmented
market. In this statement, however, the ''other things equal'' caveat is
crucial. For instance, one should not draw conclusions about integration
from stock correlations if one has not controlled for the degree of
correlation of economic fundamentals. The model that we develop can be used
to control for ''other things equal'' so that it provides us with a tool to
diagnose the degree of integration of financial markets. If the market is
segmented, the correlation of world equity returns should be excessively low
relative to the model that assumes that markets are completely integrated.
Admittedly, one could interpret a rejection (observed correlations lower
than model correlations) as either evidence against the model or against the
hypothesis of market integration. But we are able to apply the same model
construction under the hypothesis of market segmentation and, in this way,
draw a meaningful comparison. Drawing inferences about international
financial market integration is the third goal of our undertaking.
To answer the three questions posed, our intuition is simply that, if most
of the variation in economic activity in two countries is associated with
the world business cycle, then the two countries should have high equity
correlations. Hence we combine a statistical model of the business cycle
with a log-linear asset pricing framework applied to an exchange economy.
After making some choices on the form of the utility function of the
representative indidual and some distributional assumptions, we are able to
determine the model's implied level of correlation for two countries'
realized rates of return, given the measured commonality in country outputs.
The modelling of stock returns by means of an exchange economy is in the
tradition of Lucas (1978) and Mehra and Prescott (1985).\ The assumption
that world output equals world consumption is evidently simplistic and,
worse yet, prevents us from drawing useful information from the physical
investment time series.\footnote{%
See Cochrane (1991), Restoy and Rockinger (1994).} In the international
context, however, the empirical behavior of each country's consumption is,
in fact, embarassingly close to the behavior of the country's production,
much more so than it should be in an internationally integrated world.%
\footnote{%
See Lewis (1999).} Furthermore, there is no doubt that the pure-exchange
setting is a useful shortcut and that calibration exercises in this
tradition have produced many insights concerning stock returns.\ Two of
these insights, recognized as the ``equity-premium puzzle''\ and the
``excess-volatility puzzle''\ already mentioned, would actually be
sufficient to reject the pure-exchange, representative-agent, form of
modelling.\ In the present paper, we ask the reader to suspend the disbelief
that arises from these puzzles,\footnote{%
On that issue, please, refer to the calibration in Section \ref{calibration_}%
.} in order to allow us to decide whether or not cross-moments do also cause
difficulties for this kind of modelling.
Our paper is thus intermediate between a macroeconomic real-business-cycle
paper and a Finance paper.\footnote{%
See also Canova and de Nicolo (1995).}\ A\ real-business-cycle paper would
attempt to explain observed facts such as that outputs across countries are
more highly correlated than consumptions.\ No equity returns would be
measured.\ A\ Finance paper would attempt to explain return correlations
across countries with asset pricing model and variables like cash flows to
equity that may not be directly or contemporaneously related to output.
A purely financial approach of stock returns correlations has been proposed
by Ammer and Mei (1996) and Campbell and Mei (1993). They decompose the
innovations in stock returns into three or four components: news about
future dividends, interest rates, possibly news about exchange rates and
news about future excess returns, the latter being calculated as a residual
only, as opposed to being determined by a dynamic pricing model. In Ammer
and Mei, inferences about rising or falling financial-market integration are
made on the basis of the rise or fall in the correlation between news about
future excess returns. No theoretical benchmark is provided to indicate
whether the observed value of that correlation is compatible with full
integration.\ A similar question had been raised earlier by Shiller (1989)
and Beltratti and Shiller (1993).\ Their asset pricing model was a
``present-value''\ model with unspecified stochastic discount rates which
were used to generate upper and lower bounds on the values of correlations.\
The upper and lower bounds were quite far apart.\ In the present paper, the
valuation equation is derived from optimal portfolio choices based on an
explicit stochastic process for the payoff series.
Another purely financial approach consists in using the framework of a
partial equilibrium model. Carrieri, Errunza and \ Hogan (2001)\ build on an
asset pricing model derived under a known type of segmentation, the
mild-segmentation, whereby some securities are restricted to some investors.
It allows them to compute an \textquotedblleft integration
index\textquotedblright\ which captures the degree to which securities known
to be inaccessible can be proxied by accessible securities. But the
calculation of their index requires the specification of the set of
securities which is not accessible to all investors.\ Our model, on the
other hand, fully endogenizes stock returns in a general equilibrium
framework so they only depend on the economic activity.
There have also been several previous attempts to understand the interplay
between the real economy and stock returns.\ They have been mostly focused
on the determination of conditional first moments of returns. A number of
empirical papers (see, for example, Fama, 1990, Schwert, 1990, Choi \textit{%
et al.}, 1999) show that there is a relation between expected output and
stock returns. Asset pricing tests offer another possible route of
examination. These tests specify common factors which each country has
sensitivity to (see Ferson and Harvey, 1993, Cheung, He and Ng, 1997). One
can deduce from the estimated sensitivities to the common factors what the
correlation of equity returns should be. Correlations are determined by a
statistical model that captures the relative movement of each country's
return versus some global benchmarks.\ They are not endogenized.\ The
associated pricing model is not solved out over time; it only provides
expected returns from exogenously measured covariances. In principle, the
resulting expected returns can be used to test the null hypotheses of
integration or segmentation, as in Jorion and Schwartz (1986).\ Most often,
however, expected returns are not estimated with sufficient precision to be
able to reject either null hypothesis.\ We feel that correlation
measurements hold the potential of providing more powerful tests of
integration.
Our work is finally also related to, but unfortunately does not encompass,
those studying time-varying correlations.\ We aim to understand why
correlations are different across countries, not how they differ from year
to year. In fact, the correlations are modelled as being constant over time.%
\footnote{%
We also execute calibrations (and, later, statistical tests) using
unconditional moment conditions. But that choice is unrelated to the
assumptions of the model since any model can be tested on the basis of its
unconditional.predictions.}\ Longin and Solnik (1995) show by means of a
statistical model, how correlations change through time.\footnote{%
Hodrick (1989) derives the multivariate GARCH\ process followed by stock
prices when dividends themselves follow a multivariate GARCH\ process.}\
Both Longin and Solnik (1995) and Erb, Harvey and Viskanta (1994) try
empirically to explain, on the basis of economic variables, how correlations
vary over time.\footnote{%
For instance, non US stock returns tend to have a higher correlation with US
stock returns while the US is in a recession than while it is in an
expansion. Volatility of returns is also larger while the US is in a
recession.\ See also Perez-Quiros and Timmermann (1996) and Ang and Bekaert
(1999).}. The analysis in Erb \textit{et al.} shows that while there is some
time-variation in the correlations of the G7 countries' equity returns
through time, the ranking of the correlations rarely changes. That is, while
there is variation in both the U.S.-U.K. and U.S.-Japan correlations through
time, the U.S.-U.K. correlation is always higher than the U.S.-Japan
correlation. Similarly, the U.S.-Canada correlation is always higher than
the U.S.-U.K. correlation. While it is clear that correlations are not
constant, our assumption should not interfere with the main point of our
paper, which is to explain why correlations are different across different
countries.
The paper is organized as follows. Section \ref{firstlook} explores the data
and the phenomena that we are trying to explain. In Section \ref%
{common_trend}, we develop the dynamic single-index model of Stock and
Watson (1993) which we will use to define each country's business cycle.\
The log-linear pricing kernel of Restoy and Weil (1993) is explained in
Section \ref{kernel}. Section \ref{combined} applies the log-linear pricing
kernel to the dynamic single-index business cycle model to derive
equilibrium security returns. We then examine, in Section \ref{calibration_}%
, the correlations implied by the model and the actual correlations observed
in the data. Section \ref{test} develops a statistical test of the
hypothesis of financial market integration. Some concluding remarks are
offered in the final section.
\bigskip
\textit{Page 6, paragraph on international operations, called inot question
by the referee.}
There is a severe drawback to using output as a proxy for the cash flows
generated by stock securities.\ In several countries, many of the companies
listed in the stock exchange typically have levels of foreign activities
markedly larger than the share of exports in the corresponding output
series. To assess the extent of the problem, we measured the percent of
foreign sales for the companies in each of the 12 countries in 1997. Using
the Worldscope universe, we constructed country aggregates by
value-weighting these ratios by the total revenues of each firm. Belgium,
Canada, and the Netherlands have the highest proportions (64.7\%, 64.2\% and
65.2\% respectively). The same ratio averages only 40.1\% for the other
countries in our sample.\ The share of exports in GDP is typically a lower
number; in December 1997, it ranges from 7\% for the U.S. to 49\%\ in the
Netherlands. It is tempting to make a scale adjustment to each country's
correlation based on the level of foreign activity, to bring that level down
to equal the share of exports in GDP. This adjustment would have to change
through time. For example, in 1991 the weighted proportion of foreign sales
in Canada was 47.2\% and it has increased to 64.2\% in 1997. But the
proportion of sales is an imperfect measure because it only measures one
part of earnings -- the revenues. We have no information as to the
extranational costs of the firms.\ We choose not to apply a scaling factor
of that type. First, we felt that imposing the scaling factors based on
these measures would be arbitrary as we do not observe for each country the
composition of foreign trade by destination. Second, we were worried about
introducing another level of estimation error.
\bigskip
\textit{Page 10, discussion of Figure 2, called into question by the referee.%
}
Many alternative specifications of the statistical model could have been
considered.\ For instance, a moving-average component might have been useful
in representing the persistence of the world business cycle.\ The number of
lags in the autoregressive specification could be varied.\footnote{%
A specification with three lags produced parameter estimates for the
additional lags that were not significant.}\ A multi-index model, with a
regional index for Europe, might be considered.\ Or the world business cycle
could have been pre-specified as, for instance, a weighted average of
country output growth rates.\ We cannot afford to try all specifications and
some of them do not lead to convergence of the algorithm so that no
comparison is possible.\ Furthermore, comparison of models, some of which
are not nested, requires the use of somewhat \textit{ad hoc} goodness-of-fit
criteria.\ Ultimately, what we must demonstrate is our ability to capture
almost all the common dynamic variation in output by means of the single
index, while the residuals $\eta _{t}$ and $\mathbf{\varepsilon }_{t}$ are
almost uncorrelated.\ As a measure of the descriptive quality of the output
model, we present Figure \ref{goodfit} which compares the correlations of
each country's output with the rest of the world to correlations obtained by
a simulation performed under the assumptions of the model, including the
zero-correlation of residuals assumption. The model does a good job of
matching these correlations. For a number of countries (Canada, Germany,
Italy, Netherlands), the simulated correlations are somewhat lower than the
actual ones. This indicates that our dynamic common factor does not
completely capture the correlation between rates of growth in output.\ Some
of it remains in the purely synchronous, static correlation of residuals.\
But the reader should keep in mind that, in subsequent analysis, we use the
actual residuals rather than the simulated ones. This provides an even
closer match. The statistical model really only serves to determine what
component in the joint behavior of outputs is due to a long-lasting dynamic
factor and what component can be captured by the synchronous, static
correlation.
\bigskip
\textit{Conclusion.}
One often hears the assertion that higher global stock market correlations
indicate increased global financial-market integration.\ That assertion is
problematic because it does not control for the economic fundamentals of
each country.
Our framework allows us to give international stock market correlations an
interpretation in terms of the degree of \ integration \textit{vs. }%
segmentation.\pagebreak\ It also allows us to decide whether or not
correlations are larger even than they should be under full integration, in
which case a general asset-pricing puzzle would have to be recognized.
We have linked the correlations of stock returns to their fundamental
determinants. These determinants were taken to be the behavior of output in
the various countries.\ We have represented the behavior of output
(actually, industrial production) in twelve OECD countries by means of a
\textquotedblleft dynamic single-index\textquotedblright\ statistical model,
designed to capture the \textquotedblleft covariation\textquotedblright\ of
outputs in a dynamic framework, over the business cycle.\ Over the sample
period January 1970\ to June 1996, the estimated values of the coefficients
of the statistical model seem reasonable, and produce a common world cycle
which is fairly persistent.
Assuming that output and securities' payoff are closely linearly related to
each other, we have applied a dynamic representative-agent asset-pricing
kernel to the estimated behavior of output.\ Within that framework,
implemented under the hypothesis of integrated financial markets, we have
been able simulatenously to match the levels of theoretical correlations of
realized rates of return with the measured correlations, and some of the
theoretical and realized correlations between stock returns and output.
Hence, there is no \textquotedblleft excess-correlation
puzzle\textquotedblright .\ The hypothesis of financial-market segmentation,
however, has produced correlations markedly lower than the actual ones.\ The
likely interpretation of these two comparisons is that the stock markets of
the world are reasonably integrated.
One type of correlation, however, has not been explained satisfactorily by
our model.\ It is the correlation of each country's stock return with the
own-country industrial production.\ The theoretical value is quite a bit
higher than the observed one, at the value of the unknown parameter
(elasticity of intertemporal substitution) that matches the other
correlation moments.\ This is the single reason for which, in a formal GMM\
test of all moment conditions, the full-integration model was rejected by
the data.
While the idea of using cross-moments to gauge the degree of integration
seems to have generated powerful tests, we have run into practical
difficulties which further research will have to solve.\ The main practical
difficulty is an accounting one.\ It has arisen from the data inputs
themselves -- outputs on the one hand, stock returns on the other -- which
are not sufficiently well classified at the present time to allow a clean
match of their definitions.
\bigskip
\textit{Additional references:}
\bigskip
Carrieri, F., V. Errunza and K.\ Hogan, 2001, ``Characterizing World Market
Integration Through Time,''\ working paper, McGill University.
Karolyi, G. A. and R. M. Stulz, 1996, ``Why do Markets move Together? An
Investigation of U.S.-Japan Stock Return Comovements,'' Journal of Finance,
51, 951-986.
Rodriguez, R., F.\ Restoy and J.\ I.\ Pe$\widetilde{n}$a, 2002, ``A\ General
Equilibrium Approach to the Stock Returns and Real Activity Relationship,''
forthcoming Journal of International Money and Finance. (or published in
April)
\end{document}