WORKING PAPER NO 8
EMPIRICAL MODELLING
OF CONTAGION:
A REVIEW OF METHODLOGIES
MARDI DUNGEY, RENÉE FRY,
BRENDA GONZÁLEZ-HERMOSILLO,
VANCE L. MARTIN
The Working Paper is intended as a means whereby researchers’ thoughts and findings
may be communicated to interested readers for their comments. The paper should be
considered preliminary in nature and may require substantial revision. Accordingly, a
Working Paper should not be quoted nor the data referred to without the written consent
of the author. All rights reserved.
© 2003 Mardi Dungey, Renée Fry, Brenda González-Hermosillo and Vance L. Martin
Comments and suggestions would be welcomed by the authors:
e-mail: mardi.dungey@anu.edu.au
Em pirical M odelling of Con tagion: A Review of
M ethodologies
∗
Mardi Dungey
+%
, Renée Fry
+
,
Brenda González-Hermosillo
∗
and Vance L. Martin
#
+
Australian National Univ ersity
%
CERF, Cam bridge Universit y
∗
In ternational Monetary Fund
#
University of Melbourne
October 2003
Abstract
The existing literature promotes a n umber of alternative methods to test for
the presence of contagion during Þnancial market crises. This paper reviews those
methods, and shows how they are related in a uniÞed framework. A number of
extensions are also suggested which allow for multivarite testing, endogeneity
issues and structural breaks.
Key words: Contagion, Financial Crises.
JEL Classification: C15, F31
∗
This project was funded under AR C large gran t A00001350. We are grateful for commen ts from
David Cook, Jon Danielsson, Amil Dasgupta, Barry Eic hengreen, Charles Goodhart, P aul Masson,
Hashem Pesaran, Andreas Pick, Roberto Rigobon, Hyun Shin, Demosthenes Tambakis and partici-
pan ts at the Warwick Summer Workshop 2003. The paper was partly written while Mardi Dungey
w as a Visiting Fellow at CERF. The authors contact details are: mardi.dungey@an u.edu.au; re-
nee.fry@anu.edu.au; bgonzalez@imf.org; vance@unimelb.edu.au.
1
1Introduction
There is now a reasonably large body of empirical w ork testing for the existence of
contag ion during Þnancial crises. A range of different methodologies are in use, mak-
ing it difficu lt to assess the evidence for and against contagion, and particularly its
signiÞcance in transmitting crises bet ween count ries.
1
The origins of current empirical studies of con tag ion stem from Sharpe (1964) and
Grubel and Fadner (1971), and more recently from King and Wadhwani (1990), Engle,
Ito and Lin (1990) and Bekaert and Hodric k (1992). Man y of the m ethods pro posed in
these papers are adapted in some form to the curren t em pirical literature on measuring
con tagion.
The aim of the present paper is to provide a unifying framework to highlight the
key similarities an d differences between the various approac hes. For an overview of the
literature see Pericoli and Sbracia (2003) and Dornb u sch, Claessens and Park (2000).
The proposed framework is based on a latent factor structure whic h forms the basis of
the models of Dungey and Martin (2001), Corsetti, Pericoli and Sbracia (2001, 2003)
and Bekaert, Harvey and Ng (2003). This framew ork is used to compare directly the
correlation analysis appro ach pop u larised in this literature b y Forbes and Rigo bon
(2002), the VAR appro ach of Favero and Giava zzi (2002), the probability models of
Eic h engr een, Rose and Wyp losz (1995, 1996) and the co-exceedance approac h of Bae,
Karolyi and Stulz (2003).
An important outcome of this paper is that differenc es in the deÞnitions used to
test for contagion are minor and under certain conditions are even equivalent. In par-
ticular, all papers are interpreted as w or king from the same m odel, with the differences
stemming from the amo unt of information used in the data to detect contagion. In-
terpreting the approaches in this way pro vides a natural ordering of models across the
information spectrum with some models representing full information methods and
others represen ting partial information methods.
The paper proceeds as follow s. In Section 2 a framework draw n from basic rela-
tionship s between asset retu r n s is used to model returns in a non-crisis environment.
This framework is a ugmented in Sec t ion 3 to give a model which includes an avenue for
contagion during a crisis. Th e relationship between this model and the correlation tests
for con tagion are examined in Section 4 which includes a generalisation of the Forbes
and Rigobon bivariate test to a multivariate en viron m e nt. The remaining non-linear
1
The literature on Þnancial crises themselv es is m uch wider than that can vassed here and is reviewed
in Flood and Marion (1998) while more recent papers are represented by Allen and Gale (2000), Calvo
and Mendoza (2000), Kyle and Xiong (2001) and Kodres and Pritsker (2002).
2
tests are exam in e d in Section 5 and additional meth ods are canvassed in Section 6.
Each of the tests is show n to be a test of the signiÞcance of a slope dumm y. Section 7
concludes.
2 A M odel of I n terdependence
Before developing a model of con tagion, a model of in terdependence of asset mark ets
dur ing non -crisis periods is speciÞed as a latent factor model of asset returns. The
model has its origins in the the factor models in Þnance based on Arbitrage Pricing
Theory for example, where asset returns are determined by a set of common factors and
a set of idiosyncratic factors represen ting non-diversiÞable risk (Sharpe (1964); Solnik
(1974)). Similar latent factor models of contagion are used by Dungey and Martin
(2001), Dungey, Fry, Gonzalez-Hermos illo and Martin (2002a), Forbes and Rigobon
(2002) and Bekaert, Harvey and Ng (2003).
To simplify the analysis, the number of assets considered is three. Exte nd in g the
model to N assetsisstraightforwardwithanexamplegivenbelow.Letthereturnsof
three asset mark ets during a non-crisis period be deÞned as
{x
1,t
,x
2,t
,x
3,t
} . (1)
All returns are assumed to hav e zero means. The returns could be on currencies, or
national equity mark ets, or a combination of currency and equity returns in a partic-
ular coun try or across countries. The follow ing trivariate factor model is assumed to
summarise the dynamics of the three processes during a period of tranquility
x
i,t
= λ
i
w
t
+ δ
i
u
i,t
,i=1, 2, 3. (2)
The v ariable w
t
represents common shocks that impact upon all asset returns with
loadings λ
i
. These shocks could represen t Þnancial shoc ks arising from c h anges to the
risk aversion of international in vestors, or changes in wo rld endowments (Mahieu and
Sc h otm an (1994), Rigobon (2003b)). In general, w
t
represen ts market fundamentals
which determine the ave rage level of asset re t urns across internat i o nal markets during
“norm al”, that is, tranquil, times. Th is variable is commonly referred to as a world
factor, which may or ma y not be observed. For simplicit y, the world facto r is assumed
to be a latent stoc hastic process with zero mean and unit variance
w
t
∼ (0, 1) . (3)
The properties of this factor are extended below to capture ric her dynamics including
both autocorrelation and time-varying volatilit y. Th e terms u
i,t
in equation (2) are
3
idiosyncratic factors that are unique to a speciÞc asset mark et. The con tribution of
idiosyn cra tic shocks to the volatility of asset markets is determined by the loadings
δ
i
> 0. These factors are also assumed to be stochastic processes with zero mean and
unit variance
u
i,t
∼ (0, 1) . (4)
To complete the speciÞcation of the model, all factors are assumed to be independen t
E [u
i,t
,u
j,t
]=0, ∀i 6= j (5)
E [u
i,t
,w
t
]=0, ∀i. (6)
To highligh t the interrelationships amongst the three asset returns in (2) during a
non-crisis period, the covariances are given by
E [x
i,t
x
j,t
]=λ
i
λ
j
, ∀i 6= j, (7)
whilst the variances are
E
£
x
2
i,t
¤
= λ
2
i
+ δ
2
i
∀i. (8)
Expression (7) show s that any dependence bet ween asset returns is solely the result of
the inßuence of common shocks arising from w
t
, that simultaneously impact upon all
markets. Setting
λ
1
= λ
2
= λ
3
, (9)
results in independen t asset markets with all mo vements determined b y the idiosyn-
cratic shocks, u
i,t
.
2
The iden tifying assumption used by Mahieu and Schotman (1994)
in a similar problem is to set λ
i
λ
j
to a constant value, L,foralli 6= j.
3 Unanticipated Shoc k M odels of Con tagion
The deÞnition of the term contagio n varies widely across the literature. In this paper
conta gion is represented by the transm ission of unanticipated local shocks to another
country or market. This deÞnition is consistent with that of Masson (1999a,b,c), who
divides shocks to asset markets as either commo n, spillovers that result from some
identiÞable chann el, local or con tagion, and as sho wn below that of other approaches,
such as Forbes and Rigobon (2002) wh ere con tag ion is represented by an increase in
correlation during periods of crisis.
The Þrst model discussed is based on the factor structure dev eloped b y Dungey, Fry,
Gon zalez-Hermo sillo and Ma rtin (2002a,b) among st others, where con tagion is deÞned
2
Of course, just t wo of the restrictions in (7) are sufficient for independence of asset mark ets.
4