a new approach to measuring financial contagion...rate changes, and conditional stock return...
TRANSCRIPT
A New Approach to Measuring Financial
Contagion
Kee-Hong Bae
Korea University
G. Andrew Karolyi
Ohio State University
Rene M. Stulz
Ohio State University and NBER
This article proposes a new approach to evaluate contagion in financial markets. Our
measure of contagion captures the coincidence of extreme return shocks across
countries within a region and across regions. We characterize the extent of contagion,
its economic significance, and its determinants using a multinomial logistic regression
model. Applying our approach to daily returns of emerging markets during the 1990s,
we find that contagion is predictable and depends on regional interest rates, exchange
rate changes, and conditional stock return volatility. Evidence that contagion is
stronger for extreme negative returns than for extreme positive returns is mixed.
Since 1997, economists, policymakers, and journalists have talked aboutthe `̀ Asian flu.'' It has generally been perceived that the adverse currencyand stock market shock that first affected Thailand in July 1997 propa-gated across the world with little regard for economic fundamentals in theaffected countries. Before the Asian flu, there was the 1994 Mexican``Tequila crisis,'' and since then, the 1998 ``Russian virus.'' Emergingmarkets economic crises, in general, have been characterized ascontagious. According to Webster's dictionary, contagion is defined as``a disease that can be communicated rapidly through direct or indirectcontact.'' Emerging markets economic crises have led to massive bailoutsto quell contagion and have reduced support for free capital mobility.
Bae and Karolyi grateful to the Dice Center for Research on Financial Economics for support; Bae alsoappreciates the financial support of the SK Research Award. We thank Tom Santner, Mark Berliner, BobLeone, and Stan Lemeshow for useful discussions on methodology, Steve Cecchetti, Peter Christoffersen,Craig Doidge, Barry Eichengreen, Vihang Errunza, David Hirshleifer, Matthew Pritsker, RobertoRigobon, Richard Roll, Karen Wruck, and, especially, an anonymous referee, and the editor, CamHarvey, for comments. Comments from seminar participants at Hong Kong University of Science andTechnology, Korea University, McGill University, Yale University, Michigan State University,Universiteit Maastricht, Ohio State University, Rice University, Monte Verita Risk Management Con-ference, Federal Reserve Bank of Chicago Annual Conference on Bank Structure and Competition,Global Investment Conference on International Investing, and the NYSE Conference on Global EquityMarkets in Transition improved the article. Address correspondence to Ren�e M. Stulz, Ohio StateUniversity, Fisher College of Business, 2100 Neil Ave. 806 A Fisher Hall, Columbus, OH 43210, ore-mail: stulz@cob. osu.edu.
The Review of Financial Studies Fall 2003 Vol. 16, No. 3, pp. 717±763, DOI: 10.1093/rfs/hhg012ã 2003 The Society for Financial Studies
The International Monetary Fund (IMF) deputy managing director at thetime, Stanley Fischer, rationalized the 1994 Mexican bailout in this way:`̀ Of course, there was another justification: contagion effects. They werethere and they were substantial.''1 Contagion has led Bhagwati (1998) toargue that `̀ capital flows are characterized . . . by panics and manias.'' Ifmarkets work this way, it is not surprising that Stiglitz (1998) called forgreater regulation of capital flows, arguing that `` . . . developing countriesare more vulnerable to vacillations in international flows than everbefore.''
Even though this contagion connotes powerful images of economic andfinancial plagues, it is difficult to study scientifically. Evidence of thisdifficulty is that there is little agreement on even defining what financialcontagion means.2 Since equity market valuations reflect future economicactivity, much of recent research attempts to learn about contagion byinvestigating whether equity markets move more closely together in tur-bulent periods. There are considerable statistical difficulties involved intesting hypotheses of changes in correlations across quiet and turbulentperiods and recent investigations of this issue find at best mixed results [seeBaig and Goldfajn (1999) and Forbes and Rigobon (2001)]. Nevertheless,there does not seem to be strong evidence that stock returns in one countryare more highly correlated with returns in other countries during crisisperiods once one takes into account the fact that correlation estimates arelikely biased. A related literature demonstrates that, even though correla-tions change over time, it is difficult to explain changes in correlations.3
Perhaps the most important limitation of these investigations of finan-cial contagion is that they focus on asset return correlations in the firstplace. None of the concerns expressed about contagion seem to be basedon linear measures of association for macroeconomic or financial marketevents. In fact, these concerns are generally founded on the presumptionthat there is something different about extremely bad events that leads toirrational outcomes, excess volatility, and even panics. In the context ofstock returns, this means that if panic grips investors as stock returns falland leads them to ignore economic fundamentals, one would expect large
1 See his statement in Calvo (1996, p. 323).
2 For a review of the difficulties in defining contagion, see Dornbusch, Park, and Claessens (2001). A recentbook by Claessens and Forbes (2001) published this and more than 20 other articles from a February2000 World Bank/IMF conference, International Financial Contagion: How it Spreads and How it Can beStopped. These articles include theoretical models, a conceptual contribution, country case studies, andbroad-based empirical studies. Other important recent contributions include Eichengreen, Rose, andWyplosz (1996), Glick and Rose (1999), Masson (1999), Kaminsky and Reinhart (2000), Allen and Gale(2000), and Kyle and Xiong (2001). Eichengreen, Rose, and Wyplosz (1996) estimate probit regressions torelate the occurrence of a currency crisis in a country to predictive variables. Though their seminalanalysis is a precursor of our approach, it is not focused on the probability of the joint occurrence ofextreme events across countries.
3 See, for instance, Erb, Harvey, and Viskanta (1995), King, Sentana, and Wadhwani (1995), Longin andSolnik (1995, 2001), and Karolyi and Stulz (1996). See also the recent survey by Karolyi and Stulz (2003).
The Review of Financial Studies / v 16 n 3 2003
718
negative returns to be contagious in a way that small negative returns arenot. Correlations that give equal weight to small and large returns are notappropriate for an evaluation of the differential impact of large returns. Itcould be that large shocks, because they exceed some threshold or gen-erate panic, propagate across countries, but this propagation is hidden incorrelation measures by the large number of days when little of impor-tance happens.
To address these concerns, a number of recent studies have extendedmodels of international asset return volatilities and correlations to allowfor these observed threshold (large absolute return) and asymmetric(negative return) effects. Some researchers have employed univariateand multivariate extreme value theory (EVT) from statistics [Longin(1996), Danielsson and de Vries (2000), Longin and Solnik (2001),Straetmans (1998), Starica (1999), Kaminsky and Schmuckler (1999),Pownall and Koedijk (1999), and Hartman, Straetmans, and de Vries(2001)]. Others have developed multivariate GARCH-M models allowingasymmetry [Ang and Chen (2002), Bekaert and Wu (2000)], Poisson jumps[Das and Uppal (2002)], and even Hamiltonian regime-switching [Angand Bekaert (2002)] in the joint dynamics of returns. In contrast, in thisarticle we abandon the correlation framework that previous researchershave focused on to study contagion and direct our attention instead tothe large positive and negative return days. To avoid a situation where ourresults are dominated by a few observations, we do not compute correla-tions of large returns, but instead measure the joint occurrences of largereturns. In order to determine whether there are more frequent jointoccurrences of large absolute value returns than expected, we calibratethese outcomes using Monte Carlo simulations of the joint returns-generating processes of international stock market returns with differentassumptions about their structure. We then develop an econometricmodel of the joint occurrences of large absolute value returns using multi-nomial logistic regression.
In part, we are influenced in our choice of methodology by theextensive use of multinomial logistic analysis in epidemiology researchon contagious diseases [Hosmer and Lemeshow (1989)]. In epidemiology,the model is used to answer questions such as: Given that N persons havebeen infected by a disease, how likely is it that K or more other personswill be affected by that disease? We use multinomial logistic regres-sions to model occurrences of large returns, which we refer to as ``excee-dances.'' With this model we can determine how likely it is that twoLatin American countries will have large returns on a particular daygiven that two countries in Asia have large returns on that day or thepreceding day.
An important advantage of this multinomial logistic analysis, especiallyrelative to those based on EVT, is that we can condition on attributes and
Measuring Financial Contagion
719
characteristics of the exceedance events using control variables (or covari-ates) measured with information available up to the previous day. We findthat exchange rate changes, interest rate levels, and regional conditionalvolatility of equity market returns are statistically important covariatesthat help explain and predict exceedances in this model. We definecontagion within regions as the fraction of exceedance events that isnot explained by our covariates (exchange rates, interest rates, marketvolatility). We find that contagion differs across regions. Contagionappears to be much stronger within Latin America than it is withinAsia. Further, large positive and large negative returns are equallycontagious in Asia, but not in Latin America, where large negative returnsare more contagious.
Another advantage of our approach is that it enables us to considercontagion across regions as well as within regions. An earlier literature haslooked extensively at the transmission of information across advancedmarkets during the calendar day.4 Our investigation is related to thisliterature in that we consider the impact of exceedances among countriesin one region on the probability of observing exceedances among coun-tries in other regions. More specifically, we define contagion acrossregions as the fraction of the exceedance events in a particular regionthat is left unexplained by its own covariates but that is explained by theexceedances from another region. We find evidence of cross-regionalcontagion. Remarkably, the United States seems completely insulatedfrom any Asian contagion, even during the Asian crisis in 1997.
To apply our approach, we construct daily index returns from stocks inthe monthly investible indices of the International Finance Corporation(IFC indices) from April 1992 to December 1995 and then use the dailyindex returns provided by the IFC from January 1996 to December 2000for 17 Asian and Latin American markets of the Emerging MarketsDatabase (EMDB, now owned by Standard & Poor's). The sample periodextends from April 1992 through December 2000. These returns areparticularly well suited to our analysis because they correspond to thereturns of portfolios that can be held by foreign investors.
The article proceeds as follows. In Section 1 we present our data,provide statistics on joint occurrences of extreme returns, and calibratethe joint occurrences of extreme returns using Monte Carlo simulationevidence. In Section 2 we motivate the use of a multinomial logit model toexplain joint occurrences of extreme events and estimate such a model.The model is then used to show how contagion takes place within regions.
4 Important investigations of international `̀ spillovers'' of returns and volatility include studies by Eun andShim (1989), Hamao, Masulis, and Ng (1990), King and Wadhwani (1990), Engle, Ito, and Lin (1990),Bae and Karolyi (1994), Lin, Engle, and Ito (1994), and Susmel and Engle (1994). More recent contribu-tions include Ramchand and Susmel (1998), Ng (2000), Connolly and Wang (2003) and Dumas, Harvey,and Ruiz (2003).
The Review of Financial Studies / v 16 n 3 2003
720
In Section 3 we investigate contagion across regions. We conclude inSection 4.
1� Measuring Financial Contagion as Coexceedances
In this section we first discuss our data and its properties. We then turn tothe distribution of extreme returns that we use throughout the study andcalibrate using Monte Carlo simulations whether the frequency of jointextreme returns within regions is consistent with various assumptionsabout the joint dynamics of returns.
1.1 Data
A number of explanations of contagion are based on actions by foreigninvestors. We therefore use indices that are representative of the capitali-zation of stocks that foreign investors can hold. Originally the Interna-tional Finance Corporation (IFC) produced such indices for emergingmarkets; currently these indices are produced by Standard & Poor's.5 Weuse the IFC indices from Asia and Latin America. To study the extent towhich contagion affects the United States and Europe, we also use theS&P 500 index for the United States and the Datastream InternationalEurope index for Europe. Our focus is on daily returns. Daily returns areavailable for the IFC indices since December 31, 1995. Using these data,the sample of daily returns therefore starts on December 31, 1995, andends on December 29, 2000 (1305 observations). While the sample perioddoes include the 1997 Asian crisis as well as the 1998 Russian crisis, we areconcerned that the sample is too short and that it excludes anotherimportant crisis event, namely, the Mexican peso devaluation ofDecember 1994. As a result, we proceed to construct value-weightedindexes of the stocks in the respective emerging markets using dailystock prices from Datastream International. Our effort is also facilitatedby the availability of the monthly IFC indexes from the EMDB 2000CD-ROM. Our index construction procedure follows a series of stepsand checks and is detailed in the appendix.
Table 1 provides sample statistics, including correlations for the fullsample periodÐApril 1, 1992, to December 29, 2000 (2283 observations).Not surprisingly, the properties of the indices vary dramatically acrosscountries. China has the highest average daily return (0.087%), but Brazilhas the highest daily return standard deviation (3.370%), almost fourtimes that of the United States and Europe. The largest positive extremereturn (58.708%) obtains for Pakistan, whereas Peru experienced the
5 Detailed information can be obtained from The IFC Indexes: Methodology, Definitions and Practices(February 1998, International Finance Corporation, Washington, DC) or Standard & Poor's EmergingMarket Data Base EMDB 2000TM Version 6.0 (CD-ROM).
Measuring Financial Contagion
721
Table
1S
um
mary
stati
stic
sof
dail
yre
turn
son
Inte
rnati
onal
Fin
anci
al
Corp
ora
tion
(IF
C)
emer
gin
gm
ark
ets
indic
es,
Apri
l1,
1992,
toD
ecem
ber
29,
2000
CH
NK
OR
PH
IT
WN
INA
IND
MA
LP
AK
SR
IT
HA
AR
GB
RA
CH
IC
OL
ME
XP
ER
VE
NU
SE
uro
pe
Mea
n(%
)0
.08
70
.01
90
.01
20
.01
7ÿ
0.0
30
0.0
02
0.0
21
0.0
37
0.0
16ÿ
0.0
29
0.0
26
0.0
44
0.0
25
0.0
05
0.0
29
0.0
54
0.0
39
0.0
60
0.0
53
Std
.D
ev.
(%)
2.8
88
2.7
23
1.7
58
1.8
21
1.8
23
3.2
71
2.1
03
2.5
02
1.3
73
2.4
26
2.1
07
3.3
70
1.2
46
1.2
67
2.0
73
2.4
71
2.5
44
0.9
38
0.8
26
Med
ian
(%)
0.0
00
0.0
00
0.0
00
0.0
00
0.0
00
0.0
06
0.0
01
0.0
00
0.0
00ÿ
0.0
29
0.0
05
0.0
20
0.0
00ÿ
0.0
13
0.0
03
0.0
01
0.0
00
0.0
33
0.0
89
Min
imu
m(%
)ÿ
38
.09ÿ
21
.71ÿ
10
.14ÿ
10
.80ÿ
18
.74ÿ
37
.54ÿ
22
.78ÿ
17
.74ÿ
8.7
1ÿ
16.0
8ÿ
14.1
3ÿ
27.5
1ÿ
6.7
0ÿ
6.9
3ÿ
20.8
5ÿ
41.9
0ÿ
14.8
7ÿ
7.1
0ÿ
4.1
1
Maxim
um
(%)
48
.08
27
.03
21
.59
7.3
614
.26
27.2
123
.90
58.7
017
.97
16.6
313
.35
35.2
99.2
69
.23
16.7
315.7
921.8
54.9
93.6
0
Co
rrel
ati
on
sC
HN
KO
RP
HI
TW
NIN
AIN
DM
AL
PA
KS
RI
TH
AA
RG
BR
AC
HI
CO
LM
EX
PE
RV
EN
US
Eu
rop
e
CH
N1
.00
0.0
90.0
10
.03ÿ
0.0
10.0
70.0
5ÿ
0.0
10.1
10.0
5
KO
R0
.07
1.0
00
.13
0.1
00
.11
0.0
00.1
50.0
50.0
60.2
00.1
7
PH
I0
.06
0.1
71
.00
0.2
00.1
40
.17
0.0
60.1
80.0
50.0
90.2
30.2
2
TW
N0
.02
0.1
20
.17
1.0
00
.12
0.0
50
.08
0.0
40.1
10.0
30.0
50.1
60.1
2
INA
0.0
50
.10
0.0
90
.04
1.0
00
.05
0.0
40
.06
0.0
10.0
40.0
2ÿ
0.0
10.0
60.0
5
IND
0.0
40
.15
0.3
60
.13
0.0
61.0
00.1
30
.09
0.1
40
.05
0.1
30.0
70.0
70.1
60.1
2
MA
L0
.04
0.1
80
.28
0.1
60
.08
0.3
61
.00
0.1
00.0
60
.09ÿ
0.0
10.0
90.0
30.0
50.2
10.1
0
PA
K0
.01
0.0
10
.07
0.0
50
.04
0.0
60
.08
1.0
00.0
20
.01
0.0
20
.03
0.0
30.0
00.0
90.0
30.0
3
SR
I0
.00
0.0
20
.07
0.0
20
.00
0.0
30
.04
0.0
41
.00
0.0
30.0
50
.03
0.0
60.0
20.0
10.0
30.0
20.0
3
TH
A0
.10
0.2
50
.36
0.1
50
.10
0.3
30
.38
0.0
70
.07
1.0
00
.16
0.1
00
.13
0.0
40.1
30.0
60.0
60.1
80.1
6
0.1
20.0
70.1
30.1
1
AR
G0
.03
0.1
00
.07
ÿ0
.01
0.0
20.0
70
.10
0.0
2ÿ
0.0
20
.10
1.0
0
BR
Aÿ
0.0
10
.09
0.0
50
.02
0.0
60
.05
0.0
50
.03
0.0
10.0
70
.39
1.0
0
CH
I0
.02
0.1
20
.15
0.0
90
.06
0.1
10
.11
0.0
50
.00
0.1
60
.42
0.3
11
.00
CO
L0
.05
0.0
40
.07
0.0
30
.02
0.0
70
.03
0.0
40
.04
0.0
50
.05
0.0
70
.09
1.0
0
ME
X0
.01
0.1
20
.11
0.0
40
.04
0.0
60.1
00
.06ÿ
0.0
10.0
90
.47
0.3
40
.39
0.0
71.0
0
PE
R0
.00
0.0
60
.05
0.0
30
.07
0.0
40.0
50
.01
0.0
20.0
50
.16
0.1
60
.17
0.0
30.1
71.0
0
VE
N0
.06
0.0
80
.07
0.0
30
.02
0.0
80
.07
0.0
00
.00
0.0
80
.17
0.1
40
.17
0.0
80.1
80.0
61.0
0
0.0
50.1
9
US
ÿ0
.02
0.0
80
.07
0.0
10
.02
0.0
20.0
10
.01
0.0
10.0
40
.39
0.2
70
.29
0.0
50.4
00.1
10.0
91.0
0
0.0
30.2
3
Eu
rop
e0
.07
0.1
60
.16
0.0
70
.04
0.1
20.1
70
.03
0.0
40.1
70
.27
0.1
70
.27
0.0
80.2
80.1
40.1
40.3
11.0
0
0.1
00.1
9
Each
ind
exfr
om
the
Em
ergin
gM
ark
etD
ata
base
(EM
DB
)is
ad
just
edto
refl
ect
acc
essi
bil
ity
of
the
mark
etan
din
div
idu
al
sto
cks
for
fore
ign
inves
tors
.S
um
mary
stati
stic
sin
clu
de
the
mea
n,
med
ian
,st
an
dard
dev
iati
on
,m
inim
um
,m
axim
um
,an
dco
rrel
ati
on
so
fd
ail
yin
dex
retu
rns.
EM
DB
cou
ntr
ies
incl
ud
eC
hin
a(C
HN
),K
ore
a(K
OR
),P
hil
ipp
ines
(PH
I),
Taiw
an
(TW
N),
Ind
ia(I
NA
),In
do
nes
ia(I
ND
),M
ala
ysi
a(M
AL
),P
ak
ista
n(P
AK
),S
riL
an
ka
(SR
I),
Th
ail
an
d(T
HA
),A
rgen
tin
a(A
RG
),B
razi
l(B
RA
),C
hil
e(C
HI)
,C
olo
mb
ia(C
OL
),M
exic
o(M
EX
),P
eru
(PE
R),
an
dV
enez
uel
a(V
EN
).W
eals
oin
clu
de
dail
yre
turn
so
fS
&P
500
ind
exfo
rU
.S.
an
dD
ata
stre
am
Inte
rnati
on
al
Eu
rop
ein
dex
.T
he
corr
elati
on
sin
the
up
per
righ
tm
atr
ixare
bet
wee
nd
ail
yre
turn
so
fA
sian
ind
ices
inca
len
dar
tim
et
an
dth
ose
of
Lati
nA
mer
ica,
Un
ited
Sta
tes,
an
dE
uro
pe
ind
ices
inca
len
dar
tim
etÿ
1.A
ver
ages
of
corr
elati
on
sare
pre
sen
ted
init
ali
csan
dare
ass
oci
ate
dw
ith
the
blo
cko
fco
rrel
ati
on
sab
ove
an
dad
jace
nt
toth
est
ati
stic
.
722
largest negative extreme return (ÿ 41.908%). All IFC indices have agreater standard deviation than indices for the United States and Europe.
Correlations within regions are higher than correlations across regions.However, none are particularly high except for the correlations amongBrazil, Argentina, Chile, and Mexico, which are all above 0.30. Anothercluster of moderately high correlations includes the markets of SoutheastAsia (Philippines, Indonesia, Malaysia, and Thailand). On a given day,trading starts in Asia and ends in the Americas. Consequently informationthat becomes available in Latin America at noon cannot affect stockprices in Asia the same day. We consider, therefore, correlations betweenreturns in Asia and Latin America on the same day as well as thosebetween returns in Asia today and Latin America on the preceding day.The correlations between returns in Asia and Latin America separated byone day (upper right matrix with average correlation of 0.07) are roughlythe same size as the same day correlations (lower left matrix with averagecorrelation of 0.05). But the correlations of returns in Asia andthose of the United States lagged by one day are greater (average correla-tion of 0.13) than the contemporaneous correlations (average correlationof 0.03).
1.2 Exceedances and coexceedances
Correlations have been much studied. We focus instead on occurrences ofextreme returns. At this point we arbitrarily define an extreme return, orexceedance, as one that lies either below (above) the 5th (95th) quantile ofthe marginal return distribution. Alternative definitions are used later.6
We treat positive extreme returns separately from the negative extremereturns. In Table 2 we report our counts of the number of joint occur-rences of extreme returns, or coexceedances, within a region on a parti-cular day. The left side of the table focuses on negative return (``bottomtail'') exceedances and the right side on positive return (``top tail'') excee-dances. We define a coexceedance count of i units for negative returns asthe joint occurrence of i exceedances of negative returns on a particularday. The table is to be read in four parts for the top and bottom tails of theAsian (top panel) and Latin American (bottom panel) regional markets.In each part, the 2283 days in the sample period are divided into those inwhich there are no exceedances in any country (e.g., 1526 such days inAsia for negative extreme returns), only one country exceedance (e.g., 530such days in Asia for negative extreme returns), and multicountry coex-ceedances. Note that we count not only the total number of days with
6 Longin (1996), Kaminsky and Schmukler (1999), Pownall and Koedijk (1999), and Longin and Solnik(2001) employ conditional parametric or nonparametric measures of extreme returns. Later we employ aconditional approach as a robustness check on our (co-)exceedances using an EGARCH model ofconditional volatility. We also employ different sizes for the tails.
Measuring Financial Contagion
723
Table
2S
um
mary
stati
stic
sof
(co-)
exce
edance
sfo
rdail
yem
ergin
gm
ark
etin
dex
retu
rns,
Apri
l1,
1992,
toD
ecem
ber
29,
2000
Mea
nre
turn
wh
en�
6
Nu
mb
ero
fn
egati
ve
(co
-)ex
ceed
an
ces
Nu
mb
ero
fp
osi
tive
(co
-)ex
ceed
an
ces
Mea
nre
turn
wh
en�
6(%
)�
65
43
21
00
12
34
5�
6(%
)
CH
Nÿ
7.5
62
21
327
79
1526
1507
76
23
10
31
15.0
3K
OR
ÿ8.2
24
10
615
35
44
1526
1507
41
33
21
85
68.0
5P
HI
ÿ6.7
23
13
15
14
24
45
1526
1507
43
32
18
11
37
7.0
9T
WN
ÿ4.9
54
46
633
61
1526
1507
66
24
15
41
46.1
1IN
Aÿ
5.8
43
55
10
28
63
1526
1507
61
34
85
33
3.6
1IN
Dÿ
9.5
55
14
14
11
35
35
1526
1507
42
27
23
13
45
18.5
2M
AL
ÿ6.1
75
12
17
16
33
31
1526
1507
41
30
22
12
36
9.3
5P
AK
ÿ10.1
34
36
430
67
1526
1507
61
34
94
33
3.8
2S
RI
ÿ3.7
63
33
823
74
1526
1507
79
25
62
11
2.4
1T
HA
ÿ7.8
55
14
15
21
28
31
1526
1507
36
34
21
10
67
10.6
8T
ota
lÿ
7.0
85
16
22
36
148
530
1526
1507
546
148
51
18
67
7.4
7
AR
Gÿ
8.9
67
610
15
31
45
1754
1691
52
35
13
85
17.1
2B
RA
ÿ11.3
26
612
17
27
46
1754
1691
58
31
13
74
110.8
1C
HI
ÿ4.7
97
611
18
24
48
1754
1691
45
41
17
55
16.6
2C
OL
ÿ3.6
65
15
12
18
73
1754
1691
86
19
52
20
--M
EX
ÿ7.5
67
67
17
34
43
1754
1691
65
28
97
41
7.3
2P
ER
ÿ5.8
45
011
11
27
60
1754
1691
65
29
11
44
15.7
9V
EN
ÿ6.6
76
54
12
31
56
1754
1691
77
25
73
11
7.3
7T
ota
lÿ
6.9
77
615
34
96
371
1754
1691
448
104
25
95
17.5
1
Ap
osi
tive
(neg
ati
ve)
or
`̀to
p-t
ail
''(`̀
bo
tto
m-t
ail
'')
exce
edan
cefo
rd
ail
yin
dex
retu
rns
corr
esp
on
dto
the
sub
set
of
ord
ered
retu
rns
that
com
pri
seth
eh
igh
est
(lo
wes
t)fi
ve
per
cen
to
fall
retu
rns.
Co
exce
edan
ces
rep
rese
nt
join
to
ccu
rren
ces
of
exce
edan
ces
acr
oss
cou
ntr
yin
dic
esb
yd
ay.
Aco
exce
edan
ceo
fi
mea
ns
that
ico
un
trie
sh
ave
an
exce
edan
ceo
nth
esa
me
day.
Co
exce
edan
ces
are
rep
ort
edfo
ri�
1,.
..,5
sep
ara
tely
an
dfo
ri
equ
al
tosi
xo
rm
ore
as
``�
6.''
Fo
rex
am
ple
,o
f2283
trad
ing
days,
ther
eare
148
occ
urr
ence
so
fn
egati
ve
or
bo
tto
m-t
ail
coex
ceed
an
ces
for
Asi
aw
ith
two
cou
ntr
ies
on
ly,
an
d27
of
tho
seo
ccu
rren
ces
incl
ud
eC
hin
aas
on
eo
fth
etw
oco
un
trie
sw
ith
bo
tto
m-t
ail
coex
ceed
an
ces.
The Review of Financial Studies / v 16 n 3 2003
724
coexceedances of a given count, but we also identify which countriesparticipate in those events and how often.
In Asia, the distribution of coexceedances is mostly symmetric betweennegative and positive extreme returns. There are five days with six or morecountries in the bottom tail and seven days with six or more countries inthe top tail. The same symmetry holds for other numbers of coexcee-dances. The one case where there is a substantial difference between thebottom-tail coexceedances and the top-tail coexceedances is for the cate-gory of five coexceedances. In that case, there are 16 days withfive countries in the bottom tail and only 6 days with five countries inthe top tail. Indonesia was in the bottom tail for 14 of the 16 days with fivecountries and all 5 days with six or more countries. Malaysia was the nextmost regular participant in bottom-tail coexceedance events. During theAsian crisis, crisis countries (Thailand, Korea, Malaysia, and Indonesia)seem more likely to be in the bottom tail when other countries are in thebottom tail. Looking at the correlations of Table 1, these patterns inextreme returns are not a complete surprise since the crisis countrieshave higher correlations among themselves than with the noncrisis coun-tries. We report in Table 2 the average returns for each of the 10 Asiancountries when six or more Asian countries experience an exceedance on agiven day. Surprisingly the crisis countries do not always have largernegative returns on such days than noncrisis countries. The absolutevalue average return is higher for positive returns (7.47%) than for nega-tive returns (ÿ 7.08%) on such days.
Though Latin America has only seven countries, there are 7 days wheresix or more countries are in the bottom tail at the same time and 28 days intotal when four countries or more have extreme negative returns. Thiscontrasts with the case for positive extreme returns in which there is onlyone day when six countries or more have returns in the positive tail. InLatin America, and unlike Asia, there is clearer evidence of asymmetry inthat coexceedances of negative returns are more likely than coexceedancesof positive returns. Argentina, Chile, and Mexico are in each of thebottom-tail events with five or more coexceedances; by contrast,Colombia has a disproportionately large number of single-country excee-dances (73 out of 371). Among top-tail coexceedance counts, Colombia isagain less likely to be involved with other Latin American countries, likeArgentina, Chile, and Mexico, but much more likely to experience atop-tail event alone (86 of 448).
We compare but do not report coexceedance counts during the periodsbefore and after the July 1997 devaluation of the Thai Baht for Asia andbefore and after the December 1994 devaluation of the Mexican peso. Allbut five of the Asian bottom-tail and all but one of the top-tail coexcee-dances involving four countries or more (38 and 30, in total, respectively)take place after the devaluation of the Thai Baht. There are also clusters of
Measuring Financial Contagion
725
large numbers of coexceedances in Latin America but they are distributedmore evenly over the period. Latin American coexceedances involvingfour countries or more experiencing negative extreme returns take placein early 1994 (four events) and around the December 1995 Mexican pesocrisis (seven events), but two more clusters appear in July 1997 andespecially in August 1998, the Russian default crisis period. The differ-ences before and after the Thai Baht devaluation for Asia and around theMexican peso and Russian default periods for Latin America reflect thesame result as that observed by Forbes and Rigobon (2002) and others ofan increase in correlations during the crisis periods. Indeed, such a result isdifficult to interpret because we should naturally see higher correlationsonce we condition on the occurrence of large returns. The reason for this isthat, in the presence of a common factor, large returns are more likely tobe associated with large realizations of the common factor. To understandwhether the existence of coexceedances can be explained by conditioningon large absolute value returns, we have to investigate what the distribu-tion of coexceedances would be if correlations were constant during thesample period. To this end we perform Monte Carlo simulation experi-ments.7
1.3 Contagion versus coexceedances: Monte Carlo simulation evidence
We now consider the following experiment. Suppose that the covariancematrix of returns is stationary over the sample period and that the returnsfollow a multivariate normal or Student's t distribution. Using that co-variance matrix, we simulate 5000 random realizations of the time series of2283 daily returns for the Asian countries. For each realization we identifythe returns below (above) the 5th (95th) percent quantile returns for thebottom (top) tail of the return distributions and perform the same non-parametric count across countries by region as in Table 2. Doing soprovides us with a distribution of exceedances and coexceedances. Weuse that distribution to calibrate the observed sample of coexceedances.The results are shown in Table 3 and for each scenario we report thesimulated mean, standard deviation, 5% and 95% quantiles, and thesimulated p-value of the 5000 replications.
The distribution of the coexceedances will depend on the assumptionsmade about the returns-generating process. To this end we perform theMonte Carlo simulation with three scenarios. The first scenario assumesthat returns are jointly distributed as multivariate normal. The secondscenario allows for the possibility of fatter tails with the multivariateStudent's t distribution. The degrees of freedom equal N�Kÿ 1, where
7 Susmel (2001) also documents the unusually large number of extreme negative returns among LatinAmerican index returns. His focus is on the implication of safety-first principles for U.S. investors whocreate a diversified portfolio using Latin American markets added to their purely domestic portfolio.
The Review of Financial Studies / v 16 n 3 2003
726
Table
3M
onte
Carl
osi
mula
tion
resu
lts
of
(co-)
exce
edance
sfo
rdail
yem
ergin
gm
ark
etre
turn
s
Nu
mb
ero
fn
egati
ve
(co
-)ex
ceed
an
ces
Nu
mb
ero
fp
osi
tive
(co
-)ex
ceed
an
ces
�6
54
32
10
01
23
45
�6
Pan
elA
:A
sia
Act
ual
516
22
36
148
530
1526
1507
546
148
51
18
67
Mo
nte
Carl
osi
mu
lati
on
sA
.M
ult
ivari
ate
no
rmali
tyS
imu
late
dm
ean
0.6
12.7
912.0
546.0
7170.1
5595.6
01455.7
31450.2
6598.0
8172.0
346.8
412.3
32.8
40.6
2S
tan
dard
dev
iati
on
0.7
71.6
43.2
66.0
010.6
418.9
911.9
112.0
519.0
410.4
96.0
03.3
01.6
60.7
85th
qu
an
tile
00
736
153
565
1436
1430
567
155
37
70
095th
qu
an
tile
26
18
56
188
627
1475
1470
629
189
57
18
62
p-v
alu
e0.0
00.0
00.0
00.9
60.9
81.0
00.0
00.0
01.0
00.9
90.2
70.0
70.0
60.0
0
B.
Mu
ltiv
ari
ate
t-d
istr
ibu
tio
n(d
egre
eo
ffr
eed
om�
5)
Sim
ula
ted
mea
n7.2
012.3
728.5
264.8
6153.7
5415.8
11600.4
81595.2
8418.5
2155.0
165.4
328.9
612.5
07.3
0S
tan
dard
dev
iati
on
2.5
63.3
14.8
37.0
710.8
918.6
414.0
914.1
918.4
711.0
37.0
94.8
43.3
52.5
55th
qu
an
tile
37
21
54
136
385
1577
1572
388
137
54
21
73
95th
qu
an
tile
12
18
37
77
172
447
1624
1619
448
173
77
37
18
12
p-v
alu
e0.8
60.1
70.9
31.0
00.7
20.0
01.0
01.0
00.0
00.7
50.9
90.9
90.9
90.6
0
C.
Mu
ltiv
ari
ate
GA
RC
HS
imu
late
dm
ean
1.1
64.9
615.5
65
0.0
6167.5
0560.5
61483.2
01484.2
0554.9
2167.0
054.2
216.4
04.8
41.4
2S
tan
dard
dev
iati
on
1.3
63.5
54.0
26.7
014.6
123.6
720.4
522.5
727.6
912.7
66.7
74.7
13.1
41.9
35th
qu
an
tile
01
839
135
517
1448
1450
502
144
42
10
10
95th
qu
an
tile
412
21
59
187
597
1519
1525
601
186
65
25
10
5p
-valu
e0.0
40.0
20.0
40.9
80.9
20.9
20.0
40.1
60.6
00.9
40.7
40.3
20.3
60.0
4
Pan
elB
:L
ati
nA
mer
ica
Act
ual
76
15
34
96
371
1754
1691
448
104
25
95
1M
on
teC
arl
osi
mu
lati
on
sA
.M
ult
ivari
ate
no
rmali
tyS
imu
late
dm
ean
0.1
71.4
17.4
92
9.4
2110.2
9451.1
01683.1
21678.7
5453.8
3111.1
729.9
87.6
31.4
60.1
8S
tan
dard
dev
iati
on
0.4
11.1
72.5
74.8
48.7
816.4
510.3
110.2
416.4
28.5
84.8
32.5
81.1
90.4
25th
qu
an
tile
00
322
96
424
1666
1662
426
97
22
40
095th
qu
an
tile
14
12
37
125
478
1700
1696
481
126
38
12
41
p-v
alu
e0.0
00.0
00.0
10.2
00.9
51.0
00.0
00.1
20.6
50.8
20.8
70.3
50.0
20.1
6
Measuring Financial Contagion
727
Table
3(c
onti
nu
ed)
Nu
mb
ero
fn
egati
ve
(co
-)ex
ceed
an
ces
Nu
mb
ero
fp
osi
tive
(co
-)ex
ceed
an
ces
�6
54
32
10
01
23
45
�6
B.
Mu
ltiv
ari
ate
t-d
istr
ibu
tio
n(d
egre
eo
ffr
eed
om�
5)
Sim
ula
ted
mea
n1.7
96.0
917.2
742.9
3109.6
7339.3
61765.8
91761.5
6342.1
5110.4
943.4
017.3
96.1
81.8
3S
tan
dard
dev
iati
on
1.3
12.3
83.8
55
.69
8.9
316.2
111.4
811.7
316.4
09.2
05.8
13.8
62.4
11.3
55th
qu
an
tile
02
11
34
95
313
1747
1742
315
95
34
11
30
95th
qu
an
tile
410
24
52
125
366
1784
1781
370
126
53
24
10
4p
-valu
e0.0
00.5
80.7
60.9
50.9
50.0
30.8
61.0
00.0
00.7
71.0
00.9
90.7
50.8
4
C.
Mu
ltiv
ari
ate
GA
RC
HS
imu
late
dm
ean
0.2
92.0
59.2
632
.46
109.9
3431.7
01697.3
11693.4
8433.6
1111.0
732.8
79.5
42.1
30.3
1S
tan
dard
dev
iati
on
0.5
51.5
43.2
85
.48
9.0
620.8
914.5
414.9
121.4
39.3
05.5
93.3
01.6
00.5
95th
qu
an
tile
00
424
95
397
1674
1669
399
96
24
40
095th
qu
an
tile
15
15
42
125
466
1722
1718
470
126
42
15
51
p-v
alu
e0.0
00.0
30.0
60.4
20.9
51.0
00.0
00.5
80.2
50.7
90.9
40.6
00.0
80.2
5
Un
der
the
nu
llh
yp
oth
esis
that
nati
on
al
emer
gin
gm
ark
etin
dex
retu
rns
inA
sia
an
dL
ati
nA
mer
ica
are
dra
wn
fro
ma
sim
ula
ted
retu
rnd
istr
ibu
tio
n,
we
emp
loy
aM
on
teC
arl
osi
mu
lati
on
toev
alu
ate
the
nu
mb
ero
f(c
o-)
exce
edan
ces
wit
hin
each
regio
n.
We
com
pu
teth
esa
mp
lem
ean
an
dth
evari
an
ce-c
ovari
an
cem
atr
ixo
fre
turn
san
dgen
erate
5000
ran
do
mre
ali
zati
on
s.F
or
each
reali
zati
on
we
com
pu
teth
en
um
ber
of
(co
-)ex
ceed
an
ces
for
a5%
thre
sho
ld,
as
inT
ab
le2.
Su
mm
ary
stati
stic
sfo
rth
e5000
rep
lica
tio
ns
incl
ud
eth
em
ean
,st
an
dard
dev
iati
on
,5%
qu
an
tile
,95%
qu
an
tile
,an
dsi
mu
late
dp-v
alu
e(t
he
nu
mb
ero
fre
pli
cati
on
sw
ith
coex
ceed
an
ces
ina
giv
enca
tego
ryex
ceed
ing
the
act
ual
nu
mb
ero
fco
exce
edan
ces)
.S
imu
lati
on
sare
run
un
der
thre
ed
iffe
ren
tm
od
els
of
retu
rnd
istr
ibu
tio
ns:
am
ult
ivari
ate
no
rmal
dis
trib
uti
on
,a
mu
ltiv
ari
ate
t-d
istr
ibu
tio
nw
ith
five
deg
rees
of
free
do
m,
an
da
mu
ltiv
ari
ate
GA
RC
H.
Th
ed
yn
am
ics
of
vari
an
cean
dco
vari
an
cem
atr
ixo
fre
turn
sfo
rea
chre
gio
nu
nd
erth
em
ult
ivari
ate
GA
RC
Hm
od
elis
ass
um
edto
foll
ow
the
spec
ific
ati
on
pro
po
sed
by
Din
gan
dE
ngle
(1994).
The Review of Financial Studies / v 16 n 3 2003
728
N is the number of countries (10 for Asia, 7 for Latin America) and K is setto values ranging from 1 (significant positive excess cokurtosis) to 25 (littleexcess cokurtosis, approximating multivariate normal). We exploreda number of choices of K, but report only our analysis for K � 5.8
One of the concerns expressed by Baig and Goldfajn (1999), Dorn-busch, Park, and Claessens (2001), and Forbes and Rigobon (2001,2002) is that contagion as measured by changes in cross-market correla-tions across quiet and turbulent periods can be biased by heteroscedasti-city. Forbes and Rigobon (2002) show how the bias can be corrected bya measure of the relative increase in the volatility of market returns, say,for example, during a crisis period. Neither of these two scenarios allowsfor the possibility of conditional heteroscedasticity in the index returns.Unfortunately there are not many choices available to specify a parsimo-nious, yet reasonably general structure with time-varying conditionalvolatility for a relatively large number of markets. One such parameter-ization is the multivariate generalized autoregressive conditional hetero-scedasticity (GARCH) model of Ding and Engle (1994).9 This Ding andEngle model constitutes our third scenario. Specifically, we estimate
Rit� �0� "it "tjtÿ 1 � N�0;Ht�
Ht � H0 � ���0 ÿ��0 ÿ ��0� � ��0 � "tÿ 1"0tÿ 1 � ��0 � Htÿ 1,
where Rit is the return on asset i between time tÿ 1 and t, and tÿ 1, the setof marketwide information available at tÿ 1. �0 is a constant parameterand "it and the associated N-vector, "t, are residuals that are conditionallydistributed multivariate normal with symmetric conditional covariance(N�N) matrix, Ht. In the law of motion equation for the conditionalvariances, � is an N-vector of ones, � and � are N-vectors of parameters(where � is the Hadamard matrix product, element by element), and H0 isan unobserved starting covariance matrix which we set equal to the samplecovariance matrix of the returns. We estimate this system using maximumlikelihood and the Berndt et al. (1974) optimization algorithm for the 10Asian and 7 Latin American markets and then simulate 5000 randomrealizations given the estimated (2N� 1) parameters. It is important tonote that the Ding and Engle model does not impose constant correlation,
8 A multivariate Student's t distribution could potentially have a vector of degrees of freedom. Our choiceto impose a single value for all returns series is restrictive. We thank the referee for this point.
9 This model structure has been successfully applied by De Santis and Gerard (1997, 1998), and morerecently, Ledoit, Santa-Clara, and Wolf (2003). The goal of the Ledoit, Santa-Clara, and Wolf study,however, is to propose a numerically feasible alternative `̀ Diagonal-Vech'' multivariate GARCH model.We thank the referee for pointing out this alternative conditional covariance structure.
Measuring Financial Contagion
729
but rather guides the correlations in time by means of a constrained law ofmotion for the conditional volatilities. Readers should also be cautionedthat the law of motion does not allow for the covariance asymmetryfeatured in recent work by Ang and Chen (2002), that could generatehigh coexceedance counts following large negative return shocks.
Table 3 reports the results separately for Asia (panel A) and LatinAmerica (panel B). It is immediately apparent that we observe morecoexceedances than one would expect for Latin America, but not neces-sarily for Asia. This is true regardless of the assumption about the struc-ture of the joint returns-generating process. For example, we have fivedays where six or more countries in Asia have extreme negative returns. Inour simulations we generate an average of 0.61 days with the multivariatenormal scenario, 7.20 days on average in the multivariate Student's tscenario, and only 1.16 with the multivariate GARCH scenario.10 Thesimulation p-values indicate that the multivariate normal scenario deliversnot even one replication out of 5000 in which five or more days ofcoexceedances of negative returns of six or more countries occur. How-ever, the multivariate GARCH and Student's t scenarios do generate theactual number of coexceedances in 4% and 86% of the replications,respectively. For coexceedances of positive returns, the results are similar.In these cases, the sample has seven coexceedances involving six countriesor more and this count is larger than that generated by the multivariatenormal and GARCH scenarios (simulated p-value of 0.00 and 0.04,respectively), but it is not unusual for the Student's t scenarios ( p-valueof 0.60).
The results for Latin America are harder to reconcile with the simula-tions than the results for Asia. In these experiments, the multivariatenormal and GARCH scenarios fail to generate any (simulated p-valuesof 0.00) observations of six or more coexceedances of negative returns ofwhich there are seven in the actual sample. What is more surprising is thateven the Student's t scenario cannot deliver simulated coexceedancecounts as large as in the actual sample. By contrast, the number ofpositive-tail coexceedances in Latin America is not dramatically differentfrom the simulated counts. There is only one coexceedance event with sixor more countries, so each of the scenarios are able to offer a reasonablenumber of realizations that meet this challenge. But even the five
10 In order to check the validity of the calibration exercise, we examined the skewness and kurtosis of thesimulated returns from the three scenarios and compared them with the actual returns. Overall thekurtosis implied by the multivariate Student's t scenario for the marginal distributions of individualcountry index returns are reasonably close to the positive excess kurtosis in the actual returns. Theskewness statistics were, however, typically much lower. For the multivariate GARCH and normalscenarios, the skewness and kurtosis were even smaller than those of the Student's t. For example, Peru'sindex returns display excess positive skewness (0.26) and positive kurtosis (6.89). The average skewnesscoefficients for the three simulated scenarios (normal, Student's t, and GARCH) were 0.03, 0.28, andÿ 0.05, respectively; the average kurtosis coefficients were 0.01, 5.79, and 2.48, respectively.
The Review of Financial Studies / v 16 n 3 2003
730
coexceedance events in which five Latin American countries experiencereturns in the top 5% tail occur in more than 2% of the replications for themultivariate normal scenario, 8% for the multivariate GARCH scenario,and 75% for the multivariate Student's t scenario. This asymmetry incoexceedance events represents another challenge for a model ofcontagion.
The bottom line from our simulation experiments is that it is moredifficult to explain the distribution of coexceedances for Latin Americathan Asia. Our simulation evidence suggests that the frequency of bottom-tail and top-tail coexceedances in Asia can be generated (in a large fractionof the 5000 replications) with a somewhat strong assumption about posi-tive excess cokurtosis in the Student's t distribution (though not with thenormal or GARCH models). For Latin America, this is not the case forthe bottom-tail coexceedance events for any scenario. At the same time,however, it is important to emphasize that the number of puzzling obser-vations is small. The events that occur too often compared to the multi-variate Student's t, GARCH, or normal distribution model are those inwhich most countries in a region have extreme returns at the same time.There are few such days, but from the perspective of contagion studies,those days are the most interesting.
2� Contagion within Regions
In this section we show how our approach is useful for understandingcontagion within regions. In the first part of the section we present ourapproach of using multinomial logistic regressions. In the second part ofthe section we provide estimates of the regressions for Asia and LatinAmerica.
2.1 The logistic regression approach
Extreme value theory (EVT) has proposed three possible types of limitingdistributions for minima or maxima of a variable which are the Gumbel,Fr�echet, and Weibull distributions [Longin (1996)], and each of these hasbeen applied to time series of financial returns. These studies typicallyestimate the parameters of these distributions using parametric (maximumlikelihood) and nonparametric approaches. We know of only a few appli-cations of multivariate EVT to stock returns [Straetmans (1998), Starica(1999), Hartman, Straetmans, and de Vries (2001), Longin and Solnik(2001)]. But even in these cases, a dependence function between theFr�echet, Gumbel, or Weibull distributions across variables must beassumed and it is typically a logistic function [Longin and Solnik(2001)]. Our approach is different.
Exceedances in terms of extreme positive or negative returns in aparticular country can be modeled as a dichotomous variable. However,
Measuring Financial Contagion
731
our interest in coexceedances to capture contagion across many countrieswithin a region requires classification into many categories using a poly-chotomous variable. Multinomial logistic regression models, not verydifferent from the multivariate EVT applications, are popular approachesto estimate the probabilities associated with events captured in a poly-chotomous variable [Maddala (1983, chap. 2), Hosmer and Lemeshow(1989, chap. 8)]. If Pi is the probability associated with a category i of mpossible categories, then we can define a multinomial distribution given by
Pi � G��0ix�=�1 �Xmÿ 1
j� 1
G��0jx��, �1�
where x is the vector of covariates and �i the vector of coefficientsassociated with the covariates. Often the function G(�i
0x) is simplifiedusing a logistic function exp(�i
0x) which reduces Equation (1) to a multi-nomial logistic model. The model is estimated using maximum likelihoodwith the (log-) likelihood function for a sample of n observations given by
logL �Xn
i� 1
Xm
j� 1
IijlogPij, �2�
where Iij is an indicator variable that equals one if the ith observation fallsin the jth category, and zero otherwise. Because Pij is a nonlinear functionof the �'s, an iterative estimation procedure is employed and, for thispurpose, we choose the Broyden, Fletcher, Goldfard, and Shanno algo-rithm. The matrix of second partial derivatives delivers the informationmatrix and asymptotic covariance matrix of the maximum-likelihoodestimator for tests of significance of the individual estimated coefficients.Goodness-of-fit is measured using the pseudo-R2 approach of McFadden(1974) where both unrestricted (full model) likelihood, L!, and restricted(constants only) likelihood, L, functions are compared:11
pseudoR2� 1ÿ �logL!=logL�: �3�In our application to coexceedances across countries within Asia and
Latin America, we balance the need to have a model that is parsimoniousand yet one that richly captures the range of possible outcomes. Wetherefore choose to restrict our categories to five in number: 0, 1, 2, 3,and 4 or more coexceedances. For a simple model of constants, onlymÿ 1, or four parameters, need to be estimated. But for every covariateadded to the model, such as the conditional volatility of returns for theregional index, four additional parameters need to be estimated. Wechoose to estimate the coexceedances separately for positive and negative
11 Greene (2000, chap. 19) warns about the limitations of using pseudo-R2 for comparisons across models.
The Review of Financial Studies / v 16 n 3 2003
732
extreme returns (though we test the importance of this distinction later).Finally, we compute the probability of a coexceedance of a specific level,Pi, by evaluating the covariates at their unconditional values,
P�i � exp��0ix���
1�Xmÿ 1
j� 1
exp��0jx��" #
, �4�
where x� is the unconditional mean value of x. From this measure andfollowing Greene (2000, chap. 19), we compute the marginal change inprobability for a given unit change in the independent covariate to testwhether this change is statistically significantly different from zero.
Because it is often difficult to judge whether changes in probabilities ofa given coexceedance level are large or small economically, we furthercompute the sensitivity or response of our probability estimates to the fullrange of values associated with different covariates instead of just at itsunconditional mean. These probabilities across the five categories add upto one and we use plots to illustrate visually the changes in these prob-abilities, a new approach in finance that we call the ``coexceedanceresponse curve.''12
Note that our key hypotheses relate to the existence of contagion acrossregions as well as measuring contagion within regions. Specifically we willassess the importance of the coexceedance events within Asia and LatinAmerica for the likelihood of an exceedance in the United States andEurope. To this end we will need to estimate a logistic regression model forthe United States, but it must necessarily be for a dichotomous variable orbinomial logistic regression. This is a simple version of our multinomiallogistic regression model, and all estimation procedures, inference tests,pseudo-R2, and even ``exceedance response curve'' plots are computedaccordingly. For simplicity, we compute the analogous models for Europeas a single entity.
2.2 Contagion within regions
Table 4 provides estimates of our multinomial logistic regressions for Asiaand Latin America. We estimate the regressions separately for the bottomtails and the top tails. The first panel shows estimates for Asia and thesecond panel has estimates for Latin America. At the end of each table wealso report results for the binomial models for the United States andEurope. Column (1) reports estimates of regressions for the bottom tailsfor Asia that provide us with estimates of probabilities of coexceedances.
12 Our coexceedance response curve analysis is inspired by the epidemiology study by Gillespie, Halpern,and Warner (1994) which examines lung cancer deaths per year among ex-smokers and employs covari-ates such as age, gender, college attendance, smoker, and years since quitting for ex-smokers.
Measuring Financial Contagion
733
Table
4M
ult
inom
ial
logit
regre
ssio
nre
sult
sfo
rdail
yre
turn
coex
ceed
ance
sof
emer
gin
gm
ark
etin
dic
es,
Apri
l1,
1992,
toD
ecem
ber
29,
2000
Bo
tto
mta
ils
To
pta
ils
(1)
(2)
(3)
(4)
(5)
(6)
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Asi
ab 0
1(c
on
stan
t)ÿ
1.0
58
aÿ
0.1
24
aÿ
1.4
53
aÿ
0.1
91
aÿ
1.3
12
aÿ
0.1
70
aÿ
1.0
15
aÿ
0.1
18
aÿ
1.2
59
aÿ
0.1
60
aÿ
1.2
40
aÿ
0.1
74
a
b 02
ÿ2.3
33
aÿ
0.1
17
aÿ
2.9
84
aÿ
0.1
46
aÿ
3.0
96
aÿ
0.1
48
aÿ
2.3
21
aÿ
0.1
17
aÿ
2.8
39
aÿ
0.1
40
aÿ
2.1
86
aÿ
0.0
98
a
b 03
ÿ3.7
47
aÿ
0.0
51
aÿ
4.8
65
aÿ
0.0
51
aÿ
6.6
13
aÿ
0.0
58
aÿ
3.3
86
aÿ
0.0
64
aÿ
4.2
81
aÿ
0.0
67
aÿ
3.8
65
aÿ
0.0
57
a
b 04
ÿ3.5
69
aÿ
0.0
57
aÿ
4.9
51
aÿ
0.0
52
aÿ
6.2
08
aÿ
0.0
48
aÿ
3.8
84
aÿ
0.0
46
aÿ
5.3
60
aÿ
0.0
36
aÿ
6.0
37
aÿ
0.0
32
a
b 11
(hit)
0.3
89
a0.0
58
a0.4
77
a0.0
77
a0.2
42
a0.0
33
a0.3
29
a0.0
48
a
b 12
0.5
65
a0.0
26
a0.6
07
a0.0
26
a0.4
46
a0.0
21
a0.6
18
a0.0
29
a
b 13
0.7
84
a0.0
08
a0.6
63
a0.0
05
a0.6
38
a0.0
10
a0.7
74
a0.0
11
a
b 14
0.8
74
a0.0
09
a0.8
16
a0.0
06
a0.8
31
a0.0
06
a0.8
14
a0.0
04
a
b 21
(eit)
1.0
77
a0.1
58
aÿ
1.0
03
aÿ
0.1
50
a
b 22
2.1
44
a0.1
02
aÿ
1.7
74
aÿ
0.0
82
a
b 23
2.2
16
a0.0
17
aÿ
1.8
72
aÿ
0.0
25
a
b 24
2.6
40
a0.0
19
aÿ
2.3
51
aÿ
0.0
11
a
b 31
(iit)
ÿ0.0
21
ÿ0.0
04
ÿ0.0
06
0.0
00
b 32
ÿ0.0
04
0.0
00
ÿ0.0
78
bÿ
0.0
04
b
b 33
0.1
47
a0.0
01
bÿ
0.0
53
ÿ0.0
01
b 34
0.0
83
0.0
01
0.0
46
0.0
00
Lo
g-l
ikel
iho
od
ÿ2113.8
5ÿ
2006.2
1ÿ
1919.1
6ÿ
2139.1
6ÿ
2056.8
2ÿ
1998.9
0P
seu
do
-R2
5.0
9%
9.2
1%
3.8
5%
6.5
6%
Lati
nA
mer
ica
b 01
(co
nst
an
t)ÿ
1.5
54
aÿ
0.1
74
aÿ
2.0
97
aÿ
0.2
43
aÿ
2.4
31
aÿ
0.2
90
aÿ
1.3
28
aÿ
0.1
69
aÿ
1.6
72
aÿ
0.2
22
aÿ
1.8
52
aÿ
0.2
54
a
b 02
ÿ2.9
05
aÿ
0.1
02
aÿ
3.4
70
aÿ
0.1
20
aÿ
3.9
02
aÿ
0.1
20
aÿ
2.7
89
aÿ
0.1
06
aÿ
3.4
12
aÿ
0.1
24
aÿ
3.7
35
aÿ
0.1
22
a
b 03
ÿ3.9
43
aÿ
0.0
52
aÿ
5.0
83
aÿ
0.0
53
aÿ
5.7
38
aÿ
0.0
51
aÿ
4.2
14
aÿ
0.0
41
aÿ
5.3
61
aÿ
0.0
39
aÿ
5.7
84
aÿ
0.0
38
a
b 04
ÿ4.1
37
aÿ
0.0
45
aÿ
5.3
89
aÿ
0.0
43
aÿ
5.5
31
aÿ
0.0
37
aÿ
4.7
25
aÿ
0.0
28
aÿ
6.1
49
aÿ
0.0
23
bÿ
7.5
92
aÿ
0.0
21
b
b 11
(hit)
0.3
63
a0.0
44
a0.3
45
a0.0
43
a0.2
37
a0.0
33
a0.2
32
a0.0
33
a
b 12
0.3
74
a0.0
12
a0.3
59
a0.0
10
a0.3
90
a0.0
14
a0.4
08
a0.0
13
a
b 13
0.6
14
a0.0
06
a0.6
04
a0.0
05
a0.5
86
a0.0
04
a0.6
00
a0.0
04
a
b 14
0.6
47
a0.0
05
a0.6
51
a0.0
04
a0.6
57
a0.0
02
b0.6
65
a0.0
02
b
The Review of Financial Studies / v 16 n 3 2003
734
b 21
(eit)
1.1
77
a0.1
42
aÿ
0.1
30
ÿ0.0
06
b 22
1.9
14
a0.0
59
aÿ
1.4
66
aÿ
0.0
53
a
b 23
1.9
62
a0.0
17
aÿ
1.4
88
aÿ
0.0
10
b
b 24
2.0
48
a0.0
13
aÿ
1.6
38
aÿ
0.0
05
b 31
(iit)
0.0
14
0.0
02
0.0
12
0.0
02
b 32
0.0
08
0.0
00
0.0
18
0.0
01
b 33
0.0
18
0.0
00
0.0
24
0.0
00
b 34
ÿ0.0
14
0.0
00
0.0
72
b0.0
00
Lo
g-l
ikel
iho
od
ÿ1706.9
4ÿ
1636.2
4ÿ
1573.1
6ÿ
1746.6
1ÿ
1691.2
2ÿ
1664.9
6P
seu
do
-R2
4.1
4%
7.8
4%
3.1
7%
4.6
7%
US
b 01
(co
nst
an
t)ÿ
2.9
46
aÿ
0.1
40
aÿ
3.5
35
aÿ
0.1
53
aÿ
5.7
92
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0.2
25
aÿ
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0.1
40
aÿ
4.0
04
aÿ
0.1
48
aÿ
5.1
20
aÿ
0.1
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a
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0.5
70
a0.0
25
a0.4
27
a0.0
17
a0.9
21
a0.0
34
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92
a0.0
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a
b 21
(eit)
0.4
09
0.0
16
ÿ0.6
10
bÿ
0.0
21
b
b 31
(iit)
0.4
60
a0.0
18
a0.2
16
0.0
07
Lo
g-l
ikel
iho
od
ÿ452.7
6ÿ
434.7
6ÿ
424.8
8ÿ
452.7
6ÿ
399.1
3ÿ
393.9
5P
seu
do
-R2
3.9
8%
6.1
6%
11.8
5%
12.9
9%
Eu
rop
eb 0
1(c
on
stan
t)ÿ
2.9
46
aÿ
0.1
40
aÿ
3.8
08
aÿ
0.1
58
aÿ
3.6
39
aÿ
0.1
32
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2.9
46
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40
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4.0
09
aÿ
0.1
57
aÿ
3.7
91
aÿ
0.1
25
a
b 11
(hit)
1.0
49
a0.0
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a1.1
86
a0.0
39
a
b 21
(eit)
0.9
22
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a
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(iit)
ÿ0.0
57
ÿ0.0
02
ÿ0.0
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Lo
g-l
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od
ÿ452.7
6ÿ
426.4
1ÿ
408.0
7ÿ
452.7
6ÿ
412.9
2ÿ
388.6
6P
seu
do
-R2
5.8
2%
9.8
7%
8.8
0%
14.1
6%
Th
en
um
ber
of
coex
ceed
an
ces
of
dail
yre
turn
sis
mo
del
edas
an
ord
ered
po
lych
oto
mo
us
vari
ab
lean
des
tim
ate
du
sin
ga
mu
ltin
om
ial
logit
regre
ssio
nm
od
el.
Pj
isd
efin
edas
the
pro
bab
ilit
yth
at
agiv
end
ay
isass
oci
ate
dw
ith
jco
exce
edan
ces
wh
ere
jeq
uals
0,
1,
2,
3,
4o
rm
ore
(fiv
eca
tego
ries
).T
he
mu
ltin
om
ial
logit
regre
ssio
nm
od
elis
giv
enb
yP
j�
exp
(x0 b
j)/[
1�P k
exp
(x0 b
k)]
,w
her
eb
isth
evec
tor
of
coef
fici
ents
,x
,th
evec
tor
of
ind
epen
den
tvari
ab
les,
an
dk
equ
als
1to
4.
Th
ep
rob
ab
ilit
yth
at
ther
eare
no
(co
-)ex
ceed
an
ces
equ
als
P0�
1/[
1+P k
exp
(x0 b
k)]
,w
hic
hre
pre
sen
tso
ur
base
case
.T
he
ind
epen
den
tvari
ab
les,
x,
incl
ud
eth
ein
terc
ept,
con
dit
ion
al
vo
lati
lity
of
the
regio
nal
ind
exat
tim
et
(ht)
,th
eaver
age
exch
an
ge
rate
(per
$U
S)
chan
ges
inth
ere
gio
n(e
t),
an
dth
eaver
age
inte
rest
rate
level
inth
ere
gio
n(i
t).
Th
eco
nd
itio
nal
vo
lati
lity
ises
tim
ate
das
EG
AR
CH
(1,1
)u
sin
gth
eIF
Cin
ves
tib
lere
gio
nal
ind
ex.
Th
eli
kel
iho
od
for
the
mu
ltin
om
ial
logit
mo
del
[McF
ad
den
(1975)]
isn
um
eric
all
yev
alu
ate
du
sin
gth
eB
royd
en,
Fle
tch
er,
Go
ldfa
rb,
an
dS
han
no
alg
ori
thm
.P
art
ial
der
ivati
ves
of
pro
bab
ilit
ies
wit
hre
spec
tto
the
vec
tor
of
ind
epen
den
tvari
ab
les
are
com
pu
ted
at
the
mea
ns
of
x[G
reen
e(2
000,
chap
.19)]
an
dare
rep
ort
edn
ext
toth
eco
effi
cien
tes
tim
ate
s.G
oo
dn
ess-
of-
fit
ism
easu
red
by
McF
ad
den
'sp
seu
do
-R2
equ
al
to1ÿ
(L!/L
),
wh
ere
L!
isth
eu
nre
stri
cted
lik
elih
oo
d,
an
dL
is
the
rest
rict
edli
kel
iho
od
[Mad
da
la(1
983,
chap
.2)]
.T
he
logit
regre
ssio
nis
esti
mate
dse
para
tely
for
po
siti
ve
(to
p-t
ail
)an
dn
egati
ve
(bo
tto
m-t
ail
)co
exce
edan
ces.
a,
bD
eno
tes
sign
ific
an
cele
vel
sat
the
1%
an
d5%
,re
spec
tivel
y.
Measuring Financial Contagion
735
We find (not reported) that there is a probability of 66.84% that no Asiancountry has a bottom-tail return. If bottom-tail exceedances were inde-pendent, this probability would be 59.87% (or 0.9510). The coefficient b01
is associated with the event ``Y� 1,'' or the case where one country has anextreme return, and its probability is 23.22%; for example, computed asthe special case of the logistic function, exp(b01)/[1�Pkexp(�0k)]. Sincethere are no covariates, these probabilities are the sample frequenciesreported in Table 2; for example, 530 occurrences of single-country nega-tive return exceedances in Asia during the 2283 days. In column (2) weadd the conditional volatility of the Asian index (hit) as a covariate.13 Wefind that the conditional volatility increases the probability of extremereturns significantly. To see the impact of conditional volatility, it is usefulto evaluate the marginal probability of exceedances with respect to theconditional volatility. An increase in conditional volatility increases theprobability of all exceedances, but the effect decreases as we look at highernumbers of joint occurrences. For instance, a 1% increase in the condi-tional volatility increases the probability of one exceedance by 0.058% andthe probability of four or more occurrences by 0.009%. All the partialderivatives are significant at the 5% level. The pseudo-R2 is 5.09%.
In column (3), we add the average exchange rate change in the region(eit) a well as the average interest rate level (iit) in the region.14 This allowsus to answer the question of whether the probability of co-exceedances isaffected by exchange rate shocks to the region and by the level of theinterest rates. We see that this is indeed the case if we look at the regressioncoefficients. If currencies fall on average (eit rises), extreme returns aremore likely. Few of the interest rate coefficients are significant. Thesignificant bottom-tail coefficients are positive, making it more likelythat a negative exceedance will occur when interest rates are high. Thetwo significant upper-tail coefficients are of opposite sign, which is puz-zling. Moreover, the magnitude of the partial derivatives for changes in eit
is two to three times larger than for the partial derivatives for hit. Thepartial derivatives are computed at the means of the regressors and are notsignificant for one, two, or four or more exceedances. Adding exchangerate changes and the level of interest rates almost doubles the pseudo-R2
to 9.21 percent. The economic and statistical significance of exchange ratechanges raises the question of whether the stock retun contagion we
13 The conditional volatility is estimated from a univariate EGARCH(1,1) model to the value-weightedAsian and Latin American regional indexes, as created by IFC after 1995 and reconstructed back to April1992 as described in Section 2.
14 Data on daily exchange rates relative to the U.S. dollar and mterest rates for each country are tamed fromDatastream International. The interest rate series chosen is typically the short-term rate of interestavailable in Datastream with availability back to 1992. We computed simple equally-weighted averagerate changes and average interest rates by region for these covariates.
The Review of Financial Studies / v 16 n 3 2003
736
measure is actually foreign exchange contagion since we measure returnsin dollars. To examine this issue, we estimated our models in local cur-rency returns, but do not report the results because they are similar tothose we do report.
When we look at the top-tail events (models 4±6 in Table 4), we find noevidence that coexceedance events are less likely for positive extremereturns than for negative extreme returns. A pairwise comparison of thecoefficients in columns (1) and (4) cannot reject that the coefficients areequal (Wald chi-square statistic of 0.21, p-value of 0.65, not reported).15
Hence, for Asia, there is no evidence that contagion is somehow moreimportant for negative returns than it is for positive returns. Conditionalvolatility is a statistically important covariate for positive coexcee-dances.16 The exchange rate coefficients are negative and significant. Inother words, the likelihood of seeing positive extreme returns in more thanone country increases when on average the exchange rate in the regionappreciates. The interest rate variables provide almost no information forpositive coexceedances. The pseudo-R2s are much lower for positivereturns than they are for negative returns, so that our covariates aremore successful at explaining coexceedances for negative returns thanfor positive returns.
In the second panel of Table 4 we see that the results for Latin Americadiffer substantially from those for Asia. The probability of having noextreme return on a day is much higher for Latin America than it is forAsia. We estimate the probability of having no extreme return to be76.83% for Latin America, while it is 66.84% for Asia. The probabilityof having four or more Latin American countries experience an extremereturn on the same day is higher than the corresponding probability forAsia (b04 of ÿ 4.137 implies a probability of 1.23%). The explanatoryvariables are significant for Latin America in the same way that they arefor Asia, except that interest rates do not appear to be useful in explainingcoexceedances of extreme negative returns in Latin America. The partialderivatives of the probabilities with respect to regressors are significantexcept for interest rates, but they are smaller for conditional volatility andlarger for exchange rates than those for Asia. Turning to the positiveextreme returns, we see that the probability of having no positive extremereturn is higher than the probability of having no negative extreme return.Our test of equality for the probability of positive extreme return and
15 We estimate a logit model for all coexceedances, positive or negative, and introduce a dummy variablecovariate equal to one if the coexceedance was positive. The Wald test that the coefficients on the dummyvariable are jointly equal to zero is distributed as chi-square with three degrees of freedom.
16 If high regional market volatility occurs because of high volatility in a common factor, it is not surprisingthat a large number of coexceedances arise.
Measuring Financial Contagion
737
negative extreme return coexceedances confirms the asymmetry for coex-ceedances of four or more extreme returns. Specifically coexceedances offour or more extreme returns are more likely for negative extreme returnsthan for positive extreme returns (Wald chi-square statistic of 3.17,p-value of 0.07, not reported).
We also include the United States and Europe in the third and fourthpanels of Table 4. For the United States, the coefficient on the conditionalvolatility of the market is positive and significant for both negative-and positive-tail events, but the partial derivative of the probability ofan exceedance with respect to the conditional volatility is larger forpositive-tail events. Exchange rate and interest rate levels offer onlyweak explanatory power.17 The pseudo-R2s are higher for the top tailthan in any other regression. For Europe, there is clear evidence that anincrease in the conditional volatility of returns increases the probability oftail events. The exchange rate coefficients are significant, but the interestrate coefficients are not. The pseudo-R2s are substantially higher thanthose of the emerging market regions for the positive tail events.
Figure 1 illustrates the coexceedance response curves of Asia associatedwith the model in column (3) of Table 4. Note that these plots apply onlyto the bottom-tail events. Such curves are important in understanding theimpact of the covariates on the probability of exceedances. In the tableswe provide estimates of the partial derivatives of the exceedance probabil-ities with respect to the regressors evaluating the partial derivatives at themeans of the regressors. However, these partial derivatives give an incom-plete picture of the impact of changes in the regressors because theprobabilities are not linear functions of the regressors.
Plotting the probability of exceedances as a function of a regressor overthe whole relevant range of the regressor permits us to better assess howchanges in the regressor affect the probability of exceedances. Considerthe top plot that shows the sensitivity of implied conditional probabilitiesof different numbers of coexceedances to the conditional volatility ofAsian index returns. The different areas of the plot correspond to differentcoexceedance events. Clearly the probability of various coexceedances inAsia increases with the conditional volatility, but it does so nonlinearly.When the conditional volatility of Asian markets exceeds 3% or 4% perday, for example, the probability of two or more coexceedances reachesalmost 45%. An obvious issue is that one has to be cautious in evaluatingsuch a result because we end up focusing on a subset of an already smallnumber of extreme events. The two other figures are associated with the
17 For the United States we employed the equally weighted average exchange rate for all countries in Asiaand Latin America in the binomial tests as well as the daily Federal funds rate. For Europe we used thedeutsche mark--U.S. dollar (or Euro--U.S. dollar) bilateral exchange rate and the short rate in Germanyas a proxy. All data are from Datastream International.
The Review of Financial Studies / v 16 n 3 2003
738
Figure 1Coexceedance response curves of negative extreme returns in Asia
Measuring Financial Contagion
739
model for the exchange rate change and interest rate level covariates. Ofinterest is that the sensitivity of coexceedances to interest rate levels issimilar to conditional volatility, but the sensitivity to exchange rate chan-gesÐno doubt in large part due to the Asian crisis periodÐis dramaticand highly nonlinear. The response curve slope is relatively flat unlessrather large average exchange rate depreciations of 1% or more per dayoccur, after which the probability of regional contagion (two or morecoexceedances) rises to a maximum of 50% to 80%.
Two robustness checks follow. First, we provide a full set of Wald chi-square tests of the restriction that the regression coefficients are the samefor positive exceedances and negative exceedances to which we havealready referred above. We find that for Asia we cannot reject the hypo-thesis that positive- and negative-return joint exceedances are equallylikely. For Latin America, there is an asymmetry in coexceedances offour or more where negative coexceedances are more likely. Second, wealso extended the analysis to incorporate some dynamics in coexceedancesby considering whether knowing the number of extreme returns of yester-day is helpful in predicting the number of extreme returns today. Theresults (not reported) show that the lagged values of coexceedances arestatistically significant for Latin America and Asia, and less so forEurope, but are not significant for the exceedances in the United States.This specification ignores, however, the lagged effects of the interest rate,exchange rate, and regional conditional volatility covariates or a multi-day horizon for measuring coexceedance events. We address thesesupplementary issues in the next section.
How well specified these particular models are is an open question. Ourprimary focus is on the extent of contagion across regions, so it is impor-tant that our tests condition on reasonable covariates that affect conta-gion within regions. We offer a number of sensitivity tests to address thisconcern in the next section.
3� Contagion Across Regions
In this section we investigate contagion across regions. The type of ques-tion we address is whether the number of coexceedances, or joint occur-rences of extreme returns, of a given number in Asia can help predict thenumber of coexceedances or extreme returns in Latin America or in otherregions. To the extent that there is a fraction of the coexceedances in LatinAmerica that is left unexplained by its own covariates that can beexplained by coexceedances in Asia, we will interpret this as evidence ofcontagion across regions. In the first part of the section, we answerthis type of question using a base model. In the second part of the section,we explore alternate specifications, robustness tests, and calibrationexercises.
The Review of Financial Studies / v 16 n 3 2003
740
3.1 The base model
To investigate the question we are interested in, we reestimate the modelsof Table 4 for Asia, Latin America, the United States, and Europe,respectively, but add two covariates related to coexceedances (Y �jt) andregional market volatility (hjt
� ) from each of the other regions during thepreceding trading session that day (except for the United States and LatinAmerican trading sessions, which are contemporaneous). Timing conven-tions are important since U.S. and Latin American markets open after themarkets in Asia close. Therefore we add to the Asian contagion regres-sions the number of extreme returns in Latin America on the previoustrading day and the conditional volatility of the Latin American regionalindex as of the previous day. As we are careful to condition on exceedanceevents or conditional volatility from the previous trading day, we interpretthese results as evidence of predictability of contagion.
The model for Asia is given in column (1) of Table 5 for the bottom tailsand in column (4) for the top tails. The regression coefficients on thenumber of exceedances in Latin America are significant (b5k for k equals 1to 4 are all significant at the 1% level) for all but two-country coexcee-dances. In evaluating the derivative of the exceedance probabilities (``�prob'') at the unconditional mean of the covariates, we note that anincrease in the number of exceedances in Latin America increases theprobability of all one-country and four-country-or-more exceedance out-comes in Asia for negative tail events. It seems surprising at first that thecoefficient b53 is significant while its associated change in probability isnot, but this no doubt reflects the nonlinear logistic mapping. Because theslope of the probability function depends on the covariates, the signifi-cance of this slope depends on the value of the covariates used to estimatethe slope.
A concern with these results is that the number of exceedances in LatinAmerica might proxy for an exceedance in the United States, since LatinAmerican markets are open at the same time as the U.S. market. This turnsout not to be the case. We reestimated our regressions, adding a variablethat takes a value of one if the United States has an exceedance and zerootherwise. Adding this dummy variable does not change our results. Thisindicates that there is something unique about contagion among emergingmarkets. The coefficients are significant for all exceedance outcomes forpositive tails, but the partial derivatives of the probabilities are not. We addtwo Wald chi-square statistics associated with tests of the null hypothesisthat the block of coefficients associated with the conditional volatility andthe number of exceedances in the other market are jointly zero. The con-ditional volatility of Latin America does not seem to be very helpful inpredicting exceedances in Asia. Introducing this variable weakens theestimates of the impact of changes in the conditional volatility of Asia onthe probability of exceedances in Asia.
Measuring Financial Contagion
741
Table
5C
onta
gio
nte
stre
sult
sof
mult
inom
ial
logit
regre
ssio
nfo
rdail
yre
turn
coex
ceed
ance
sof
emer
gin
gm
ark
etin
dic
es,
Apri
l1,
1992,
toD
ecem
ber
29,
2000
Bo
tto
mta
ils
To
pta
ils
(1)
(2)
(3)
(4)
(5)
(6)
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Asi
aF
rom
Lati
nA
mer
ica
Fro
mU
SF
rom
Eu
rop
eF
rom
Lati
nA
mer
ica
Fro
mU
SF
rom
Eu
rop
eb 0
1(c
on
stan
t)ÿ
1.4
14
aÿ
0.1
90
aÿ
1.6
25
aÿ
0.2
24
aÿ
1.6
70
aÿ
0.2
31
aÿ
1.2
43
aÿ
0.1
77
aÿ
1.3
20
aÿ
0.1
85
aÿ
1.4
61
aÿ
0.2
13
a
b 02
ÿ3.2
49
aÿ
0.1
55
aÿ
3.7
72
aÿ
0.1
73
aÿ
3.7
12
aÿ
0.1
70
aÿ
2.2
63
aÿ
0.1
02
aÿ
2.4
92
aÿ
0.1
13
aÿ
2.5
65
aÿ
0.1
15
a
b 03
ÿ7.1
54
aÿ
0.0
57
aÿ
7.7
04
aÿ
0.0
55
aÿ
7.5
63
aÿ
0.0
53
aÿ
3.9
09
aÿ
0.0
54
aÿ
4.6
47
aÿ
0.0
62
aÿ
4.5
72
aÿ
0.0
61
a
b 04
ÿ6.5
60
aÿ
0.0
38
aÿ
7.1
32
aÿ
0.0
43
aÿ
7.0
98
aÿ
0.0
45
aÿ
7.0
51
aÿ
0.0
28
bÿ
7.5
13
aÿ
0.0
28
bÿ
7.5
07
aÿ
0.0
21
b
b 11
(hit)
0.4
46
a0.0
73
a0
.357
a0.0
59
a0.3
52
a0.0
57
a0.3
53
a0.0
52
a0.2
84
a0.0
42
a0.2
43
a0.0
35
a
b 12
0.5
53
a0.0
24
a0
.427
a0.0
17
a0.4
45
a0.0
19
a0.6
54
a0.0
30
a0.5
23
a0.0
24
a0.5
04
a0.0
24
a
b 13
0.5
75
a0.0
04
a0
.475
a0.0
03
b0.5
00
a0.0
03
b0.8
52
a0.0
11
a0.6
29
a0.0
08
a0.6
56
a0.0
08
a
b 14
0.7
94
a0.0
04
a0
.670
a0.0
04
a0.6
47
a0.0
04
a0.7
96
a0.0
03
b0.6
45
a0.0
02
b0.7
77
a0.0
02
b
b 21
(eit)
1.0
82
a0.1
61
a0
.997
a0.1
49
a1.0
54
a0.1
57
aÿ
0.9
81
aÿ
0.1
49
aÿ
0.9
61
aÿ
0.1
47
aÿ
0.9
27
aÿ
0.1
42
a
b 22
2.1
56
a0.1
03
a2
.048
a0.0
94
a2.1
47
a0.0
99
aÿ
1.7
16
aÿ
0.0
79
aÿ
1.6
62
aÿ
0.0
76
aÿ
1.6
11
aÿ
0.0
74
a
b 23
2.2
98
a0.0
16
a2
.166
a0.0
14
a2.2
22
a0.0
14
aÿ
1.8
09
aÿ
0.0
23
aÿ
1.7
47
aÿ
0.0
21
aÿ
1.7
12
aÿ
0.0
21
a
b 24
2.7
20
a0.0
15
a2
.574
a0.0
15
a2.6
32
a0.0
16
aÿ
2.3
41
aÿ
0.0
08
aÿ
2.2
75
aÿ
0.0
08
bÿ
2.2
58
aÿ
0.0
06
b
b 31
(iit)
ÿ0.0
21
ÿ0.0
04
ÿ0.0
03
ÿ0.0
02
ÿ0.0
10
ÿ0.0
03
ÿ0.0
08
0.0
00
ÿ0.0
01
0.0
01
0.0
01
0.0
01
b 32
ÿ0.0
02
0.0
00
0.0
34
0.0
02
0.0
12
0.0
01
ÿ0.0
80
bÿ
0.0
04
bÿ
0.0
57
ÿ0.0
03
ÿ0.0
64
bÿ
0.0
04
b 33
0.1
60
a0.0
01
b0
.194
a0.0
01
b0.1
77
a0.0
01
bÿ
0.0
60
ÿ0.0
01
ÿ0.0
04
0.0
00
ÿ0.0
46
ÿ0.0
01
b 34
0.0
77
0.0
01
0.1
29
b0.0
01
0.1
17
b0.0
01
0.0
76
0.0
00
0.1
14
0.0
00
0.0
29
0.0
00
b 41(h
jt*)
0.0
55
0.0
08
0.2
43
a0.0
38
a0.5
00
a0.0
80
aÿ
0.0
52
ÿ0.0
08
0.0
62
0.0
08
0.3
33
a0.0
52
b
b 42
0.1
24
0.0
06
0.4
04
a0.0
18
a0.7
81
a0.0
34
aÿ
0.0
63
ÿ0.0
03
0.1
42
0.0
07
0.4
23
b0.0
18
b 43
0.1
90
b0.0
01
0.5
66
a0.0
04
b0.7
23
b0.0
04
ÿ0.1
85
ÿ0.0
03
0.2
41
0.0
03
0.8
79
a0.0
12
a
b 44
ÿ0.0
98
ÿ0.0
01
0.2
31
0.0
01
0.6
00
0.0
03
0.0
75
0.0
00
0.5
55
a0.0
02
b1.3
67
a0.0
04
b 51
(Yjt*
)0.1
57
b0.0
27
b0
.670
a0.0
98
b0.4
02
0.0
57
0.2
05
a0.0
29
b0.3
39
0.0
41
0.0
13
ÿ0.0
14
b 52
0.0
12
ÿ0.0
02
1.3
62
a0.0
62
a0.7
09
b0.0
31
0.4
05
a0.0
19
a0.9
50
a0.0
46
b0.8
42
a0.0
46
a
b 53
0.3
62
b0.0
03
1.8
84
a0.0
13
b1.9
89
a0.0
14
b0.6
73
a0.0
09
a1.7
28
a0.0
24
a0.7
28
0.0
10
b 54
0.8
89
a0.0
05
a2
.610
a0.0
16
b1.9
88
a0.0
13
b0.8
34
a0.0
03
b1.5
67
a0.0
06
1.4
43
a0.0
04
Lo
g-l
ikel
iho
od
ÿ1895.4
5ÿ
1884.2
0ÿ
1885.9
8ÿ
1978.2
6ÿ
1976.4
5ÿ
1967.3
1P
seu
do
-R2
10.3
1%
10.8
5%
10.7
6%
7.5
0%
7.5
9%
8.0
2%
w2(h
jt*)
8.2
3(0
.08)
21.1
4(0
.00)
31.5
0(0
.00)
5.9
0(0
.21)
12.7
4(0
.01)
37.0
2(0
.00)
w2(Y
jt*)
38.2
5(0
.00)
46.5
9(0
.00)
29.5
7(0
.00)
34.1
6(0
.00)
24.9
7(0
.00)
13.8
8(0
.01)
The Review of Financial Studies / v 16 n 3 2003
742
Lati
nA
mer
ica
Fro
mA
sia
Fro
mU
SF
rom
Eu
rop
eF
rom
Asi
aF
rom
US
Fro
mE
uro
pe
b 01
(co
nst
an
t)ÿ
2.3
57
aÿ
0.2
82
aÿ
2.1
41
aÿ
0.2
56
aÿ
2.5
07
aÿ
0.3
03
aÿ
1.8
22
aÿ
0.2
53
aÿ
1.3
87
aÿ
0.1
85
aÿ
1.9
48
aÿ
0.2
70
a
b 02
ÿ3.9
69
aÿ
0.1
15
aÿ
3.8
49
aÿ
0.1
13
aÿ
4.0
47
aÿ
0.1
24
aÿ
3.4
68
aÿ
0.1
05
aÿ
3.3
39
aÿ
0.1
06
aÿ
3.9
89
aÿ
0.1
27
a
b 03
ÿ6.0
52
aÿ
0.0
52
aÿ
6.0
94
aÿ
0.0
49
aÿ
6.4
18
aÿ
0.0
45
aÿ
5.6
85
aÿ
0.0
38
aÿ
5.3
38
aÿ
0.0
35
aÿ
5.5
93
aÿ
0.0
37
a
b 04
ÿ6.3
26
aÿ
0.0
36
aÿ
7.3
08
aÿ
0.0
25
bÿ
6.5
82
aÿ
0.0
31
aÿ
8.2
49
aÿ
0.0
17
ÿ7.7
56
aÿ
0.0
17
ÿ9.0
48
aÿ
0.0
16
b 11
(hit)
0.3
68
a0.0
47
a0.4
35
a0.0
55
a0.3
22
a0.0
41
a0.2
80
a0.0
40
a0.3
58
a0.0
52
a0.2
13
a0.0
30
a
b 12
0.3
59
a0.0
10
a0.4
44
a0.0
12
a0.3
24
a0.0
09
a0.5
30
a0.0
16
a0.5
46
a0.0
17
a0.3
70
a0.0
12
a
b 13
0.5
59
a0.0
05
a0.6
42
a0.0
05
a0.5
51
a0.0
04
a0.6
34
a0.0
04
a0.7
38
a0.0
05
a0.6
06
a0.0
04
a
b 14
0.5
48
a0.0
03
a0.6
49
a0.0
02
b0.5
67
a0.0
03
a0.7
22
a0.0
01
0.7
45
a0.0
02
0.5
62
a0.0
01
b 21
(eit)
1.1
44
a0.1
39
a1.0
86
a0.1
33
a1.1
65
a0.1
42
aÿ
0.1
71
ÿ0.0
14
ÿ0.1
92
ÿ0.0
17
ÿ0.1
11
ÿ0.0
05
b 22
1.9
09
a0.0
56
a1.8
78
a0.0
55
a1.9
16
a0.0
59
aÿ
1.4
95
aÿ
0.0
50
aÿ
1.4
60
aÿ
0.0
50
aÿ
1.4
02
aÿ
0.0
49
a
b 23
1.9
85
a0.0
16
a1.9
46
a0.0
15
a2.0
02
a0.0
13
aÿ
1.5
14
aÿ
0.0
10
bÿ
1.5
08
aÿ
0.0
10
bÿ
1.3
99
aÿ
0.0
10
b
b 24
2.1
21
a0.0
11
a2.1
23
a0.0
07
b2.1
28
a0.0
10
aÿ
1.7
47
aÿ
0.0
04
ÿ1.6
61
aÿ
0.0
04
ÿ1.6
85
aÿ
0.0
03
b 31
(iit)
0.0
12
0.0
02
0.0
04
0.0
00
0.0
17
0.0
02
0.0
10
0.0
02
ÿ0.0
05
ÿ0.0
01
0.0
15
0.0
02
b 32
0.0
11
0.0
00
0.0
06
0.0
00
0.0
13
0.0
00
0.0
10
0.0
00
0.0
03
0.0
00
0.0
27
0.0
01
b 33
0.0
26
0.0
00
0.0
30
0.0
00
0.0
36
0.0
00
0.0
22
0.0
00
0.0
06
0.0
00
0.0
22
0.0
00
b 34
0.0
04
0.0
00
0.0
38
0.0
00
0.0
07
0.0
00
0.0
84
b0.0
00
0.0
77
0.0
00
0.1
08
a0.0
00
b 41
(hjt*
)ÿ
0.1
17
bÿ
0.0
15
ÿ0.3
27
aÿ
0.0
42
a0.0
12
0.0
01
ÿ0.1
96
aÿ
0.0
27
aÿ
0.4
71
aÿ
0.0
70
a0.0
40
0.0
06
b 42
ÿ0.2
75
bÿ
0.0
08
ÿ0.3
67
bÿ
0.0
10
0.0
63
0.0
02
ÿ0.5
44
aÿ
0.0
17
aÿ
0.5
59
aÿ
0.0
16
b0.0
67
0.0
02
b 43
0.0
58
0.0
01
ÿ0.1
87
ÿ0.0
01
0.1
03
0.0
01
ÿ0.1
32
ÿ0.0
01
ÿ0.4
90
bÿ
0.0
03
ÿ0.3
49
ÿ0.0
03
b 44
0.1
61
0.0
01
ÿ0.0
44
0.0
00
0.4
17
0.0
02
ÿ0.3
33
ÿ0.0
01
ÿ0.4
80
ÿ0.0
01
0.6
62
0.0
01
b 51
(Yjt*
)0.1
01
0.0
10
0.8
35
a0.0
97
a0.9
30
a0.1
14
a0.2
55
a0.0
37
a0.8
24
a0.1
16
a0.7
56
a0.1
08
a
b 52
0.4
90
a0.0
15
a1.9
11
a0.0
57
a1.0
99
a0.0
32
b0.4
02
a0.0
12
b1.6
44
a0.0
52
a1.3
88
a0.0
44
a
b 53
0.2
80
0.0
02
2.3
52
a0.0
19
a2.6
13
a0.0
19
a0.0
70
0.0
00
1.1
24
0.0
06
1.2
05
0.0
07
b 54
0.5
13
a0.0
03
b3.8
99
a0.0
14
b2.7
57
a0.0
13
b0.8
48
a0.0
02
2.7
22
a0.0
06
2.1
45
a0.0
04
Lo
g-l
ikel
iho
od
ÿ1555.1
8ÿ
1522.9
9ÿ
1541.1
9ÿ
1640.9
4ÿ
1637.0
0ÿ
1646.9
2P
seu
do
-R2
8.8
9%
10.7
8%
9.7
1%
6.0
5%
6.2
8%
5.7
1%
w2(h� jt)
11.6
9(0
.02)
13.6
9(0
.01)
1.8
1(0
.77)
24.4
5(0
.00)
30.1
7(0
.00)
4.9
4(0
.29)
w2(Y� jt)
25.2
9(0
.00)
92.7
6(0
.00)
63.1
7(0
.00)
29.9
8(0
.00)
37.1
0(0
.00)
27.8
8(0
.01)
US
Fro
mA
sia
Fro
mL
ati
nA
mer
ica
Fro
mE
uro
pe
Fro
mA
sia
Fro
mL
ati
nA
mer
ica
Fro
mE
uro
pe
b 1(c
on
stan
t)ÿ
5.8
42
aÿ
0.2
24
aÿ
6.5
77
aÿ
0.2
05
aÿ
5.9
11
aÿ
0.2
15
aÿ
5.1
50
aÿ
0.1
78
aÿ
5.4
53
aÿ
0.1
70
aÿ
5.0
59
aÿ
0.1
63
a
b 2(h
it)
0.3
70
a0.0
14
a0.4
37
a0.0
14
a0.1
70
0.0
06
0.8
84
a0.0
31
a1.0
43
a0.0
33
a0.9
30
a0.0
30
a
b 3(e
it)
0.4
22
0.0
16
0.3
14
0.0
10
0.5
30
b0.0
19
bÿ
0.6
11
bÿ
0.0
21
bÿ
0.5
91
bÿ
0.0
18
bÿ
0.7
45
aÿ
0.0
24
a
b 4(i
it)
0.4
55
a0.0
17
a0.5
58
a0.0
17
a0.4
51
a0.0
16
a0.2
19
0.0
08
0.2
47
b0.0
08
b0.1
99
0.0
06
b 4(h� jt)
0.0
20
0.0
01
ÿ0.1
77
ÿ0.0
06
0.3
47
0.0
13
ÿ0.0
05
0.0
00
ÿ0.2
04
bÿ
0.0
06
bÿ
0.2
58
ÿ0.0
08
b 4(Y� jt)
0.1
85
0.0
07
0.9
14
a0.0
28
a1.5
51
a0.0
57
a0.0
45
0.0
02
0.6
78
a0.0
21
a1.7
56
a0.0
56
a
Lo
g-l
ikel
iho
od
ÿ423.0
1ÿ
381.0
0ÿ
409.5
5ÿ
393.8
7ÿ
378.2
8ÿ
378.5
0P
seu
do
-R2
6.5
7%
15.8
5%
9.5
4%
13.0
1%
16.4
5%
16.4
0%
w2(h� jt)
0.0
7(0
.79)
3.8
1(0
.05)
2.5
0(0
.11)
0.0
0(0
.97)
5.7
2(0
.02)
1.1
8(0
.28)
w2(Y� jt)
3.3
6(0
.07)
90.3
6(0
.00)
31.1
9(0
.00)
0.1
7(0
.68)
33.3
7(0
.00)
35.7
9(0
.00)
Measuring Financial Contagion
743
Table
5(c
onti
nu
ed)
Bo
tto
mta
ils
To
pta
ils
(1)
(2)
(3)
(4)
(5)
(6)
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Eu
rop
eF
rom
Asi
aF
rom
Lati
nA
mer
ica
Fro
mU
SF
rom
Asi
aF
rom
Lati
nA
mer
ica
Fro
mU
Sb 1
(co
nst
an
t)ÿ
4.3
11
aÿ
0.1
33
aÿ
3.6
09
aÿ
0.1
21
aÿ
4.0
17
aÿ
0.1
29
aÿ
4.2
58
aÿ
0.1
28
aÿ
3.7
81
aÿ
0.1
20
aÿ
4.1
87
aÿ
0.1
31
a
b 2(h
it)
0.9
58
a0.0
30
a0.9
83
a0.0
33
a1.0
31
a0.0
33
a0.9
87
a0.0
30
a1.0
44
a0.0
33
a0.8
96
a0.0
28
a
b 3(e
it)
0.9
80
a0.0
30
a0.9
97
a0.0
33
a1.0
08
a0.0
32
aÿ
1.1
20
aÿ
0.0
34
aÿ
1.0
81
aÿ
0.0
34
aÿ
1.0
73
aÿ
0.0
34
a
b 4(i
it)
ÿ0.0
10
0.0
00
ÿ0.0
83
ÿ0.0
03
ÿ0.0
23
ÿ0.0
01
ÿ0.0
25
ÿ0.0
01
ÿ0.0
83
ÿ0.0
03
ÿ0.0
13
0.0
00
b 4(h
jt*)
ÿ0.0
07
0.0
00
ÿ0.0
70
ÿ0.0
02
ÿ0.0
42
ÿ0.0
01
0.0
67
0.0
02
0.0
35
0.0
01
0.2
51
0.0
08
b 4(Y
jt*)
0.6
24
a0.0
19
a0.5
27
a0.0
18
a1.9
44
a0.0
62
a0.4
64
a0.0
14
a0.3
63
a0.0
12
a1.0
51
a0.0
33
a
Lo
g-l
ikel
iho
od
ÿ384.8
9ÿ
395.6
8ÿ
386.2
8ÿ
376.0
2ÿ
383.4
2ÿ
380.5
6P
seu
do
-R2
14.9
9%
12.6
1%
14.6
8%
16.9
5%
15.3
1%
15.9
5%
w2(h
jt*)
0.0
1(0
.92)
0.8
8(0
.35)
0.0
7(0
.79)
0.8
1(0
.37)
0.3
0(0
.58)
3.4
2(0
.06)
c2(Y
jt*)
45.4
0(0
.00)
27.3
6(0
.00)
52.6
6(0
.00)
21.8
5(0
.00)
9.2
4(0
.00)
11.1
4(0
.00)
Th
en
um
ber
of
coex
ceed
an
ces
of
dail
yre
turn
sis
mo
del
edas
an
ord
ered
po
lych
oto
mo
us
vari
ab
lean
des
tim
ate
du
sin
ga
mu
ltin
om
ial
logit
regre
ssio
nm
od
el.
Pj
isd
efin
edas
the
pro
bab
ilit
yth
at
agiv
end
ay
isass
oci
ate
dw
ith
jco
exce
edan
ces,
wh
ere
jeq
uals
0,
1,
2,
3,
4o
rm
ore
(fiv
eca
tego
ries
).T
he
mu
ltin
om
ial
logit
regre
ssio
nm
od
elis
giv
enb
yP
j�
exp
(x0 b
j)/[
1+P k
exp
(x0 b
k)]
,w
her
eb
isth
evec
tor
of
coef
fici
ents
,x
,th
evec
tor
of
ind
epen
den
tvari
ab
les,
an
dk
equ
als
1to
4.
Th
ep
rob
ab
ilit
yth
at
ther
eare
no
(co
-)ex
ceed
an
ces
equ
als
P0�
1/[
1+P k
�1
,4
exp
(x0 b
k)]
,w
hic
hre
pre
sen
tso
ur
ba
seca
se.
Th
ein
dep
end
ent
vari
ab
les,
x,
incl
ud
eth
ose
inT
ab
le3
plu
sth
en
um
ber
of
dail
yre
turn
coex
ceed
an
ces
fro
man
oth
erre
gio
n(Y
*)
an
da
mea
sure
of
con
dit
ion
al
vo
lati
lity
fro
man
oth
erre
gio
n(h
* j).
Th
eco
nd
itio
nal
vo
lati
lity
ises
tim
ate
das
EG
AR
CH
(1,1
)u
sin
gth
eIF
Cin
ves
tib
lere
gio
nal
ind
ex.
Part
ial
der
ivati
ves
of
pro
bab
ilit
ies
wit
hre
spec
tto
the
vec
tor
of
ind
epen
den
tvari
ab
les
are
com
pu
ted
at
the
mea
ns
of
xan
dare
rep
ort
edn
ext
toth
eco
effi
cien
tes
tim
ate
s.G
oo
dn
ess
of
fit
ism
easu
red
by
McF
ad
den
'sp
seu
do
-R2
equ
al
to1ÿ
(L!/L
),
wh
ere
L!
isth
eu
nre
stri
cted
lik
elih
oo
d,
an
dL
is
the
rest
rict
edli
kel
iho
od
[Mad
dala
(1983),
chap
.2)]
.T
he
logit
regre
ssio
nis
esti
mate
dse
para
tely
for
po
siti
ve
(to
p-t
ail
)an
dn
egati
ve
(bo
tto
m-t
ail
)co
exce
edan
ces.w2
(hjt*
)an
dw2
(Yjt*
)are
Wald
chi-
squ
are
test
sfo
rth
ere
stri
ctio
ns
that
b k1�
b k2�
b k3�
b k4�
0w
her
ek
is4
an
d5,
resp
ecti
vel
y,
wit
hp-v
alu
esin
pare
nth
eses
.
a,
bD
eno
tes
sign
ific
an
cele
vel
sat
the
1%
an
d5%
,re
spec
tivel
y.
The Review of Financial Studies / v 16 n 3 2003
744
When we turn to contagion from the United States (models 2 and 5), wesee that the coefficients on the U.S. exceedance have significant coeffi-cients, and the effect on the probability is larger than the effect from LatinAmerica. In addition, the conditional volatility of the United States ishelpful to predict exceedances in Asia. Of interest is whether the UnitedStates had an extreme return seems more helpful in predicting the numberof negative extreme returns in Asia than the number of positive extremereturns, although the Wald statistics indicate that both are significant atthe 1% level. Finally, the results from adding European exceedances ascovariates (models 3 and 6) are weaker than those obtained from addingU.S. covariates for negative returns, but they are still statistically signifi-cant. Comparing the regressions of Table 5 for Asia with those of Table 4,we see that the pseudo-R2 is higher in all cases (though, of course, it is notadjusted for degrees of freedom). We also see that we cannot reject thehypothesis that the new coefficients on the conditional variances andon the number of exceedances are significantly different from zero, exceptthat the Latin American conditional volatility does not significantly affectthe number of positive exceedances in Asia.
The contagion tests for Latin America are presented in the secondpanel. Remember that Asian markets close before the markets in LatinAmerica open on the same day; as a result, we use same-day returns inmeasuring contagion from Asia to Latin America. For the negativeextreme returns, we find that Latin America has more negative extremereturns if Asia has more negative extreme returns, at least for two-countryand four-country-or-more coexceedances. The results for conditionalvolatility are mixed and possibly negative, which suggests that there maybe complex interaction effects among the conditional volatility processesof the different regions. The exceedance shocks from the United Statesand Europe have a larger and more consistent impact than those fromAsia. The effect of the conditional volatility from the United States is alsostrangely negative, though not from Europe. The pseudo-R2s of the LatinAmerican regressions increase more by adding covariates from anotherregion than the pseudo-R2s of Asia. For all the regressions, we cannotreject the hypothesis that the coefficients on the additional variables aresignificant.
Finally, we turn to the United States and Europe in the third and fourthpanels of Table 5. Asian extreme returns or conditional volatility havelittle effect on the probability of a negative extreme return for the UnitedStates and none on the probability of a positive extreme return for theUnited States. In contrast, extreme returns from Latin America and fromEurope have a significant effect. Since markets in Latin America are openwhen markets in the United States are open, a concern is that contagionfrom Latin America is really contagion indirectly from the UnitedStates itself. Finally, Europe's probability of negative extreme returns is
Measuring Financial Contagion
745
significantly affected by extreme returns in all other regions. Again, how-ever, we have to be concerned about the interpretation of this result, sinceEuropean markets are open part of the time when U.S. and Latin Amer-ican markets are open.
The coexceedance response curve plots in Figure 2 for Asia show howthe conditional volatility and the number of extreme returns in LatinAmerica, the United States, and Europe affects the probability of extremereturns in Asia. The plots for Latin America are given in Figure 3. We cansee that the probability of exceedances in Asia increases as the conditionalvolatility of the Latin American returns increases and as the number ofexceedances in Latin America increases. However, the impact of anincrease in the number of Latin American exceedances on the probabilityof four or more exceedances in Asia never reaches 10%. The impact ofAsian exceedances on the probability of one or two exceedances in LatinAmerica (Figure 3) seems modest and the impact of Asian exceedances onthree and four or more exceedances in Latin America is weaker than theimpact of Latin American exceedances on the probability that Asia willhave three or four or more exeedances. Viewed from this perspective,contagion seems sharper from Latin America to Asia than from Asia toLatin America. Further, contagion affecting emerging markets is strongerthan contagion affecting developed countries. Similar plots (not reportedto save space) show that the United States is largely unaffected by coex-ceedances or conditional volatility from Asia. It is somewhat more dra-matically affected by coexceedances in Latin America, but as discussedearlier, the relation between exceedances in Latin America and an excee-dance in the United States is hard to interpret. Europe is more insulatedthan the United States from contagion in Latin America, but more sensi-tive to contagion from Asia than the United States.
3.2 Calibration, robustness tests, and alternative specifications
The returns among countries of the regions we consider are correlated asevidenced by Table 1. One would therefore expect that extreme returns inone region are more likely to be accompanied by extreme returns inanother region and that the coexceedance patterns are just another mani-festation of these correlations. To evaluate this hypothesis we extend thesimulation experiment in Section 1.3 to evaluate our multinomial logisticregression model results. In this experiment we perform Monte Carlosimulations of 2283 daily returns (corresponding to the April 1, 1992, toDecember 29, 2000, period) for each country in Asia and Latin Americausing 1000 replications of the historical mean vector and variance-covariance matrix and assumptions about the joint returns-generatingprocess. As before, we propose the multivariate normal, multivariateStudent's t (with five degrees of freedom), and the multivariate GARCH
The Review of Financial Studies / v 16 n 3 2003
746
using the Ding and Engle (1994) specification. This time, however, thesimulation is for all 17 countries in both regions. For each replication wecount coexceedance events in both regions and estimate a simplifiedversion of the multinomial logistic regression model of Table 5. To pro-ceed with the experiments, we only examine whether the number of coex-ceedances in one region can be forecast with the number of coexceedancesin another region. We only perform the experiments for contagion fromLatin America to Asia and from Asia to Latin America.
From Latin America to Asia
Figure 2Coexceedance response curves of negative extreme returns in Asia to the conditional volatility andnumber of coexceedances of overseas market.
Measuring Financial Contagion
747
The results are available from the authors. Basically we cannot explainthe coefficients on coexceedances from the other region for Asia or LatinAmerica. For the multivariate normal and Student's t scenarios, wecannot explain the magnitude of the bj coefficients associated with Y �jtcoexceedances for positive or negative extreme returns. The multivariateGARCH model has only moderate success delivering simulation p-valuesof at most 5% for top-tail exceedances and 16% for the bottom tails. The
From Latin America to Asia
Figure 2Continued
The Review of Financial Studies / v 16 n 3 2003
748
pseudo-R2 statistics in the simulations reach values as large as in the actualdata in at most 1% of the replications. For Latin America, in particular,the highest simulation p-value for any coexceedance coefficient is 3% forthe top tail in the multivariate GARCH scenario and 23% in the bottomtail also for the multivariate GARCH scenario. Perhaps even more strik-ing for Latin America, the pseudo-R2 is at least four times higher in thedata than it is in any of the simulations.
Figure 3Coexceedance response curves of negative extreme returns in Latin America to the conditional volatilityand number of coexceedances of overseas market
Measuring Financial Contagion
749
We consider a battery of robustness checks. We reestimated our multi-nomial logistic regressions with Monday dummies. These dummies areinsignificant. We also reestimated the models of Table 5 using localcurrency returns. The results are virtually unchanged, except that thepseudo-R2 are lower in Asia and Latin America. In Table 6 we reportour contagion tests using lagged conditioning variables. Though it is anin-sample experiment, it allows us to investigate further the predictabilityof contagion. We see immediately that the pseudo-R2 falls. However, the
Figure 3Continued
The Review of Financial Studies / v 16 n 3 2003
750
significance of yesterday's coexceedances from the other regions is not lessthan the significance of same day coexceedances. The table providesevidence that contagion across regions is predictable and that the numberof coexceedances of another region provides useful information in pre-dicting contagion.
A concern we have expressed is that contagion is just the outcome ofhigh volatility. We investigated this concern in a preliminary way with ourMonte Carlo simulations using multivariate GARCH scenarios. Anotherapproach to investigate this concern is to define exceedances differentlyfrom how we have defined them so far. With the exceedances defined interms of the sample period returns, we necessarily have an outcome wherewe have more exceedances in periods of higher conditional volatility.Alternatively we can define exceedances using conditional volatility itself,so that the probability of observing an exceedance is always the same(assuming multivariate normality for returns and a constant conditionalmean). In Table 7 we define positive extreme returns to be those thatexceed 1.65 times the conditional volatility and negative extreme returnsthose that are below ÿ 1.65 times the conditional volatility. The mainimpact of defining extreme returns this way is that a region's conditionalvolatility is no longer useful in predicting that region's coexceedances.However, coexceedances in one region still provide useful information inpredicting coexceedances in another region. For instance, the number ofcoexceedances in Latin America helps explain the number of coexcee-dances in Asia. Surprisingly, with this definition of exceedances, interestrates are no longer useful to predict exceedances, but exchange ratechanges still are.
We use two more definitions of exceedances. We reestimate (notreported) the base model regression, but use exceedances computed overthree days instead of over one day as regressors. That is, a coexceedanceevent is defined as one in which more than one market experiences anextreme return within a moving three-day window. The objective of thisrobustness check is to assess in a rough way the nature of the dynamics incoexceedances within a region. Overall, the results are similar to those ofthe base case in Table 5 for Asia, but weaker for Latin America.18 Finally,we define exceedances by the 2.5% quantile rather than the 5% quantile.Proceeding this way, we have fewer exceedances. The results (again, notreported) reveal a similar pattern in coefficients, partial derivatives ofprobabilities relative to covariates, and coexceedance responses to Table 5,but inference tests lose power.
18 Another possible concern that we do not investigate with the alternative specifications using multidayhorizons and lagged covariates is with nonstationarity of the explanatory variables. Park and Phillips(2000) demonstrate the complications in the limiting distributions for binary choice models with expla-natory variables generated as integrated processes. The potential impact on multinomial logit models isan open question, however. We thank Richard Roll and our referee for pointing this out.
Measuring Financial Contagion
751
Table
6C
onta
gio
nte
stre
sult
sof
mult
inom
ial
logit
regre
ssio
nfo
rdail
yre
turn
coex
ceed
ance
sof
emer
gin
gm
ark
etin
dic
esusi
ng
lagged
condit
ionin
gva
riable
s,A
pri
l1,
1992,
toD
ecem
ber
29,
2000
Bo
tto
mta
ils
To
pta
ils
(1)
(2)
(3)
(4)
(5)
(6)
Co
eff.
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rob
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oef
f.�
pro
b.
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Co
eff.
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rob
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oef
f.�
pro
b.
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aF
rom
Lati
nA
mer
ica
Fro
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SF
rom
Eu
rop
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mer
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Fro
mU
SF
rom
Eu
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eb 0
1(c
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stan
t)ÿ
1.2
41
aÿ
0.1
53
aÿ
1.4
91
aÿ
0.1
92
aÿ
1.5
18
aÿ
0.1
98
aÿ
1.1
71
aÿ
0.1
57
aÿ
1.2
43
aÿ
0.1
65
aÿ
1.3
90
aÿ
0.1
94
a
b 02
ÿ3.0
08
aÿ
0.1
51
aÿ
3.5
66
aÿ
0.1
73
aÿ
3.4
39
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0.1
67
aÿ
2.3
37
aÿ
0.1
08
aÿ
2.5
69
aÿ
0.1
20
aÿ
2.6
46
aÿ
0.1
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a
b 03
ÿ7.2
66
aÿ
0.0
58
aÿ
7.9
37
aÿ
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56
aÿ
7.6
28
aÿ
0.0
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4.0
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aÿ
0.0
59
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4.7
23
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0.0
67
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4.7
37
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0.0
66
a
b 04
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27
aÿ
0.0
50
aÿ
7.1
39
aÿ
0.0
55
aÿ
6.9
67
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0.0
56
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6.9
77
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0.0
35
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7.2
89
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7.4
93
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0.0
26
b
b 11
(hit)
0.4
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a0.0
63
a0
.312
a0.0
49
a0.3
07
a0.0
48
a0.3
15
a0.0
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a0.2
50
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36
a0.2
09
a0.0
29
a
b 12
0.5
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a0.0
25
a0
.408
a0.0
18
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31
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a0.6
00
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a0.4
75
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a0.4
56
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22
a
b 13
0.4
57
a0.0
03
b0
.349
a0.0
02
0.3
92
a0.0
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b0.8
05
a0.0
11
a0.5
98
a0.0
08
a0.6
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a0.0
08
a
b 14
0.7
04
a0.0
05
a0
.571
a0.0
04
a0.5
63
a0.0
04
a0.7
94
a0.0
04
a0.6
65
a0.0
03
b0.7
72
a0.0
03
b
b 21
(eitÿ
1)
0.2
46
0.0
36
0.2
37
0.0
35
0.2
52
0.0
37
ÿ0.4
10
aÿ
0.0
60
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0.3
88
aÿ
0.0
57
bÿ
0.3
41
bÿ
0.0
50
b
b 22
0.3
52
0.0
16
0.3
46
0.0
15
0.3
62
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ÿ0.8
75
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0.0
43
aÿ
0.8
61
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0.0
42
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0.7
73
aÿ
0.0
38
a
b 23
0.9
39
a0.0
07
a0
.948
a0.0
07
a0.9
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a0.0
07
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0.5
75
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0.0
07
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0.0
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ÿ0.4
32
ÿ0.0
05
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0.8
22
a0.0
06
a0
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a0.0
06
a0.8
76
a0.0
07
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0.8
01
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0.0
03
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0.7
70
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0.0
03
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0.6
72
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0.0
02
b 31
(iitÿ
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ÿ0.0
33
ÿ0.0
07
ÿ0.0
12
ÿ0.0
03
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08
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06
0.0
00
b 32
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0.0
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28
0.0
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0.0
04
0.0
00
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0.0
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0.0
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55
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0.1
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.226
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98
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0.1
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b0.0
01
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68
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49
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b0.0
86
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01
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0.0
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0.0
48
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(h� jt)
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0.0
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0.2
48
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a0.5
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07
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a0.6
91
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b
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0.1
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02
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97
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75
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03
0.2
65
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0.9
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0.2
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0.0
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b
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0.1
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a0.0
31
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70
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10
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ÿ0.0
14
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1.4
30
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46
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94
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b
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0.3
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70
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a0.7
11
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0.8
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a2
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ÿ1959.8
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1942.9
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2003.6
3P
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do
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1%
8.5
0%
8.3
2%
5.7
4%
5.8
5%
6.3
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w2(h� jt)
8.5
5(0
.07)
22.9
0(0
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28.7
6(0
.00)
5.0
4(0
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13.5
7(0
.01)
41.2
6(0
.00)
w2(Y� jt)
36.0
1(0
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52.3
2(0
.00)
35.7
1(0
.00)
37.5
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28.1
5(0
.00)
15.3
6(0
.00)
The Review of Financial Studies / v 16 n 3 2003
752
Lati
nA
mer
ica
Fro
mA
sia
Fro
mU
SF
rom
Eu
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Asi
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(co
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2.2
63
aÿ
0.2
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1.9
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2.4
11
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0.2
86
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1.8
38
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48
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1.4
07
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81
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65
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65
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18
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0.1
13
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3.1
91
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66
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0.0
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.00)
94.3
1(0
.00)
69.5
5(0
.00)
29.9
5(0
.00)
42.5
9(0
.00)
33.1
7(0
.01)
US
Fro
mA
sia
Fro
mL
ati
nA
mer
ica
Fro
mE
uro
pe
Fro
mA
sia
Fro
mL
ati
nA
mer
ica
Fro
mE
uro
pe
b 1(c
on
stan
t)ÿ
5.5
10
aÿ
0.2
16
aÿ
6.3
17
aÿ
0.2
02
aÿ
5.6
20
aÿ
0.2
10
aÿ
5.1
08
aÿ
0.1
80
aÿ
5.4
51
aÿ
0.1
73
aÿ
5.0
43
aÿ
0.1
67
a
b 2(h
it)
0.4
26
a0.0
17
a0.4
61
a0.0
15
a0.2
40
0.0
09
0.8
68
a0.0
31
a1.0
31
a0.0
33
a0.8
87
a0.0
29
a
b 3(e
itÿ
1)
ÿ0.3
00
ÿ0.0
12
ÿ0.2
47
ÿ0.0
08
ÿ0.2
49
ÿ0.0
09
ÿ0.3
46
ÿ0.0
12
ÿ0.4
14
ÿ0.0
13
ÿ0.3
17
ÿ0.0
11
b 4(i
itÿ
1)
0.3
83
a0.0
15
a0.5
01
a0.0
16
a0.3
85
a0.0
14
a0.2
17
0.0
08
0.2
49
b0.0
08
b0.2
05
0.0
07
b 4(h� jt)
0.0
17
0.0
01
ÿ0.1
61
ÿ0.0
05
0.3
53
0.0
13
0.0
03
0.0
00
ÿ0.1
97
bÿ
0.0
06
bÿ
0.2
09
ÿ0.0
07
b 4(Y� jt)
0.1
83
0.0
07
0.9
12
a0.0
29
a1.4
42
a0.0
54
a0.0
43
0.0
01
0.6
95
a0.0
22
a1.5
83
a0.0
52
a
Lo
g-l
ikel
iho
od
ÿ425.5
6ÿ
383.0
3ÿ
413.2
7ÿ
396.0
8ÿ
379.7
3ÿ
382.4
5P
seu
do
-R2
6.0
0%
15.3
9%
8.7
1%
12.5
1%
16.1
2%
15.5
2%
w2(h� jt)
0.0
5(0
.92)
3.1
9(0
.07)
2.6
4(0
.10)
0.0
0(0
.99)
5.5
3(0
.02(
0.8
1(0
.37)
w2(Y� jt)
3.3
1(0
.00)
91.1
7(0
.00)
28.6
3(0
.00)
0.1
5(0
.69)
34.7
6(0
.00)
32.0
8(0
.01)
Measuring Financial Contagion
753
Table
6(c
onti
nued
)
Bo
tto
mta
ils
To
pta
ils
(1)
(2)
(3)
(4)
(5)
(6)
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Eu
rop
eF
rom
Asi
aF
rom
Lati
nA
mer
ica
Fro
mU
SF
rom
Asi
aF
rom
Lati
nA
mer
ica
Fro
mU
Sb 1
(co
nst
an
t)ÿ
4.2
01
aÿ
0.1
53
aÿ
3.5
46
aÿ
0.1
39
aÿ
3.9
44
aÿ
0.1
49
aÿ
4.2
37
aÿ
0.1
54
aÿ
3.8
41
aÿ
0.1
45
aÿ
4.2
28
aÿ
0.1
57
a
b 2(h
it)
0.9
31
a0.0
34
a0.9
72
a0.0
38
a1.0
00
a0.0
38
a1.0
34
a0.0
38
a1.0
75
a0.0
41
a0.9
19
a0.0
34
a
b 3(e
itÿ
1)
0.0
41
0.0
01
0.1
08
0.0
04
0.1
23
0.0
05
0.2
83
0.0
10
0.2
86
0.0
11
0.2
96
0.0
11
b
b 4(i
it1)
0.0
11
0.0
00
ÿ0.0
56
ÿ0.0
02
0.0
02
0.0
00
0.0
01
0.0
00
ÿ0.0
51
ÿ0.0
02
0.0
15
0.0
01
b 4(h
jt*)
ÿ0.0
14
0.0
00
ÿ0.0
76
ÿ0.0
03
ÿ0.0
40
ÿ0.0
01
0.0
90
0.0
03
0.0
68
0.0
03
0.2
97
b0.0
11
b
b 4(Y
*jt)
0.5
80
a0.0
21
a0.4
66
a0.0
18
a1.7
77
a0.0
67
a0.3
83
a0.0
14
a0.2
83
b0.0
11
b0.8
04
a0.0
30
a
Lo
g-l
ikel
iho
od
ÿ405.3
2ÿ
415.9
5ÿ
407.1
2ÿ
400.7
5ÿ
406.6
7ÿ
403.7
0P
seu
do
-R2
10.4
7%
8.1
2%
10.0
7%
11.4
8%
10.1
7%
10.8
3%
w2(h
jt*)
0.0
3(0
.86)
0.9
8(0
.320
0.0
7(0
.79)
1.5
4(0
.21)
1.3
0(0
.25)
5.1
1(0
.02)
w2(Y
jt*)
40.9
6(0
.00)
22.6
5(0
.00)
45.8
0(0
.00)
16.0
4(0
.00)
5.8
0(0
.02)
6.7
7(0
.01)
Th
en
um
ber
of
coex
ceed
an
ces
of
dail
yre
turn
sis
mo
del
edas
an
ord
ered
po
lych
oto
mo
us
vari
ab
lean
des
tim
ate
du
sin
ga
mu
ltin
om
ial
logit
regre
ssio
nm
od
el.
Pj
isd
efin
edas
the
pro
bab
ilit
yth
at
agiv
end
ay
isass
oci
ate
dw
ith
jco
exce
edan
ces,
wh
ere
jeq
uals
0,
1,
2,
3,
4o
rm
ore
(fiv
eca
tego
ries
).T
he
mu
ltin
om
ial
logit
regre
ssio
nm
od
elis
giv
enb
yP
j�
exp
(x0 b
j)/[
1+
�kex
p(x0 b
k)]
,w
her
eb
isth
evec
tor
of
coef
fici
ents
,x
isth
evec
tor
of
ind
epen
den
tvari
ab
les,
an
dk
equ
als
1to
4.
Th
ep
rob
ab
ilit
yth
at
ther
eare
no
(co
-)ex
ceed
an
ces
equ
als
P0�
1/[
1+
�kex
p(x0 b
k)]
wh
ere
keq
uals
1to
4,w
hic
hre
pre
sen
tso
ur
base
case
.T
he
ind
epen
den
tvari
ab
les,
x,in
clu
de
the
inte
rcep
t,co
nd
itio
nal
vo
lati
lity
of
regio
nal
ind
exat
tim
et
(ht)
,th
ela
gged
aver
age
exch
an
ge
rate
(per
$U
S)
chan
ges
inth
ere
gio
n(e
tÿ
1),
the
lagged
aver
age
inte
rest
rate
level
inth
ere
gio
n(i
tÿ
1),
the
nu
mb
ero
fd
ail
yre
turn
co-
exce
eda
nce
sfr
om
an
oth
erre
gio
n(Y
* j),
an
da
mea
sure
of
con
dit
ion
al
vo
lati
lity
fro
man
oth
erre
gio
n(h
* j).
Th
eco
nd
itio
nal
vo
lati
lity
ises
tim
ate
das
EG
AR
CH
(1,1
)u
sin
gth
eIF
Cin
ves
tib
lere
gio
nal
ind
ex.
Fo
rth
eco
nta
gio
nte
stfr
om
Lati
n,
US
,an
dE
uro
pe
toA
sia,
lagged
h* j
an
dY
* jare
use
dto
ad
just
for
the
no
nsy
nch
ron
ou
str
ad
ing.
Part
ial
der
ivati
ves
of
pro
bab
ilit
ies
wit
hre
spec
tto
the
vec
tor
of
ind
epen
den
tvari
ab
les
are
com
pu
ted
at
the
mea
ns
of
xan
dare
rep
ort
edn
ext
toth
eco
effi
cien
tes
tim
ate
s.G
oo
dn
ess-
of-
fit
ism
easu
red
by
McF
ad
den
'sp
seu
do
-R2
equ
al
to1ÿ
(L!/L
),
wh
ere
L!
isth
eu
nre
stri
cted
lik
elih
oo
d,
an
dL
is
the
rest
rict
edli
kel
iho
od
[Mad
dala
(1983,
chap
.2)]
.T
he
logit
regre
ssio
nis
esti
mate
dse
para
tely
for
po
siti
ve
(to
p-t
ail
)an
dn
egati
ve
(bo
tto
m-t
ail
)co
exce
edan
ces.w2
(hjt*
)an
dw2
(Yjt*
)are
Wald
chi-
squ
are
test
sfo
rth
ere
stri
ctio
ns
thatb k
1�b k
2�b k
3�b k
4�
0,w
her
ek
is4
an
d5,
resp
ecti
vel
y,
wit
hp
-valu
esin
pare
nth
eses
.
19
a,
bD
eno
tes
sign
ific
an
cele
vel
sat
the
1%
an
d5%
,re
spec
tivel
y.
The Review of Financial Studies / v 16 n 3 2003
754
Table
7C
onta
gio
nte
stre
sult
sof
mult
inom
ial
logit
regre
ssio
nfo
rdail
yre
turn
coex
ceed
ance
sfr
om
condit
ional
extr
eme
retu
rns,
Apri
l1,
1992
toD
ecem
ber
29,
2000
Bo
tto
mta
ils
To
pta
ils
(1)
(2)
(3)
(4)
(5)
(6)
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Asi
aF
rom
Lati
nA
mer
ica
Fro
mU
SF
rom
Eu
rop
eF
rom
Lati
nA
mer
ica
Fro
mU
SF
rom
Eu
rop
eb 0
1(c
on
stan
t)ÿ
1.3
12
aÿ
0.1
79
aÿ
1.4
63
aÿ
0.2
05
aÿ
1.3
93
aÿ
0.1
92
aÿ
0.9
92
aÿ
0.1
48
aÿ
0.9
76
aÿ
0.1
45
aÿ
1.1
10
aÿ
0.1
65
a
b 02
ÿ2.9
12
aÿ
0.1
14
aÿ
2.8
62
aÿ
0.1
11
aÿ
2.7
38
aÿ
0.1
06
aÿ
1.5
07
aÿ
0.0
59
aÿ
1.4
40
aÿ
0.0
57
aÿ
1.7
60
aÿ
0.0
72
a
b 03
ÿ6.3
93
aÿ
0.0
33
aÿ
6.5
15
aÿ
0.0
35
bÿ
6.6
36
aÿ
0.0
37
aÿ
4.5
97
aÿ
0.0
53
aÿ
5.0
17
aÿ
0.0
52
aÿ
4.7
28
aÿ
0.0
51
a
b 04
ÿ4.9
61
aÿ
0.0
20
bÿ
4.7
75
aÿ
0.0
17
bÿ
5.2
95
aÿ
0.0
22
bÿ
4.4
90
aÿ
0.0
15
bÿ
4.2
30
aÿ
0.0
17
bÿ
4.4
23
aÿ
0.0
20
b
b 11
(hit)
ÿ0.0
25
ÿ0.0
04
ÿ0.0
75
ÿ0.0
14
ÿ0.0
42
ÿ0.0
08
ÿ0.0
99
ÿ0.0
17
ÿ0.1
03
ÿ0.0
17
ÿ0.1
49
aÿ
0.0
24
b
b 12
0.0
33
0.0
02
0.0
73
0.0
04
0.0
97
0.0
05
ÿ0.1
24
ÿ0.0
05
ÿ0.1
47
ÿ0.0
06
ÿ0.2
72
bÿ
0.0
12
b 13
ÿ0.1
97
ÿ0.0
01
ÿ0.0
82
0.0
00
ÿ0.1
54
ÿ0.0
01
ÿ0.1
09
ÿ0.0
01
ÿ0.2
61
ÿ0.0
03
ÿ0.1
66
ÿ0.0
01
b 14
0.2
15
0.0
01
0.3
52
0.0
01
0.1
95
0.0
01
0.4
59
b0.0
02
0.3
74
b0.0
02
0.3
25
0.0
02
b 21
(eit)
0.7
88
a0.1
15
a0
.781
a0.1
14
a0.7
80
a0.1
14
aÿ
0.4
01
aÿ
0.0
54
ÿ0.4
01
aÿ
0.0
53
ÿ0.3
94
aÿ
0.0
51
b 22
1.3
96
a0.0
53
a1
.318
a0.0
50
a1.3
07
a0.0
50
aÿ
1.2
12
aÿ
0.0
55
aÿ
1.2
52
aÿ
0.0
59
aÿ
1.2
45
aÿ
0.0
58
a
b 23
1.7
96
a0.0
09
a1
.746
a0.0
09
a1.7
43
a0.0
09
aÿ
1.2
79
aÿ
0.0
14
aÿ
1.3
67
aÿ
0.0
13
aÿ
1.3
29
aÿ
0.0
14
a
b 24
1.6
43
a0.0
06
b1
.678
a0.0
06
b1.5
91
a0.0
06
bÿ
1.4
28
aÿ
0.0
04
bÿ
1.5
13
aÿ
0.0
06
bÿ
1.4
52
aÿ
0.0
06
b
b 31
(iit)
ÿ0.0
04
0.0
00
0.0
09
0.0
01
0.0
02
0.0
00
0.0
16
0.0
04
0.0
13
0.0
03
0.0
19
0.0
04
b 32
ÿ0.0
18
ÿ0.0
01
ÿ0.0
13
ÿ0.0
01
ÿ0.0
17
ÿ0.0
01
ÿ0.0
62
ÿ0.0
03
ÿ0.0
71
ÿ0.0
04
ÿ0.0
54
ÿ0.0
03
b 33
0.1
08
0.0
01
0.1
23
0.0
01
0.1
21
0.0
01
0.0
44
0.0
01
0.0
71
0.0
01
0.0
42
0.0
00
b 34
ÿ0.0
64
0.0
00
ÿ0.0
69
0.0
00
ÿ0.0
20
0.0
00
ÿ0.1
23
0.0
00
ÿ0.1
17
ÿ0.0
01
ÿ0.1
17
ÿ0.0
01
b 41
(hjt*
)0.0
61
0.0
08
0.2
11
a0.0
34
a0.1
97
0.0
32
ÿ0.0
64
ÿ0.0
09
ÿ0.0
71
ÿ0.0
12
0.1
13
0.0
15
b 42
0.1
69
a0.0
07
b0
.120
0.0
03
0.0
00
ÿ0.0
02
ÿ0.2
25
bÿ
0.0
11
ÿ0.1
74
ÿ0.0
08
0.2
43
0.0
11
b 43
0.2
06
0.0
01
0.3
52
0.0
02
0.8
01
b0.0
04
0.1
19
0.0
02
0.4
60
b0.0
05
b0.5
83
b0.0
06
b 44
0.0
19
0.0
00
ÿ0.2
51
ÿ0.0
01
0.1
28
0.0
00
ÿ0.1
67
ÿ0.0
01
ÿ0.0
60
0.0
00
0.6
07
0.0
03
b 51
(Yjt*
)0.1
43
0.0
21
0.3
63
0.0
47
0.6
80
a0.1
01
a0.1
51
b0.0
21
0.6
78
a0.1
09
a0.2
55
0.0
44
b 52
0.1
31
0.0
04
0.8
94
b0.0
35
b0.8
09
b0.0
29
0.4
13
a0.0
18
a0.7
88
b0.0
30
ÿ0.0
65
ÿ0.0
08
b 53
0.8
31
a0.0
04
b2
.210
a0.0
12
b1.9
65
a0.0
10
b0.3
82
0.0
04
1.8
64
a0.0
18
b1.3
05
a0.0
15
b
b 54
0.8
63
a0.0
04
b2
.590
a0.0
10
b2.2
38
a0.0
09
b1.1
27
a0.0
04
b2.5
78
a0.0
10
b0.9
34
0.0
04
Lo
g-l
ikel
iho
od
ÿ1744.3
3ÿ
1744.5
2ÿ
1747.4
1ÿ
1960.7
3ÿ
1963.5
5ÿ
1976.0
9P
seu
do
-r2
3.7
8%
3.7
7%
3.6
1%
2.8
5%
2.7
1%
2.0
8%
w2(h
jt*)
9.3
3(0
.05)
9.1
0(0
.06)
7.6
3(0
.11)
8.6
4(0
.07)
8.9
9(0
.06)
7.9
7(0
.09)
w2(Y
jt*)
33.9
3(0
.00)
37
.32
(0.0
0)
29.6
2(0
.00)
41.3
7(0
.00)
36.8
9(0
.00)
8.5
5(0
.07)
Measuring Financial Contagion
755
Table
7(c
onti
nued
)
Bo
tto
mta
ils
To
pta
ils
(1)
(2)
(3)
(4)
(5)
(6)
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Co
eff.
�p
rob
.C
oef
f.�
pro
b.
Lati
nA
mer
ica
Fro
mA
sia
Fro
mU
SF
rom
Eu
rop
eF
rom
Asi
aF
rom
US
Fro
mE
uro
pe
b 01
(co
nst
an
t)ÿ
1.9
75
aÿ
0.2
43
aÿ
1.9
07
aÿ
0.2
36
aÿ
2.0
63
aÿ
0.2
58
aÿ
1.2
61
aÿ
0.1
54
aÿ
0.9
69
aÿ
0.1
14
aÿ
1.2
65
aÿ
0.1
54
a
b 02
ÿ4.2
25
aÿ
0.0
90
aÿ
4.4
79
aÿ
0.0
92
aÿ
4.1
80
aÿ
0.0
90
aÿ
3.1
93
aÿ
0.1
10
aÿ
2.5
76
aÿ
0.0
86
aÿ
3.1
83
aÿ
0.1
13
a
b 03
ÿ4.8
72
aÿ
0.0
24
aÿ
4.8
70
aÿ
0.0
22
bÿ
5.3
63
aÿ
0.0
23
bÿ
5.2
51
aÿ
0.0
39
aÿ
5.9
57
aÿ
0.0
46
aÿ
5.6
31
aÿ
0.0
42
a
b 04
ÿ6.5
46
aÿ
0.0
27
bÿ
6.9
53
aÿ
0.0
23
bÿ
7.1
26
aÿ
0.0
20
bÿ
6.2
44
aÿ
0.0
16
bÿ
5.5
43
aÿ
0.0
19
bÿ
6.5
86
aÿ
0.0
17
b
b 11
(hit)
0.1
69
a0.0
22
a0.1
89
a0.0
25
a0.1
43
a0.0
19
a0.0
15
0.0
01
0.0
37
0.0
05
ÿ0.0
21
ÿ0.0
03
b 12
0.1
77
b0.0
03
0.1
52
0.0
03
0.1
85
b0.0
04
0.0
52
0.0
02
0.1
12
0.0
04
ÿ0.0
21
ÿ0.0
01
b 13
0.0
95
0.0
00
0.2
07
0.0
01
0.0
53
0.0
00
0.1
47
0.0
01
0.0
22
0.0
00
0.0
70
0.0
01
b 14
0.2
17
b0.0
01
0.2
39
0.0
01
0.1
67
0.0
00
0.4
31
a0.0
01
0.3
89
a0.0
01
0.3
07
a0.0
01
b 21
(eit)
0.9
76
a0.1
24
a0.9
91
a0.1
27
a1.0
05
a0.1
29
aÿ
0.2
03
ÿ0.0
19
ÿ0.2
12
ÿ0.0
23
ÿ0.1
64
ÿ0.0
14
b 22
1.6
02
a0.0
33
a1.6
39
a0.0
33
a1.5
71
a0.0
33
aÿ
1.4
49
aÿ
0.0
53
aÿ
1.3
67
aÿ
0.0
49
aÿ
1.3
96
aÿ
0.0
54
a
b 23
1.4
99
a0.0
07
b1.4
83
a0.0
06
b1.4
59
a0.0
06
b0.3
55
0.0
04
1.1
90
a0.0
11
a0.3
87
0.0
04
b 24
1.7
25
a0.0
07
b1.7
59
a0.0
06
b1.7
36
a0.0
05
bÿ
1.8
39
aÿ
0.0
05
ÿ1.6
50
aÿ
0.0
06
ÿ1.7
53
aÿ
0.0
05
b 31
(iit)
0.0
01
0.0
00
ÿ0.0
01
0.0
00
0.0
05
0.0
01
ÿ0.0
03
ÿ0.0
01
ÿ0.0
12
ÿ0.0
02
ÿ0.0
01
0.0
00
b 32
ÿ0.0
01
0.0
00
0.0
12
0.0
00
0.0
01
0.0
00
0.0
11
0.0
00
ÿ0.0
07
0.0
00
0.0
16
0.0
01
b 33
ÿ0.0
56
0.0
00
ÿ0.0
48
0.0
00
ÿ0.0
39
0.0
00
0.0
43
0.0
00
0.0
63
b0.0
01
0.0
50
0.0
00
b 34
0.0
13
0.0
00
0.0
32
0.0
00
0.0
23
0.0
00
ÿ0.0
11
0.0
00
ÿ0.0
11
0.0
00
0.0
07
0.0
00
b 41
(hjt*
)ÿ
0.0
72
ÿ0.0
11
ÿ0.0
89
ÿ0.0
14
0.0
74
0.0
08
ÿ0.2
06
aÿ
0.0
29
aÿ
0.3
54
aÿ
0.0
50
aÿ
0.1
90
ÿ0.0
30
b 42
0.1
38
0.0
03
0.2
86
0.0
07
0.2
67
0.0
06
ÿ0.1
18
ÿ0.0
03
ÿ0.4
76
bÿ
0.0
15
0.1
20
0.0
06
b 43
0.3
25
b0.0
02
0.0
61
0.0
00
0.8
25
b0.0
04
ÿ0.3
41
ÿ0.0
02
0.1
13
0.0
02
0.0
04
0.0
00
b 44
0.3
95
a0.0
02
b0.3
76
0.0
01
0.8
31
b0.0
02
ÿ0.0
56
0.0
00
ÿ0.1
07
0.0
00
0.6
47
0.0
02
b 51
(Yjt*
)0.2
60
a0.0
33
a0.8
40
a0.1
03
a0.7
62
a0.0
95
a0.1
85
b0.0
23
b0.3
74
0.0
40
0.4
92
b0.0
63
b 52
0.4
62
a0.0
10
b2.0
57
a0.0
42
a1.4
25
a0.0
30
a0.5
03
a0.0
18
a1.6
50
a0.0
58
a0.9
43
a0.0
33
b
b 53
0.5
79
b0.0
03
2.8
18
a0.0
13
b2.6
68
a0.0
12
b0.1
62
0.0
01
1.8
78
a0.0
14
b1.3
47
b0.0
10
b 54
0.5
68
b0.0
02
3.3
54
a0.0
11
b3.4
64
a0.0
10
b0.9
23
a0.0
02
1.5
73
b0.0
05
2.3
03
a0.0
06
Lo
g-l
ikel
iho
od
ÿ1426.1
4ÿ
1411.0
4ÿ
1414.2
6ÿ
1627.5
5ÿ
1635.2
5ÿ
1638.9
5P
seu
do
-R2
5.4
0%
6.4
1%
6.1
9%
3.2
0%
2.7
4%
2.5
2%
w2(h
jt*)
21.9
8(0
.00)
6.2
8(0
.18)
8.4
7(0
.08)
12.6
9(0
.01)
15.7
2(0
.00)
5.5
4(0
.24)
w2(Y
jt*)
26.0
8(0
.00)
81.7
2(0
.00)
69.0
8(0
.00)
36.9
2(0
.00)
42.6
0(0
.00)
23.6
8(0
.01)
The Review of Financial Studies / v 16 n 3 2003
756
US
Fro
mA
sia
Fro
mL
ati
nF
rom
Eu
rop
eF
rom
Asi
aF
rom
Lati
nF
rom
Eu
rop
eb 1
(co
nst
an
t)ÿ
3.9
01
aÿ
0.1
70
aÿ
4.3
81
aÿ
0.1
62
aÿ
4.2
41
aÿ
0.1
70
aÿ
3.3
77
aÿ
0.1
52
aÿ
3.8
86
aÿ
0.1
60
aÿ
3.3
62
aÿ
0.1
51
a
b 2(h
it)
ÿ0.0
99
ÿ0.0
04
ÿ0.2
63
ÿ0.0
10
ÿ0.4
70
bÿ
0.0
19
b0.0
84
0.0
04
0.0
39
0.0
02
0.0
81
0.0
04
b 3(e
it)
0.3
54
0.0
15
0.2
34
0.0
09
0.5
09
b0.0
20
bÿ
0.6
93
aÿ
0.0
31
aÿ
0.6
57
aÿ
0.0
27
aÿ
0.7
38
aÿ
0.0
33
a
b 4(i
it)
0.1
89
0.0
08
0.2
14
b0.0
08
b0.2
14
b0.0
09
b0.0
63
0.0
03
0.0
98
0.0
04
0.0
57
0.0
03
b 4(h
jt*)
ÿ0.0
21
ÿ0.0
01
0.0
70
0.0
03
0.5
50
b0.0
22
bÿ
0.0
22
ÿ0.0
01
0.0
39
0.0
02
ÿ0.0
29
ÿ0.0
01
b 4(Y
*jt)
0.1
07
0.0
05
0.8
44
a0.0
31
a1.6
65
a0.0
67
a0.0
35
0.0
02
0.6
38
a0.0
26
a0.4
52
0.0
20
Lo
g-l
ikel
iho
od
ÿ428.8
6ÿ
395.8
4ÿ
414.8
0ÿ
442.5
4ÿ
425.1
6ÿ
442.0
5P
seu
do
-R2
0.7
1%
8.3
5%
3.9
6%
0.9
7%
4.8
6%
1.0
8%
w2(h
jt*)
0.0
5(0
.82)
0.7
9(0
.37)
4.4
8(0
.03)
0.0
6(0
.81)
0.1
2(0
.73)
0.0
1(0
.92)
w2(Y
jt*)
0.6
3(0
.43)
73.8
4(0
.00)
32.6
6(0
.00)
0.0
7(0
.79)
39.8
4(0
.00)
1.2
1(0
.27)
Eu
rop
eF
rom
Asi
aF
rom
Lati
nA
mer
ica
Fro
mU
SF
rom
Asi
aF
rom
Lati
nA
mer
ica
Fro
mU
Sb 1
(co
nst
an
t)ÿ
3.4
71
aÿ
0.1
21
aÿ
2.9
97
aÿ
0.1
12
aÿ
3.3
32
aÿ
0.1
15
aÿ
2.9
92
aÿ
0.1
00
aÿ
2.8
41
aÿ
0.0
94
aÿ
3.0
70
aÿ
0.1
01
a
b 2(h
it)
0.0
82
0.0
03
ÿ0.0
91
ÿ0.0
03
0.0
39
0.0
01
ÿ0.5
49
bÿ
0.0
18
bÿ
0.5
01
ÿ0.0
17
bÿ
0.8
16
bÿ
0.0
27
b
b 3(e
it)
1.0
11
a0.0
35
a1.0
40
a0.0
39
a1.0
95
a0.0
38
aÿ
1.5
81
aÿ
0.0
53
aÿ
1.5
91
aÿ
0.0
53
aÿ
1.5
83
aÿ
0.0
52
a
b 4(i
it)
ÿ0.0
43
ÿ0.0
01
ÿ0.0
86
ÿ0.0
03
ÿ0.0
38
ÿ0.0
01
ÿ0.0
30
ÿ0.0
01
ÿ0.0
53
ÿ0.0
02
ÿ0.0
05
0.0
00
b 4(h� jt)
0.0
77
0.0
03
0.1
15
0.0
04
0.1
28
0.0
04
0.1
06
0.0
04
0.0
53
0.0
02
0.3
33
0.0
11
b 4(Y� jt)
0.7
70
a0.0
27
a0.5
87
a0.0
22
a2.3
67
a0.0
82
a0.2
53
b0.0
08
b0.3
04
b0.0
10
b0.9
89
a0.0
33
a
Lo
g-l
ikel
iho
od
ÿ402.8
4ÿ
415.7
2ÿ
399.2
5ÿ
406.4
8ÿ
407.0
2ÿ
405.3
4P
seu
do
-R2
10.4
4%
7.5
8%
11.2
4%
12.4
9%
12.3
7%
12.7
3%
w2(h� jt)
0.9
7(0
.32)
3.1
4(0
.08)
0.4
5(0
.50)
1.7
9(0
.18)
0.4
5(0
.50)
2.8
7(0
.09)
w2(Y� jt)
58.5
6(0
.00)
28.5
6(0
.00)
77.7
2(0
.00)
4.6
5(0
.03)
5.5
5(0
.02)
7.7
6(0
.01)
Extr
eme
retu
rns
are
def
ined
inte
rms
of
exce
edan
ces
bey
on
da
thre
sho
ldth
at
vari
eso
ver
tim
ew
ith
the
con
dit
ion
al
vo
lati
lity
of
regio
nal
mark
etre
turn
s.S
pec
ific
all
y,
the
tim
e-se
ries
of
con
dit
ion
al
vo
lati
liti
es,
hit,
for
each
cou
ntr
yin
dex
iat
tim
et
are
ob
tain
edu
sin
gE
GA
RC
H(1
,1)
mo
del
.T
hen
,a
retu
rn,
r it,
isd
efin
edas
extr
eme
ifjr itj>
1.6
5h
it.
Th
en
um
ber
of
coex
ceed
an
ces,
of
dail
yre
turn
sis
mo
del
edas
an
ord
ered
po
lych
oto
mo
us
vari
ab
lean
des
tim
ate
du
sin
ga
mu
ltin
om
ial
logit
regre
ssio
nm
od
el.
Pjis
def
ined
as
the
pro
bab
ilit
yth
at
agiv
end
ay
isass
oci
ate
dw
ith
jco
exce
edan
ces,
wh
ere
jeq
uals
0,
1,
2,
3,
4o
rm
ore
(fiv
eca
tego
ries
).T
he
mu
ltin
om
ial
logit
regre
ssio
nm
od
elis
giv
enb
yP
j�
exp
(x0 b
j)/[
1+
�kex
p(x0 b
k)]
,w
her
eb
isth
evec
tor
of
coef
fici
ents
,x
,th
evec
tor
of
ind
epen
den
tvari
ab
les,
an
dk
equ
als
1to
4.
Th
ep
rob
ab
ilit
yth
at
ther
eare
no
(co
-)ex
ceed
an
ces
equ
als
P0�
1/
[1+P k
exp
(x0 b
k)]
,w
her
ek
equ
als
1to
4,
wh
ich
rep
rese
nts
ou
rb
ase
case
.T
he
ind
epen
den
tvari
ab
les,
x,
incl
ud
eth
ose
inT
ab
le5.
Th
eco
nd
itio
nal
vo
lati
lity
ises
tim
ate
das
EG
AR
CH
(1,1
)u
sin
gth
eIF
Cin
ves
tib
lere
gio
nal
ind
ex.
Part
ial
der
ivati
ves
of
pro
bab
ilit
ies
wit
hre
spec
tto
the
vec
tor
of
ind
epen
den
tvari
ab
les
are
com
pu
ted
at
the
mea
ns
of
xan
dare
rep
ort
edn
ext
toth
eco
effi
cien
tes
tim
ate
s.G
oo
dn
ess
of
fit
ism
easu
red
by
McF
ad
den
'sp
seu
do
-R2
equ
al
to1ÿ
(L!/L
),
wh
ere
L!
isth
eu
nre
stri
cted
lik
elih
oo
d,
an
dL
is
the
rest
rict
edli
kel
iho
od
[Mad
dala
(1983,
chap
.2)]
.T
he
logit
regre
ssio
nis
esti
mate
dse
para
tely
for
po
siti
ve
(to
p-t
ail
)an
dn
egati
ve
(bo
tto
m-t
ail
)co
exce
edan
ces.w2
(hjt*
)an
dw2
(Yjt*
)are
Wald
chi-
squ
are
test
sfo
rth
ere
stri
ctio
ns
thatb k
1�
b k2�
b k3�
b k4�
0,
wh
ere
kis
4an
d5,
resp
ecti
vel
y,
wit
hp-v
alu
esin
pare
nth
eses
.
a,
bD
eno
tes
sign
ific
an
cele
vel
sat
the
1%
an
d5%
,re
spec
tivel
y.
Measuring Financial Contagion
757
Finally, we consider alternative estimation approaches for our problem.Because our multinomial logit model fails to account for the ordinalnature of our coexceedance measure as the dependent variable, we maylose efficiency compared to an ordered logit model, which is explicitlydesigned to capture the ordering information. The ordered logit, alsoknown as a proportional-odds ordered logit model, requires the odds ofadjacent categories, defined by different threshold or cutoff points alongthe ordinal scale, to have the same ratio for all independent variablecombinations. As a result, there is only one set of coefficients estimatedfor the covariates instead of four sets separately for each outcome in themultinomial logit. However, this model implies that the odds of observingfive coexceedances instead of four are equivalent to the odds of observingthree coexceedances instead of two. Such a constraint will generate less-efficient estimates if the odds are not proportional [Brant (1990), Petersonand Harrell (1990)]. With this concern in mind, we chose to featurethe unordered multinomial logit. However, in unreported results, wereplicated our contagion tests across regions using the ordered modeland found that our inferences about the coexceedance variable Y�j (coeffi-cients and marginal effects) and the pseudo-R2 were consistent and verysimilar. Some propose diagnostic tests for ordered logit models relative tomultinomial (unordered) logit models based on the differences in the log-likelihood values [Brant (1990)]. One such test is referred to as a`̀ likelihood ratio test.'' It is computed as ÿ 2(LoÿL), where Lo (L) isthe log-likelihood of the ordered (unordered) logit, which is distributed asa chi-square with p(cÿ 2) degrees of freedom, where c is the number ofcategories (c� 5 for Asia and Latin America) and p is the number ofcovariates ( p� 5 in our case). This diagnostic regularly rejects the orderedlogit model in favor of the multinomial, with only one exception. Notethat this diagnostic cannot be used as a formal measure of fit, as themodels are not nested.
Another alternative is the negative binomial model, which is a generali-zation of the Poisson regression model used mainly for count data. Thismodel specifies that each observation is drawn from a Poisson distributionwith an expected number of events per period that is related to indepen-dent variables, or covariates. The advantage of the negative binomialmodel is that it does not assume equality of the expected mean andvariance. We hesitate to employ this model, as it is typically used incross-sectional analysis and less often with time-series data [Greene(2000, section 19.9)]. In this model we do not need to assign categories,as in the ordered and unordered logit models, and as a result, the system issmaller, with only one coefficient estimated for each covariate.19 We
19 We tested the restriction in the multinomial logit models in Section 4.1 that the coefficients across the categoriesof one, two, three, and four or more coexceedances are equal and rejected these restrictions easily for the caseof Asia and Latin America. These restricted models are closest in spirit to the negative binomial model.
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replicate our tests for contagion across regions with this model (unre-ported) and find that our inferences about contagion effects are evenstronger between Asia and Latin America and between the emergingmarket regions and Europe. Contagion from Asia and Latin America tothe United States is measurably lower, however.
Our multinomial logistic regression model results for contagion withinand across regions are not simply manifestations of the correlations ofreturns in those markets, even if we allow for returns-generating processeswith excess kurtosis and time-varying volatility. The findings are robust tospecifications with seasonal dummies, lagged conditioning information,local currency (versus U.S. dollar) denominated returns, multiday hori-zons for exceedance counts, and even conditional measures of extremesbased on conditional volatility. We also explore other econometricmethods including ordered logit, proportional odds, and negative bi-nomial regression models. If anything, these alternative specificationslikely strengthen our main findings on the existence of contagion effectsacross regions.
4� Conclusion
In this article we propose a new approach to the study of financialcontagion. The key presumption of our approach is that contagion is aphenomenon associated with extreme returns: if there is contagion, small-return shocks propagate differently from large-return shocks. We there-fore investigate the propagation of large-return shocks within regions andacross regions. Such an approach faces two problems. First, focusing onlarge-return shocks, by definition, decreases sample size and limits thepower of our tests. One must be careful not to let inferences be dominatedby a few datapoints. As a result, we choose to focus on counts of coin-cidences of extreme returns rather than on correlations of joint extremereturns. Our modeling approach employs the multinomial logistic regres-sion approach to reflect this new and different focus. Second, one wouldexpect large returns to be more highly correlated than small returns. As aresult, one has to make sure that the apparent contagion of large returns isnot simply the outcome of conditioning a study on large returns. We useMonte Carlo simulations to calibrate our results with different scenariosaccording to what one would find if returns were distributed as multi-variate normal, Student's t, and even with GARCH effects. We find thatwe have too many cases where large negative returns occur in mostcountries of a region. Further, we find that the number of large negativereturns in one region is more useful to predict the number of large negativereturns in another region than if the returns in the two regions weredistributed multivariate normal, Student's t, or GARCH. We also findthat the number of joint occurrences of extreme returns within a region
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can be explained by regional conditional volatility, the level of interestrates, and exchange rate changes.
Contagion is a source of great concern for policymakers and has gen-erated a large and growing academic literature. We find in our study ofemerging markets that the propagation of large negative returns acrossregions is anomalous if stock return indices follow a joint returns-generating model with normal or fat tails or even if the conditionalvolatility of returns varies over time. Whether this anomalous propaga-tion should be a matter of serious concern will depend on the views ofreaders. Nevertheless, our article has a number of clear results:
1. Contagion is more important in Latin America than in Asia.2. Contagion from Latin America to other regions of the world is
more important than contagion from Asia.3. The United States is largely insulated from contagion from Asia.4. Contagion is predictable conditional on prior information.
A natural extension of our study would be to investigate whetheralternate distributional assumptions could explain our results. Further,our study uses daily returns and focuses on same-day, lagged one-day, andeven three-day contagion. But a useful extension of the study would be tolook at longer-horizon contagion. Such an analysis would make it possibleto investigate whether there are thresholds of cumulative returns abovewhich propagation of returns becomes more intense. It would also beuseful to apply the approach to a broader cross section of individualstock or sector index returns within countries. The approach developedin this article would be well suited for such analyses. There is a longtradition that focuses on modeling the properties of extreme returns.A factor model might capture both the properties of extreme returns andof other returns. It would be a challenge to develop a model that wouldcapture the nonlinearities that we emphasize, but such a model couldprovide useful insights about the contagion quantified in this article.
Appendix
Every three month, stocks in the EMDB Global Index for each market are identified and
sorted by market capitalization (adjusted for the free-float if cross-holding data is provided).
Stocks are included until 50 stocks are included or until the threshold of 90% of the EMDB
Global Index capitalization is met. Daily returns are computed from daily log differences of a
value-weighted portfolio of constituent stocks and both local currency and U.S. dollar-
denominated (net of log difference of daily exchange rate) returns. Though we start the
procedure as far back as December 1989, the official start date for all markets is April 1, 1992.
We verify our selection and construction criteria by examining the statistical attributes of the
index series and the correlations with the actual IFC indexes after December 31, 1995.
Overall, the coverage in terms of market capitalization is well over 90% even if the 50 stock
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limit is not met, due to the skewness of the composition in many of these emerging markets.
Most correlations between the constructed and actual IFC indexes are well over 0.95 (median
0.988) for all but three exceptional cases (Colombia, 0.88; India, 0.89; Peru, 0.83) indicating
the construction process is reasonably sound. We report only the results using our con-
structed indexes, but all the tests reported in this article are estimated using the actual IFC
indexes also. Further details on the scope of coverage and components is available from the
authors upon request.
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