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VOLATILITY TRANSMISSION AND FINANCIAL CRISES By Guglielmo Maria Caporale, Nikitas Pittis, and Nicola Spagnolo ~ Abstract In this paper we examine the international transmission of the 1997 South East Asia financial crisis. We estimate a bivariate GARCH-BEKK model and carry out LR tests for causality-invariance with bootstrapped critical values. Three pairwise models are estimated for US, European, Japanese and South East Asian daily stock market returns. Volatility spillovers are found in all cases. The dynamics of the conditional volatilities differ, but causality links in the variance are found to be strong and bidirectional in normal periods, and unidirectional (from the markets in turmoil to the others)following the onset of the crisis, consistently with crisiscontingent models. (JEL C32, G15)

Introduction The relative importance of macroeconomic and financial sector linkages in explaining contagion between countries or regions following the onset o f a financial crisis is often debated. At the time of the 1997 South East Asia crisis, both the O E C D and the IMF tried to quantify its likely adverse effects on output growth in the industrial economies by focusing on trade linkages. For instance, the OECD estimated that a slowdown in trade with Asia could result in a fall of nearly 1 percent in the level of G D P over two years in the OECD area as a whole (see OECD, 1997). Other studies argued that, because trade is mainly regional, contagion tends to be between economies within the same region; this is true both of countries which are competitors, having similar exports (see Glick and Rose, 1999), and of countries which are complements, being at different stages of economic development (see Diwan and Hoekman, 1998). However, whether trade linkages are a crucial channel for contagion is an empirical matter, and the evidence is not unequivocally supportive of this idea. The O E C D itself acknowledged that trade flows are only one of the possible transmission mechanisms - it is vital to take into account spillovers across global financial markets when analysing the possible repercussions o f financial turbulence in one region on other regions of the world. In fact a study by the IMF, which tested for financial market contagion within South East Asia, found an increase in the correlations between financial markets during a crisis compared to a tranquil period (see Baig and Goldfajn, 1998). Admittedly, the nature of contagion is difficult to identify. For instance, although there is evidence that asset prices are highly correlated across South East Asia, it is not clear whether this reflects similarities in fundamentals or is a consequence of spillovers (see Alba et al, 1998). However, there is a growing consensus that analysing financial contagion is essential to understanding financial crises, especially in view of the increasing degree of integration of international financial markets. For instance, Masson (1999) developed a model in which contagion generates a crisis through its capital account effects (even though the underlying The authors are grateful to an anonymous referee, Graciela Kaminsky, Marco Barassi, Andrea Cipollini and participants in the 2001 AEA Meetings, New Orleans, January 5-7, 2001, and in the Australasian Meeting of the Econometric Society, Auckland, New Zealand, July 6-8, 2001 for useful comments and suggestions. Financial assistance from Leverhulme grant F/71 l/A, "Volatility of share prices and the macroeconomy:real effects of financial crises", is also gratefully acknowledged. Corresponding author: Professor Guglielmo Maria Caporale, Brunel Business School, Brunel University, Uxbridge, Middlesex UB8 3PH, UK. Tel.: +44 (0)1895 266713. Fax: +44 (0)1895 269770. E-mall: GuglielmoMaria.Caporale @brunel.ac.uk

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mechanism works through trade channels). Kaminsky and Schmukler (1999) emphasised the possible "herding" behaviour of investors who just follow th~ market believing that asset prices contain relevant information; as a result, there could be a stock market crisis in one country simply because of the collapse which has occurred in another country. Clearly, a surge in the volatility of stock prices can then have a significant impact on the real economy through, e.g., wealth effects and the cost of capital. Direct reallocation of resources and halted overseas activities, or resource reallocation involving the banking sector, can also be very important as a transmission mechanism from the financial to the real sector. This was certainly the case in South East Asia in 1997, with the crisis affecting overseas subsidiaries and subcontractors of Asian companies, and thus the local economies. Existing empirical studies analyse primarily dynamic linkages between developed markets, with only some of them focusing on linkages between emerging markets, or between these and other foreign markets. Furthermore, most empirical studies only consider linkages between first moments, namely they look at correlations, i.e. first-order dependence in a linear regression framework (see, e.g., Hilliard (1979), Eun and Shim (1989) and Koch and Koch (1991), who all examined the contemporaneous and lagged correlation in daily price changes across major stock markets). The possibility of higher-order dependence, arising out of the interactions between the second moments, has hardly been investigated, even though the importance of second conditional moments in modelling high frequency financial time series has been recognized ever since Engle (1982) introduced the class of ARCH models. In terms of estimation techniques, the GARCH framework in various forms predominates. A few exceptions use VAR or cointegration analysis. For instance, Liu and Pan (1997) estimated a VAR to examine the dynamic relationships between Asian-Pacific stock markets. Sander and Kleimeier (2003) carried out cointegration and Granger causality tests to analyse contagion between sovereign bond spreads as a measure of perceived country risk in four Asian crisis episodes. They considered linkages within the Asian region, and also between Asia and other emerging economies, and found evidence for changed causality patterns on a regional level, and also on a global level as the Russian crisis started. Studies focusing on the developed markets are numerous. For instance, Hamao et al. (1990) employed autoregressive conditionally heteroscedastic models to study the dynamics of spillover effects in price changes and volatility between the US and Japan, and found that shocks that originate in the US are larger and more persistent. Lin et al. (1994), using a signal extraction model with GARCH processes, studied the New York and Tokyo stock markets and found feedback effects between these two markets. Susmel and Engle (1994) analysed the interrelationship between the New York and London stock markets and did not find much evidence of either mean or volatility spillovers. They argued that earlier findings to the contrary were due to the use of non-robust estimators with the associated standard errors being too small. Karolyi (1995) examined the dynamic relationship between US and Canadian stock market returns and return volatilities using a bivariate generalized autoregressive conditional heteroscedastic model. He found that the effects of shocks from the S&P 500 index returns on the TSE 300 index returns and volatility are smaller and less persistent than those measured with traditional vector autoregressive models. Theodossiou and Lee (1993) studied the relationship between the US, UK, Canadian, German and Japanese stock markets using a multivariate GARCH-in-mean model and found mean and volatility spillovers between some of those markets. A minority of studies focus on volatility spillovers within individual developed stock markets (see, e.g., Reyes, 2001, considering the Tokyo stock exchange), or on linkages between financial markets (commodity, foreign exchange, bond and stock markets) in the same country (see, e.g., Darbar and Deb, 1999, analysing the US case). Once again, they are based on some type of GARCH model - bivariate exponential GARCH (EGARCH) and bivariate Logistic EGARCH (LEGARCH) respectively. Fewer papers have looked at linkages between emerging markets. One example is the already mentioned VAR analyis by Liu and Pan (1997) examining information transfers between Japan and neighbouring Asian-Pacific markets. Worthington et al. (2001) look at price linkages in Asian

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equity markets using a multivariate cointegration procedure. Sola et al. (2002) propose a new procedure for analyzing volatility links between different markets based on a bivariate Markov switching model. They find that volatility spillovers become unidirectional following the onset of the t997 crisis, running from Thailand (the market in turmoil) to South Korea, whilst Brazil was hardly affected. Similarly, only a few papers have investigated the relationship between developed and emerging markets. Liu et al. (1998) using a VAR methodology examine the structure of international transmissions in daily returns for six national stock markets. Their results indicate that the US market plays a dominant role in influencing the Pacific-Basin markets; Japan and Singapore together have a significant persistent impact on the other Asian markets, while the markets in Taiwan and Thailand are not efficient in processing international news. Furthermore, Cheung et al. (2002) study the interactions between the US, Japan and four East Asian markets. They reported that the US market led the Asian markets before and after the crisis, but was Granger-caused by these markets during the crisis period. During the same period, the East Asian market were affected by the Japanese one. Walti (2003) also tested for the existence of contagion during the recent Asian crises using the framework of Favero and Giavazzi (2002) and found that the hypothesis of no contagion is widely rejected. Given the fact that all recent currency and financial crises originated in emerging markets (e.g., Mexico in 1994, and South East Asia in 1997), before affecting the developed economies, and invariably led to substantially more volatile stock prices, it is of particular interest to focus on volatility transmission across emerging and developed stock markets, as the present paper does. In line with the vast majority of existing studies, we take a GARCH modeling approach. Specifically, we estimate a bivariate GARCH model ~, for which a BEKK representation is adopted (see Engle and Kroner, 1995), and then test for the relevant zero restrictions on the conditional variance parameters by means of likelihood ratio (LR) tests, as in other studies such as Cheung et al., 2002. However, rather than relying on asymptotic distributions, we use appropriately bootstrapped critical values. This is because empirical distributions can differ from the asymptotic ones, and therefore for the purpose of statistical inference it is of paramount importance to obtain the former. In this respect, our study improves significantly on earlier ones, which do not address the finite sample issues, and hence it provides more reliable evidence. We use this framework to analyze the 1997 South East Asia crisis, and ask the question whether its onset affected the volatility transmission mechanism and changed international financial linkages. We find that, prior to the crisis, there were bidirectional volatility spillovers between the South East Asian, European, Japanese and US stock markets. By contrast, in the post-crisis periods causality links became unidirectional, running only from the South East Asian markets, where the crisis originated, to the others. The layout of the paper is as follows. The next section outlines the bivariate GARCH model used to study volatility spillovers between stock markets. Section 3 describes the data and the procedure used to calculate the appropriate bootstrap calibrated likelihood ratio test, and reports the empirical estimates. The final section offers some concluding remarks.

1The concept of causality in the second moments can be thought of as an extension of the well-establishednotion of Granger causalitybetween the first moments,and it could be tested empiricallyby employingthe test recentlyproposedby Cheung and Ng (1996).

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The Model In this section, we introduce the multivariate G A R C H process we employ to estimate the international transmission of stock returns' volatility. We model the joint processes governing the rates of returns of two stock indices with the following bivariate G A R C H model 2 9 rt = a ' + / ~ r t _ 1 + u ,

where

the

residual

G I 1'-I D (0, H t )with

(1)

vector

u~ = (e~.~,e2. , )

is

bivariate

and

normally

distributed

its corresponding conditional variance covariance matrix given by:

(2)

The parameter vector of the mean return equation (1) is defined by the constant O~ = (O~l , O'2 ) and the autoregressive term f l = ( i l l , f12 ) , while the parameter matrices for the variance equation (2) are defined as C o , which is restricted to be upper triangular, and two unrestricted matrices, All and GI~. Therefore, the second moment will take the following form:

H, =CoCo+( all \a21

a121' I e~''-I el"-le2't-1)( all a22) \el,,_le2,t_, e2,,_1 )~azl

a12 /

a22J (3)

\g:l

gz2J

~.gzl

gzzJ

Equation (2) models the dynamic process of

Ht_ 1 and

past values of the squared innovations

Ht

as a linear function of its own past values

ekr_1, e2,t_ 1

, in both cases allowing for own-

market and cross-market influences in the conditional variance. The important feature of this specification is that it allows the conditional variances and covariances of the two series to affect each other, thereby enabling one to test the null hypothesis of no volatility spillover effects in one or even both directions. Furthermore, it does not require the estimation of m a n y parameters (eight for the bivariate system excluding constant, without any loss of generality). Even more

2 The model is based on the bivariate GARCH(1 ,t)-BEKK representation proposed by Engle and Kroner (1995).

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importantly, the B E K K model guarantees by construction that the covariance matrices in the system are positive definite. 3 Given a sample of

T

observations, a vector of u n k n o w n parameters /9 and a 2 x l vector of

returns rr , the conditional density function for the model (1) is:

f(r l,_l;a)=(2x)-'H , - 1 / 2 e x p l

(4)

The log likelihood function T

L:Zlogf(r, ll,_;O)

(5)

t-I

is maximized numerically using the Broyden, Fletcher, Goldfarb and Shanno algorithm to yield m a x i m u m likelihood estimates. Standard errors are calculated using the quasi-maximum likelihood methods of Bollerslev and Wooldridge (1992), which is robust to the distribution of the underlying residuals.

An Application to the South East Asia Crisis In this section we employ the model described above to investigate the casual relations between stock returns volatility in the South East Asian market and other main markets. Testing for causality-in-variance is the goal of our analysis. After describing the data and the bootstrapping LR test procedure, we discuss the results.

Data The data on stock indices are daily (five days per week). The original series were used for the US and Japan; in addition, two aggregate indices were built, one for Europe (including Italy, France, U K and Germany) and the other for South East Asia (including South Korea, Singapore, Taiwan, Philippines, Malaysia, Thailand, Hong Kong and Indonesia). The indices are weighted averages, where the weight is the GDP of individual countries converted to US dollars at market

s Note that the BEKK-GARCHspecificationemployed in our study implies a joint restrictionon the variance and covariance. This is shown by Darbar and Deb (1997), who employthe Engle and Kroner specification(1995) to examine the co-movementsof equity returns in four major internationalmarkets. This allows them to decompose the conditional covariance into two components. The first, permanent component is the historical (unconditional)mean covariance between the returns. A fluctuation of the conditional covariance around this permanent componentis the second. To distinguish between the existence of nonzero permanent and transitory components, they propose the joint restrictions Ho:c12=a12=g12=0. Although we are aware of this issue and of the resulting difficulties in interpretingtests for volatility spillovers based on joint restrictions,we have decided to use the standard approach found in the literaturein order to make our results comparableto those from previous studies. Furthermore,Darbar and Deb (1997) acknowledgethat their method suffers from the "Davies problem" (i.e. identification).Nevertheless, they rely on asymptoticcritical values. Studying the properties of their test by means of bootstrappingtechniqueswould undoubtedlybe an interestingresearch topic, but it is beyond the scope of the present paper.

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exchange rates 4, averaged over the preceding three years 5 (see Figure 1), over the period 1/1/1986 - 11/10/2000, for a total of 3855 observations. The data were all obtained from Datastream. F i g u r e I: S t o c k R e t u r n I n d i c e s 420-2-

-6 .........~;8'4~:~.........~ , ~ 1/0" ~""'""q'i~';h'~

...........

1

/

0

1

~

,.~ ,d..,,.,LL~. . . . . . . . . . .

d..k,,S

204

-2 -4 -6

1/01/86

11/0~1/8.q '

9/0"~33'

Y/02/97

1/0'/86

11/01/89

9/01 ~3

7/02/97

We define daily returns as logarithmic differences o f stock indices. Table 2 presents a wide range of descriptive statistics for the four series under investigation, for the full sample and for two sub-periods, namely the pre-1997 and the post-1997 period. The sample moments for the whole sample returns show heavy skewness and kurtosis; consequently, Jarque-Bera statistics indicate rejections o f the null hypothesis that stock market returns are normally distributed. The statistics indicate that the nature of the data is substantially different in the two sub-samples. Specifically, there appears to be a statistically significant increase in volatility starting from the middle of 1997, as shown by tests for variance equality (see Table 1). Such an increase does not always convey useful information, given the fact that financial markets have generally become more volatile in recent years, and investors have become more accustomed to big swings in stock prices. However, in this case the higher volatility of stock prices undoubtedly coincides with the onset of the South East Asian crisis, which began in Thailand in the late spring o f 1997 with sustained speculative attacks on the local currency, and continued with its flotation in early July 1997. Within days, speculators had attacked the currencies of Malaysia, the Philippines and Indonesia. The Korean currency was attacked later on. The empirical distributions in fact seem to be dramatically influenced by the break which occurred in the middle of 1997. Visual inspection of the data suggests that G A R C H effects are present in the whole sample as well as in the two sub-periods. Ljung-Box portmanteau statistics

4 The analysis has also been performed with own currency returns. The results have not been reported as they are qualitatively similar and are available from the authors. 5 We followed the procedure used in the World Economic Outlook Statistical Appendix for constructing aggregate indices.

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(LB) for serial correlation in the standardized squared returns are also reported. They confirm that the null hypothesis of white noise residuals can easily be rejected. The magnitude of the autocorrelation values suggests a non-linear dependence pattern; indeed, the significant persistence in the squared returns is consistent with the volatility clustering commonly observed in financial series. Overall, the summary statistics confirm the well-known stylized facts for financial time series data.

Resampling LR Test This section reports the procedure we use to calculate the bootstrap calibrated critical values of the likelihood ratio test. We assume that u t follows a martingale difference, dynamically heteroscedastic process as in equation (3). Imposing zero constraints on the off-diagonal coefficient is equivalent to the null hypothesis of no Granger causality from one variable to the other and viceversa. In particular, under the null hypothesis H 0 : a21 = g21 = 0 , we have that h2, does not Granger cause ha,, whereas ha, does cause h2. Therefore, the equation for H, will take the following form: 6 '/It = C21 +allel,_ 2 2 l +gHt~,-1 9

(6)

2 ~2, = CllCl2 + atlal2elt-z + alta22el,-le2t-i + gllgl2]~t-1 + gllgeJ~2,-i 2 2 2 2 2 h2t =C22+C22+at2el,_l + 2a12a22elt_le2,_l + a22e2r_, + g~2hl,_t + 2g12g22h12,_t + g~2h2,_l The likelihood ratio test, LR henceforth, compares the maximum value of the likelihood function under the assumption that the null hypothesis is correct to the maximum value of the unrestricted likelihood function. Then, if the null is true:

LR=-2(LR-I_ v ) where L R and L v

(7)

are the restricted and the unrestricted maximized likelihood function

respectively. Therefore, under the null hypothesis the test is asymptotically distributed as a x 2 ( j ) with degrees of freedom j equal to the number of restrictions. However, note that, since the distribution of (ref :LRtest) under H 0 will depend upon nuisance parameters (a2~ and g2~) which cannot be conditionated away, the Monte Carlo test method does not apply exactly. Therefore, in order to take into account the presence of nuisance parameters we resort to bootstrap resampling. More specifically, we use a bootstrap procedure analogous to that described in Davison and Hinkley (1997, p.148); our results are obtained from 999 artificial time series generated from the fitted model (ref: BEKKRESTR) for the observed series of interest using innovations resampled from the residuals {/~, } .

6 Similarrestrictions can be imposedin the oppositedirection; in that case All and G1t would be uppertriangular.

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383

W e f i n d that the L R test h a s f i n i t e - s a m p l e T y p e - I e r r o r p r o b a b i l i t i e s that d o n o t d i f f e r s i g n i f i c a n t l y f r o m the n o m i n a l v a l u e o f 0.05 w h e n T = ( 8 5 4 , 3 0 0 0 , 3 8 5 4 ) 7 , w i t h e m p i r i c a l r e j e c t i o n f r e q u e n c i e s r e a s o n a b l y c l o s e to the c o r r e s p o n d i n g a s y m p t o t i c ones. 8

Table 1: Summary Descriptive Statistics Whole-Sample Country Asia

Europe

Japan

USA

Statistics Mean Std. dev. Skewness Kurtosis

Sub-samples

LB~_~)~

1/1/86--11/10/00 0.0160 0.5346 -0.2744 9.2940 645.84*

1/ 1/86-1/7/97 0.0301 0.4776 -0.5452 9.809 187.01 *

2/7/97-11/10/00 -0.0331 0.6965 0.1693 7.0042 114.45"

LB2o)~

868.41 *

223.20*

147.21 *

JB

6411 *

5945"

575*

Mean Std. dev. Skewness Kurtosis

LB~)_

0.0154 0.4278 - 1.043 14.343 178.59"

0+0148 0.4062 - 1.4456 20.187 128.11 *

0.0t 82 0.4966 -0.2378 3.892 63.770*

LB21o) ~

209.36*

143.04*

121.41 *

JB

21363"

37973*

36*

Mean Std. dev. Skewness Kurtosis

--LB25)

0.0091 0.6826 -0.0379 11.317 223.04*

0.0143 0.6454 -0.3388 13.746 481.96*

-0.0103 0.8003 0.5431 6.6869 40.686*

LB2o)~

278.17"

636.79*

54.312"

JB

11110"

14494*

526*

Mean Std. dev. Skewness Kurtosis

LB,_s)__

0.0213 0.4521 -3.121 69.116 231.85*

0.0208 0.4247 -4.6263 109.20 180.07*

0.0233 0.5377 -0.3741 6.6866 57.633 *

LB~o )-

245.65*

189.97"

86.168"

JB

70823 *

142062"

504*

Notes: The star indicates rejection at the 5% level. LB(m2 and LBoo)2 are respectively the Ljung-Box test of significance of autocorrelations of five and ten lags in the standardized squared residuals. Variance equality tests have been carried out (Levene, 1960) with the null hypothesis of equal pre-crisis and post-crisis variance being rejected in all four cases. The tests yielded values of 18.48, 7.78, 11.43 and 8.87 respectively, all of which are bigger than the corresponding F (1, 3852) critical values.

7 These are the sample sizes corresponding to the pre- and post-crises samples respectively. s Since the percent rejections at the 0.01, 0.05 and 0.10 significance levels are qualitatively similar, we focus our discussion on the properties of 0.05-level test.

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JOURNAL OF ECONOMICS AND FINANCE 9 Volume 30 9 Number 3 9 Fall 2006

Table 2: Bootstrapped Likelihood Ratio Test

Whole sample

Europe and East Asia 13.15

USA and East Asia 14.77

Japan and East Asia 19.01

16.22

38.64

15.69

6.63

14.77

6.31

T = 3854 Pre-crisis sample

T = 3000 Post-crisis sample

T = 854 Notes: Bootstrappedlikelihood ratio Type-Ierrorprobabilityof 0.05-Level are reported.

Empirical Results The estimated conditional variances with associated robust standard errors and likelihood function values for the South East Asian and the European, US and Japanese stock market returns are presented in Tables 3, 4 and 5 respectively. For each model, the Akaike, Bayesian and Hannan-Quinn information criteria have been employed to determine the conditional variance lag lengths. These suggest that a GARCH(1,1)BEKK specification is appropriate for the conditional variance. Hypothesis testing is performed on the models using the likelihood ratio test, and comparing the test statistics with the empirical critical values reported in Table 1. We carry out tests for causality-in-variance for each model, alternatively constraining the matrices A~] and Gll to be upper triangular and lower triangular, thereby allowing for causality only in one direction at a time. We report the LR statistics and the associated p-values only when the restriction is accepted. The null hypothesis of unidirectional cross-market spillovers is rejected when the full sample or the pre-1997 period are considered, but it cannot be rejected in the post-1997 period for all the three models. The patterns in the conditional variance coefficients are not substantially different across models. The estimates are in most cases statistically significant. 9. In order to test the adequacy of the models, Ljung-Box portmanteau tests (LB) were performed on standardized and standardized squared residuals. Overall the results indicate that the GARCH(1,1) specification captures satisfactorily the persistence in squared returns in the series, with the null hypothesis of no autocorrelation being rejected in just one case at the five per cent level. The coefficient values for own-market volatilities indicate high persistence in the stock returns, with coefficient estimates that are all bigger than 0.9. Interestingly, though, in the pre-crisis sample the GARCH parameters are less persistent in all the models, with values ranging from 0.77 to 0.93.

9The covariancestationarycondition is satisfiedby all the estimated models.

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T a b l e 3: E s t i m a t e d G A R C H (1,1) Models for the E u r o p e a n d S o u t h E a s t Asia Stock

Returns Whole sample 1 / l / 8 6 - 11/10/00

Pre-crisis sample 1/1/86- 1/7/97

Post-crisis sample 2/7/97 - 11/10/00

S.E,

Coef.

S.E.

Coes

S.E.

.0245

.0056

,0177

.0068

.0298

.0145

fll

,0577

.0777

,0790

.0181

.0201

,0207

~2

.0315

.0054

.0300

,0070

-,0211

.0208

f12

.1067

.0567

.0487

,0308

,2748

.0319

Cll

-,0573

.0125

-.1013

.0243

.0673

,0032

C12

-.0424

.0104

-,0159

.0400

.0151

.0071

C22

,0607

,0149

-.0411

.0249

.1657

.0074

gll

,9979

.0149

.7915

.0390

-.9635

.0010

g12

.4700

,0824

-.7583

.1195

g21

-.1670

,0635

-.1616

.0540

.0149

.0050

g22

.9879

,0129

.8861

.0659

-.8831

.0038

all

.2391

.0329

.2002

.0460

.2316

.0058

a12

.0962

.0381

.1044

.0946

a21

.0048

,0260

.1997

.0609

.1658

.0174

a22

.2665

,0363

.3242

.0307

.3386

,0t06

Parameters

LogLik

Coef,

2737.021

2569.826

LR Test p-vMue

LBE(IO ) 2

LBE(IO )

249.486 6.36 (.0415)

4.5905 13,012

8,609 18.389

LBA(IO )

3.2374

6.0582

LBA2(10)

3.8243

6,6242

3.6088 14.691 4,2074 10.302

Notes: Quasi maximumlikelihood standard errors (S,E.) based on Bollerslevand Wooldridge (1992) are reported. A * indicates rejectionat the 5% level, LR test p-valuesare in parentheses. LB(10) and l.,BZ(10)are respectivelythe LjungBox test of significanceof autocorrelations of ten lags in the standardized and standardized squared residuals. The covariance stationary condition is also satisfied by all the estimated models, all the eigenvalues of A11 | AI 1 + GI 1 | G11 being less than one in modulus.

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Table 4: Estimated G A R C H (1,1) Models for the USA and South East Asia Stock Returns Whole sample 1/1/86 - 11/10/00 Parameters

Coef.

Pre-crisis sample

Post-crisis sample

1/1/86- 1/7/97

2/7/97 - 11/10/00

S.E.

Coef.

S.E.

Coef.

S,E.

al

.0261

.0052

.0234

.0068

.0227

.0167

fll

.0343

.0171

.0471

.0234

.0353

.0394

O~2

.0301

.0069

.0298

.0102

-.0176

.0211

f12

.1041

.0186

.0555

.0171

.2705

.0458

Cll

-.0447

.0009

.0315

.0252

.1294

.0417

C12

-.0067

.0019

-.0852

.0474

-.0058

.0242

C22

.0554

.0021

.0000

.0974

.1672

.0561

gll

.9666

.0003

.9272

.0226

.9402

.0319

g12

.0168

.0007

.3832

.0134

g21

-.0112

.0004

-.2642

.0103

.0045

.0011

g22

.9544

.0006

.8882

.0414

.9023

.0515

all

.2320

.0015

.1961

.0839

-.2330

.0616

a12

-.1016

.0033

-.0881

.0262

a21

.0473

.0019

.0631

.0347

.0531

.0149

a22

.2779

.0028

.2264

.0713

.3630

.0905

LogLik

2757.107

2683.087

LR Test p-v~ue

121.562 7.1 (.0287)

LSu(5)

7.657

6.297

2

22.649*

15.276

7.9737

8.114

9.3755

9.1776

15.795

9.5730

LBuo0) LBA(5)

9( LB

10)

Notes: See Notes for Table 3.

6.6488 15.445

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Table 5: Estimated GARCIt (1,1) Models for the Japanese and South East Asia Stock Returns Whole sample 1/1/86 - 11/10/00

Pre-crisis sample 1/1/86- t/7/97

Post-crisis sample 2/7/97 - 11/10/00

Parameters

Coef.

S.E.

Coef.

S.E.

Coef.

S.E.

~1

.0289

.0150

.0332

.0120

.0112

.0209

~2

.0341

.0110

.0406

.0085

-.0060

.0220

C11

.1036

.0213

.1135

.0180

.0801

.0426

C12

.0432

.1254

.0780

.0573

.0049

.0666

C22

.0778

.0488

.0766

.0116

.1454

.0895

.9503

.0153

.9382

.0162

.9659

.0091

-.0004

.0115

-.0101

.0071

-.0407

.1641

-.0656

.0699

.0499

.0473

.9308

.1127

.9128

.0542

.9168

.0820

.2724

.0376

.3049

.0374

-.1586

.0912

-.0052

.0173

.0157

.0148

.1206

.2928

.1315

.1120

.0890

.0599

.3357

.2305

.3454

.0987

.3509

.1521

&

gll g12 g21 g22 all a12 a21 a22 Lo~Lik LR Test p-value

1222.272

LBj(IO )

0.7754

0.6134

2 LBj(IO)

1.8023

2.0050

LBA(IO )

5.4850

LB

(

18.126 10)

Notes: See Notes for Table 3.

1033.967

10.295 18.639

t65.930

7.1997 10.336 3.7501 12.848

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Cross-market volatility dependence varies in magnitude and sign across markets. We find feedbacks in variance in both directions in all the models over the whole sample as well as in the pre-crisis sample, a result which-is consistent with the growing degree of integration of financial markets over the last two decades. However, there are asymmetries in volatility spillovers across markets. In particular, the South East Asian conditional variance depends positively on shocks originating in the European markets, while innovations in the US market decrease the South East Asian conditional variance. Shocks which occurred in the Japanese market have a positive effect on the South East Asian conditional variance over the full sample, while in the pre-crisis period their influence is negative and smaller. The positive sign found in the cross-market conditional variance suggests that the volatility of South East Asian stock returns has a positive cluster effect on the other markets. In particular, positive South East Asian shocks have a stronger influence in the pre-crisis period compared with the whole sample. On the other hand, in the post-crisis sample cross-market dependence is just in one direction, with the South East Asian market affecting positively the European and US markets. The bidirectional spillover found in the case of Japan is not surprising, as the collapse of some mid-size Japanese banks with the resulting financial problems and higher volatility in the Japanese markets were possibly expected a priori to have an impact on volatility in the other Asian markets. The LR statistics associated with the null of zero cross-market volatility spillovers from the US, European, and Japanese to the South East Asian market cannot be rejected. The x 2 ( j ) statistics yielded values of 6.36, 7.1 and 8.1, all of which have corresponding p-values bigger than the corresponding bootstrapped critical values. Furthermore, the positive sign suggests that financial turbulence, reflected in higher stock returns volatility, has a positive cluster effect on the other markets. Our findings are consistent with those of other studies taking a similar approach, such as Cheung et al. (2002), who found interactions between the US, the Japan and four East Asian markets. In particular, our analysis also indicates that the developed markets were Granger-caused by the South East Asian ones during the crisis period, even though we employ aggregate indices for the European and South East Asian stock markets, rather than indices for individual countries as in the aforementioned study.

Conclusions In this paper we have examined volatility transmission across emerging and developed stock markets, which, we have argued, is of crucial importance for understanding how financial crises spread (contagion effects possibly reflecting the "herding" behaviour of investors, as pointed out by Kaminsky and Schmukler, 1999), and has not been duly investigated. In particular, we have analysed the effects of the 1997 South East Asia crisis on other major stock markets. In line with other papers, we have adopted a BEKK representation of a bivariate GARCH model (see Engle and Kroner, 1995). However, we have improved on earlier contributions, which had overlooked finite sample issues, by constructing appropriate confidence intervals for the LR test by means of bootstrapping in order to test for causality-in-variance, thereby obtaining more reliable statistical results. The adopted framework has been applied to daily data on stock returns. In particular, three pairwise models have been estimated providing some empirical evidence on the transmission of volatility across US, European, Japanese and South East Asian financial markets. The empirical results can be summarised as follows. There is evidence of volatility spillovers in all cases, though it is also clear that there are significant differences in the nature of the transmission mechanisms (and the size of the shocks). More in detail, there appear to be bidirectional feedbacks in the second moment over the whole sample as well as the pre-crisis sample, though the dynamics of the conditional volatilities differ. On the other hand, causality links in the variance become unidirectional following the onset of the crisis, running from the markets in turmoil to the others. This suggests that an important feature of financial crises is that, after the crisis has spread internationally, the countries originally affected become unresponsive to

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developments in other financial markets. This is consistent with the idea that, though the build-up in vulnerability (due to financial weaknesses) in such countries might be gradual (see Alba et al., 1999), the precipitation of the crisis represents a regime switch, with a jump from one equilibrium to another (see Jeanne and Masson, 2000). In other words, it gives support to crisis-contingent models, in which the behaviour of investors, and consequently the transmission mechanism, change after a shock hits the economy. This is in contrast to non-crisis-contingent models, in which shocks are propagated through stable linkages (e.g. trade links - see Glick and Rose, 1999), and the transmission mechanism is the same in crisis and tranquil periods. It also suggests that international diversification in reducing portfolio risk during a crisis will be only relatively effective if it is based on pre-crisis estimates. Finally, it can be seen as an argument for IMF interventions and bail-outs, though there is, of course, a moral hazard problem (see Forbes and Rigobon, 2002, for more details). As a natural extension of the bivariate analysis conducted in the present paper, it would be useful to estimate a k-variate model and to examine volatility spillovers among all four markets; also, recursive techniques could be used for each market to detect the exact timing of any breaks. This will be the object of future work.

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