A statistical framework closely related Forbes and Rigobon’s test is pre-
sented by Boyer et al. (1999) and Loretan and English (2000), who assume that
(τiyrj) is a normal bivariate random variable. The equivalence between the two
approaches can be easily understood by referring to the following property: if
(ri,rj) is a normal bivariate random variable, one can write13
Г = ai + 7i ■ r.j + υi
(7)
rj = a J + Tj ■ T
where v-ι and Vj are orthogonal and normally distributed random variables. It
is apparent that, as in Forbes and Rigobon, the country-specific shock in j is
the global factor, up to an affine transformation.
The test statistic adopted by Boyer et al. (1999) and Loretan and English
(2000), which follows from the model (7), is the same as the one adopted by
Forbes and Rigobon (1999a,b):
1 + δ ]1/2
1 + δp2~
(8)
This is the correlation between two jointly normal random variables as a function
of the increase in the variance of one of them, δ — also known in the literature
as ‘normal correlation theorem’. Note that (8) coincides with our measure of
interdependence (3) when there is no idiosyncratic shock in country j; that is,
when λ1' = λj = 0. Thus, the measures of interdependence (2) and (3) could
be interpreted as a generalization of the normal correlation theorem.
In these models, the test strategy consists in verifying whether the statistic
(8) is significantly different from pɑ. The drawback of tests using the statistic
(8) is quite clear. In equation (6), r depends linearly on rj-, so that there is
no component of the variance of r7 that is country-specific. The stock market
return in country j is specified as a ‘global’ or ‘regional’ factor. The test statistic
(8) is therefore only applicable when every single shock in country j has global
or regional repercussions. Do we really believe that the rate of return in Hong
Kong or Thailand is (or coincide with) a global or even a regional factor both
before and after a crisis?
The specification of r7 as a global factor has important implications for the
test. To the extent that the increase in the variance of the market in coun-
try j is due to idiosyncratic shocks in this country, the theoretical correlation
coefficient (8) will be biased. Such bias will be larger, the larger the share of
variance in r7 that can be attributed to country-specific shocks. As apparent
from equation (6), specifying r7 as a global factor magnifies the theoretical cor-
relation φ between the two markets, and increases the chances that its variance
will explain the observed correlation during the crisis. Hence, the test will be
biased towards the null hypothesis of interdependence. It may not come entirely
as a surprise that this kind of tests hardly find any evidence of Contagionfi In
the next section, we will indeed provide empirical evidence showing that many
strong results in the literature are severely affected by the test bias discussed
above.
13These tests have been sometimes used by financial market paricipants. See Deutsche Bank
(2000).
14See for instance Boyer et al. (1999) and Forbes and Rigobon (1999a,b).
14