‘instantaneous’ correlation coefficient between stock market returns in Hong
Kong and the Philippines, both measured in US dollars, during 1997. The daily
correlation provides a proxy for p (during tranquil periods) and pɑ (during
crises). Note that, before October 20, which is the starting day of the crisis,
we only report the instantaneous correlation, pt; from October 20 on, we report
both the instantaneous correlation, pɛ, and a set of coefficients of instantaneous
correlation under the null hypothesis of interdependence, calculated assuming
different values of λj∙.
For the purpose of the graph, we find it useful to calculate and plot an inverse
transformation of φ, instead of φ itself. This transformation, denoted by φt(λj■'),
is given below
pɑ
Φi (ʌ,) = I ʌ ʌ P2
ʌ/l + s - S [pf )
^sx1 (p>? )
where S is estimated from the sample data.9 According to the logic of our test,
this coefficient of correlation is adjusted so as to allow for the fact that changes
in the volatility of stock prices in Hong Kong will per se affect cross-border
comovements during the Hong Kong crisis. Thus, the observed pɑ is adjusted
on the basis of the estimated increase in the variance of rj-, that is S. Given S,
a smaller λj (shifting weight towards an increase in the variance of the global
factor) entails a smaller adjusted coefficient.
A visual inspection of figure 5 suggests that the unadjusted correlation co-
efficient pɑ increased significantly during the Hong Kong crisis in October 1997
relative to the previous months. Is this evidence of contagion? In light of what
discussed in the previous section, we can test of contagion vs. interdependence
by comparing φt (λj) and pt. Specifically, the null hypothesis of interdependence
is accepted when φi(λj) is not significantly larger than pt. Figure 5 plots differ-
ent estimates of φt (λj) conditional on values of λj between 0 and 5. The graph
shows that the adjusted coefficient φt (Xl) is close to pt for low values of the
variance ratio, while it gets significantly larger for values of λj around 5. The
graph thus suggests that the hypothesis of interdependence could be accepted
conditional on some λj smaller than 5.
The literature provides a few examples of conditional correlation tests of
contagion — but in most cases the maintained assumption on the Xs is only
implicit. In the following section, we will review these tests, nesting them in
our framework.
4.1 Tests based on sample correlation coefficient or A =
l∕p2 - 1
Early contributions on contagion, such as King and Wadhwani (1990), acknowl-
edge the problem of controlling for the relationship between volatility of return
and correlation, but implement no correction of their empirical tests.10 It is
9The coefficient φ' is obtained by substituting φ with ρc in equation (2), and then solving
the resulting expression for ρ.
10King and Wadhwani (1990) are aware of the relationship between volatility and correlation
as they write: “we might expect that the contagion coefficients would be an increasing function
of volatility” (pp. 20). However, in calculating correlation between markets, they do not
correct for the increase in volatility.
11