by pɑ, and the theoretical measure of interdependence φ are the main elements
of our test.
The coefficient φ is derived under the null hypothesis of interdependence: if
7i, 7j Vαr(ε⅛) and Cov(ε-i,ε1) do not change during the crisis, pɑ and φ will
coincide. Conversely, if there is contagion in the form of an increase in the mag-
nitude of factor loadings or a positive correlation between idiosyncratic risks
(e.g., because some country-specific factor becomes global during the crisis in
country j), pɑ will be larger than φ. Then, under the identifying assumption
that contagion from international crises does not alter the variance of idiosyn-
cratic shocks in countries other than j (i.e. Var(ε∙i) is constant), a statistical
analysis on contagion vs. interdependence can be performed by testing whether
pɑ is significantly higher than φ.
We should stress a notable feature of this approach to testing. During an
international crisis originating in one country, shocks to the global factor tend to
induce large comovements of prices. Yet, the country where the crisis originates
may also be subject to large shocks that are and remain country-specific. Overall
cross-market correlation may fall. The fact that during a crisis correlation falls
(as it often does in the data, see Section 2) is by no means evidence against
contagion. In other words, testing for contagion needs not be conditional on
observing a hike in correlation. In line with this remark, the test is symmetrical;
namely, it can also be applied to structural breaks and contagion consisting in
looser interdependence (e.g. falling factor loadings). There is no reason why
the concept of contagion should be confined to the hypothesis of stronger than
normal ties.
4 A review of the literature
This section analyzes recent empirical contributions on contagion, identifying
a set of tests that can be interpreted as special cases of our framework. To
introduce our discussion, it is useful to simplify our test statistic φ by assuming
that the variance ratio defined in the previous section does not vary across
periods, λj' = λ1∙. Assuming a constant ratio means that the variance of the
global factor and the variance of the country-specific risk increase by the same
proportion during the crisis in j:
Var(rj I C) = Var(f ∣ C) = Var(εj ∣ C) = ɪ .
Var(r3) Var(f ) Var(εj) ^∣^
Then, the coefficient of interdependence φ simplifies to:
φ(⅛Λp) = p
1 + δ 11/2
(3)
1 + sp (1 + ʌ,■')_
Other things equal, a larger variance-ratio λj reduces the effect of an increase
in the variance of r7 on the coefficient of interdependence. This is because a
larger fraction of this variance is due to the country-specific component, hence
weakening cross-market linkages.
To clarify this point, we consider once again the case-study analyzed at the
end of Section 2, that is the spread of financial instability in the stock market
from Hong Kong to the Philippines on October 1997. Figure 5 below shows the
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