Correlation Analysis of Financial Contagion: What One Should Know Before Running a Test



believes that the variance ratio in Hong Kong during 1997 were constant and
lower than the value
λ solving the above equation, one should also accept the
null hypothesis of interdependence.

The first two columns of table 1 report the correlation between two-day
rolling averages of stock market returns in US dollars of Hong Kong with each
country in the sample during the tranquil,
p, and the crisis period, pc. The
third column of table 1 reports the threshold level of the variance ratio,
λ,
corresponding to (10). It is apparent that
λ tends to be larger, the smaller
the difference between
p and p; in other words, if the correlation between two
stock markets does not increase sharply during the crisis period, the null of
interdependence can be rejected only for very high values of the variance ratio.
Note also that, when correlation decreases between the tranquil and the crisis
period, the null of interdependence cannot be rejected at all (
λ = +∞). When
the correlation in the tranquil period is about zero, as in the case of Italy, the
null of interdependence is rejected for any value of
λj.

Table 1 shows that the null hypothesis of interdependence will be rejected
for ‘low’ values of λj in the case of Italy, France, Singapore, the UK, and the
Philippines. For instance, if one believes that λj = 3 (a value that we will
find in one of our estimates), our test would reject interdependence for all the
countries listed above. At λj = 7 (that will be our highest estimated value), the
test would also reject for Germany.

We stress the consequence of setting λj = λj' = 0, as implicitly done in
some of the literature reviewed in the previous section. Under such maintained
assumption, the test would reject interdependence only in the case of Italy -
that is, there would be almost no evidence of contagion. Yet, there are at least
four countries for which the strong result of “no contagion” is quite dubious.

Table 1 also reports the results of the Fisher test, based on unadjusted
correlation coefficients, so that the null hypothesis is
Ho : p. We have
shown that this test corresponds to our conditional correlation analysis if λj
happens to be exactly equal to l
∕p2 — I.17 Interpreting the table, observe that
this test rejects the null whenever l
∕p2 — l λ. This is the case for Indonesia,
the Philippines, Singapore, Russia and, among the G7, Germany, France, the
UK and Italy. Relative to the results from a test conditional on a positive but
low
λ (say λ = 4), there is some weak evidence of contagion for two countries
that do not appear in our list of ‘suspects’ above, Indonesia and Russia. So,
there is a substantial, although not perfect, overlap of results.

Nonetheless, note that the required variance ratio for the Fisher test on
unadjusted correlation coefficients to be consistent with our framework (that is,
the magnitude of l
∕p2 — l) is extremely — and unrealistically — high for most
countries. Only in two cases, Singapore and Indonesia, l
∕p2 — l is smaller then
10.

17Recall that there is only one value of the variance ratio that is true for Hong Kong. Then,
the Fisher test will be correct for at most one of the country pairs (or for a set of countries
whose stock markets happen to be equally correlated with Hong Kong’s).

17



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