How Do Economists Quantify Contagion? In the context of international financial crises, what mathematical methods have Economists employed in order to quantify financial contagion?



Note: For a working definition of contagion I'll use the description supplied by Kaminsky, Reinhart &amp; Vegh (2003):


  We refer to contagion as an episode in which there are significant immediate effects in a number of countries following an event—that is, when the consequences are fast and furious and evolve over a matter of hours or days. This “fast and furious” reaction is a contrast to cases in which the initial international reaction to the news is muted.
I believe the single most commonly used metric for contagion is a sharp increase in the correlation of returns in various countries, either within a country (e.g., the correlation of daily returns in the markets for stocks, bonds, and commodities) or across countries (e.g, the correlation of daily returns in the stock markets in Europe, North and South America, Asia, etc). 

While correlation is an easily understood measure, and while it's true that pairwise correlations do tend to rise during crisis periods, using correlations in this manner is not without pitfalls. In particular, sampling correlation coefficients will rise during periods of heightened market volatility (and this is a major difference to, say, regression coefficients), irrespective of whether there's a real crisis or not. For more on these pitfalls see, e.g.,

Forbes and Rigobon, 2002, "No Contagion, Only Interdependence: Measuring Stock Market Comovements", Journal of Finance, vol. 57, pp. 2223-2281.

and

Loretan and English, Evaluating changes in correlations during periods of high market volatility, BIS Quarterly Review, 2000, June, pp. 29-36.