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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 & 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.

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It might be hard for answerers to answer your question, if we don't know which particular meaning of "contagion" you have in mind. And additionally, it seems to me that some words have their greatest utility in their ambiguity of meaning, and in such cases, quantification might be tricky, if not meaningless. Are you interested in the circumstances in which markets that had been negatively-correlated, uncorrelated or weakly correlated, find their correlations trending towards 1? –  EnergyNumbers Nov 26 at 6:59
You should define contagion first or at least restrict it to macroeconomics/econometrics. To me contagion is related to networks (e.g. public opinion formation) but that is clearly not what you are talking about. Maybe pick one or more definitions from papers that are related to your question. –  The Almighty Bob Nov 26 at 9:36
The question seems fine to me. EN, you should post your comment as an answer, plus any other possible meanings the word has to you in other circumstances. Because that is one sense in which contagion is used. (I can think of three different meanings in use!) Now, I typically think of contagion in relation to networks, like TAB, especially as a parameter associated with an event in a percolation question. Anyway: "you don't choose if you cannot..." If there are several meaning in different contexts all of which are possible answers, then the answer is a list of all possible meanings, I suggest. –  Guido Jorg Nov 26 at 13:49
Another word that describes this kind of phenomena is cascade failure, from wikipedia: "A cascading failure is a failure in a system of interconnected parts in which the failure of a part can trigger the failure of successive parts. Such a failure may happen in many types of systems, including power transmission, computer networking, finance, human bodily systems, and bridges." –  Lumi Nov 26 at 16:23

2 Answers 2

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.


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

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If i understand the meaning of the question correctly, i would suggest that the benchmark model in this kind of stories is the so-called BGG [1999], Handbook of Macroeconomics, Volume 1,Part C,Chapter 21, which introduces and explains the financial accelerator effect, which essentially states that endogenous "developments" in credit markets work to amplify and propagate shocks in macroeconomy. Following this model there is a huge literature which identifies quantitatively the financial accelerator in various models and proposes linkages with financial crisis, credit networks and macroeconomy. A good paradigm is the paper of Delli Gati et al, Journal of Economic Dynamics and Control, [2012].

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A financial accelerator effect is not the same as contagion. –  Mico Nov 26 at 20:36

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