# Contagion Effect - A Simple Empirical Model

A Simple Empirical Model

The empirical literature on testing for contagion has focused on increases in the correlation of returns between markets during periods of crisis. Forbes and Rigobon (2002) begin by discussing the current imprecision and disagreement surrounding the term contagion. It proposes a concrete definition, a significant increase in cross-market linkages after a shock, and suggests using the term “interdependence” in order to differentiate this explicit definition from the existing literature. It shows the elementary weakness of simple correlation tests: with an unchanged regression coefficient, a rise in the variance of the explanatory variable reduces the coefficient standard error, causing a rise in the correlation of a regression. The regression underlying contagion tests is as follows:

Xt=θ(L)Xt+Θ(L)Itt (1) Xt={xtc,xtj} (2) It={itc, itUS, itj} (3)

where t is the time period for all variables; xc is the stock market return in the crisis country;, xj is the stock market return in another market j; Xt is a transposed vector of returns in the same two stock markets; Θ(L) and θ(L) are vectors of lags; ic, ius, and ij are short-term interest rates for the crisis country, the United States, and country j, respectively; and ξt is a vector of reduced-form disturbances. For each series of tests, they first use the VAR (vector autoregression) model in equations (1) through (3) to estimate the variance-covariance matrices for each pair of countries during the stable period, turmoil period, and full period. Then they use the estimated variance-covariance matrices to calculate the cross-market correlation coefficients (and their asymptotic distributions) for each set of markets and periods.

As Pesaran and Pick (2007) observe, however, financial contagion is a difficult system to estimate econometrically. To disentangle contagion from interaction effects, county-specific variables have to be used to instrument foreign returns. Choosing the crisis period introduces sample selection bias, and it has to be assumed that crisis periods are sufficiently long to allow correlations to be reliably estimated. In consequence, there appears to be no strong consensus in the empirical literature as to whether contagion occurs between markets, or how strong it is.

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