Correlation in Corporate Defaults: Contagion or Conditional Independence?

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Abstract
We revisit a method used by Das, Duffie, Kapadia, and Saita (2007) (DDKS) to test the doubly stochastic assumption in intensity models of default. We show that using a different specification of the default intensity, and using the same test as DDKS, we cannot reject using an almost identical set of default histories recorded by Moody's in the period from 1982 to 2006. We propose additions to the procedure as well as a Hawkes process alternative to test for violations of conditional independence but cannot detect contagion. We then observe that the test proposed by DDKS is mainly a misspecification test in that it will not detect contagion effects as long as individual firms have default intensities and there are no simultaneous jumps to default. Specifically, contagion spread through the explanatory variables ('covariates') that determine the default intensities of individual firms will not be detected. We therefore perform different tests to see if firm-specific variables are affected by occurrences of defaults. Regression tests show that there is no influence from defaults on quick ratios, but some influence on distance-to-default.

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