Correlation in Corporate Defaults: Contagion or Conditional Independence?
32 Pages Posted: 21 Mar 2008
Date Written: March 18, 2008
We revisit a test for conditional independence proposed by Das, Duffie, Kapadia, Saita (2007) (DDKS) applied to US corporate defaults. They reject the conditional independence assumption but also observe that the test is a joint test of the specification of the default intensity of individual firms and the assumption of conditional independence. We show that using a different specification of the default intensity, and using the same test as DDKS, we cannot reject the assumption of conditional independence for default histories recorded by Moody's in the period from 1982 to 2006. We propose additions to the DDKS procedure as well as a Hawkes process alternative to test for violations of conditional independence but are still unable to reject. We then show, that the test proposed by DDKS is not able to detect all violations of conditional independence. Specifically, the tests will not capture contagion effects which are spread through the explanatory variables ('covariates') used as conditioning variables in the Cox regression and which determine the default intensities of individual firms. We therefore propose a different test in which only the truly 'macro-economic' variables are used as exogenous variables, but firm specific variables are left out. The specification then checks whether there is additional downgrade activity following defaults. The idea is that if firm specific covariates are affected by defaults of other firms, then we should not condition on these in the Cox regression but rather check if they deteriorate after defaults. We use rating downgrades as a proxy for deteriorating firm specific variables. These tests show that defaults indeed trigger rating downgrades of other firms. This suggests, that the reason for violations of conditional independence is the worsening of balance sheet variables. Hence if we can model the way in which balance sheets are affected by defaults of other firms, we do not need unobserved factors to explain default clustering.
Keywords: Default correlation, intensity estimation, Hawkes process
JEL Classification: G33, G32, C52
Suggested Citation: Suggested Citation