We revisit a test for conditional independence in intensity models of default proposed by Das, Duffie, Kapadia, and Saita (2007) (DDKS). Based on a sample of 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 perform different tests to see if firm-specific variables are affected by occurrences of defaults. As a first simple test we check whether there is additional downgrade activity following defaults. The idea is that if firm-specific covariates are affected by defaults of other firms, then this is reflected in subsequent rating changes and consequently we should see more rating downgrades than what can be explained by economy-wide covariates. While these tests show that defaults indeed are followed by more downgrades of other firms, the results may reflect rating agency behavior and the omitted covariates. We therefore also consider regression tests to see if quick ratios and distance-to-default are affected by defaults. We find no influence from defaults on Quick ratios, but some influence on distance-to-default. This suggests, that violations of conditional independence do indeed arise from balance sheet effects.
Joint paper with Mads Stenbo Nielsen (Copenhagen Business School), August 7, 2008