Can we think of time variation in the frequency of corporate defaults as controlled by ’exogenous’ factors with no feedback from actual defaults to these factors? Or can we statistically document ’contagion effects’ by which one firm’s default increases the likelihood of other firms defaulting?
In a recent paper Das, Duffie, Kapadia, and Saita (2007) (DDKS) test whether default events in an intensity-based setting can reasonably be modeled as ’doubly stochastic’, i.e. as dependent solely on ’exogenous’ factors. Their approach is to transform the time scale using the sum of the default intensities estimated for individual firms and then test whether defaults on this transformed time scale behave as a standard Poisson process. Based on a time series of U.S. corporate defaults, they strongly reject that defaults can be modeled as doubly stochastic. DDKS view this test as a joint test of the specification of the default intensities of the individual firms and the doubly stochastic assumption. A core message of our paper is that the time transformation test should be thought of mainly as a misspecification test. We need - and propose - other tests to look for contagion effects that violate the doubly stochastic assumption.
Our first contribution is to show that a different specification of the intensity will in fact make us unable to reject the tests performed by DDKS. That is, using our specification of the intensity there is no excess default clustering. As DDKS we use the sample of firms listed in Moody’s default database. To make sure that the different conclusion is not merely a consequence of deviations in the data, we show that specifying the explanatory variables as in DDKS, we reject the assumption of conditional independence but using our specification, we are not able to reject using a large variety of tests. In essence, our change in specification consists in replacing a measure of the short rate with a measure of steepness of the term structure, adding industrial production (a variable also examined in DDKS) and adding the following three firm specific variables: quick ratio, short-to-long debt and the book value of assets. We will discuss this choice of the explanatory variables below.
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Correlation in corporate defaults: Contagion or conditional independence?
