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The authors analyze the size-dependence and temporal stability of firm bankruptcy risk in the US economy by applying Zipf scaling techniques. They focus on a single risk factor - the debt-to-asset ratio R - in order to study the stability of the Zipf distribution of R over time. They find that the Zipf exponent increases during market crashes, implying that firms go bankrupt with larger values of R. Based on the Zipf analysis, they employ Bayes' theorem and relate the conditional probability that a bankrupt firm has a ratio R with the conditional probability of bankruptcy for a firm with a given R value.
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