Zipf Law in Firms Bankruptcy

TL;DR

This paper analyzes the distribution of firm bankruptcies in Japan, revealing a Zipf law for liabilities, and models the bankruptcy process through debtor-creditor dynamics to explain these empirical patterns.

Contribution

It demonstrates the Zipf law in firm liabilities and links size and debt distributions, supported by a debtor-creditor dynamic model.

Findings

Liabilities follow a Zipf law in high debt range.

Firm lifetime distribution is exponential.

Debt correlates strongly with firm size.

Abstract

Using an exhaustive list of Japanese bankruptcy in 1997, we discover a Zipf law for the distribution of total liabilities of bankrupted firms in high debt range. The life-time of these bankrupted firms has exponential distribution in correlation with entry rate of new firms. We also show that the debt and size are highly correlated, so the Zipf law holds consistently with that for size distribution. In attempt to understand ``physics'' of bankruptcy, we show that a model of debtor-creditor dynamics of firms and a bank, recently proposed by economists, can reproduce these phenomenological findings.