Ebook A Theory of Credit Scoring and Competitive Pricing of Default Risk (Preliminary and Incomplete)
It is well known that lenders use credit scores to regulate the extension of consumer credit. People with high scores are offered credit on more favorable terms. People who default on their loans experience a decline in their scores and, therefore, lose access to credit on favorable terms. People who run up debt also experience a decline in their credit scores and have to pay higher interest rates on new loans. While credit scores play an important role in the allocation of consumer credit they have not been adequately studied in the consumption smoothing literature. This paper attempts to remedy this gap.
We propose a theory of unsecured consumer credit where: borrowers have the legal option to default;defaulters are not exogenously excluded from future borrowing; there is free entry of lenders; and lenders cannot collude to punish defaulters. In our framework, limited credit or credit at higher interest rates following default arises from the lender’s optimal response to limited information about the agent’s type and earnings realizations. The lender learns from an individual’s borrowing and repayment behavior about his type and encapsulates his reputation for not defaulting in a credit score. Our underlying framework is broadly consistent with the way real-world unsecured consumer credit markets work. The framework can be used to shed light on household consumption smoothing with respect to transitory income shocks and to examine the welfare consequences of legal restrictions on the length of time adverse events can remain on one’s credit record.
The legal environment surrounding the U.S. unsecured consumer credit market is characterized by the following features. Individual debtors have can file for bankruptcy under Chapter 7 which permanently discharges net debt (liabilities minus assets above statewide exemption levels). A Chapter 7 filer is ineligible for a subsequent Chapter 7 discharge for 6 years. During that period, the individual is forced into Chapter 13 which is typically a 3-5 year repayment schedule followed by discharge. Over two-thirds of household bankruptcies in the U.S. are Chapter 7. The Fair Credit Reporting Act requires credit bureaus to exclude the filing from credit reports after 10 years (and all other adverse items after 7 years).
Beginning with the work of Athreya, there has been a growing number of papers that have tried to understand bankruptcy data using quantitative, heterogeneous agent models (for example Chatterjee, et. al., Livshits, et. al.). For simplicity, these models have assumed that an individual is exogenously excluded from borrowing while a bankrutpcy remains on his credit record. This exclusion restriction is often modelled as a Markov process and calibrated so that on average the household is excluded for 10 years, after which the Fair Credit Reporting Act requires that it be stricken from the household’s record. This assumption is roughly consistent with the findings by Musto who documents the following important facts: households with low credit ratings face very limited credit lines (averaging around $215) prior to and $600 following the removal of a bankruptcy flag; for households with medium and high credit ratings, their average credit lines were a little over $800 and $2000 respectively prior to the year their bankruptcy flag was removed from their record; and for households with high and medium credit ratings, their average credit lines jumped nearly doubled to $2,810 and $4,578 in the year that the bankruptcy flag was removed from their record.
While this exogenous exclusion restriction is broadly consistent with the empirical facts, a fundamental question remains. Since a Chapter 7 filer is ineligible for a subsequent Chapter 7 discharge for 6 years (and at worst forced into a subsequent Chapter 13 repayment schedule), why don’t we see more lending to those who declare bankruptcy? If lenders believe that the Chapter 7 bankruptcy signals something relatively permanent about the household’s unobservable characteristics, then it may be optimal for lenders to limit future credit. But if the circumstances surrounding bankruptcy are temporary (like a transitory, adverse income shock), those individuals who have just shed their previous obligations may be a good future credit risk. Competitive lenders use current repayment and bankruptcy status to try to infer an individual’s future likelihood of default in order to correctly price loans. There is virtually no existing work embedding this inference problem into a quantitative, dynamic model.
Given commitment frictions, it’s important for a lender to assess the probability that a borrower will fail to pay back that is, assess the risk of default. In the U.S., lenders use credit scores as an index of the risk of default. The credit scores most commonly used are produced by a single company, the Fair Isaac and Company, and are known as FICO scores. These scores range between 300 and 850, where a higher score signals a lower probability of default. The national distribution of FICO scores are given in Figure 1. Scores under 620 are considered high risk, often called “subprime.”
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