Federal Reserve Bank of Minneapolis White Paper: 'A Quantitative Theory of the Credit Score'

MINNEAPOLIS, Minnesota, Aug. 4 -- The Federal Reserve Bank of Minneapolis issued the following Economic Research white paper entitled "A Quantitative Theory of the Credit Score". Here are excerpts of the report co-authored by Satyajit Chatterjee, vice president and economist at the Federal Reserve Bank of Philadelphia, consultant Dean Corbae, professor of economics at the University of Wisconsin, Kyle Dempsey, assistant professor at the Ohio State University, and Jose-Victor Rios-Rull, professor at the University of Pennsylvania:

Abstract

What is the role of credit scores in credit markets? We argue that it is a stand in for a market assessment of a person's unobservable type (which here we take to be patience). We pose a model of persistent hidden types where observable actions shape the public assessment of a person's type via Bayesian updating. We show how dynamic reputation can incentivize repayment without monetary costs of default beyond the administrative cost of filing for bankruptcy. Importantly we show how an economy with credit scores implements the same equilibrium allocation. We estimate the model using both credit market data and the evolution of individual's credit scores. We find a 3% difference in patience in almost equally sized groups in the population with significant turnover and a shift towards becoming more patient with age. If tracking of individual credit actions is outlawed, the benefits of bankruptcy forgiveness are outweighed by the higher interest rates associated with lower incentives to repay.

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Introduction

Credit scores are a fundamental ingredient of a borrower's access to credit. In the United States, credit bureaus and credit rating agencies serve this function for individual and business credit by creating and maintaining credit scores for individual borrowers. Similar agencies exist in many other countries.

Credit scores affect borrowing terms and change with credit use and repayments. Despite the widespread use of credit scores in actual credit markets, they are conspicuously absent from standard quantitative models of consumer default which are typically more concerned with allocations than the contractual arrangements that generate them.

In this paper we provide a theory of the joint behavior of unsecured credit and credit scores, that is, both allocations and arrangements, over the lifetime that is based on hidden information about some persistent, credit-relevant individual characteristic - which we take to be patience - and where maintaining a good reputation plays a central role.

Our theory is founded on the premise that an individual's true propensity to repay -- i.e., the individual's true type -- is hidden from her creditors, and it is the presence of this persistent hidden information that makes an individual's history of actions relevant for lenders. Our theory is dynamic: at any point in time, lenders use a person's observable history of actions to perform a Bayesian update of her type; individuals understand this and choose actions mindful of the consequence any action has on the future beliefs of lenders. A loss of reputation, rather than stigma or exogenous exclusion from future borrowing, is the only dynamic punishment from default. Specifically, an individual's credit score falls upon default and she subsequently faces worse borrowing terms. Our theory is competitive: information available to any lender is assumed to be available to all lenders and there is free entry into the business of lending. Finally, our theory respects a key feature of the institutional arrangement under which unsecured consumer credit is extended in the United States: at some monetary cost, individuals can choose to have their debts discharged via Chapter 7 bankruptcy.

We make several contributions. First, we extend the theory of unsecured credit to accommodate persistent hidden information about individual types. Our model environment is rich enough to cover four of the five characteristics lenders use to assess creditworthiness: character (reflected in credit history), capacity (reflected in debt-to-income ratio), capital (wealth), and conditions (amount of the loan).1 Competition drives lending contracts to be indexed by all observable borrower and loan characteristics relevant for predicting the probability of default on a loan. When there is hidden information, a new individual characteristic becomes relevant: a Bayesian update of the borrower's type probability -- in the terminology of this paper, the borrower's type score -- indicating the probability that a person is of each of the different types existing in the economy. The update conditions on all relevant observables: the individual's current type score, their current net wealth, all the relevant information to forecast future earnings, and, of course, their current action, be that to save, borrow or default. One way to interpret the large number of conditioning variables is that the lender is using "big data." Our framework easily encompasses "small data" cases in which lenders observe only some strict subset of actions.

Second, after proving an equilibrium with type scores exists, we show that a market arrangement which uses credit scores as in modern societies replicates the same equilibrium allocation without any reference to type scores. Specifically, we use the type score to define a credit score - an object that yields a ranking of individuals with regard to their probability of default on a particular contract. Such an ordinal ranking is widely used by credit bureaus. We provide a sufficient condition such that the equilibrium of the arrangement that uses credit scores to index contracts has the same allocation as the equilibrium of our baseline economy with type scores. Just as agents take prices as given in standard competitive equilibrium models, in our equilibrium with credit scores individuals and lenders take credit score dependent prices and the distribution of future credit scores conditional on their actions as given; they do not need to know what is behind such functions, just that they exist. In doing so, we provide a theory of the credit score itself and of how it evolves over time in response to fundamentals of the economy. In this context, we take to heart that the actual market arrangement is a form of data and our equivalence result allows for the use of such data for empirical purposes.

Third, we take our model to the data, estimating preference parameters from the joint behavior of credit scores over an individual's lifetime and aggregate credit market moments. It is here that our decision to model age variation in the evolution of earnings and hidden characteristics pays off. For these estimates, we verify that the sufficient condition which guarantees equivalence between the type score economy and credit score economy holds. We find what we believe are important properties of the U.S. population with regard to (hidden) patience as revealed by the properties of the credit market: the difference between patient and impatient people are 3% annually, slightly less than three quarters of people are born impatient while slowly tilting towards patience (by age 60 slightly less than half of them have become patient), and patience is highly persistent. Nevertheless, these infrequent changes in type, along with the estimated small variation in extreme value shocks, prevent excessively fast learning about an individual's type.2

Fourth, we use our estimates to explore the role of hidden information in the U.S. unsecured credit market. We start by considering a policy counterfactual in which lenders are prohibited from keeping track of the history of an individual's asset market actions but can condition on the observable length of an individual's credit history (effectively their age). In this case, impatient types are pooled with patient types without having to bear the costs of imitating them in order to obtain better borrowing terms. Since young adults wish to borrow against their higher expected future income, and most start their adult life impatient, the policy has the possibility of improving the welfare of those young adults.

However, the policy removes the incentives to maintain a good reputation which leads to individuals facing higher interest rate offerings. We find the negative incentive effects offset the potential pooling benefits for impatient young adults such that all young adults are made worse off.

Our second counterfactual considers an economy where one's type is perfectly observable. The findings are intuitive. Since the impatient are now known, they face a more adverse situation; their interest rates are higher and they borrow less. The contrary is true for the patient. As people age, this knowledge becomes less relevant because people accumulate precautionary balances and rarely borrow.

We also find that whatever changes do occur at the individual level roughly offset each other at the aggregate level so that the aggregate differences between the hidden and full information worlds are minor.

Fifth, we make a couple of methodological contributions. First, we combine both screening and dynamic signalling where these screening and signalling opportunities are constrained by noise which we introduce via extreme value shocks.3 The shocks ensure that beliefs held by lenders following any feasible action are determined in equilibrium (reminiscent of Selten (1975) and Myerson (1978)).4 Second, we extend quantitative theory models of default to include hidden information which requires us to index the pricing of credit to the market assessment of individual types.5,6,7 While previous quantitative theory models imposed exogenous punishment, we incorporate dynamic reputation as a means of disciplining borrowers.

The paper is organized as follows. Section 2 describes our baseline economy with private information. Section 3 describes the equilibrium problems faced by our agents. Section 4 studies the properties of the baseline model. Section 5 describes how we map the model to the data. Section 6 compares our baseline economy to alternative economies with different information structures. Section 7 concludes. There is an accompanying online appendix where we provide additional theoretical, computational, and data results.

Full white paper: https://www.minneapolisfed.org/research/wp/wp770.pdf

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Conclusion and Directions for Future Research

In this paper, we present a hidden information model of unsecured consumer credit with risk of default. People are subject to unobserved persistent and transitory shocks and the history of people's asset market actions help forecast future defaults. The setup is possibly the simplest environment to quantitatively study the role of credit scores in regulating consumer credit. We showed how this can be done using shocks drawn from an extreme value distribution and recursive updating of beliefs.

Our quantitative model with persistent hidden heterogeneity in types is capable of not only accounting for aggregate credit market moments but also the joint behavior of the age profile of credit rankings.

Furthermore, the model generates an age profile of credit ranking patterns like those in U.S. data. In this sense, our model provides a quantitative theory of the credit score.

Table 6: Comparison of Full Information vs. Baseline Ratio to BASE (in %)

[Table omitted]

View table at https://www.minneapolisfed.org/research/wp/wp770.pdf

Notes: All numbers are reported in percentages.

Two implications of our theory are worth highlighting. First, we found that restricting lenders' access to an individual's history of asset market actions (no tracking) leads to a welfare loss for all young adults. Since the young tend to borrow against their future income, the negative incentive effects from not having to maintain a good reputation raises interest rates faced by the young which offsets any benefits from pooling afforded to the low types. Our "big data" baseline model affords all of the young with better intertemporal insurance at the expense of worse intratemporal insurance for a subset of the population in a "small data" economy.

Second, even though our model allowed lenders unrestricted access to the history of all actions relevant for inferring an individual's type, the equilibrium allocations at an individual level remain far removed from those of a full information economy. This stems from the fact that individuals select actions that only partially reveal their type while in the full information economy they get that revelation for free. Despite big differences at the micro level, the macro (aggregate) differences are small.

Where next? First, type does not have to correspond to an individual's hidden time preference.

Alternatively, it could correspond to hidden ability differences that exogenously affect earnings. Furthermore, hidden time preference could affect a hidden human capital decision (i.e. moral hazard) to endogenously affect earnings or to a variety of other personal traits. Second, while the theory is written for many types, the quantitative work assumed two types since it was adequate for the task at hand. Extending the analysis to higher dimensional type differences is left for future research. Third, to keep the state space reasonable, we restricted attention to a model with one asset so that we consider simply positions of net debt. A model with separate debt and assets (e.g. housing) can generate stronger reputation effects. In Online Appendix C we provide a simple example where reputation in the unsecured credit market spills over to other asset markets, reinforcing reputation effects. More generally, a person's reputation (or type score) in the unsecured credit market may have implications for other markets (e.g. insurance, labor) and other interactions (marriage) that are worth exploring.

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Full white paper: https://www.minneapolisfed.org/research/wp/wp770.pdf