The Free Installment Puzzle†

We analyze a new dataset on borrowing decisions of a sample of customers of a credit card company. This credit card allows customers to pay for their purchases via installment credit over terms up to 12 months at an interest rate that depends on the customer’s credit score and the duration of the installment loan. We use these data to estimate the effect of interest rates on consumers’ demand for credit. We show that conventional econometric methods (including regression, instrumental variables, and matching estimators) predict that the demand for installment credit is an increasing function of the interest rate, an inference we dismiss as spurious due to the endogeneity of the interest rate and the effect of unobserved credit constraints that cause customers with worse credit scores to have higher demand for installment credit. To make more credible inferences about the effect of interest rates on the demand for credit we exploit a novel feature in our data: customers are more or less randomly offered free installments, i.e. the opportunity to pay back a given purchase over a fixed term ranging from 2 to 12 months at an interest rate of zero. We exploit these free installment offers as a quasi-random experiment the help identify the demand for credit by estimating a discrete choice model of the installment credit decision that accounts for censoring (choice based sampling) in observed free installments. Despite the significant censoring, we show that it is possible to identify consumers’ choice probabilities and the probability they are offered free installments. The free installment puzzle results from our finding that less than 3% of the transactions in our sample were made as free installments, even though our model predicts that the average probability of being offered a free installment in our sample is approximately 20%. Our model predicts a high incidence of “pre-commitment behavior” even among the minority of individuals who do take the free installment offers. For example, the model predicts that 88% of individuals who were offered (and chose) a 10 month free installment offer pre-commited at time of purchase to pay the balance in fewer than 10 installments. This pre-commitment behavior is puzzling since there are no pre-payment penalties, and traditional economic models predict that consumers should choose the maximum loan duration when a loan is offered at a 0% interest rate. This puzzling consumer behavior raises questions about the company’s behavior: why does it make so many free installment offers if the response to them is so poor? We also present evidence that the increasing interest rate schedule the company offers its customers may not be profit-maximizing. †We are grateful to David McArthur for research assistance at an early stage of this project and for feedback from presentations of earlier versions of this paper at the University of Maryland in fall 2010, at the CEAR Workshop in Denver, January 2011, and at the State University of New York at Albany and Penn State University in September 2011. Please send comments to SungJin Cho at Department of Economics, Seoul National University, Seoul, Korea, email: [email protected] or John Rust at Department of Economics, University of Maryland, College Park, MD 20742 e-mail: [email protected].