An Empirical Bargaining Model with Left-Digit Bias: A Study on Auto Loan Monthly Payments

This paper studies price bargaining when both parties have left-digit bias when processing numbers. The empirical analysis focuses on the auto finance market in the United States, using a large data set of 35 million auto loans. Incorporating left-digit bias in bargaining is motivated by several intriguing observations. The scheduled monthly payments of auto loans bunch at both $9- and $0-ending digits, especially over $100 marks. In addition, $9-ending loans carry a higher interest rate, and $0-ending loans have a lower interest rate. We develop a Nash bargaining model that allows for left-digit bias from both consumers and finance managers of auto dealers. Results suggest that both parties are subject to this basic human bias: the perceived difference between $9- and the next $0-ending payments is larger than $1, especially between $99- and $00-ending payments. The proposed model can explain the phenomena of payments bunching and differential interest rates for loans with different ending digits. We use counterfactuals to show a nuanced impact of left-digit bias, which can both increase and decrease the payments. Overall, bias from both sides leads to a $33 increase in average payment per loan compared with a benchmark case with no bias.

This paper was accepted by Matthew Shum, marketing.