Does consumer behavior exhibit time inconsistency? This is an essential, yet difficult question to answer. Since the pioneering contribution of Samuelson (1937), it has become a standard assumption in dynamic economics models that consumers have an exponential time discount function, {1, ?, ?2, ...}, which implies that consumer behavior is time consistent. A significant body of evidence in experimental psychology and economics literature, however, suggests that consumers discount the future hyperbolically, not exponentially. The essential feature of hyperbolic discounting is that consumers are time inconsistent. In the last decade, a particular kind of hyperbolic discounting, the quasi-hyperbolic discount function, {1, ??,??2, ...}, has been widely studied due to its analytic simplicity.1 Many researchers have applied this discount function to explain various economic anomalies, such as procrastination, retirement, addiction and credit card borrowing.2 This paper also adopts this formulation, which shall be simply referred to as hyperbolic discounting in later discussion.

The recent use of hyperbolic discounting has been criticized for lack of convincing empirical evidence.3 An ideal test is to compare consumers’ long-run plans with their later actions, which will be consistent for exponential consumers but inconsistent for hyperbolic consumers. In the real world, it is difficult to track long-run plans or later actions — especially long-run plans. This paper examines time inconsistency using a large-scale randomized experiment in the credit card market, with which we have a unique opportunity to conduct a reasonably good test. In the experiment, 600,000 consumers were each randomly assigned to one of six different groups, denoted as Market Cells A to F, which were mailed six different credit card offers. The six offers had different introductory interest rates and different durations: Market Cell A (4.9% for 6 months), B (5.9% for 6 months), C (6.9% for 6 months), D (7.9% for 6 months), E (6.9% for 9 months) and F (7.9% for 12 months). All other characteristics of the solicitations were identical across the six market cells. Consumer responses and subsequent usage of respondents for 24 months were observed.