Time Inconsistency in the Credit Card Market



Does consumer behavior exhibit time inconsistency? This is an essential, yet dicult question to answer. This dissertation attempts to answer this question based on a large-scale randomized experiment in the credit card market. Specifically, we apply both time consistent preferences (exponential) and time inconsistent preferences (hyperbolic) to study two puzzling phenomena in the experiment. The two puzzling phenomena seem to suggest time inconsistency in consumer behavior. First, more consumers accept an introductory o er that has a lower interest rate with a shorter duration than a higher interest rate and a longer duration. However, ex post borrowing behavior reveals that the longer duration o er is better, because respondents keep on borrowing on the credit card after the introductory period. Second, consumers are reluctant to switch, and many of those consumers who have switched before fail to switch again later.

A multi-period model with complete information is studied analytically, which shows that standard exponential preferences cannot explain the observed behavior because they are time consistent. However, hyperbolic preferences that are time inconsistent come closer to rationalizing the observed behavior. In particular, two special cases of hyperbolic discounting are carefully examined, sophisticated and naive. Sophisticated consumers prefer the short offer because it serves as a selfcommitment device. Naive consumers prefer the short o er because they underestimate their future debt.

The exponential discounted utility model (DU) proposed by Samuelson (1937) is a standard theoretical model for consumer intertemporal choices. The central assumption of the DU model is that consumer intertemporal impatience can be condensed
into one parameter, a constant discount rate per period. Constant discounting implies that consumers' intertemporal preferences are time consistent. A signi cant body of evidence, however, has been gathered in experimental psychology and economics studies, that consumers have a declining rate of time preferences. Researchers nd that a hyperbolic functional form, which imposes declining discount rates, ts such experiment data much better that the exponential function. Declining discount rates imply that consumers are time inconsistent.

Studies of Time Discounting

Intertemproal choices, decisions involve tradeo s among costs and bene ts occurring at di erent time, are important and ubiquitous. Such decisions not only a ect one's wealth, but may also, as Adam Smith rst recognized, determine the economic
prosperity of nations. Jonh Rae's The Sociology Theory of Capital discusses the underlying psychologic motives, which determines a nation's the effective desire of accumulation", which in turn decides a society's level of saving. He believed that intertemporal choices was the joint product of four factors, two promoting and the other two limiting the desire of saving. The two main factors which promoted the desire are the bequest motives and the propensity to exercise self-restraint. One limiting factor is the uncertainty of human life. The second factor that limited the e ective desire was the excitement of immediate consumption.

Eugen von Bohm-Bawerk began modeling intertemporal choices in the same terms as other economic tradeo s, as a 'technical' decision about allocating resources over di erent points of time, much as one would allocate resources between housing and food. This treatment was formalized by Irving Fisher. Fisher plotted the intertemporal consumption decision on a two-good indi erence diagram, with current consumption on the abscissa and the second period consumption on the ordinate.

This representation made clear that a person's intertemporal allocation depends on both time preferences and diminishing marginal utility. Pure time preference can be interpreted as the marginal rate of substitution on the diagonal where consumption is equal in both periods.

Author: Haiyan Shui, Doctor of Philosophy, 2004, Economics Department, University of Maryland

Source: http://drum.lib.umd.edu/bitstream/1903/2082/1/umi-umd-2049.pdf






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