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Participants (N = 17) chose between smaller, immediate and larger, delayed hypothetical money amounts in two laboratory sessions separated by 1 week. The choice procedure yielded equivalence points at which participants were indifferent between the smaller, immediate and the larger, delayed reward for eight different delays of the larger reward. These equivalence points then were used to estimate temporal discounting parameters according to three different discounting functions. A hyperbolic discounting function accounted for more of the variance than an exponential function, which replicated earlier research. Correlations across sessions showed that the discounting parameters were reliable, and that the equivalence points were reliable for delays greater than 1 month.
Many behavioral events involve choosing between acts that have consequences of different value and delay. For example, one must choose between sleeping a bit longer and rising to be at work on time, or between attending a party and studying for an important exam, or between seeking employment after high school and attending college. In each case, one choice option results in a relatively smaller but earlier reward, and the other choice option results in a relatively larger but later reward. Laboratory preparations that model such situations have become critically important in behavioral research on the psychological phenomena of impulsiveness and self-control (e.g., Ainslie, 1975; Rachlin & Green, 1972); choice of the smaller, earlier reward or of the larger, later reward can be labeled as instances of impulsiveness or self-control, respectively The ubiquity of apparently impulsive choices indicates that persons often behave in ways that serve their short-term rather than their long-term interests.
A key problem for understanding impulsiveness and self-control is understanding the manner in which the value of delayed rewards are discounted. In general, future rewards are less valuable than present rewards. For example, given a choice between $10 now and $20 next year, most people would choose the former even though it is only one half the amount of the latter. Describing change in reward value as a function of delay has been a long-standing and important issue in psychological research (e.g., Ainslie, 1975). Two types of discount functions have received the most research attention: (1) exponential,
which is common in the psychological literature (e.g., Ainslie, 1992; Mazur, 1987; Rachlin, Rained, & Cross,...





