Econometrica: Jan, 2012, Volume 80, Issue 1
Timing and Self‐Control
Drew Fudenberg, David K. Levine
The standard dual‐self model of self‐control, with a shorter‐run self who cares only about the current period, is excessively sensitive to the timing of decisions and to the interpolation of additional “no‐action” time periods in between the dates when decisions are made. We show that when the shorter‐run self is not completely myopic, this excess sensitivity goes away. To accommodate the combination of short time periods and convex costs of self‐control, we introduce a cognitive resource variable that tracks how the control cost depends on the self‐control that has been used in the recent past. We consider models with both linear and convex control costs, illustrating the theory through a series of examples. We examine when opportunities to consume will be avoided or delayed, and we consider the way in which the marginal interest declines with delay.
Supplement to "Timing and Self Control"
This appendix has several sections. W1 is another example/application of the model. W2 is a brief proof of something asserted in the text. W3 provides a foundation for the model in terms of a game between the long run self and a sequence of shorter one selves. W4 explores an alternative model; it shows that the alternative makes no difference with linear control sets but leads to odd conclusions when the cost is convex.