Publication Date: August 2017
Revision Date: February 2018
We introduce and characterize a recursive model of dynamic choice that accommodates naivete about present bias. While recursive representations are important for tractable analysis of in nite-horizon problems, the commonly-used Strotz model of time inconsistency presents well-known technical diﬀiculties in extensions to dynamic environments. Our model incorporates costly self-control in the sense of Gul and Pesendorfer (2001) to overcome these hurdles. The important novel condition is an axiom for naivete. We ﬁrst introduce appropriate deﬁnitions of absolute and comparative naivete for a simple two-period model, and explore their implications for the costly self-control model. We then develop suitable extensions of these deﬁnitions to in nite-horizon environments. Incorporating the deﬁnition of absolute naivete as an axiom, we characterize a recursive representation of naive quasi-hyperbolic discounting with self-control for an individual who is jointly overoptimistic about her present-bias factor and her ability to resist instant gratiﬁcation. We also study the implications of our proposed comparison of naivete for this recursive representation and uncover new restrictions on the present-bias and self-control parameters that characterize comparative naivete. Finally, we discuss the subtleties that preclude more general notions of naivete, and illuminate the impossibility of a deﬁnition that simultaneously accommodates both random choice and costly self-control.
Naive, Sophisticated, Self-control, Quasi-hyperbolic discounting
JEL Classification Codes: D11, D15, D91