We introduce and characterize a recursive model of dynamic choice that accommodates naiveté about present bias. The model incorporates costly self-control in the sense of Gul and Pesendorfer (2001) to overcome the technical hurdles of the Strotz representation. The important novel condition is an axiom for naiveté. We first introduce appropriate definitions of absolute and comparative naiveté for a simple two-period model, and explore their implications for the costly self-control model. We then extend this definition for infinite-horizon environments, and discuss some of the subtleties involved with the extension. Incorporating the definition of absolute naiveté 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 study the implications of our proposed comparison of naiveté for the parameters of the recursive representation. Finally, we discuss the obstacles that preclude more general notions of naiveté, and illuminate the impossibility of a definition that simultaneously incorporates both random choice and costly self-control.
We propose nonparametric definitions of absolute and comparative naivete. These definitions leverage ex-ante choice of menu to identify predictions of future behavior and ex-post (random) choices from menus to identify actual behavior. The main advantage of our definitions is their independence from any assumed functional form for the utility function representing behavior. An individual is sophisticated if she is indifferent ex-ante between retaining the option to choose from a menu ex-post or committing to her actual distribution of choices from that menu. She is naive if she prefers the flexibility in the menu, reflecting a mistaken belief that she will act more virtuously than she actually will. We propose two definitions of comparative naivete and explore the restrictions implied by our definitions for several prominent models of time inconsistency.