Identifying Present-Biased Discount Functions in Dynamic Discrete Choice Models

TL;DR

This paper develops a method to identify present-biased discount functions in dynamic discrete choice models, providing bounds on their possible values using polynomial equations derived from data.

Contribution

It introduces a novel approach to identify present bias and discount factors in dynamic choice models under exclusion restrictions, applicable to both finite and infinite horizons.

Findings

Discount factors are usually identifiable but hard to estimate precisely.

The method bounds the set of possible present-bias parameters.

Solutions exist for both finite and infinite horizon models.

Abstract

We study the identification of dynamic discrete choice models with sophisticated, quasi-hyperbolic time preferences under exclusion restrictions. We consider both standard finite horizon problems and empirically useful infinite horizon ones, which we prove to always have solutions. We reduce identification to finding the present-bias and standard discount factors that solve a system of polynomial equations with coefficients determined by the data and use this to bound the cardinality of the identified set. The discount factors are usually identified, but hard to precisely estimate, because exclusion restrictions do not capture the defining feature of present bias, preference reversals, well.