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Competitive Credit and Present Bias: A Stochastic Discounting Approach

Siddharth Chatterjee, Daniel F. Garrett

TL;DR

The paper develops a model where agents have time-consistent preferences but face privately observed, stochastic discount factors, enabling overestimation of future patience. In competitive credit markets, dynamic mechanisms are designed by firms to maximize profits subject to incentive compatibility and a break-even constraint, with agent beliefs potentially misspecified. A central finding is that equilibrium contracts often backload consumption and penalize early consumption, and this persists even when agents hold correct beliefs about future discounting in richer-type settings. The framework connects to and generalizes quasi-hyperbolic models, derives inverse Euler-type conditions, and has normative implications: regulation cannot easily improve welfare once beliefs and profit constraints are accounted for, highlighting the role of belief-driven distortions in intertemporal contracting.

Abstract

A prominent theme in behavioural contract theory is the study of present-biased agents represented through quasi-hyperbolic discounting. In a model of competitive credit provision, we study an alternative to this framework in which the agent has a private stochastic discount factor and may overestimate the likelihood of more patient values. Agent preferences, however, are timeconsistent. While a limiting case of our model corresponds to a "fully naive" agent in work on quasi-hyperbolic discounting, another case is where the agent has correct beliefs about future discounting. In equilibrium, the agent selects options with earlier consumption in case of less patient discount factor realisations, but is penalised by receiving worse terms. Our model thus accounts for an important feature of equilibrium contracts identified in Heidhues and Kőszegi (2010). Unlike Heidhues and Kőszegi, our framework often predicts excessively backloaded consumption, including when the agent holds correct beliefs about future discounting.

Competitive Credit and Present Bias: A Stochastic Discounting Approach

TL;DR

The paper develops a model where agents have time-consistent preferences but face privately observed, stochastic discount factors, enabling overestimation of future patience. In competitive credit markets, dynamic mechanisms are designed by firms to maximize profits subject to incentive compatibility and a break-even constraint, with agent beliefs potentially misspecified. A central finding is that equilibrium contracts often backload consumption and penalize early consumption, and this persists even when agents hold correct beliefs about future discounting in richer-type settings. The framework connects to and generalizes quasi-hyperbolic models, derives inverse Euler-type conditions, and has normative implications: regulation cannot easily improve welfare once beliefs and profit constraints are accounted for, highlighting the role of belief-driven distortions in intertemporal contracting.

Abstract

A prominent theme in behavioural contract theory is the study of present-biased agents represented through quasi-hyperbolic discounting. In a model of competitive credit provision, we study an alternative to this framework in which the agent has a private stochastic discount factor and may overestimate the likelihood of more patient values. Agent preferences, however, are timeconsistent. While a limiting case of our model corresponds to a "fully naive" agent in work on quasi-hyperbolic discounting, another case is where the agent has correct beliefs about future discounting. In equilibrium, the agent selects options with earlier consumption in case of less patient discount factor realisations, but is penalised by receiving worse terms. Our model thus accounts for an important feature of equilibrium contracts identified in Heidhues and Kőszegi (2010). Unlike Heidhues and Kőszegi, our framework often predicts excessively backloaded consumption, including when the agent holds correct beliefs about future discounting.
Paper Structure (7 sections, 14 theorems, 144 equations, 3 figures)

This paper contains 7 sections, 14 theorems, 144 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Further literature
  3. General Model
  4. Discussion of relationship to quasi-hyperbolic discounting
  5. Agent with degenerate impatience
  6. Findings for the richer model
  7. Conclusions

Key Result

Lemma 1

Consider any direct mechanism $M^{D}=\left(v_{t}\right)_{t=1}^{T}$ that, if chosen by the agent, results in non-negative profits for the firm. Then there is another mechanism $\bar{M}^{D}=\left(\bar{v}_{t}\right)_{t=1}^{T}$ that gives the firm non-negative profits in which, for all $t\geq2$ and all

Figures (3)

  • Figure 1: NPV of firm's date-2 continuation cost
  • Figure 2: Equilibrium and efficient date-2 consumption
  • Figure 3: Equilibrium and efficient date-2 consumption

Theorems & Definitions (30)

  • Lemma 1
  • Lemma 2
  • Proposition 1
  • Proposition 2
  • Corollary 1
  • Proposition 3
  • Proposition 4
  • Proposition 5
  • Lemma 3
  • Lemma 4
  • ...and 20 more