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Complexity and Misspecification

Drew Fudenberg, Florian Mudekereza

TL;DR

The paper develops a tractable framework that combines concerns about model misspecification with a preference for simplicity by penalizing the entropy of worst-case distortions. This leads to Gibbs-type distortions and a dynamic learning environment in which complexity aversion can eliminate cycles and steer decisions toward safer actions, with welfare gains when safety aligns with the true data-generating process. The approach yields microfoundations for empirical phenomena such as scale heterogeneity in discrete choice, probability neglect, and home bias in international finance, and connects to rational inattention and stochastic growth literature through an information-theoretic lens. Methodologically, the paper derives closed-form distortions, envelope results, and ARC representations, and provides a rich set of applications and welfare implications for long-run decision making under uncertainty.

Abstract

We propose a tractable unified framework to study the evolution and interaction of model-misspecification concerns and complexity aversion in repeated decision problems. This aims to capture environments where decision makers worry that their models are misspecified while also disliking overly complex models. We find that pathological cycles caused by endogenous concerns for misspecification can be eliminated by penalizing complex models and show that such preferences for simplicity tend to favor safety, which can enhance welfare in the long run. We use our framework to provide new microfoundations for pervasive empirical phenomena such as "scale heterogeneity" in discrete-choice analysis, "probability neglect" in behavioral economics, and "home bias" in international finance.

Complexity and Misspecification

TL;DR

The paper develops a tractable framework that combines concerns about model misspecification with a preference for simplicity by penalizing the entropy of worst-case distortions. This leads to Gibbs-type distortions and a dynamic learning environment in which complexity aversion can eliminate cycles and steer decisions toward safer actions, with welfare gains when safety aligns with the true data-generating process. The approach yields microfoundations for empirical phenomena such as scale heterogeneity in discrete choice, probability neglect, and home bias in international finance, and connects to rational inattention and stochastic growth literature through an information-theoretic lens. Methodologically, the paper derives closed-form distortions, envelope results, and ARC representations, and provides a rich set of applications and welfare implications for long-run decision making under uncertainty.

Abstract

We propose a tractable unified framework to study the evolution and interaction of model-misspecification concerns and complexity aversion in repeated decision problems. This aims to capture environments where decision makers worry that their models are misspecified while also disliking overly complex models. We find that pathological cycles caused by endogenous concerns for misspecification can be eliminated by penalizing complex models and show that such preferences for simplicity tend to favor safety, which can enhance welfare in the long run. We use our framework to provide new microfoundations for pervasive empirical phenomena such as "scale heterogeneity" in discrete-choice analysis, "probability neglect" in behavioral economics, and "home bias" in international finance.
Paper Structure (85 sections, 23 theorems, 198 equations)

This paper contains 85 sections, 23 theorems, 198 equations.

Table of Contents

  1. Introduction
  2. Related Work
  3. Robust control and misspecification.
  4. Expected utility and complexity.
  5. Narratives and coarse reasoning.
  6. Information-theoretic preferences.
  7. Model selection and learning.
  8. Static Environment
  9. Primitives and running example
  10. Robust criterion with complexity aversion
  11. Static illustration in the running example
  12. Dynamic Environment and Long-Run Behavior
  13. Dynamic environment
  14. Mixed $c$--robust equilibria for the $\bar{\mu}$--criterion
  15. Correct specification and the Bayesian limit
  16. ...and 70 more sections

Key Result

Lemma 2.1

Suppose Assumption ass:full_support holds and define If $\kappa>0$ (i.e., $\mu<1/\lambda$), then for every $(a,q)\in A\times Q$, eq:static_criterion has a unique minimizer Moreover, $v_{\lambda,\mu}(a;q)$ and $\hat{p}_{\lambda,\mu}(a;q)$ are continuous in $(\lambda,\mu,q)$ on $\{\kappa>0\}$, and the following envelope identities hold for all $(\lambda,\mu,q)$ with $\kappa>0$:

Theorems & Definitions (44)

  • Example 2.1: Safe vs risky arm
  • Lemma 2.1
  • Proposition 2.1: Entropy strictly decreasing in complexity aversion
  • Example 2.2
  • Definition 3.1: $\bar{\mu}$--optimal policies
  • Definition 3.2: $\Lambda$-limit frequencies
  • Definition 3.3: Mixed $c$--robust equilibrium
  • Proposition 3.1
  • Proposition 3.2
  • Lemma 3.1
  • ...and 34 more