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Universal Inference for Incomplete Discrete Choice Models

Hiroaki Kaido, Yi Zhang

TL;DR

The paper tackles inference in incomplete discrete choice models that yield set-valued predictions by developing a finite-sample valid, tuning-parameter-free procedure based on a robust universal inference framework. It builds a tailor-made likelihood using a least-favorable pair and employs cross-fitting to achieve universal size control for testing composite hypotheses and constructing confidence sets for subvectors and counterfactuals. Key contributions include finite-sample validity under broad selection mechanisms, tractable computation via convex programs for the LFP, and applicability to models with mixed data types and nuisance components. The method delivers practical, reliable inference in a wide class of incomplete models and demonstrates competitive power and computation in Monte Carlo experiments.

Abstract

A growing number of empirical models exhibit set-valued predictions. This paper develops a tractable inference method with finite-sample validity for such models. The proposed procedure uses a robust version of the universal inference framework by Wasserman et al. (2020) and avoids using moment selection tuning parameters, resampling, or simulations. The method is designed for constructing confidence intervals for counterfactual objects and other functionals of the underlying parameter. It can be used in applications that involve model incompleteness, discrete and continuous covariates, and parameters containing nuisance components.

Universal Inference for Incomplete Discrete Choice Models

TL;DR

The paper tackles inference in incomplete discrete choice models that yield set-valued predictions by developing a finite-sample valid, tuning-parameter-free procedure based on a robust universal inference framework. It builds a tailor-made likelihood using a least-favorable pair and employs cross-fitting to achieve universal size control for testing composite hypotheses and constructing confidence sets for subvectors and counterfactuals. Key contributions include finite-sample validity under broad selection mechanisms, tractable computation via convex programs for the LFP, and applicability to models with mixed data types and nuisance components. The method delivers practical, reliable inference in a wide class of incomplete models and demonstrates competitive power and computation in Monte Carlo experiments.

Abstract

A growing number of empirical models exhibit set-valued predictions. This paper develops a tractable inference method with finite-sample validity for such models. The proposed procedure uses a robust version of the universal inference framework by Wasserman et al. (2020) and avoids using moment selection tuning parameters, resampling, or simulations. The method is designed for constructing confidence intervals for counterfactual objects and other functionals of the underlying parameter. It can be used in applications that involve model incompleteness, discrete and continuous covariates, and parameters containing nuisance components.

Paper Structure

This paper contains 18 sections, 6 theorems, 68 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Relation to the literature
  3. Set-up
  4. Examples
  5. An Overview of the Main Results
  6. Unrestricted Estimator
  7. How to Construct $\mathcal{L}_0$
  8. Finite Sample Validity
  9. Illustration
  10. Theory behind the Robustness and Finite-sample Validity
  11. Universal inference with Least Favorable Pair
  12. Monte Carlo experiments
  13. Discussion
  14. Proofs
  15. Preliminaries
  16. ...and 3 more sections

Key Result

Theorem 1

Suppose Assumption as:iidF holds. Then, for any $n\in\mathbb N$,

Figures (2)

  • Figure 1: Level sets of $G(\cdot|x;\theta)$ with $\beta^{(j)}< 0,j=1,2$.
  • Figure 2: Power of the Cross-fit LR and Moment-based Tests: ($S=1000$ replications)

Theorems & Definitions (20)

  • Example 1: Discrete Game
  • Example 2: Heterogeneous Choice Sets
  • Example 3: Panel Binary Choice Model
  • Remark 2.1
  • Definition 2.1: LFP-based parametric model
  • Remark 2.2
  • Theorem 1
  • Corollary 1
  • Remark 3.1
  • Example 1: Discrete Game
  • ...and 10 more