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Designing Around Selection: Identification and Estimation Under Multi-Dimensional Unobserved Heterogeneity

Author

Listed:
  • Brent R. Hickman
  • John A. List
  • Ian Muir
  • Gregory K. Sun

Abstract

We study identification and optimal policy design within principal-agent models. The modal empirical specification is equivalent to a potential-outcomes framework augmented with three assumptions: treatment-effect monotonicity, extrapolative structure, and rank invariance (RI), which restricts unobserved heterogeneity to be one-dimensional. This decomposition isolates identifying content of each assumption. The first two assumptions are interpretable and testable; RI is untestable and rules out economically plausible behaviors. We derive sharp counterfactual bounds when RI is relaxed. We estimate empirical bounds and apply them to optimal nonlinear pricing. The robust policy fully insures against worst-case latent selection while still enabling profit and consumer-surplus gains.

Suggested Citation

  • Brent R. Hickman & John A. List & Ian Muir & Gregory K. Sun, 2026. "Designing Around Selection: Identification and Estimation Under Multi-Dimensional Unobserved Heterogeneity," NBER Working Papers 35547, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:35547
    Note: IO TWP
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    Cited by:

    1. Aaron L. Bodoh-Creed & Brent R. Hickman & John A. List & Ian Muir & Gregory K. Sun, 2026. "Salience and (Non-)Buyer's Remorse: Optimal Nonlinear Pricing with Cognitively Constrained Consumers," NBER Working Papers 35003, National Bureau of Economic Research, Inc.

    More about this item

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C93 - Mathematical and Quantitative Methods - - Design of Experiments - - - Field Experiments
    • D04 - Microeconomics - - General - - - Microeconomic Policy: Formulation; Implementation; Evaluation
    • J2 - Labor and Demographic Economics - - Demand and Supply of Labor
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
    • L5 - Industrial Organization - - Regulation and Industrial Policy

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