Designing Around Selection: Identification and Inference Under Multi-Dimensional Unobserved Heterogeneity
NBER Working Papers · 2026 · Brent R. Hickman、John A. List、Ian Muir、Gregory K. Sun
中文摘要
我们研究一大类委托—代理模型中的识别与最优政策设计。我们表明，文献中最常见的经验框架等价于一个无结构的潜在结果模型，并附加三项具体假设：需求定律（LoD），即处理效应单调性；外推式模型结构（EMS），它排除了代理人对价格变化作出块状反应；以及秩不变性（RI），它将不可观测异质性（UH）限制为一维。这一分解分离出每项假设的识别内容，并厘清其经济作用。LoD 与 EMS 可利用外生价格变动进行实证检验；另一方面，RI 是一项强假设，排除了许多经济上合理的行为，且同样无法进行实证检验。我们在放松 RI 时推导出反事实结果的尖锐界。传统的单维模型给出规划者目标的上界，而下界——允许任意多维 UH——在政策设计上具有对抗性解读。我们估计经验界，并将其应用于网约车服务的非线性定价。由此得到的稳健定价政策完全防范最坏情形的潜在选择，同时保留了传统模型所预测的大部分利润与消费者剩余收益。我们的框架为逆向选择情形下的稳健政策设计提供了一种易于处理的方法，这些情形包括 Mirrlees 式税收、规制、劳动供给与采购。
Abstract
We study identification and optimal policy design in a broad class of principal-agent models. We show that the most common empirical framework within the literature is equivalent to an unstructured potential-outcomes model augmented with three specific assumptions: the Law of Demand (LoD), or treatment-effect monotonicity; extrapolative model structure (EMS), which rules out lumpy agent responses to price changes; and rank invariance (RI), which restricts unobserved heterogeneity (UH) to be one-dimensional. This decomposition isolates the identifying content of each assumption and clarifies its economic role. The LoD and MS are empirically testable using exogenous price variation; RI, on the other hand, is a strong assumption ruling out many economically plausible behaviors, and also not empirically testable. We derive sharp bounds on counterfactual outcomes when RI is relaxed. The conventional 1-dimensional model delivers an upper bound on planner objectives, while the lower bound, which allows for arbitrary multi-dimensional UH, has an adversarial interpretation for policy design. We estimate empirical bounds and apply them to nonlinear pricing of rideshare services. The resulting robust pricing policy fully insures against worst-case latent selection while preserving most of the profit and consumer-surplus gains predicted by the conventional model. Our framework provides a tractable approach to robust policy design in adverse-selection settings including Mirrleesian taxation, regulation, labor supply, and procurement.