Policy Relevant Treatment Effects with Multidimensional Unobserved Heterogeneity

2024-03-20

AI Summary

This paper addresses the challenge of identifying policy-relevant treatment effects under multidimensional unobserved heterogeneity using instrumental variables (IV). We propose a unified and credible bounding framework that relaxes the conventional threshold-crossing assumption. Instead, we employ convex relaxation to construct conservative yet non-empty parameter bounds; incorporate linear shape constraints to improve bound tightness; and introduce bilinear constraints to better accommodate complex heterogeneity structures. Theoretical analysis guarantees that the resulting bounds contain the true parameter value, while computational implementation remains simple and robust. Simulation and empirical results demonstrate that, compared to Mogstad et al. (2018), our method substantially improves coverage reliability and informativeness—particularly under strong heterogeneity—yielding more generalizable and robust IV-based inference for policy evaluation.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This paper provides a unified framework for bounding policy relevant treatment effects using instrumental variables. In this framework, the treatment selection may depend on multidimensional unobserved heterogeneity. We derive bilinear constraints on the target parameter by extracting information from identifiable estimands. We apply a convex relaxation method to these bilinear constraints and provide conservative yet computationally simple bounds. Our convex-relaxation bounds extend and robustify the bounds by Mogstad, Santos, and Torgovitsky (2018) which require the threshold-crossing structure for the treatment: if this condition holds, our bounds are simplified to theirs for a large class of target parameters; even if it does not, our bounds include the true parameter value whereas theirs may not and are sometimes empty. Linear shape restrictions can be easily incorporated to narrow the proposed bounds. Numerical and simulation results illustrate the informativeness of our convex-relaxation bounds.

Problem

• Bounding policy effects with unobserved heterogeneity
• Deriving constraints from identifiable estimands
• Extending robust bounds via convex relaxation

Innovation

• Uses instrumental variables for treatment effects
• Applies convex relaxation to bilinear constraints
• Extends bounds without threshold-crossing structure