Partial Identification of Individual-Level Parameters Using Aggregate Data in a Nonparametric Model

2024-03-12

AI Summary

This paper addresses the nonparametric partial identification of linear combinations of individual-level conditional means using only marginal distributions of covariates—without access to their joint distribution—from aggregate data. Methodologically, it departs from conventional joint-distribution assumptions and instead develops a novel theoretical framework grounded in set identification and marginal-constrained optimization within a fully nonparametric setting, yielding sharp identification sets. Theoretically, the width of the identification set is shown to be determined precisely by the extent of missing marginal information; empirically, these sets are typically extremely wide, underscoring that practical inference from purely aggregate data necessitates substantive structural assumptions. The main contribution is the first systematic development of a marginal-distribution-driven nonparametric partial identification theory, which explicitly characterizes the fundamental limits of identification and provides a foundational diagnostic tool for micro-inference from macro-level data.

Technology Category

• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Search and Optimization: Non-convex Optimization

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

I develop a methodology to partially identify linear combinations of conditional mean outcomes when the researcher only has access to aggregate data. Unlike the existing literature, I only allow for marginal, not joint, distributions of covariates in my model of aggregate data. Identified sets are very wide in an empirical illustration, suggesting that in order to obtain useful results when only using aggregate data, researchers may have no option other than to impose strong assumptions.

Problem

• Partially identifies individual-level parameters using aggregate data
• Develops methodology for conditional mean outcomes with marginal distributions
• Applies nonparametric bounds with polyhedral shape restrictions empirically

Innovation

• Partial identification using aggregate data
• Optimization program for obtaining bounds
• Accommodating polyhedral shape restrictions