Privacy-aware identification

TL;DR

This paper redefines econometric identification under differential privacy constraints, introducing a new framework that accounts for randomness and uncertainty inherent in privacy-preserving data analysis.

Contribution

It develops a novel theoretical framework combining differential privacy, random set theory, and econometric identification, enabling analysis of parameters under privacy constraints.

Findings

Introduces a new interpretation of identification as a limit of random sets.

Proposes decision mappings to recover point identification.

Highlights the role of randomness and uncertainty in privacy-aware econometrics.

Abstract

The paper redefines econometric identification under formal privacy constraints, particularly differential privacy (DP). Traditionally, econometrics focuses on point or partial identification, aiming to recover parameters precisely or within a deterministic set. However, DP introduces a fundamental challenge: information asymmetry between researchers and data curators results in DP outputs belonging to a potentially large collection of differentially private statistics, which is naturally described as a random set. Due to the finite-sample nature of the DP notion and mechanisms, identification must be reinterpreted as the ability to recover parameters in the limit of this random set. In the DP setting this limit may remain random which necessitates new theoretical tools, such as random set theory, to characterize parameter properties and practical methods, like proposed decision mappings by data curators, to restore point identification. We argue that privacy constraints push econometrics toward a broader framework where randomness and uncertainty are intrinsic features of identification, moving beyond classical approaches. By integrating DP, identification, and random sets, we offer a privacy-aware identification.