🤖 AI Summary
This paper addresses a fundamental challenge in econometric identification under differential privacy (DP): conventional point or set identification fails to accommodate the information asymmetry and inherent randomness introduced by DP mechanisms. To resolve this, the paper pioneers the systematic application of random set theory, redefining identification as the ability to recover parameters within the limit of a sequence of random sets induced by DP statistics. It proposes a data curator–driven decision mapping framework that achieves provably consistent point identification in finite samples. The approach rigorously characterizes the identifiability boundary under DP, balancing controlled bias against statistical consistency. By shifting the paradigm from deterministic sets to stochastic limits, the framework endogenizes privacy into identification analysis—extending classical identification theory to formally incorporate privacy constraints as an intrinsic dimension of inference.
📝 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.
