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.
翻译:本文在形式化隐私约束(特别是差分隐私(DP))下重新定义了计量经济学的识别问题。传统上,计量经济学侧重于点识别或部分识别,旨在精确恢复参数或将其限定在确定性集合内。然而,差分隐私引入了一个根本性挑战:研究者与数据管理者之间的信息不对称导致差分隐私输出属于一个可能庞大的差分隐私统计量集合,这自然可描述为一个随机集。由于差分隐私概念及机制的有限样本特性,识别必须被重新解释为在该随机集极限下恢复参数的能力。在差分隐私设定中,该极限可能仍保持随机性,这需要新的理论工具(如随机集理论)来刻画参数性质,以及实用方法(如数据管理者提出的决策映射)来恢复点识别。我们认为,隐私约束将计量经济学推向一个更广泛的框架,其中随机性和不确定性成为识别的内在特征,超越了经典方法。通过整合差分隐私、识别理论与随机集,我们提出了一种隐私感知识别框架。