Identification, Data Combination and the Risk of Disclosure

Abstract

It is commonplace that the data needed for econometric inference are not contained in a single source. In this paper we analyze the problem of parametric inference from combined individual-level data when data combination is based on personal and demographic identi fiers such as name, age, or address. Our main question is the identi fication of the econometric model based on the combined data when the data do not contain exact individual identifi ers and no parametric assumptions are imposed on the joint distribution of information that is common across the combined dataset. We demonstrate the conditions on the observable marginal distributions of data in individual datasets that can and cannot guarantee identi fication of the parameters of interest. We also note that the data combination procedure is essential in the semiparametric setting such as ours. Provided that the (non-parametric) data combination procedure can only be de ned in finite samples, we introduce a new notion of identi fication based on the concept of limits of statistical experiments. Our results apply to the setting where the individual data used for inferences are sensitive and their combination may lead to a substantial increase in the data sensitivity or lead to a de-anonymization of the previously anonymized information. We demonstrate that the point identi fication of an econometric model from combined data is incompatible with restrictions on the risk of individual disclosure. If the data combination procedure guarantees a bound on the risk of individual disclosure, then the information available from the combined dataset allows one to identify the parameter of interest only partially, and the size of the identi cation region is inversely related to the upper bound guarantee for the disclosure risk. This result is new in the context of data combination as we notice that the quality of links that need to be used in the combined data to assure point identi cation may be much higher than the average link quality in the entire dataset, and thus point inference requires the use of the most sensitive subset of the data. Our results provide important insights into the ongoing discourse on the empirical analysis of merged administrative records as well as discussions on the disclosive nature of policies implemented by the data-driven companies (such as Internet services companies and medical companies using individual patient records for policy decisions).