Identification and Formal Privacy Guarantees

The use of highly sensitive individual datasets in empirical economic research and the increasing availability of public individual-level data creates privacy risks. To deal with such risks, the computer science research proposed differential privacy (DP) -- a formal criterion for the evaluation of non-disclosure guarantees for released statistics and a related methodology to ensure such guarantees. The impact of DP on identification of parameters of interest determined from the population distribution has not, however, been studied. This paper bridges this gap.

We find that there is a broad class of population parameters that are not identified and, moreover, not even partially identified as one cannot construct a deterministic set that would contain their values. Population parameters can be only characterized as elements of random sets which then requires the application of the toolkit of the random set theory to analyze their properties. We argue that
identification becomes possible if the target parameter can be deterministically mapped within the random set. In that case, a full exploration of the support of the distribution of the random set of the weak limits of differentially private estimators can allow the data curator to find a selection procedure that will guarantee identification. We provide a decision-theoretic approach to this selection.

Our results indicate that expansion of formal privacy guarantees to socio-economic datasets requires further work on integrating data analysis with results
and concepts from the random set theory as well as techniques for partial identification and inference.