Identification and privacy guarantees
Abstract This paper investigates the impact of differential privacy (DP), a leading criterion for evaluation of statistical disclosure limitation, on the identification of a broad class of econometric parameters. We provide two sets of contrasting results. First, we show that without involvement of the data curator the parameters of interest are generally not point or partially identified when statistics computed from the data must satisfy the DP guarantee. Population parameters can only be characterized as elements of random sets. Second, we demonstrate that when a data curator can evaluate and select data statistics, the parameters can become point identified. This can be achieved by fully exploring the distribution (capacity) of the random set of the weak limits of differentially private estimators. Our first set of results stems from the fact that the properties of a particular statistic providing DP guarantee depend on the underlying population data distribution, which is typically not known a priori. In contrast, the second set of our results does not rely on particular distributional assumptions. It enables the application of a rich set of existing “generic” algorithms from computer science literature to provide DP guarantees. Parameter identification is ensured by post-processing the outputs of those algorithms using a powerful apparatus of the random set theory. Our findings suggest that providing DP guarantees for the analysis of economic data has the potential to retain the identification of possibly all statistics and parameters of interest but may require integration with techniques for partial identification and inference.
Bio Denis Nekipelov is an Associate Professor of Economics and Computer Science (by courtesy) and an Amazon Scholar with PXT Central Science division. Nekipelov’s work is aimed at the analysis and theory of scalable and efficient techniques that can be used to estimate the models of strategic behavior. This work combines statistical inference tools available in Econometrics and scalable algorithms coming from Computer Science. His work also analyzes the limitations in empirical implementation of strategic behavior models. In particular, some models may be sufficiently rich to provide a good description of the data, but provide non-robust predictions regarding the behavior of Economic agents making the policy analysis and implementation very hard if not impossible. Nekipelov received his B.Sc. and M.Sc. in Applied Physics and Mathematics at Moscow Institute of Physics and Technology and his Ph.D. in Economics from Duke University.