Identification of Regressions with Missing Covariate Data

• Activity Number: 276
• Type: Invited
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: JBES-Journal of Business & Economic Statistics
• Author(s): Federico Bugni*+ and Joseph Hotz and Esteban Aucejo
• Companies: Duke University and Duke University and Duke University
• Keywords: missing data ; outer identified sets ; sharp sets

Abstract

This paper examines the problem of identification and inference on parametric models when there are missing data, with special focus on the case when covariates, denoted by X, are missing. Our econometric model is given by a conditional moment condition implied by the assumption that X is strictly exogenous. At the same time, we assume that the distribution of the missing data is unknown. We confront the missing data problem by adopting a worst case scenario approach. We characterize the sharp identified set and argue that this set is usually prohibitively complex to compute or to use for inference. Given this difficulty, we consider the construction of outer identified sets (that is, supersets of the identified set) that are easier to compute and can still provide a characterization of the parameter of interest. Two different outer identification strategies are discussed. Both of these strategies are shown to contain non-trivial identifying power and are relatively easy to compute and to be used for inference.