Published online by Cambridge University Press: 02 September 2015
This paper examines the problem of identification and inference on a conditional moment condition model with missing data, with special focus on the case when the conditioning covariates are missing. We impose no assumption on the distribution of the missing data and we confront the missing data problem by using a worst case scenario approach.
We characterize the sharp identified set and argue that this set is usually too complex to compute or to use for inference. Given this difficulty, we consider the construction of outer identified sets (i.e. supersets of the identified set) that are easier to compute and can still characterize the parameter of interest. Two different outer identification strategies are proposed. Both of these strategies are shown to have nontrivial identifying power and are relatively easy to use and combine for inferential purposes.
We thank useful comments and suggestions from Arie Beresteanu, Ivan Canay, Shakeeb Khan, and the participants at the presentations in the 2010 World Congress in Shanghai, the 2010 Triangle Econometrics Conference, the 2011 Joint Statistical Meetings in Miami, and at the Statistics Seminar at Duke University. Bugni thanks the National Science Foundation for research support via grant SES-1123771. We also thank the co-editors and the two anonymous referees for several comments and suggestions that have significantly improved this paper. Takuya Ura provided excellent research assistance. Any and all errors are our own.