To “ Efficiency Bounds for Missing Data Models with Semiparametric Restrictions ” : Proofs

THIS APPENDIX CONTAINS PROOFS of the results contained in the main paper. All notation is as defined in the main text unless explicitly noted otherwise. Equation numbering continues in sequence with that established in the main text. To simplify notation, let β denote the true parameter value β0 unless explicitly stated otherwise; similarly, the 0 subscript is removed from other objects, such as the propensity score, when doing so does not cause confusion.