SEMIPARAMETRIC EFFICIENCY BOUNDS FOR CONDITIONAL MOMENT RESTRICTION MODELS WITH DIFFERENT CONDITIONING VARIABLES
研究了不同条件变量下条件矩限制模型的半参数效率界，将其表示为递减的无条件矩限制模型效率界的极限，并提供了近似有效得分的迭代方法，适用于缺失数据回归、供需联立方程等模型。
This paper addresses the problem of semiparametric efficiency bounds for conditional moment restriction models with different conditioning variables. We characterize such an efficiency bound, that in general is not explicit, as a limit of explicit efficiency bounds for a decreasing sequence of unconditional (marginal) moment restriction models. An iterative procedure for approximating the efficient score when this is not explicit is provided. Our theoretical results provide new insight for the theory of semiparametric efficiency bounds literature and open the door to new applications. In particular, we investigate a class of regression-like (mean regression, quantile regression,…) models with missing data, an example of a supply and demand simultaneous equations model and a generalized bivariate dichotomous model.