Semiparametric efficiency bounds for seemingly unrelated conditional moment restrictions

TL;DR

This paper derives semiparametric efficiency bounds for models with conditional moment restrictions involving different conditioning variables, providing a method to approximate these bounds and extending theoretical understanding.

Contribution

It characterizes efficiency bounds as limits of unconditional models and offers an iterative procedure for approximating the efficient score in complex models.

Findings

Efficiency bounds expressed as limits of unconditional models

Iterative procedure for efficient score approximation

Application to regression models with missing data

Abstract

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 complete and extend existing results in the literature, 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.