Over-identified Doubly Robust identification and estimation

Ensemble Learning with Statistical and Structural Models

“…The DRSS builds on the GDR method of Lewbel et al (2019). In this section, we discuss the estimator first in the context of statistical prediction and then in causal inference.…”

“…Under regularity conditions, as long as one of the two models, h or g, is correctly specified, it can be shown that µ (x) → p µ (x). The proof is based on Theorem 1 of Lewbel et al (2019) (see Appendix A.1). The intuition is simple: if one of the models, say h, is correctly specified but g is not, then Q h θ h → p 0 while Q g θ g will have a nonzero limit.…”

“…The doubly robust estimator is consistent if either of the two models is correctly specified, thus providing an insurance against model misspecification. Lewbel et al (2019) generalized the classic doubly robust method to allow the combination of any parametric models. Their method provides a basis for our DRSS estimator.…”

“…Chernozhukov et al (2016Chernozhukov et al ( , 2017 showed that the doubly robust estimator can be viewed as being based on Neyman-orthogonal moment conditions that are first-order robust to errors in nuisance parameter estimation. More recently, Lewbel et al (2019) proposed the general doubly robust (GDR) method that provides a general technique for constructing a doubly robust combination out of any parametric models, which forms the basis of our DRSS estimator.…”