Semiparametric Estimation and Inference Using Doubly Robust Moment Conditions

By Christoph Rothe, Sergio Firpo. 2013

27 citations recorded by the source corpus.

We study semiparametric two-step estimators which have the same structure as parametric doubly robust estimators in their second step, but retain a fully nonparametric specification in the first step. Such estimators exist in many economic applications, including a wide range of missing data and treatment effect models. We show that these estimators are ?n-consistent and asymptotically normal under weaker than usual conditions on the accuracy of the first stage estimates, have smaller first order bias and second order variance, and that their finite-sample distribution can be approximated more accurately by classical first order asymptotics. We argue that because of these refinements our estimators are useful in many settings where semiparametric estimation and inference are traditionally believed to be unreliable. We also illustrate the practical relevance of our approach through simulations and an empirical application.

Subfields: Statistics and Probability

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Citations in the corpus

Program evaluation and causal inference with high-dimensional data (2013, methodology): “…) := ψ α V,z,gV ,mZ (W,αV (z)) and (3.12) ψαV,z,g,m(W,α) := 1(Z = z)(V − g(z,X)) m(z,X) + g(z,X)− α. (3.13) This efficient influence function was derived by Hahn (1998); it has recently been used by Cattaneo (2010) in the series context (with p n) and Rothe and Firpo (2013) in the kernel context.”
Program evaluation with high-dimensional data (2013, methodology): “…) := ψ α V,z,gV ,mZ (W,αV (z)) and (3.12) ψαV,z,g,m(W,α) := 1(Z = z)(V − g(z,X)) m(z,X) + g(z,X)− α. (3.13) This efficient influence function was derived by Hahn (1998); it has recently been used by Cattaneo (2010) in the series context (with p n) and Rothe and Firpo (2013) in the kernel context.”
The Value of Knowing the Propensity Score for Estimating Average Treatment Effects (2016, background): “16 An inspection of the proof of Theorem 2, which follows directly from a result in Rothe and Firpo (2016), shows that both terms on the right-hand side of the previous equation have mean zero, which means that τ̂kps is second-order unbiased.”