Uniformly Semiparametric Efficient Estimation of Treatment Effects With a Continuous Treatment

By Antonio F. Galvao, Liang Wang. 2015

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This article studies identification, estimation, and inference of general unconditional treatment effects models with continuous treatment under the ignorability assumption. We show identification of the parameters of interest, the dose–response functions, under the assumption that selection to treatment is based on observables. We propose a semiparametric two-step estimator, and consider estimation of the dose–response functions through moment restriction models with generalized residual functions that are possibly nonsmooth. This general formulation includes average and quantile treatment effects as special cases. The asymptotic properties of the estimator are derived, namely, uniform consistency, weak convergence, and semiparametric efficiency. We also develop statistical inference procedures and establish the validity of a bootstrap approach to implement these methods in practice. Monte Carlo simulations show that the proposed methods have good finite sample properties. Finally, we apply the proposed methods to estimate the unconditional average and quantile effects of mothers’ weight gain and age on birthweight. Supplementary materials for this article are available online.

Subfields: Economics and Econometrics, Statistics and Probability

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Citations in the corpus

Double/De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers (2018, background): “Prominent examples of the debiased CTE literature include Rubin and van der Laan (2006), Dı́az and van der Laan (2013), Galvao and Wang (2015), Kennedy et al. (2017), Kallus and Zhou (2018), and Colangelo and Lee (2020).”
Non‐parametric methods for doubly robust estimation of continuous treatment effects (2015, background): “Hirano and Imbens (2004), Imai and van Dyk (2004), and Galvao and Wang (2015) adapted propensity score-based approaches to the continuous treatment setting, but these similarly rely on correct specification of at least a model for treatment (e.g., the conditional treatment density). In contrast, sem”
Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments (2019, unknown): “In low-dimensional settings, see Imbens (2000), Hirano and Imbens (2004), Flores (2007), and Lee (2018) for examples of a class of regression-type estimators n (cid:5) (cid:5) Galvao and Wang (2015) and Hsu et al. (2020) study a class of inverse probability weighting estimators.”