Semi-parametric estimation of multi-valued treatment effects for the treated: Estimating equations and sandwich estimators - Johan Zetterqvist; Ingeborg Waernbaum (Institute for Evaluation of Labour Market and Education Policy (IFAU), 2020)
An estimand of interest in empirical studies with observational data is the average treatment effect of a multi-valued treatment in the treated subpopulation. We demonstrate three estimation approaches: outcome regression, inverse probability weighting and inverse probability weighted regression, where the latter estimator holds a so called doubly robust property. Here, we define the estimators in the framework of partial M-estimation and derive corresponding sandwich estimators of their variances. The finite sample properties of the estimators and the proposed variance estimators are evaluated in simulations that reproduce designs from a previous simulation study in the literature of multi-valued treatment effects. The proposed variance estimators are investigated and compared to a bootstrap estimator.
Keywords: C14; 330; ATT; causal inference; inverse probability weighting; doubly robust; weighted ordinary least squares