Semi-parametric estimation of multi-valued treatment effects for the treated: estimating equations and sandwich estimators

Published: 03 March 2020

Author: Ingeborg Waernbaum, And Johan Zetterqvist, And

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.


IFAU Working paper 2020:4 "Semi-parametric estimation of multi-valued ATTs" is written by Johan Zetterqvist (Karolinska institutet) and Ingeborg Waernbaum  (IFAU and Uppsala university). For further information, plesae contact  Ingeborg;