Primary Submission Category: Instrumental Variables
Identification and Estimation with Deconfounded Instruments under Index Sufficiency
Authors: Christian Tien,
Presenting Author: Christian Tien*
This paper extends a novel methodology for identifying and estimating the causal effects of endogenous (treatment) variables on an outcome variable with partially endogenous instrumental variables. A crucial estimation step called “deconfounding” recovers variation in the instruments, which is unassociated with some observed variables called proxies, and consequently with any unobserved variables that explain the association between the instruments and proxies. These unobserved variables are called common confounders of the instruments and proxies. This paper explores the role of index sufficiency as a minimal parametric assumption, which naturally fits in with the deconfounding approach and permits the identification and estimation of causal effects in the common confounding setup. Novel semiparametric estimation theory is provided. Root-n-estimation of causal effects under index sufficiency in otherwise nonparametric models is shown to be possible, combining ideas from debiasing with respect to sequentially dependent nuisance functions [Singh, 2021, Chernozhukov et al., 2022] with recent results on strong identification subject to nuisance functions, which are defined as solutions to possibly ill-posed inverse problems [Bennett et al., 2022]. An empirical application on the returns to education with NLS97 data demonstrates the appeal of this approach in practical settings with partially endogenous instruments.