High-Dimensional Model-Assisted Inference for Local Average Treatment Effects With Instrumental Variables

Abstract

Consider the problem of estimating the local average treatment effect with an instrument variable, where the instrument unconfoundedness holds after adjusting for a set of measured covariates. Several unknown functions of the covariates need to be estimated through regression models, such as instrument propensity score and treatment and outcome regression models. We develop a computationally tractable method in high-dimensional settings where the numbers of regression terms are close to or larger than the sample size. Our method exploits regularized calibrated estimation for estimating coefficients in these regression models, and then employs a doubly robust point estimator for the treatment parameter. We provide rigorous theoretical analysis to show that the resulting Wald confidence intervals are valid for the treatment parameter under suitable sparsity conditions if the instrument propensity score model is correctly specified, but the treatment and outcome regression models may be misspecified. In this sense, our confidence intervals are instrument propensity score model based, and treatment and outcome regression models assisted. For existing high-dimensional methods, valid confidence intervals are obtained for the treatment parameter if all three models are correctly specified. We evaluate the proposed method via extensive simulation studies and an empirical application to estimate the returns to education. The methods are implemented in the R package RCAL.

Keywords:

• Calibrated estimation
• Complier average causal effect
• Causal inference
• Doubly robust estimation
• Instrumental variable
• Lasso penalty
• Model misspecification
• Propensity score
• Regularized M-estimation

Acknowledgments

The authors thank an AE and two referees for constructive comments leading to improvement of the article.

Additional information

Funding

The research of B. Sun was supported in part by National University of Singapore Start-Up Grant R-155-000-203-133. The research of Z. Tan was supported in part by PCORI Grant ME-1511-32740.