[Paper Review] High-dimensional Model-assisted Inference for Local Average Treatment Effects with Instrumental Variables

Baoluo Sun, Zhiqiang Tan|arXiv (Cornell University)|Sep 19, 2020

Advanced Causal Inference Techniques4 citations

TL;DR

This paper proposes a high-dimensional model-assisted method for estimating local average treatment effects (LATE) using instrumental variables, leveraging regularized calibrated estimation with Lasso penalties to handle sparsity in high-dimensional covariates. The method ensures valid Wald confidence intervals under weaker conditions—specifically, correct specification of the instrument propensity score model—while allowing for potential misspecification in treatment and outcome regression models, extending doubly robust inference to high-dimensional settings.

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, which involves Lasso penalties but carefully chosen loss functions for estimating coefficient vectors in these regression models, and then employs a doubly robust estimator for the treatment parameter through augmented inverse probability weighting. 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. 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 methods via extensive simulation studies and an empirical application to estimate the returns to education.

Motivation & Objective

• To develop a computationally tractable method for estimating local average treatment effects (LATE) in high-dimensional settings where the number of covariates is comparable to or exceeds sample size.
• To extend doubly robust estimation to high-dimensional instrumental variable models by incorporating regularized calibrated estimation with Lasso penalties.
• To establish theoretical validity of Wald confidence intervals for LATE under weaker conditions: correct instrument propensity score model, while allowing misspecification in treatment and outcome regression models.
• To provide a rigorous theoretical framework for high-dimensional model-assisted inference in causal inference with instrumental variables.

Proposed method

• Employs regularized calibrated estimation with carefully chosen loss functions for estimating coefficient vectors in three regression models: instrument propensity score, treatment regression, and outcome regression.
• Uses Lasso penalties to achieve sparse estimation in high-dimensional settings under sparsity assumptions, selecting only relevant covariates.
• Applies a doubly robust estimator for LATE in the form of a ratio of two augmented inverse probability weighted (AIPW) estimators.
• Incorporates calibrated estimation techniques from Tan (2020b) adapted for high-dimensional settings to improve estimation efficiency and robustness.
• Derives theoretical bounds on estimation error using decomposition of influence functions and concentration inequalities under regularity conditions on design matrices and error terms.
• Establishes asymptotic normality of the estimator under sparsity and appropriate rate conditions on tuning parameters.

Experimental results

Research questions

• RQ1 Can valid confidence intervals for LATE be constructed when the number of covariates is large relative to sample size?
• RQ2 Does the proposed method maintain validity when treatment and outcome regression models are misspecified, provided the instrument propensity score model is correctly specified?
• RQ3 How does regularized calibrated estimation with Lasso improve estimation efficiency and robustness in high-dimensional instrumental variable models?
• RQ4 What are the theoretical conditions under which the resulting Wald confidence intervals for LATE are asymptotically valid?

Key findings

• The proposed method yields valid Wald confidence intervals for the local average treatment effect under the condition that the instrument propensity score model is correctly specified, even if the treatment and outcome regression models are misspecified.
• The method achieves asymptotic normality and valid inference under sparsity conditions, where only a small subset of covariates have non-zero coefficients in the relevant regression models.
• Theoretical analysis shows that estimation error in the influence function decomposition is bounded by terms involving the Lasso tuning parameters and sparsity levels, ensuring convergence under appropriate rate conditions.
• Simulation studies confirm the method's robustness and coverage properties under model misspecification, outperforming existing high-dimensional IV methods that require all three models to be correctly specified.
• Empirical application to returns to education demonstrates the method’s practical utility in real-world causal inference with high-dimensional covariates.