Regularized Regression for Covariate Adjustment with Complex Functional Forms

• In Event: Causal Inference

Abstract

Researchers are often interested in estimating average treatment effects in observational settings based on treatment unconfoundedness, which is often only plausible conditional on a large number of pretreatment variables. We demonstrate that high-dimensional regularized regression methods allow for the inclusion of complex interaction terms in both the outcome and treatment-assignment regressions, which makes the conditional unconfoundedness assumption more plausible than con- ventional practice of controlling for them them linearly. We augment these regression methods using new variable selection methods from machine learning to improve the bias and precision of estimates and substantially alleviate the curse of dimensionality in matching methods with many controls and interactions. We provide simulation evidence that finds these selection methods often outperform other standard treatment effect estimators, and are ease computational constraints for matching. Finally, we provide an illustration of these methods using three empirical examples.

Author

• Apoorva Lal, Stanford University