Primary Submission Category: Matching, Weighting
Inference for weighting-based effect estimators: Residualization produces smaller standard errors with correct coverage
Authors: Arisa Sadeghpour, Erin Hartman, Chad Hazlett,
Presenting Author: Arisa Sadeghpour*
Balancing weight procedures are used in observational causal inference to adjust for covariate imbalance within the sample. Common practice for inference is to estimate robust standard errors from a weighted regression of outcome on treatment. However, it is well known that weighting can inflate variance estimates, sometimes significantly, leading to standard errors and confidence intervals that are overly conservative. Motivated by linearized standard errors from the survey literature, we instead propose using robust standard errors from a weighted regression that additionally includes the balancing covariates and their interactions with treatment. We show that these standard errors are more precise and asymptotically correct when balancing weights target exact balance, such as with entropy balancing. Gains to precision can be quite significant when the balancing weights adjust for prognostic covariates. For procedures that balance in expectation, such as inverse propensity weighting, our proposed method improves precision by reducing residuals through the parametric model. We also consider implications for other estimands such as the ATT and for approximate balancing weights. We demonstrate our approach through simulation and re-analysis of multiple empirical studies.