Globally Efficient Non-Parametric Inference of Average Treatment Effects by Empirical Balancing Calibration Weighting

Abstract

Summary The estimation of average treatment effects based on observational data is extremely important in practice and has been studied by generations of statisticians under different frameworks. Existing globally efficient estimators require non-parametric estimation of a propensity score function, an outcome regression function or both, but their performance can be poor in practical sample sizes. Without explicitly estimating either functions, we consider a wide class calibration weights constructed to attain an exact three-way balance of the moments of observed covariates among the treated, the control, and the combined group. The wide class includes exponential tilting, empirical likelihood and generalized regression as important special cases, and extends survey calibration estimators to different statistical problems and with important distinctions. Global semiparametric efficiency for the estimation of average treatment effects is established for this general class of calibration estimators. The results show that efficiency can be achieved by solely balancing the covariate distributions without resorting to direct estimation of propensity score or outcome regression function. We also propose a consistent estimator for the efficient asymptotic variance, which does not involve additional functional estimation of either the propensity score or the outcome regression functions. The proposed variance estimator outperforms existing estimators that require a direct approximation of the efficient influence function.

Approximate Residual Balancing: Debiased Inference of Average Treatment Effects in High Dimensions

“…Our approximately balancing weights (5) are inspired by the recent literature on balancing weights (Chan et al ., ; Deville and Särndal, ; Graham et al ., ; Hainmueller, ; Hellerstein and Imbens, ; Hirano et al ., ; Imai and Ratkovic, ; Zhao, ). Most closely related, Zubizarreta () proposed to estimate τ by using the reweighting formula as in Section 2.2.1 with weightswhere the tuning parameter is t ; he called these weights stable balancing weights .…”

“…The finding that weights designed to achieve balance perform better than weights based on the propensity score is consistent with findings in Chan et al . (), Graham et al . (), Hainmueller (), Imai and Ratkovic () and Zubizarreta ().…”

“…The methods that were considered by Chan et al . (), Graham et al . (), Hainmueller (), Zubizarreta (), etc.…”

“…This approach also bears a close conceptual connection to work by Chan et al . (), Deville and Särndal (), Graham et al . (), Hainmueller (), Hellerstein and Imbens (), Imai and Ratkovic () and Zhao (), who fitted propensity models to the data under a constraint that the resulting inverse propensity weights exactly balance the covariate distributions between the treatment and control groups and found that these methods outperform propensity‐based methods that do not impose balance.…”

The Right Tool for the Job

“…Several other techniques similar to the covariate balancing propensity method that estimate propensity score weights with methods beyond logistic regression have been proposed 22;23;24 . Many of them design weights that are not equal to the inverse of the propensity score but are chosen explicitly to optimize balance between the covariate distributions in the exposed and control groups.…”