Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting

By Kwun Chuen Gary Chan, Sheung Chi Phillip Yam, Zheng Zhang. 2015

235 citations recorded by the source corpus.

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 function, we consider a wide class of 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 the 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 variance estimator proposed outperforms existing estimators that require a direct approximation of the efficient influence function.

Subfields: Statistics and Probability

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Citations in the corpus

Approximate residual balancing: debiased inference of average treatment effects in high dimensions (2016, methodology): “This approach also bears a close conceptual connection to work by Chan et al. (2015), Deville and Särndal (1992), Graham et al. (2012, 2016), Hainmueller (2012), Hellerstein and Imbens (1999), Imai and Ratkovic (2014) and Zhao (2016), who effectively fit propensity models to the data under a constra”
Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations (2017, methodology): “This result is related to Chan et al. (2016), Fan et al.”
Matching for Balance (2019, background): “Examples of weighting methods for covariate balance include Hainmueller (2012), Imai and Ratkovic (2014), Zubizarreta (2015), Chan et al. (2016), Fan et al. (2016), Zhao and Percival (2017), Athey et al. (2018), Hirshberg and Wager (2018), Zhao (2019), and Wang and Zubizarreta (2017).”
Covariate balancing propensity score by tailored loss functions (2016, methodology): “To derive design-based inference of WATE, we assume strong ignorability (Assumption 1) and Yi ∼ N(gTi(Xi), σ2).”
Entropy Balancing is Doubly Robust (2015, background): “The primal optimization problem of EB amounts to an empirical calibration estimator (Deville and Särndal, 1992; Särndal and Lundström, 2005), which is widely popular in survey sampling but perhaps not sufficiently recognized in causal inference (Chan et al., 2015).”
Propensity Score Weighting for Causal Inference with Clustered Data (2017, background): “Chan et al. (2015) showed that estimation of average treatment effects by empirical balancing calibration weighting can achieve global efficiency.”
A unifying approach for doubly-robust $\ell_1$ regularized estimation of causal contrasts (2019, methodology): “For parameters in the Chernozhukov et al. (2018b) class for which, as indicated earlier, one of the nuisance functions is the conditional mean of an outcome on covariates, our specially chosen loss function yields the usual `1 penalized least squares of this nuisance function when the working model ”
Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data (2018, background): “where φ() is defined in (7), π̂0 RCAL(X) = π(X; γ̂ 0 RCAL), m̂ 0 RWL(X) = m0(X; α̂ 0 RWL), and γ̂0 RCAL and α̂ 0 RWL are defined as follows.”
Robust Estimation of Causal Effects via High-Dimensional Covariate Balancing Propensity Score. (2018, methodology): “…by optimizing covariate balance between the treatment and control groups (e.g., Hainmueller, 2012; Graham et al., 2012; Imai & Ratkovic, 2014; Chan et al., 2016; Zubizarreta, 2015; Zhao, 2019; Fan et al., 2016).80 The proposed methodology extends the covariate balancing propensity score of…”
Covariate balancing propensity score for a continuous treatment: Application to the efficacy of political advertisements (2018, background): “In recent years, several researchers have proposed methods that estimate propensity scores by optimizing covariate balance (e.g., McCaffrey et al., 2004; Tan, 2010; Hainmueller, 2012; Graham et al., 2012; Imai and Ratkovic, 2014; Chan et al., 2015; Hazlett, 2016; Fan et al., 2016; Zhao, 2016).”
The Balancing Act in Causal Inference (2021, result): “Examples of proposals in line with this approach include Athey et al. (2018), Breidt, Opsomer, et al. (2017), Chan et al. (2016), Deville and Särndal (1992), Graham et al. (2012), Hainmueller (2012), Hirshberg and Wager (2018), Imai and Ratkovic (2014), Kallus (2020), Li et al. (2018), Tan (2020),…”
Augmented minimax linear estimation (2017, methodology): “…there has been considerable interest in practical methodologies that emphasize balance when paired with AIPW methodology (Athey et al., 2016; Chan et al., 2015; Graham et al., 2012, 2016; Hainmueller, 2012; Hirano et al., 2001, 2003; shows that our weights γ̂ will, if our tuning parameter σ…”