Primary Submission Category: Matching, Weighting
Weighted average treatment effect with unknown weights
Authors: Georgy Kalashnov,
Presenting Author: Georgy Kalashnov*
I derive semi-parametrically efficient estimate of a weighted average treatment effect, where weights depend on the data generating process and therefore are unknown. Examples of such estimates include average treatment on the treated, overlap weights. The need to (whether explicitly, or implicitly) estimate the weights restricts the outcome adjustment function we can use to keep the efficiency. E.g. for ATE we should use the prediction of the countrerfactual that is not observed as an adjustment function, for ATT — the prediction of control outcome, for overlap weights, the prediction of observed Y. This restriction creates three interpretable terms in the asymptotic variance of the estimate: a weighted variance of the idiosyncratic error, a (weighted) variance of the conditional average treatment effect, and most importantly, the systematic error created by the forced choice of adjustment function. This results is useful in several ways: 1) it nests and extends a large number of results, which either concentrate on some specific weights, e.g. Hahn (1998), Freedman (2009), Lin (2013), or on a known weighting function, e.g. Li, Morgan, Zaslavsky (2018), Chernozhukov, Newey, Singh (2022) 2) it allows to inform bias variance tradeoff in the task of choosing an estimand to pursue (e.g. should we use ATE or ATT, or overlap weights), under different additional assumptions on the data generating process.