Primary Submission Category: Weighting
Semiparametric inference for sample treatment effects on the treated
Authors: Andrew Yiu,
Presenting Author: Andrew Yiu*
Causal effects are most often defined in terms of a target superpopulation from which the observed data were drawn. This includes classic estimands such as the (population) average treatment effect on the treated (ATT). A possible alternative is to replace certain components of the population estimand with their sample analogues–for instance, we could define our causal effect by averaging over the observed covariates in the sample rather than over the unknown superpopulation covariate distribution. This could be implemented after the sample characteristics have been adjudged to be adequately representative of the target population. An advantage of these sample estimands is that we can estimate them more precisely than their population counterparts (i.e. smaller asymptotic variances, tighter confidence sets). Despite this, the theory for treatment effects on the treated is underdeveloped. We fill this gap by categorizing the family of sample estimands and establishing asymptotic properties with respect to a semiparametric efficient estimator. Our results include some surprising findings: the asymptotic variance of the popular “sample treatment effect on the treated” (SATT) is point-identified and can hypothetically exceed that of its population ATT counterpart; we also introduce a new estimand that can always be estimated at least as efficiently as both the ATT and the SATT.