Primary Submission Category: Heterogeneous Treatment Effects
Adaptive experiment design for efficient semiparametric estimation in the partially linear model
Authors: Harrison Li, Art Owen,
Presenting Author: Harrison Li*
We propose an adaptive procedure to optimally choose binary treatment assignments in a multi-stage randomized experiment based on semiparametric efficient estimation in a partially linear model for heterogeneous treatment effects. The asymptotic covariance matrix of the treatment effect estimator depends on both propensity scores and nuisance functions such as conditional variances. We show that we can use data from previous stages of the experiment to consistently estimate propensity scores for future stages that optimize a scalar functional of this covariance matrix, with possible constraints on the fraction of subjects treated at each stage. Allowable functionals include standard “design criteria” from the classical theory of experiment design, such as D-optimality. With appropriate cross fitting, the data from this adaptive experiment can be used to efficiently estimate the treatment effect under weak conditions on nuisance function estimation, even if there is bounded covariate shift between stages. Here, efficiency means achieving the same first-order asymptotic behavior as a semiparametric efficient estimator that uses data collected non-adaptively according to the optimal propensity scores and knows all nuisance functions exactly. Our running example evaluates a targeting algorithm for the Reemployment Services and Eligibility Assessment (RESEA) program, a U.S. government service to help unemployment insurance recipients resume their careers.