Semiparametric Estimation of Treatment Effects in Randomized Experiments
Abstract
We develop new semiparametric methods for estimating treatment effects. We
focus on a setting where the outcome distributions may be thick tailed, where treatment
effects are small, where sample sizes are large and where assignment is completely random. This setting is of particular interest in recent experimentation in tech companies.
We propose using parametric models for the treatment effects, as opposed to parametric models for the full outcome distributions. This leads to semiparametric models for
the outcome distributions. We derive the semiparametric efficiency bound for this setting,
and propose efficient estimators. In the case with a constant treatment effect one of the
proposed estimators has an interesting interpretation as a weighted average of quantile
treatment effects, with the weights proportional to (minus) the second derivative of the log
of the density of the potential outcomes. Our analysis also results in an extension of Huber’s model and trimmed mean to include asymmetry and a simplified condition on linear
combinations of order statistics, which may be of independent interest.
focus on a setting where the outcome distributions may be thick tailed, where treatment
effects are small, where sample sizes are large and where assignment is completely random. This setting is of particular interest in recent experimentation in tech companies.
We propose using parametric models for the treatment effects, as opposed to parametric models for the full outcome distributions. This leads to semiparametric models for
the outcome distributions. We derive the semiparametric efficiency bound for this setting,
and propose efficient estimators. In the case with a constant treatment effect one of the
proposed estimators has an interesting interpretation as a weighted average of quantile
treatment effects, with the weights proportional to (minus) the second derivative of the log
of the density of the potential outcomes. Our analysis also results in an extension of Huber’s model and trimmed mean to include asymmetry and a simplified condition on linear
combinations of order statistics, which may be of independent interest.
Research Areas
