Expectile treatment effects: An efficient alternative to compute the distribution of treatment effects

The distribution of treatment e ects extends the prevailing focus on average treatment e ects to the tails of the outcome variable and quantile treatment effects denote the predominant technique to compute those effects in the presence of a confounding mechanism. The underlying quantile regression is based on a L1-loss function and we propose the technique of expectile treatment effects, which relies on expectile regression with its L2-loss function. It is shown, that apart from the extreme tail ends expectile treatment effects provide more efficient estimates and these theoretical results are broadened by a simulation and subsequent analysis of the classic LaLonde data. Whereas quantile and expectile treatment effects perform comparably on extreme tail locations, the variance of the expectile variant amounts in our simulation on all other locations to less than 80% of its quantile equivalent and under favourable conditions to less than 2/3. In the LaLonde data expectile treatment effects reduce the variance by more than a quarter, while at the same time smoothing the treatment e ects considerably.