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 e ects denote the predominant technique to compute those e ects 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 e ects, which relies on expectile regression with its L2{loss function. It is shown, that apart from the extreme tail ends expectile treatment e ects provide more ecient estimates and these theoretical results are broadened by a simulation and subsequent analysis of the classic LaLonde data. Whereas quantile and expectile treatment e ects 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 e ects reduce the variance by more than a quarter, while at the same time smoothing the treatment e ects considerably.