Economists frequently estimate average treatment effects (ATEs) for transformations of the outcome that are well-defined at zero but behave like $\log(y)$ when $y$ is large (e.g., $\log(1+y)$, $\mathrm{arcsinh}(y)$). We show that these ATEs depend arbitrarily on the units of the outcome, and thus cannot be interpreted as percentage effects. Moreover, we prove that when the outcome can equal zero, there is no parameter of the form $E_P[g(Y(1),Y(0))]$ that is point-identified and unit-invariant. We discuss sensible alternative target parameters for settings with zero-valued outcomes that relax at least one of these requirements.

翻译：经济学家经常估计结果变异的平均治疗效果(ATE),这些结果定义明确为零,但当美元数额很大(例如$\log(1+y),$\mathrm{arcsinh}(y)美元)时,其表现方式像$\log(y)美元。我们发现,这些ATE任意依赖结果的单位,因此不能被解释为百分比效应。此外,我们证明,当结果等于零时,没有美元[(Y(1),Y(0)]表格的参数,而美元则是点名和单位变量。我们讨论了具有零价值结果的环境的合理替代目标参数,这些结果至少可以放松其中一项要求。