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 should not be interpreted as percentage effects. In line with this result, we find that estimated treatment effects for $\mathrm{arcsinh}$-transformed outcomes published in the American Economic Review change substantially when we multiply the units of the outcome by 100 (e.g., convert dollars to cents). To help delineate alternative approaches, we prove that when the outcome can equal zero, there is no average treatment effect of the form $E_P[g(Y(1),Y(0))]$ that is point-identified and unit-invariant. We conclude by discussing sensible alternative target parameters for settings with zero-valued outcomes that relax at least one of these requirements.

翻译：经济学家经常对结果变量的变换形式（这些变换在零处有定义，且当y较大时表现类似于log(y)，例如log(1+y)、arcsinh(y)）估计平均处理效应（ATE）。我们证明这些ATE任意依赖于结果变量的单位，因此不应被解释为百分比效应。与此结论一致的是，我们发现美国经济评论（American Economic Review）中发表的基于arcsinh变换结果的估计处理效应，在将结果变量单位乘以100（例如将美元转换为美分）时发生了显著变化。为厘清替代方法，我们证明当结果变量可能为零时，不存在形如E_P[g(Y(1),Y(0))]且可点识别且单位不变的平均处理效应。最后，我们针对零值结果变量的情景，讨论放宽至少一个约束条件的合理替代目标参数。