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量变换后的平均处理效应（ATEs），这些变换在零处有定义，但在 $y$ 较大时近似于 $\log(y)$（例如 $\log(1+y)$、$\mathrm{arcsinh}(y)$）。我们证明这些ATEs任意地依赖于结果的单位，因此不能解释为百分比效应。此外，我们证明当结果可能等于零时，不存在形如 $E_P[g(Y(1),Y(0))]$ 的既满足点识别又满足单位不变性的参数。我们讨论了针对零值结果场景下至少放宽其中一个要求的合理替代目标参数。