Applied work often studies the effect of a binary variable (“treatment”) using linear models with additive effects. I study the interpretation of the OLS estimands in such models when treatment effects are heterogeneous. I show that the treatment coefficient is a convex combination of two parameters, which under certain conditions can be interpreted as the average treatment effects on the treated and untreated. The weights on these parameters are inversely related to the proportion of observations in each group. Reliance on these implicit weights can have serious consequences for applied work, as I illustrate with two well-known applications. I develop simple diagnostic tools that empirical researchers can use to avoid potential biases. Software for implementing these methods is available in R and Stata. In an important special case, my diagnostics only require the knowledge of the proportion of treated units.

中文翻译：

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当治疗效果异质时解释 OLS 估计值：较小的群体获得较大的权重

应用工作通常使用具有累加效应的线性模型来研究二元变量（“处理”）的影响。当治疗效果异质时，我研究了此类模型中 OLS 估计量的解释。我表明处理系数是两个参数的凸组合，在某些条件下可以解释为处理和未处理的平均处理效果。这些参数的权重与每组中的观察比例成反比。依赖这些隐含的权重会对应用工作产生严重的后果，正如我用两个众所周知的应用程序所说明的那样。我开发了简单的诊断工具，经验研究人员可以使用这些工具来避免潜在的偏见。实现这些方法的软件在 R 和 Stata 中可用。在一个重要的特殊情况下，