Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights
研究了当处理效应存在异质性时，线性模型中OLS估计量的解释问题，发现处理系数是处理组和未处理组平均处理效应的凸组合，且权重与各组样本比例成反比，可能导致偏差，并提供了诊断工具。
Abstract 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 require only the knowledge of the proportion of treated units.