Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights

• 成果类型: Article
• 署名作者: Sloczynski, Tymon
• 署名单位: Brandeis University
• 刊物名称: REVIEW OF ECONOMICS AND STATISTICS
• ISSN/ISSBN: 0034-6535
• DOI: 10.1162/rest_a_00953
• 发表日期: 2022-05
• 页码: 501-509
• 关键词: origins; IMPACT

摘要

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.