Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/219149 
Year of Publication: 
2020
Series/Report no.: 
CESifo Working Paper No. 8331
Publisher: 
Center for Economic Studies and Ifo Institute (CESifo), Munich
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 only require the knowledge of the proportion of treated units.
Subjects: 
heterogeneity
linear regression
model diagnostics
model misspecification
ordinary least squares
propensity score
treatment effects
JEL: 
C21
C31
Document Type: 
Working Paper
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