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

Tymon Słoczyński

No 8331, CESifo Working Paper Series from CESifo

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.

Keywords: heterogeneity; linear regression; model diagnostics; model misspecification; ordinary least squares; propensity score; treatment effects (search for similar items in EconPapers)
JEL-codes: C21 C31 (search for similar items in EconPapers)
Date: 2020
New Economics Papers: this item is included in nep-ore
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Citations: View citations in EconPapers (4)

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Related works:
Journal Article: Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights (2022)
Working Paper: Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights (2020)
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