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

By Tymon Słoczyński. Review of Economics and Statistics, 2018

77 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e60d86f29ee22edbec1b7fbfea26e082c0a9ec33

Citations in the corpus

• Quantifying Positional Biases in Text Embedding Models (2024, unknown): “Our model choice is notable for its direct interpretability [25], though we acknowledge and check for potential issues posed by OLS, such as multicollinearity.”