Heterogeneous treatment effects: what does a regression estimate?

Regressions that control for confounding factors are the workhorse of evaluation research. When treatment effects are heterogeneous, however, the workhorse regression leads to estimated treatment effects that lack behavioral interpretations even when the selection on observables assumption holds. Regressions that use propensity scores as weights and regressions based on random coefficients or hierarchical models provide alternative estimators that have clear behavioral interpretations. Assuming selection on the observables and heterogeneous treatment effects, this article (a) shows what is identified as the treatment effect in the workhorse model, (b) shows what is identified as the treatment effect by propensity score models and models based on random coefficients/ hierarchical models, and (c) provides advice for evaluators.