New Evidence on Linear Regression and Treatment Effect Heterogeneity

Tymon Słoczyński

No 9491, IZA Discussion Papers from Institute of Labor Economics (IZA)

Abstract: It is standard practice in applied work to rely on linear least squares regression to estimate the effect of a binary variable ("treatment") on some outcome of interest. In this paper I study the interpretation of the regression estimand when treatment effects are in fact heterogeneous. I show that the coefficient on treatment is identical to the outcome of the following three-step procedure: first, calculate the linear projection of treatment on the vector of other covariates ("propensity score"); second, calculate average partial effects for both groups of interest ("treated" and "controls") from a regression of outcome on treatment, the propensity score, and their interaction; third, calculate a weighted average of these two effects, with weights being inversely related to the unconditional probability that a unit belongs to a given group. Each of these steps is potentially problematic, but this last property – the reliance on implicit weights which are inversely related to the proportion of each group – can have particularly severe consequences for applied work. To illustrate the importance of this result, I perform Monte Carlo simulations as well as replicate two applied papers: Berger, Easterly, Nunn and Satyanath (2013) on the effects of successful CIA interventions during the Cold War on imports from the US; and Martinez-Bravo (2014) on the effects of appointed officials on village-level electoral results in Indonesia. In both cases some of the conclusions change dramatically after allowing for heterogeneity in effects.

Keywords: heterogeneity; linear regression; ordinary least squares; propensity score; treatment effects (search for similar items in EconPapers)
JEL-codes: C21 C52 D72 F14 O17 (search for similar items in EconPapers)
Pages: 44 pages
Date: 2015-11
New Economics Papers: this item is included in nep-sea
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Citations: View citations in EconPapers (2)

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Working Paper: New Evidence on Linear Regression and Treatment Effect Heterogeneity (2012)
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