Słoczyński, Tymon (2014): New Evidence on Linear Regression and Treatment Effect Heterogeneity.
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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 threestep 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 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 devastating consequences for applied work. To illustrate the severity of this issue, I perform Monte Carlo simulations as well as replicate two prominent 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 MartinezBravo (2014) on the effects of appointed officials on villagelevel electoral results in Indonesia. In both cases some of the conclusions change dramatically after allowing for heterogeneity in effects.
Item Type:  MPRA Paper 

Original Title:  New Evidence on Linear Regression and Treatment Effect Heterogeneity 
Language:  English 
Keywords:  treatment effects; linear regression; ordinary least squares; heterogeneity 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C31  CrossSectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions ; Social Interaction Models C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C21  CrossSectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  60810 
Depositing User:  Tymon Słoczyński 
Date Deposited:  21. Dec 2014 16:47 
Last Modified:  08. Jan 2015 19:23 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/60810 
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New Evidence on Linear Regression and Treatment Effect Heterogeneity. (deposited 27. Jun 2012 14:54)
 New Evidence on Linear Regression and Treatment Effect Heterogeneity. (deposited 21. Dec 2014 16:47) [Currently Displayed]