New Evidence on Linear Regression and Treatment Effect Heterogeneity

Arbeitspapier

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.

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• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: IZA Discussion Papers ; No. 9491

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Single Equation Models; Single Variables: Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions ; Model Evaluation, Validation, and Selection ; Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior ; Empirical Studies of Trade ; Formal and Informal Sectors; Shadow Economy; Institutional Arrangements
• Thema: heterogeneity ; linear regression ; ordinary least squares ; propensity score ; treatment effects

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Sloczynski, Tymon
• Ereignis: Veröffentlichung
• (wer): Institute for the Study of Labor (IZA)
• (wo): Bonn
• (wann): 2015

Weitere Informationen

• Handle: http://hdl.handle.net/10419/125005