arXiv 5 Mar 2024 · Statistics — Methodology
arXiv:2403.03299 · PDF · DOI · OpenAlex · Extracted main text
Researchers frequently estimate treatment effects by regressing outcomes (Y) on treatment (D) and covariates (X). Even without unobserved confounding, the coefficient on D yields a conditional-variance-weighted average of strata-wise effects, not the average treatment effect. Scholars have proposed characterizing the severity of these weights, evaluating resulting biases, or changing investigators' target estimand to the conditional-variance-weighted effect. We aim to demystify these weights, clarifying how they arise, what they represent, and how to avoid them. Specifically, these weights reflect misspecification bias from unmodeled treatment-effect heterogeneity. Rather than diagnosing or tolerating them, we recommend avoiding the issue altogether, by relaxing the standard regression assumption of "single linearity" to one of "separate linearity" (of each potential outcome in the covariates), accommodating heterogeneity. Numerous methods--including regression imputation (g-computation), interacted regression, and mean balancing weights--satisfy this assumption. In many settings, the efficiency cost to avoiding this weighting problem altogether will be modest and worthwhile.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Winston Lin (2013) Agnostic notes on regression adjustments to experimental data: Reexamining Freedman’s critique | 1.000 | 6 | 4 | 100% |
| 2 | Peter M. Aronow and Cyrus Samii (2016) Does Regression Produce Representative Estimates of Causal Effects? | 1.000 | 6 | 3 | 100% |
| 3 | Patrick Kline (2011) Oaxaca-blinder as a reweighting estimator | 1.000 | 6 | 3 | 100% |
| 4 | Ambarish Chattopadhyay and José R Zubizarreta (2023) On the implied weights of linear regression for causal inference | 1.000 | 5 | 3 | 100% |
| 5 | Tymon Słoczyński (2022) Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights | 1.000 | 5 | 3 | 100% |
| 6 | Jinyong Hahn (2023) Properties of least squares estimator in estimation of average treatment effects | 0.928 | 4 | 3 | 100% |
| 7 | Guido W. Imbens and Jeffrey M. Wooldridge (2009) Recent Developments in the Econometrics of Program Evaluation | 0.928 | 4 | 3 | 100% |
| 8 | Joshua D. Angrist (1998) Estimating the Labor Market Impact of Voluntary Military Service Using Social Security Data on Military Applicants | 0.874 | 6 | 2 | 100% |
| 9 | Joshua D. Angrist and Jörn-Steffen Pischke (2009) Mostly Harmless Econometrics: An Empiricist's Companion | 0.874 | 6 | 2 | 100% |
| 10 | William A Belson (1956) A technique for studying the effects of a television broadcast | 0.843 | 3 | 3 | 100% |
Showing the top 10 of 39 scored citations.