arXiv 17 Jan 2020 · Econometrics · publishedEconometrica (2023)
arXiv:2001.06118 · PDF · DOI · OpenAlex · Extracted main text
This article extends the widely-used synthetic controls estimator for evaluating causal effects of policy changes to quantile functions. The proposed method provides a geometrically faithful estimate of the entire counterfactual quantile function of the treated unit. Its appeal stems from an efficient implementation via a constrained quantile-on-quantile regression. This constitutes a novel concept of independent interest. The method provides a unique counterfactual quantile function in any scenario: for continuous, discrete or mixed distributions. It operates in both repeated cross-sections and panel data with as little as a single pre-treatment period. The article also provides abstract identification results by showing that any synthetic controls method, classical or our generalization, provides the correct counterfactual for causal models that preserve distances between the outcome distributions. Working with whole quantile functions instead of aggregate values allows for tests of equality and stochastic dominance of the counterfactual- and the observed distribution. It can provide causal inference on standard outcomes like average- or quantile treatment effects, but also more general concepts such as counterfactual Lorenz curves or interquartile ranges.
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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 | Abadie, Diamond \ Hainmueller (2010) `Synthetic control methods for comparative case studies: Estimating the effect of california's tobacco control program', Journal… | 1.000 | 14 | 5 | 100% |
| 2 | Athey \ Imbens (2006) `Identification and inference in nonlinear difference-in-differences models', Econometrica 74(2), 431–497 | 1.000 | 8 | 4 | 100% |
| 3 | Abadie, Diamond \ Hainmueller (2015) `Comparative politics and the synthetic control method', American Journal of Political Science 59(2), 495–510 | 1.000 | 7 | 5 | 100% |
| 4 | Abadie \ Gardeazabal (2003) `The economic costs of conflict: A case study of the basque country', American economic review 93(1), 113–132 | 1.000 | 6 | 3 | 100% |
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| 6 | Agueh \ Carlier (2011) `Barycenters in the wasserstein space', SIAM Journal on Mathematical Analysis 43(2), 904 – 924 | 0.928 | 4 | 3 | 100% |
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| 8 | Chen (2020) `A distributional synthetic control method for policy evaluation', Journal of Applied Econometrics 35(5), 505–525 | 0.737 | 3 | 2 | 100% |
| 9 | Gastwirth (1971) `A general definition of the lorenz curve', Econometrica: Journal of the Econometric Society pp. 1037–1039 | 0.737 | 3 | 2 | 100% |
| 10 | Hsieh \ Turnbull (1996) `Nonparametric and semiparametric estimation of the receiver operating characteristic curve', Annals of statistics 24(1), 25–40 | 0.737 | 3 | 2 | 100% |
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