arXiv 11 Sep 2019 · Econometrics · publishedJournal of Econometrics (2021) · 10 citations (OpenAlex)
arXiv:1909.05093 · PDF · DOI · OpenAlex · Extracted main text
We analyze the properties of matching estimators when there are few treated, but many control observations. We show that, under standard assumptions, the nearest neighbor matching estimator for the average treatment effect on the treated is asymptotically unbiased in this framework. However, when the number of treated observations is fixed, the estimator is not consistent, and it is generally not asymptotically normal. Since standard inference methods are inadequate, we propose alternative inference methods, based on the theory of randomization tests under approximate symmetry, that are asymptotically valid in this framework. We show that these tests are valid under relatively strong assumptions when the number of treated observations is fixed, and under weaker assumptions when the number of treated observations increases, but at a lower rate relative to the number of control observations.
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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 | Otsu, T. and Rai, Y (2017) Bootstrap inference of matching estimators for average treatment effects | 0.843 | 5 | 4 | 60% |
| 2 | Canay, I. A., Romano, J. P., and Shaikh, A. M (2017) Randomization tests under an approximate symmetry assumption | 0.830 | 7 | 4 | 57% |
| 3 | Heckman, J. J., Ichimura, H., and Todd, P. E (1997) Matching as an econometric evaluation estimator: Evidence from evaluating a job training programme | 0.644 | 2 | 2 | 100% |
| 4 | Conley, T. G. and Taber, C. R (2011) Inference with Difference in Differences with a Small Number of Policy Changes | 0.511 | 4 | 2 | 25% |
| 5 | Huber, M., Lechner, M., and Wunsch, C (2013) The performance of estimators based on the propensity score | 0.511 | 2 | 2 | 50% |
| 6 | Smith, J. A. and Todd, P. E (2001) Reconciling conflicting evidence on the performance of propensity-score matching methods | 0.511 | 2 | 1 | 100% |
| 7 | Abadie, A. and Imbens, G. W (2011) Bias-corrected matching estimators for average treatment effects | 0.511 | 2 | 1 | 100% |
| 8 | Abadie, A., Diamond, A., and Hainmueller, J (2010) Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program | 0.511 | 2 | 1 | 100% |
| 9 | Imbens, G. and Wooldridge, J (2009) Recent developments in the econometrics of program evaluation | 0.511 | 2 | 1 | 100% |
| 10 | Armstrong, T. B. and Kolesár, M (2021) Finite-sample optimal estimation and inference on average treatment effects under unconfoundedness | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 45 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Inference with few treated units | 0.693 | 6 | 1 |
| 2 | Randomization Inference Tests for Shift-Share Designs | 0.405 | 1 | 1 |