arXiv 15 Nov 2023 · Econometrics
arXiv:2311.09435 · PDF · DOI · OpenAlex · Extracted main text
Many causal parameters depend on a moment of the joint distribution of potential outcomes. Such parameters are especially relevant in policy evaluation settings, where noncompliance is common and accommodated through the model of Imbens & Angrist (1994). This paper shows that the sharp identified set for these parameters is an interval with endpoints characterized by the value of optimal transport problems. Sample analogue estimators are proposed based on the dual problem of optimal transport. These estimators are root-n consistent and converge in distribution under mild assumptions. Inference procedures based on the bootstrap are straightforward and computationally convenient. The ideas and estimators are demonstrated in an application revisiting the National Supported Work Demonstration job training program. I find suggestive evidence that workers who would see below average earnings without treatment tend to see above average benefits from treatment.
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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, A (2003) Semiparametric instrumental variable estimation of treatment response models | 0.874 | 5 | 2 | 100% |
| 2 | Imbens, G. W., & Angrist, J. D (1994) Identification and estimation of local average treatment effects | 0.843 | 3 | 3 | 100% |
| 3 | Fan, Y., & Park, S. S (2010) Sharp bounds on the distribution of treatment effects and their statistical inference | 0.644 | 2 | 2 | 100% |
| 4 | Firpo, S., & Ridder, G (2019) Partial identification of the treatment effect distribution and its functionals | 0.644 | 2 | 2 | 100% |
| 5 | Villani, C (2009) Optimal transport: old and new\/, vol. 338 | 0.550 | 6 | 3 | 17% |
| 6 | Staudt, T., Hundrieser, S., & Munk, A (2022) On the uniqueness of kantorovich potentials | 0.511 | 3 | 2 | 33% |
| 7 | Heckman, J. J., Smith, J., & Clements, N (1997) Making the most out of programme evaluations and social experiments: Accounting for heterogeneity in programme impacts | 0.511 | 2 | 1 | 100% |
| 8 | Ji, W., Lei, L., & Spector, A (2023) Model-agnostic covariate-assisted inference on partially identified causal effects | 0.511 | 2 | 1 | 100% |
| 9 | Allcott, H., Braghieri, L., Eichmeyer, S., & Gentzkow, M (2020) The welfare effects of social media | 0.405 | 1 | 1 | 100% |
| 10 | Callaway, B (2021) Bounds on distributional treatment effect parameters using panel data with an application on job displacement | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 39 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Generalized Optimal Transport | 0.941 | 6 | 3 |
| 2 | Model-Agnostic Covariate-Assisted Inference on Partially Identified Causal Effects | 0.405 | 1 | 1 |
| 3 | An econometrician's guide to optimal transport | 0.405 | 1 | 1 |
| 4 | Partial Identification of Policy-Relevant Treatment Effects with Instrumental Variables via Optimal Transport | 0.405 | 1 | 1 |