Carolina Caetano, Gregorio Caetano, Leonard Goff, Eric Nielsen
arXiv 7 Jul 2025 · Econometrics
arXiv:2507.05210 · PDF · OpenAlex · Extracted main text
We show that causal effects can be identified when there is bunching in the distribution of a continuous treatment variable, without imposing any parametric assumptions. This yields a new nonparametric method for overcoming selection bias in the absence of instrumental variables, panel data, or other popular research designs for causal inference. The method leverages the change of variables theorem from integration theory, relating the selection bias to the ratio of the density of the treatment and the density of the part of the outcome that varies with confounders. At the bunching point, the treatment level is constant, so the variation in the outcomes is due entirely to unobservables, allowing us to identify the denominator. Our main result identifies the average causal response to the treatment among individuals who marginally select into the bunching point. We further show that under additional smoothness assumptions on the selection bias, treatment effects away from the bunching point may also be identified. We propose estimators based on standard software packages and apply the method to estimate the effect of maternal smoking during pregnancy on birth weight.
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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 | Caetano, C (2015) A Test of Exogeneity Without Instrumental Variables in Models With Bunching self | 1.000 | 7 | 4 | 100% |
| 2 | Almond, D., Chay, K. Y., and Lee, D. S (2005) The Costs of Low Birth Weight | 0.969 | 11 | 3 | 91% |
| 3 | Goff, L (2023) Treatment Effects in Bunching Designs: The Impact of Mandatory Overtime Pay on Hours self | 0.928 | 4 | 3 | 100% |
| 4 | Pinkse, J. and Schurter, K (2023) Estimates of Derivatives of (Log) Densities and Related Objects | 0.874 | 6 | 2 | 100% |
| 5 | Schennach, S (2022) Measurement systems | 0.843 | 4 | 4 | 75% |
| 6 | Caetano, C., Caetano, G., and Nielsen, E (2024) Correcting for Endogeneity in Models with Bunching self | 0.843 | 4 | 3 | 75% |
| 7 | Bertanha, M., Caetano, C., Jales, H., and Seegert, N (2024) Bunching Estimation Methods self | 0.843 | 3 | 3 | 100% |
| 8 | Schennach, S. M (2019) Convolution Without Independence | 0.737 | 3 | 2 | 100% |
| 9 | Caetano, C., Caetano, G., Nielsen, E., and Techio, O (2024) Partial Identification in Models with Bunching self | 0.644 | 2 | 2 | 100% |
| 10 | Bertanha, M., McCallum, A. H., and Seegert, N (2023) Better Bunching, Nicer Notching | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 65 scored citations.