arXiv 15 Jul 2026 · Econometrics
arXiv:2607.14414 · PDF · DOI · OpenAlex · Extracted main text
Experiments may, by design, prevent one from observing on a single subject both the response to a treatment and to its absence. Because of this, marginal distributions for both cases may be observable but not their joint distribution, thus obscuring the distribution of the treatment effect. We examine the case where we impose that the treatment effect is nonnegative, also called monotone treatment response, a common assumption relevant to many practical applications. We solve the problems of best- and worst-case probabilities that the treatment effect exceeds a given value, using an explicit construction for the dependence scheme in each case. Such problems can equivalently be described, in different contexts, as risk aggregation under dependence uncertainty and an order constraint, and as optimal transport with a particular cost function.
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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 | Nutz, M. and Wang, R (2022) The directional optimal transport self | 0.737 | 5 | 4 | 40% |
| 2 | Arnold, S., Molchanov, I. and Ziegel, J. F (2020) Bivariate distributions with ordered marginals | 0.737 | 3 | 3 | 67% |
| 3 | Chen, Y., Lin, L. and Wang, R (2022) Risk aggregation under dependence uncertainty and an order constraint self | 0.644 | 5 | 2 | 40% |
| 4 | Froehlich, G. W (1999) What is the chance that this study is clinically significant? A proposal for Q values | 0.644 | 4 | 1 | 100% |
| Manski | unmatched citation key Manski | 0.644 | 4 | 1 | 100% |
| 6 | Rachev, S. T. and Rüschendorf, L (2006) Mass Transportation Problems, Volume 1: Theory | 0.511 | 2 | 2 | 50% |
| 7 | Villani, C (2009) Optimal Transport: Old and New | 0.511 | 2 | 2 | 50% |
| 8 | Dawid, A. P (2000) Causal inference without counterfactuals | 0.511 | 2 | 1 | 100% |
| 9 | Dawid, A. P (2015) Statistical causality from a decision theoretic perspective | 0.511 | 2 | 1 | 100% |
| Dawid | unmatched citation key Dawid | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 93 scored citations. 2 of these could not be matched to a bibliography entry, so only the citation key is shown.