Daisuke Kurisu, Yuta Okamoto, Taisuke Otsu
arXiv 1 Aug 2026 · Econometrics
arXiv:2608.00772 · PDF · Extracted main text
Monotone treatment response (MTR), monotone treatment selection (MTS), and monotone instrumental variable (MIV) assumptions are widely used to partially identify counterfactual mean outcomes, but existing analyses have focused almost exclusively on scalar outcomes. We develop a unified framework for partial identification with outcomes that take values in a general metric space under these monotonicity restrictions by embedding the metric space into an $L^2$ space and imposing coordinatewise monotonicity on the embedded functions. The proposed framework yields valid identified sets for Fréchet means in a broad class of random-object spaces and further delivers sharp identification results for distributional outcomes under the Wasserstein metric, interval-valued outcomes represented by support functions, and compositional outcomes under the Aitchison metric. We also establish a support-free characterization of the identified set under the joint MTR--MTS assumption. Numerical and empirical illustrations based on Job Corps earnings data and periodontal health distributions from the National Health and Nutrition Examination Survey demonstrate the empirical usefulness of the proposed framework.
appendix boundary found by appendix_command · 54% of the source is main text. Read the extracted text to check this.
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 | Manski, Charles F. and Pepper, John V (2000) Monotone Instrumental Variables: With an Application to the Returns to Schooling | 0.977 | 15 | 6 | 93% |
| 2 | Charles F. Manski (1997) Monotone Treatment Response | 0.950 | 7 | 4 | 86% |
| 3 | Wooyoung Kim AND Koohyun Kwon AND Soonwoo Kwon AND Sokbae Lee (2018) The identification power of smoothness assumptions in models with counterfactual outcomes | 0.874 | 5 | 2 | 100% |
| 4 | Kurisu, Daisuke and Okamoto, Yuta and Otsu, Taisuke (2025) Random sets from the perspective of metric statistics self | 0.811 | 4 | 2 | 100% |
| 5 | Richard Blundell AND Amanda Gosling AND Hidehiko Ichimura AND Costas… (2007) Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds | 0.737 | 3 | 2 | 100% |
| 6 | Aitchison, John (1982) The statistical analysis of compositional data | 0.644 | 2 | 2 | 100% |
| 7 | Bigot, Jérémie and Gouet, Raúl and Klein, Thierry and López, Alfredo (2017) Geodesic PCA in the Wasserstein space by convex PCA | 0.644 | 2 | 2 | 100% |
| 8 | Manski, Charles F. and Tamer, Elie (2002) Inference on Regressions with Interval Data on a Regressor or Outcome | 0.644 | 2 | 2 | 100% |
| 9 | Kurisu, Daisuke and Okamoto, Yuta and Otsu, Taisuke (2026) Lee Bounds for Random Objects self | 0.644 | 2 | 2 | 100% |
| 10 | Beresteanu, Arie and Molinari, Francesca (2008) Asymptotic properties for a class of partially identified models | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 28 scored citations.