{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T11:12:02Z","timestamp":1790680322862,"version":"4.1.0"},"reference-count":40,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T00:00:00Z","timestamp":1736121600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001695","name":"JST","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001695","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100025019","name":"SPRING","doi-asserted-by":"publisher","award":["JPMJSP2110"],"award-info":[{"award-number":["JPMJSP2110"]}],"id":[{"id":"10.13039\/501100025019","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,9,22]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>In the presence of sample selection, Lee\u2019s (2009, Review of Economic Studies 76, 1071\u2013102) non-parametric bounds are a popular tool for estimating a treatment effect. However, the Lee bounds rely on the monotonicity assumption, the empirical validity of which is sometimes unclear. Furthermore, the bounds are often regarded to be wide and less informative even under monotonicity. To address these issues, this study introduces a stochastic version of the monotonicity assumption alongside a non-parametric distributional shape constraint. The former enhances the robustness of the Lee bounds with respect to monotonicity, while the latter helps tighten these bounds. The obtained bounds do not rely on the exclusion restriction and can be root-n consistently estimable, making them practically viable. The potential usefulness of the proposed methods is illustrated by their application to experimental data from an after-school instruction programme.<\/jats:p>","DOI":"10.1093\/ectj\/utaf001","type":"journal-article","created":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T15:16:44Z","timestamp":1735917404000},"page":"482-501","source":"Crossref","is-referenced-by-count":1,"title":["Robustify and tighten the Lee bounds: a sample selection model under stochastic monotonicity and symmetry assumptions"],"prefix":"10.1093","volume":"28","author":[{"given":"Yuta","family":"Okamoto","sequence":"first","affiliation":[{"name":"Graduate School of Economics, Kyoto University , Kyoto 606-8501 ,","place":["Japan"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,1,6]]},"reference":[{"key":"2026020907314993300_bib1","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1093\/restud\/rdac062","article-title":"Managerial quality and productivity dynamics","volume":"90","author":"Adhvaryu","year":"2022","journal-title":"Review of Economic Studies"},{"key":"2026020907314993300_bib2","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1086\/689774","article-title":"Stochastic choice and preferences for randomization","volume":"125","author":"Agranov","year":"2017","journal-title":"Journal of Political Economy"},{"key":"2026020907314993300_bib3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1353\/dem.0.0049","article-title":"Height and the normal distribution: evidence from Italian military data","volume":"46","author":"A\u2019Hearn","year":"2009","journal-title":"Demography"},{"key":"2026020907314993300_bib4","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1257\/aer.20180511","article-title":"Maternal depression, women\u2019s empowerment, and parental investment: evidence from a randomized controlled trial","volume":"110","author":"Baranov","year":"2020","journal-title":"American Economic Review"},{"key":"2026020907314993300_bib5","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1162\/edfp_a_00228","article-title":"Financial incentives and educational investment: the impact of performance-based scholarships on student time use","volume":"13","author":"Barrow","year":"2018","journal-title":"Education Finance and Policy"},{"key":"2026020907314993300_bib6","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/j.jeconom.2021.11.011","article-title":"Identifying marginal treatment effects in the presence of sample selection","volume":"234","author":"Bartalotti","year":"2023","journal-title":"Journal of Econometrics"},{"key":"2026020907314993300_bib7","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1086\/648995","article-title":"Why is consumption more log normal than income? 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