{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T11:01:50Z","timestamp":1761649310742,"version":"3.40.5"},"reference-count":38,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T00:00:00Z","timestamp":1709769600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:p>This paper proposes a nonparametric test to assess whether there exist heterogeneous quantile treatment effects (QTEs) of an intervention on the outcome of interest across different sub-populations defined by covariates of interest. Specifically, a consistent test statistic based on the Cram\u00e9r\u2013von Mises type criterion is developed to test if the treatment has a constant quantile effect for all sub-populations defined by covariates of interest. Under some regularity conditions, the asymptotic behaviors of the proposed test statistic are investigated under both the null and alternative hypotheses. Furthermore, a nonparametric Bootstrap procedure is suggested to approximate the finite-sample null distribution of the proposed test; then, the asymptotic validity of the proposed Bootstrap test is theoretically justified. Through Monte Carlo simulations, we demonstrate the power properties of the test in finite samples. Finally, the proposed testing approach is applied to investigate whether there exists heterogeneity for the QTE of maternal smoking during pregnancy on infant birth weight across different age groups of mothers.<\/jats:p>","DOI":"10.1017\/s0266466624000045","type":"journal-article","created":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T10:20:01Z","timestamp":1709806801000},"page":"660-687","source":"Crossref","is-referenced-by-count":2,"title":["A NONPARAMETRIC TEST OF HETEROGENEITY IN CONDITIONAL QUANTILE TREATMENT EFFECTS"],"prefix":"10.1017","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8988-8779","authenticated-orcid":false,"given":"Zongwu","family":"Cai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2621-6216","authenticated-orcid":false,"given":"Ying","family":"Fang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ming","family":"Lin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengfang","family":"Tang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2024,3,7]]},"reference":[{"key":"S0266466624000045_r12","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1111\/j.1468-0262.2005.00570.x","article-title":"An IV model of quantile treatment effects","volume":"73","author":"Chernozhukov","year":"2005","journal-title":"Econometrica"},{"key":"S0266466624000045_r26","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1111\/1468-0262.00442","article-title":"Efficient estimation of average treatment effects using the estimated propensity score","volume":"71","author":"Hirano","year":"2003","journal-title":"Econometrica"},{"key":"S0266466624000045_r31","unstructured":"Lee, S. , Song, K. , & Whang, Y.-J. 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