{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T21:19:35Z","timestamp":1790025575345,"version":"4.0.1"},"reference-count":27,"publisher":"The Econometric Society","issue":"3","license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>In this paper, we study the estimation and inference of the quantile treatment effect under covariate\u2010adaptive randomization. We propose two estimation methods: (1) the simple quantile regression and (2) the inverse propensity score weighted quantile regression. For the two estimators, we derive their asymptotic distributions uniformly over a compact set of quantile indexes, and show that, when the treatment assignment rule does not achieve strong balance, the inverse propensity score weighted estimator has a smaller asymptotic variance than the simple quantile regression estimator. For the inference of method (1), we show that the Wald test using a weighted bootstrap standard error underrejects. But for method (2), its asymptotic size equals the nominal level. We also show that, for both methods, the asymptotic size of the Wald test using a covariate\u2010adaptive bootstrap standard error equals the nominal level. We illustrate the finite sample performance of the new estimation and inference methods using both simulated and real datasets.<\/jats:p>","DOI":"10.3982\/qe1323","type":"journal-article","created":{"date-parts":[[2020,7,16]],"date-time":"2020-07-16T06:48:03Z","timestamp":1594882083000},"page":"957-982","source":"Crossref","is-referenced-by-count":23,"title":["Quantile treatment effects and bootstrap inference under covariate\u2010adaptive randomization"],"prefix":"10.3982","volume":"11","author":[{"given":"Yichong","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Economics, Singapore Management University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xin","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Economics, Singapore Management University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2020]]},"reference":[{"key":"quan200096-bib-0001","doi-asserted-by":"crossref","DOI":"10.2307\/j.ctvcm4j72","volume-title":"Mostly Harmless Econometrics: An Empiricist's Companion","author":"Angrist","year":"2008"},{"issue":"1","key":"quan200096-bib-0002","first-page":"22","volume":"7","author":"Banerjee","year":"2015","journal-title":"American Economic Journal: Applied Economics"},{"issue":"4","key":"quan200096-bib-0003","first-page":"200","volume":"1","author":"Bruhn","year":"2009","journal-title":"American Economic Journal: Applied Economics"},{"issue":"524","key":"quan200096-bib-0004","doi-asserted-by":"crossref","first-page":"1741","DOI":"10.1080\/01621459.2017.1375934","volume":"113","author":"Bugni","year":"2018","journal-title":"Journal of the American Statistical Association"},{"issue":"4","key":"quan200096-bib-0005","doi-asserted-by":"crossref","first-page":"1747","DOI":"10.3982\/QE1150","volume":"10","author":"Bugni","year":"2019","journal-title":"Quantitative Economics"},{"issue":"3","key":"quan200096-bib-0006","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1162\/rest_a_00695","volume":"100","author":"Byrne","year":"2018","journal-title":"Review of Economics and Statistics"},{"issue":"4","key":"quan200096-bib-0007","doi-asserted-by":"crossref","first-page":"1564","DOI":"10.1214\/14-AOS1230","volume":"42","author":"Chernozhukov","year":"2014","journal-title":"The Annals of Statistics"},{"issue":"4","key":"quan200096-bib-0008","first-page":"222","volume":"8","author":"Chong","year":"2016","journal-title":"American Economic Journal: Applied Economics"},{"issue":"1","key":"quan200096-bib-0009","first-page":"123","volume":"7","author":"Cr\u00e9pon","year":"2015","journal-title":"American Economic Journal: Applied Economics"},{"issue":"2","key":"quan200096-bib-0010","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1214\/aos\/1176342662","volume":"2","author":"Doksum","year":"1974","journal-title":"The Annals of Statistics"},{"key":"quan200096-bib-0011","doi-asserted-by":"crossref","first-page":"3895","DOI":"10.1016\/S1573-4471(07)04061-2","volume":"4","author":"Duflo","year":"2007","journal-title":"Handbook of Development Economics"},{"issue":"4","key":"quan200096-bib-0012","doi-asserted-by":"crossref","first-page":"1499","DOI":"10.1093\/qje\/qjt024","volume":"128","author":"Duflo","year":"2013","journal-title":"The Quarterly Journal of Economics"},{"issue":"3","key":"quan200096-bib-0013","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1093\/biomet\/58.3.403","volume":"58","author":"Efron","year":"1971","journal-title":"Biometrika"},{"issue":"1","key":"quan200096-bib-0014","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1111\/j.1468-0262.2007.00738.x","volume":"75","author":"Firpo","year":"2007","journal-title":"Econometrica"},{"issue":"1","key":"quan200096-bib-0015","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1198\/jbes.2009.08161","volume":"29","author":"Hahn","year":"2011","journal-title":"Journal of Business & Economic Statistics"},{"issue":"2","key":"quan200096-bib-0016","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1017\/jpr.2016.3","volume":"53","author":"Hu","year":"2016","journal-title":"Journal of Applied Probability"},{"issue":"3","key":"quan200096-bib-0017","doi-asserted-by":"crossref","first-page":"1794","DOI":"10.1214\/12-AOS983","volume":"40","author":"Hu","year":"2012","journal-title":"The Annals of Statistics"},{"key":"quan200096-bib-0018","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139025751","volume-title":"Causal Inference in Statistics, Social, and Biomedical Sciences","author":"Imbens","year":"2015"},{"key":"quan200096-bib-0019","unstructured":"Ma, W., Y. 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