[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-201893-105":59,"doc-detail-201893-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","efficient-semiparametric-estimation-of-quantile-treatment-effects","Efficient Semiparametric Estimation of Quantile Treatment Effects","","This paper develops semiparametric efficiency bounds for quantile treatment effects when treatment assignment depends on observable characteristics. It proposes three two-step estimation procedures combining nonparametric estimation with a difference between solutions to two distinct minimization problems. For one estimator, the work establishes Root-N consistency, asymptotic normality, and attainment of the semiparametric efficiency bound. The empirical application to job training highlights heterogeneous effects concentrated in upper earnings quantiles.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/efficient-semiparametric-estimation-of-quantile-treatment-effects/201893/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/efficient-semiparametric-estimation-of-quantile-treatment-effects/201893.png","ImageObject",300,407,{"name":92,"@type":93},"Rowan","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-04",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",18,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What problem does the paper address for quantile treatment effects?","Question",{"text":113,"@type":114},"It derives semiparametric efficiency bounds for quantile treatment effects when selection into treatment is based on observable characteristics, and it develops estimators for these parameters.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How are the quantile treatment effects defined in the paper?",{"text":118,"@type":114},"For a fixed percentile, QTE is described as the horizontal distance between two cumulative distribution functions, and it is linked to a rank invariance assumption in the individual-level interpretation.",{"name":120,"@type":111,"acceptedAnswer":121},"What do the results and empirical application show about treatment effect heterogeneity?",{"text":122,"@type":114},"The paper proves Root-N consistency, asymptotic normality, and efficiency bound attainment for one estimator. The job training application indicates that treatment effects are heterogeneous and concentrated in the upper quantiles of the earnings distribution.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},201893,1788539889,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145,"preview_page_count":4},1099514067415,"https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502","E¢ cient Semiparametric Estimation of  \nQuantile Treatment E§ects􀀃  \nSergio Firpoy  \nFirst Draft: November 2002  \nThis Draft: January 2004  \nAbstract  \nThis paper presents calculations of semiparametric e¢ ciency bounds for quantile treatment e§ects parameters when selection to treatment is based on observable characteristics. The paper also presents three estimation procedures for these parameters, all of which have two steps: a nonparametric estimation and a computation of the di§erence between the solutions of two distinct minimization problems. Root-N consistency, asymptotic normality, and the achievement of the semiparametric e¢ ciency bound is shown for one of the three estimators. In the Önal part of the paper, an empirical application to a job training program reveals the importance of heterogeneous treatment e§ects, showing that for this program the e§ects are concentrated in the upper quantiles of the earnings distribution.  \nKeywords: Quantile Treatment E§ects, Propensity Score, Semiparametric E¢ ciency Bounds, E¢ cient Estimation, Semiparametric Estimation  \n1 Introduction  \nIn program evaluation studies it is often important to learn not only about the average treatment e§ects, but about the distributional e§ects of a treatment. In particular, the policy-maker might be interested in the e§ect of the treatment on the dispersion of the outcome, or its e§ect on the lower tail of the outcome distribution.  \nOne way of capturing this e§ect in a setting with binary treatment and scalar outcomes is by computing the quantiles of the distribution of the treated and of the control outcomes. Using quantiles, discretized versions of the distribution functions of treated and controls can be calculated. Also, quantiles are used in many inequality measurements as, for instance, quantile ratios, inter-quantile ranges, concentration functions, and the Gini coe¢ cient. Finally, di§erences in quantiles are important as the e§ects of a treatment may be heterogeneous, varying along the outcome distribution.  \n􀀃 I am indebted to Guido Imbens and to Jim Powell for their advice, support and many suggestions. I am also grateful to Marcelo Fernandes, Fernando Ferreira, Carlos Flores, Gustavo Gonzaga, Jinyong Hahn, Michael Jansson, David Lee, Thierry Magnac, Rosa Matzkin, Dan McFadden, Jo„o Pinho de Mello, Deb Nolan, David Reinstein, Paul Ruud, Je§rey Wooldridge and participants of seminars at EPGE-FGV, Georgetown, MSU, PUCRio, UBC, UC-Berkeley, UC-Davis, University of Miami, University of Toronto and University of Washington for comments. Financial support from CAPES-Brazil is acknowledged. All errors are mine.  \ny The University of British Columbia, Department of Economics, \\#997-1873 East Mall, Vancouver, B. C. , Canada, V6T 1Z1, Ö[rpo@interchange.ubc.ca](rpo@interchange.ubc.ca).  \nSeveral parameters can be deÖned in order to capture the e§ects of a treatment. In most cases, the focus is on the average treatment e§ect (ATE) deÖned as the di§erence in the means of the potential outcomes. One reason that many program evaluation studies focus on average treatment e§ects is that for the special case in which the treatment has a homogeneous e§ect, it is possible to interpret ATE as the e§ect of the treatment on a single observation. Note, however, that the average treatment e§ect does not depend on homogeneity assumptions to be well-deÖned.  \nIndeed, treatment e§ects may be heterogeneous, varying greatly along the outcome distribution. The presence of heterogeneity in treatment e§ects is very important when evaluating programs, as policy-makers are often interested in the distributional consequences of the treatment. This is true, for example, for a wide range of social programs such as welfare, unemployment insurance, subsidized job training, the minimum wage, agrarian reform, and micro-credit provision.  \nA parameter of interest in the presence of heterogeneous treatment e§ects is the quantile treatment e§ect (QTE) . As originally deÖned by","cbCainOESgmtSpLn","https://ap.wps.com/l/cbCainOESgmtSpLn","pdf",403658,52,"English","# Introduction\n## Quantile effects and distributional impacts\n## Average treatment effects and heterogeneity\n## Quantile treatment effects and rank invariance\n## Handling violations via bounds and marginal distributions","[{\"question\":\"What problem does the paper address for quantile treatment effects?\",\"answer\":\"It derives semiparametric efficiency bounds for quantile treatment effects when selection into treatment is based on observable characteristics, and it develops estimators for these parameters.\"},{\"question\":\"How are the quantile treatment effects defined in the paper?\",\"answer\":\"For a fixed percentile, QTE is described as the horizontal distance between two cumulative distribution functions, and it is linked to a rank invariance assumption in the individual-level interpretation.\"},{\"question\":\"What do the results and empirical application show about treatment effect heterogeneity?\",\"answer\":\"The paper proves Root-N consistency, asymptotic normality, and efficiency bound attainment for one estimator. The job training application indicates that treatment effects are heterogeneous and concentrated in the upper quantiles of the earnings distribution.\"}]","Efficient Semiparametric Estimation of Quantile Treatment Effects | PDF",131]