[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-201996-105":59,"doc-detail-201996-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","a-closed-form-estimator-for-quantile-treatment-effects-with-endogeneity","A Closed-Form Estimator for Quantile Treatment Effects with Endogeneity","","This paper studies the estimation of quantile treatment effects under endogeneity using the instrumental variable quantile regression (IVQR) framework. It proposes a class of flexible plug-in estimators built from closed-form solutions derived from IVQR moment conditions, maintaining root-n consistency and tractable computation. The paper proves functional central limit theorems and establishes bootstrap validity for quantile treatment effect functionals. Monte Carlo simulations show favorable finite-sample performance and robustness to misspecification, and the method is applied to reanalyze the causal effect of 401(k) plans.",{"@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/a-closed-form-estimator-for-quantile-treatment-effects-with-endogeneity/201996/",{"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/a-closed-form-estimator-for-quantile-treatment-effects-with-endogeneity/201996.png","ImageObject",300,407,{"name":92,"@type":93},"Levi","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-27","2026-09-04",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What estimation approach does the paper propose for quantile treatment effects with endogeneity?","Question",{"text":113,"@type":114},"It develops flexible plug-in estimators based on closed-form solutions derived from instrumental variable quantile regression (IVQR) moment conditions.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the method avoid difficulties from the IVQR GMM objective?",{"text":118,"@type":114},"By using the derived closed-form solutions, it bypasses the need to optimize the non-smooth and non-convex IVQR GMM objective while still achieving tractable estimation.",{"name":120,"@type":111,"acceptedAnswer":121},"What inference results are established for the proposed estimators?",{"text":122,"@type":114},"The paper proves functional central limit theorems and validates the exchangeable bootstrap, enabling uniform confidence bands and functional hypothesis tests.","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},201996,1788540825,{"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":26,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144,"preview_page_count":4},7971461740909,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","A closed-form estimator for quantile treatment e􀀋ects with  \nendogeneity  \nKaspar W􀁿uthrich∗  \nRevised: January 30, 2019  \nAbstract  \nThis paper studies the estimation of quantile treatment e􀀋ects based on the instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen, 2005) . I develop a class of 􀀍exible plug-in estimators based on closed-form solutions derived from the IVQR moment conditions. The proposed estimators remain tractable and root-n-consistent, while allowing for rich patterns of e􀀋ect heterogeneity. Functional central limit theorems and bootstrap validity results for the estimators of the quantile treatment e􀀋ects and other functionals are provided. Monte Carlo simulations demonstrate favorable 􀀌nite sample properties of the proposed approach. I apply my method to reanalyze the causal e􀀋ect of 401(k) plans.  \nJEL Classi􀀌cation: C21, C26  \nKeywords: instrumental variables, conditional and unconditional quantile treatment e􀀋ects, distribution regression, exchangeable bootstrap  \n∗ UC San Diego, Department of Economics, 9500 Gilman Dr. , La Jolla, CA 92093, email: [kwuthrich@ucsd.edu](kwuthrich@ucsd.edu).  \n1 Introduction  \nQuantile regression is a powerful tool for characterizing the heterogeneous impact of policy variableson di􀀋erent points of an outcome distribution. However, as with ordinary least squares, endogeneity renders standard quantile regression methods inconsistent for estimating quantile treatment e􀀋ects (QTE) . One approach to overcome this problem is to use instrumental variable (IV) methods.  \nThe goal and main contribution of this paper is to develop a 􀀍exible yet tractable approach for estimating conditional and unconditional QTE based on the instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen, 2005) with binary endogenous variables and binary instruments. The principal feature of the IVQR model is the rank similarity assumption, a restriction on the evolution of individual ranks across treatment states. Rank similarity implies a conditional moment restriction that can be used for constructing estimators of population QTE. However, estimation based on this moment restriction is complicated by the non-smoothness and non-convexity of the corresponding generalized method of moments (GMM) objective function, which occurs even for linear-in-parameters quantile models (Chernozhukov and Hansen, 2013; Chernozhukov et al. , 2017) .  \nIn this paper, I derive closed-form solutions for the IVQR estimands of the potential outcome cumulative distribution functions (cdfs) .1 These closed-form solutions are compositions of observable conditional cdfs and probabilities. I estimate the conditional cdfs using distribution regression (DR) and the conditional probabilities using parametric binary choice models. I then apply the closed-form solutions to obtain plug-in estimators of the conditional potential outcome cdfs and the conditional QTE. Finally, unconditional QTE are estimated by integrating the estimators of  \nthe conditional potential outcome cdfs with respect to the empirical distribution of the covariates.2  \n1 These identi􀀌cation results generalize W􀁿uthrich (2018), who derives similar closed-from solutions under more restrictive assumptions.  \n2 I refer to Firpo (2007) or Fr􀁿olich and Melly (2013) for a discussion of the di􀀋erences between conditional and unconditional QTE.  \nThis plug-in estimation strategy naturally bypasses the challenges associated with optimizing the IVQR GMM objective function. As a result, the proposed estimators are easy to implement and remain computationally tractable, while allowing for rich patterns of treatment e􀀋ect heterogeneity with respect to observables covariates. Moreover, unlike other IVQR estimators, the plug-in approach does not require practitioners to model the counterfactual structural quantile function. Instead, they only need to specify and estimate the observable conditional probabilities and cdfs with well-est","cbCaiuoWy00uNjmb","https://ap.wps.com/l/cbCaiuoWy00uNjmb","pdf",546347,"English","# Abstract\n# Introduction\n## Related literature","[{\"question\":\"What estimation approach does the paper propose for quantile treatment effects with endogeneity?\",\"answer\":\"It develops flexible plug-in estimators based on closed-form solutions derived from instrumental variable quantile regression (IVQR) moment conditions.\"},{\"question\":\"How does the method avoid difficulties from the IVQR GMM objective?\",\"answer\":\"By using the derived closed-form solutions, it bypasses the need to optimize the non-smooth and non-convex IVQR GMM objective while still achieving tractable estimation.\"},{\"question\":\"What inference results are established for the proposed estimators?\",\"answer\":\"The paper proves functional central limit theorems and validates the exchangeable bootstrap, enabling uniform confidence bands and functional hypothesis tests.\"}]","A Closed-Form Estimator for Quantile Treatment Effects with Endogeneity | PDF",151]