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The paper builds on L1-based quantile regression but introduces expectile treatment effects using expectile regression with an L2 loss. Expectile treatment effects deliver more efficient estimates except at extreme tail ends, supported by simulation and analysis of LaLonde data. In simulations the expectile variance is below 80% of the quantile counterpart across most locations, and in favorable cases drops below about two thirds.",{"@graph":69,"@context":122},[70,84,105],{"@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/expectile-treatment-effects-an-efficient-alternative-to-compute-the-distribution-of-treatment-effects/202027/",{"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/expectile-treatment-effects-an-efficient-alternative-to-compute-the-distribution-of-treatment-effects/202027.png","ImageObject",300,407,{"name":92,"@type":93},"Taylor Morgan","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-21","2026-09-04",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does the paper address in treatment effect analysis?","Question",{"text":112,"@type":113},"It targets how to compute and interpret the distribution of treatment effects, emphasizing tail behavior rather than only average effects.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do expectile treatment effects relate to quantile treatment effects?",{"text":117,"@type":113},"They build on regression ideas for distributional effects, but use expectile regression with an L2 loss instead of quantile regression with an L1 loss.",{"name":119,"@type":110,"acceptedAnswer":120},"What do the results claim about efficiency and variance?",{"text":121,"@type":113},"The paper shows expectile treatment effects are more efficient than quantile treatment effects except at extreme tail ends, with lower variance in simulations and reduced variance in the LaLonde analysis.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},202027,1788541146,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"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":129,"read_time":26,"preview_page_count":4},1099523885336,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","SFB 649 Discussion Paper 2014-059  \nExpectile Treatment Effects: An efficient alternative to compute the distribution of treatment  \neffects  \nStephan Stahlschmidt* Matthias Eckardt* Wolfgang K. Härdle*  \n* Humboldt-Universität zu Berlin, Germany  \nThis research was supported by the Deutsche Forschungsgemeinschaft through the SFB 649 \"Economic Risk\" .  \n[http://sfb649.wiwi.hu-berl](http://sfb649.wiwi.hu-berl)[in.de](in.de)  \nISSN 1860-5664  \nSFB 649, Humboldt-Universität zu Berlin Spandauer Straße 1, D-10178 Berlin  \nExpectile Treatment E􀀋ects: An e􀀎cient alternative to compute the distribution of treatment e􀀋ects 􀀃  \nStephan Stahlschmidt  \nSchool of Business and Economics Humboldt{Universit􀁿at zu Berlin Germany  \nMatthias Eckardt  \nDepartment of Computer Science Humboldt{Universit􀁿at zu Berlin Germany  \nWolfgang K. H􀁿ardle  \nC.A.S.E Center for Applied Statistics and Economics Humboldt{Universit􀁿at zu Berlin Germany  \nWorking Paper Version: 20141014  \n􀁿  \n􀀃 The 􀀌nancial support from the Deutsche Forschungsgemeinschaft via SFB 649 \\Okonomisches Risiko\", Humboldt{Universit􀁿at zu Berlin, and IRTG 1792 \\High Dimensional Non Stationary Time Series\", Humboldt{Universit􀁿at zu Berlin, is gratefully acknowledged.  \nAbstract  \nThe distribution of treatment e􀀋ects extends the prevailing focus on average treatment e􀀋ects to the tails of the outcome variable and quantile treatment e􀀋ects denote the predominant technique to compute those e􀀋ects in the presence of a confounding mechanism.  \nThe underlying quantile regression is based on a L 1{loss function and we propose the technique of expectile treatment e􀀋ects, which relies on expectile regression with its L2{loss function. It is shown, that apart from the extreme tail ends expectile treatment e􀀋ects provide more e􀀎cient estimates and these theoretical results are broadened by a simulation and subsequent analysis of the classic LaLonde data. Whereas quantile and expectile treatment e􀀋ects perform comparably on extreme tail locations, the variance of the expectile variant amounts in our simulation on all other locations to less than 80% of its quantile equivalent and under favourable conditions to less than 2=3 . In the LaLonde data expectile treatment e􀀋ects reduce the variance by more than a quarter, while at the same time smoothing the treatment e􀀋ects considerably.  \nKeywords: distributional treatment e􀀋ects, e􀀎ciency, expectile treatment e􀀋ects, LaLonde data, quantile treatment e􀀋ects  \nJEL codes: C21, C31, C54, J64  \n1 Introduction  \nThe analysis of a particular intervention and especially the e􀀋ect it exhibits on a speci􀀌c outcome variable has been a central issue in statistical data analysis and several classic techniques were invented to answer this question (Fisher, 1935) . Whereas at 􀀌rst the design and analysis of experiments were of much interest, more recently the focus in social sciences has shifted to the evaluation of treatment e􀀋ects from observational data, as in many circumstances the execution of experiments is infeasible or too costly. In this context treatment e􀀋ects quantify causal outcomes arising from a clearly identi􀀌able intervention and are for example applied to assess new policies or programmes (e.g. LaLonde, 1986; Dehejia and Wahba, 1999) .  \nThese applications most often concentrate on an average e􀀋ect on the population or some subgroup thereof. However, the predominant Rubin Causal Model (Rubin, 1974) allows for heterogeneity in response to a treatment and the focus on average a􀀋ects inhibits the disclosure of possibly deviant e􀀋ects in the tails of the outcome distribution. Contrary quantile treatment e􀀋ects (Doksum, 1974; Lehmann, 1974) allow to analyse the e􀀋ect distribution and, given covariates, apply quantile regression techniques (Koenker and Bassett, 1978) to infer the causal e􀀋ect. Quantile treatment e􀀋ect have been applied to such diverse topics as teacher shortage in African countries (Bourdon et al. , 2010), returns to education in China (Mess","cbCaig1VWcjxah0e","https://ap.wps.com/l/cbCaig1VWcjxah0e","pdf",740918,24,"English","# Abstract\n# Keywords\n# 1 Introduction","[{\"question\":\"What problem does the paper address in treatment effect analysis?\",\"answer\":\"It targets how to compute and interpret the distribution of treatment effects, emphasizing tail behavior rather than only average effects.\"},{\"question\":\"How do expectile treatment effects relate to quantile treatment effects?\",\"answer\":\"They build on regression ideas for distributional effects, but use expectile regression with an L2 loss instead of quantile regression with an L1 loss.\"},{\"question\":\"What do the results claim about efficiency and variance?\",\"answer\":\"The paper shows expectile treatment effects are more efficient than quantile treatment effects except at extreme tail ends, with lower variance in simulations and reduced variance in the LaLonde analysis.\"}]","Expectile Treatment Effects - An Efficient Alternative to Compute the Distribution of Treatment Effects | PDF"]