[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122584-en":3,"doc-seo-122584-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},122584,7971461741311,"Ophelia","https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826",8,"Research & Report","Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments","Nonparametric inference for causal effects of continuous treatment variables is developed under unconfoundedness and with high-dimensional or nonparametric nuisance components. The proposed double debiased machine learning (DML) estimators target the average dose-response (average structural function) and partial effects, attaining asymptotic normality alongside nonparametric convergence rates. Kernel-based doubly robust influence functions and cross-fitting yield tractable conditions ensuring nuisance estimation does not alter first-order large-sample distributions. Kernel localization via the Gateaux derivative is justified, and ML procedures are validated in Monte Carlo simulations and a job training evaluation.","View metadata, citation and similar [papers at ](papers at core.ac.uk)[core.ac.uk](papers at core.ac.uk) brought to you by CORE  \n[provided by](provided by arXiv.org)[ arXiv.org](provided by arXiv.org) e-Print Archive  \narXiv :2004 .03036v1 [ econ .EM] 6 Apr 2020  \nDouble Debiased Machine Learning Nonparametric Inference with  \nContinuous Treatments 􀀃  \nKyle Colangelo Ying-Ying Leey  \nUniversity of California Irvine  \nApril 2020  \nAbstract  \nWe propose a nonparametric inference method for causal e􀀋ects of continuous treatment variables, under unconfoundedness and in the presence of high-dimensional or nonparametric nuisance parameters. Our double debiased machine learning (DML) estimators for the average doseresponse function (or the average structural function) and the partial e􀀋ects are asymptotically normal with nonparametric convergence rates. The nuisance estimators for the conditional expectation function and the conditional density can be nonparametric kernel or series estimators or ML methods. Using a kernel-based doubly robust in􀀍uence function and cross-􀀌tting, we give tractable primitive conditions under which the nuisance estimators do not a􀀋ect the 􀀌rst-order large sample distribution of the DML estimators. We justify the use of kernel to localize the continuous treatment at a given value by the Gateaux derivative. We implement various ML methods in Monte Carlo simulations and an empirical application on a job training program evaluation.  \nKeywords: Average structural function, cross-􀀌tting, dose-response function, doubly robust, high dimension, nonseparable models, partial mean, post-selection inference.  \nJEL Classi􀀌cation: C14, C21, C55  \n􀀃 The 􀀌rst version was circulated as Lee (February 2019), \\Double machine learning nonparametric inference on continuous treatment e􀀋ects.\" We are grateful to Max Farrell, Whitney Newey, and Takuya Ura for valuable discussion. We also thank seminar participants at Harvard-MIT and UC Irvine, conference participants in 2019: Barcelona Summer Forum workshop on Machine Learning for Economics, North American Summer Meeting of the Econometric Society, Vanderbilt/CeMMAP/UCL conference on Advances in Econometrics, Midwest Econometrics Group, California Econometrics Conference, and 2020 North American Winter Meeting of the Econometric Society.  \ny Department of economics, 3151 Social Science Plaza, University of California Irvine, Irvine, CA 92697 . E-mail: [yingying.lee@uci.edu](yingying.lee@uci.edu)  \n1 Introduction  \nWe propose a nonparametric inference method for continuous treatment e􀀋ects on the outcome Y , under the unconfoundedness assumption 1 and in the presence of high-dimensional or nonparametric nuisance parameters. We focus on the heterogenous e􀀋ect with respect to the continuous treatment or policy variables T. To identify the causal e􀀋ects, it is plausible to allow the number of the control variables X to be large relative to the sample size n. To achieve valid inference and to employ machine learning (ML) methods, we use a double debiased ML approach that combines a doubly robust moment function and cross-􀀌tting.  \nWe consider a fully nonparametric outcome equation Y = g (T; X; \") . No functional form assumption is imposed on the unobserved disturbances \", such as restrictions on dimensionality, monotonicity, or separability. The potential outcome is Y(t) = g(t; X; \") indexed by the hypothetical treatment value t. The object of interest is the average dose-response function as a function oft, de􀀌ned by the mean of the potential outcome across observations with the observed and unobserved heterogeneity (X; \"), i.e., 􀀌t = E[Y(t)] =R R g(t; X; \")dFX\". It is also known as the average structural function in nonseparable models in Blundell and Powell (2003) . The well-studied average treatment e􀀋ect of switching from treatment t to s is 􀀌s 􀀀 􀀌t. We further de􀀌ne the partial (or marginal) e􀀋ect of the 􀀌rst component of the continuous treatment T at t = (t1 ; :::tdt)0 to beth","cbCaigHqGbWpOcsH","https://ap.wps.com/l/cbCaigHqGbWpOcsH","pdf",616247,1,34,"English","en",105,"# Abstract\n# Introduction\n## Causal estimands and identification under unconfoundedness\n## Double debiased ML estimator with cross-fitting","[{\"question\":\"What causal quantities does the method estimate for continuous treatments?\",\"answer\":\"It estimates the average dose-response function (equivalently the average structural function in nonseparable models) and the partial (marginal) effect of the continuous treatment at a given value.\"},{\"question\":\"How does the approach handle high-dimensional or nonparametric nuisance parameters?\",\"answer\":\"It uses a double debiased machine learning framework with a doubly robust moment function and cross-fitting, allowing nuisance estimators to be kernel/series/nonparametric or ML based without affecting the first-order distribution.\"},{\"question\":\"Why is cross-fitting and kernel localization used in the estimator?\",\"answer\":\"Cross-fitting via sample splitting ensures valid asymptotic inference when flexible nuisance learners are employed. Kernel weighting localizes the continuous treatment around the target value, and its use is justified through the Gateaux derivative.\"}]","Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments | PDF",1785811478,86,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"double-debiased-machine-learning-nonparametric-inference-with-continuous-treatments","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/double-debiased-machine-learning-nonparametric-inference-with-continuous-treatments/122584/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What causal quantities does the method estimate for continuous treatments?","Question",{"text":75,"@type":76},"It estimates the average dose-response function (equivalently the average structural function in nonseparable models) and the partial (marginal) effect of the continuous treatment at a given value.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the approach handle high-dimensional or nonparametric nuisance parameters?",{"text":80,"@type":76},"It uses a double debiased machine learning framework with a doubly robust moment function and cross-fitting, allowing nuisance estimators to be kernel/series/nonparametric or ML based without affecting the first-order distribution.",{"name":82,"@type":73,"acceptedAnswer":83},"Why is cross-fitting and kernel localization used in the estimator?",{"text":84,"@type":76},"Cross-fitting via sample splitting ensures valid asymptotic inference when flexible nuisance learners are employed. Kernel weighting localizes the continuous treatment around the target value, and its use is justified through the Gateaux derivative.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]