[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-202170-105":59,"doc-detail-202170-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","tobit-rd-regression-discontinuity-designs-with-sample-selection-lecture-slides","Tobit RD - Regression Discontinuity Designs with Sample Selection - Lecture Slides","","Regression Discontinuity (RD) designs are extended to handle sample selection or missing outcomes, addressing the key RD threat of sample selection and the resulting incomparability around the cutoff. The framework identifies both extensive and intensive margins of the treatment effect: changes in participation probability and shifts in the conditional distribution of observed outcomes given participation. The approach delivers subgroup treatment-effect bounds and also characterizes subgroup features, including always-participating versus quitting compliers, enabling policy-relevant interpretation.",{"@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/tobit-rd-regression-discontinuity-designs-with-sample-selection-lecture-slides/202170/",{"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/tobit-rd-regression-discontinuity-designs-with-sample-selection-lecture-slides/202170.png","ImageObject",300,407,{"name":92,"@type":93},"Lute","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02","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},"Why does sample selection create problems for standard RD designs?","Question",{"text":113,"@type":114},"Sample selection makes observations above and below the RD cutoff incomparable, which can invalidate the standard RD design. The paper motivates this by showing how the treatment effect cannot be interpreted in the usual way when outcomes are only observed for selected individuals.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What does the method identify regarding the RD treatment effect?",{"text":118,"@type":114},"It identifies two margins: an extensive margin effect on the participation probability and an intensive margin effect on the distribution of the observed outcome among participants. It also provides subgroup treatment-effect bounds and identifies subgroup characteristics useful for policy.",{"name":120,"@type":111,"acceptedAnswer":121},"What assumptions are used for identification?",{"text":122,"@type":114},"Assumption 1 requires discontinuity at the cutoff, monotonicity (Pr(T1 ≥ T0)=1), and smoothness/continuity of relevant conditional distributions and type probabilities at the cutoff, along with continuity and strict positivity of the running variable density.","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},202170,1788543185,{"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},137454149569,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Regression Discontinuity Designs with Sample Selection  \nYingying Dong  \nUniversity of California Irvine  \n Y . Dong (University of California Irvine)  Tobit RD  03/2017 1 / 43   \nMotivation: Recent Examples  \nOne frequently encountered issue in empirical applications of RD design ñ Sample selection!  \nRecent Examples:  \n McCrary and Royer (2011) investigate e§ects of womenís education on fertility and infant health (observed only if giving birth) .  \n Kim (2012) estimates e§ects of taking remedial courses on performance in subsequent main courses (observed only if completing subsequent courses) .  \n Other: Martorell and McFarlin (2011), Sampaio et al. (2013) ...  \n Y . Dong (University of California Irvine)  Tobit RD  03/2017 2 / 43   \nMotivation: Illustration of the Issue  \n Sample selection ñ> incomparability of observations above/ below the RD cuto§.  \n Standard RD design (Hahn et al. 2001) is invalid.  \n Y . Dong (University of California Irvine)  Tobit RD  03/2017 3 / 43   \nWhat Does This Paper Do?  \nExtends the standard RD design to allow for sample selection or missing outcomes.  \n Point identiÖes extensive and intensive margins of the RD treatment e§ect.  \n Extensive margin: e§ect on the participation probability.  \n Intensive margin: e§ect on the observed outcome distribution conditional on participation.  \n Provides subgroup treatment e§ect bounds.  \n Also point identiÖcation of characteristics of subgroups (e.g. always participating vs . quitting compliers) -useful for policy.  \n Y . Dong (University of California Irvine)  Tobit RD  03/2017 4 / 43   \nWhat Does This Paper Do?  \nIdentiÖcation here  \n does not require exclusion restrictions in the selection equation.  \n Standard sample selection correction requires exclusion restrictions or functional form/distributional assumptions: Heckman (1979, 1990), Ahn and Powell (1993), Lee (1994), Andrews and Schafgans (1998), Das, Newey and Vella (2003) and Lewbel (2007) etc .  \n does not require specifying the selection mechanism.  \n Sample selection could be caused by non-participation, dropout, survey  \nnonresponse, or other reasons (e.g. , censoring by death) .  \nApplies these results to examine e§ects of academic probation on college persistence and GPA.  \n Y . Dong (University of California Irvine)  Tobit RD  03/2017 5 / 43   \nNotation  \nT =Treatment; T 2 f0 , 1g.  \nS =Sample selection indicator; S 2 f0 , 1g. Y 􀀃 = (Partially observed) outcome.  \nObserve Y = Y 􀀃 if S = 1; missing if S = 0.  \nYt􀀃 , t = 1 , 0 is potential outcome under treatment or no treatment.  \nSt , t = 1 , 0 is potential sample selection under treatment or no treatment.  \n Y . Dong (University of California Irvine)  Tobit RD  03/2017 6 / 43   \nNotation  \n Let T1 (r ) and T0 (r ) be potential treatment status above or below the RD cuto§, respectively.  \nLet T = h (R , V ) for unobservables V , which can be a vector.  \nWLG, rewrite T = h 1 (R , V ) Z + h 0 (R , V ) (1 􀀀 Z ), where Z = 1 (R 􀀕 r0) . Then deÖne T1 (r ) 􀀑 h 1 (r , V ) and T0 (r ) 􀀑 h 0 (r , V ) .  \n Individual types  \nAlways takers (A): T1 (r ) = T0 (r ) = 1 , Never takers (N ):  \nT1 (r ) = T0 (r ) = 0, Compliers (C ): T1 (r ) > T0 (r ), DeÖers (D):  \nT1 (r ) \u003C T0 (r ) (Angrist, Imbens, and Rubin, 1996) .  \n Y . Dong (University of California Irvine)  Tobit RD  03/2017 7 / 43   \nDeÖnitions  \nTwo Margins of the RD treatment e§ect  \n Extensive margin 􀀑E [S1 􀀀 S0 jR = r0 , C ] .  \n e .g. change in the dropout rate with or without the probation policy.  Intensive margin  \n􀀑 E [Y1􀀃 jS1 = 1 , R = r0 , C ] 􀀀 E [Y0􀀃 jS0 = 1 , R = r0 , C ] .  \n e .g. , how the quality (training) of college graduates di§ers with or  \nwithout the probation policy, regardless of composition.  causal only from the distributional point of view.  \n Y . Dong (University of California Irvine)  Tobit RD  03/2017 8 / 43   \nIdentifying Assumption  \nASSUMPTION 1: The following assumptions hold for r 2 (r0 􀀀 \\# , r0 + \\#)  \nfor some small \\# > 0.  \nA1 . (Discontinuity): limr\"r0","cbCaivhZlTQzOQ48","https://ap.wps.com/l/cbCaivhZlTQzOQ48","pdf",475989,43,"English","# Motivation: Sample selection in RD\n# Illustration: Why standard RD can be invalid\n# What the paper does\n## Extensive and intensive margins\n# Identification approach\n## No exclusion restrictions in selection equation\n## Potential outcomes and sample selection\n# Notation and assumptions\n## Discontinuity, monotonicity, smoothness\n# Point identification results\n## Theorem: Extensive vs. intensive margin identification","[{\"question\":\"Why does sample selection create problems for standard RD designs?\",\"answer\":\"Sample selection makes observations above and below the RD cutoff incomparable, which can invalidate the standard RD design. The paper motivates this by showing how the treatment effect cannot be interpreted in the usual way when outcomes are only observed for selected individuals.\"},{\"question\":\"What does the method identify regarding the RD treatment effect?\",\"answer\":\"It identifies two margins: an extensive margin effect on the participation probability and an intensive margin effect on the distribution of the observed outcome among participants. It also provides subgroup treatment-effect bounds and identifies subgroup characteristics useful for policy.\"},{\"question\":\"What assumptions are used for identification?\",\"answer\":\"Assumption 1 requires discontinuity at the cutoff, monotonicity (Pr(T1 ≥ T0)=1), and smoothness/continuity of relevant conditional distributions and type probabilities at the cutoff, along with continuity and strict positivity of the running variable density.\"}]","Tobit RD - Regression Discontinuity Designs with Sample Selection - Lecture Slides | PDF",108]