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This arises when treatment is assigned at the group level (e.g., firms, schools) but the objects of interest are within-group distributions (e.g., employee wages, student test scores). Standard RDDs are not designed for this two-level structure, as they assume scalar outcomes observed at the same level as treatment assignment. To address this, I develop a novel approach based on random distributions and show that, under a mild continuity condition on the average quantile function, the jump at the cutoff identifies a local average quantile treatment effect. To estimate it, I propose a distribution-valued local polynomial estimator, which fits the full quantile curve with a single bandwidth, avoids quantile crossing, and yields a meaningful \u201caverage distribution\u201d. I derive uniform asymptotic normality, valid multiplier bootstrap confidence bands, and a data-driven bandwidth selection method. Simulations demonstrate strong performance and reveal that standard quantile RDD is biased and inconsistent in this setting. An application to U.S. gubernatorial close elections (1984\u20132010) uncovers an equality\u2013efficiency trade-off under Democratic control, driven by income reductions at the top of the distribution.", "occurrence_notes":null, "guid":"140189-21886718@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/140189", "building_id":"1000154", "building_name":"Lorch Hall", "campus_maps_id":"88", "room":"301", "location_name":"Lorch Hall", "has_livestream":0, "cost":"", "tags":["Econometrics","Economics","Metrics","seminar"], "website":"http:\/\/www.lsa.umich.edu\/econ", "sponsors":[ { "group_name":"Department of Economics", "group_id":"3302", "website":"http:\/\/www.lsa.umich.edu\/econ" }, { "group_name":"Econometrics", "group_id":"3546", "website":"" }, { "group_name":"Department of Economics Seminars", "group_id":"3566", "website":"" } ], "image_url":"https:\/\/events.umich.edu\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "styled_images":{ "event_thumb":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_thumb\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "event_large":"https:\/\/events.umich.edu\/media\/cache\/event_large\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "event_large_2x":"https:\/\/events.umich.edu\/media\/cache\/event_large_2x\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "event_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/event_large_lightbox\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "group_thumb":"https:\/\/events.umich.edu\/media\/cache\/resolve\/group_thumb\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "group_thumb_square":"https:\/\/events.umich.edu\/media\/cache\/resolve\/group_thumb_square\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "group_large":"https:\/\/events.umich.edu\/media\/cache\/resolve\/group_large\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "group_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/group_large_lightbox\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "event_large_crop":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_large_crop\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "event_list":"https:\/\/events.umich.edu\/media\/cache\/event_list\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "event_list_2x":"https:\/\/events.umich.edu\/media\/cache\/event_list_2x\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "event_grid":"https:\/\/events.umich.edu\/media\/cache\/event_grid\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "event_grid_2x":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_grid_2x\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "event_feature_large":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_feature_large\/media\/attachments\/2025\/10\/event_140189_original-1.jpg", "event_feature_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_feature_thumb\/media\/attachments\/2025\/10\/event_140189_original-1.jpg" }, "occurrence_count":1, "first_occurrence":21886718 } , "140206-21886737": { "datetime_modified":"20251024T123202", "datetime_start":"20251009T150000", "datetime_end":"20251009T160000", "has_end_time":1, "date_start":"2025-10-09", "date_end":"2025-10-09", "time_start":"15:00:00", "time_end":"16:00:00", "time_zone":"America\/Detroit", "event_title":"Called to Teach & Equipped to Serve: Memphis Teacher Residency Virtual Info Session", "occurrence_title":"", "combined_title":"Called to Teach & Equipped to Serve: Memphis Teacher Residency Virtual Info Session", "event_subtitle":"", "event_type":"Careers \/ Jobs", "event_type_id":"2", "description":"Discover how you can earn a fully funded Master\u2019s in Teaching, with free housing, mentorship, and coaching support, in a community that is rooted in our mission of Christian love expressed in equal education. Join our virtual info session to learn more about the Memphis Teacher Residency, Tennessee's top-rated teacher training program, and the options we have for you!\u00a0100% of attendees said our info session was worth their time! Here's what to expect:\u00a0\nMTR's mission, history, and strategy\nOverview of the residency and summer programs\nFinancial Benefits\nApplication Process\nVirtual tour of housing & MTR offices\nHear from a current teaching resident\nQ&A\nGiveaway\n", "occurrence_notes":null, "guid":"140206-21886737@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/140206", "building_id":"", "building_name":"", "campus_maps_id":"", "room":"", "location_name":"", "has_livestream":0, "cost":"", "tags":[], "website":"", "sponsors":[ { "group_name":"University Career Center UCC", "group_id":"1140", "website":"http:\/\/careercenter.umich.edu" } ], "image_url":"", "styled_images":{ "event_thumb":"", "event_large":"", "event_large_2x":"", "event_large_lightbox":"", "group_thumb":"", "group_thumb_square":"", "group_large":"", "group_large_lightbox":"", "event_large_crop":"", "event_list":"", "event_list_2x":"", "event_grid":"", "event_grid_2x":"", "event_feature_large":"", "event_feature_thumb":"" }, "occurrence_count":1, "first_occurrence":21886737 } }