{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/balancing-regression-difference-in","title":"Balancing, Regression, Difference-In-Differences and Synthetic Control Methods: A Synthesis","arxiv_id":"1610.07748","date":"2016-10-25","proceeding":null,"authors":["Nikolay Doudchenko","Guido W. Imbens"],"abstract":"In a seminal paper Abadie, Diamond, and Hainmueller [2010] (ADH), see also\nAbadie and Gardeazabal [2003], Abadie et al. [2014], develop the synthetic\ncontrol procedure for estimating the effect of a treatment, in the presence of\na single treated unit and a number of control units, with pre-treatment\noutcomes observed for all units. The method constructs a set of weights such\nthat selected covariates and pre-treatment outcomes of the treated unit are\napproximately matched by a weighted average of control units (the synthetic\ncontrol). The weights are restricted to be nonnegative and sum to one, which is\nimportant because it allows the procedure to obtain unique weights even when\nthe number of lagged outcomes is modest relative to the number of control\nunits, a common setting in applications. In the current paper we propose a\ngeneralization that allows the weights to be negative, and their sum to differ\nfrom one, and that allows for a permanent additive difference between the\ntreated unit and the controls, similar to difference-in-difference procedures.\nThe weights directly minimize the distance between the lagged outcomes for the\ntreated and the control units, using regularization methods to deal with a\npotentially large number of possible control units.","url_abs":"http://arxiv.org/abs/1610.07748v2","url_pdf":"http://arxiv.org/pdf/1610.07748v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"balancing-regression-difference-in","repo_url":"https://github.com/hollina/scul","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}