{"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/flexible-analysis-of-individual-heterogeneity","title":"On Causal Inference with Model-Based Outcomes","arxiv_id":"2403.19563","date":"2024-03-28","proceeding":null,"authors":["Dmitry Arkhangelsky","Kazuharu Yanagimoto","Tom Zohar"],"abstract":"We study a causal inference problem with group-level outcomes, which are themselves parameters identified from microdata. We formalize these outcomes using population moment conditions and demonstrate that one-step Generalized Method of Moments (GMM) estimators are generally inconsistent due to an endogenous weighting bias, where policy affects the implicit GMM weights. In contrast, two-stage Minimum Distance (MD) estimators perform well when group sizes are sufficiently large. While MD estimators can still be inconsistent in small groups due to a policy-induced sample selection, we demonstrate that this can be addressed by incorporating auxiliary population information. An empirical application illustrates the practical importance of these findings.","url_abs":"https://arxiv.org/abs/2403.19563v4","url_pdf":"https://arxiv.org/pdf/2403.19563v4.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":"flexible-analysis-of-individual-heterogeneity","repo_url":"https://github.com/kazuyanagimoto/unitdid","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"causal-inference","task_name":"Causal Inference"},{"task_slug":"model","task_name":"model"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}