{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T11:06:43Z","timestamp":1789211203028,"version":"build-2803163510"},"reference-count":0,"publisher":"Oxford University Press (OUP)","license":[{"start":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T00:00:00Z","timestamp":1789084800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Difference-in-differences (DID) is a widely used quasi-experimental design for causal inference, traditionally applied to scalar or Euclidean outcomes, while extensions to outcomes residing in non-Euclidean spaces remain limited. Existing methods for such outcomes have primarily focused on univariate distributions, leveraging linear operations in the space of quantile functions, but these approaches cannot be directly extended to outcomes in general metric spaces. In this paper, we propose geodesic DID, a novel DID framework for outcomes in uniquely geodesic metric spaces that admit a geodesic transport structure, including distributions, networks, and manifold-valued data. To address the absence of algebraic operations in these spaces, we use geodesics as proxies for differences and introduce the geodesic average treatment effect on the treated (ATT) as the causal estimand. We establish the identification of the geodesic ATT and derive the convergence rate of its sample versions, employing tools from metric geometry and empirical process theory. This framework is further extended to the case of staggered DID settings, allowing for multiple time periods and varying treatment timings. To illustrate the practical utility of geodesic DID, we analyze health impacts of the Soviet Union\u2019s collapse using age-at-death distributions and assess effects of U.S. electricity market liberalization on electricity generation compositions.<\/jats:p>","DOI":"10.1093\/biomet\/asag054","type":"journal-article","created":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T11:38:25Z","timestamp":1788867505000},"source":"Crossref","is-referenced-by-count":0,"title":["Geodesic difference-in-differences"],"prefix":"10.1093","author":[{"given":"Yidong","family":"Zhou","sequence":"first","affiliation":[{"name":"University of Minnesota School of Statistics, , 224 Church St S.E., Minneapolis, Minnesota 55455, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daisuke","family":"Kurisu","sequence":"additional","affiliation":[{"name":"The University of Tokyo Faculty of Economics, , 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033,","place":["Japan"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Taisuke","family":"Otsu","sequence":"additional","affiliation":[{"name":"London School of Economics Department of Economics, , Houghton Street, London, WC2A 2AE, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hans-Georg","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"University of California Department of Statistics, , Davis, One Shields Avenue, Davis, California 95616, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,9,11]]},"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asag054\/71035060\/asag054.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asag054\/71035060\/asag054.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T10:27:10Z","timestamp":1789208830000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article\/doi\/10.1093\/biomet\/asag054\/8790844"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,11]]},"references-count":0,"URL":"https:\/\/doi.org\/10.1093\/biomet\/asag054","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,11]]},"article-number":"asag054"}}