Geodesic difference-in-differences

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ID: 328570
2026
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Abstract
Summary 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’s collapse using age-at-death distributions and assess effects of U.S. electricity market liberalization on electricity generation compositions.
Reference Key
openalex_W4406975438 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Yidong Zhou, Daisuke Kurisu, Taisuke Otsu, Hans‐Georg Müller
Journal jurnal biometrika dan kependudukan
Year 2026
DOI
10.1093/biomet/asag054
URL
https://doi.org/10.1093/biomet/asag054
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