 Design-Based Inference under Random Potential OutcomesAbstract: We introduce a design-based framework for causal inference that accommodates random potential outcomes without introducing outcome models, thereby extending the classical Neyman--Rubin paradigm in which outcomes are treated as fixed. Each unit's potential outcome is modelled as a structural mapping $\tilde{y}_i(z, \omega)$, where $z$ denotes the treatment assignment and $\omega$ represents latent outcome-level randomness. Inspired by recent work linking design-based inference to the Riesz representation theorem, we embed random potential outcomes in a Hilbert space and define treatment effects as linear functionals, leading to estimators characterised by their Riesz representers. This approach preserves the core identification logic of randomised assignment while enabling valid inference under stochastic outcome variation. We establish consistency and asymptotic normality under local dependence, and develop feasible variance estimators that remain valid under weaker structural assumptions, including partially known dependence. A simulation study illustrates the robustness and finite-sample behaviour of the estimators. The proposed framework extends design-based causal inference to settings in which outcome-level randomness and local dependence are intrinsic features of the data. Date: 2025-05, Revised 2025-12 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2505.01324 Access Statistics for this paper More papers in Papers from arXiv.org |
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