Design-Based Inference under Random Potential Outcomes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915724761497600 |
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| author | Yang, Yukai |
| author_facet | Yang, Yukai |
| contents | We develop 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. By modelling potential outcomes as random functions driven by a latent stochastic environment, causal estimands are defined as expectations over this mechanism rather than as functionals of a single realised potential-outcome schedule. We show that under local dependence, cross-sectional averaging exhibits an ergodic property that links a single realised experiment to the underlying stochastic mechanism, providing a fundamental justification for using classical design-based statistics to conduct inference on expectation-based causal estimands. We establish consistency, asymptotic normality, and feasible variance estimation for aggregate estimators under general dependency graphs. Our results clarify the conditions under which design-based inference extends beyond realised potential-outcome schedules and remains valid for mechanism-level causal targets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01324 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Design-Based Inference under Random Potential Outcomes Yang, Yukai Methodology Econometrics Statistics Theory 62D05, 62G05, 60F05 We develop 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. By modelling potential outcomes as random functions driven by a latent stochastic environment, causal estimands are defined as expectations over this mechanism rather than as functionals of a single realised potential-outcome schedule. We show that under local dependence, cross-sectional averaging exhibits an ergodic property that links a single realised experiment to the underlying stochastic mechanism, providing a fundamental justification for using classical design-based statistics to conduct inference on expectation-based causal estimands. We establish consistency, asymptotic normality, and feasible variance estimation for aggregate estimators under general dependency graphs. Our results clarify the conditions under which design-based inference extends beyond realised potential-outcome schedules and remains valid for mechanism-level causal targets. |
| title | Design-Based Inference under Random Potential Outcomes |
| topic | Methodology Econometrics Statistics Theory 62D05, 62G05, 60F05 |
| url | https://arxiv.org/abs/2505.01324 |