Treatment Effects with Correlated Spillovers: Bridging Discrete and Continuous Methods
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914219826348032 |
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| author | Kikuchi, Tatsuru |
| author_facet | Kikuchi, Tatsuru |
| contents | This paper develops a continuous functional framework for treatment effects propagating through geographic space and economic networks. We derive a master equation from three independent economic foundations -- heterogeneous agent aggregation, market equilibrium, and cost minimization -- establishing that the framework rests on fundamental principles rather than ad hoc specifications. The framework nests conventional econometric models -- autoregressive specifications, spatial autoregressive models, and network treatment effect models -- as special cases, providing a bridge between discrete and continuous methods. A key theoretical result shows that the spatial-network interaction coefficient equals the mutual information between geographic and network coordinates, providing a parameter-free measure of channel complementarity. The Feynman-Kac representation characterizes treatment effects as accumulated policy exposure along stochastic paths representing economic linkages, connecting the continuous framework to event study methodology. The no-spillover case emerges as a testable restriction, creating a one-sided risk profile where correct inference is maintained regardless of whether spillovers exist. Monte Carlo simulations confirm that conventional estimators exhibit 25-38% bias when spillovers are present, while our estimator maintains correct inference across all configurations including the no-spillover case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_12653 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Treatment Effects with Correlated Spillovers: Bridging Discrete and Continuous Methods Kikuchi, Tatsuru Econometrics Theoretical Economics Methodology This paper develops a continuous functional framework for treatment effects propagating through geographic space and economic networks. We derive a master equation from three independent economic foundations -- heterogeneous agent aggregation, market equilibrium, and cost minimization -- establishing that the framework rests on fundamental principles rather than ad hoc specifications. The framework nests conventional econometric models -- autoregressive specifications, spatial autoregressive models, and network treatment effect models -- as special cases, providing a bridge between discrete and continuous methods. A key theoretical result shows that the spatial-network interaction coefficient equals the mutual information between geographic and network coordinates, providing a parameter-free measure of channel complementarity. The Feynman-Kac representation characterizes treatment effects as accumulated policy exposure along stochastic paths representing economic linkages, connecting the continuous framework to event study methodology. The no-spillover case emerges as a testable restriction, creating a one-sided risk profile where correct inference is maintained regardless of whether spillovers exist. Monte Carlo simulations confirm that conventional estimators exhibit 25-38% bias when spillovers are present, while our estimator maintains correct inference across all configurations including the no-spillover case. |
| title | Treatment Effects with Correlated Spillovers: Bridging Discrete and Continuous Methods |
| topic | Econometrics Theoretical Economics Methodology |
| url | https://arxiv.org/abs/2512.12653 |