arXiv 14 Dec 2025 · Econometrics
arXiv:2512.12653 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Callaway, Brantly and Pedro H. C. Sant'Anna (2021) Difference-in-Differences with Multiple Time Periods | 1.000 | 5 | 3 | 100% |
| 2 | Bramoullé, Yann, Habiba Djebbari, and Bernard Fortin (2009) Identification of Peer Effects through Social Networks | 0.928 | 4 | 3 | 100% |
| 3 | Sun, Liyang and Sarah Abraham (2021) Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects | 0.928 | 4 | 3 | 100% |
| 4 | Hirano, Keisuke and Guido W. Imbens (2004) The Propensity Score with Continuous Treatments | 0.874 | 5 | 2 | 100% |
| 5 | Kennedy, Edward H., Zongming Ma, Matthew D. McHugh, and Dylan S. Small (2017) Non-parametric Methods for Doubly Robust Estimation of Continuous Treatment Effects | 0.811 | 4 | 2 | 100% |
| 6 | Acemoglu, Daron, Vasco M. Carvalho, Asuman Ozdaglar, and Alireza Tah… (2012) The Network Origins of Aggregate Fluctuations | 0.737 | 3 | 2 | 100% |
| 7 | Barrot, Jean-Noël and Julien Sauvagnat (2016) Input Specificity and the Propagation of Idiosyncratic Shocks in Production Networks | 0.644 | 2 | 2 | 100% |
| 8 | Borusyak, Kirill, Xavier Jaravel, and Jann Spiess (2024) Revisiting Event Study Designs: Robust and Efficient Estimation | 0.644 | 2 | 2 | 100% |
| 9 | Conley, Timothy G (1999) GMM Estimation with Cross Sectional Dependence | 0.644 | 2 | 2 | 100% |
| 10 | LeSage, James and R. Kelley Pace (2009) Introduction to Spatial Econometrics | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 35 scored citations.