标题： 动态空间处理效应作为连续泛函：理论与医疗保健可及性的证据 显示英文标题

标题： Dynamic Spatial Treatment Effects as Continuous Functionals: Theory and Evidence from Healthcare Access

摘要： 我开发了一个基于Navier-Stokes偏微分方程的空间处理效应连续函数框架。 与离散处理参数不同，该框架将处理强度表征为随时间和空间变化的连续函数$\tau(\mathbf{x}, t)$，从而能够对边界演变、空间梯度和累积暴露进行严格的分析。 使用32,520个美国邮政编码进行实证验证，显示医疗保健可及性存在指数空间衰减（$\kappa = 0.002837$每公里，$R^2 = 0.0129$），在37.1公里处有可检测的边界。 该框架成功诊断了范围条件是否成立：正的衰减参数验证了医院附近的扩散假设，而负的参数正确地表明了城市混杂效应。 异质性分析显示，老年人群的距离效应强2-13倍$\times$，并且存在显著的教育梯度。 模型选择强烈支持对数衰减而非指数衰减（$\Delta \text{AIC} > 10,000$），它代表了指数衰减和幂律衰减之间的中间地带。 应用范围涵盖环境经济学、银行业和医疗政策。 连续函数框架提供了预测能力（$d^*(t) = \xi^* \sqrt{t}$）、参数敏感性（$\partial d^*/\partial \nu$）以及传统双重差分方法中无法获得的诊断测试。 显示英文摘要

摘要： I develop a continuous functional framework for spatial treatment effects grounded in Navier-Stokes partial differential equations. Rather than discrete treatment parameters, the framework characterizes treatment intensity as continuous functions $\tau(\mathbf{x}, t)$ over space-time, enabling rigorous analysis of boundary evolution, spatial gradients, and cumulative exposure. Empirical validation using 32,520 U.S. ZIP codes demonstrates exponential spatial decay for healthcare access ($\kappa = 0.002837$ per km, $R^2 = 0.0129$) with detectable boundaries at 37.1 km. The framework successfully diagnoses when scope conditions hold: positive decay parameters validate diffusion assumptions near hospitals, while negative parameters correctly signal urban confounding effects. Heterogeneity analysis reveals 2-13 $\times$ stronger distance effects for elderly populations and substantial education gradients. Model selection strongly favors logarithmic decay over exponential ($\Delta \text{AIC} > 10,000$), representing a middle ground between exponential and power-law decay. Applications span environmental economics, banking, and healthcare policy. The continuous functional framework provides predictive capability ($d^*(t) = \xi^* \sqrt{t}$), parameter sensitivity ($\partial d^*/\partial \nu$), and diagnostic tests unavailable in traditional difference-in-differences approaches.