This paper develops a dual-channel framework for analyzing technology diffusion that integrates spatial decay mechanisms from continuous functional analysis with network contagion dynamics from spectral graph theory. Building on our previous studies, which establish Navier-Stokes-based approaches to spatial treatment effects and financial network fragility, we demonstrate that technology adoption spreads simultaneously through both geographic proximity and supply chain connections. Using comprehensive data on six technologies adopted by 500 firms over 2010-2023, we document three key findings. First, technology adoption exhibits strong exponential geographic decay with spatial decay rate $\kappa \approx 0.043$ per kilometer, implying a spatial boundary of $d^* \approx 69$ kilometers beyond which spillovers are negligible (R-squared = 0.99). Second, supply chain connections create technology-specific networks whose algebraic connectivity ($\lambda_2$) increases 300-380 percent as adoption spreads, with correlation between $\lambda_2$ and adoption exceeding 0.95 across all technologies. Third, traditional difference-in-differences methods that ignore spatial and network structure exhibit 61 percent bias in estimated treatment effects. An event study around COVID-19 reveals that network fragility increased 24.5 percent post-shock, amplifying treatment effects through supply chain spillovers in a manner analogous to financial contagion documented in our recent study. Our framework provides micro-foundations for technology policy: interventions have spatial reach of 69 kilometers and network amplification factor of 10.8, requiring coordinated geographic and supply chain targeting for optimal effectiveness.

翻译：本文构建了一个双通道框架来分析技术扩散，该框架将连续函数分析中的空间衰减机制与谱图理论中的网络传染动力学相结合。基于我们先前的研究——这些研究建立了基于纳维-斯托克斯方程的空间处理效应和金融网络脆弱性分析方法，我们证明了技术采纳同时通过地理邻近性和供应链连接进行传播。利用2010年至2023年间500家公司采纳六项技术的全面数据，我们记录了三个关键发现。首先，技术采纳表现出强烈的指数型地理衰减，空间衰减率$\kappa \approx 0.043$每公里，这意味着空间边界$d^* \approx 69$公里，超出此范围溢出效应可忽略不计（R平方 = 0.99）。其次，供应链连接形成了特定于技术的网络，其代数连通性（$\lambda_2$）在技术扩散过程中增加了300-380%，且在所有技术中$\lambda_2$与采纳率之间的相关性均超过0.95。第三，忽略空间和网络结构的传统双重差分法在估计处理效应时存在61%的偏差。围绕COVID-19的事件研究表明，冲击后网络脆弱性增加了24.5%，通过供应链溢出放大了处理效应，其方式类似于我们近期研究中记录的金融传染。我们的框架为技术政策提供了微观基础：干预措施的空间影响范围为69公里，网络放大因子为10.8，需要协调地理和供应链目标以实现最佳效果。