Technology Adoption and Network Externalities in Financial Systems: A Spatial-Network Approach

This paper develops a unified framework for analyzing technology adoption in financial networks that incorporates spatial spillovers, network externalities, and their interaction. The framework characterizes adoption dynamics through a master equation whose solution admits a Feynman-Kac representation as expected cumulative adoption pressure along stochastic paths through spatial-network space. From this representation, I derive the Adoption Amplification Factor -- a structural measure of technology leadership that captures the ratio of total system-wide adoption to initial adoption following a localized shock. A Levy jump-diffusion extension with state-dependent jump intensity captures critical mass dynamics: below threshold, adoption evolves through gradual diffusion; above threshold, cascade dynamics accelerate adoption through discrete jumps. Applying the framework to SWIFT gpi adoption among 17 Global Systemically Important Banks, I find strong support for the two-regime characterization. Network-central banks adopt significantly earlier ($\rho = -0.69$, $p = 0.002$), and pre-threshold adopters have significantly higher amplification factors than post-threshold adopters (11.81 versus 7.83, $p = 0.010$). Founding members, representing 29 percent of banks, account for 39 percent of total system amplification -- sufficient to trigger cascade dynamics. Controlling for firm size and network position, CEO age delays adoption by 11-15 days per year.