Technology Adoption and Network Externalities in Financial Systems: A Spatial-Network Approach
Tatsuru Kikuchi
TL;DR
The paper tackles coordination failures in technology diffusion within financial networks, where adoption value depends on both geographic proximity and network connections. It develops a unified spatial-network diffusion framework built on a master equation with a Feynman-Kac representation, enabling a path-based interpretation of adoption pressure and the derivation of the Adoption Amplification Factor. A Lévy jump-diffusion extension with state-dependent intensity captures critical mass and cascade dynamics, unifying gradual diffusion and abrupt cascades under a two-regime picture. The empirical application to SWIFT gpi adoption among 17 Global Systemically Important Banks confirms the key predictions: network-central banks adopt earlier, founding members contribute disproportionately to amplification, and a two-regime pattern with pre-threshold diffusion and post-threshold cascades is evident. The findings have practical policy implications, highlighting how targeting high-amplification institutions and designing timely interventions can efficiently overcome coordination frictions in financial infrastructure.
Abstract
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 ($ρ= -0.69$, $p = 0.002$), 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.