My Personal Tribute to Professor Taizo Yakushiji

Time-Scale Dependence in Defense-Spending Interdependence:

Evidence from the United States, China, and Japan Using Generalized RPC

This article is a personal tribute to my academic mentor in Japan, Professor Taizo Yakushiji, who passed away on January 9, 2026. It reflects the analytical techniques I learned from him in the early 1990s and demonstrates how I have built upon that foundation in light of recent academic literature.

（本稿は、2026年1月9日に逝去された恩師・薬師寺泰蔵教授に捧げる追悼草稿であり、学術誌等を通じた正式な出版・公刊を目的としたものではありません。）

Abstract

This article revisits the Richardson-type arms race model by introducing a frequency-domain perspective on strategic interaction. Using SIPRI military expenditure data for Japan, the United States, and China from 1990 to 2024, it develops a generalized relative power contribution (RPC) framework that integrates order-invariant identification with time-scale decomposition. The analysis yields three findings. First, low-frequency dynamics exhibit stronger cross-national contributions, indicating structural interdependence alongside domestic institutional constraints, whereas high-frequency dynamics are increasingly dominated by own contributions, reflecting short-run internal adjustment. Second, conventional orthogonalized RPC introduces systematic directional bias due to ordering dependence, particularly by understating China’s influence. Third, bootstrap inference shows that while the qualitative structure of interaction is robust, the magnitude of estimated effects varies across frequencies, especially at higher frequencies. These results suggest that arms competition is better understood as a multi-scale and probabilistic process rather than a single reaction relationship. By providing an order-invariant and frequency-specific measure of contribution, the framework offers a more precise characterization of defense-spending interdependence, with implications for empirical studies of deterrence, strategic interaction, and policy responsiveness in contemporary security environments.