Does the growth of military hard power back up the growth of monetary soft power via data-driven probabilistic optimal relations?

The research of how economic growth and military expenses affect each other could be found in the literature, but a comprehensive quantitative study of the degree of interaction between military expenses and money currency is not fully investigated. In this study, we borrow the concepts of hard power and soft power and quantify these concepts by associating military hard power with military expenses over GDP and monetary soft power with growth rate of exchange rate over growth rate of broad money from 1961 to 2019. We study the causal relation between these two powers by mathematical and statistical approaches. We keep track of the time-series of Hausdorff distances between their empirical optimal relations and absolute linear relations and analyse their stability. The absolute linear relations serve as the benchmark for measuring the causality between military hard power and monetary soft power, while the empirical optimal relations reveal their actual interaction. Our result shows there is a clear causal relation that military hard power backs up monetary soft power, but not the other way around. This indicates that proper military spending over GDP would stabilise and promote the currency value of a country.