This research explores the intricate dynamics of economic integration in Asia and Europe, assessing the degree of real exchange rate (RER) convergence. Departing from conventional bilateral RER calculations based on the Consumer Price Index (CPI), we utilize industry-specific RER based on the Producer Price Index (PPI) to evaluate RER convergence towards regional key currencies—the Chinese renminbi (RMB) in Asia and the Deutsche Mark (DEM) in Europe. Our study focuses on evaluating RERs within three pivotal machinery industries—general machinery, electric machinery, and transport equipment—as significant drivers of regional and global supply chains. Employing a state space model, we estimate industry-specific RER convergence and discern nuanced time variations in RER adjustment speeds across regional countries. Additionally, the dynamic factor model (DFM) decomposes RER convergence dynamics for each regional country, identifying relative contributions from common global, regional (Asia or Europe), and idiosyncratic (country-specific) factors. Our analysis reveals nuanced patterns in RER convergence dynamics across regional countries. Notably, the DFM results for general machinery, electric machinery, and transport equipment unveiled distinctive trends within each sector. For instance, while certain regions exhibited stronger convergence driven by common global or regional factors, others displayed higher sensitivity to idiosyncratic country-specific influences.