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 euro in Europe. We specifically focus on RERs in 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 aim to estimate industry-specific RER convergence and discern nuanced time variations in RER adjustment speeds across regional countries. The dynamic factor model (DFM) decomposes RER convergence dynamics for each regional country, identifying relative contributions from common global (US), regional (Asia or Europe), and idiosyncratic (country-specific) factors. This approach provides comprehensive insights into the intricacies of economic integration in Asia and examines the role of the RMB as a regional key currency.