We propose a simple method for estimating multiple natural rates in a system of simultaneous equations. Our estimators of natural rates are closely related to the HP filter and accessible by many practitioners. As an application, Japan’s potential output and natural foreign exchange rate are estimated. It is shown that Japan’s potential output has been growing, but the natural foreign exchange rate has experienced stepwise downward shifts since the beginning of the 21st century. While Japan suffered the long-lasting stagnation, emerging markets, particularly China, achieved tremendous economic growth. The declines in the natural foreign exchange rate indicate Japan’s lost competitiveness in the world economy clearly.