How the old saying “when the United States sneezes, the world catches a cold” holds true has been the subject of many research papers on global and country group business cycle synchronization and divergence. Instead of business cycle linkages, however, this paper examines the evolution of the dependence of ASEAN-5 and other Asian economies on their traditional and emerging growth engines (the United States, EU, Japan, China, and India). For this we use a structural vector autoregression model that yields time-varying growth multiplier effects. Although China has overtaken others as a major export destination for ASEAN-5 and despite the United States losing much of its relative economic clout in Asia, the multiplier effects show that the United States is still about 1.5 times more growth-enhancing than China for ASEAN-5. The EU has also not lost out completely to China as a growth engine. China, however, has overtaken Japan to become about 1.88 times more growth enhancing than Japan for ASEAN-5. India has yet to become a significant growth engine, although it is of increasing importance to Singapore, Malaysia, and Indonesia. These results call for new initiatives to balance the rising over-dependence on China.