The last 150 years have been a period of unusual demographic change. Baby booms occurred in the aftermath of wars in some countries. In others, baby booms occurred as a result of falling infant mortality rates and subsequent reductions in fertility. Baby boom generations produce an echo, in the form of a large cohort of children a generation later, creating long-term demographic disequilibria. These destabilized age structures, together with improvements in health and longevity among the elderly, are producing, for the first time in history, populations with large and growing rates of old age dependency. We argue that transitions from high mortality and fertility to low mortality and fertility can be beneficial to economies as the large baby boom cohorts enter the workforce and save for retirement, while rising longevity has perhaps increased both the incentive to invest in education and to save for retirement. We present estimates of a model of economic growth that highlights the positive effects of demographic change during 1960-95. We also show how Ireland benefited from lower fertility in the form of higher labor supply per capita and how Taiwan benefited through increased savings rates. We emphasize, however, that the realization of the potential benefits associated with the demographic transition appears to be dependent on institutions and policies, requiring the productive employment of the potential workers and savings the transition generates.