BEIJING — China’s birth rate fell to its lowest level in the country’s modern history, hastening the aging of the population and the shrinking of the workforce, despite the government’s efforts to reverse the trend.

Already, nearly a fifth of China’s population is age 60 or older. A shrinking working-age population can dent the economy through lower productivity and higher labor costs, while an increasing number of elderly pushes up health-care costs. South Korea and Japan are facing similar problems but on a much smaller scale.