When China put in place its one-child policy four decades ago, policy makers said they would simply switch gears if births dropped too much. That has turned out to be not so easy. “In 30 years, the current problem of especially dreadful population growth may be alleviated and then [we can] adopt different population policies,” the Communist Party said in a 1980 open letter to members and young people. With the number of births declining year after year, China is now racing in the opposite direc-tion, closing abortion clinics and expanding services to help couples conceive. But a legacy of...