The U.S. economy, already struggling with stagnant wages and lackluster spending, faces another obstacle to growth: missing babies.

The nation’s fertility rate edged down last year to a record low, the latest notch in a long decline made worse by the recent recession. For every 1,000 women of childbearing age, there were just 62.5 births, down from 63 births in 2012, according to the Centers for Disease Control and Prevention.

Lower...