For decades, researchers have repeated a simple fact about income and family size: The higher the family income, the fewer children you have.

But in recent years, that trend has started to reverse; wealthier families are beginning to have more children than middle-class families. And a new analysis suggests that, in the United States, having a third child might be more than a sign of being wealthy. In an analysis of the Federal Reserve’s recent Survey of Consumer Finances, Mike Konczal, vice president of policy and research at the left-leaning nonprofit Economic Security Project, found that 49 percent of U.S. families in the top 1 percent of incomes had three or more children, compared with 40 to 43 percent for most other income groups.