The unemployment rate dropped to 3.5% in September, a rate not seen since December 1969. That is undoubtedly good news for workers, but it has left economists puzzling over how low joblessness can fall and for how long.

For years, a widely held economic theory predicted falling unemployment should eventually push up wages and inflation. With the U.S. economic expansion now in its 11th year, the jobless rate has continued to fall and year-over-year inflation remains shy of the Federal Reserve’s 2% target.

This...