Full-service restaurant meals rose the most, at 3.8%. Limited-service meals, the category that covers fast food, rose 3.2%. Food-at-home costs fell 0.1% in September alone.

The gap is hitting households whose pay has fallen behind prices. Overall consumer prices rose 3.7% over the past year while average hourly wages rose 3%, which left real hourly wages down 0.7%. Families now compare a $35 or $40 fast-food order with what the same money buys at a grocery store. Consumers have not stopped dining out overall.

McDonald's, Yum Brands and Domino's Pizza are among the chains whose growth is being held back by the price gap. In September, McDonald's warned that persistent inflation could keep customer traffic flat in its major markets. The company has announced an $8.5 billion plan, spread over a decade, to help franchisees improve their economics. It is also relying on its McValue platform, which includes a menu of items under $3 and $4 breakfast offers, to keep customers seeing it as good value.

Yum Brands' KFC chain is testing smaller portions sold as "Go Buckets." Domino's is concentrating on promotions and smaller menu offers.

Investors now pay more attention to order volume and customer traffic than to headline comparable-sales growth, because higher menu prices can push sales figures up even when fewer customers come through the door.