Time limits represent a substantial departure from previous welfare policy. Theory suggests that their effects should vary according to the age of the youngest child of the family. I test this prediction using data from the Current Population Survey and find that time limits indeed have larger effects on families with younger children. I further estimate that anticipatory responses to time limits have decreased welfare use by 6 to 7 percent, accounting for 12 to 13 percent of the decline in welfare use during the late 1990s.