When can the gauge of wire change in a household circuit?
Pigtails are referred to as tap conductors in the NEC. 

Unlike tap conductors for some luminaries, ovens, and other appliances, which can be smaller than the OCPD, it is not permitted to use a smaller tap for general wall receptacle outlets.

NEC 2014 210.19 (A)(4)(Exception C) Individual outlets, **other than receptacle outlets**, with taps not over 450 mm (18 in.) long.

Here's a good example of tap conductors on a dimmer: