Traditionally, estimation of demand systems is predicated on the validity of several axioms of consumer behavior. While such abstractions make empirical work easier, they can also overlook important economic behavior. Because the price of a good does not reflect the total cost of purchase, there is reason to believe that consumer responses to changes in price are not continuous. Utilizing a regime switching model, we show that there are indeed important threshold effects, and that these effects bias elasticity estimates toward zero.