We analyse the behaviour of an economy characterized by staggered pricing, with price contracts either specified in nominal terms (Taylor, 1980), or in real terms (Fuhrer and Moore, 1995). We focus on the response of these models to a permanent and unexpected disinflation policy. It is advanced that this policy implies very different responses from the two models, with the former being unable to reproduce any inflation persistence or output depression, while the latter is able to generate it. We argue that this result builds on the unjustified neglect of a structural error term present in both models. Taking into account this term partly erases the differences between the models, who display comparable inflation persistence and output costs in response to a disinflation.