This paper estimates and compares new-Keynesian DSGE monetary models of the business cycle derived under two different pricing schemes - Calvo, Rotemberg - and a positive trend inflation rate. Our empirical findings (i) support trend inflation-equipped models as better fitting during the U.S. great moderation period, (ii) provide evidence in favor of the statistical superiority of the Calvo setting, and (iii) suggest the absence of price indexation under the Calvo mechanism only. Possibly, the superiority of the Calvo model (against Rotemberg) is due to the restrictions implied by such pricing scheme for the aggregate demand equation. The determinacy regions associated to the two estimated models indicate relevant differences in the implementable simple policies. Our findings call for the development of monetary policy models consistently embedding a positive trend inflation rate and possibly based on a Calvo pricing scheme.