This paper presents some new estimates for the relationship between inflation and unemployment in Brazil based on a new Keynesian hypothesis about the behavior of the economy. Four main hypotheses are tested and sustained throughout the study: i) agents do not have perfect rationality; ii) the imperfection in the agents expectations generating process may be an important factor in explaining the high persistence (inertia) of Brazilian inflation; iii) inflation does have an autonomous inertial component, without linkage to shocks in individual markets; iv) a non-linear relationship between inflation and unemployment is able to provide better explanations for the inflation-unemployment relationship in the Brazilian economy in the last 12 years. While the first two hypotheses are tested using a Markov Switching based model of regime changes, the remaining two are tested in a context of a convex Phillips Curve estimated using the Kalman filter. Despite the methodological and estimation improvements provided in the paper, the impulse-response functions for the monetary policy presented the same properties shown in the literature that uses Brazilian data.