This paper estimates the Brazilian NAILO (Nonaccelerating Inflation Level of Output), obtains (Bayesian) probability bands for the Nailo and for its growth rate, and investigates the relationship between deviations of output with respect to the Nailo and the acceleration of inflation. As explained in the text, the NAILO should not be confused with the country`s potential output. This study innovates by changing the specification of the Phillips Curve, adopted by Gordon (1997 and 1998) and by Staiger, Stock and Watson (1997a, 1997b and 2002), to allow for a stochastic rate of growth of the NAILO and for a variance of residuals which changes over time according to a hidden Markov chain specification. These improvements are essential to deal with the instability of the Brazilian economy. Considering 68% probability bands, the annual growth rate of Nailo in the last quarter of 2007 was between 2.5 and 4.4% (3.5% being the most likely value). A value of GDP 1% higher than that of the NAILO, for more than four quarters and adopting 68% probability bands, generates an increase in the annual inflation rate between 0.5 and 0.7 pp (percentage points). We also observed a very close relationship between changes in the output gap and changes in the installed capacity utilization measured either by the Getulio Vargas Foundation (FGV) or by the National Confederation of the Industry (CNI).