We analyze the positive and normative effects of a progressive tax on wages in a nonlinear New Keynesian DSGE model in the presence of demand and technology shocks. The non-linearity allows us to disentangle the effects of the progressive tax on the volatility and the level of macroeconomic variables, for both intertemporally optimizing ("Ricardian") and non-Ricardian ("rule-of-thumb") households. We find that the interaction of the two household types is of crucial importance. When only Ricardian households are considered, progressive taxes increase welfare (compared to at taxes) in the presence of technology shocks. Aggregate welfare falls, however, when rule-of-thumb households are added to the analysis. The progressive tax increases the welfare of the latter household by lowering its consumption volatility, but this is overcompensated for by the destabilization of Ricardian household consumption. Under demand shocks, progressive taxes reduce the welfare of both household types, with the welfare of rule-of-thumb households falling despite a decline in their consumption volatility. The reason is a lower average consumption level which is related to the changed curvature of the marginal cost function.