The relevance of direct supply-side effects of monetary policy in a New Keynesian DSGE model is studied. We extend a model with several nominal and real frictions by introducing a cost channel of monetary transmission and allowing for non-separability of money and consumption in the utility of the representative household. These fea- tures have important theoretical consequences for the output-inflation trade-off and indeterminacy of interest rate rules. The empirical evidence for these effects are then examined using a Bayesian maximum likelihood framework complemented with GMM single-equation estimation. Both estimation strategies point to weak evidence for the cost channel and non-separable utility.