This paper investigates in a non-linear setting the impact on the real economy of frictions stemming from the financial sector. We develop a medium scale DSGE model with a banking sector where an occasionally binding constraint on banks' capital induces a relevant non-linearity. The model - estimated on Italian data from 1999 to 2015 via a likelihood-free method - is able to generate business cycle asymmetries as in actual data that cannot replicated by linear models. Lastly, the role of macroprudential policies in smoothing the cycle is discussed.