This paper presents a New Keynesian model that dwells on the role of banks in the cost channel of monetary policy. Banks extend loans to firms in an environment of monopolistic competition by setting the loan rate according to a Calvo-type staggered price setting approach, which means that the adjustment of the aggregate loan rate to a monetary policy shock is sticky. We estimate the model for the Euro area by adopting a minimum distance approach. Our findings exhibit that, first, frictions on the loan market influence the propagation of monetary policy shocks as the pass-through of a change in the money market rate to the loan rate is incomplete, and, second, the cost channel is operating, but the effect is weak since inflation is driven by real unit labor costs rather than the loan rate. Our main conclusion is that the strength of the cost channel is mitigated as banks shelter firms from monetary policy shocks by smoothing lending rates.