We analyse the effects of central bank government bond purchases in an estimated DSGE model for the euro area. In the model, central bank asset purchases are relevant in so far as agency costs distort banks asset allocation between loans and bonds, and households face transaction costs when trading government bonds. Such frictions in the banking sector induce inefficient time-variation in the term premia and open up for a credit channel of central bank government bond purchases. Considering first ad hoc asset purchase programmes like the one implemented by the ECB, we show that their macroeconomic multipliers are stronger as the lower bound on the policy rate becomes binding and when the purchasing path is fully communicated and anticipated by economic agents. From a more normative standpoint, interest rate policy and asset purchases feature strong strategic complementarities during both normal and crisis times. In a lower bound environment, optimal policy conduct features long lower bound periods and activist asset purchase policy. Our results also point to a clear sequencing of the exit strategy, stopping first the asset purchases and later on, lifting off the policy rate. In terms of macroeconomic stabilisation, optimal asset purchase strategies bring sizeable benefits and have the potential to largely offset the costs of the lower bound on the policy rate.