This issue might sound very familiar to you – the Federal Reserve System was confronted with a similar issue a while ago. It stopped buying large quantities of assets in October 2014 and, since then, it has kept the size of its balance sheet constant, buying just enough to replace maturing securities.
The Fed has stated that it will not begin shrinking the central bank’s balance sheet until normalisation of the federal funds rate is well underway. As for the Eurosystem, the ECB Governing Council is to decide upon the sequencing of such measures.