Are expansionary monetary and fiscal policies substitutable or complementary?

The usual theory is that there is substitutability between expansionary monetary policy and expansionary fiscal policy: if governments implement a sufficiently stimulatory fiscal policy, then central banks will be able to end their highly stimulatory monetary policies. This theory is often put forward currently for the United States (if the Biden administration runs up massive fiscal deficits, the Federal Reserve will be able to stop buying securities) and for the euro zone (the ECB's support will be less necessary thanks to the recovery plans implemented by individual countries and the European Union). But the opposite theory is that expansionary monetary policy and expansionary fiscal policy complement each other. The higher the fiscal deficits and the higher the public debt, the more expansionary monetary policy must be to keep governments fiscally solvent (there is "fiscal dominance"). If the substitutability theory is correct, in 2022 we will see the beginning of a tapering of central bank government bond purchases in the United States and the euro zone. But if the complementarity theory is correct, government bond purchases will remain extremely large for many years to come. We examine the likelihood of the two scenarios.