Central bank digital currency and monetary policy

Many central banks are contemplating whether to issue a central bank digital currency (CDBC). CDBC has certain potential benefits, including the possibility that it can bear interest. However, using CBDC is costly for agents, perhaps because they lose their anonymity when using CBDC instead of cash. I study optimal monetary policy when only cash, only CBDC, or both cash and CBDC are available to agents. If the cost of using CBDC is not too high, more efficient allocations can be implemented by using CBDC than with cash, and the first best can be achieved. Having both cash and CBDC available may result in lower welfare than in cases where only cash or only CBDC is available. The welfare gains of introducing CBDC are estimated as up to 0.64% for Canada.