That is the topic of my latest Bloomberg column, and here is one excerpt, related to earlier ideas from the New Monetary Economics:
The most common worry is that a central bank digital currency, or CBDC, would lead to disintermediation, with individuals or wholesalers putting their money into a CBDC system rather than commercial banks. The result would be fewer loans and less private-sector economic activity.
CBDC proponents typically say regulation can fix this problem. They favor some combination of issuance limits on CBDC units, CBDC access for wholesalers and major players only, or penalty interest rates or fees on CBDC holdings.
Yet all of these ideas create barriers — you might even call them “capital controls” — between ordinary dollars and CBDC dollars. If there are limits or barriers to dollar-to-CBDC conversion, dollars and CBDC units will not sell for the same price. Why should they? They perform different functions for different clienteles. Of course if the Fed allows unrestricted conversions, a one-to-one price would be enforced by arbitrage. But such open and unfettered privileges are precisely what policy advocates are seeking to limit.
The result would be a bit like the Chinese system. The yuan has for a long time had one value within China and another in world markets, with the difference being enforced by capital controls. And with a Chinese digital currency on the way, China may soon have (at least) three different currency prices.
In this new world, people will ask whether the U.S. dollar unit of account refers to “ordinary dollars” or to CBDC dollars. There might be two competing “dollar units of account” — or, more plausibly, retail prices would continue to be denominated in terms of ordinary dollars and the CBDC would have a floating exchange rate with respect to these “retail dollars.”
…the price of the CBDC dollar would become both a major policy variable and a major indicator of where central bank policy is headed. To what extent does the Fed wish to allow transactions, intermediation and resources to flow into the CBDC-linked sector? Current debates about open-market operations or interest on reserves will become arcane and outdated. The regulations roping off the CBDC sector from the retail-dollar sector would become truly significant, and would give the Fed (and other regulatory parties) much greater influence over sectoral allocation.
Over time, the CBDC financial sector would become much larger, as more of the economy digitizes and demands the hypermodern CBDC payment and settlement system. That would mean that the dominant U.S. currency — the CBDC dollar —would be fully separate from the mainstream accounting unit, namely the retail dollar.
There is further relevant analysis at the link.