Various proposals for "central bank digital currency" (CBDC) have been under discussion for several years now. The central bank of Ecuador launched a digital currency in 2015 — and shut down the failed project three years later. A number of economists have addressed the topic.
What is a CBDC? It is a payment medium that would be denominated in the established fiat money unit, not in any new unit. There are two main models: (1) a digital token that, like traditional coins and currency notes, and like Bitcoin, passes peer-to-peer without going through the interbank clearing system, presumably validated by a distributed-ledger blockchain system; and (2) account balances that individuals and businesses can directly hold on the books of the central bank, retail versions of the balances that commercial banks presently hold there for interbank payments. The latter model is not really properly called a currency, being a deposit-transfer system, but it is put under the "digital currency" umbrella because it resembles fiat currency notes in being a liability of the central bank, and as such a "final" means of payment, and because transactions would settle nearly instantly on a single balance sheet.
The debate over CBDCs was recently revived by the IMF's Managing Director Christine Lagarde in a speech suggesting, rather tentatively, that central banks should consider issuing some kind of digital currency so as to keep up with the times. (Why on earth the IMF continues to exist, long after the demise of the Bretton Woods system that it was created to support, is a question for another time.)
Lagarde begins her speech with a potted history of money. Although she does not attribute the origin of money to the state, she suggests that the state helps to improve money. Once bank-issued money arose, "spearheaded by the Italian bankers and merchants of the Renaissance," trust in the issuer became important. Thus: "Trust became essential—and the state became the guarantor of that trust, by offering liquidity backstops, and supervision." The timeline matters here. In fact, Italian bankers began providing money payments via transferable account balances some time before 1200 AD, whereas European states provided nothing in the way of "liquidity backstops, and supervision" until many centuries later. So state guarantees were not essential to the spread of bank-issued money historically. Nor was the popularity or safety of private banknotes, as issued by 17th century London goldsmiths, or by 18th and 19th-century Scottish or Canadian bankers, historically dependent on state guarantees.
Lagarde rightly notes that "the fintech revolution … questions the role of the state in providing money." She points to the recent proliferation of digital private payment providers "from AliPay and WeChat in China, to PayTM in India, to M-Pesa in Kenya" and namechecks "cryptocurrencies such as Bitcoin, Ethereum, and Ripple." She expresses her own position on the desirable monetary role of the state in surprisingly tentative language: "Some suggest the state should back down. Still, I am not entirely convinced. … I believe we should consider the possibility to issue digital currency. There may be a role for the state to supply money to the digital economy."
On the plus side of the CBDC ledger, Lagarde proposes that a central bank digital currency "could satisfy public policy goals, such as (i) financial inclusion, and (ii) security and consumer protection; and to provide what the private sector cannot: (iii) privacy in payments." Wait, what? It is of course laughable that a government would itself provide greater privacy in payments than it allows private institutions to provide. Could this have been a joke intended to lighten the mood of the speech? The private sector can in fact provide as much financial privacy as customers desire, as numbered Swiss bank accounts once did, and as "privacycoin" crypto projects today remind us. Lack of privacy stems from government restrictions, not from private-sector inability.
Lagarde says that "There may be scope for governments to encourage private sector solutions" to the problem of financial inclusion "by providing funding, or improving infrastructure." More effective ways to encourage private sector solutions to banking the unbanked would be (a) deregulation, especially not requiring permission for innovations in mobile and other payment platforms, (b) guarantees not to interfere in private payment platforms once launched, and (c) guarantees on the privacy of private sector accounts from government surveillance, which might help to attract some of the warily unbanked to deposit use.
To her credit, Lagarde recognizes that people value the privacy provided by currency: "Cash, of course, allows for anonymous payments. We reach for cash to protect our privacy for legitimate reasons: to avoid exposure to hacking and customer profiling, for instance." But she is vague at best, and dissembling at worst, on how deposits on the central bank's books would insure privacy. She promises that customer identities "would not be disclosed to third parties or governments unless required by law," but adds: "Anti-money laundering and terrorist financing controls would nevertheless run in the background. If a suspicion arose it would be possible to lift the veil of anonymity and investigate." Would any suspicion by a policeman or tax collector be enough to lift the veil? If so, then the CBDC would be no more private than ordinary current-day bank deposits. J. P. Koning not unfairly characterizes what Lagarde offers as a "Faustian bargain": "The state will issue digital currency that protects us from information snoops in the private sector, on the condition that it gets a back door."
In the US and Europe, at least, banks today are required to notify regulators of large or "suspicious" deposit and withdrawal activities, and are expected to surrender account information to the authorities on a written request, without a court order or a search warrant. It is hard to imagine that any government would instruct or allow its central bank to create accounts with greater privacy protection against the national government than commercial bank accounts have.
In the background to Lagarde's speech is a November 2018 IMF staff discussion note on CBDC that she cites.  The note itself does not offer a brief for CBDC, but rather enumerates plusses and minuses. Comparing CBDC to cash, demand deposits, and non-bank private digital payment media, the note's authors find that "CBDC would not strictly dominate any of these alternative forms of money."
The staff discussion note emphasizes the hope of Keynesian macroeconomists that "interest-bearing CBDC would eliminate the effective lower bound on interest rate policy," but points out that it would have this effect "only with constraints on the use of cash." It is the abolition of easily stored cash that allows a central bank to impose negative interest rates, not the introduction of CBDC in either form.
The IMF note acknowledges a case for stronger payments privacy:
There are legitimate reasons people may prefer at least some degree of anonymity—potentially when it comes to everyone except the government, and regarding the government unless a court order unlocks encrypted transaction information. It is a way to avoid customer profiling—commercial use of personal information, for example, to charge higher mortgage rates to people who purchase alcohol. Another advantage of anonymity is limiting exposure to hacking. Moreover, anonymity is often associated with privacy—widely recognized as a human right (as stated in the Universal Declaration of Human Rights [Article 12] and elsewhere).
The note also observes that a central bank offering retail deposits "could increase risks to financial intermediation. It would raise funding costs for deposit-taking institutions."
Just as importantly on the minus side, although not mentioned in either Lagarde's speech or the IMF staff note, is that diverting deposits from commercial banks to the central bank will shrink the funding for the economic-growth-enhancing small business loans that commercial banks provide, in favor of central bank holdings of sovereign debts and government-favored private securities (for the Fed at present, mortgage-backed securities). The IMF authors of the note observe that in a world where CBDC accounts replace both currency and ordinary checking deposits "only the commercial bank could create money." Correspondingly, in a world of CBDC alone, only the central bank would direct the loanable funds marshalled by checking deposits.
 Bordo and Levin (2017) have suggested that private commercial banks should provide the front end for access to the central bank's balance sheet, because they are better at customer service. Designated "digital cash" account balances at commercial banks would differ from ordinary account balances only in that balance transfers between accounts would be nearly instantly settled. Near-instant settlement would be enabled by the commercial banks holding "segregated reserve accounts" at the central bank, linked to their customers digital cash accounts, and presumably backed by high or even 100-percent, reserves. Under their proposal commercial banks would act as so many central bank branch agencies. Their proposed system would have all the same drawbacks of outright CBDC accounts discussed herein.
 Under the Right to Financial Privacy Act of 1978, a bank or other financial institution is protected from customer lawsuits for disclosing customer account information to a US federal agency (BATF, DEA, FBI, IRS, etc.) that subpoenas it in connection with suspected illegal activity. The agency is required only to notify an individual customer (but not a business customer) of the request, giving the customer ten days to seek legal redress. In court the agency does not need to meet the Fourth Amendment standard of probable cause. Under later statutes including the Patriot Act, notice is not required where the individual is suspected of drug trafficking, espionage, or terrorism. In a recent law review article, W. F. McElroy notes that today "the privacy of financial records from unwarranted government intrusion is under siege."
 Tommaso Mancini-Griffoli, Maria Soledad Martinez Peria, Itai Agur, Anil Ari, John Kiff, Adina Popescu, and Celine Rochon, "Casting Light on Central Bank Digital Currency," IMF Staff Discussion Note (November 2018).