On the Equivalence of Private and Public Money is a 2019 working paper by Brunnermeier and Niepelt that addresses this issue:
We propose a generic model of money and liquidity. We provide
sufficient conditions under which a swap of private (inside) against
public (outside) money leaves the equilibrium allocation and price
system unchanged. We apply the results to Central Bank Digital
Currency, the “Chicago Plan,” and the Indian de-monetization
experiment.
This is their exercise:
As a result of these developments, debates about the “right” monetary
architecture resurface and classic questions about the nature of money
return to the fore. A key point of contention concerns the optimal
balance between public and private money. Proponents of a strong
government role fear that private money creation breeds instability
and shifts seignorage rents from taxpayers to shareholders. In the
“Chicago Plan” of the 1930s and the recently rejected Swiss
constitutional referendum on “Vollgeld” (sovereign money), they
propose to severely restrict or even ban money creation by anyone
except the central bank. Less drastic proposals aim at electronic
Central Bank Digital Currency (CBDC) for use by non-banks. Monetary
authorities in countries such as Canada, Singapore, and Sweden
currently evaluate the introduction of such “Reserves for All;” the
Banco Central del Uruguay has successfully tested the model; and other
central banks consider it.
Skeptics, on the other hand, warn of severe macroeconomic risks due to
the replace- ment of private by public means of payment. In their
view, a reduction of bank issued inside money will hamper credit
extension by banks to firms and households, with negative
implications for growth; and the introduction of CBDC will provide a
safe haven asset for depositors to run into at the slightest hint of a
crisis, rendering bank runs more likely and thereby threatening
financial stability.
To assess these arguments, we develop a generic model of money and
liquidity. Within this framework, we establish sufficient conditions
under which it is irrelevant whether the public or the private
sector issues means of payment.
They summarize their results as follows:
We apply our results to two proposals for monetary reform:
CBDC, and the more drastic “Chicago Plan.” We find that the
introduction of CBDC need not change macroeconomic outcomes,
independently of whether deposits are subject to bank runs or not. If
bank runs are a feature of the current system then the equivalent
monetary regime with CBDC has state contingent transfers from the
private sector to the central bank; if it does not, for instance due
to a generous deposit insurance scheme, then no such transfers are
needed.
Contrary to the prevailing view that CBDC would make bank runs more
likely, our analysis concludes that it might well make them less
likely. With pass-through funding, the central bank becomes a large
depositor that internalizes run externalities, unlike small
depositors. This makes the financial system less fragile. Regarding
the Chicago Plan, we also find that the conditions for equivalence are
met provided that banks receive appropriate compensation for lost
seignorage rents, or that the ownership structure of banks is
aligned with the distributions of tax burdens. An important
motivation for the “Vollgeld” proposal to outlaw banks from creating
liquid assets was that banks should be forced to relinquish
these rents. This would transfer seignorage from bank
shareholders to taxpayers, undermining wealth-neutrality.
We also apply our results to the recent Indian de-monetization
experiment. We find that it could not have been neutral because
cash-based transactions at black-market prices could not have been
replaced by deposit-based transactions.
In contrast, there is a Bank of England working paper that strongly disagrees.The macroeconomics of central bank issued digital currencies by Barrdear and Kumhof (2016):
We study the macroeconomic consequences of issuing central bank
digital currency (CBDC) -- a universally accessible and
interest-bearing central bank liability, implemented via distributed
ledgers, that competes with bank deposits as medium of exchange. In a
DSGE model calibrated to match the pre-crisis United States, we find
that CBDC issuance of 30% of GDP, against government bonds, could
permanently raise GDP by as much as 3%, due to reductions in real
interest rates, distortionary taxes, and monetary transaction costs.
Countercyclical CBDC price or quantity rules, as a second monetary
policy instrument, could substantially improve the central bank’s
ability to stabilise the business cycle.
