Abstract
I discuss private and central-bank-issued digital currencies, summarizing my prior research. I argue that prices of private digital currencies such as bitcoin follow random walks or, more generally, risk-adjusted martingales. For central bank digital currencies, I argue that they enhance the trilemma facing a central bank. Of the three objectives, price stability, efficiency, and monetary trust, the central bak can achieve at most two.
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Notes
This is akin to an anthropic principle.
Obviously, there is an overall increase in price since 2018 until the time of writing, February 2024. It may be harder to decide whether that price increase is due to chance or an upward drift in the bitcoin price.
The term “hodler” rather than “holder” was introduced by a typo on https://bitcointalk.org/index.php?topic=375643.0 and is now firmly part of the vocabulary, describing individuals holding on to a cryptocurrency rather than spending or exchanging it.
There is a large literature on the details of monetary policy implementation, and they are not the focus of our paper. We simply assume that the central bank can achieve this price path exactly.
From an asset pricing perspective, one can think of liquidity services as the dividend of money. One still needs to be careful when applying an asset pricing approach since doubling the price of bitcoin also doubles its liquidity services.
The boundedness condition arises from the feature that the total value of bitcoin cannot exceed the total value of all goods when all bitcoins are always spent.
Note that the seller becomes a buyer in \(t+1\), i.e., it is the utility function of the current seller on the right-hand side of Eq. (5). The risk compensation can also take the form of an “insurance premium”, i.e., there are generally price processes \(Q_t\) so that the expected return on bitcoin is below unity.
With cash and a CBDC, there is a “boring” run where agents exchange CBDC for cash or vice versa. This is a rather benign scenario and not our focus.
The paper also includes a discussion of the price level \(P_2\). Briefly, note that any price level \(P_2\) can be achieved by the appropriate choice of the interest rate policy i(n).
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Acknowledgements
This is my Presidential Address, delivered at theInternational Atlantic Economic Conference in Philadelphia on Friday, October 6, 2023. I am very grateful to Katherine Virgo for her supportthroughout. I am grateful to my co-authors on the research I am reporting here, particularly Linda Schilling and Jesús Fernández-Villaverde.
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Uhlig, H. On Digital Currencies. Atl Econ J 52, 1–14 (2024). https://doi.org/10.1007/s11293-024-09792-1
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DOI: https://doi.org/10.1007/s11293-024-09792-1