How well can a cryptocurrency serve as a means of payment? Since the creation of Bitcoin in 2009,
many critics have denounced cryptocurrencies as fraud or outright bubbles. More nuanced opinions
have argued that such currencies are only there to support payments for illegal activities or simply
waste resources. Advocates point out, however, that – based on cryptographic principles to ensure
security – these new currencies can support payments without the need to designate a third-party
that controls the currency or payment instrument possibly for its own profit.1
We take up this discussion and develop a general equilibrium model of a cryptocurrency that
uses a blockchain as a record-keeping device for payments. Although Bitcoin in its current form
has immense welfare costs, an optimally designed cryptocurrency can potentially support payments
rather well. First, using Bitcoin transactions data, we show that the welfare cost of a cryptocurrency
can be comparable to a cash system with moderate inflation. Second, using summary statistics for
US debit card transactions, we find that a cryptocurrency can perform nearly as well as a low-value,
retail payment system operating with very low fees.2
Economics research so far has provided little insight into the economic relevance of cryptocurrencies.
Most existing models of cryptocurrencies are built by computer scientists who mainly focus on the
feasibility and security of these systems. Crucial issues such as the incentives of participants to
cheat and the endogenous nature of some key variables such as the real value of a cryptocurrency
in exchange have been largely ignored.
Such considerations, however, are pivotal for understanding
the optimal design and, hence, the economic value of cryptocurrency as a means of payment.
Our focus is primarily on understanding how the design of a cryptocurrency influences the interactions among participants and their incentives to cheat. These incentives arise from a so-called
“double-spending” problem. Cryptocurrencies are based on digitial records and, thus, can be copied
easily and costlessly which means that they can potentially be used several times in transactions (for a more detailed description see Section 2 below). We formalize this double-spending problem
and show how this problem is being addressed by (i) a resource-intensive competition for updating
the records of transaction – a process commonly referred to as mining – and (ii) by introducing confirmation lags for settling transactions in cryptocurrency. This implies that a cryptocurrency faces
a trade-off between how fast transactions settle and a guarantee (or “finality”) for their settlement.
Consequently, crytocurrencies cannot achieve immediate and final settlement of transactions.
A strength of our analysis is that we take into account the costs of operating a cryptocurrency
that prohibits double-spending. This allows us to quantitatively assess how efficient Bitcoin as a
medium of exchange can be relative to existing means of payment. Calibrating our model to Bitcoin
data, we find that from a social welfare perspective using Bitcoin is close to 500 times more costly
than using traditional currency in a low inflation environment.
This is, however, a result of the inefficient design of Bitcoin as a cryptocurrency. Bitcoin uses
both currency growth and transaction fees to generate rewards for mining. In its current form, the
cryptocurrency reward structure is too generous so that too many resources are being used to rule
out double-spending and making it a secure form of payment.
We show that the optimal way of
providing rewards for mining is exclusively via currency creation at a very low rate rather than by
using transaction fees. The optimal design of Bitcoin would generate a welfare cost of only about
0.08% of consumption which is equivalent to a cash system with moderate inflation.
We also evaluate the efficiency of using a cryptocurrency system to support large-value and retail
transactions. Using summary data for Fedwire and US Debit cards, we confirm that cryptocurrencies are a much better alternative for low value, high-volume transactions than for large value
payments. This is intuitive, as double spending incentives increase with the size of transactions.
Hence, more mining and longer confirmation lags (which are both costly) are required when supporting large-value payments in a cryptocurrency.
Our exercise shows that cryptocurrency systems
can potentially be a valid alternative to retail payment systems that operate at very low fees, as
soon as limits on the scale of such systems can be resolved.
The economic literature on cryptocurrencies is very thin. We are not aware of any work that
has formalized the design features of a cryptocurrency and that has studied its optimal design
under the threat of double spending attacks. We model bilateral exchange based on money, we
follow the recently promoted framework of Lagos and Wright (2005) and enrich it by modelling a
mining competition to update the blockchain. For formalizing the blockchain itself, we rely on the theoretical literature of payment systems as a record-keeping device.3
Our work is thus a first attempt to explicitly model the distinctive technological features of a
cryptocurrency system which are a blockchain, mining and double-spending incentives within a
quantitative economic model. We are also first to theoretically analyze the optimal design of a
cryptocurrency and giving a quantitative answer to the efficiency properties of cryptocurrencies.
Some recent contribution have analyzed – from a qualitative perspective – whether Bitcoin can
function as a real currency given its security features and lack of usage for making frequent payments
(see for example Yermack (2013) and B¨ohme et al. (2015)). One question in this line of research
is to empirically explain the valuation of cryptocurrencies. Gandal and Halaburda (2014) look at
network effects associated with cryptocurrencies and investigate how such effects are reflected in
their relative valuation. Glaser et al. (2014) look at how media coverage of Bitcoin drives part of
the volatility in its valuation.4
Another area of research investigates how digital currencies can influence the way monetary policy is
conducted. But none of this work can be applied to cryptocurrencies that are based on a blockchain
and operate without a designated third-party to issue the currency. Agarwal and Kimball (2015)
advocate here that the adoption of digital currencies can facilitate the implementation of a negative
interest rate policy, while Rogoff (2016) suggests that phasing out paper currency can undercut
undesirable tax evasion and criminal activities. Our findings complements this work as we establish
some potential bounds on the costs that can be levied on people through central bank issued
digital currency.5 Finally, Fern´andez-Villaverde and Sanches (2016) model cryptocurrencies as
privately issued fiat currencies and analyze – in the tradition of the literature on the free banking
era – whether competition among different currencies can achieve price stability and efficiency of
exchange.