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Jonathan Chiu†    Bank of Canada

Thorsten V. Koeppl‡. Queen’s University

First version: March, 2017

This version: September, 2018

Abstract

How well can a cryptocurrency serve as a means of payment? We study the optimal design of 

cryptocurrencies and assess quantitatively how well similar currencies can support bilateral trade. 

 The challenge for cryptocurrencies is to overcome double- spending by counting on competition 

 to modernize the blockchain( expensive mining) and by delaying agreement. We estimate that the 

 current Bitcoin scheme generates a large weal loss of1.4 of consumption. This weal loss 

 can be lowered mainly to0.08 by espousing an optimal design that reduces mining and 

 relies simply on plutocrat growth rather than sale freights to finance mining prices. We 

 also point out that cryptocurrencies can potentially challenge retail payment systems handed 

 scaling limitations can be addressed. 

 Keywords Cryptocurrency, Blockchain, Bitcoin, Double Spending, Payment Systems 

 JEL Bracket E4, E5, L5 

 ∗ The views expressed in this paper aren’t inescapably the views of the Bank of Canada. We thank the cult 

 at numerous forums and conferences for their commentary. This exploration was supported by SSHRC Insight Grant 435- 

 2014- 1416. The authors declare that they’ve no applicable or material fiscal interests that relate to the exploration 

 described in this paper. 

 † Bank of Canada, 234 Wellington St, Ottawa, ON K1A 0H9, Canada(e-mailjchiu@bankofcanada.ca). 




 ‡ Queen’s University, Department of Economics, Kingston, K7L 3N6, Canada(e-mailthor@econ.queensu.ca).

(1) Introduction

 How well can a cryptocurrency serve as a means of payment? Since the creation of Bitcoin in 2009, 

 numerous critics have denounced cryptocurrencies as fraud or outright bubbles. further nuanced opinions 

 have argued that similar currencies are only there to support payments for illegal conditioning or simply 

 waste coffers. lawyers point out, still, that – grounded on cryptographic principles to insure 

 security – these new currencies can support payments without the need to designate a third- party 

 that controls the currency or payment instrument conceivably 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 weal costs, an optimally designed cryptocurrency can potentially support payments 

 rather well. First, using Bitcoin deals data, we show that the weal cost of a cryptocurrency 

 can be similar to a cash system with moderate affectation. Second, using summary statistics for 

 US disbenefit card deals, we find that a cryptocurrency can perform nearly as well as a low- value, 

 retail payment system operating with veritably low freights.2 

 Economics exploration so far has handed little sapience into the profitable applicability of cryptocurrencies. 

 utmost being models of cryptocurrencies are erected by computer scientists who substantially concentrate on the 

 feasibility and security of these systems. pivotal issues similar as the impulses of actors to 

 cheat and the endogenous nature of some crucial variables similar as the real value of a cryptocurrency 

 in exchange have been largely ignored. similar considerations, still, are vital for understanding 

 the optimal design and, hence, the profitable value of cryptocurrency as a means of payment. 

 Our focus is primarily on understanding how the design of a cryptocurrency influences the inter- 

 conduct among actors and their impulses to cheat. These impulses arise from a so- called 

 “ double- spending ” problem. Cryptocurrencies are grounded on digitial records and, therefore, can be copied 

 fluently and costlessly which means that they can potentially be used several times in deals 

 1Some central banks have lately started to also explore the relinquishment of cryptocurrency and blockchain technolo- 

 gies for retail and large- value payments. exemplifications are the People’s Bank of China who aims to develop a civil 

 digital currency grounded on blockchain technology; the Bank of Canada and the Monetary Authority of Singapore who 

 are studying its operation for interbank payment systems; and the Deutsche Bundesbank who has developed a primary 

 prototype for blockchain- grounded agreement of fiscal means. 

 2This raises the issue that numerous cryptocurrencies presently can not be gauged sufficiently to serve as a true 

 relief of large retail payment networks. We abstract fully from similar scalability issues that substantially arise from technological constraints.

 and operate without a designated third- party to issue the currency. Agarwal and Kimball( 2015) 

 advocate then that the relinquishment of digital currencies can grease the perpetration of a negative 

 interest rate policy, while Rogoff( 2016) suggests that phasing out paper currency can undercut 

 undesirable duty elusion and felonious conditioning. Our findings complements this work as we establish 

 some implicit bounds on the costs that can be levied on people through central bank issued 

 digital currency.5 Eventually, Fern´andez- Villaverde and Sanches( 2016) model cryptocurrencies as 

 intimately issued edict currencies and dissect – in the tradition of the literature on the free banking.

Cryptocurrencies A detail preface 

Our ultramodern frugality relies heavily on digital means of payments. Trade in the form ofe-commerce 

 for illustration necessitates the operation of digital commemoratives. In a digital currency system, the means of 

 payment is simply a string of bits. This poses a problem, as these strings of bits as any other 

 digital record can fluently be copied andre-used for payment. Basically, the digital commemorative can be 

 counterfeited by using it doubly which is the so- called double- spending problem. 

 Traditionally, this problem has been overcome by counting on a trusted third- party who manages 

 for a figure a centralized tally and transfers balances by crediting and debiting buyers and merchandisers ’ 

 accounts. This third- party is frequently the issuer of the digital currency itself, one prominent illustration 

 being PayPal, and the value of the currency derives from the fact that druggies trust the third- party 

 to enjoin double- spending( top of Figure2.1). 

 Cryptocurrencies similar as Bitcoin go a step further and remove the need for a trusted third- party. 

 rather, they calculate on a decentralized network of( conceivably anonymous) validators to maintain and 

 update clones of the tally( bottom of Figure2.1). This necessitates that agreement between the 

 validators is maintained about the correct record of deals so that the druggies can be sure to 

 admit and keep power of balances. But such a agreement eventually requires that( i) druggies do 

 not double- spend the currency and( ii) that druggies can trust the validators to directly modernize the 

 tally. 

 How do cryptocurrencies similar as Bitcoin attack these challenges? Trust in the currency is grounded 

 on a blockchain which ensures the distributed verification, streamlining and storehouse of the record of 

 sale histories.6 This is done by forming a blockchain. A block is a set of deals 

 that have been conducted between the druggies of the cryptocurrency. A chain is created from these 

 blocks containing the history of once deals that allows one to produce a tally where one 

 can intimately corroborate the quantum of balances or currency a stoner owns. Hence, a blockchain is like a 

 book containing the tally of all once deals with a block being a new runner recording all the 

 current deals. 

 Figure2.2 illustrates how the blockchain is streamlined. To insure agreement, validators contend for 

 In this sense it’s different from traditional plutocrat which is simply a partial memory of once deals as it 

 only records the current distribution of balances and doesn’t record how once deals induce the current 

 distribution.

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- ferocious competition for streamlining 

 the records of sale – a process generally appertained to as mining – and( ii) by introducing con- 

 firmation lags for settling deals in cryptocurrency. This implies that a cryptocurrency faces 

 a trade- off between how fast deals settle and a guarantee( or “ futurity ”) for their agreement. 

 Accordingly, crytocurrencies can not achieve immediate and final agreement of deals. 

 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 effective Bitcoin as a 

 medium of exchange can be relative to being means of payment. Calibrating our model to Bitcoin 

 data, we find that from a social weal perspective using Bitcoin is close to 500 times more expensive 

 than using traditional currency in a low affectation terrain. 

 This is, still, a result of the hamstrung design of Bitcoin as a cryptocurrency. Bitcoin uses 

 both currency growth and sale freights to induce prices for mining. In its current form, the 

 cryptocurrency price structure is too generous so that too numerous coffers are being used to rule 

 out double- spending and making it a secure form of payment. We show that the optimal way of 

 furnishing prices for mining is simply via currency creation at a veritably low rate rather than by 

 using sale freights. The optimal design of Bitcoin would induce a weal cost of only about 

 of consumption which is original to a cash system with moderate affectation. 

 We also estimate the effectiveness of using a cryptocurrency system to support large- value and retail 

 deals. Using summary data for Fedwire and US disbenefit cards, we confirm that cryptocur- 

 rencies are a much better volition for low value, high- volume deals than for large value 

 payments. This is intuitive, as double spending impulses increase with the size of deals. 

 Hence, further mining and longer evidence lags( which are both expensive) are needed when drag- 

 porting large- value payments in a cryptocurrency. Our exercise shows that cryptocurrency systems 

 can potentially be a valid volition to retail payment systems that operate at veritably low freights, as 

 soon as limits on the scale of similar systems can be resolved. 

 The profitable literature on cryptocurrencies is veritably thin. We aren’t apprehensive of any work that 

 has homogenized the design features of a cryptocurrency and that has studied its optimal design 

 under the trouble of double spending attacks. We model bilateral exchange grounded on plutocrat, we 

 follow the lately promoted frame of Lagos and Wright( 2005) and enrich it by modelling a 

 mining competition to modernize the blockchain. For standardizing the blockchain itself, we calculate on the theoretical literature of payment systems as a record- keeping device.3 

 Our work is therefore a first attempt to explicitly model the distinctive technological features of a 

 cryptocurrency system which are a blockchain, mining and double- spending impulses within a 




 quantitative profitable model. We’re also first to theoretically dissect the optimal design of a 

 cryptocurrency and giving a quantitative answer to the effectiveness parcels of cryptocurrencies. 

 Some recent donation have anatomized – fr

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