Abstract
How well can a cryptocurrency serve as a means of payment? We study the optimal design of cryptocurrencies and assess quantitatively how well such currencies can support bilateral trade. The challenge for cryptocurrencies is to overcome double-spending by relying on competition to update the blockchain (costly mining) and by delaying settlement.
We estimate that the current Bitcoin scheme generates a large welfare loss of 1.4% of consumption. This welfare loss can be lowered substantially to 0.08% by adopting an optimal design that reduces mining and relies exclusively on money growth rather than transaction fees to finance mining rewards. We also point out that cryptocurrencies can potentially challenge retail payment systems provided scaling limitations can be addressed.
Key Insight: While Bitcoin in its current form has immense welfare costs, an optimally designed cryptocurrency can potentially support payments rather well. Cryptocurrencies work best when the volume of transactions is large relative to the individual transaction size, making them more suitable for retail payments than large-value settlements.
Key Findings
Key Insights Summary
Double-Spending Problem
Cryptocurrencies face a fundamental double-spending problem where digital tokens can be copied and reused. This is addressed through mining competition and confirmation lags, creating a trade-off between settlement speed and finality.
Immediate vs Final Settlement
For any cryptocurrency based on a Proof-of-Work protocol, settlement cannot be both immediate and final. There's an inherent trade-off between transaction speed and security against double-spending attacks.
Optimal Cryptocurrency Design
The optimal reward structure sets transaction fees to zero and relies exclusively on seignorage (money growth). This minimizes distortions and improves overall efficiency of the cryptocurrency system.
Retail vs Large-Value Payments
Cryptocurrencies are much better suited for low-value, high-volume retail transactions than for large-value payments due to the relationship between transaction size and double-spending incentives.
Mining Costs
Current Bitcoin mining generates substantial costs ($360M annually in the model), but optimal design could reduce this to $6.9M while maintaining security.
Scalability Challenge
The efficiency of cryptocurrencies increases with scale, putting scalability front and centre as the main technological challenge to be overcome for widespread adoption.
Paper Overview
Document Contents
1. Introduction
Since the creation of Bitcoin in 2009, cryptocurrencies have sparked intense debate about their economic relevance. Critics have denounced them as fraud or bubbles, while advocates point to their potential to support payments without designated third-parties that control currency for profit.
This paper develops a general equilibrium model of a cryptocurrency that uses a blockchain as a record-keeping device for payments. We formalize the double-spending problem and show how it is addressed through resource-intensive mining competition and confirmation lags.
Our analysis reveals that although Bitcoin in its current form has significant welfare costs, an optimally designed cryptocurrency can support payments efficiently. We quantitatively assess how well cryptocurrencies can facilitate transactions compared to traditional payment systems.
The paper contributes to the thin economic literature on cryptocurrencies by being the first to formally model the distinctive technological features of cryptocurrency systems - blockchain, mining, and double-spending incentives - within a quantitative economic framework.
2. Cryptocurrencies: A Brief Introduction
Cryptocurrencies such as Bitcoin remove the need for a trusted third-party by relying on a decentralized network of validators to maintain and update copies of the ledger. Trust is based on a blockchain which ensures distributed verification, updating and storage of transaction histories.
The blockchain is updated through a competitive process called mining, where miners compete to solve computationally costly proof-of-work problems. The winner updates the chain with a new block and receives rewards financed by new coin creation and transaction fees.
The fundamental challenge is the double-spending problem: after conducting a transaction, a user may attempt to convince validators to accept an alternative history where the payment wasn't made. This is discouraged by confirmation lags - sellers wait for multiple confirmations before delivering goods, making successful double-spending attacks more difficult.
3. The Double Spending Problem
We develop a model to study mining and double-spending decisions within a payment cycle. The model shows that to undo a transaction with a confirmation lag of N subperiods, a dishonest buyer needs to win the mining game N+1 times consecutively.
This leads to our fundamental result: For any cryptocurrency based on a Proof-of-Work protocol, settlement cannot be both immediate and final. There is an inherent trade-off between transaction speed and security against double-spending.
The model derives a no-double-spending constraint: d < R(N+1)N, where d is the transaction size, R is the mining reward, and N is the confirmation lag. This constraint shows the relationship between transaction size, confirmation lag, and the mining rewards needed to deter double-spending.
4. General Equilibrium Framework
We incorporate the cryptocurrency structure into a monetary general equilibrium framework based on Lagos and Wright (2005). This step is essential because cryptocurrency is a closed-loop system - its value depends on circulation in the economy, which determines mining rewards, which in turn affect mining effort and double-spending incentives.
The framework allows us to explore optimal cryptocurrency design. We find that the optimal reward structure sets transaction fees to zero and relies solely on seignorage (money growth). This minimizes distortions and improves efficiency.
We prove that a double-spending proof cryptocurrency equilibrium exists when the user pool is sufficiently large, highlighting that cryptocurrencies become more efficient with scale.
5. A Numerical Analysis of Bitcoin
We calibrate our model using Bitcoin trading data from 2015. The analysis reveals that the current Bitcoin design is very inefficient, generating a welfare loss of 1.4% relative to an efficient cash system.
The main source of inefficiency is large mining costs, estimated at $360 million per year. This translates to people being willing to accept a cash system with 230% inflation before being better off using Bitcoin.
However, an optimally designed Bitcoin would reduce the welfare cost to 0.08% by lowering money growth and eliminating transaction fees. The equivalent inflation rate would drop to 27.51%.
We also evaluate cryptocurrency efficiency for retail payments (using US debit card data) and large-value settlements (using Fedwire data). Cryptocurrencies show much smaller welfare losses for retail payments (0.00052%) compared to large-value systems (0.0060%).
6. Conclusion
Distributed record-keeping with blockchain based on consensus through Proof-of-Work is an intriguing concept. The economics of this technology are driven by individual incentives to double-spend and the costs of controlling these incentives.
As the scale of a cryptocurrency increases, it becomes more efficient. This explains why double-spending proof equilibrium exists only with a sufficiently large user pool, and why cryptocurrencies work best when transaction volume is large relative to individual transaction size.
Bitcoin is not only expensive in terms of mining costs but also inefficient in its long-run design. Efficiency can be significantly improved by optimizing the rate of coin creation and minimizing transaction fees.
Cryptocurrency systems can potentially challenge retail payment systems once scalability limitations are addressed. There remains much to be learned about the economic potential and efficient design of blockchain technology.
Appendix
The paper includes extensive appendices with proofs, derivations, and additional analyses including:
- Micro-foundation for the proof-of-work problem
- Complete proofs of lemmas and propositions
- Analysis of Proof-of-Stake as an alternative consensus mechanism
- Formal description of the blockchain
Note: The above is a summary of the paper's key content. The complete document contains extensive mathematical derivations, formal proofs, and detailed economic analysis. We recommend downloading the full PDF for comprehensive understanding.