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An equilibrium model of the market for bitcoin mining
We propose a model which uses the Bitcoin/US dollar exchange rate to predict the computing power of Bitcoin’s network. We show that free entry places an upper-bound on mining revenues and we devise a structural framework to measure its value. Calibrating the model’s parameters allows us to accurately forecast the evolution of the network computing power over time. We establish the accuracy of the model through out-of-sample tests and investigation of the entry rule. We find that around one third of seigniorage income is dissipated in electricity consumption. The model indicates that a slowing down in the rate of technological progress will significantly increase Bitcoin’s carbon footprint.
Bitcoin and the market for mining
This section describes the tasks accomplished by miners and the rewards they get in return. Since it iswell beyond the scope of this paper to explain the overall architecture of Bitcoin, we only cover the elements that are required for the understanding of our model, and refer readers interested in a more comprehensive treatment to Nakamoto (2008) and Antonopoulos (2014).
The function of miners.— Bitcoin is a decentralized cryptocurrency which operates without a central authority. Decentralization is achieved through the recording of transactions in a public ledger called the blockchain. The main challenge for a decentralized currency is to maintain consensus among all participants on the state of the blockchain (who owns what) in order to prevent double spending of the same coin. A user spends a coin twice when one of her payments is accepted because the recipient is not aware of a previous payment spending the same coin. In order to avoid such conflicts, transactions are added to the blockchain by blocks and producing a valid block is made so difficult that the time it takes to build a block is, on average, much longer than the time it takes for a block to propagate across the network. This ensures that, in most instances, the whole network agrees on which transactions are part of the blockchain.
Blocks are cryptographically chained according to their dates of creation. This incremental process implies that the information contained in a given block cannot be modified without updating all subsequent blocks. Nakamoto’s groundbreaking insight was to recognize that the cost of manipulation would increase dramatically in the number of modified blocks, thus ensuring that tampering with a given block becomes prohibitively expensive as more blocks are added on top of it. To be accepted by other Bitcoin users, a new block must be stamped with a « proofof- work ». Each block possesses a header, which contains both a « nonce », i.e. an arbitrary integer, and a statistic summing up the transactions of the block, the time the block was built and the header of the previous block. Finding a valid proof-of-work boils down to finding a nonce satisfying the condition h(header) t, where h is the SHA-256 hash function applied twice in a row and t is a threshold value. The hash function h has the property of being numerically non-invertible. Moreover knowing h(n), for any n 2 N, yields no information on h(m) for all m 6= n. Hence the only way to find a valid nonce is to randomly hash guesses until the condition above is satisfied. This activity is called mining and it requires few special skills besides the means to spend resources on the mining process. The average time it takes to mine a valid block can be made arbitrarily long by lowering the threshold t. Since Bitcoin’s protocol specifies that one valid block should be found every 10 minutes, the threshold is updated every 2016 blocks to account for changes in the computing power, or hashpower, deployed by miners .
Mothballing and scrapping options.
We now relax Assumption 2 according to which miners always keep their hardware in mining mode. In practice, miners have the option to switch off their machines, and they can switch them back on should mining become profitable again. We assume that the hardware can be kept idle at zero costs. Thus the mothballing decision is fully reversible, and as such does not involve any forward-looking component. Machines are mining whenever their flow revenues are higher than their operating costs.
Table of contents :
Résumé substantiel en français
Remerciements
General introduction
1 An equilibrium model of the market for bitcoin mining
1.1 Introduction
1.2 Bitcoin and the market for mining
1.3 TheModel
1.4 Calibration
1.5 Extensions
1.5.1 Model with halvings.
1.5.2 Mothballing and scrapping options.
1.6 Conclusion
1.7 Appendix
2 How to make the Bitcoin network more environmentally friendly
2.1 Introduction
2.2 Bitcoin and the miners
2.3 The model
2.4 Numerical analysis
2.5 Conclusion
3 Identification and estimation of the average marginal effect in a panel data fixed effects logit model
3.1 Introduction
3.2 Identification results
3.2.1 The parameters of interest
3.2.2 Sharp bounds
3.2.3 A nicer characterization for the bounds
3.2.4 Computation of the bounds
3.3 Estimation
3.3.1 The use of an index
3.3.2 A first idea
3.3.3 A second idea
3.3.4 More than two periods are available
3.4 Monte-Carlo simulations
3.5 Conclusion
General conclusion
Bibliography
