SUPPORTED BY UNIGESTION Bitcoin as Decentralized Money : Prices , Mining , and Network Security

We address the determination and evolution of bitcoin prices in a simple monetary economy that captures the salient features of a decentralized network. Network users forecast the transactional and resale value of bitcoin holdings and consider the risk of a network attack. Miners contribute resources that enhance network security and compete for mining rewards received in units of the same unbacked token. In equilibrium, the overall production of network security and the bitcoin price are jointly determined. We characterize how the network technologies and participants, users and miners, affect the number and dynamic stability properties of equilibria. We find that the relation between bitcoin prices and the supply growth rate is not monotonic: the same price is consistent with different rates. The model’s outcomes demonstrate how intrinsic price–security feedback effects can amplify or moderate the price volatility effect of demand shocks. We find rational patterns of price momentum, and that small and large stochastic bubbles can exist in general equilibrium and show how the probability of bursting decreases with the bitcoin price. JEL Codes: E40; E42; G12; G15; G18 First draft : July 12, 2018. Current draft : December 12, 2018 ∗Imperial College London. Email: epagnott@ic.ac. uk. †This paper builds on previous work in “Pricing Satoshis” presented at the 2018 Finance Theory Group London meeting, the 2018 NBER Asset Pricing Summer Institute, the Einaudi Institute for Economics and Finance and Imperial College London. For helpful conversations and comments I thank Franklin Allen, Fernando Alvarez, Andrea Buraschi, Jonathan Chiu, Will Cong, Jason Donaldson, Maryam Farboodi, Harrison Hong, Marcin Kacperczyk, Andrei Kirilenko, Francesco Lippi, Hanno Lustig, Alex Michaelides, David Miles, Monika Piazzesi, Jose Scheinkman, Michael Sockin, Savi Sundaresan, Nick Szabo, and Stijn Van Nieurburgh and participants at the 2019 American Economic Association meetings, the 2019 American Financial Association Meetings, and the Bloomberg Crypto Summit. The usual disclaimers apply. The rapid growth of Bitcoin has sparked heated debates. The issue of bitcoin1 price determination and price volatility is particularly elusive. On the one hand, in investment and entrepreneurial circles, it is often argued that the price reflects fundamental factors such as the growth in the number of network participants and the quality of the underpinning technology. A prominent view in the academic and policy communities, on the other hand, is that bitcoins are just a bubble that will eventually burst and, therefore, bitcoin prices are meaningless. Reaching a consensus on these issues is challenged by the fact that traditional monetary and asset pricing models were not designed around a decentralized network (DN), such as Bitcoin, but a centralized network (CN) run by an institution such as a central bank, government, or a corporation.2 What is different about Bitcoin? Any financial network needs to be secured. Digital transfers of ownership, in particular, require some form of verification and it should be difficult for a malicious attacker to manipulate the recorded history. In a CN, a specific trusted node assumes such operational responsibility and, in exchange, charges users with fees. In the Bitcoin DN, verification and updates to the system ledger (blockchain) are not delegated to a single node but, rather, to a set of miners. Miners validate new blocks of bitcoin transfers every 10 minutes, on average, and add them to the system ledger. Which miner adds the new block is the result of a non-cooperative competitive process where each miner uses computer power, measured as the hash rate, to solve a mathematical problem based on a cryptographic algorithm. The reward to the winning miner consists of newly minted bitcoins and is awarded provided the winning miner respected a set of consensus rules that prevents frauds; otherwise, the investment in computer power is entirely lost.3 This system of incentives is a breakthrough innovation by Nakamoto (2008) and has the property that, for a given level of miner decentralization, network security is increasing in the amount of total computer power in the network, the system hash rate. Figure 1 shows that, since its inception, We follow the standard practice in the developer community of using a lowercase b for the token (bitcoin) and a capital B for the protocol or network (Bitcoin). Excellent up-to-date surveys of traditional monetary models are provided by Rocheteau and Nosal (2017) and Walsh (2017). The solution to the problem is included in each new block and proves that the miner solved the problem—thus the term proof of work (PoW). See Antonopoulos (2017) for an excellent summary of the consensus rules. The reward to the winning miner is the first transfer in each block (the Coinbase transaction) and consists, as of 2018, of 12.5 bitcoins and fees that users making transfers in that block pay to the winning miner.