Digital Currency Price Formation: A Production Cost Perspective

Abstract

The paper investigates the long-run relationship between the bitcoin-USD exchange rate and its marginal cost between July 2010 and July 2022. We derive Bitcoin's marginal cost from a model of Bitcoin mining grounded in the Bitcoin code, and show that its production cost is a function of only two variables, the electricity price and the mining hardware efficiency. We then estimate a time-varying vector error correction model, and also the cointegration between bitcoin's price and Bitcoin network's hash rate, a commonly used production cost proxy. Our results show that the time-varying cointegration between the cryptocurrency's price and its hash rate is permanently in disequilibrium, bar a short time interval between March 2017 and January 2018. Consequently, although bitcoin's price and the hash rate are cointegrated, it is clear that the latter does not function as a stable long-run explanatory variable for its price. On the contrary, we found that bitcoin and its marginal cost of production have been cointegrated since inception, and that their time-varying long-run relationship always reverts towards equilibrium - and often to equilibrium- after long periods of divergence. These results contrast with most of the empirical literature that attempted to model the relationship betweeen bitcoin and its fundamentals in a time-invariant framework, but are consistent with recent research showing a significant role for production cost in the determination of bitcoin's price dynamics.

Keywords: Bitcoin's price formation, production cost, time-varying VECM, mining hardware efficiency

JEL Classification: G12, D21, D22