| Summary: | The paper investigates the long-run relationship between bitcoin and its marginal cost between July 2010 and July 2022. We derive Bitcoin's marginal cost of production 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 bitcoin'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 bitcoin price dynamics. On the contrary, we found that bitcoin's price and its marginal cost of production have been cointegrated since its 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.
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