Does Metcalfe's Law Explain Bitcoin Prices? A Time Series Analysis

Abstract

Metcalfe's Law argues the value of a network is proportional to the square of its users. Bitcoin and other cryptocurrencies can be modeled as such: if Metcalfe's Law is true, then it is possible to forecast prices using the size of the network. I test this assertion by a cointegration test between price and an adjusted number of wallets' connections. It is stated that the series do not cointegrate, rejecting the Metcalfe's Law. A first-differences model is employed to further analyse the relation between returns and variations in the number of wallets. It is stated that Metcalfe's Law consistently predicts the trend in the value of Bitcoin; nevertheless, it is not possible to reject the reverse causation of Bitcoin returns leading to new wallets.