The economics of bitcoin exchange rate: A quantal response statistical equilibrium model

This paper provides economic foundations for the pattern of the Bitcoin exchange rate against the US dollar using a Quantal Response Statistical Equilibrium (QRSE) model. This model integrates bounded rationality and heterogeneous agent behavior to explain the statistical distribution of Bitcoin’s log-return exchange rates. Compared to classical statistical distributions, the QRSE model not only delivers a good empirical fit but also transforms abstract statistical parameters into a coherent behavioral narrative. The estimated parameters reveal a market driven by moderately attentive agents who do not instantly exploit arbitrage opportunities, allowing pricing biases to persist. A moderate feedback strength indicates that mean-reverting forces exist but act too slowly to prevent the accumulation of deviations, generating excess volatility. The estimated slight misalignment between individual expectations and the market’s social anchor produces the asymmetric return distributions and fat left tails characteristic of cryptocurrency markets. By linking micro-level strategic behavior under bounded rationality to macro-level distributional properties, our paper provides novel insights into the behavioral foundations of Bitcoin’s unique price dynamics, offering regulators and policymakers a deeper understanding of the mechanisms driving market instability, speculative bubbles, and volatility clustering.