Energy Risk and Bitcoin Valuation Across Protocol-Defined Regimes

This study examines Bitcoin valuation within a regime-dependent framework that combines macro-financial conditions, investor attention, and energy-related drivers. We develop a semi-structural representation in which Bitcoin market capitalization is linked to an equilibrium-consistent set of fundamentals. The analysis is conducted separately across four halving regimes, allowing the valuation mapping to evolve with Bitcoin’s protocol and market maturation. Long-run relations are estimated using Dynamic Ordinary Least Squares (DOLS) as a linear benchmark and complemented by XGBoost as a flexible nonlinear in-sample approximator. In the short run, residual-based valuation gaps are incorporated into an error-correction framework to assess whether deviations from the estimated benchmark help explain subsequent adjustments in Bitcoin market capitalization. The results show that Bitcoin valuation is regime-dependent. Equity-market conditions provide the most stable valuation anchor across specifications, pointing to a growing integration of Bitcoin into the broader financial system. Investor attention is more relevant in the early regimes, while energy-related variables become more informative when they are linked to production-side incentives. In particular, mining profitability emerges as the strongest empirical energy-related signal. In the short run, valuation gaps display mean-reverting dynamics, and nonlinear gaps yield stronger and faster adjustment signals than the linear benchmark. Bitcoin valuation is best understood through a regime-specific framework combining macro-financial integration, protocol-driven scarcity, and miner-related incentives.