Proof-of-Stake Dynamics: The Elusive Price Anchor and Endogenous Volatility Harvesting

In this paper, we develop an open-economy macroeconomic model of a Proof-of-Stake network to analyze nominal token-price dynamics and the systemic effects of speculative capital. We first consider a network populated solely by active utility users, who finance network activity through a steady exogenous inflow of fiat currency. We prove the existence of a unique, globally asymptotically stable steady-state equilibrium with a well-defined nominal token price and derive a closed-form expression for the network's relaxation time. Calibrating the model using parameters representative of the current Ethereum network, we estimate a relaxation half-life of approximately 46 years. This extreme macroeconomic inertia implies that the token price may remain persistently displaced from its evolving steady-state benchmark, producing sustained price overshooting as the network adjusts to changing fundamentals. We then introduce an Investor class to examine the effects of passive and active speculative capital. We show that passive institutional staking compresses the native staking yield and creates a structural imbalance that systematically raises the nominal token price while shifting consensus ownership away from active utility users. Active speculative capital has a qualitatively different effect. In response to capital shocks, the Consumer class's rigid preference for fiat-denominated consumption generates an endogenous constant-value strategy. This mechanism shifts staked-token ownership from the Investor class toward active utility users, with potentially favorable implications for consensus decentralization.