Does Crypto Sentiment Extremity Widen Estimated Spreads? Evidence Depends on the Specification

We examine whether extreme values of the Crypto Fear & Greed Index are associated with a daily high-low spread estimate for Bitcoin. The sample contains 2,896 BTC/USDT observations from February 2018 to January 2026. We find an unconditional extreme-minus-neutral gap of 61.99 basis points. After close-to-close realised-volatility-quintile demeaning it is 24.79 basis points, although none of the five separate quintile contrasts survives Holm correction. With quadratic realised-volatility and strictly lagged momentum controls, the HAC estimate is 11.81 basis points (95% CI [-2.31,25.93], p=.101). A fixed non-parametric stratification gives 20.44 basis points (p=.0195 under circular shifts), while separate models for a zero-floored estimate's incidence and positive magnitude are imprecise. The results therefore show only a descriptive, specification-dependent association. We conclude that they do not establish a stable or causal liquidity premium.