Since crypto asset have no exposure to domestic commodities there is no evidence of anti-correlation with a basket of goods that would be inversely to the national currency in times of inflation. Instead crypto assets seem largely correlated with the broader stock market and as such are not a hedge against any macroeconomic factors of either inflation or equity markets.
Crypto assets are also not a reliable store of value in times of market instability, and as such do not provide a safe haven of any form since they are largely correlated with the broader market and exposed to the same shocks.
In his whitepaper Bitcoin, Currencies, and Fragility, Nassim Taleb deconstructs the "inflation hedge" thesis:
The experience of March 2020, during the market panic upon the onset of the pandemic, when bitcoin dropped farther than the stock market —and subsequently recovered with it upon the massive injection of liquidity is sufficient evidence that it cannot remotely be used as a tail hedge against systemic risk. Furthermore, bitcoin appears to respond to liquidity, exactly like other bubble items. It is also uncertain what could happen should the internet experience a general, or an even a regional, outage — particularly if it takes place during a financial collapse.
- Shaffer, Daniel S. 2010. Profiting in Economic Storms: A Historic Guide to Surviving Depression, Deflation, Hyperinflation, and Market Bubbles. John Wiley & Sons.
- Taleb, Nassim Nicholas. 2021. ‘Bitcoin, Currencies, and Fragility’. ArXiv:2106.14204 [Physics, q-Fin], July. http://arxiv.org/abs/2106.14204.
- Wang, Gangjin, Yanping Tang, Chi Xie, and Shou Chen. 2019. ‘Is Bitcoin a Safe Haven or a Hedging Asset? Evidence from China’. Journal of Management Science and Engineering 4 (3): 173–88. https://doi.org/10.1016/j.jmse.2019.09.001.
- Cembalest, Michael. 2022. ‘The Maltese Falcoin: On Cryptocurrencies and Blockchains’.
- Frisch, Helmut. 1983. Theories of Inflation. Cambridge University Press.