More precisely – “will central banks allow decentralized digital currencies to exist over the long-term?”
The short answer is we do not know for sure, but there certainly is an incentive for the Federal Reserve and other central banks to want to tame any currency that falls outside of central banks’ sphere of control. Central banks are obviously in the “control” business as it relates to interest rates and of course the money supply.
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Decentralized currencies by definition can not be controlled and are difficult to track. Further, the Federal Reserve has expressed interest in pursuing its own digital currency.
Were the proverbial gun put to our head we would guess that “Yes”, at some point the Federal Reserve will try to tame Bitcoin either by outlawing the currency or by working with Treasury to establish regulation whereby the Federal Government may monetize Bitcoin and other digital currencies. The trigger for Fed action could be a market cap-based threshold where if Bitcoin or digital currencies in the aggregate grow to reach $X value, the Fed will act. At present Bitcoin enjoys a market cap of approximately $297 billion. The top 5 digital currencies have an aggregate market cap of approximately $384 billion.