The rise of digital money may bring about privately issued money that circulates across borders and coexists with public money. This paper uses an open-economy search model with multiple currencies to study the impact of such global money on monetary policy autonomy -- the capacity of central banks to set a policy instrument. I show that the circulation of global money can entail a loss of monetary policy autonomy, but it can be preserved if government policy that limits the amount or use of global money for transactions is introduced or if the global currency is subject to counterfeiting. The result suggests that global digital money and monetary policy autonomy can be compatible.
