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The rise of digital currencies may result in domestic parallel currencies.
Their exchange rate shocks present new challenges for
monetary policy. We analyze these issues in a New Keynesian
framework. Firms set prices in one of the currencies. A one-time
appreciation of a parallel currency results in persistent redistributions
toward the dollar sector output and inflation. We calculate
optimal monetary policy. When price stickiness is homogeneous, it
is optimal to leave nominal interest rates unchanged. We compare
optimal policy to three Taylor rules. Higher dollar price rigidity
may lead to an increase rather than a decrease of the dollar sector.
