Parallel Digital Currencies and Sticky Prices

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 in the Dollar sector. (JEL E12, E23, E31, E42, E52, F33)