Parallel Digital Currencies and Sticky Prices

The recent rise of digital currencies opens the door to their use in parallel alongside official currencies ("dollar'') for pricing and transactions. We construct a simple New Keynesian framework with parallel currencies as pricing units and sticky prices. Relative prices become a state variable. Exchange rate shocks can arise even without other sources of uncertainty. A one-time exchange rate appreciation for a parallel currency leads to persistent redistribution towards the dollar sector and dollar inflation. The share of the non-dollar sector increases when prices in the dollar sector become less sticky and when firms can choose the pricing currency