We propose and solve a small-scale New-Keynesian model with Markov sunspot shocks that move the economy between a targeted-inflation regime and a deflation regime and fit it to data from the U.S. and Japan. For the U.S. we find that adverse demand shocks have moved the  economy to the zero lower bound (ZLB) in 2009 and an expansive monetary policy has kept it there subsequently. In contrast, Japan has experienced a switch to the deflation regime in 1999 and remained there since then, except for a short period.