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. The two scenarios have drastically different implications for macroeconomic policies. Fiscal multipliers are about 20% smaller in the deflationary regime, despite the economy remaining at the ZLB. While a commitment by the central bank to keep rates near the ZLB doubles the fiscal multipliers in the targeted-inflation regime (U.S.), it has no effect in the deflation regime (Japan).