This paper develops and estimates a dynamic stochastic general equilibrium (DSGE) model representing several key characteristics of Japan, namely, a large open economy, large fiscal deficits increasing amounts of debt held by domestic residents, as well as monopolistically-competitive pricing in traded goods. The economy is driven by recurring sets of shocks to productivity, government spending, quality of capital, foreign interest rates, domestic consumption, global demand, and export and import markup price setting. We compare optimal simple rules for consumption tax rates, a Taylor rule with negative interest rates (and thus not subject to the zero lower bound) and a quantitative easing rule, for reducing government debt held by the banking system, as well as optimizing welfare. In times of crisis, we show that all three rules do very well in mitigating the adverse effects of negative shocks. QE rules have a comparative advantage for reducing debt, while tax-rate rules have the advantage for stabilizing consumption in adverse periods. Both of these policy rules are close to the results prevailing in a Taylor-rule world with no zero bound, with sticky prices.