Global learning dynamics for price-level targeting (PLT) monetary policy are analyzed and compared to inflation targeting in a nonlinear New Keynesian model. Domain of attraction of target steady state is a new robustness criterion for policy regimes. Robustness of PLT depends on whether a known target path is incorporated into learning. Credibility is measured by accuracy of this forecasting method relative to simple statistical forecasts evolving through reinforcement learning. Initial credibility and target price are key factors influencing performance. Model results are in line with the Swedish experience of price stabilization in1930's.