We examine global dynamics under learning in a nonlinear New Keynesian model when monetary policy uses price-level targeting and compare it to inflation targeting. Domain of attraction of the targeted steady state gives a robustness criterion for policy regimes. Robustness of price-level targeting 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. Credibility evolves through reinforcement learning. Initial credibility and initial level of target price are key factors influencing performance. Results match the Swedish experience of price level stabilization in 1920's and 30s.