The macroeconomic implications of downward nominal wage rigidities are analyzed via a dynamic stochastic general equilibrium model featuring aggregate and idiosyncratic shocks. A closed-form solution for a long-run Phillips curve relates average output gap to average wage inflation: it is virtually vertical at high inflation and flattens at low inflation. Macroeconomic volatility shifts the curve outwards and reduces output. The results imply that stabilization policies play an important role, and that optimal inflation may be positive and differ across countries with different macroeconomic volatility. Results are robust to relaxing the wage constraint, for example, when large idiosyncratic shocks arise.