Standard New Keynesian (NK) models feature an optimal inflation target well below 2 percent, limited welfare losses from business cycle fluctuations and long-term monetary neutrality. We develop a NK framework with endogenous productivity and downward nominal wage rigidity (DNWR) which challenges these results. The interaction between endogenous growth and DNWR generates asymmetric hysteresis effects on unemployment and R&D. As a consequence, the model features a non-vertical long-run Phillips curve and a trade-off between price distortions and output hysteresis that changes the welfare-maximizing inflation rate to above 2 percent. Deviations from the optimal target carry welfare costs multiple times those in traditional NK models. Taylor rules that respond to the unemployment rate address more effectivelythe asymmetric hysteresis in our model. Results are robust to the inclusion of the effective lower bound on interest rates.