This paper has two aims. First, it provides simple theoretical models that highlight two channels whereby monetary shocks have permanent real effects and the interactions between these channels. Second, it presents an empirical dynamic model, covering a panel of EU countries, and derives the implied long-run inflation-unemployment tradeoff. Our results suggest that the tradeoff is far from vertical. We also find that wage persistence plays a larger role than price persistence in generating the tradeoff, but that the two forms of persistence are complementary in giving monetary policy its long-run real effects. Our results call for a reassessment of the European macroeconomic experience.