We examine the global dimension of inflation in 24 OECD countries between 1980 and 2007 in a traditional Phillips curve framework. We decompose output gaps and changes in unit labor costs into common (or global) and idiosyncratic components using a factor analysis and introduce these components separately in the regression. Unlike previous studies, we allow global forces to affect inflation through (the common part of) domestic demand and supply conditions. Our most important result is that the common component of changes in unit labor costs has a notable impact of inflation. We also find evidence that movements in import price inflation affect CPI inflation while the impact of movements in the common component of the output gap is unclear. A counterfactual experiment illustrates that the common component of unit labor cost changes and non-commodity import price inflation have held down overall inflation in many countries in recent years whereas commodity import price inflation has only raised the short-run volatility of inflation. In analogy to the Phillips curves, we estimate monetary policy rules with common and idiosyncratic components of inflation and the output gap included separately. Central banks have indeed reacted to the global components.