This paper shows how persistent world inflation shocks hitting a small open economy can re-weight the importance of domestic and foreign factors in the determination of prices. In particular, we study why a global disinflation environment may imply a weakening of the channels whereby domestic shocks affect inflation. We derive a state-dependent Phillips curve based on translog preferences that make the elasticity of substitution of domestic goods sensitive to foreign prices. With this approach we are able to replicate this dragging effect of global disinflation on domestic inflation. We also provide empirical evidence from a wide panel of countries to support the significance of such an effect.