The dramatic decline in inflation across the world over the last 20 years has been largely credited to improved monetary policy. The universal nature of the phenomenon and its simultaneity with globalization however indicate that there might also be a "real" side to it. We build a model based on Melitz (2003) in which falling transport cost lead to greater openness, higher productivity and lower inflation. Following a decline in transport cost openness increases and firm selection eliminates the least productive domestic firms. The consequent increase in average productivity leads to falling relative prices for goods. A cash-in-advance constraint allows to analyse how falling relative prices can lead to lower inflation. Using a dataset of macroeconomic variables for 107 countries from all world regions we are able to show that openness-induced productivity growth leads to a significant decline in inflation world wide.