Measuring productivity premia with many modes of internationalization

•We study how to estimate productivity premia for internationalization modes.•This requires information compression when firms can choose from many modes.•We compare different approaches of information compression.•We illustrate these options by using survey data on 9541 European companies.•We advice researchers to choose from these methods consciously and check robustness.

We show that estimating productivity premia for internationalization modes requires information compression when firms can choose from many modes. Using a unique database of European firms we illustrate the different approaches and suggest that researchers should deliberately choose from them.