Using carefully designed discrete choice surveys, we measure how much individuals care whether their data are stored domestically, i.e., the premium people place on limiting the sharing of their data to their home country compared to elsewhere. We conduct this measure across countries (United States, United Kingdom, South Korea, Japan, Italy, India, and France) and data types (home address and phone number, personal information on finances, biometrics, health status, location, networks, communications, and music preferences). We find only modest evidence of added value resulting from data localization; to the extent that there is added value from localization, it appears to largely come for data types where privacy (i.e., full restrictions on data sharing) is already of high value: financial (account balance) and biometric (facial image) data, and home address and phone number. We also find that, for the U.S., U.K., Italy, India and France, there is no evidence that excluding China and Russia when allowing for international data sharing impacts data localization premium. Interestingly, for Japan and South Korea, we find evidence of a preference against excluding China and Russia if data are to be shared internationally. We discuss privacy policy implications.