Great question! Unfortunately, I think there are not going to be great answers. Three ideas have come up in my discussions with users of registry data:
Describe data access procedures completely: Be as transparent as you possibly can be about how you acquired the data, how others can acquire them, and what the policies and costs associated with acquisition would be.
Show everything that you can: While you cannot share the raw data, you can likely share a considerable amount of information from the data. For example, you can include descriptive statistics and graphics that convey the univariate and multivariate patterns in the data. You may also be able to share certain aggregated statistics (e.g., data aggregated at a block or city level).
Offer to collaborate: You may have privileged access to data (i.e., other simply will not be able to access it). In that case, to the extent allowed by data access rules, you should offer the ability to run analyses for others and collaborate with them using the data. This would mean that even your critics can use the data in a meaningful public exchange of ideas, even if the data themselves cannot be made public.
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