Multiple imputation for combining confidential data owned by two agencies

Summary.  Statistical agencies that own different databases on overlapping subjects can benefit greatly from combining their data. These benefits are passed on to secondary data analysts when the combined data are disseminated to the public. Sometimes combining data across agencies or sharing these data with the public is not possible: one or both of these actions may break promises of confidentiality that have been given to data subjects. We describe an approach that is based on two stages of multiple imputation that facilitates data sharing and dissemination under restrictions of confidentiality. We present new inferential methods that properly account for the uncertainty that is caused by the two stages of imputation. We illustrate the approach by using artificial and genuine data.