An emerging concern in algorithmic fairness is the tension with privacy interests. Data minimization can restrict access to protected attributes, such as race and ethnicity, for bias assessment and mitigation. Less recognized is that for nearly 50 years, the federal government has been engaged in a large-scale experiment in data minimization, limiting (a) data sharing across federal agencies under the Privacy Act of 1974, and (b) data collection under the Paperwork Reduction Act. We document how this “privacy-bias tradeoff” has become an important battleground for fairness assessments in the U.S. government and provides rich lessons for resolving these tradeoffs. President Biden’s 2021 racial justice Executive Order 13,985 mandated that federal agencies conduct equity impact assessments (e.g., for racial disparities) of federal programs. We conduct a comprehensive assessment across high-volume claims agencies that affect many individuals, as well as all agencies filing “equity action plans,” with three findings. First, there is broad agreement in principle that equity impact assessments are important, with few parties raising privacy challenges in theory and many agencies proposing substantial efforts. Second, in practice, major agencies do not collect and may be affirmatively prohibited under the Privacy Act from linking demographic information. This has led to pathological results: until 2022, for instance, the US Dept. of Agriculture imputed race by “visual observation” when race information was not collected. Data minimization has meant that even where agencies want to acquire demographic information in principle, the legal, data infrastructure, and bureaucratic hurdles are severe. Third, we derive policy implications to address these barriers.