Reconstruction of age distributions from differentially private census data

The age distribution of a population is important for understanding the demand and provision of labor and services, and as a denominator for calculating key age-specific rates such as fertility and mortality. In the US, the most important source of information on age distributions is the decennial census, but a new disclosure avoidance system (DAS) based on differential privacy will inject noise into the data, potentially compromising its utility for small areas and minority populations. In this paper, we explore the question whether there are statistical methods that can be applied to noisy age distributions to enhance the research uses of census data without compromising privacy. We apply a non-parametric method for smoothing with naive or informative priors to age distributions from the 2010 Census via demonstration data which have had the US Census Bureau's implementation of differential privacy applied. We find that smoothing age distributions can increase the fidelity of the demonstration data to previously published population counts by age. We discuss implications for uses of data from the 2020 US Census and potential consequences for the measurement of population dynamics, health, and disparities.