Migrant age profiles reconciling digital trace and survey data: an example of the United Kingdom in 2018 and 2019

Accurate estimates of migrant population stocks by age and sex are essential for demographic analysis and policy. This study develops a hierarchical Bayesian model that integrates survey data from the Labour Force Survey with digital trace data from the Facebook Advertising Platform to improve estimation of migrant age–sex distributions. The approach applies reduced Rogers–Castro age schedules as first-stage smoothing and harmonizes profiles within a multinomial-Dirichlet–Dirichlet framework. We illustrate the model using data on the 10 largest European migrant groups in the United Kingdom in 2018–2019. Results reveal 3 broad patterns: younger age structures among Western and Southern European migrants, slightly older working-age profiles for Central and Eastern Europeans, and a predominantly older Irish migrant population. External validation against Census 2021 country-of-birth data for England and Wales shows that the proposed model more closely matches benchmark age–sex distributions than a specification inspired by the area model of Wiśniowski et al. (2016. Integrated modelling of age and sex patterns of European migration. Journal of the Royal Statistical Society: Series A (Statistics in Society), 179(4), 1007–1024. https://doi.org/10.1111/rssa.12177). Facebook data improve representation of younger migrants, who are often underrepresented in surveys, while the Labour Force Survey provides broader demographic structure. Overall, the findings demonstrate the value of combining traditional and digital data to address gaps in migration statistics and produce timely, detailed population estimates.