Migrant Age Profiles Reconciling Digital Trace and Survey Data: An Example of the United Kingdom in 2018 and 2019

Accurate and timely estimates of migrant population stocks, disaggregated by age and sex, are critical for population projections and for understanding migration dynamics. This study proposes a hierarchical Bayesian model that extends previous work by incorporating age and sex disaggregation, using data from the Labour Force Survey (LFS) and digital traces from the Facebook Advertising Platform. A Bayesian multinomial–Dirichlet–Dirichlet model harmonizes age and sex profiles from the two sources, leveraging the Rogers–Castro framework to characterize migration age schedules and utilizing the conjugate nature of Dirichlet priors to ensure computational efficiency. We illustrate the framework using data on migrant populations in the United Kingdom for 2018 and 2019, based on the two sources: the Labour Force Survey and Facebook. The analysis identifies three distinct migrant groups with differing age and sex profiles: younger Western and Southern European migrants, slightly older Central and Eastern Europeans, and a predominantly older Irish migrant population. Facebook data enhances the coverage of younger migrants, who are often underrepresented in traditional surveys, while the LFS provides broader demographic context and helps benchmark the estimates to standard population definitions. The findings highlight the utility of integrating traditional and digital data sources to address gaps in migration statistics. This framework enables more accurate disaggregation of migrant population stock data and offers a scalable, computationally efficient methodology for improving migration estimates, particularly in contexts lacking ground-truth data. The approach also yields insights into migration patterns and demographic structures, with potential applications in policy planning and demographic research.