Estimating and conditional forecasting bilateral migration flows between South America and Europe, 1985-2050

South America and Europe have a history of reversals in the directionality of migration. While South America was a major destination for European migrants in the early 20th century, migration flows have reversed in recent decades, with increasing South American emigration to Europe. However, inconsistencies in bilateral migration data hinder empirical assessments of migration systems between these regions. This study addresses this gap by (1) estimating a complete, comparable, reliable and consistent time series of bilateral migration flows between South America and Europe from 1985 to 2018 and (2) generating conditional forecasts until 2050. Using a two-level hierarchical Bayesian model, it integrates one-year and five-year transition census data, corrects for undercounting of native-born migrants, adjusts for census approaches and data quality, and incorporates key migration drivers, including demographics, socioeconomic disparities, historical ties, and environmental factors. By producing reliable migration data, this study provides a robust foundation for analysing the persistence and evolution of migration patterns between South America and Europe across time. It contributes to migration systems theory by integrating theoretical insights with empirical modelling, assessing whether South America-Europe flows form a structured, evolving network, whilst also serving as a valuable reference for analysing future migration trajectories.