Reconciling Bilateral Migration Flows with Net Migration Totals

Thomas M. Menino Convention & Exhibition Center 

The Human Migration Database (HMigD) at the Max Planck Institute for Demographic Research estimates international migration flows by integrating diverse data sources within a hierarchical Bayesian framework. A persistent challenge is that estimated bilateral flows are often inconsistent with external, high-quality country-level net migration totals, and reconciling these without modifying the underlying model is difficult. This paper introduces an information-projection (I-projection) approach as a post-processing step: starting from the posterior over bilateral flows, we compute the Kullback–Leibler–minimizing update that satisfies net-migration accounting constraints to obtain a consistent joint distribution. Unlike earlier solutions limited to independent Poisson flows, this method handles arbitrary joint distributions, preserves dependence structure, and provides evidence lower bound (ELBO)-like guarantees. We demonstrate scalable implementation and show that incorporating net-migration constraints improves HMigD estimates.

Migration Statistics

Constrained Estimation

Data Reconciliation

Information Projection

Kullback–Leibler Divergence 

Social Statistics Section