Bilateral Migration Flow Imputation

Bilateral migration flow imputation fills in the complete origin-destination matrix of how many people moved between every pair of countries when the directly reported data cover only a fraction of those pairs and are defined inconsistently from one reporter to the next. The reporting problem is severe: some countries count migrants by intended duration of stay, others by change of registration, others not at all, and a flow reported by the sending country rarely matches the same flow reported by the receiving country. Abel and Cohen's 2019 work, building on Abel's 2013 stock-based estimation, treats this as a matrix-completion problem: harmonize whatever fragments exist, derive consistent row and column totals — often from migrant-stock change — and then fill the empty and unreliable cells so the finished matrix matches those totals. The cells are filled with iterative proportional fitting and a pseudo-Bayesian estimator that blends sparse counts toward a structured prior, and the resulting flows can be refined into sex- and age-specific tables. The output is a single, internally consistent, fully populated bilateral flow table for all country pairs.