Residual Method for Unauthorized Population

The residual method estimates the size of the unauthorized migrant population by subtraction: it takes the total foreign-born population counted in a census or large survey and removes the part that can be accounted for as legally resident, treating whatever remains as the unauthorized residual. Robert Warren and Jeffrey Passel introduced and validated the approach in their landmark 1987 Demography article, which matched undocumented aliens counted in the 1980 United States census against administrative records of legal immigrants. The arithmetic is deceptively simple, but the credibility of the estimate lives entirely in the adjustments. The legally resident stock must be aged forward from admission records and reduced for those who have since died or emigrated, and the resulting residual must be inflated to account for the share of unauthorized migrants the census itself failed to count. Done carefully and computed within detailed demographic cells — by age, sex, country of birth, and period of entry — the method turns two imperfect data sources that each say nothing directly about legal status into a defensible national estimate. It remains the dominant approach used by United States statistical agencies and research centers to size the unauthorized population.