Compare methods

	Multiregional Migration Projection	Migration Flow Estimation from Stocks
Field	Migration Studies	Migration Studies
Family	Regression model	Process / pipeline
Year of origin	1975	2013
Originator	Andrei Rogers; Frans Willekens	Guy J. Abel; Guy J. Abel & Joel E. Cohen
Type	Matrix cohort-component projection model for multiple interacting regions	Demographic-accounting pipeline for deriving migration flows from stocks
Seminal source	Rogers, A. (1975). Introduction to Multiregional Mathematical Demography. John Wiley & Sons, New York. ISBN: 9780471729945	Abel, G. J. (2013). Estimating Global Migration Flow Tables Using Place of Birth Data. Demographic Research, 28, 505-546.
Aliases	Multiregional Cohort-Component Projection, Multistate Population Projection, Spatial Population Projection, Rogers Multiregional Projection	Stock-to-Flow Migration Estimation, Demographic Accounting of Migrant Stocks, Flow-from-Stock Method, Abel Stock-Differencing Method
Related	3	3
Summary	Multiregional migration projection extends the classic cohort-component method from a single closed population to a system of several regions that exchange migrants. Developed principally by Andrei Rogers in his 1975 Introduction to Multiregional Mathematical Demography, it replaces the ordinary Leslie matrix with a generalized growth matrix whose blocks carry not only survival and fertility within each region but also the age-specific probabilities of moving from every region to every other. Advancing a stacked population vector — population by age for each region — through repeated multiplication by this matrix projects all regions simultaneously and consistently, so that an out-migrant from one region becomes an in-migrant somewhere else and the system stays closed. The same matrix yields multistate life-table quantities such as expected lifetime spent in each region and the long-run stable spatial distribution of the population. Because the method demands smooth age-specific migration inputs, it is usually paired with Rogers-Castro model schedules, and the comparative findings of Rogers and Willekens's 1986 Migration and Settlement project established it as the standard apparatus of formal spatial demography.	Migration flow estimation from stocks reconstructs the unobserved movement of people between countries from something that is observed: how many foreign-born residents each country holds, broken down by country of birth, at two points in time. Most countries report migrant stocks — the number of people living abroad by where they were born — far more reliably than they report flows, the year-by-year counts of who moved where. Guy Abel's 2013 method, refined in the Abel and Cohen 2019 release covering 200 countries, treats the change in these bilateral stock tables between two censuses as the net result of migration plus births and deaths, and solves for the smallest set of origin-to-destination flows that could have produced the observed change. The approach rests on demographic accounting: a stock at the end of a period equals the stock at the start, plus births into the group, minus deaths, plus arrivals, minus departures. By fixing the demographic margins and minimizing flows, it turns a fragmentary stock record into a complete, comparable flow table. This has become the standard way to build globally consistent five-year migration flow estimates where direct flow data simply do not exist.