Compare methods

	Bilateral Migration Flow Imputation	Place-to-Place Migration Model
Field	Migration Studies	Migration Studies
Family	Process / pipeline	Regression model
Year of origin	2019	1966
Originator	Guy J. Abel & Joel E. Cohen; Guy J. Abel	Ira S. Lowry; (gravity antecedent: George K. Zipf)
Type	Imputation pipeline for completing origin-destination migration matrices	Econometric origin-destination flow model
Seminal source	Abel, G. J., & Cohen, J. E. (2019). Bilateral international migration flow estimates for 200 countries. Scientific Data, 6, 82.	Lowry, I. S. (1966). Migration and Metropolitan Growth: Two Analytical Models. Chandler Publishing, San Francisco. ISBN: 9780810200135
Aliases	Origin-Destination Flow Imputation, Country-Pair Migration Matrix Completion, Harmonized Bilateral Flow Estimation, Migration Matrix Imputation	Origin-Destination Migration Model, Lowry Migration Model, Econometric Gross-Flow Model, Modified Gravity Migration Model
Related	3	3
Summary	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.	The place-to-place migration model explains and predicts the gross number of people moving from each origin region to each destination region as a function of conditions at both ends and the distance between them. It descends from the gravity analogy popularized by George Zipf in 1946, in which movement between two cities rises with the product of their populations and falls with the distance separating them, but it adds behavioral economic content. Ira Lowry's 1966 formulation is the canonical example: he modeled interregional migration as driven by relative labor-market conditions — wages, unemployment, and the size of the labor force at origin and destination — modified by distance, and estimated the relationship econometrically from observed flows. Cast in log-linear or, in modern practice, Poisson form, the model recovers interpretable elasticities showing how flows respond to a wage gap or an unemployment differential, and it can reproduce or forecast the entire origin-destination matrix. It bridges the descriptive gravity tradition and explicit regression-based migration econometrics, and remains a workhorse for analyzing why people move where they do.