Place-to-Place Migration Model
Also known as: Origin-Destination Migration Model, Lowry Migration Model, Econometric Gross-Flow Model, Modified Gravity Migration Model
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.
Key highlights
- Gives interpretable elasticities showing how migration flows respond to wages, unemployment, and distance, not just a fitted pattern.
- Embeds well-established gravity regularities while adding behavioral economic content, combining empirical fit with causal interpretation.
- Predicts the full origin-destination matrix, supporting forecasting and counterfactual scenarios about changing economic conditions.
- Estimable with standard tools, and the Poisson-with-fixed-effects form handles count flows and zero cells robustly.
Intuition
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How it works
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When to use it
Use the place-to-place migration model when you have a gross origin-destination flow matrix together with measurable conditions at origins and destinations — wages, unemployment, employment, amenities — and you want to explain why flows go where they do, estimate the responsiveness of migration to economic drivers, or predict how the matrix would change under different conditions. It suits internal migration between regions, interstate or inter-metropolitan flows, and any setting where flows and place covariates are observable and a behavioral labor-market interpretation is plausible. It is the natural choice when you need interpretable elasticities or counterfactual forecasts rather than a purely descriptive index. It is less appropriate when only net migration is available, when flows are dominated by non-economic forces such as conflict or family reunification that the covariates cannot capture, when the origin-destination matrix is mostly zeros and sparsely populated, or when reverse causality between local economies and migration is severe and unaddressed by the design.
Strengths & limitations
- Gives interpretable elasticities showing how migration flows respond to wages, unemployment, and distance, not just a fitted pattern.
- Embeds well-established gravity regularities while adding behavioral economic content, combining empirical fit with causal interpretation.
- Predicts the full origin-destination matrix, supporting forecasting and counterfactual scenarios about changing economic conditions.
- Estimable with standard tools, and the Poisson-with-fixed-effects form handles count flows and zero cells robustly.
- Local economic conditions and migration are jointly determined, so coefficients can be biased by reverse causality without an identification strategy.
- Log-linear estimation is undefined for zero flows and assumes a multiplicative error that the data may not satisfy.
- Results depend on the spatial units chosen, with the modifiable areal unit problem affecting distance and flow definitions.
- Observed wages and unemployment proxy expected opportunities imperfectly, and omitted amenities or networks can confound the economic effects.
Common pitfalls
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Applications
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Frequently asked
How does the place-to-place model relate to the gravity model of migration?
The gravity model is its starting point: flows scale with the product of origin and destination masses and decay with distance, as in Zipf's formulation. Lowry's place-to-place model keeps the distance-decay structure but replaces raw population mass with behavioral economic determinants — wages, unemployment, and labor-force size — so the coefficients describe how migration responds to labor-market conditions rather than just to size. In effect it is a modified, economically interpretable gravity model, and modern Poisson spatial-interaction models nest both by adding origin and destination fixed effects to the gravity-style bilateral terms.
Why estimate the model with Poisson regression instead of log-linear OLS?
Migration flows are non-negative counts, and origin-destination matrices typically contain many zero cells, especially between small or distant regions. Logging the flows for OLS is impossible when the flow is zero, and ad hoc fixes like adding a constant or dropping zeros bias the estimates. Poisson regression models the expected count directly through a log link, accommodates zeros naturally, and remains consistent under mild assumptions even if the variance is not exactly the mean. It also lets you include origin and destination fixed effects to absorb unobserved push and pull, which is why it has become the standard estimator for gross-flow models.
Can the model predict net migration and how migration reshapes regions?
Yes. Because it predicts the full origin-destination matrix, you can sum each region's predicted inflows and subtract its predicted outflows to obtain net migration, and you can run counterfactuals by changing the economic covariates and re-predicting. The resulting predicted balances can be summarized with migration-impact measures such as effectiveness and the aggregate net rate from the cross-national toolkit. This connects the behavioral, regression-based explanation of why flows occur to the descriptive question of how strongly migration redistributes population across the regional system.
Sources
- 1.Lowry, I. S. (1966). Migration and Metropolitan Growth: Two Analytical Models. Chandler Publishing, San Francisco.ISBN 9780810200135
- 2.Zipf, G. K. (1946). The P1 P2 / D Hypothesis: On the Intercity Movement of Persons. American Sociological Review, 11(6), 677-686.
- 3.Bell, M., Blake, M., Boyle, P., Duke-Williams, O., Rees, P., Stillwell, J., & Hugo, G. (2002). Cross-national comparison of internal migration: issues and measures. Journal of the Royal Statistical Society: Series A, 165(3), 435-464.
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ScholarGate. (2026, June 23). Place-to-Place Migration Model. ScholarGate. https://scholargate.app/migration-studies/place-to-place-migration-model