Migration Model Simulator: Gravity Model & Push-Pull Dynamics

simulator intermediate ~10 min
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M = 75,000/yr — predicted annual migration flow

With a wage differential of 3×, distance of 2000 km, and origin population of 50M under moderate border friction, the gravity model predicts approximately 75,000 migrants per year — a migration rate of 1.5‰.

Formula

M_ij = k × P_i × Δw / (d^α × f) — gravity migration model
m = M / P₀ × 1000 — migration rate per thousand
R = β × M × w_d — remittance flow estimate

The Laws of Migration

In 1885, Ernst Georg Ravenstein published the first systematic 'laws of migration,' observing that most migration is short-distance, that migrants from rural areas move to towns then cities, and that every migration stream produces a counter-stream. These empirical regularities, remarkably durable across 140 years, form the foundation of modern migration modeling and the gravity framework that quantifies them mathematically.

The Gravity Model

Borrowed from Newtonian physics, the gravity model predicts migration flow as proportional to the 'mass' (population, economic output) of origin and destination and inversely proportional to the distance between them. The distance exponent α captures how sharply migration decays with separation — typically 1.0 to 2.0, with higher values for less mobile populations. Despite ignoring politics, culture, and networks, this simple model explains the majority of observed migration patterns.

Push-Pull Dynamics

Every migration decision reflects a calculation — conscious or intuitive — of expected gains versus costs. Economic differentials (wage ratios, employment rates) are the strongest quantifiable drivers, but conflict, environmental degradation, and political persecution create push factors that defy simple economic models. Network effects amplify flows: the presence of earlier migrants in a destination lowers the costs and risks for subsequent movers, creating self-reinforcing corridors.

Consequences and Policy

Migration reshapes both sending and receiving societies. Destination countries gain labor, youth, and often entrepreneurial energy. Origin countries lose human capital but gain remittances — now exceeding $600B annually worldwide, dwarfing foreign aid. Policy tools (visa quotas, points systems, border enforcement) modulate flows but cannot eliminate the fundamental forces driving them. The tension between sovereign border control and the human response to opportunity remains central to 21st-century politics.

FAQ

What is the gravity model of migration?

The gravity model, adapted from Newton's law of gravitation, predicts that migration flow between two regions is proportional to the product of their populations (or economic indicators) and inversely proportional to the distance between them. M_ij = k × P_i × P_j / d_ij^α, where α (typically 1-2) captures distance decay. Despite its simplicity, it explains 60-80% of observed migration variance.

What are push and pull factors in migration?

Push factors drive people away from their origin: poverty, conflict, environmental disaster, political repression. Pull factors attract them to destinations: higher wages, job opportunities, safety, family networks. The gravity model quantifies these as economic differentials (pull) and distance/friction (impedance). Real migration decisions involve complex combinations of both.

How does distance affect migration?

Distance is the strongest predictor of migration volume — doubling distance typically halves migration flow. This 'distance decay' reflects monetary moving costs, information barriers, cultural differences, and the psychological cost of separation from family and community. However, diaspora networks can partially overcome distance by reducing information and settlement costs.

What is brain drain?

Brain drain (skilled emigration) occurs when highly educated workers disproportionately leave developing countries for wealthier ones. The wage premium for education is typically larger in destination countries, creating stronger pull for skilled workers. Estimates suggest 10-30% of tertiary-educated citizens from small developing nations live abroad. Remittances and return migration partially offset the loss.

Sources

Embed

<iframe src="https://homo-deus.com/lab/demography/migration-model/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub