“Diaspora dynamics” refers to a model of migration flows and stocks between countries that considers various factors that affect the rates of migration between the countries. The model was discussed by Paul Collier in his book Exodus: How Migration is Changing Our World.

• The incentive to migrate is dependent on the income gap between the source country and the target country.
• Other barriers, such as social, legal, and cultural barriers, mean that initial migration flows are a lot less than what polling data and economic models would suggest.
• One factor that significantly reduces the social, legal, and cultural barriers to migration is the presence of a large diaspora, i.e., a lot of people from the source country who are in the target country. The legal barrier is reduced because of family reunification law as well as political channels where existing members may lobby for more migration for people from their source country. Other barriers are overcome through one-on-one help as well as the presence of ethnic enclaves or other sources of cultural interchange that make the transition more gradual.

The size of the diaspora itself depends on these factors:

• The flow of migrants since migration began: The stock of migrants can be obtained by looking at the flow of migrants up to the point.
• Birth and death rates for migrants, to give a picture of how the migrant community evolves in size over time in the target country.
• The rate of assimilation of migrants (and their descendants) to their host country, to the point where they no longer identify as part of the diaspora and are of no use to would-be migrants either directly (by sponsoring them through family reunification or helping them settle down) or indirectly (by interacting with them in ethnic/cultural settings).

Equilibria

One obvious equilibrium is where migration flow is zero and the stock of migrants is zero. Other equilibria may or may not exist.

An equilibrium occurs where:

(Rate of new migration) + (Rate of growth of migrant descendant population (that still identifies as part of the diaspora)) = (Rate of return migration) + (Rate of decline in diaspora population due to migrants assimilating to the new country completely and forgetting their old affiliation) + (Rate of death of past migrants)

The model could be made more complicated, and more terms could be added to both sides. The model could also be simplified. For instance, if return migration is negligible, the rate of return migration can be dropped. If children of migrants are completely assimilated to the new country from the get-go, then we can ignore the rate of growth of the migrant descendant population. If the migrant flow has just started and most migrants are young, the death rate of migrants may be negligible, so we can ignore it.

It is possible that no equilibrium exists, i.e., the rate of assimilation is never fast enough to catch up with the rate of migration, so the critical constraining factor in this case is just the population of the source country. Note that even if no equilibrium exists, migration rate may still take a very long time to pick up.

Gradual acceleration

We expect that, at least initially, the rate of migration is greater than the rate of assimilation. Therefore, the diaspora grows initially. Since the size of the diaspora is positively related to the rate of future migration, the rate of migration itself increases. Thus, diaspora dynamics suggests that migration accelerates initially. This process is expected to continue till equilibrium.

There are many other possibilities that could arise, particularly since the economic incentive to migrate as well as legal, social, and cultural barriers to migration are themselves in flux and are themselves responsive to the size of the migrant stock and flow.

Discussions by others of diaspora dynamics and its implications for migration policy

• Paul Collier’s Exodus and the risks of migrant diasporas by Paul Crider, Open Borders: The Case, November 4, 2013.
• Diasporas, Swamping, and Open Borders Abolitionism by Bryan Caplan, EconLog, February 5, 2014.
• The Swamping that Wasn’t: The Diaspora Dynamics of the Puerto Rican Open Borders Experiment by Bryan Caplan, EconLog, March 27, 2014.