Giovanni Peri & Francisco Requena have a new NBER working paper:

There is abundant evidence that immigrant networks are associated with larger exports from the country where they settle to their countries of origin. The direction of causality of this association is less clearly established… Using micro data on individual trade transactions from Spanish provinces between 1995 and 2008 and data on the stock of immigrants in those provinces by country of origin… we find that immigrants significantly increase exports (elasticity of 0.10), that the effect is almost entirely due to an increase in the extensive margin and that the effect is somewhat stronger for differentiated goods.