I don’t know much about the topic of mass migration, especially historical migrations. But, it’s interesting that what was at one time a relatively “frequent” phenomena is seemingly no longer relevant.
The two big mass migrations, on the scale I have in mind, that I can think of are the “Sea Peoples” (and Dorian) migration, ca. 1200 B.C.E., and the west- and southward migrations that took place between ~300–500 C.E. Both events were huge game changers demographically, economically and politically. The Sea Peoples migration, with the exception of Egypt, caused the collapse of various, once very powerful, Bronze Age societies: Mycenae, the Hittites, the Levant, et cetera. The migrations that took place during the late Roman Empire are similar in that it, ultimately, played a large role in ending the Roman era, and thus led to a new political era in Europe, the Middle East, and North Africa. From what I know, this latter event was far less catastrophic (in terms of cultural and economic significance) than that of the Sea Peoples. Still, the two are very similar in that waves of displaced peoples ultimately change the political landscape of up to three continents (although Asia and Africa to a much lesser extent than Europe).
There are other examples. Late during the 2nd and 1st centuries B.C., Rome had to deal with an early, and much more limited, migratory threat. This became known as the Cimbrian War, where the Romans defeated a migratory “horde” estimated to include ~300,000–500,000 people. This short historical overview is euro-centric, but I’m sure there were similar experiences in other areas of the world where strong central governments developed (e.g. China?). Some mass migrations don’t fit the category, since they didn’t expand into areas with strong, established political entities — they simply populated relatively open land. (Although, I wonder if the European displacement of Native American polities is analogous to the Bronze Age and pre-Medieval Era migrations.)
Following the Middle Ages, however, the way mass migrations have impacted societies has sharply changed. There are still mass migrations: the significant immigration trends. But, whereas 1,000+ years ago this would have caused political upheaval, societal displacement, and sharp declines in long-distance trade, nowadays migrants — even those which form part of mass human movements — are assimilated into existing societies. The mass European migration to the U.S., for example, fed the latter’s industrial revolution. It was thanks to the migration that the U.S. was able to expand its productive capacity, by making use of a much larger labor force than otherwise would be the case. Generally, people think that immigrants are a burden to the nation they migrate to, but the truth is the exact opposite: they help improve our standard of living. It’s all because societies have become more cosmopolitan, and mass migrations no longer lead to war, genocide, social displacements, et cetera.
I’m sure that historians and sociologists have theories that help explain this phenomenon. Is it that modern society is more sedentary? The large polities that ceased to exist following ancient mass migrations were also sedentary. It doesn’t explain why nowadays migrants are complements to existing populations, and back then migrants displaced existing populations. Maybe conflict has become so costly that the benefits of violent migrations are no longer large enough. This has a degree of plausibility, doesn’t it? (Maybe only to the untrained eye, however.) The Sea Peoples migration coincides with the transition from the Bronze to the Iron Age, and the Sea Peoples took advantage of new technology in their armaments. Similarly, there were significant military changes that occurred during the period of the fall of Rome. Maybe technologies spread less quickly at that time, so certain societies had longer-term advantages over others. Or, maybe societal stagnation was more common back then — established polities were more likely to become too burdensome for the size of their economies. Another explanation have something to do with how recipient societies have learned to respond to mass migrations.
I think it’s an interesting question. Does it have something to do, even indirectly, with the post-1700s growth spurt? Does it have anything to do with the cultural and/or intellectual change that Deidre McCloskey has in mind in Bourgeois Dignity?