One of the ways of arguing that migration yields benefits to migrants is to look at the stated preferences (i.e., words) and revealed preferences (i.e., actions) of migrants and potential migrants.
Stated preference: how many claim to wish to move?
Worldwide polls suggest that over 600 million people wish to move to a different country from where they currently are, and would do so if the visa or regulatory regime were more relaxed. More information on these polls is available at the polling data on migration page.
One objection is that these are merely stated preferences — and talk is cheaper than action. True, but this effect cuts both ways. Many people who say they wish to migrate may not do so, but many people who aren’t considering migration right now (with no realistic chance of this) may consider migrating, and actually follow through on it, if a realistic opportunity is presented. The key to determining the net effect would be to consider whether the so-called “preference falsification” (see here and here) would cut more in one direction or the other. It seems that, given the social importance of affirming loyalty to one’s nation and community, preference falsification is more likely to understate people’s desire to migrate than to overstate it.
Revealed preference: how many move, and how much do they pay for the privilege?
The presence of large-scale “illegal” immigration, often achieved by paying hefty coyote fees, suggests that a lot of people perceive significant gains from migration that would offset the costs. More at the coyote fees page.
A counter-argument to this is that people who migrate are doing so only based on what they think the target country has to offer them, not on the reality in that target country. Various versions of this counter-argument depict migrants as people who have been misled by “false advertising” and are exploited in many ways.
It’s true that there are migrants who often regret their decision to migrate, and some choose to return to their homeland or try their luck in yet another country. There are also migrants who started out aiming to be temporary migrants but ended up settling permanently. Overall, there do seem to be many migrants who stick with their decision to migrate. There are two other lines of evidence to support this: a lot of the migration pressure comes from countries that have already sent large numbers of migrants. This means that those who wish to migrate probably have friends and relatives in the land they wish to migrate to, and hence have a better picture of what life is like post-migration. The second is that guest workers in seasonal agricultural programs are often repeat workers; see here, for instance.