One possible reply is that present immigrants do not in fact come for welfare--that on average they receive less from government relative to the taxes they pay than those already here. Julian Simon has made this argument, and provided a good deal of evidence for it. Its principle weakness is that it describes the people who immigrate under our present immigration laws--laws which make it hard for the sort of people who would go on welfare to immigrate legally and risky for illegal immigrants to apply for welfare. The situation might be quite different in a regime of free immigration.
A second answer is that the argument, although correct, tells only half the story. The redistributionist tendencies of modern states are an argument against free immigration, but also an argument for it. The argument against takes the level of redistribution as given and points out its effect on who migrates where and why. The other half of the argument reverses the causation by considering the effect of migration on levels of redistribution. The harder it is for people to move from one country to another, the more attractive redistributional policies are. The possibility of redistribution tends to increase inefficient migration, but the possibility of migration tends to decrease inefficient redistribution.
Consider a government in a world of free migration, trying to decide whether to increase or decrease the level of welfare. Giving people money may be politically attractive, but collecting the taxes to pay for it is not. A ten percent increase in levels will attract indigents from abroad, swell the welfare rolls, and increase costs by much more than ten percent. A ten percent decrease will cause some indigents presently on welfare to migrate to countries with more generous policies, reducing costs by much more than ten percent. The existence of easy migration makes welfare state policies less attractive, with the result that levels of redistribution are likely to be lower.
While I have not seen this argument used in discussions of international migration, it is a commonplace in discussions of interstate migration. American supporters of the welfare state routinely argue that welfare ought to be Federal rather than state, precisely because state welfare is held down by the threat of interstate migration. Indeed, one possible explanation for why the U.S. moved more slowly than Europe countries towards a welfare state is that European redistribution was by national governments with control over immigration, whereas American redistribution was largely by state governments without such control.
The argument is also relevant to future trends in Europe. The EEC is currently moving towards complete freedom of internal migration. If the argument I have given is correct, one result will be to put pressure on national governments to reduce their level of transfer payments. The result will be either a reduction in the european welfare states or a transfer of authority for redistribution from the national to the supra-national level.
Published in Liberty Magazine, reprinted by permission