Do migrants, especially those from within the European Union, get a better deal in Britain than they would elsewhere in the EU? And do they therefore impose a disproportionate burden on UK taxpayers? The answer to the first question is yes, at least compared with some countries, because of the nature of the UK benefit system. But despite this, the answer to the second is a definitive no. When Iain Duncan Smith describes the inflow of EU nationals to claim benefits as a "crisis", the only rational reaction is: "Crisis? What crisis?".

The UK benefit system is indeed relatively friendly to migrants from within the EU. Migrants from outside generally have to pass a "no recourse to public funds" test, and of course skilled migrants and foreign students are pretty unlikely to end up on benefits. But migrants from within the EU, once they are "habitually resident", have to be treated similarly to UK citizens. And given that our benefit system, for those of working age, is now mostly means-tested – that is, based on income and residence, not contributions – that means EU citizens do better here than they would in some other countries, such as Germany, that have more contributory systems, as Dominic Raab pointed out in the Times.

Similarly, the NHS, unlike in many continental European systems that have some element of co-payment, is generally free at the point of use for all residents. And the combination of child benefit and child tax credits is considerably more generous than, say, Italy, where benefits are lower and fall away sharply with income.

Of course, it's not quite as simple as that. The UK has far from the most generous social security system in Europe, both in terms of benefit levels and overall spending. In France, for example, unemployment benefits are considerably higher for most people than they are in the UK, while contribution conditions are, if anything, somewhat weaker; a French teacher or banker losing their job in London might well be shocked by how little they would be entitled to here.

So, overall, the picture is mixed, but certainly some migrants – especially those from the relatively poor new member states – do better here than they would at home. But that doesn't mean British taxpayers are the losers from migration. Quite the opposite. All the evidence suggests that migrants – especially migrants from the new EU member states – are net contributors to the public purse, not a drain. The most comprehensive study on this topic found that the latter paid in via taxes about 30% more than they cost our public services. In particular, they were far less likely to claim benefits and tax credits, and far less likely to live in social housing.

Focusing more specifically on the benefit system, the contrast becomes even starker. Raab claims that there are more than half a million "unemployed" EU citizens in the UK (compared with the national total of about 2.5 million). This is wrong: there are half a million EU citizens who are not in work, but some are retired, and some out of the labour market for other reasons. By Raab's definition, there would be more than 15 million unemployed Britons! In fact, employment rates for EU citizens – especially those from the new member states – are considerably higher than for the UK-born.

And even those who aren't working are considerably less likely than those born in the UK to claim benefits. According to figures from the Department for Work and Pensions (DWP), of the roughly 1.8 million people from elsewhere in the EU of working age, about 90,000 are claiming an "out of work benefit", or about 5%. That compares with about 13% for natives. Equally, migrants from outside the EU are much less likely to claim benefits than natives. And as for Bulgarians and Romanians, although there are already at least 140,000 in the UK, neither shows up in the top 20 countries of origin for foreign benefit claimants, suggesting the numbers to date are minimal.

What about other public services? NIESR research for the government's Migration Advisory Committee found that migrants imposed less than proportionate costs on the health and education system. This is mostly a natural consequence of the fact that migrants are more likely to be young and healthy, and health spending goes overwhelmingly on the old and sick. Of course migrants will, over time, age too (although many EU migrants are likely to return to their countries of origin) but the net balance over time is still likely to be positive.

So, on average, "benefit tourism" (or indeed "health tourism") doesn't appear to be a significant economic problem – migrants, including EU migrants, more than pay for themselves. Without migration, our fiscal position would be even worse, and public services even more stretched for cash. But that doesn't mean that there aren't cases of real abuse, nor does it mean it's unreasonable for people to think there's something wrong with, for example, people coming here but claiming child benefit – at UK rates, and paid for by UK taxpayers – for children in other countries where the cost of living is lower.

Raab's prescription – and that of Frank Field – for this problem is a return to the "contributory principle", where benefits would be much more closely related to national insurance contributions. There are good arguments for and against this – but it would be a major reversal of the policy pursued by governments of all parties for at least the last 30 years, largely in attempts to save money.

Ever since Margaret Thatcher abolished the earnings-related supplement to unemployment benefit in 1982, the contributory principle has become less and less a part of the UK welfare system. Indeed, the largest single welfare savings measure so far introduced by this government was the time-limiting of contributory employment and support allowance, which will save £2bn per year and in effect means the end of the largest remaining part of the working-age benefit system that could meaningfully be described as contributions-based.

Now there are good arguments for and against contributory benefits – and to give Field credit, he has been arguing the case for years. But reversing the tide of history on this to deal with a relatively minor set of issues looks like a very large sledgehammer directed at a very small nut.