IMMIGRATION is a sensitive subject at the best of times, and this is not one of them. The economic crisis has destroyed millions of jobs in rich countries, making their governments especially touchy about the impact of immigration on the demand for indigenous labour.

Such concerns are illogical, because immigration is counter-cyclical. Recession in rich countries has discouraged some would-be incomers from trying their luck. America, for instance, has seen a sharp decline in Mexicans trying to cross its southern border. Immigration to Europe has slowed. Some studies also suggest that increased inflows of migrants are a leading indicator of a pickup in growth.

Yet governments are often reluctant to leave migration flows to the labour market. In recessions, they tend to take steps to discourage new migrants and even get rid of existing ones. Over the past year the Danish, French and Italian governments have rolled back the Schengen passport-free zone and reintroduced limited border controls. Even Australia and Canada, which pioneered the “points system” to give preference to skilled workers, have cut back on work permits. David Cameron, Britain's prime minister, has imposed a “migration cap” for those from outside the EU. Countries including Spain, Japan and Denmark have taken this to its logical conclusion, with “pay as you go” schemes, under which migrants get cash handouts to return to their countries of origin.

Concerns about immigration are understandable, especially at a time when jobs are in such short supply. Polling in both Europe and America suggests that a majority of locals think immigrants do more harm than good and damage locals' chances in the job market. Evidence that immigration hurts indigenous workers is, however, weak. In seasonal work and construction, cheap foreign labour can depress wages and make it harder for the low-skilled to find work, but the flexibility and willingness of new workers can also boost productivity and encourage innovation.

Strains on public services can sorely test the patience of locals, especially when budget cuts are making it hard to maintain such services. In Britain, for instance, a contingency fund to help cash-strapped local authorities facing pressure on public services has been scrapped. Yet over time immigrants more than repay the extra short-term burden they impose on education, health and other budgets.

Keep the gates open

Politicians often say that they want a sensible debate about immigration; but too often they pander to voters' fears of immigrants rather than attempting to allay them. They should be particularly wary of doing so now. There is growing competition for their skills elsewhere (see article): Asia is fast becoming the new magnet for migrants.

China, which used to be closed to immigrant labour, is now handing out residency permits to professionals, academics and entrepreneurs. In 2009 Shanghai recorded 100,000 foreigners living there. A similar number have settled in the southern port of Guangzhou, drawn from Europe, the Middle East and Africa. South Korea has also witnessed a rise in incomers since 2007 and is particularly keen to attract American-educated graduates.

Immigration is, on the whole, good for economies; and right now, rich countries can do with all the economic help they can get. Rather than sending immigrants home, with their skills, energy, ideas and willingness to work, governments should be encouraging them to come. If they don't, governments elsewhere will.