If only it were so simple.

For we do not actually have anything like tight control on immigration numbers, even though the main political parties are always keen to create an impression that we do.

A net total of 500,000 people have poured in over the past year, not counting tourists, compared with 240,000 in 2018-19, the last year unaffected by the pandemic.

For advocates of a larger population, such as this column, the thundering pace of arrivals should be joyful news. It's not. Housing in this country is costing far too much.

Also, if we do not bring immigration down for a few years, Australians, especially younger ones who rent, will learn to loathe it. Maintaining powerful long-term population growth would then become politically impossible.

In June, the Institute of Public Affairs forecast that we'd need 45,200 extra homes this year to accommodate natural population growth and 160,000 more for immigrants. But we were likely to build only 148,500 homes, the think tank found. We don't have enough construction workers, materials are costly, and anti-development nimbies have been running wild, especially in NSW.

So the institute forecast a shortfall of 56,700 homes, with a similar degree of under-supply in the following three years. Actually, it's turning out to be worse than that, because the immigration flow is stronger than the institute assumed.

Meanwhile, September-quarter rents were 7.6 per cent higher than a year earlier, and Reserve Bank governor Michelle Bullock expects annual rises to hit 10 per cent, far above general inflation and even further above wage rises. So, yes, the housing crisis will get even worse.

So, let's restrict immigration for a few years. But how?

The great bulk of the inward flow of people is feeding the education sector with students, so that's where most of the solution should be. Yet the government hardly controls student visa numbers. If someone with enough money wants to come here for education, and if a university or other school issues a certificate of enrolment, a student visa generally follows.

Brendan Coates of the Grattan Institute, another think tank, suggests the simple measure of increasing the $710 application fee for the visa. Doubling it would reduce foreign demand for Australian education (not much, I think) and, more importantly, pay for a 10 per cent increase in rent assistance for eligible Australians, he calculates.

It's a good idea, but long-term support for immigration would still suffer the political damage of frequent media reports about population driving up rents.

Probably more effective would be excluding some of our education sector's junkier courses from eligibility for visas, another suggestion from Coates. Some of those courses seem to be basically conduits for immigration, which would be fine if they delivered highly qualified immigrants - but they generally don't.

And the Grattan Institute has previously suggested getting tough with international students who have already graduated but are failing to develop careers here while lingering on visas that are too readily extended. We need to start telling them it's time to go home.

Handing out plenty of working-holiday visas sounds like a good idea, since we need more workers. But the long stays in Australia by those visa holders are less about working than holidaying. For a while, we should accept fewer of them.

Maybe the measure we really need to take is to get actual control of student numbers, by setting an annual quota - something not advocated by the Grattan Institute. Again, it's one of those ideas that sounds simple but is actually hard to put into operation. How many students would be allocated to each university or other school, and on what basis?

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Notice that the best foreign students overwhelmingly want to study at our most highly rated universities, half of which are in Melbourne and Sydney, the cities that are suffering most from population growth.

While immigration is the main problem in housing demand, it can also be part of the solution for supply.

The Master Builders Association has urged the government to remove obstacles to bringing in skilled workers, which would mean more foreigners enjoying good wages on Australian construction sites, building those homes we need.

The association calls for a simpler visa system with lower costs and quicker processing, plus the inducement of easier pathways to permanent residency. Language requirements for some skilled workers should be lowered, the association says, noting that a tradesperson is currently required to have the same English skills as a journalist.

It also wants the government to look at creating an apprenticeship visa. Actually, it's inexplicable that we have no visa that allows foreigners to do apprenticeships here. We've known for years that not enough Australians are interested in trades.

We can also increase supply of housing by redirecting construction capacity towards it. The painful conclusion is that we need to cut infrastructure spending for a while.

Infrastructure, especially for transportation, is always thought to be inadequate, so calling for less spending on it seems sacrilegious. But Australians need homes before they need better roads.

So the federal government's axing of 50 infrastructure projects this week will not only save money; to the extent that some of that construction would have begun soon, workers, managers and equipment will now be diverted to building bungalows or, better, townhouses and flats.

We can get back to the job of catching up on infrastructure later - after we've caught up on housing supply.