Theresa May, the home secretary, has given a keynote speech on immigration to the centre-right Policy Exchange thinktank, in which she has announced new interviews for foreign students. But do her arguments add up?

1. Migration and jobs

In her speech, May says:

"So we asked the Migration Advisory Committee to look at the effects of immigration on jobs, and their conclusions were stark. They found a clear association between non-European immigration and employment in the UK. Between 1995 and 2010, the committee found an associated displacement of 160,000 British workers. For every additional 100 immigrants, they estimated that 23 British workers would not be employed."

This is highly selective at best, as I explain here. In fact, the MAC analysis found that, overall, looking at all immigrants over the entire time period for which data was available, there was no statistically significant impact of migration on employment. They then cut the data in various different ways, and ran 15 different regressions. For 11, there was no statistically significant impact; for four, there was. May is highlighting one of the four. It is also worth noting that the MAC noted that their findings were far from robust – all they had to do was change the variables slightly, look at a somewhat different time period, or change the technical specifications of the model – and the results were quite different (and statistically insignificant). Finally, they concluded:

"In particular, any link between immigration and employment of British-born people cannot be proved to be causal. Rather, it should be thought of as an association."

So to say, as May does, that the results were "stark" is going well beyond what the MAC said or what the research actually found. It is also worth noting that most other research continues to find no statistically significant impact of migration on employment. As Ian Preston, professor of economics at UCL and one of the leading researchers in this area, puts it:

"Viewing the totality of new evidence, it is difficult to see a persuasively robust empirical case for long-run harmful effects of immigration on employment of the UK-born."

2. Migration and wages

May says:

"There is evidence, too, that immigration puts a downward pressure on wages. Drawing on several academic studies, the committee found that immigration can increase wages for the better-off, but for those on lower wages, more immigration means more workers competing for a limited number of low-skilled jobs. The result is lower wages – and the people who lose out are working-class families, as well as ethnic minority communities and recent immigrants themselves."

The implication here, in the first and third sentences, is that immigration lowers average wages. This is not what the evidence suggests, and not what the MAC found: they concluded that it was reasonable to assume that immigration had little or no impact on average wages. The second sentence is correct, but omits the point that the estimated impacts are rather small; the MAC's preferred study suggests that the impact on annual growth in hourly wages of the lowest earners was 0.7p-30p a week for a full-time worker – which they describe as "very modest". By comparison, the Institute for Fiscal Studies estimates that the losses to the poorest decile resulting from the measures in the chancellor's autumn statement will be £3.34 a week.

3. Migration and housing

May says:

"One area in which we can be certain mass immigration has an effect is housing. More than one third of all new housing demand in Britain is caused by immigration. And there is evidence that without the demand caused by mass immigration, house prices could be 10% lower over a 20-year period."

The first sentence is supported by the official projections. The source of the second sentence is unclear. The MAC found that estimates of the impact of migration on house prices were highly uncertain, but that it was likely to be small. However, if by "caused by mass immigration" May means "compared with what would happen if there was zero immigration", then this does not seem an unreasonable estimate over a 20-year period; the implication is that migration increases house prices by 0.5% per year, which seems plausible enough.

4. Migration, language, and social cohesion

May says:

"You only have to look at London, where almost half of all primary school children speak English as a second language, to see the challenges we now face as a country. This isn't fair to anyone: how can people build relationships with their neighbours if they can't even speak the same language?"

This appears to confuse "speaking English as a second language" with "can't even speak the same language". It is true that almost half of all primary school children in London speak English as a second language. But this doesn't mean that they, or their parents, can't speak English with their friends and neighbours. In fact, census data shows that only one in eight households in London (and one in 25 in the country) don't include someone for whom English is a "main" language; and even some of those will have people who can communicate perfectly well in English. Moreover, it is also worth noting that despite the very high numbers of children with English as a second language, London school performance is excellent relative to the rest of the country, particularly for more deprived pupils.