Where did all the immigrants go? A fascinating puzzle with a mundane solution.

There are two ways of finding out how many immigrants there are in Canada. One is through administrative data, that is, by using landing records (the forms filled in when new immigrants arrive in Canada) to track immigrants. Another through survey data: to carry out a survey of a selected sample of the Canadian population, and ask people “are you an immigrant?”

Administrative data on immigration levels can be found on the Immigration, Refugees and Citizenship Canada (IRCC) website here: http://www.cic.gc.ca/english/resources/statistics/.Using the data on new permanent residents by source area, I calculated this table on the number of new immigrants to Canada between 2006 to 2011.

The best survey data on immigration to Canada is obtained through the Census, which is carried out every five years. Usually filling out the Census is mandatory. Because almost everyone fills out the Census, it is an almost perfectly representative sample of the population, so extremely useful for economists. In 2011, however, the mandatory Census was temporarily replaced with a voluntary National Household Survey.

The NHS provides an alternative estimate the number of people who have immigrated to Canada between 2006 and 2011. Using the data from table 99-010-X2011026, and manipulating it to create categories comparable to the ones above, I produced the following estimate of the number of Canadian immigrants by region of birth:

What is immediately striking is the difference between the total number of immigrants to Canada as estimated by the IRCC administrative data as compared to the NHS survey data. There are about 350,000 people who apparently arrived as permanent residents between 2006 and 2011, but who are not in the NHS numbers. What could be the reason?

One possibility is that the difference is caused by non-response bias. If, for example, immigrants were less likely to respond to the National Household Survey, that would cause their numbers to be underestimated in the NHS. Arguing against the non-response bias explanation, however, is the fact that the distribution of immigrants by region of birth across the two tables is roughly the same. If non-response was the issue, I would expect to see bigger differences between the administrative and survey numbers in regions where trust in government - and thus willingness to fill out government surveys - is low.

Another possible explanation of the difference is return migration. Possibly people are coming to Canada as permanent residents, finding that life here is not all that it is cracked up to be, and then leaving again. After all, the Immigration, Refugees and Citizenship Canada administrative data counts people who arrive, but does not count people who leave.

A third possible explanation is that the difference is due to some quirk of the data. Indeed, data quirks almost certainly explain at least half of the discrepancy between the two numbers. The National Household Survey asked respondents, “In what year did this person first become a landed immigrant?”. The numbers in the National Household Survey table above represent people who reported any year between 2006 and 2011.  Yet the National Household Survey was carried out in May, 2011, so anyone who arrived in the second half of the year would not have been included in the NHS counts. Given that almost 250,000 people immigrated to Canada in 2011, at least half that number, or 125,000 people, would have arrived in Canada after the 2011 NHS had been filled out.

Thus a good portion of the difference between the estimates in the two tables above is due to the NHS not counting people who arrived in the second half of 2011. The remainder of the difference is, I suspect, attributable to some mixture of return migration and non-response.

The first moral of this story is that when it comes to data, details matter. How, precisely, was the data gathered? What, precisely, is being measured? What was the exact question asked to survey respondents? The second moral of this story is just how hazardous merging and comparing data from two different sources can be. Here the two data sources being compared were both measuring immigration to Canada, so the non-comparability was immediately obvious. But suppose, for example, Canadian administrative data was being compared to US census data instead of Canadian NHS data. The non-comparability of the numbers might not have been spotted.

Note: this is taken from a series of notes I am writing up for a professional practice for economists course I am teaching this fall. 

Comments

[Mike]

I wish Stat Can produced something like what you have done here. It has taken me almost a decade to understand the differences between most of the common data series they produce.

[Frances Woolley]

Mike, I just wish that Stat Can didn't use such a bizarre time frame for the data making comparisons impossible. Here are the different ways the immigrant numbers can be categorized:

Before 1971
1971 to 1980
1981 to 1990
1991 to 2000
2001 to 2011
2001 to 2005
2005 to 2011

Now thinking about it I'm guessing there might be residual disclosure issue if the 2001 to 2010 numbers are reported along with the total numbers because possibly someone could pick out a person who came in May? But it would be nice to have at least some of the big aggregate numbers available on a consistent time frame so that one could track trends over time and not be off by a half year.

[Dave D'Rave]

I suspect that many of these people are now in the United States.
The practice of immigrating to Canada with the intention of eventually
moving to the US is so widespread that it even has a slang term:
"Touching Base".

For a while there, 85% of "Canadians" coming to work in the US on a TN-1 visa
were actually Chinese or Indian nationals who had "immigrated" to Canada and
then used their "Canadian" identity papers to get a NAFTA visa to move South.
While this particular loophole has been plugged, I do not doubt that the whole
concept of using Canadian "immigration" as a foot in the door for the US
is very much still happening.

[Joseph]

Dave makes a good point and it is one that is not just US-specific. The willingness to immigrate for economic or personal reasons probably doesn't attenuate quickly after arriving in Canada, so these folks might be the leading edge of those willing to go on to other countries when options exist. I know that expats were targeted as people might set up a foreign business office when when I worked for a corporation as they were seen as much more likely to agree to go.

[Frances Woolley]

Dave and joseph -

There isn't a lot of info on return migration, but this OECD report gives some estimates, though they're fairly dated now: https://www.oecd.org/migration/mig/43999382.pdf. Canada actually does a fairly good job of holding onto its immigrants compared to a lot of other countries:

On Canadians in the US: a lot of the Canadians working in tech in the US (be they first, second, or 10th generation immigrants) are there because of simple economics. Tech salaries are higher in the US (see thishttps://www.investinontario.com/information-technology#IT-Companies-thrive-here). Canada has a number of large and highly respected software engineering and computer science programs. They're producing lots of graduates, and the best and brightest go where the salaries are highest and the opportunities for learning are the greatest, and that's often the US.. The fact that a number of Canada's tech companies are located in cities that fall in into the "nice place to raise a family" category doesn't help with the retention of young talent.

[Jacques René Giguère]

You wanted an integrated North American economy. Then it means that Canada will be in the periphery (boondocks in human english) the way Nova Scotia is a a beautiful place for the 1% to buy a cottage on the sea.
The consequence is you mistakenly believe Canada is a "more equal" society than the US. No: your true 1% percenters are in New York and San Francisco. We're just the loser on the rez.

[Frances Woolley]

Jacques Rene -

That's actually something that's really important to bear in mind when comparing Canadian and US income inequality numbers. The US taxes people on the basis of citizenship, so it's not possible to avoid paying US taxes except by giving up US citizenship. Canada taxes people on the basis of residence, creating strong incentives for rich Canadians to take up residence elsewhere. I'm not sure how much of the difference between Cdn and US inequality numbers this accounts for, but it is part of the story.

You're making a slightly different point - that the most talented Cdns go south and earn their fortunes in the US. Not sure how much of the inequality difference that would account for.

[Jacques René Giguère]

The whole point of the National Policy was to create a whole society up north.
Otherwise, Manitoba is North North Dakota with all the prosperity and influence that ensues.
In an integrated North American economy,apart from space stations for the mining and gas-oil extraction, the only locale that is relevant is Montréal as Chicago's northern harbor. The same as New Orleans which Chicago's southern shore. Just colder and less crime. And both french-speaking as my ancestors knew the value of location,location,location.
As for inequality, the Canadian real high earners live in the US,both individually and as members of the biggest businesses. The "Big Five " (that is Anglo) banks divide a market smaller than Texas. And the next two (Nationale and Desjardins) share a market barely the size of Arizona. Would barely count as regional banks in the US (with commensurate compensations...)
Inequality in the North Atlantic is not about ordinary proles (including professors at municipal universities, sorry McGill,I knew McGill, I worked with McGill but you're no Harvard...) earning less but about the real top stealing much more. And the stealing is done mostly in New York and San Francisco. The "CEO" of GM Canada is merely a foreman of the branch office without authority to blow its own nose or a young trainee for the show down south.