Are babies in Denmark becoming relatively more Danish?

It looks that way, but not really

Over on Twitter we have this claim by Marko Jukic about the speed of the Danish population replacement is getting a lot of attention:

It sounds unlikely given that migration to Denmark continues, some of which are children. So let's have a closer look.

The question is difficult because the statistical categories do not perfectly proxy genetic categories. "Danish origin" or "Danish ancestry" (depending on the table and the translation) does not mean 100% Danish ancestry. This comes down to just Danish Statistics counts persons, and it gets complicated for mixed-origin people and immigrants later than 2nd generation. First, the main definitions:

Ancestry (herkomst)
Persons of Danish origin
Persons of at least one parent who is a Danish citizen, born in Denmark.

Immigrants
Immigrants are born abroad. None of the parents are both Danish citizens and born in Denmark. If no information is available about either parent and the person was born abroad, the person is also considered an immigrant.

Descendants
Descendants are born in Denmark. None of the parents are both Danish citizens and born in Denmark. If no information is available about either parent and the person is a foreign citizen, the person is also considered a descendant. When one or both parents who were born in Denmark acquire Danish citizenship, their children will not be classified as descendants, but as persons of Danish origin. However, if Danish-born parents both retain a foreign citizenship, their children will be classified as descendants.

So we see the fist issue namely that persons with 1 Danish parent and 1 foreign counts as Danish. Second, notice that to count as Danish, the parent merely needs to have Danish citizenship and be born in Denmark. Any children they get will also be counted as Danish, even if they are only 25% (3. generation) or 12.5% Danish (4th generation). Mainly this affects counts for children born to mixed marriages and 3+ generation migrants. I am not sure what happens if a couple of 2 generation immigrants have a child while not having Danish citizenship, making the child classified as descendant (2. gen) but then gain Danish citizenship. Will the 3rd gen children change to Danish or not?

With that said, let's look at some of the data from the table he looked at FOLK1C (People 1C). The database gives raw counts, so I have analyzed them in R as percentages as well. His central claim is that the very young cohorts are more Danish or at least European than the older ones. Here's the main data of interest:

It is pretty difficult to see, so let's just look at the Danish %:

There is indeed a reversal from around 2019 to now. Magic COVID effect. Granted, it is tiny, since Danish % of 0-4 year olds increased only from 85.2% to 85.9%.

We can think of this as reflecting many things that could have changed:

1. Fertility rates, including those specific to particular ages. If immigrants are delaying childbirth more (towards Danish), then this will happen.

2. Emigration, if they leave the country.

3. If they somehow change their categorization from foreign to Danish.

There is data for us to look at for fertility rates. First, we can look at the estimates of total fertility rates. This is a model-forecast of the number of children per woman if current age-specific fertility trends are constant (they never hold):

There is indeed a remarkable decline in fertility of 1st generation. Their fertility was above 3.5 children per woman in 1992, but converged with Danes in 2009. The new migrants around 2015 then caused an increase, but it immediately declined and indeed after 2021 their fertility is lower than Danes'.

These model forecasts, however, are known to be faulty when age-specific birth rates change. We know they have been changing, women have children later now. OWID has a great page on this:

Indeed, looking at total fertility rates can be grossly misleading:

Insofar as population decline is concerned, there is no cause for concern in Sweden and USA, while Japan and Spain still have issues.

Going back to the Danish situation, we can look at cohort fertility rates instead:

It is similar to the Sweden data, but Denmark is still in the negative, though it was more positive until 1935, and has been increasing since 1955.

These data concern all persons in Denmark, and there doesn't seem to be any cohort fertility rates by origin, so we will have to look at age-specific birth rates:

We can start by noting that teenage births are incredibly rare in Denmark among Danes, approximately 1 in a 1000 (0.001, 0.1%). There has been a drastic decline among 1st generationers as well, from about 1.7% to 0.25%. There are differences across all age groups, but since most women have their children between 25-39, these subsets are of the most importance. Danish women clearly have higher fertility in the 30-34 category, which is the most important (largest values on y axis), and they are about the same as 2nd generation women in 25-29. Danish women have also been catching up in the 35-39 and 40-44 groups. To get the full picture, we can compute a weighted mean across the age groups:

I think this means that of all women of fertile age (15-64 in this dataset), about 3% of the Danish have a child a given year (multiple births reduce this slightly since it only counts as one new mother but multiple new babies), whereas for 2nd generationers it's about 4.6% and 3.3% for 1st generationers. The forecast is not that positive here as it was in the prior table, and I think the reason why is that most 2nd generationers just aren't old enough to have that many children yet.

Edited to add: After sleeping on this, it occurred to me that we can remove the age distribution confound by using the Danish population's age composition to compute the weighted mean for all groups in a given year. This answers the question: what would be the weighted mean birth rate of origin groups be at that year given they all had the Danish age composition (very close to the long term equilibrium given no immigration or emigration). Doing this gives this plot:

This shows that 1st generationers have indeed declined below Danes, though 2+ generationers still have some advantage. The numbers are a bit noisy given the small numbers of women involved. Furthermore, it seems that one should be able to make a cohort fertility forecast based on this, again assuming those age-specific birth rates hold in a woman's reproductive career. Since my age span here is 15-64, this is 50 years. Thus about 0.03 * 50 = 1.5 should be the current Danish fertility rate for such a hypothetical woman. This is marginally lower than the total fertility rate Danish Statistics calculates for the same year (2024: mine = 1.46, DST = 1.52), so I am not sure exactly how they differ in methodology.

We can also look at the origin of the newborns' mothers as a percentage:

These data are not consistent with the results we got simply from counting persons. I think the reason why is that 3rd generations are usually counted as Danish origin, and though they are relatively small in number, they grow year by year. Danish Statistics notes in their annual report (2024):

Children of descendants have at least one parent who is a descendant and no parent of Danish origin. There are 39,123 children of descendants on 1 January 2024 – of which 93 per cent are from non-Western countries. 59 per cent of children of descendants from non-Western countries are under 10 years old.

Children of descendants from Western countries have a different age distribution than children of descendants from non-Western countries, and although they are clearly outnumbered overall, among children of descendants who have reached the age of 30, more than twice as many are from Western countries as from non-Western countries.

Ishøj, Vallensbæk, Brøndby, Albertslund and Høje-Taastrup are the five municipalities with the largest shares of children of descendants. The proportions are 191 per thousand in Ishøj, 130 per thousand in Vallensbæk, 126 per thousand in Brøndby, 120 per thousand in Albertslund and 96 per thousand in Høje-Taastrup. In Ishøj Municipality, this corresponds to 1,692 out of 8,862 0-29-year-olds being children of descendants.

In the compulsory tests at the primary school leaving examination in 2023, the average grade for children of descendants from non-Western countries is 5.5 for boys and 6.3 for girls. The corresponding averages for boys and girls of Danish origin are 6.7 and 7.4.

Specifically, concerning the categorization:

In Statistics Denmark's classification of ancestry, there are three groups: 1) Danish origin, 2) immigrants and 3) descendants. These are the ones that have been used in this publication so far. In this chapter, we will look at a fourth group: children of descendants. Children of descendants are limited to people who have parents of whom at least one is a descendant, and where neither parent has Danish origin. At the same time, children of descendants in Statistics Denmark's normal definition of ancestry must be either people of Danish origin or descendants.

It is not possible to add the group to the existing categories in the definition of ancestry. This is because children of descendants are calculated according to their parents' ancestry classification (whether the parents are immigrants, descendants or people of Danish origin). The groups in the normal definition of ancestry are calculated according to the parents' country of birth and citizenship and therefore not according to the parents' ancestry classification.

The two different calculation methods mean that children of descendants can also appear in several groups at the same time (e.g. both be classified as a person of Danish origin and be children of descendants). In other words, there is overlap between the categories if children of descendants are added to the ancestry classification.

Thus, they generally count as Danish for the purposes of the above categories. This adds at least another 40k migrants from the Danish category to the non-Danish category, messing up with the results above. Their grades in school are about the same as 2nd generation, so there is no hope there either:

(Google translate can't translate everything correctly here, gnst. = average, character = grade, eftk. = 2nd generation.) (Notice also the big COVID-related decline combined with overall grade inflation.)

Overall findings:

• Marko Jukic is sort of correct about the composition in the 0-4 age range, but this is an artifact of how Danish statistics counts 3rd generation immigrants I think.

• There has been a strong convergence in total fertility rate, but this is very problematic given the changes in age-specific fertility rates. My calculation of a weighted mean fertility rate shows a consistent advantage of 2nd generation immigrants to Danish women. There is a decline in 1st generation immigrant fertility rates following the 2015 migration wave.

• By using the origin of the mother of newborns, we can more consistently count the Danish % of the young cohort, and this shows a gradual decline, though it is relatively stable since 2016.