I feel like there's a confusion between school size, scale, and country size.
Imagine a Norway with a single high school, which is a boarding school for all of the high school students in the country. In that case Norway is small, compared to the US, and the school system is small, with a single very large high school.
Or the other way around, if the average school in Sweden has 20 students per grade, while the "small" schools for NYC have ~80 students per grade (both papers use ~100 as the threshold between small and not-small), then since the population of Sweden and NYC are about the same, this would mean that Sweden would have more schools, and so work on a larger scale than NYC.
Without knowing what the school sizes for the Nordic countries, I don't think you can make a conclusion from the information you presented.
> The average school size in our sample was about 450 in 1986, decreasing to about 400 students in the middle of the 1990s (mainly due to small birth cohorts born in the 1980s) and then increasing to 450 again in 2004,
The schools in that Danish study cover grades 0-9, so fall well into the "small" category. They conclude (emphasis is mine)
> With these reservations in mind, we find that for students attending grade 9 in Danish public schools, school size tends to have no effect or even a positive effect on educational outcomes and earnings later in life, at the age of 30. This result is different from the results found in a number of studies from mainly the UK and the US. However, Danish schools are on average much smaller than schools in the US and the UK. The average school size in this study which covers almost all public schools with grade 9 in Denmark was about 460 students. Another interesting result is that the positive effects of school size tend to be larger for boys when we consider educational outcomes like the probability of completing high school or a vocational education and training program, and for children who have fathers with a low education level. Thus, students who are traditionally considered more vulnerable seem to benefit from larger schools. Finally, part of the non-negative or positive school size effect seems to be driven by schools in urban areas contrary to rural areas.
Imagine a Norway with a single high school, which is a boarding school for all of the high school students in the country. In that case Norway is small, compared to the US, and the school system is small, with a single very large high school.
Or the other way around, if the average school in Sweden has 20 students per grade, while the "small" schools for NYC have ~80 students per grade (both papers use ~100 as the threshold between small and not-small), then since the population of Sweden and NYC are about the same, this would mean that Sweden would have more schools, and so work on a larger scale than NYC.
Without knowing what the school sizes for the Nordic countries, I don't think you can make a conclusion from the information you presented.
I found the information which closes that loop, for Denmark, at http://ftp.iza.org/dp8032.pdf :
> The average school size in our sample was about 450 in 1986, decreasing to about 400 students in the middle of the 1990s (mainly due to small birth cohorts born in the 1980s) and then increasing to 450 again in 2004,
The schools in that Danish study cover grades 0-9, so fall well into the "small" category. They conclude (emphasis is mine)
> With these reservations in mind, we find that for students attending grade 9 in Danish public schools, school size tends to have no effect or even a positive effect on educational outcomes and earnings later in life, at the age of 30. This result is different from the results found in a number of studies from mainly the UK and the US. However, Danish schools are on average much smaller than schools in the US and the UK. The average school size in this study which covers almost all public schools with grade 9 in Denmark was about 460 students. Another interesting result is that the positive effects of school size tend to be larger for boys when we consider educational outcomes like the probability of completing high school or a vocational education and training program, and for children who have fathers with a low education level. Thus, students who are traditionally considered more vulnerable seem to benefit from larger schools. Finally, part of the non-negative or positive school size effect seems to be driven by schools in urban areas contrary to rural areas.