[ODP] Increasing inequality in general intelligence and socioeconomic status as a res
Title:
Increasing inequality in general intelligence and socioeconomic status as a result of immigration in Denmark 1980-2014

Authors:
Emil O. W. Kirkegaard, Bo Tranberg

Abstract:
We argue that if immigrants have a different mean general intelligence (g) than the host country and if immigrants generally retain their level of mean g, then immigration will increase the standard deviation of g. We further argue that inequality in g is an important cause of social inequality, so increasing it will increase social inequality.

We build a model to analyze change in the mean and standard deviation of g over time and use it on data from Denmark. The simplest model, which assumes no immigrant gains in g, shows that g has fallen from 97.1 to 96.4 and the standard deviation has increased from 15.04 to 15.40 in the time span 1980 to 2014 due to immigration.

Files:
PDF: https://osf.io/dei73/
Other files: https://osf.io/r5a2x/files/
MH:

I think you should write "better correlate" if it's a correlation analysis. By saying this, you make clear that you are talking about correlations, and people will never get confused about if it's correlation or regression.

Changed the word from "predictor" to "correlate" when the context was correlations as opposed to MR.

Revision #6
https://osf.io/dei73/
Is there any empirical data for SD trends over time? You cite a study of the IQ in 2003, but no cohort-based studies of changes in SD.

g should be italicized in a paper. "Authors" as a plural should not have an apostrophe (as on p. 4). "Gini" (as in "Gini coefficient") should be capitalized.
The army has data, but they are not public.

One could try the PISA data. These are scholastic, not g data. PISA is also affected by changes in the exclusion rate and schooling practices.

Anyway, the PISA data are:

source("merger.R")DF.mega = read.mega("Megadataset_v1.8.csv")DF.pisaSD = DF.mega[,seq(29,61,2)]t(DF.pisaSD["DNK",])

 DNKMath00SD 87.00000Read00SD 98.00000Sci00SD 103.00000Math03SD 103.00000Read03SD 88.00000Sci03SD 102.00000Sci06SD 93.13443Read06SD 89.26528Math06SD 84.81061Read09SD 83.58587Math09SD 87.01057Sci09SD 91.91580Finance12SD NAMath12SD 82.09977Read12SD 85.61966Sci12SD 92.66652CPS12SD 92.31454

Results are all over the place. PISA SD's are not very stable from year to year. Too much noise or exclusion rate changes or something.

I prefer not to bother with italicization of g.
Changed "author's" to "authors".
Changed all "gini"s to "Gini"s.
It's not all over the place. For reading and science, SDs tend to decrease over time. It's clearly different from the pattern displayed in figure 6. Although PISA is not intelligence test, I wasn't expecting this.
1) "Fifth, comparisons between full-siblings living together show that"

should be reared/raised together

2) "to calculate the composing of populations"

Composing? Rephrase.

3) "we show the out using step sizes of"

Show the outPUT?

4) "Adding two normal distributions together with different means always results in a greater SD."

Wouldn't the SDs of the distributions have to be similar for that to be true?

5) You should add some descriptive statistics on the countries of origin of the immigrant population in Denmark.

1) "Fifth, comparisons between full-siblings living together show that"

should be reared/raised together

Changed to "reared".

2) "to calculate the composing of populations"
Composing? Rephrase.

Changed to "to calculate the aggregation of populations".

3) "we show the out using step sizes of"
Show the outPUT?

Fixed.

4) "Adding two normal distributions together with different means always results in a greater SD."

Wouldn't the SDs of the distributions have to be similar for that to be true?

Changed to "Adding two equal sized, equal SD normal distributions together with different means always results in a greater SD.".

We have been trying to prove this theorem deductively, but it is not easy. We consulted some mathematicians who were also unable to prove it. It is easy to show by illustration of course.

5) You should add some descriptive statistics on the countries of origin of the immigrant population in Denmark.

I can add a table in the appendix with their relative size over select years. Is that what you desire? E.g. percent of the population by each country of origin 1980, 1985, 1990, 1995, 2000, 2005, 2010?

-

New revision added: https://osf.io/dei73/ dated 14th Nov. 2014. #7

1) "Fifth, comparisons between full-siblings living together show that"

should be reared/raised together

Changed to "reared".

2) "to calculate the composing of populations"
Composing? Rephrase.

Changed to "to calculate the aggregation of populations".

3) "we show the out using step sizes of"
Show the outPUT?

Fixed.

4) "Adding two normal distributions together with different means always results in a greater SD."

Wouldn't the SDs of the distributions have to be similar for that to be true?

Changed to "Adding two equal sized, equal SD normal distributions together with different means always results in a greater SD.".

We have been trying to prove this theorem deductively, but it is not easy. We consulted some mathematicians who were also unable to prove it. It is easy to show by illustration of course.

5) You should add some descriptive statistics on the countries of origin of the immigrant population in Denmark.

I can add a table in the appendix with their relative size over select years. Is that what you desire? E.g. percent of the population by each country of origin 1980, 1985, 1990, 1995, 2000, 2005, 2010?

-

New revision added: https://osf.io/dei73/, dated 14th Nov. 2014. #7

Delete the comma from the link
Introduction. Constant Danes population size could be due to lowered mortality due to increased lifespan. You should also plot number of deaths or death rate against year in figure 2.
Population t+1= Populationt+Naturalincreaset+Netmigrationt
Naturalincreaset= Birthst+Deathst
This model should be incorporated in the paper.
“The reason for the apparent paradox is that there is a constant conversion of people from the
’foreign origin’ category to the ’Danish origin’ category”
You cannot state this if you do not include the number of deaths in your demographic model.
Section 4.3. > I would like to see this tested on an existing population with long lasting and widespread migration history, such as the US. How did the SD in IQ or average height in the US change over the last 100 years or so? Is it higher than countries with more homogeneous ethnic background, such as Iceland or Finland?
For example we know the ethnic composition of White Americans (e.g. 25% German, 10 % Irish, etc.) and the average heights and SDs of the European countries from which they descend. This will enable you to test your model.
Duxide,

Thank you for reviewing our paper.

Introduction. Constant Danes population size could be due to lowered mortality due to increased lifespan. You should also plot number of deaths or death rate against year in figure 2.
Population t+1= Populationt+Naturalincreaset+Netmigrationt
Naturalincreaset= Birthst+Deathst
This model should be incorporated in the paper.

We don't want to get into more complex modeling. It is possible to have constant population size only if average lifespan increase quite a bit every year. This doesn't happen, altho it increases a bit.

“The reason for the apparent paradox is that there is a constant conversion of people from the
’foreign origin’ category to the ’Danish origin’ category”
You cannot state this if you do not include the number of deaths in your demographic model.

Sure we can. The reason it happens is quite obvious from the legalistic definition of "country of origin" that the DST employs. If you desire more complex modeling, you should look up Nyborg's paper. His predictions were wrong however since he used UN birth rates for immigrants in Denmark, not adjusting for the fact that they decline sharply once they get here and in the second generation especially. For that reason his predictions are too pessimistic.

Section 4.3. > I would like to see this tested on an existing population with long lasting and widespread migration history, such as the US. How did the SD in IQ or average height in the US change over the last 100 years or so? Is it higher than countries with more homogeneous ethnic background, such as Iceland or Finland?

For example we know the ethnic composition of White Americans (e.g. 25% German, 10 % Irish, etc.) and the average heights and SDs of the European countries from which they descend. This will enable you to test your model.

If you have links to data useful for that purpose, that would be good. However, it is for another study. In this one we tried to model the SD of g using population level data. There is only one real datapoint to compare against (2003 army data) and the model fits nicely with it both in terms of the mean and the SD.

This seems to be another case of the reviewer wanting the paper to be about something other than it is. It is not reasonable to demand a new complex analysis of deaths for the simple claim that conversion of people from "foreign origin" to "Danish origin" is happening. This is plainly obvious from the definition. A child born to 1 genetic Dane and 1 foreign origin will be counted at 1 "Danish origin" in their data. That person would of course be 50% Danish genetically, but since s/he is counted as 1, it introduces error in estimates such as ours.
This seems to be another case of the reviewer wanting the paper to be about something other than it is. It is not reasonable to demand a new complex analysis of deaths for the simple claim that conversion of people from "foreign origin" to "Danish origin" is happening. This is plainly obvious from the definition. A child born to 1 genetic Dane and 1 foreign origin will be counted at 1 "Danish origin" in their data. That person would of course be 50% Danish genetically, but since s/he is counted as 1, it introduces error in estimates such as ours.

Yes, I agree. That's why I don't understand why you took the trouble of plotting birth rate. That way you set yourself up for elaborating more and doing complex modelling. If you offer half cake people will want the other half.
In my opinion you should keep it simple and just say that the conversion of people from foreign origin to Danish origin is happening introduced error in the estimate.Otherwise you'll shoot yourself in the foot.

Dear Emil,

Unfortunately my time is too limited to look through all the papers. Here a few brief suggestions for the paper about immigration and inequality:

1. One thing you could work out is that there is a predicted direct effect of ability distribution on socio-economic inequalities simply because you get more variance in IQ, therefore more variance in SES. But there is also the more insidious but possibly more potent effect that rising cognitive inequality, when it is on racial or ethnic lines, reduces solidarity. In America, for example, one side effect of efforts to integrate the “disadvantaged minorities” and of the relaxed immigration policies that had been introduced during the 1960s was a virulent anti-poor and anti-welfare movement that virtually ended federally funded welfare programs during the 1980s and 90s. All this on the background of steep rises in social inequality. The main victims of this development were working-class Whites, whose standard of living has declined since the 1970s. And still, most Americans today (even the poor!) believe that those who are poorer than themselves are treated too well in their country. If there is massive low-IQ immigration in Europe, within a generation or so we will see the same massive shift in political preferences in Europe. Some have made this shift already.

2. You do not dwell much on the selectivity of migration. For example, immigrants from India seem to be doing well in the UK although the average IQ in India is most likely a bit below 80. One reason is almost certainly that rich Hindus are more likely to migrate than poor ones. This does not seem to be the case for people from Pakistan and Bangladesh, who do poorly in Britain. It is not entirely clear what causes this difference, but different selectivity of migration is likely to be one factor.

3. I noticed that you did not cite Rindermann’s recent study about immigrant performance, which I am attaching.

4. I guess the data that you are presenting, for example in Figure 2, are TFR, not cohort fertility. The difference is that TFR is affected by changes in the timing of reproduction, and is therefore not an accurate measure of actual demographic trends. There was a trend for delayed childbearing in Europe during the last decades. Therefore the cohort fertility is a bit higher than the TFR. This means the Danes are still breed themselves out of existence, but a bit more slowly than suggested by their TFR.

5. On page 2 you find that the constant number of Danes is hard to square with the fertility data in Figure 2. In addition to the non-identity of TFR and cohort fertility rate, another reason is rising life expectancy.

6. Page 3: Modify premise 1 by specifying immigrants “in Denmark”. Otherwise it looks like immigrants always have lower g than natives. This is not the case, for example in the Arab oil countries.

7. Premise 3 is offered without clear proof. Typical correlations of g with adult income are about 0.3, which means they are not very high, unlike correlations with education which are 0.5 to 0.6. Whether this is “important” is debatable. As far as I know there is no empiric study showing unequivocally that there is a connection between cognitive inequality and income inequality in comparisons between countries.

8. Page 4, last bullet point: Principal axis factoring, not principle axis factoring.

9. Page 8: Here you mention people rich enough to hire human smugglers. Those who migrate and who are bright enough and solid enough to make a positive contribution to the host countries do not need human smugglers. They can hire an immigration lawyer, and they get support from their employers. Immigration is driven mainly by businesses who either want cheap labor, or who cannot find enough native talent for highly qualified work. Their needs determine in large part whether the immigrants that manage to settle in the country are of the low-IQ or the high-IQ type. Every good libertarian applauds this state of affairs because it is good for business and brings people to the places where they are needed.

Hope this s at least of some help.

Gerhard
Although I understand the basic idea of the article, I'm not even sure what your model depicted in figure 3 is trying to say. Is that a simulation study (in figure 3) ? Can you translate this passage here ? I don't understand it.

Briefly put, the model works by dividing normal distributions into intervals and finding the density of each interval. Normal distributions with different means will thus add differently to each interval, and each can be weighted by its size.

Consider the case where we want to model the merging of two equal sized populations with means of -.5 and .5. Suppose that we want to model it in the region -5 to 5. The effect of the step size is to increase the resolution and make the estimates from the intervals closer to the true normal distributions. Below, we show the out using step sizes of 2, 1, .5, and .1.

I have also never heard about "interval means" (in your R syntax).

And, some few other things :

Figure 3 appears in your article but not cited/mentioned in your text. At page 6, you write "Where x-bar is the mean value and xi is the i 'th value." You should also say that Σ is "sum of".

Finally, your graphs at figures 8-9 are pictures published in econometric papers by the usual group of economists who look at the trend in inequality (Piketty and co.). But are you sure you won't have problem with copyright or something ? In some books, it's common to read annotations (below the graphs) such as "reprinted with permission of xxx".
Meng Hu,

The results are from a simulation based on population data from public databases.

I don't know what you don't understand. One takes a normal distribution, cuts it into intervals, and then weighs the intervals by their size to obtain weighted means and weighted SDs.

"interval means" is just another term for "interval midpoint". The latter term seems to be more common, so I will change it to that.

Figure 3 is mentioned right in the text you quoted ("Below, we show"). However, I will add an explicit reference to it.

Using images like that is fair use under Danish law. Don't need permission.

I will try to get a new draft out later tonight which also includes updates based on Meisenberg's review above. :)
Ok.

About this, "Since we consider the no gains (100% heritability) implausible, we place our money on something akin to the weak gains model." I don't think what is written in parentheses is true. It could be that the absence of gain is consistent with <100% heritability if environmentality, for some reasons, keep the IQ levels constant. Some rGE (G-E correlation) theorists used that argument (although wrong in my opinion) to explain why compensatory educational intervention does not improve IQ.

And, finally, can you describe in your text how you make the four models presented in table 2 ?
Admitting that the g-relevant environment is not better in Denmark than lower scoring host countries, means the difference between host countries and DK is 100% heritable. As such I don't see how the claim can be found, unless we assume wildly implausible GE-interaction models.

We explained it in Section 6. However, I will add an example to make it more clear.
New draft. #8

Changed "interval mean" to "interval midpoint".

Made a direct reference to Figure 3 in the text.

Added an example to better explain how results in Table 2 are derived.

Added a discussion of the second route of increased inequality to the discussion:

In the paper, we argued that inequality in g leads to inequality in socioeconomic outcomes due to the relevance of g as a cause of these. However, a reviewer pointed out that increased racial or ethnic heterogeneity within society may cause people to adopt less egalitarian policies which could itself increase socioeconomic inequality, see among others\cite{Meisenberg07,Meisenberg08,putnam2007pluribus,roth2010perils}.

2. You do not dwell much on the selectivity of migration. For example, immigrants from India seem to be doing well in the UK although the average IQ in India is most likely a bit below 80. One reason is almost certainly that rich Hindus are more likely to migrate than poor ones. This does not seem to be the case for people from Pakistan and Bangladesh, who do poorly in Britain. It is not entirely clear what causes this difference, but different selectivity of migration is likely to be one factor.

We discuss selection a few times. However, there is no obvious dataset to use to test selection effects. The conclusion discusses that future studies may look into this.

3. I noticed that you did not cite Rindermann’s recent study about immigrant performance, which I am attaching.

It was not published when we submitted this article. :) I have added it to the discussion of premise 2.

4. I guess the data that you are presenting, for example in Figure 2, are TFR, not cohort fertility. The difference is that TFR is affected by changes in the timing of reproduction, and is therefore not an accurate measure of actual demographic trends. There was a trend for delayed childbearing in Europe during the last decades. Therefore the cohort fertility is a bit higher than the TFR. This means the Danes are still breed themselves out of existence, but a bit more slowly than suggested by their TFR.

They are TFR, yes. I agree. I have added a clarification to the table caption.

5. On page 2 you find that the constant number of Danes is hard to square with the fertility data in Figure 2. In addition to the non-identity of TFR and cohort fertility rate, another reason is rising life expectancy.

Yes, this is already mentioned, we write:

As can be seen, the fertility of women with Danish origin is well below replacement levels (about 2.1). Given reasonable assumptions about population age structure, sex distribution and increases in lifespan, the demographic data appears to be inconsistent with the fertility data.

6. Page 3: Modify premise 1 by specifying immigrants “in Denmark”. Otherwise it looks like immigrants always have lower g than natives. This is not the case, for example in the Arab oil countries.

Changed text to:

Premise 1: Immigrants have a lower average g than the western host countries.

One if is really nit-picky, one may point to Australia as a country where the immigrants are not lower (because Chinese etc.), but for almost all of them, they are lower on average. We can hopefully be forgiven this minor imprecision.

7. Premise 3 is offered without clear proof. Typical correlations of g with adult income are about 0.3, which means they are not very high, unlike correlations with education which are 0.5 to 0.6. Whether this is “important” is debatable. As far as I know there is no empiric study showing unequivocally that there is a connection between cognitive inequality and income inequality in comparisons between countries.

Premise 3 concerns within country socioeconomic inequality, not between country. We think the .3 correlation is important. .3 only seems weak if one looks at individual level data. If one examines grouped data*, such an effect size is clearly important.

* Lubinski, D., & Humphreys, L. G. (1996). Seeing the forest from the trees: When predicting the behavior or status of groups, correlate means. Psychology, Public Policy, and Law, 2(2), 363.

8. Page 4, last bullet point: Principal axis factoring, not principle axis factoring.

Fixed.
Admitting that the g-relevant environment is not better in Denmark than lower scoring host countries, means the difference between host countries and DK is 100% heritable.

It's an unlikely assumption. Ok, environments among high IQ (developed) countries are probably not very different, and between-country environmental gap is large only if you compare developed and undeveloped countries. However, small environmental difference can generate small IQ gains/losses. How do you know that "the g-relevant environment is not better in Denmark than lower scoring host countries" ?

We applied these gains only to countries with an IQ lower than Denmark.

I would like you to give more information about the mean IQ (max. and min.) of these countries. How much lower ? Information about SD of IQ may also be useful.

In your figure 3, i noticed that the first graph displays two non-normal distribution. Both groups have skewed IQ distribution.

Fifth, comparisons between full-siblings reared together show that the higher IQ ones tend to do better in society. This cannot be attributed to shared environmental factors since these are shared by the siblings.

You can add Nedelec et al. (2012).

Nedelec, J. L., Schwartz, J. A., Connolly, E. J., & Beaver, K. M. (2012). Exploring the association between IQ and differential life outcomes: Results from a longitudinal sample of monozygotic twins. Temas em Psicologia, 20(1), 31-43.

It shows that non-shared environment has no predictivity. However, the direction of the correlations is more consistent with a conclusion of inconsistent finding than with a conclusion of null finding. They also do not correct for measurement errors, e.g., by using latent variable approach. So, you may or may not cite it.
I was reading an older review by Loehlin (2000) and found an apparently forgotten study of the heritability of SES:

Tambs, K., Sundet, J. M., Magnus, P., & Berg, K. (1989). Genetic and environmental contributions to the covariance between occupational status, educational attainment, and IQ: A study of twins. Behavior genetics, 19(2), 209-222.

Scores of occupational status, educational attainment, and IQ were obtained for 507 monozygotic and 575 dizygotic male twin pairs born 1931–1935 and 1944–1960. A multivariate genetic analysis with statistics from different cohorts showed heterogeneity between cohorts, and analyses were performed in four separate cohorts. The only set of results which departed clearly from the rest was found for the group born 1931–1935, where the ratio of environmental to genetic effects exceeded those of the other groups. Typical heritability values in the three youngest groups (weighted means) were .43, .51, and .66 for occupation, education, and IQ, respectively. The values in the oldest group were .16, .10, and .37, but this sample is small and the estimates are unstable. Genetic variance influencing educational attainment also contributed approximately one fourth of the genetic variance for occupational status and nearly half the genetic variance for IQ. The values for the between-families variances (reflecting family environment and assortative mating) varied from 2 to 35% in the three youngest groups but were higher for education (62%) and IQ (45%) in the oldest groups. All the between-families variance was common to all three variables. For educational attainment and IQ, the bulk of this between-families variance is probably genetic variance due to assortative mating. The common-factor environmental within-family variances were generally small, and the specific estimates seemed to contain mainly measurement error.
Meng Hu,

It's an unlikely assumption. Ok, environments among high IQ (developed) countries are probably not very different, and between-country environmental gap is large only if you compare developed and undeveloped countries. However, small environmental difference can generate small IQ gains/losses. How do you know that "the g-relevant environment is not better in Denmark than lower scoring host countries" ?

I don't know that. We did not claim that either, so I don't know why you ask. We model environmental gains in a simple way, by up-adjusting immigrants from lower-scoring country, but not down-adjusting immigrants from higher-scoring countries on the theory that environment does not explain the differences between these.

One could remove that assumption and adjust all immigrants towards the Danish IQ. It will make little difference since there are not so many large immigrant countries with IQs higher than the Danish (97.2), and those there are (e.g. Germany), have IQs only slightly higher, so the adjustment would be very small (DEU = 98.8, GBR = 99.1).

I would like you to give more information about the mean IQ (max. and min.) of these countries. How much lower ? Information about SD of IQ may also be useful.

You are asking for the SD, min and max IQ of all countries with IQs below Danish. Attached is a histogram. Descriptive stats are:

 vars n mean sd median trimmed mad min max range skew kurtosis seIQ 1 87 83.9 8.72 85 84.44 9.93 62 96.6 34.6 -0.53 -0.6 0.93

In your figure 3, i noticed that the first graph displays two non-normal distribution. Both groups have skewed IQ distribution.

This is a statistical artifact. The population is normally distributed. This shows what happens if one uses a resolution too low in modeling. We did not use steps of 2, we used .1 (#4). Changing it to .01 makes no noticeable difference on results or plots. We used .1 for computational reasons.

You can add Nedelec et al. (2012).

Nedelec, J. L., Schwartz, J. A., Connolly, E. J., & Beaver, K. M. (2012). Exploring the association between IQ and differential life outcomes: Results from a longitudinal sample of monozygotic twins. Temas em Psicologia, 20(1), 31-43.

It shows that non-shared environment has no predictivity. However, the direction of the correlations is more consistent with a conclusion of inconsistent finding than with a conclusion of null finding. They also do not correct for measurement errors, e.g., by using latent variable approach. So, you may or may not cite it.

Thank you. We were not familiar with this study.