This paper is quite well-written and finished for publication from my point of view.


1. I would like to see the graph depicting how the average IQ of immigrants to Denmark has declined from 1980-2014. As Table 1 describes, the early immigrants were mostly from nearby Europeans countries (IQ >95), but in this century, they consisted of more middle easterners such as Lebanon, Iraq, Pakistan, Somalia, and Iran (IQ<90).

(This point was already addressed and the manuscript now contains a graph that shows how the average IQ of the Danish immigrants has fallen down to the worldwide mean of IQ90.)


2. The widening income disparity has been observed worldwide. Most economists think that the technology has changed so fast so that more intelligent people create vastly more valuables compared to the last century, when a blue-collared worker could play a fairly important part in producing anything valuable. We will see intelligence and creativity will increase their importance since more and more robots (and soon 3D printers) does those formerly blue-collared jobs.

Another explanation is the slowed growth rate of the world economy. If the rich accumulates their assets faster than the general wage rate growth, the rich get richer and unskilled workers get poorer, as described in "Le Capital" by Tomas Piquet. Of course, this is related to the lower time discount rate (=patience), which is another key factor closely correlated with a person's IQ.

As the authors acknowledge, it would be extremely difficult to separate the underlying genetic changes causing the economic outcomes from those of technological ones. Nonetheless, I believe that this kind of biological simulation analysis does clarify the changes in all aspects of societies in the long run (such as more than 30 years of time span).

I don't think we will reach agreement on this semantic issue.

I would like to know why you didn't give me any counter-argument. You seemed to imply that "my" definition is not shared by anyone else. I showed the proof that this is untrue. And that your wiki-quote you gave me earlier is imprecise, as it does not say how a statistical model is placed with regard to the observed data (unlike the bunch of references I've cited). Unfortunately, that was your only argument. So, I ask you to cite a reference (or several, preferably) that a statistical model can be = to observed data, that statistically modeling needs not be different from a descriptive stats (e.g., means or correlations) since that is your argumentation.

The position you ascribe to me is not mine (i.e. straw man).

I didn't ascribe whatever definition to yours. That was the opposite, in fact. You said :

You are again arguing for some narrow definition of model. This is not the only way the word is used in science.

One does not need actual comparison data for modeling. In many cases, such data are not actually available... which is also why one is doing the modeling in the first place. In this case, there are population data available and one data point from the army study, which the model results can and is compared to in the study. So, by your narrow definition, it is still modeling.

This ...

"One does not need actual comparison data for modeling"

... is what I was answering to (from a long time now). There's no straw man.

If you have any doubts that your model is equivalent to the data, I have two answers : 1) you have never denied I was wrong in saying this 2) a simple calculation of means and SDs is necessarily a descriptive stats, and thus, is equivalent to the observed data.

To see the difference, here's an illustration.
https://humanvarietiesdotorg.files.wordpress.com/2014/12/how-to-calculate-and-use-predicted-y-values-in-multiple-regression-2.png
https://humanvarietiesdotorg.files.wordpress.com/2014/12/how-to-calculate-and-use-predicted-y-values-in-multiple-regression-6.png

The first one is a loess curve (descriptive stats, means of wordsum by age by groups).
The second one modeled, by using squared terms of age.

Also, you're the one who said that my definition is not the one shared by others. You said it clearly by arguing that "This is not the only way the word is used in science". I responded to this, in that your description is wrong. I explained that all in details, with citations and references, that modeling is not equivalent to observed data, and indeed its purpose is to fit that model to the data. So, obviously, modeling implies calculation (i.e., prediction) to produce numbers that are not observables in the data. That is what is meant to say "all models are wrong, but some are useful". Your model with no gain does not satisfy the very definition of statistical modeling, because there is not uncertainty. A model is a mental tool that helps to approximate the real world outcomes. All statisticians know that models are approximations, which is why they are wrong. Since the goal of a model is to measure how well it approximates the data, or alternatively to measure the degree of inexactness of these models, the equivalency between observed data and a specific model does not and cannot permit to satisfy the purpose of modeling, because in that situation, your model with no gain is necessarily correct instead of being wrong. The very definition of a model is to be wrong. That's why your model is not actually a model.

These are proofs of what I say :

http://wmbriggs.com/blog/?p=13721
http://andrewgelman.com/2008/06/12/all_models_are/

The first link says explicitly that you need actual comparison data for modeling.

I would like to thank K. Kura for the comment, as it makes me realize how bad a reviewer I can be. I already knew all along that the conclusion of the present paper was wrong, but still didn't make the connection with inequality and capital when reading it. But thanks to Kura mentioning Thomas Piketty's super best-seller "Capital", I now remember my early writings on that subject, and I'm now able to detect the core of the problem with the paper's main idea.

So, the comment I was referring to is ...

Another explanation is the slowed growth rate of the world economy. If the rich accumulates their assets faster than the general wage rate growth, the rich get richer and unskilled workers get poorer, as described in "Le Capital" by Tomas Piquet. Of course, this is related to the lower time discount rate (=patience), which is another key factor closely correlated with a person's IQ.

I will have to debunk that hypothesis, first, before presenting my argument. So let's go.

The main idea of Piketty is this : r>g, or the "law" that the returns on invested capital (r) rises faster than economic growth (g), in the context of rising proportion of capital incomes in the total income and of capital incomes being more unequally distributed than labor incomes. This creates an ever-increasing rise in inequality, mainly due to the top 1% and 0.1% incomes (and even higher).

In general, there are lot of criticisms to Piketty, some bad (no need to be mentioned), some excellent (<a href="http://www.economicpolicyresearch.org/images/docs/research/political_economy/Pikettys_Elasticity_of_Substitution_A_Critique_WP_2014_8.pdf"; rel="nofollow">here</a>, <a href="http://aida.wss.yale.edu/smith/piketty1.pdf"; rel="nofollow">here</a>, <a href="http://www.dissentmagazine.org/article/kapital-for-the-twenty-first-century"; rel="nofollow">here</a>, <a href="http://larrysummers.com/2014/05/14/piketty-book-review-the-inequality-puzzle/"; rel="nofollow">here</a>, <a href="http://georgecooper.org/2014/05/24/the-horrible-history-of-mr-piketty/"; rel="nofollow">here</a>, <a href="http://debrajray.blogspot.co.uk/2014/05/nit-piketty.html"; rel="nofollow">here</a>, <a href="http://www.nber.org/feldstein/wsj05152014.pdf"; rel="nofollow">here</a>)

One devastating critique to Piketty relates to the Cambridge Capital Controversy (CCC), an old debate about capital between UK Cambridge theorists (e.g., Robinson, Sraffa, Pasinetti) against neoclassical theorists (e.g., Solow and Samuelson). The argument of Cambridge was that you cannot add up the values of capital goods to get an aggregate, common quantity of capital without knowing the prior rate of interest (or rate of profit) which must come from the financial world (or sphere). The problem is that the rate of interest is determined by the amount of capital being used, which capital is itself determined by a prior interest rate. This raises an impossible circularity problem. Here's how Burmeister (<a href="http://ebooks.cambridge.org/chapter.jsf?bid=CBO9781139166881&cid=CBO9781139166881A016"; rel="nofollow">2000</a>) described the end of the debate : "However, the damage had been done, and Cambridge, UK, 'declared victory': Levhari was wrong, Samuelson was wrong, Solow was wrong, MIT was wrong and therefore neoclassical economics was wrong". Yet, Piketty barely mentioned CCC, as he did not understand the implication of the CCC. The CCC is problematic to Piketty's 1st and 2nd laws of capitalism (the core of his r>g theory, i.e., the third law of capitalism), which rely directly on the notion of aggregate stock of capital, which has been debunked by the Cambridge theorists. Piketty indeed claims that the economy is using "more" capital in the aggregate sense. As noted by Galbraith (<a href="http://www.dissentmagazine.org/article/kapital-for-the-twenty-first-century"; rel="nofollow">2014</a>), that makes no sense.

Another fatal blow comes from a study, in which Bonnet et al. (<a href="https://docs.google.com/file/d/0B0VDoaXaIou8NkVGR19nVVhCQ0k/edit"; rel="nofollow">2014</a>) show that the increase in the share of capital in total income is entirely accounted for by housing capital (thus demolishing Piketty). When housing capital is measured in rent instead of housing prices (as Piketty did), there is no increasing trend for capital/income ratio. The reason to rely of rent is because rent is more inclusive and accurate. For example, landlords earn incomes from renting, whereas owner-occupiers do not receive any income but still receive an implicit return as rent that is saved or economized by these owner-occupiers. Rowthorne (<a href="http://www.tcf.org/assets/downloads/A_Note_on_Thomas_Piketty3.pdf"; rel="nofollow">2014</a>) makes an argument that is not too far off.

Finally, even Piketty himself admitted that the income inequalities today have little to do with his "r > g" theory. See <a href="http://www.slate.com/blogs/moneybox/2014/10/15/piketty_igm_forum_economists_did_not_just_reject_capital_in_the_21st_century.html"; rel="nofollow">here</a>.

Having rejected Piketty's theory, I can (and I will) propose mine. I have summarized the main idea in one of <a href="http://menghublog.wordpress.com/2014/07/25/a-growth-in-inequality-together-with-growth-in-financial-market-activities-probably-not-a-mere-coincidence/"; rel="nofollow">my blog article</a>, 6 months ago. I found several studies showing that since the 1980s, the increased income inequality has something to do with the growth in financial activities and housing boom, i.e., that wealth concentration tend to be skewed toward these kinds of activities and sectors. It also has a pattern of economic cycles (i.e., inequalities growing during the boom and diminishing during the bust; think about the dotcom and subprime episodes). One hypothesis usually invoked to explain the sudden explosion in inequality starting from 1980s is that financial deregulation (at the beginning of the 1980s) is responsible for that pattern (notably in UK and US) but given what free banking theorists (White, Selgin, Dowd) have demonstrated, theoretically and empirically, banking deregulation itself is not the problem because it was found to be historically compatible with economic growth and stability. Instead, the cause originates from the monetary policy of excessive money supply (which has started in the beginning of 1970s, especially with Bretton Woods). Banking regulation (if appropriately applied) can indeed mitigate the banking crises and, thus, economic cycles, but the real trigger is the monetary policy.

Here comes my hypothesis. It has something to do with the Austrian Business Cycle Theory (ABCT), which has strong theoretical relevance as well as empirical relevance. That theory says (among many other things) that an economic boom due to excessive money supply involves a relatively stronger expansion in capital-intensive industries (e.g., capital/durable good industries, which may include housing) than in industries of low capital intensity and of non-durable goods, which must be followed by an economic recession, with capital/durable good industries being more severely affected than the non-durable goods sectors. Since Bonnet et al. (2014) suggest that housing is almost solely responsible to the increasing capital/income ratio, which Piketty takes as being responsible to income inequality when r>g, and since that housing prices seem to follow a pattern of economic cycles, the ABCT is perfectly relevant here. On the other hand, I do not see how an increasing disparity (SD) in IQ can account for the increasing inequality due to housing capital. That seems impossible. The ABCT also predicts that the sectors being closer to the source of new money (created by the banking system) to be booming relatively more than other sectors of the economy. One such sector is obviously financial activities (thanks to cheap credits). Many studies summarized in my blog article (see above) shows this is true, as financial wages go up relatively much more than in nonfinancial sectors, since the early 1980s, and following a pattern of economic cycles. But, then again, how can IQ(SD) explain this pattern of cycles ? Difficult, if not impossible, in my opinion.

What you see in these series of graphs (in my blog post above), is that the trend in inequality has a pattern of economic cycles. It grows during years of boom, diminishing during years of bust. The flow of low-IQ immigrant, however, is not subjected to these kind of shocks. This, not only rejects Piketty's argument, but also the idea that low-IQ immigrant is mainly responsible for this. Here's an illustration. If you think about immigration, the flow of low-IQ immigrant should be rising at a constant rate. If you correlate the trend in immigration with the trend in inequality, you'll see a positive correlation. This is what economists call a spurious regression in time series analyses. These variables are correlated only because they share a common factor : time effect (i.e., trend, which is a type of non-stationarity that you need to get rid of). If you partial out time effect, there is no causality at all. For instance, using a Granger causality test, with inequality (trend) in dependent var, and lagged values of inequality (trend) and lagged values of IQ(SD) variable in independent var, you'll see that IQ(SD) variable has no independent effect. Thus, it does not Granger-cause income inequality. The reason is because when time effect is removed, IQ(SD) variable has now a flat line, while inequality still has a pattern of positive shocks (boom) and negative shocks (bust). What's happening is that the IQ(SD) variable does not respond to any positive/negative shocks to inequality, thus rejecting the idea that IQ(SD) has anything to do with inequality.

Finally, if my explanation above is a little bit complex, there is another thing (much easier) that definitely refutes the IQ(SD) hypothesis. It's the fact that, as Piketty et al. demonstrate, the income inequality is due mainly due to the very top incomes (0.1% and 1%). I don't see why the large share of low-IQ people would have anything to do with it.

Of course, I'm not saying that IQ(SD) has no effect on inequality. Theoretically, it's unbeatable. However, I'm saying here that the kind of inequality you're having today, in advanced modern countries, has to do mainly with monetary policy; i.e., central banks (e.g., Fed for U.S., ECB for Europe, BoJ for Japan).

So, the remaining question is... what do we have in Denmark ? Looking through Piketty's (2014) book, at page 318, I see that the trend in inequality (i.e., the share of top percentile in total income) seems to follow a pattern of economic cycles, although it only has small fluctuations over time. Perhaps too small ? In any case, it is interesting to compare that graph from the one displayed in Figure 4.1 from Anker (2011). Around the period of 2005-2009, inequality in Denmark has increased along with the ratio of actual real GDP to natural real GDP (which indicates an economic boom). Furthermore, in 2009-2010, there is a decline in that GDP ratio along with a decline in inequality. I do not believe that the IQ(SD) hypothesis can explain this pattern of economic cycles. Of course, the fluctuations in inequalities in Denmark are extremely small, so it may not be easy enough to tell. Another question is what kind of inequality prevails in Denmark. If inequality is mainly the result of housing boom, as in the case in other European/US countries, I am afraid that the hypothesis of increasing IQ(SD) must be rejected for a second time.

Even if you disagree with my skepticism about the Denmark, and even accept your hypothesis for Denmark only, the IQ(SD) hypothesis would have a very limited interest because it couldn't apply to other countries (european/US).

One can say, of course, that the correlation between income and the typical SES variable is not so high, but it is still high enough for me to believe that if the IQ(SD) hypothesis cannot apply to income, it is unlikely to explain SES differences over time. This is even more so in scandinavian countries, where you have lot of "administrative" data of income, which has a reliability of 100%.

In the paper, it is written that :

If one looks at income data, then generally inequality has been decreasing since the beginning of the century, but there is an upwards trend in the recent period from perhaps the mid 1980s to now.

But it needs to be mentioned explicitly that in most western countries, 1) most of the inequality is due to the top income shares, 2) and of which most (probably) is due to housing boom and the expansion of financial activities. If the hypothesis of growing IQ disparities cannot explain these pattern, I want it to be said. And even if the proposed hypothesis is applicable to Denmark, I want the authors to explain how it can explain the pattern of inequalities seen in countries such as the United States and the UK.

If you correlate the trend in immigration with the trend in inequality, you'll see a positive correlation. This is what economists call a spurious regression in time series analyses. These variables are correlated only because they share a common factor : time effect (i.e., trend, which is a type of non-stationarity that you need to get rid of). If you partial out time effect, there is no causality at all. For instance, using a Granger causality test, with inequality (trend) in dependent var, and lagged values of inequality (trend) and lagged values of IQ(SD) variable in independent var, you'll see that IQ(SD) variable has no independent effect. Thus, it does not Granger-cause income inequality.

Emil, can you verify if this is the case? (I will look at the paper this weekend.)

Emil, it seems you're eluding all of my objections again. And yet, I was clear, and I cannot be clearer than this. To repeat, my questions were :

1) Does your theory only apply to Denmark ? If yes, the theory has little value if only applicable to Denmark. If not, there are additional questions. Such as :

2) How can you explain the explosion in inequalities started from the early 1980s, notably in US and UK, which has perfectly coincided with the expansion of the financial activities ?

3) How can you explain that the great majority of those income inequalities, as evidenced in the data collected by Piketty et al., is due to the share of incomes going towards the 1% and 0.1% top incomes ? What the data indicate is that the "super elites" own the major portion of the national wealth. How is it related to the arrivals of low-IQ immigrants ?

4) How the hypothesis of low-IQ immigrant (and the resulting increase in IQ's SD) can explain that most of those income inequalities (going to the very top incomes) are related to housing capital and financial activities ?

5) How can your theory explain the tremedous growth in inequalities which generally coincides with the periods of economic boom and the marked decline in inequalities coinciding with economic bust ?

There is also something you need to keep in mind. As I noted in this article : "Lemann (p. 323) also says that as income rises above $100,000, the % of it derived from salaries and wages and business/profession is steadily declining, replaced by long-term capital gains. In other words, Lemann has the impression that the top income shares are composed of inheritors and financiers but not high-IQ professionals." I insist on this because most psychologists who argue about IQ believe that SES differences have something to do with professions (I also got that feeling when reading section 2.3 of Emil/Bo paper). That's not even the case.

There was a reason why I have mentioned the ABCT, despite being an economic theory. It's to show you how this theory can explain easily the pattern of inequalities, compared to your proposed theory which has, no doubt, a very, very poor explanatory power. The major explanation for the income inequalities, is related to financial boom and housing boom. And these can be easily explained by the ABCT. This concerns within-country inequalities however. My impression is that IQ dispersion (or SD) is the major cause of between-country inequality in wealth. But within and between group variations need not have the same causes. A lot of people, either in economics or psychology, tend to make that mistake, usually called ecological fallacy (or individualistic fallacy, for the reverse). It's tempting to believe the two have the same causes, but it's not always the case.

With regard to Granger causality, I didn't do the test in Stata, and I don't think it's needed. I know how the technique works and I can explain it. Take this graph for instance.



The blue line is the observed data, the green is the same but "detrended" (i.e., time effect partialed out). Let's imagine these two lines correspond to the movements of inequalities. Imagine also that the red line is the proportion of low-IQ immigrant or the IQ's SD (choose whichever you want) over time. In the above graph, you see the red and blue lines have an upward trend. They are correlated. Econometricians call it a spurious regression. They will ask you to detrend the two variables. You get the green line, which has a mean of zero (because it's detrended). Unfortunately, the other line is missing, but I couldn't find a better graph (although you can try this one). It's not a problem anyway; when you detrend the red line, what you have, typically, is a line that is flat, with mean of zero. So even if it's absent in the above graph, you can imagine it. So now, what you see is that the flat line (IQ's SD) does not respond to any positive/negative shocks to the inequality variable (green line). When inequalities go up, or down, the variable IQ's SD (a flat line with mean value of zero) gives no "answer". So, from the perspective of the econometricians, there is no causality between them, not even a correlation.

The reason why I have imagined that the red line is the IQ's SD or the % of low-IQ immigrants is because, in the Figure 1 given in the present paper of Emil/Bo, you see that the upward trend in the % of foreign people increases at a constant rate, exactly like in the red line shown above.

We don't want to delve deeper into economics territory in which neither author is well-read. This is a paper for a psychology journal, not an economy journal, so it seems reasonable that requirements should be along those appropriate for the former, not the latter.

This is a well written paper.

Regarding formatting, could you consistently either put a space before the citation or put no space? e.g.

"No one denies the first any longer[24, chapter 4], so we turn to the second."
"That this is so was one of the points of The Bell Curve, and had also been made by one of its authors already by 1971[25]."

Regarding your discussion:

"The first part of our argument is that immigrants have different levels of average g...."

Which immigrants? A number of migrant groups (e.g., to the middle east) discussed by Rindermann and Thompson scored above the native mean. Also, the conclusion does not necessarily follow since immigrants, even from low IQ countries, could be selected. Clarify this section e.g., "The first part of our argument is that national groups vary in levels of g and that immigrant groups will accordingly insofar as they are more or less representative of their nation of origin..." I know what you mean, but some readers might not.

Related:

"Premise 1: immigrants [from low cognitive countries] have a lower average g than the Western host countries."
"Conclusion 2: Immigration [of the present type] will cause higher socioeconomic inequality in the countries, everything else equal"

Regarding your results:

For section 9, what would the Gini coefficient table look like with/without the proposed immigrant effects? Can you estimate this? You imply that immigration contributing to the stalling of the secular decline in inequality. But this is difficult to judge without seeing projected graphs with and without immigration.

If you can't do this, that's is fine.

Make the clarification noted above, though.

Emil, it seems you're eluding all of my objections again. And yet, I was clear, and I cannot be clearer than this. To repeat, my questions were :

Meng,

I confess that I do not see the relevance of you criticisms. The phenomenon that the authors concern themselves with is intuitively obvious. What the paper adds is that it models the phenomenon and so provides a method for quantifying its social effect. The authors note that social inequality is affected by many factors. And they noted that an immigrant effect can be masked by other social effects. They concern themselves with a hypothetical immigrant effect ceteris paribus. Since they did not attempt to test whether the immigrant effect noticeably contributed the staling of the secular decline in inequality in Denmark, your criticisms seem out of place.

I confess that I do not see the relevance of you criticisms.

Same thing for me, because this comment here "The authors note that social inequality is affected by many factors." means you have not read my comment carefully (or you are also in denial in full awareness), and yet I said it clearly, and I said it twice in my comments, that the main factor behind the variation in income inequalities has something to do financial and housing boom. In general, I'm disappointed in your argument as well because you're literally ignoring everything I said. Notably the most critical comment which was that Piketty et al.'s data show that the big factor behind income inequalities is the tremedous share of national income going to the top incomes.

I repeat again : main factor. That should be clear, no ? Everything that has nothing to do with the above must have a poor predictive power in explaining inequality. Unless, of course, you can show me (or explain) how the % of low-IQ immigrants is related to the above.

Same thing for me, because this comment here "The authors note that social inequality is affected by many factors." means you have not read my comment carefully (or you are also in denial in full awareness), and yet I said it clearly, and I said it twice in my comments, that the main factor behind the variation in income inequalities has something to do financial and housing boom. In general, I'm disappointed in your argument as well because you're literally ignoring everything I said. Notably the most critical comment which was that Piketty et al.'s data show that the big factor behind income inequalities is the tremedous share of national income going to the top incomes...I repeat again : main factor. That should be clear, no ? Everything that has nothing to do with the above must have a poor predictive power in explaining inequality. Unless, of course, you can show me (or explain) how the % of low-IQ immigrants is related to the above.

Perhaps you could briefly restate your argument. My impression is that the authors were making the following case:

A mismatch between the cognitive ability of immigrants and natives will lead to an increase in (intranational) social inequality.

This is not a novel point. It has been made, for example, by Gregory Clark (with reference to a different latent ability):

The American Dream Is an Illusion Immigration and Inequality
By Gregory Clark AUGUST 26, 2014

"The evidence shows that immigrant groups tend to retain the social status that they arrive with. The same goes with more recent immigrants to the United States...The effects have been dire: there can be no doubt that immigration is widening social inequality in the United States."

What is novel, in this paper, is not the idea, but the modeling in terms of increased g variance.

Do we agree with the above?

If so, we can only disagree about the "significance" of the effect.

Now, the authors only claim -- if I correctly recall what they wrote -- that the effect is significant in the sense that economists, like Clark, would, if unbiased, consider it to be a non-trivial factor. And people like Clark do.

So where it the room for disagreement?

Perhaps you could briefly restate your argument.

I already did, in this comment, to which you have responded, but ignored all of my objections and all of my questions addressed to Emil.

What is novel, in this paper, is not the idea, but the modeling in terms of increased g variance.

Do we agree with the above?

I don't disagree of course, but it's not my point.

Now, the authors only claim -- if I correctly recall what they wrote -- that the effect is significant in the sense that economists, like Clark, would, if unbiased, consider it to be a non-trivial factor. And people like Clark do.

So where it the room for disagreement?

The explanation for my disagreement has been developed in this comment, and summarized in this comment, both of which you have already responded to, but without answering any of my objections.

The only hope for the theory proposed in the paper, is that IQ(SD) due to low-IQ immigrants has a good explanatory power in accounting for educational/occupational differences, despite accounting (probably) for almost nothing of the income differences. I'm skeptical of it. My most optimistic guess is that low-IQ immigrants explain (at best) only a modest portion of educational/occupational differences. But the authors proposed that their theory explain the lion's share of these inequalities.

Although I found it some time ago, I have looked at that paper a little bit more :
http://www.emod.ox.ac.uk/sites/emod.ox.ac.uk/files/Denmark_Atkinson_S%C3%B8gaard_2013.pdf

It's the Atkinson & Søgaard (2013) mentioned in the submitted article by Kirkegaard and Tranberg. But in the Figure A2 "Total stock income and the top 10 per cent income share" of the above paper I found, you have 3 curves, two that have incorporated the stock income (capital+dividends) and one without such stock income. What is interesting is that income inequalities were almost flat between 1980 and 2010 for the latter curve. But when you incorporate the stock income, you have a sensible increase in the inequalities. So, my suspicion was accurate. The increase in inequalities in Denmark has causes similar to what happened in other european countries, and the United States. So, if it is the inheritors that gobble up the lion's share of the national income, how can your theory low-IQ immigration explain that ?

Another question is worth mentioning. What kind of inequalities the low-IQ immigration would have predicted ? I would say, obviously, low- versus high-IQ jobs. It goes without saying. So now, in what way is it related to capital gains and inheritors ? What I'm trying to say is that what causes incomes inequalities is at the source of capital gains (e.g., financial boom). And this has something to do with market regulation, not immigration.

Also, the comment by Chuck as well this passage "Of course, there are many factors that affect social inequality, and the predicted effect size is probably small, so it may not be visible in actual data yet. If one looks at income data, then generally inequality has been decreasing since the beginning of the century, but there is an upwards trend in the recent period from perhaps the mid 1980s to now." from the present article really bother me a lot. The argument is that since the causes of income inequalities are so complicated that they involve many factors. But then, in the paper, it is said that only the period of mid-1990 to 2010 (and not mid-1980s as wrongly stated in the submitted paper; at least, when you look at Figure 9) is consistent with the prediction of the low-IQ immigrants theory.

Now, let me ask you a question. Why do you think that inequalities have decreased between 1970 and 1990 ? And between 1920 and 1960 ? What are the causes ? Perhaps market regulations, perhaps an increase in education (since it's an hypothesis usually in high regards among economists, even though I don't share their enthusiasm), or some other things still related to public policies. So, what makes you believe that the same factors have stopped operating since mid-1990s ? Maybe the regulations have changed in a way that causes inequalities to increase, which would explain the very slight increase in inequalities since mid-1990s. To say that the last 2 decades (almost) have seen a slight increase in inequalities is consistent with your hypothesis is a confirmation bias. Such affirmation is acceptable only if everything else is constant. But that is not the case. If there are many additional factors (e.g., public policies) that have an impact on inequalities, you have to take them into account. That is not even an easy task. The impact of public policies is extremely complex, and all economists can tell that.

What about the following revision:

\section{A policy conundrum}
We think that immigration as it is happening right now to Western countries leads to a policy conundrum for some policy makers. Our argument is as follows:

First, people who migrate to Western countries generally have a lower average level of g than the countries they migrate to and that selection effects do not substantially alter this for most countries. Second, migrants generally retain their average levels of g from their home countries. Third, g is an important cause of socioeconomic inequality within countries.

From these three premises, we draw the following conclusions: Immigration causes increased inequality in g within countries, and as a result of this, immigration causes higher socioeconomic inequality within countries.

If the argument is sound, then policy makers who prefer high rates of immigration and who want to decrease, or at least keep stable, socioeconomic inequality within their country face a problem.

In the next three subsections we provide evidence for our three premises.

I think that you should rewrite section 2.1. Try something like:

"The first part of our argument is that immigrants to the West often hail from countries which have lower levels of measured g than do Western countries. We derive this premise from reported immigration rates in conjunction with well validated measure of national average cognitive ability. As for the latter, Richard Lynn has pioneered the study of national IQs and collected a huge database of studies. The latest dataset and the global correlates of these are reported in his and Vanhanen’s 2012 book Intelligence: A unifying construct for the social sciences[4]. There is no reasonable doubt left as to whether members of different nations have different cognitive profiles, although there is room left for discussion about the exact magnitude of the differences [5, 6, 7, 8, 9] and the precise psychometric nature of them (e.g., to what exact extent they are in g)."

I have to say that I was surprised to read: "There is no reasonable doubt
left as to whether nations have different average g levels". Really? In a recently submitted paper I said: "Firstly, the psychometric nature of the measured differences is not well investigated; simply, it is not clear to what extent they are psychometrically unbiased in the sense of having the same meaning as those differences, ones which are known to have a substantial genetic basis, within nations and regions." One of the problems is that we don't know to what extent the measured g differences are really g differences. I thought that we had discussed this before.