I will note that I still find the graph (and related discussion) presented in section 9 to be problematic -- just now much less so than before -- since the authors fail to determine the relationship between Gini and g variance, leaving us with no means of interpreting the changes in Gini in context to the phenomenon which they discuss. According to Young (2011):

"Aitchison and Brown (1957) showed that if a population’s income is ln-normally distributed, then its Gini coefficient is given by G = 2N[σ/√2]-1, where σ is the standard deviation of ln income."

Others give similar formulas.

Based on these formulas and assuming that increased SES variance is commensurate with increased g variance one could calculate the expected change in GINI coefficient (due to increased g variance). One could then compare it with the secular change and place the importance of the potential immigrant effect in context to that. I appreciate that the authors decided not to do this. In this situation, though, I do not feel that it is wise to discuss the GINI data.

That said, section 9 is but one of ten. On account of the other nine sections, my conditions being filled, I approve.

Chuck asked me what are my conditions of approvals, and my main complaints. I would say :

1. If the paper is about Chuck's point (a), i.e., purely theoretical, then Emil must remove section 9 entirely, and he must also explain if, given his theory, he expects the effect size to be small/medium/large or even near-zero. In the paper, this is not clearly explained. As I said, in section 2.3 and other sections as well (e.g., section 10) Emil makes it sound as if IQ is important in explaining SES gaps. Yet in one sentence at the beginning of section 9 he says maybe the effect size is small with regard to changes in inequalities. This is too confusing. In other words, what I'm asking is simple : Emil must make it clear both in the abstract and conclusion section, whether IQ is important or not in accounting for changes in inequalities over time.

2. My opinion, however, is that (a) is not necessary and I won't recommend it. The use of data is fine, because any theory must be tested empirically; otherwise that theory has no value. But Emil still needs to explain if he expects a large, medium or small effect size, and clarify once and for all (since this has never been done) if IQ is important or not in accounting for changes in inequalities over time (note here: I'm not talking about IQ-SES correlation but the effect that the % of low IQs should have on the changes in inequalities over time). And he must make it clear both in the abstract and conclusion section. Given that Emil wrote that "the recent increase in economic inequality may be due to many things that have nothing to do with increased variation in g from immigration" then he must also admit that the data he is using does not lend credibility to his theory because he does not identify these confounding factors and their expected effects on the changes in inequalities over time. Consequently, he cannot know if these factors could have really "masked" the expected effect size. Maybe they didn't, and maybe the expected size was, as I suspected, near-zero. Indeed, Emil has no means of quantifying the effect (perhaps it's large, medium, small, perhaps it's near-zero) : this is my most critical point, and I want it to be clearly stated. If possible, Emil can also add my opinion in a footnote, e.g., "A reviewer (Meng Hu) argued that the trend in income inequalities are qualitatively different from what would be expected given the authors' proposed theory. He says that a theory based on low-IQ immigration expects inequalities to be related with the % of low-IQ jobs and dispersion of low- and high-IQ jobs while the data shows that when the factors of top income shares (Piketty, 2014) or capital gains (Atkinson & Søgaard, 2013) are removed, the trend in income inequalities becomes flat". Emil can also add "The present authors, however, do not share his views." if he wants to make it clear this is my view, and not his.

[EDIT]

I don't know where Chuck can still find the strength to argue once more, but in his latest mail, I have responded as follows, about Emil's paper :

Because there's no point in saying "we are arguing about inequality in g causing inequality in SES" when you can't quantify its effect. That means you cannot even tell if it's meaningfully different from zero. Thus, if they are unable to quantify its effect, Emil must say it in the abstract and conclusion sections : "However, we are unable to quantify its effect and cannot make any inference on its empirical relevance".

By "its effects" I'm obviously talking about the predicted effect size of the impact of low-IQ immigration, assuming it really has an impact different from zero.

And my feelings are true. I want Emil to be very explicit about the above, if he wants me to approve.

I will renew my approval if the authors make it explicit that section 9 is entirely speculative (that is, so weakly supported by the data as to have almost no empirical test) and this should be highlighted in the section heading by adding something like "a very preliminary hypothesis" or "a tentative scenario".

I will renew my approval if the authors make it explicit that section 9 is entirely speculative (that is, so weakly supported by the data as to have almost no empirical test) and this should be highlighted in the section heading by adding something like "a very preliminary hypothesis" or "a tentative scenario".

To be sure, the recent increase in economic inequality may be due to many things that have nothing to do with increased variation in g from immigration. [b]The present study does not attempt to show that the recent increase is due to immigration, and we merely regard the above as circumstantial evidence.[/b]

It already does.

I meant it should be added to the section title. Addo to "Has social inequality gone up?"... A tentative scenario

Well, inequality has gone somewhat up in DK in recent decades. The question is mainly whether immigration had something to do with it. Maybe, probably? Of course, the mere fact that the model predicts some increase and an increase has been observed does not imply the model is correct (affirming the consequent). However, it does somewhat increase the posterior probability of the model relatively to other models that did not predict increased inequality.

As you said, the result is entirely post-hoc, and it does not test alternative models. For this reason I think you should change the section title to make it clear it's just one of the many possible explanation of the data.

I think putting it in the section header would make it clearer.I don't want readers to be confused. And I do not want to be the tough guy either so I will ask other reviewers what they think?

I will renew my approval if the authors make it explicit that section 9 is entirely speculative (that is, so weakly supported by the data as to have almost no empirical test) and this should be highlighted in the section heading by adding something like "a very preliminary hypothesis" or "a tentative scenario".

This was also (more or less) the condition for my approval. But I have also said that Emil should say it explicitly in the conclusion section as well. Not just the abstract.

Well, inequality has gone somewhat up in DK in recent decades. The question is mainly whether immigration had something to do with it. Maybe, probably? Of course, the mere fact that the model predicts some increase and an increase has been observed does not imply the model is correct (affirming the consequent). However, it does somewhat increase the posterior probability of the model relatively to other models that did not predict increased inequality.

That's where you're wrong. I showed you that this proves nothing. Not even that the likehood of your model is increased. Not even the slightest. If anything, the data entirely disproves your model.

Anyone here can read my earlier comments. The idea was simple. The trends in income inequalities, as I have shown, are qualitatively different from what could be predicted by low-IQ immigration (which is about dispersion in SES while boom-bust cycles, housing and financial bubbles, top income shares have nothing to do with this). That means they are not confoundings. Given this, you cannot argue that if your model does not predict these patterns of very large, sudden and quick ups and downs in income inequalities, then, it must be due to confounding. As I have explained earlier, when removing the factors I have mentioned (capital gains and top income shared), the trend in income inequalities becomes perfectly flat. Even in Denmark. This rejects what you say here :

Well, inequality has gone somewhat up in DK in recent decades.

This has been disproved. Entirely.

For this reason, as I said many, many, many times before, your only hope is that the trend is flat and does not confirm your model only because there are confoundings (which are, of course, not related with either capital gains or top income shares). And that's when I asked you this question : what are these supposed confounding factors ? Suppose, as I've said before, you can identify all these confounding factors, how do you know they will have a meaningful impact ? Have you even considered undetected factors that will rise inequalities, and thus, falsely attributing the contribution of these undetected factors to low-IQ immigration ? Unless you can detect all of these unknown factors and partial out their impact on inequalities, you will not be able to reach a conclusion, not even a tentative one.

In general, what's problematic with the section 9, is that you are saying that the data may not necessarily confirm your model, but that may be due to confoundings. There is no proof this was due to confoundings. Maybe there is no such confounds. The only way to know, as I said, is to measure the relative contribution of all of these supposed confoundings. Since you never did that, there is no reason to say "perhaps it's due to confoundings" because an equally valid claim would be "perhaps it's not due to confoundings". In the latter case, your model is refuted.

If the purpose of the paper is to merely propose a model, you're safe. But as soon as you're arguing about its probability, you're wrong on about everything. Generally, the paper is speculative. So, this must be made clear, i.e., that your model needs to be evaluated and unless this task is done, there is nothing you can learn from this model.

As for this :

A reviewer objected that no g gains is compatible with less than 100% heritability if one assumes gene-environment interaction/correlation models.

I said "gene-environment correlation" but I never said "gene-environment interaction/correlation".

Duxide: I think putting it in the section header would make it clearer.I don't want readers to be confused. And I do not want to be the tough guy either so I will ask other reviewers what they think?

If the purpose of the paper is to merely propose a model, you're safe. But as soon as you're arguing about its probability, you're wrong on about everything. Generally, the paper is speculative. So, this must be made clear, i.e., that your model needs to be evaluated and unless this task is done, there is nothing you can learn from this model.

At least three of us agree that section 9 introduces a problem. Whether this section is tolerable, as is, is open to judgment. Whatever the case, I find it highly irritating that the authors do not simply make the reasonable alterations suggested by Duxide and Meng Hu but instead continue to haggle over the changes necessary.

I want to make it clear once and for all. Although I may sound as if I don't trust this theory at all, I'm just skeptical about the magnitude of its effect. I mean... I never said the theory is unsound. My impression is that when all theoretically relevant confoundings are removed, the trend in income inequalities would be either (almost) flat or increasing. But it can't have a decreasing trend. It's like the law of supply and demand. When everything else is constant, a demand for a good that is becoming greater than its own supply causes its prices to go up. If you see some data inconsistent with this economic law, the only possible explanation is that there are confounding factors causing prices to change in different ways. That's the same thing for the model proposed in the paper here. Increasing variance in IQ can't possibly cause a decline in inequalities. Only an increase. Thus, by definition, if there is a decrease in inequalities, that must be due to other factors. Although my expectation is that the effect is positive but very small, only a good empirical test can (in)validate my expectations, and just looking at the observed data can't possibly help us to understand how it works. Yet, that is what section 9 is all about. But what you need is modeling the income data.

I will renew my approval if the authors make it explicit that section 9 is entirely speculative (that is, so weakly supported by the data as to have almost no empirical test) and this should be highlighted in the section heading by adding something like "a very preliminary hypothesis" or "a tentative scenario".

To be sure, the recent increase in economic inequality may be due to many things that have nothing to do with increased variation in g from immigration. [b]The present study does not attempt to show that the recent increase is due to immigration, and we merely regard the above as circumstantial evidence.[/b]

It already does.

I meant it should be added to the section title. Addo to "Has social inequality gone up?"... A tentative scenario

I have added the requested text in draft 15.

I see you've added the text but not changed the section header.Any reasons for this?

I approve publication.

Some language issues you may still want to address:

1) "and so on than the Native populations"

native

2) "These parties can generally be characterized as nationalist and conservative but they do not necessarily favor increased economic liberty."

I would guess most everyone favors "increased economic liberty", they just use different definitions of it. "Increased economic liberalism" would be clearer.

3) In Table 1 "DEU" presumably refers to Germany. You should use "GER". Some of the other country name abbreviations used may be non-standard as well.

I see you've added the text but not changed the section header.Any reasons for this?

I forgot to compile the LATEX file. I updated the source file (.tex). It is fixed now in #16.

Fine. I approve publication.