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.

I agree with Meng Hu in a qualified sense. First, I think that the paper is interesting and that it deserves to be published shortly. That said, I do think that the inclusion of your section 9 is questionable. Here is what you say:

The results of the modeling suggest that social inequality in Denmark is increasing due to the increasing SD of g in the country (and perhaps because of falling average g too). 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. Figure 9 shows Gini coefficients from late 1800s to 2010 as estimated by Atkinson et al (2013)[49], and Figure 10 shows similar estimates by Neamtu et al (2013)[50].

The presentation of the graphs give the impression that immigration is -- or that you think it is -- causing the stalling of the secular decline in inequality. But, you don't actually commit to this position because you can't. We (at least MH and I) are left with a misleading impression. To clarify, you would have to append something like:

It is not clear why this is or if immigration had a detectable impact on this index. We were unable to model the results with and in absence of immigration so it is difficult to even speculate.

But if you added this, the superfluous nature of the section would become apparent. If you have no idea if immigration has had any detectable effect on the mentioned indexes of inequality why show those indexes?

If you wish to include the noted data pictorially, I would just include figure 9. And perhaps note that "similar estimates are presented by Neamtu et al (2013) [50]". I would then include a clarifying sentence, such as the example given above, after your Figure 9.

The section would then lend itself less to misinterpretation.

The last batch of questions is another round suited for macro economics journals, not psychology. This is not a macro economics paper. This is a psychology paper which touches on a macro economic issue. As John wrote, what is interesting in this paper is not that it's a new idea (Clark had argued the same before, just without invoking GI), but that we did modeling of population data to produce some estimates of the increase in GI. When we initially discussed this study, we waited several months trying to figure out a way to get from the GI SD to some economic inequality measure. We did not find a plausible way to do this, and hence we left it at where it is in the paper. In other words, it's a case of a reviewer who wants the paper to be about something it isn't. We have seen this a few times from different reviewers with different papers.

Let me try to clarify the matter. We now agree that the paper is interesting and that it provides some novel piece of information. Some of us disagree about the relative overall importance of immigration with respect to intranational inequality; in a similar way, others, noting that most variance is between individuals, disagree with (e.g., me) about the relative overall importance of biological race with respect to anything. But being more or less rational, here, we all would agree that immigration is not completely irrelevant to the topic of intranational inequality -- it is therefore a topic which one might reasonably pursue. Now, nothing in the paper directly says that immigration is a very important factor, in the sense of explaining a lot of the intranational inequality. In fact, some discussion in the paper e.g., section 8 suggests otherwise. So there is no problem in this respect. The only issue, I think, is that section 9 lends itself, at least when cursorily read, to the impression that immigration is explaining what it isn't necessarily. Perhaps the readers are more to blame than are the authors for this situation. Whatever the case, my reading left me with this impression. I would suggest that the authors make a few minor edits (suggested prior) to prevent this from happening to others -- I would not demand that they do this, since the fault is not clearly theirs, just suggest.

I would though ask that the authors make the previously requested changes to section 2.1; conditioned on those changes being made, I approve publication.

Not sure what you mean. Both of these have no spaces.

But we have been inconsistent with putting citations before or after the punctuation marks. I have changed it so that it is consistently before the punctuation marks (comma/dot).

I expected you to look through the paper and to notice that some of sentences have spaces before the brackets and others do not. Thus:

For an attempt, probably too pessimistic, at modeling that tries to solve this problem, see [3].

This cannot be attributed to shared environmental factors since these are the same
for both siblings[30, 31]

In Figure 9, one can start the trend line at 1985 and also get an upward trend. Meng Hu apparently chose to start it at 1995 which produces a similar trend but somewhat stronger since it does not catch the slight decrease around 1990. Who decides where one starts the trend line?

The reason why I chose 1995 is because income inequalities given Figure 9 begin to increase by around 1995. But when you write mid-1980s, you're giving the (false) impression that income inequalities have started to increase since mid-1980s.

The last batch of questions is another round suited for macro economics journals, not psychology. This is not a macro economics paper.

I'm not talking about economics here. But data. I asked : How can you explain the pattern of income inequalities over time given your proposed theory ? You didn't reply, nor did John Fuerst (even though he was the one who initiated the conversation between him and I). The reason why I have put forward the economic theories is to show you how worse your theory would fit the data, compared to, say, the ABCT. But this latter point can be ignored; I just mentioned the ABCT just for a matter of illustration but certainly not because I wanted it to be mentioned in your article (even the theory I proposed is not accepted by the majority of the economists, for reasons that remind me of why the hereditarian hypothesis is not well regarded). What is of upmost interest here is how you can answer my barrage of questions here. These are not "economic questions" however. These are questions concerning the data.

It seems both of you, Emil and Chuck, you do not understand what is an economic question. Economics is about theory, e.g., law of supply and demand. None of my question purported to such issues. I'm not that stupid.

Concerning what Chuck said, I agree obviously that a word of cautious is needed, especially due to the amount of unanswered questions that makes the theory looking bad. Again, I'm not saying it on theoretical grounds, because it's unbeatable. But based on the data you have (see, e.g., Piketty) there is no evidence today that income inequalities have anything to do with low-IQ immigration.

I'm not talking about economics here. But data. I asked : How can you explain the pattern of income inequalities over time given your proposed theory ? You didn't reply, nor did John Fuerst (even though he was the one who initiated the conversation between him and I).

I did not reply because the reason for the disagreement became obvious: you and I are reading the paper differently. Imagine if Emil wrote a paper on dysgenic trends; and in the papers he argued that present breeding patterns were depressing IQ, but also noted that differences would be small and could be masked by other factors.

(a) One might read him as making a ceteris paribus claim in which case this would be trivially obvious and what would be interesting, if anything, would be the model developed. This is how I read his paper.

(b) Or one might read him as saying that dysgenic trends explain an "major" amount of cross temporal variance either in the country of reference or all countries. This reading would erroneous, since nowhere did he claim or imply this.

(c) Alternatively, one might read him as saying that dysgenic trends are resulting in lower IQs than before (and not lower IQs than would otherwise be found). This might be a plausible reading given his wording. If this reading was correct, we would have a problem since ceteris paribus effects need not be associated with actual decreases as is the case with measured IQ (the Flynn Effect). It could be, for example, that a dysgenic trend is tied to a trend (e.g., increased education) which is boosting IQ and thus more than masking any deleterious effect.

We do not need to turn to complex macro economic models to imagine such situations in the case of immigration and inequality. Perhaps immigration is and will be associated with a net decrease in inequality because, despite increasing inequality by inflating g variance, immigrants vote progressive and progressive governments engage in massive redistribution, decreasing social inequality.

If I thought that Emil wanted to show something like (c) I would request that he show that increased immigration is actually associated with increased inequality in the country of reference -- and, after, that he rule out obvious confounds. But I assume (a) -- which is why I said that what is interesting is the model. You, on the other hand, are reading the paper as (b) or (c).

Agreed?

I guess we can add below the figures something like this:

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. 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.

Once you make the alternation noted here, I will approve. (It is not established that differences are in g.)

Sorry, I forgot about that part in my rewriting.

What about?There is no reasonable doubt left as to whether members of different nations have different average IQs, although there is room left for discussion about the exact magnitude of the differences\cite{wicherts_systematic_2010,wicherts_another_2010,wicherts_dangers_2010,lynn_average_2010,rindermann_african_2013} and the precise psychometric nature of them (e.g., to what exact extent they are in g).

How about "different average measured IQs"? I would like you to convey the point that the psychometric nature of the international differences is not clear. That differences are in "little g" is not established.

We do not need to turn to complex macro economic models to imagine such situations in the case of immigration and inequality.

And here again. I thought I was clear in my response to Emil. I'm tired of repeating. My questions have nothing to do with economic theories. Only with data. My point is that the theory proposed in the paper cannot explain the pattern of the income data. There is no use to try mischaracterizing my argument and my questions in order to avoid having the difficulty to confront them directly.

Perhaps immigration is and will be associated with a net decrease in inequality because, despite increasing inequality by inflating g variance, immigrants vote progressive and progressive governments engage in massive redistribution, decreasing social inequality.

I have made an argument similar before, i.e., the one you have quoted. But what you have forgotten however is that Emil said that the increase in inequalities since mid-1990s is consistent with his proposed theory. In my earlier comment, I have said he didn't try to explain why the inequalities decreased between 1920 and 1960, and once more between 1970 and 1990. I have said that the changes in market regulations could have caused these earlier trends, but that a change in these regulations may have caused inequalities to increase since mid-1990s. I said that his affirmation about low-IQ immigration is valid only assuming "ceteris paribus". But there is no such a thing in the real world, and modeling (by partialing out confounding factors) is the only way to predict the outcome of interest. Given that he did not (or can not) clean out all of the confounding factors, it makes no sense to cite such data in order to say that the pattern of the data is consistent with the proposed theory. That's an illustration of confirmation bias. But I'm just repeating what I said before.

Even your proposed theory is entirely false and discredited by the U.S. and European data. When looking at the U.S. data (see below), the largest increase/decrease in inequalities coincided exactly with the onset of an economic boom/bust (roaring twenties in the 1920s, dot-com in the mid-1990s, subprimes in the 2000s). And yet, no one has heard about such sudden change in politics that would engage in such sudden and massive redistribution so as to cause such a drastic and sudden change during these periods, and everyone knows (or should) that these booms were all related to housing and financial booms, both of which are unrelated with income redistribution initiated by the governments. And the very fact that the strongest declines in inequalities coincided with economic crises disprove even better your proposition, as everyone knows that these crises were due to banking panics, which thing is unrelated with income redistribution by governments. There was also another strong increase in inequalities starting at the beginning of the 1980s, which was, as explained before, marked by strong market deregulation (which is at odd with your proposition of massive income redistribution by progressive governments), especially banking deregulation (interacting with a monetary policy of excessive money supply). The source of the increase in these inequalities, to repeat, is related to capital gains and financial activities, both of which are totally unrelated with your proposition. These are facts, not economics.

In order for your theory to be credible, you must discard the alternative propositions, such as those I have mentioned (e.g., boom/bust cycles, deregulation, top income shares, capital gains, financial markets). Curiously, Emil seems to believe that your theory is plausible, as he mentioned it in his last version, even though your proposition is refuted in every aspects of the data. [EDIT2 (feb,6,2015): comment in italics may be ignored]

I did not reply because the reason for the disagreement became obvious: you and I are reading the paper differently.

In reality, I'm the one who reads the paper correctly. And you're the one who misread it and also claimed that I misread it. In other words, you're making two mistakes in a row. You first make my argument look like what it is not, in order to dismiss it entirely without answering my questions. The fact that you have assigned (b) and (c) to my argumentation is the proof of it. But also the proof that you're misreading Emil's paper. Unlike what you claimed in, e.g., point (b), it is not true that the authors believe that their theory is limited to Denmark, "Many Western European countries currently have high rates of immigration. Generally speaking, immigrants do not fare well in their receiving countries.", "Immigration rates in different countries have been different over time. Per the theory employed in this study, everything else equal, those experiencing more immigration will have increased their socioeconomic inequality more (or decreased it less).". And, otherwise, they would say it, or they won't consider such a theory, since in this case, it has no value. Generally, the paper proposes a theory, not new, and then uses data to support the proposed theory. And I responded that the data, taken at its face value, actually contradicts the proposed theory, and that Emil's use of such data implies that the causes of the variation in inequalities before 1990s and since mid-1990s have changed, even though he gives no proof of it. This has nothing to do with either with your point (a), (b) or (c). I think I have also said that since the paper proposes that low-IQ immigrant has a great impact on inequalities, this claim can only be accepted if you have the data, which, however, strongly contradicts Emil's proposition.

But without reliance on data, the theory has no value if you cannot predict the magnitude of the effect of low-IQ immigration. According to the paper "Third, g is an important cause of socioeconomic inequality within countries ... Immigration causes increased inequality in g within countries, and as a result of this, immigration causes higher socioeconomic inequality within countries ... One might wonder whether the effect size is simply too small to matter ... The answer is that for the tails of the distributions, it means quite a lot" it is clear to me that the effect is not expected to be trivial, thus your point (b) should not have been applied to me. If the authors actually don't believe that low-IQ immigration has a large effect, then the interest of the paper is greatly attenuated. Assuming you believe the effect is large, you need to confirm this claim with the data. But without data, you're left with only speculations; that is, you don't know if (ceteris paribus) the effect size will be small, modest or large. In this case, the interest of the paper is once again greatly attenuated.

Your analogy, point (c), with dysgenics and Flynn effect is the worst comparison one could have made. In the Flynn effect, no one really knows what's causing it or is related to it, even though some researchers want to believe in diverse hypotheses (all of them being false, in my opinion). But in income inequality, even if there are still some debates as to the causes of it, we know already what are related to these variations in inequalities, i.e., a) capital gains, b) boom in financial sector, c) top incomes, d) economic booms, e) banking/market deregulation.

My point, again, is that the theory proposed by Emil has no relationship with either a), b), c), d), e). For this reason, and unlike what you said, everything from a) to e) cannot be considered as confounding factors. In other words, if inequalities stops varying after removing some of or all of these factors from the equation, the proposed theory must be refuted based on the actual data (but not necessarily future data). And this is what seems to be shown in the graph below.



(From Piketty's 2014 book, "Capital")

That's why, I said, it is important to answer these questions :

1. Can low-IQ immigration explain the fact that the increase in income inequalities in European/US countries is almost entirely due to the increasing share of national income gobbled up by the top incomes ?
2. Can low-IQ immigration explain the fact that the increase in those inequalities has little to do with social attainment, as one would predict from the theory, but is mainly the result of capital gains and financial activities ?
3. Can low-IQ immigration explain the violent and sudden shocks in inequalities (ups and downs) in a very short time span of just a few years, as depicted in the above graph ?

Can you try explaining why the inequalities don't increase anymore after you look at the top 10-5% instead of looking at the top 5-1% and 1% incomes ? Why the inequalities vary increasingly much more when you start looking at 5-1% instead of 10-5%, and then looking at 1% instead of 5-1% ? Why this only factor (top income shares) is able to explain (almost if not all) the entirety of the trend in income inequalities in the U.S. ? If this factor is unrelated with low-IQ immigration, it cannot be argued anymore that it acts as a confounding. Thus, Emil's theory is indeed empirically refuted.

It is not false. In Figure 10, it starts increasing around 1980 depending on which lines one follows.

Remember what you have written...

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.

What are you referring to by "decreasing since the beginning of the century" ? Figure 9, of course. And then you continue with "but there is an upwards trend ... from ... mid 1980s to now". The "but" indicates you're clearly referring to Figure 9, once again. Using mid-1980s as the starting point is false, misleading. [EDIT2 (Feb,6,2015): my comment in italics may be ignored]

By the way, talking about corrections...

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

This is incorrect. What I was talking about is G-E correlation, not GxE interaction.

In reply to Meng Hu.

MH wrote: And here again. I thought I was clear in my response to Emil. I'm tired of repeating. My questions have nothing to do with economic theories. Only with data. My point is that the theory proposed in the paper cannot explain the pattern of the income data. There is no use to try mischaracterizing my argument and my questions in order to avoid having the difficulty to confront them directly

By my (a) interpretation this point is irrelevant. Would you disagree? {Emil, could you confirm if my (a) interpretation is more or less correct?]

MH wrote: But what you have forgotten however is that Emil said that the increase in inequalities since mid-1990s is consistent with his proposed theory.

This speculation is not inconsistent with an (a) reading.

MH: Even your proposed theory is entirely false and discredited by the U.S. and European data. When looking at the U.S. data (see below), the largest increase/decrease in inequalities coincided exactly with the onset of an economic boom/bust (roaring twenties in the 1920s, dot-com in the mid-1990s, subprimes in the 2000s).

I was illustrating a theoretical possibility.

MH: In reality, I'm the one who reads the paper correctly. And you're the one who misread it and also claimed that I misread it... But also the proof that you're misreading Emil's paper.

I am waiting for proof of this. Provide textual evidence to support the claim that (b or c) are better readings than (a).

MH: The paper proposes a theory, not new, and then uses data to support the proposed theory.

My interpretation is that it explicates a simple and obvious theory:

Emil's Syllogism (compare http://www.columbia.edu/cu/psychology/terrace99/lec15/ov11.html )

--the immigration of individuals with g scores dissimilar to those of the native population will increase g variance
--increased g variance will lead to increased SES variance, ceteris paribus

And after it provides a method for quantifying one aspect of the model (the increased g-variance). My interpretation is that the authors do not commit themselves to the claim that increased immigration with everything else going on is actually associated with increased overall inequality. Of course, it would have to be associated with increased overall inequality controlling for every other factor, but the authors don't attempt to do this -- and given my (a) interpretation it is not necessary that they do.

MH: "And I responded that the data, taken at its face value, actually contradicts the proposed theory. I think I have also said that since the paper proposes that low-IQ immigrant has a great impact on inequalities, this claim can only be accepted if you have the data, which, however, strongly contradicts Emil's proposition."

This is like saying that the Flynn effect contradicts a dysgenic IQ hypothesis. If the hypothesis was (1) that dysgenic effects explain decreasing IQ it would, because the FE shows that IQ is not decreasing. But if the hypothesis was (2) that dysgenic effects are causing lower IQs than one would otherwise have without it, it wouldn't, since there can be countervailing environmental factors. My interpretations of the paper is that it is arguing (2) = a, not (1) = b,c.

MH: Furthermore, the theory has no value if you cannot predict the magnitude of its effect... it is clear that the effect is not expected to be trivial. In that case, you need to confirm this claim with the data. But without data, you're left with only speculations; that is, you don't know if (ceteris paribus) the effect size will be small, modest or large. In this case, the interest of the paper is greatly attenuated."

Without data you are left with a model. The model, with some addition data, can be used to estimate if "(ceteris paribus) the effect size will be small, modest or large". This would be done by multiplying the predicted increased g variance by an estimated correlation between increased g variance and increased SES variance. You can then apply this model and the estimate to data. You would see if controlling for a billion factors, increased g variance owing to immigration is associated with increased SES variance. The authors only lay out the theory and develop the model. I have no problem with this.

MH: Your analogy with dysgenics and Flynn effect is the worst comparison one could have made. In the Flynn effect, no one really knows what's causing it or is related to it, even though some researchers want to believe in diverse hypotheses (all of them being false, in my opinion).

It is a perfect analogy, but you misunderstood the point of it. Refer above.

But John, IQs are always measured. IQs are always an observed/manifest variable. g is the latent variable, general intelligence is the ability. Sometimes, one conflates the latter two and call them both "g". This is done in the present paper. (This practice apparently confused Flynn, since he tried to argue on the base of that identity.)

I obviously know this but your readers might not -- since, yes, "IQ" is often used as shorthand for "g". Recall, originally I asked you to replace "g" with "cognitive profiles". How about "measured cognitive ability"?

I think it is somewhat unclear what you mean with the (c) option. You used another example than the claim in the paper. So I don't know whether it is more like (a) or (c).Meng Hu is mostly spending his time on (b) which we obviously did not mean. I made this pretty clear with the latest change where I adde...The primary interest of this paper is the modeling. It is impossible to argue for (b) without lots of more data, and we never tried to do so. For what we know, the effect we discuss may be insignificant in comparison with other stuff, like changing redistributional policies over time or global crises or whatever.

The difference I was trying to get at with (a) versus (c) is that with (c) you commit yourself to the position that the gross effect of immigration is an increase in inequality (of even a small magnitude). My point was that it need not be, since immigration might be causally associated with countervailing forces. Perhaps Danes react to the sight of poor immigrants by implementing inequality reducing measures -- thus leading immigration to decrease inequality. For (c) you would have to provide evidence that increased immigration is causally related to increased inequality -- not just e.g., autocorrelated. The question would then be: Why? And increased g-variance would be a possible answer. With (a) you allow for the possibility that increased migration, of the poor sort, could have all sorts of weird and counter-intuitive effects and concern yourself with a situation in which all things are equal -- that is, putting those effects aside. In this situation, claims don't depend on the empirical data regarding changes in inequality. In (c) and more so in (b) they do. Does that clarify things? (If not, I will have to draw a diagram for you and MH with a big goofy crayon.)

By my (a) interpretation this point is irrelevant. Would you disagree?

Your point (a) makes the assumption that data is not relevant, because there is no "ceteris paribus". In the paper, I repeat, a theory is proposed, and illustrated with data. I have attacked Emil's interpretation of the data, not the theory. And I said that the data, as we observe now, contradicts Emil's prediction and interpretation, rather than confirming it. What I said has nothing to do with either (b) or (c).

This speculation is not inconsistent with an (a) reading.

Of course it is....

Because it is a proof that Emil does not see his work as you do. Emil illustrates his theory with income data (on Denmark) thus invalidating your point (a). Your (a) necessarily implies that you don't need data to evaluate the likelihood and the relevance of Emil's theory. In other words, the theory can never be empirically tested. This makes Emil's paper and proposition totally worthless.

I was illustrating a theoretical possibility.

First, Emil uses this false theory in his paper. This should be removed [EDIT2: my comment in italics should be ignored]. Second, this theoretical possibility is the approach anyone must use. As I will explain below, any possible omitted, confounding factor must be detected in order to be evaluated. Ceteris paribus is not a valid argument, as I will show.

I am waiting for proof of this. Provide textual evidence to support the claim that (b or c) are better readings than (a).

You already have your answer, in the comment you have replied. I have said that my point has nothing to do with either (b) or (c). Not even (a). To recall, I have used data to attack the proposed theory, and I did it mainly because Emil has used data (section 9) by wrongly believing that it supports the theory. That is, I criticize Emil's use and interpretation of the data.

My interpretation is that it explicates a simple and obvious theory

Yet I have strongly insisted on this point before. The theory, for being at least credible, must be evaluated using the data. The relevance of the theory cannot be expressed if the effect size cannot be evaluated (small, medium, large).

My interpretation is that the authors do not commit themselves to the claim that increased immigration with everything else going on is actually associated with increased overall inequality.

Of course they do....

They said, after all, "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."

What do you think the "but" is for ? It's obvious. What Emil says is that the period before 1990s is not consistent with the predicted effect size, but the period since mid-1990s is consistent with the predicted effect size. So indeed, they commit themselves to this claim. As I said, this is confirmation bias, e.g., implying that the factors causing inequalities before 1990s are different than those causing inequalities since mid-1990s. [see EDIT]

Without data you are left with a model.

A model has no value if it cannot be "fitted" against the data. All models have to be empirically tested. Any model or hypothesis that cannot be empirically investigated is not worthy to be called a scientific theory. Because that makes it impossible to refute, by definition. That's why I have implied that your point (a) makes no sense, because it states that the theory expressed in the theory does not need to be empirically evaluated (i.e., with data).

The model, with some addition data, can be used to estimate if "(ceteris paribus) the effect size will be small, modest or large".

Here's something you don't understand with ceteris paribus. This is best illustrated in multiple regressions. One usual bias is the so-called "omitted variable bias." This suggests you have omitted a variable of interest, i.e., a variable that has a theoretical relevance for explaining the variation in the dependent variable (e.g., income inequalities). When you spit "ceteris paribus" you're not really thinking about a plausible, theoretical relevant omitted variable. When you say that these confounding factors (not even explicited) could have masked the effect of low-IQ immigrant, you're committing the same fallacy as Emil did, when he writes, in his paper, "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.".

What are these many other factors which make the predicted effect size not visible in the data ? Your argument is devoid of meaning, since you cannot name the confounding factors. And because you cannot name these confounding factors, your "argument" can not be evaluated. Imagine in a multiple regression, in which you have included, say, 100 variables related to environment, and yet someone can say it's not enough, because we don't know if there are still no other environmental factors undetected. The researcher can still find some more environmental variables, and end up with a model with 200 variables, but someone can still say it's not enough because we don't know if all possible environmental factors have been included. Because this question can not be answered, the relevance of that theory can not be evaluated. Since in statistics, you cannot reach the ceteris paribus condition or even approximate it, your point (a) which assumes ceteris paribus when reading Emil's paper must necessarily invalidate every possible statistical methods and models, because none of them can reach the ceteris paribus assumption that you need since no one can incorporate every possible environmental factors that exist in the entire universe. In other words, you're making Emil's proposed theory impossible to evaluate.

That's why your point (a) is nonsensical. Without reliance on data, the proposed theory can be no more than a mere speculation. Something that can never be tested. If this is how you read the paper, this is not how the authors consider it. The very fact that the paper relies on data (section 9) shows that you misread it completely.

It is a perfect analogy, but you misunderstood the point of it. Refer above.

It's a bad analogy, you don't recognize it because you ignore my comment. I said that the causes and correlates of the Flynn effects are not understood and not clearly detected at all. In the case of income inequalities, we know what are related to these changes. We can single them out (unlike for the Flynn effect) and quantify their effects (unlike with the Flynn effect). And these factors related to inequalities, as I stated, have no relationship with low-IQ immigration. If you partial out these factors (from a) to e) in my earlier comment) you'll see that there is no increase in inequalities. For the U.S., eliminating the very top incomes is sufficient to cause inequalities over time (since 1970s) to stagnate. For Denmark, as I said before, eliminating the stock income is sufficient to cause the trend in inequalities to stagnate.

But now, if you attempt to respond that the stagnation of these inequalities over time, after removing some of the factors I have listed above (e.g., top incomes, capital gains...), is due to confounding factors that cause inequalities to drop over time in such a way that, as a result, there is no increasing income inequalities as predicted by continuous low-IQ immigration, then you'll have to name these factors, and we will discuss about the plausibility of these factors as possible confoundings. Because if you say that you don't know these confounding factors, you're making Emil's proposition impossible to test, because ceteris paribus can never be reached. In multiple regression, the inclusion of an additional, omitted variable (i.e., confounding factor) must always be something having theoretical relevance.

Because otherwise, your argument implies that whatever additional confounding factors could have been added into the equation, it is never enough because there still might be some undetected and unknown factors causing variation in income, and these will cause the predicted effect size (of low-IQ immigration) to be entirely masked. This kind of argument is a no-end loop.

Meng Hu is mostly spending his time on (b) which we obviously did not mean.

Is that so ? If you haven't read my comment, here again :

According to the paper "Third, g is an important cause of socioeconomic inequality within countries ... Immigration causes increased inequality in g within countries, and as a result of this, immigration causes higher socioeconomic inequality within countries ... One might wonder whether the effect size is simply too small to matter ... The answer is that for the tails of the distributions, it means quite a lot" it is clear to me that the effect is not expected to be trivial.

Everything quoted above indicates the paper has some reliance on (b). This refutes everything Chuck has said about the paper having nothing to do with (b). The section 2.3 of your paper proves what I say; you were expecting IQ (g) to be an important cause in income inequalities. [see EDIT]

Even if we accept the idea that Emil is not assuming (b), this in itself defeats the purpose and relevance of the paper. If you have forgotten, here's what Chuck's point (b) was about :

(b) Or one might read him as saying that dysgenic trends explain an "major" amount of cross temporal variance either in the country of reference or all countries. This reading would erroneous, since nowhere did he claim or imply this.

Thus, if Emil says that (b) is not affirmed in the paper, this means that Emil does not affirm that the predicted effect size is great and that his theory does not need to be confirmed in all countries. In other words, the implication of what Emil and Chuck were saying is that the proposed theory is worthless because the predicted effect size is not large and that this effect is not generalizeable to other countries. [see EDIT]

For what we know, the effect we discuss may be insignificant in comparison with other stuff

Interesting...

But this is not even stated in the paper. Instead, what is implied in the paper is that the effect size is not expected to be trivial. [see EDIT]

We also wanted to argue the idea that immigration leads to increased variance which leads to increased socioeconomic inequality everything else equal.

Like Chuck, you don't understand the implication of "everything else equal". You should have rephrased it as follows : "leads to increased socioeconomic inequality, holding constant every other theoretically relevant factors". The question, then, would be, what are those theoretically relevant factors which, according to you, causes the predicted effect size not to be seen in the income data ?

In this case, we are arguing along (a) not (c), and definitely not (b).

Assuming what you say is true (which is not), why are you using data to say that it's consistent with your theory ? This mere fact proves that you're not arguing about (a), unlike what you claimed...

[EDIT : I have focused my attention mainly on section 2.3 and related. But in one sentence "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" I have forgotten to retain the middle in my mind, and which passage recognizes that the effect may be small, so at least one portion of point (b) in Chuck may be valid after all. However, this is still confusing, while you have many cues in the paper (especially at the beginning) which argue that IQ is an important cause of inequalities, and then saying finally that the effect size may be small. This is confusing, and should be corrected. Furthermore, if the effect size is predicted to be small, then, the relevance of this theory is very limited, unlike what the authors make it sound to be, throughout the text. This also needs to be corrected.]

[EDIT again: I have corrected two approximations in my earlier comment, after re-reading the paper. Look for EDIT2 in bold]

It is interesting to see that I have no answer to the graph I have displayed above. Not to mention my questions/objections. Instead, the discussion derives toward my "supposed" misreading.

John,

I added "measured" as requested in draft #14.

I also made a correction Meng HU's complaint about "This is incorrect. What I was talking about is G-E correlation, not GxE interaction."

https://osf.io/dei73/

I approve on condition of one more alteration. In the paper, you wrote:

"The results of the modeling suggest that social inequality in Denmark is increasing due to the increasing SD of g in the country (and perhaps because of falling average g too). 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."

Could you rewrite this as e.g.,
...

"The results of the modeling indicate that g-variance is increasing in Denmark and that average g is falling too. Conditioned on both factors, one would predict that
social inequality is increasing. Of course, there are many factors that affect social inequality, and the predicted effect size due to increased g variance is probably small, so any effect might not yet be readily visible in actual data; moreover, immigration could potentially be causally associated with other factors that increase equality, so one can not conclude that net inequality will increase due to the present type of immigration. One might, though, suspect that it would."

...

I would like you to explicitly acknowledge in the paper that whether immigration will tend to lead to a net increase in inequality is unclear. This will eliminate any potential for misreading.

John,

What about:

Change to:

The results of the modeling suggest that inequality in g is increasing and that g is falling too. Based on especially the first factor, one would expect that socioeconomic inequality is increasing. Of course, there are many factors that affect socioeconomic inequality, and the expected effect size is probably small, so it may not be detectable in actual data yet.

And in the discussion:

The net effect of immigration might not be to increase socioeconomic inequality. Other effects may counteract the effect from increased inequality in g. One reviewer (John Fuerst) suggested that immigrants may vote for parties that favor increased wealth distribution. In fact, one survey from 2010 among a representative sample of 1055 immigrants in Denmark showed that they vote almost exclusively for left of center parties. This is excluding the immigration critical \textit{Danish People's Party} which is economically left-wing.\cite{Information2010indv}

Finally, it should be pointed out that the policy conundrum applies even if immigrants did not differ in mean g levels from the native population or quickly catched up. As long as they fare poorly in society, one may expect socioeconomic inequality to increase. Economist Gregory Clark has in fact argued that immigration of people who fare poorly in society will lead to increased economic inequality without making reference to g\cite{ClarkInequality2014}.

I prefer what I said, but I am OK with this.