• Arden, R., Gottfredson, L. S., Miller, G., & Pierce, A. (2009). Intelligence and semen quality are positively correlated. Intelligence, 37(3), 277-282.

• Pierce, A., Miller, G., Arden, R., & Gottfredson, L. S. (2009). Why is intelligence correlated with semen quality? Biochemical pathways common to sperm and neuron function and their vulnerability to pleiotropic mutations: Biochemical pathways common to sperm and neuron function and their vulnerability to pleiotropic mutations. Communicative & Integrative Biology, 2(5), 385-387.

Using the Vietnam Experience Study (US military veterans aged ca. 38), one of the only datasets that ever measured these two phenotypes together, they found correlations like these:

As far as I can tell, there is only one replication of this and it’s n=41 and didn’t find anything.

Since I have this dataset, I decided to look again. Arden et al did not show the scatterplot, but they should have because it looks like this:

This is the full sample, no adjustments or exclusions aside from missing data. The correlation is there, 0.14, vs. their 0.19, but if you look at the deciles on the right, you can see that the signal is entirely in the bottom 10% of men. This is more or less the case for every sperm metric that shows any signal:

Some of these metrics are interdependent since normal + small + large + tapered + amorphous = 100%. Thus, the simplest way to analyze that is just to use normal%.

So is this a real thing? Maybe the bottom 5-10% of men really do have quite a bit worse semen quality, or maybe there is some problem. Perhaps they were drunk at or before the testing, so their cognitive scores are bad and so is their semen quality. Or perhaps they didn’t stick to the rule of abstinence before ejaculation day. But before that, let’s examine the semen measures + covariates:

We can see moderate correlations among the semen metrics in an expected way. Factor analysis also confirms a 2-factor solution for volume and quality, so I will use those going forward. For good measure, here are the decile plots for semen quality and volume:

After looking closely at the 5% bins (not shown here), there is only an apparent effect in the bottom 10% of men sorted by g (intelligence), so I will use a binary for this group in the models. Here are some model results:

The results are pretty interesting. The bottom 10% men by intelligence have about 0.85 standard deviations worse semen quality, but only 0.35 SD less volume (p < 5% only). The quality link does not go away even with extensive controls, while the volume link became weaker and non-significant. The bottom 10% is only 48 men, so there is a limit to how much statistical precision we have to work with here, and we can’t say for sure about the volume. Note that Blacks have less semen volume than Whites, as may be expected by their smaller testicles -- a finding we previously reported from this dataset. Nothing predicts semen quality as well as low intelligence, though strangely abstinence predicts it mildly, perhaps not a biological link but a behavioral. A crude count of medical history (lifetime diagnosed conditions) predicts it slightly perhaps, while smoking, drinking, and BMI had no detectable effect. Concerning volume, abstinence is a decent predictor.

So it seems somewhat safe to say that intelligence does predict semen quality, but apparently only because the bottom 10% have really terrible quality. This is less easy to explain than positing some general fitness factor that underlies both, as done originally.

You can click any of the green cells to look at the scatterplots. For instance, French vocabulary (0-10 part of the 15-language test) and US-centric general knowledge test:

You can also discover weird stuff, like maybe Greek speakers aren’t very irritable (self-report):

I am trying to encourage users to take more than 1 test, so that the data can be linked. Many of these scales have never been studied together before, so new analyses become possible this way.

Have fun!

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A number of researchers have used these simple tests to examine various race differences. Lynn & Holmshaw 1990 reported these findings from South Africa:

350 black South African 9-year-old children were compared with 239 white British children on the Standard Progressive Matrices and 12 reaction time tests giving measures of decision times, movement times and variabilities in tasks of varying complexity. The black children obtained a mean IQ of approximately 65. They also had slower decision times and greater variabilities than the white children, but they had faster movement times. The magnitude of the white advantage on decision times was 0.68 of a standard deviation, about one-third of the white advantage on the Progressive Matrices. The result suggests that around one-third of the white advantage on intelligence tests may lie in faster information processing capacity.

Similarly, Lynn et al 1991 reported gaps in favor of Chinese (Hong Kong) over British:

239 British and 118 Chinese Hong Kong nine-year-old children, each representative for intelligence of Britain and Hong Kong, were tested on the Standard Progressive Matrices and on reaction times. The reaction time apparatus measured simple and complex reaction times proper (i.e., decision times), movement times, and variabilities. The results showed that all the reaction time measures were associated with intelligence and that Hong Kong children had a higher mean IQ and faster reaction times than British children. This suggests that the difference in mean IQ between Hong Kong and British children has a neurological basis. However, the British children showed faster movement times and lower variabilities, contrary to expectation. This suggests independent neurological processes may underlie reaction times, movement times, and variabilities.

And Lynn & Shigehisa 1991 (2nd study) reported that the Japanese also outperformed the British:

Japanese and British 9-year-old children were compared on the standard progressive matrices and twelve reaction time parameters providing measures of simple and complex decision times, movement times and variabilities. The mean of the Japanese children on the progressive matrices exceeded that of the British children by 0.65 SD units and on the decision times component of reaction times by 0.50 SD units, suggesting that the high Japanese mean on psychometric intelligence is largely explicable in terms of the more efficient processing of information at the neurological level. Japanese children also showed faster movement times but, contrary to expectation, had greater variabilities than British children.

The hypothesis that reaction times are positively associated with intelligence was tested on 444 nine-year-old Japanese children. Intelligence was measured by the Raven’s Standard Progressive Matrices, and 12 reaction time parameters were obtained to give measures of movement times, reaction times proper (decision times), differentiated into simple and complex reaction times, and variabilities. Factor analysis of the reaction time tasks indicated the presence of a general factor and three primary factors identifiable as movement times, simple reaction times, and complex reaction times. Of these, only complex reaction times showed significant associations with intelligence.

And it’s not just Lynn. Sen & Jensen 1983 reported that Americans outperformed Indians. Jensen & Whang 1993 examined White and Chinese Americans and found the Chinese did better.

Common to all the above studies is that they relied on various convenience samples, not large representative samples. Given the consistency of the results, we aren’t really in doubt that the larger representative samples would replicate the patterns, but nevertheless, it is good to know for sure. I recently found that there is reaction time data from the simplest version available in the NHANES III (1988-1994), a large representative American sample of older people. NHANES in general are a goldmine because they are completely public and have many interesting variables. Unfortunately, the older datasets are only available in the obnoxious fixed-width data format that was commonly used for recording data on tapes (as it is very compact). Modern AIs have made accessing and using this data much easier, so now I can quickly do an analysis that would otherwise have taken many hours. In the dataset, subjects took the simple reaction time test 50 times, so each person has 50 values available. The distribution of which can look like this:

These are from the first 9 subjects with data (only adult subjects took the reaction times as part of medical examination). Note the shapes of the distributions differ, and the presence of outliers (3 subjects have inattentive trials at 1000+ ms). There is also a learning effect, which we can see if we plot reaction times as a function of trial count:

Most subjects get better with practice, but some appear to get tired or bored towards the end. One could fit individual learning rate models to the data, but from the data you can see that these models would give rather nonsensical results in many cases. Bottom left subject appears to be learning if one looks at the red line fit, but not really, just their first trial was extremely slow.

Most of the studies above reported various summary statistics by race. The analytic choices are actually nontrivial because we have 2 decisions to make regarding summary statistics to use: 1) within-person, and 2) between-person. For within person, I can think of a number of options depending on what we care most about. It is known that the dispersion (variability) of the distribution is itself indicative of cognitive ability. The presence of severe outliers means we should also explore robust statistics, or use exclusion rules. I’ve opted for the simplest approach of including all data, so if subjects were inattentive at first, or bored at the end, this is part of their real performance, just like they might be inattentive or bored when driving a car. For the choice of summarizing between-persons, I’ve used the mean. We can judge to which extent that is sensible by looking at the distributions of the various within-person metrics by race:

All the between-person distributions have the same kind of right tail as they do within person. Thus, using the mean is somewhat misleading. The distribution doesn’t appear to differ in shape by race however. In every case, the Whites (European Americans) do better, which we can see (barely) by the blue lines being taller and towards the left (more clustered at faster reaction times). If we nevertheless use the means to summarize the distributions, we can calculate the familiar Cohen’s d gaps here in terms of the White between-person SD for consistency. In general, Cohen’s ds are calculated using average SDs or occasionally using the total sample SD. The latter is more inappropriate as the presence of ethnic diversity increases the total sample SD and reduces any Cohen d gap sizes (for instance, Wechsler’s SD are based on total sample SDs, so their IQ gaps shrink as the norm sample becomes less White over cohorts resulting in a phantom gap narrowing). However, to keep things most consistent, I’ve long decided to report all Cohen’s d’s using the White SD, so that the reference population stays the most consistent between samples and studies. With that said, here are the gaps on these metrics:

So despite the data being somewhat irregular, it doesn’t matter too much whether we try to deal with this or not. The Black-White d gaps are 0.57 for a mean, 0.51 for the median, 0.57 for the mean of the slowest 20% trials, 0.41 d for the fastest, 0.41 for the standard deviation (SD), 0.49 for the robust version (MAD), and about 0.30 d for 2 other metrics. The Mexican-White results tell a similar story.

Finally, though the samples were pretty representative, we can adjust for age and sex, the Whites were older, which goes against them slightly, and there is even a temperature measurement of the room, which turns out to be surprisingly important:

Taking into account these factors (lest someone claims that maybe the non-Whites did poorly because of lack of AC communism), we can use this model: metric(RT) ~ race + spline(age) + sex + room_temp. This gives us these results:

So in line with slight age confounding (Whites are older and older people are worse), the gaps are somewhat larger after the adjustment. In general, it made little difference.

Finally, NHANES 3 administered a number of other tests, though not to each age group, but we can still compute the Cohen’s d gaps for each test:

The other tests also show sensible gap sizes, some of them even exceeding 1.0 d. This is somewhat suspicious, but for the Mexicans, it probably has to do with language. NHANES has a question for administration language (recall, this is in the 1980s), so we can split by English vs. Spanish:

The results somehow make less sense than before. The gaps on reaction time are also much larger when using Spanish as administration language, even though language cannot affect performance on a simple reaction time test. This thus suggests that Spanish language is more a proxy for something else that is going on here. This oddity aside, overall, the results were normal for the reaction time gaps in general. The R notebook is available here.

In German, it shows the performance of Turks on PISA math by year and destination country. It can be seen they all cluster and show no improvement over time. The natives are slowly declining in the comparison European countries, presumably because the ‘native’ category increasingly includes non-Europeans.

Since the PISA data are all public, we can redo this exercise but expand it to be worldwide. From a human capital perspective we can think of the world as a migration matrix of performance. Columns can be destination countries, and rows are origin countries, and each cell has the mean score seen on PISA. In an ideal world, we would have this complete matrix, but due to sample size limitations in PISA studies, privacy protection (not all origin countries are listed), unequal population sizes (larger countries can send more migrants), and differential migration (some countries send more migrants per population size), we end up with this matrix:

To give some examples:

• Turks in Austria (413), Germany (427), Denmark (424), Switzerland (447), Belgium (430), Netherlands (460), Finland (416), Liechtenstein (471).

• Indians in Australia (549), Canada (515), UK (510), Brunei (509), New Zealand (527)

• Chinese in Macao (542), Hong Kong (549), Australia (583), Canada (603), New Zealand (577), Kazakhstan (433), Finland (488), Panama (401), Netherlands (519)

These are all PISA math scores listed in order of largest samples (e.g. only 60 Chinese in Panama). I have analyzed the reading and science as well, but math seems the least prone to language bias in theory, so we will stick with it.

The simplest model we can posit is that migrants perform as they do at home, and they stay at that level. This is essentially the strict global hereditarian model. In this simple model, the score means are identical in expectation no matter where a given group of people are located. Insofar as this is accurate, it is a simple matter of predicting migrant performance since we can simply regress it on the national IQ of their home country:

We see that several countries don’t participate in PISA but send migrants (marked in red), so their home PISA scores were imputed using the NIQ converted to PISA scale. India is the biggest outlier as they perform far better in non-India than they do in India. This suggests that Indian migrants are either not representative or India’s IQ is severely underestimated. However, let’s first consider the next simplest model: score ~ origin + destination (dummy). In this case, we allow for the fact that some countries are better at integrating migrants in some way that affects PISA scores. Positive values for the destination dummy thus means that migrants in that country perform better than expected by the origin countries’ NIQ. I would show these models but given that it is just 2 sets of values by country, it is too long to show. I can show the simplified model where we use the NIQs of the country as stand-in for the relevant values. Thus, each subject has an origin NIQ (the mean of their parents’ values, or if there is only 1 parent origin listed, that parent), and the NIQ of the destination country: score ~ origin_NIQ + destination_NIQ + year:

Thus surprisingly, perhaps, we see that destination NIQ is a much better predictor of how migrants perform on PISA than their home country’s NIQ according to the standardized betas. For the model with dummy variables, it is possible to compare the joint effects of the dummies for destination with the origin effects in terms of r2, so that we can get an idea of what is more important in the broad perspective:

Both approaches tell roughly the same story in that destination beats the origin as a predictor, whether we let both ‘roam freely’ or force them into NIQ terms. So what is going on? It’s our old friend the migrant selectivity issue. We can compare the origin effects versus the migrant selection index which we can calculate from the IAB Brain Drain database. This database contains information about the educational level (3 classes) of people who left various countries and migrated to the OECD. Using this, we can compute a selectivity index by comparing highly educated % among the emigrants vs. the country for the same year and age group. Then we get this result:

Now things make sense again. The countries that send relatively elite migrants compared to their populations are the same ones that perform well on PISA in other countries. If we don’t add the destination country dummies, we get a weighted correlation of 0.73 and 0.77 if we control for destination country even if this is uninterpretable. From a statistical perspective, this is somewhat of an annoying approach because we now have a complex 2-level model:

• score ~ destination + origin + year + residual

• origin ~ migrant_selection_index + residual2

India is the biggest outlier, Indians around the Western world perform roughly at 105 IQ on PISA math given an origin NIQ of 76 or so. This is close to the other results seen for Indians in the USA in my prior post. Note also that other countries show interesting selection effects. Pakistanis are also selected, just less so than the Indians, and they end up underperforming the Europeans despite the selection. Possibly with stronger selection, the UK wouldn’t have so big a discussion about the grooming gangs, though I suspect a lot of this difference has to do with the additional factor of Islam vs. Hinduism.

There is a way to simplify the models above into a single model, namely by converting origins to origin_NIQ expectation, destination_NIQ and then adding the selection index. Furthermore, we can exploit the fact that selection index differs also by destination, not just origin. Thus, we compute every origin x destination selection index and use this. Thus the model becomes:

• score ~ origin_NIQ + dest_NIQ + selection

Here’s the models using natural units slopes:

Reading the table takes some care. In the first model (O), we only use NIQ of origin as the predictor. The expected value begins at 65 IQ (in PISA units but here converted to NIQ), and rises 0.34 for every IQ point in the origin country. It’s not a great model, 12% variance. This model would predict, for instance, that a Dane in Sweden would get a score of 65+100*0.34=99, which is about right. A Somali in Denmark would get 65 + 70 * 0.34 = 89 IQ, too high. The second model (D) uses only the destination country IQ. Strangely, it has a slope larger than 1 and combined with a very negative intercept. Thus a Somali in Denmark is predicted to have a score of -86 + 100 * 1.86 = 100 IQ. In fact, it just predicts ~100 IQ for any migrant in Denmark or any other Western country. Models with S show that the slope for selection index is about 4 IQ/logit of selection (3.6 to 4.6). Curiously, destination IQ combines poorly with selection (model D+S), but origin + selection (O+S) is almost as good (65 vs. 69%) as the full model (O+D+S) despite the fact that destination beats origin alone (models O vs. D). In terms of parsimony, then, we could use the O+S model. This is what it predicts vs. what we see:

Looks pretty good, and this model essentially only uses the origin IQs and modifies them by the degree of selection we estimated using the independent Brain Drain dataset.

Referring back to the diaspora vs. home NIQs, readers may have noticed the unusual result that Americans underperform. Their mean PISA math outside the USA was only 440, on par with Portugal. Why is that? Performance by destination:

• Israel, 102 IQ, American Jews moving to Israel

• Canada, 102 IQ, Anglo-exchange

• Australia, 100 IQ, Anglo-exchange

• Mexico, 70 IQ, Mexican returnees

• USA (home), 97 IQ

The small numbers of Americans (50) who presumably returned to Mexico did extremely poorly and pulled down the average, and because it was using inverse-variance weights (like in random effects meta-analysis), it had a disproportionally large effect. The weighted mean is 480, which is not so far from expectations.

Another visible outlier in the plot is PHL or Filipinos. They scored about 100 IQ outside of their home country. PISA does not provide any ethnic data, but it does provide home language. Of the Filipinos migrants, 56% speak English at home even when they move to non-English speaking countries such as Macao. They bring English with them as the premier language and it isn’t just assimilation. In contract, of Filipinos living in their home country, only 7% speak English at home.

Concerning the Malaysians (MYS), 39% of the migrants speak Chinese (Mandarin+Cantonese+other Chinese) at home, but it’s 23% of Malaysians, so close to 2x the rate. Another 32% speak English at home, which is uncommon among normal Malaysians. Reversely, we can say that about 70% speak Malay at home in Malaysia, but only 21% among the migrants.

One can keep going through the outliers to attempt to figure out a plausible story of what is going on, but I’m not too interested in the particular cases, but in the overall pattern of results.

Regarding the math vs. other domains, here’s the O+S models for the others in comparison:

Thus surprisingly, perhaps, it turns out that the weakest model is the one with math as the outcome, the other 2 domains give somewhat stronger model fits as does the composite (average) score. The PISA people pretend that their tests are measuring 3-4 related constructs, but their scores correlate on average 0.89 with each other, so they are effectively unidimensional measures of some kind of scholastic-colored g factor. See Pokropek et al 2022 for more on this.

Conclusions

• PISA worldwide data can be used to study country of origin effects with regards to national IQs.

• However, due to biased data coverage, only 2.2% of possible origin-destination pairs have at least 25 students, so interpretation is difficult.

• It turns out that emigrant selection is the major factor explaining differences from expectations, especially because Indians overperform compared to Indians at home.

• Using just NIQ of origin + selection index explains about ~70% of variation in migrant PISA performance.

Yes, I could have included more databases, but AI tells me these are the most commonly used, and for the approach I develop below, it would not matter much to include more. The next step is to count the number of top universities by country. If we arbitrarily pick top 200, then we get the following top countries:

The results are reasonably, but not perfectly, correlated. USA has the most top universities in each database, but is the number 45 or 62? Asian countries show extreme divergence, South Korea has between 1 and 7 depending on the system. Which numbers are more sensible? It’s not obvious. Either China has already overtaken the UK (ARWU) or it is still far behind (QS and THE). Thus the main problem with the above findings is that we have 3 different databases of university rankings, so how are these best combined? Rank-order data is limited because we can’t say how much better rank X is than X+1 or X-1. We need interval data. Fortunately, it turns out the methods for computing these rankings are public and so are the underlying quantitative indicators. Thus, we can treat this as an ordinary factor analysis problem. We simply pool the available indicators and see what their correlations look like:

We unsurprisingly find a positive manifold, every quality indicator relates positively to every other indicator. The pattern is not that great though, there are a number of very weak indicators with correlation down to 0.08. This does not appear to be a bug, it’s just a bad measure, at least insofar as any general quality is concerned. Given the positive manifold, we can at least pragmatically treat the data as being explained (reflective) or well-summarized by (formative) a general factor or index, and then score every university on this university-g scale. Technically, the g here only refers to it being the general factor of these indicators of university quality, but you could also think of it as a proxy for the average human g -- general intelligence -- at the universities, or just think about it as university goodness. We also notice in the correlation matrix that some variables are near duplicates, which will inflate the variance related to that specific aspect of university quality. For instance, there are 3 closely related variables across 2 databases of internationalization, students/faculty/outlook, the latter which includes the former as well as international collaborations (joint authorships). Decent to half-decent arguments can also be made against each of the indicators as potentially measuring something other than university quality (number in parens is their assigned weight):

• Alumni (10%) — “The total number of the alumni of an institution winning Nobel Prizes and Fields Medals.”

• Award (20%) — “The total number of the staff of an institution winning Nobel Prizes in Physics, Chemistry, Medicine and Economics and Fields Medal in Mathematics.”

• HiCi (20%) — “The number of Highly Cited Researchers selected by Clarivate.”

• N&S (20%) — “The number of papers published in Nature and Science between 2016 and 2020.”

• PUB (20%) — “Total number of papers indexed in Science Citation Index-Expanded and Social Science Citation Index in 2020.”

• PCP (10%) — “The weighted scores of the above five indicators divided by the number of full-time equivalent academic staff.”

• Teaching (30%) — the learning environment: a reputation survey plus staff-to-student ratio, doctorate-to-bachelor ratio, doctorates-awarded-to-academic-staff, and institutional income.

• Research (30%) — volume, income and reputation: a research-reputation survey, research income (scaled to staff), and research productivity (publications per staff).

• Citations (30%) — research influence: captures how often a university’s published work is cited by scholars globally.

• International Outlook (7.5%) — staff, students and research: the proportion of international students, the proportion of international staff, and the proportion of papers with at least one international co-author.

• Industry Income (2.5%) — knowledge transfer: research income an institution earns from industry, scaled against the number of academic staff.

• Academic Reputation (40%) — based on a global survey asking academics to name the institutions where the best work is being done in their field.

• Employer Reputation (10%) — based on a survey asking employers to identify the institutions producing the best, most competent graduates.

• Faculty/Student Ratio (20%) — the number of academic staff relative to students, used as a proxy for teaching capacity.

• Citations per Faculty (20%) — total citations to an institution’s papers over five years, divided by its number of faculty.

• International Faculty Ratio (5%) — the proportion of faculty members who are international.

• International Students Ratio (5%) — the proportion of students who are international.

You can make arguments against each of them. Alumni measures raw counts, so just having more students in general will make these numbers higher. A small, elite and focused university is beaten by one with more students. Award measures ability to hire expensive staff, so one can consider it a measure of wealth of the university. Citations per faculty punishes hiring teaching focused professors. The ideal university by this metric has 0 students and 3 top researchers. Internationalization metrics punish larger countries since they have an easier time collaborating within country (USA, China), and one submeasure rewards joining papers with 100+ authors. It can also be gamed by intentionally attracting foreign students, even if these are below average. This is a typical strategy for many UK universities I’ve been told. Generally, though, gaming all metrics at the same time is not so easy, so their joint effect is probably a fair estimate of the general factor.

There are various ways to deal with such overlapping or strong group factors. One common approach is to score the data using the bifactor model. In this case, we posit that a few underlying unobserved (latent) variables cause the pattern we see. One of them we posit is general, so it affects every indicator, whereas the others only affect some subset (the group factors). In our case, we can fit this model:

The uni-g has reasonably high omega h. But some of the other factors are not that great, especially not the last one which only has 1 indicator loading at 0.45. However, it doesn’t really matter much because alternative models produce essentially the same score estimates with correlations all above 0.99. Even just taking the mean z-score of variables (so called unit-weight factor analysis) correlates ~0.97 with the factor analytic scores. Thus this single score represents the quality fairly well as a single dimension and with that we have a single number for each university in this joint database, 621 universities that were included in each of these databases. However, there are many more universities in the world, and this is important as we shall see later. Here’s the sample sizes by database unions and intersections:

Above we used the full intersection to get the 621 universities with full data. However, given the strong correlations among the variables, we can also make reasonable estimates of uni-g for the union of all 3 databases using whichever variables are available. There are different approaches here, but a simple and principled approach is to fit the 1-factor EFA model using FIML which uses the available data and provides scores for every university. I tried alternative approaches such as building subset specific regression models, but the results were correlated 0.99 or so. Thus, we have obtained uni-g estimates for 2000+ universities.

Having integrated our estimates into a single best estimate we move to the next problem with the university counts by country: having more people in your country means you have more universities, and thus more chances to have top ones, even if there are no average quality differences between countries’ universities. Here are the correlations across different thresholds for “top” university:

If the question is just who has more top universities, and thus where global research talent is concentrated, then it will tend to be whichever country has a large population, a good human talent average, as well as suitable political conditions. There are also historical lags, as new talent moves towards existing talent clusters, so even if some countries no longer have good political conditions (like the UK), then they can rely on the system’s self-reinforcing feature for some time. If the question is instead who is good at making top universities in relative terms, then we have to use some kind of the dreaded per capita analysis. Ignoring those other factors for now, here are the by country counts using the final model for the combined dataset and the per-million rankings for top 200:

USA moves from global 1st to 16th. In other words, America doesn’t actually produce a lot of top universities taking their population into account using the naive approach.

The problem with per-person estimates for rare cases is that the estimates are very unstable. A small country like Iceland (400k population) might have a good university or might not, just like it might have a single Nobel Prize winner or not. A single positive observation would result in a very high per-person rate (2.5 top universities per million people) and 0 positive observations would result in the lowest rate of 0 per million. Hypothetically, if we were to magically scale every country’s population to 1 billion, we would learn the true rates without uncertainty, and this true rate would lie far from the observed rate. In other words, for rare cases/events, it is impossible to even arrive at a correct estimate as any observation would lead to a very wrong result compared to this counterfactual. The general solution to this issue is to use better models. There are two main approaches. First, we can adjust the observed per-person rate towards a plausible value, typically the global mean (weakly informative prior) using something like Empirical Bayes. Second, we can use count models to predict the expected count for each country as a joint effect of the variables we use for prediction + population size. This latter approach fixes the standard errors at the cost of interpretability of the model results. Yes, I know, some will object philosophically to this statistical approach. There is only 1 Iceland, and it only has the current number of top universities (0), so its observed rate is the true one. From this perspective, there is no possibility of estimating model uncertainty because we already observe all the data, it’s not a sample but the population. This means there is no point of doing any standard errors or inferential statistics at all. While perhaps philosophically defensible, no one actually follows this approach in practice. Everybody reports p values for regressions for US states, even though we also observe all 50 of them, and not a random sample of 50 states from a hypothetical infinite rerun of US history where they would be different numbers and kinds of states. But I digress. Anyway, in our list above, the 4 last entries on the per person list have exactly 1 university in top 200, their country’s top university.

Concerning the causal explanation of the worldwide distribution of universities and their quality levels, one could of course take many approaches. I posit that the most foundational approach consists of 2 root causes: national intelligence average (national IQ, or NIQ) and the population size in a distributional model. NIQ and population size are not closely causally connected. My causal model of the data is that given a sufficiently large population size (say, 1 billion), every country would have a distribution of universities with a mean uni-g of some value. The population size affects the number of universities but not mean uni-g. NIQ affects both the mean uni-g and the number of them. Thus, it moves the distribution towards the higher end of the university quality dimension and makes it larger. In theory, then, if we measured all universities in the world, then NIQ should be very highly correlated with mean uni-g for the country, since this is not affected by population size. However, the university databases do not measure all universities. There are about 20k accredited universities worldwide of which we observe data for about 2000 or 10%. The problem is that we are measuring them from the right tail, best first, so not a random sample. Thus, for countries with medium to low mean uni-g, we don’t observe the entire distribution of their universities so their mean uni-g will be inflated by sampling bias. For instance, Denmark has 7 broad universities, 3 are in top 200, 6 in top 500 and all 7 in top 1000. Adding more universities to the database would thus not expand this list and Denmark’s uni-g mean would remain unchanged. However, adding more universities to the database would add many more for India, Brazil, China etc., lowering their estimates of mean uni-g. From the perspective of statistical modeling, thus, I can think of 3 approaches:

1. Count of top N -- Per-person rate of top-N universities, where top N is a tuning parameter. Best modeled using count models. This avoids the selection bias from not observing the left tail at the cost of statistical uncertainty and model interpretability.

2. Mean uni-g -- Mean score of all observed universities from that country. Biased upwards for low human talent and large population size countries. Avoids the arbitrariness of the top N tuning parameter.

3. Max uni-g -- Single highest scoring university. Avoids both issues but has even more statistical uncertainty and may be affected by historical factors relating to concentration of talent inside countries. Many countries put almost all talent in capital region, others split it up more evenly, and the former is much better for this metric.

I don’t know which approach is best, so I tried all of them. The simplest is average uni-g by country vs. NIQ, we don’t need to adjust for population size, so it’s just a scatterplot:

There is bias in that large countries are overestimated. E.g. USA has 1000s of unmeasured, low quality but accredited universities, all of which would substantially lower the mean uni-g if we had seen them. The same is true for low NIQ counties because we only observe their top universities. This general approach has issues with defining what is included as a university, and the data includes somewhere between 62% and 10% of American universities depending on these definitions.

The next idea is just to look at the single best scoring university by country (max uni-g) predicted from population size and NIQ. Population size makes the distribution larger, so there is greater chance of seeing a far right tail value, and NIQ moves the distribution towards the right and makes it larger, substantially increasing the max value seen. Since we have to control for population size, we can use the partial residuals for the plot:

This gives a better model, with sensible signal also among the low to average NIQ countries. The top positive outliers with regards to NIQ are those that are 1) large, and or 2) attract top talent from other countries, USA, UK, Switzerland, Singapore, and Canada. 4 of 5 of these are Anglos, and we have issues with English-speaking world granting high prestige to internationally known universities. Everybody knows Harvard etc. because they are commonly featured in American movies. Alternatively, maybe the modeling of the effect of population size is not quite right. After all, no one really thinks that log (population size) is the exactly right mathematical specification for how population size affects the likely right tail value.

Finally, the count models. I’ve chosen to stick with the top 200 N threshold, though one can tune/hack this parameter to get slightly better fit. There is a choice of what count model to use, ranging from the classic Poisson to negative binomial to 2-step hurdle-like models. Fortunately, the data does not suggest excess number of 0’s, so we can stick with the negative binomial. The issue here for the blogpost is that it doesn’t really give us a nice plot to show the model, only 30 out of ~200 countries have any top 200 university, so almost all countries just have a 0 observed rate. The most visual approach I can think of is using the empirical Bayes adjusted rates per million, which since they are directly adjusted for population size, can be shown with a simple scatterplot:

The grey values are the imputed values, that is, what the model expects the rate to be even though 0 was observed.

Overall, then, it is not entirely clear which approach is best for modeling this, but no matter the chosen approach, NIQs clearly predict university quality and quantity. One can go into models that control for confounders, spatial autocorrelation, or controlling for mediators like income/wealth, however, I am short on time, so this is it for today. Well, except for paying subscribers, who also get a fully searchable and downloadable dataset, so they can look up any university in database.

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The main analytic leverage for guessing at causality here is that countries changed status for the putative causal variables, and this is easy to measure. That is, the single market started with the European Economic Community in 1957 (Treaty of Rome), the initial customs union (Belgium, France, Italy, Luxembourg, the Netherlands and West Germany). It then gradually expanded over time to include more countries and more internal free trade. Thus, we can use the same country’s data from before and after they entered this union. Similarly, for the Eurozone, we can use the year they joined the Euro and adopted the currency. Thus, we don’t need to worry about between country differences so much because we are using within country variation and with year fixed effects. These are the dates for joining the two systems:

The dataset includes only countries that could plausibly join the European Union, so only European ones, including the ones that so far haven’t joined. These don’t affect the models much since they don’t have any within country variation to use to estimate the main predictor, but are shown here for completion’s sake.

The outcome variable is typically some kind of measure of economic growth. Typically GDP/cap is used, but it has severe issues for the European countries due to the tax haven problems (Ireland) and EU bureaucrats, lobbyists, and employees (Luxembourg), as covered in the prior post on economic growth as function of national IQ and poverty since 2000. The alternatives to GDP/person are GNI/person (foreign workers’ production is counted in their home countries, not their resident countries), and consumption/person (actual spending/person). The GDP/person time series covers more years, but at the cost of being ambiguous. Thus, a typical trade-off between measurement quality and data coverage. My preferred metric, median income, had too few years of coverage to be useful here, which was also true for GNI/person, so we were left with only consumption/person as a more clean metric.

Concerning the data source, for the oldest running time series, we have to use the Maddison database, and for later data we can use PWT‘s. These providers don’t provide the same metrics, so this choice also affects the metric used (GDP/consumption).

A number of other choices presented themselves. For instance, we saw before that being initially poor predicts faster growth, in particular if the IQ is relatively high for the current economic performance. This is a typical catch-up effect, also seen with children who have been out of school for a while. Since we are using fixed effects for countries, any stable characteristic is already controlled for, so there is no need (or possibility) of including the presumed stable NIQs (one could use varying PISA scores but coverage is not great and neither is the meaning of the changes clear). But we can still include a control for current economic performance (for that country x year). I decided to try 3 options: 1) no control, 2) last year’s economic performance, 3) last year’s relative economic performance (1 = average of countries that year).

Since the answers to which combinations of metrics, years, data sources, outlier handling etc. were not obvious, I ran a multiverse/specification curve model with these researcher degrees of freedom:

1. Data + metric: PWT+GDP, PWT+consumption, Maddison-GDP

2. Time: full (1950-present), 1991-present

3. Prior performance: none, lag(econ perf), lag(relative econ perf)

4. Outliers: none, trimmed

5. Greece: include, exclude

6. Estimator: double FE, Sun-Abraham (heterogeneity robust)

7. Single market coding: accession year, max(accession year, 1993), 1968 (Treaty of Rome in full effect)

8. Brexit: UK out in 2021, or still in

9. Croatia: included, excluded (it has only 2 years of data after joining the Eurozone, confounded with post-COVID lockdown recovery)

These choices result in 100s of models for both of the putative causal variables (single market, Eurozone), but fortunately, we can fit all of them quickly:

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Tackling first the matter of political leaning. There are some websites and academics sources that have published occupation level results for political leanings, mainly based on political donations. The most extensive I could find was Verdant Labs results from 2016 with results for 549 occupations. This is actually more than those in my ACS list (311), and Claude was able to match up 515 of them to the ACS occupation codes (OCCP). Here’s the most extremely skewed political occupations:

AI wrote 2008-2014 on the image, but actually it was just guessing. The website doesn’t appear to be updated since 2016, so the data are from around that time. This is somewhat before the Republican change into the populist party, so it is possible that some occupations have moved substantially since then. However, for our fertility estimates, the time is sensible because the fertility data is from 2013-2022. To note about these data based on donations is that they reflect people who actually donate money to politicians, which are those who are more invested in politics, and richer. This demographic skews Democrat in modern USA. There may also be issues with shy Republicans who don’t donate publicly (out of fear of reprisals), or just don’t donate at all (surveys show Democrat voters are more interested in politics in general). At least, there seems to be a dearth of activist class jobs with ~100% Republican donations emerging. Every single occupation in the top Democrat list is more skewed towards Democrats than the most Republican occupation is towards Republicans (10% Democrat for Miners vs. 1-9% Republican in all top 25 for Democrats). This is also why many occupations aren’t seen at all despite being large. There are 600k American women working with hand packing things, but they don’t donate a lot of money to politicians, so their leaning cannot be estimated this way.

One of the lowest female fertility occupations was in fact librarian (various subtypes), which we see is in the top list for most left-wing occupations. Using the matching overlap of occupations we get this simple result:

The correlation is a bit better than the other ones we tried, r = -0.23.

Regarding the modeling, there are some thorny questions about measurement/sampling error and representativeness:

• The fertility rates are estimates, with some error bars. If these were measured better, the model itself would fit better. Thus, our results are underestimates compared to the hypothetical situation where we sampled an infinite number of women in each occupation.

• The simplest way to counteract this bias is to use precision weights, that is, 1/standard error. However, because precision is directly a function of the sample size and the sample size is a function of the size of the occupations, weighing by precision also weighs results towards the larger occupations. This thus changes what is being modeled from being “the universe of all jobs” to “the universe of jobs relative to their size”.

• Alternatively, one can use the cool SIMEX method, which should produce about the same results.

• By joining more variables to the dataset, we are losing some occupations that couldn’t be mapped confidently. This thus represents another subset of the number of occupations which itself can affect the results aside from the introduction of another predictor.

With these caveats in mind, here are some model results:

I’ve tried every modeling approach I could think of, which are:

• OLS, no weights. This is the cookie cutter and identical to the method used before.

• WLS, weighted. This weighs each occupation by the precision with which we have measured its fertility (the outcome variable), and thus its size in the workforce.

• FGLS, also weighted, but less so. This is a poor man’s alternative to the multi-level model. The difference being that we add a constant to the denominator to prevent large occupations from having almost all the weight. This is akin to random effects meta-analysis.

• HLM, also weighted but using a multi-level model that uses the fact that the occupations are part of 25 clusters to stabilize the results (23 with data post merge).

• SIMEX, which uses simulated extra errors to the variables to try to back-estimate the effects of the variables at SE=0. The clever thing about this is that it can use cell-level error estimates in any variable, and thus we can also account for the estimation error in the political leaning variable (100 total donors for occupation X and 90% gave to Democrats vs. 10000 total donors for occupation Y and 90% gave to Democrats, these estimates are not equally precise, the former may be quite wrong but the latter is not likely to be).

Looking across the models, we see at least some consistency. All models find that female% of occupations predict higher fertility with about the same effect size around 0.25. The relatively unweighted models find large negative effects of Democrat% support, but these are smaller or not above chance levels in the weighted models. I think this is because the high Democrat% occupations are numerically small and thus imprecise and thus have small importance when using weights. Artistic jobs predict lower fertility with fairly stable slopes around -0.30, but varying p values. These models have only 143 cases because many occupations could not be matched with the OCCP codes or the ones with political donation data, and with weights, the effective sample size is much smaller and thus the results will become unstable.

Regarding the male results, it is tricky. There is a variable for cohabiting opposite sex partner, which is then the father presumably. Any non-cohabiting father is not counted this way. There is another method which is the count of resident children below the age of 1, but this would presumably give about the same result. With this in mind, here are the results across sex:

The correlation is not very strong 0.30. However, this is downwards biased by both the estimation errors for women and the even larger ones for men. The doubly adjusted correlation is 0.45, about 50% larger, based on reliabilities of 0.78 for women and 0.67 for men. Interestingly, the cross-wave stability for both sexes was 0.74 corrected for reliability, so the temporal changes seem to be happening at the same speed in both sexes (between the 2013-2017 and 2018-2022 datasets). Here’s the top and bottom male occupations:

Funny that even men in nurse-like roles are high fertility. And for good measure, here are the same models fit on the male data:

Note that Democrat% predicts negatively also for men regardless of the model, while female% does not reliably predict, though it is p<5% in 2 models. Conventional and artistic also show up as negative predictors, the same as for women. These models with politics added did not have sufficient precision to estimate the nonlinear effects of complexity, or at least, it was not detectable with this reduced sample and extra covariates.

Overall, the differences in fertility across occupations are generally explainable in sensible terms for both men and women, and largely due to the same factors. Of course, we cannot be confident about causality with these cross-sectional results, but the results do point in some directions of interest.

These are just the top and bottom 25 occupations. There are some questions about the causation. The most obvious interpretation is that some jobs are easier to combine with family making than others, so this would represent a causal effect from occupation to fertility. The second most obvious interpretation is that women who want to make families don’t choose their occupations at random, but choose those that are compatible with family life or otherwise preferred by (would be) mothers, and that’s why some occupations are higher in fertility. The third interpretation is that having children caused women to move into specific occupations afterwards, thus violating the stability assumption. This third option is most likely the case for telemarketer, which is presumably something women decide to do to make some money while staying at home with young children (a good working from home/remote job). However, for many other jobs, changing jobs is not so easy. Working as a nurse or physician (both in top 25) requires a long-ish degree and passing some test, so it is not so easy to just decide to change to that job tomorrow. Regarding family life compatibility, the interpretation is not so obvious for some jobs. In the low fertility group, we see flight attendants, which makes a lot of sense. They keep traveling around and pregnancy while working in mid-air sounds unwise (in fact, often prohibited). On the other hand, web development is easy to combine with family formation, but they are among the least fertile women. In the high fertility group, we see a lot of healthcare jobs, which I guess may have flexible hours, but also many are physical labor intensive (butcher, packaging, machine filling, agricultural workers) that don’t sound like they would make for good jobs compatible with motherhood. Overall, it doesn’t immediately seem that between job fertility rates are caused by the jobs themselves but rather must mainly be due to self-selection of preexisting differences among the women who choose them.

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• Van Pelt, D., & Kirkegaard, E. O. (2026). Big Data, Deep Roots: Correlating Surname Genetic Ancestry and Socioeconomic Status across Millions of Americans. Comparative Sociology, 25(2), 239-280. https://doi.org/10.1163/15691330-bja10162

Genetic variation plays a significant role in shaping socioeconomic status. Conventional census racial categories (Black, White, Asian, Hispanic) obscure substantial variation among ancestry groups. Surnames reflect ancestral lineage and genetic heritage, enabling finer measurement. The authors combined 23andMe genetic ancestry data on surnames with surnames yielded from government financial records, criminal databases, Wikipedia entries, and physician licensure records. They found that genetic ancestry strongly predicted surname-level outcomes across all metrics, with substantial differences in social standing among ethnic groups. Ashkenazi Jews and Indians ranked highest; British/Irish and Iberian ranked lowest among Europeans; highly selected immigrant groups such as Arabs and Iranians scored above Europeans.

Ancestry-related social gaps are much researched in the USA. Most of the research focuses on the relatively crude racial categories of Black, White, Hispanic, Asian. But there is also some research on the more fine-grained differences. The origin of the study was that some people posted 23andme’s surname page on X. You can look up almost any surname found in the American population there to see statistics about it, including ancestry results from 23andme customers. For instance, looking up “Brown”, we can see that the mean ancestry for this group of customers is:

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Skin pigmentation is a central element of most discussions on ‘race’ and genetics. Research on the genetic basis of population variation in this phenotype, which is important in mediating both social experiences and environmental exposures, is sparse. We studied the relationship between pigmentation and ancestry in five populations of mixed ancestry with a wide range of pigmentation and ancestral proportions (African Americans from Washington, DC; African Caribbeans living in England; Puerto Ricans from New York; Mexicans from Guerrero; and Hispanics from San Luis Valley). The strength of the relationship between skin color and ancestry was quite variable, with the correlations ranging in intensity from moderately strong (Puerto Rico, ρ = 0.633) to weak (Mexico, ρ = 0.212). These results demonstrate the utility of ancestry-informative genetic markers and admixture methods and emphasize the need to be cautious when using pigmentation as a proxy of ancestry or when extrapolating the results from one admixed population to another.

The correlation was 0.44 in African Americans, but this old study only used a few SNPs to estimate ancestry. Another study (Beleza et al 2013) of people from Cape Verde (islands off the coast of west Africa) reported a correlation of 0.66. The size of the correlation will depend on multiple factors including the amount of admixture (the correlation would be very weak if done on European Americans with negligible African ancestry), and the accuracy of the measurements (few vs. whole genome variants, objective skin brightness in a non-tanned area vs. self or interviewer report).

That aside, there is a sizable literature in sociology arguing that societies are very racist and this discrimination is based mainly on skin pigmentation. They publish studies with titles like “The Persistent Problem of Colorism: Skin Tone, Status, and Inequality“. Of course, there is a question of why it is so related. The hereditarians have used it mainly as a proxy for genetic ancestry and thus looked for correlations with intelligence. Richard Lynn reported a correlation of 0.17 in a 2002 study.

It would be interesting to note how well such findings generalize. Our studies of ancestry at the national and subnational levels suggest it replicates fairly well:

But these aggregate data may be misleading for findings concerning individuals. So I sought a dataset that has skin color -- any measure -- and intelligence -- also any measure -- for a number of countries. LAPOP (Latin American Public Opinion Project) gives some public data. Among them, there are some questions that measure intelligence, if poorly:

• gi1: “Name of the US President” (correct = name the current US president) - 87% get it right (pass rate)

• gi2: “Name of the President of the [country’s] National Assembly / Parliament” (country-specific person) - 52% pass rate

• gi3: “How many states does the United States have?” (50) - 71% pass rate

• gi4: “How long is the [presidential / prime-ministerial / government’s] term of office in [country]? (country-specific number) - 87% pass rate

• gi5: “What is the name of the president of Brazil?” (varies) - 35% pass rate

• gi7: “How many representatives/members/MPs does the lower house (or parliament/congress) have? (country-specific number) - 18% pass rate

• gix4: “On which continent is Nigeria?” (Africa) - 58% pass rate

Even if they were all given in each wave, it would be a pretty bad intelligence test. But actually each wave only had a subset of them, making it a positively terrible test. Nevertheless, it is better than nothing. Skin color was not measured objectively but rather using an interviewer scale that looks like this:

It’s not great because human sight is not flawless, sun exposure changes the color of the skin, and interviewers might be influenced by other factors, for instance, responses during the interview. Nevertheless, this method has been used in many surveys. So combining these two measures, we can score our very primitive intelligence test as the % correct answers of the ones in the given survey and correlate it with the skin color variable:

The correlation is overall very weak as might be expected from the terrible measures, -0.04. More strange is that 2 countries show a positive correlation larger than expected by chance (Guyana and Belize) and others show nominally positive correlations. Guyana perhaps has an explanation. Generally speaking, lighter skin correlates with more European ancestry relative to something else, usually African (in USA) or Amerindian (most Latin America). However, if there is not a lot of European ancestry in the population, lighter skin becomes a proxy for whichever ethnic group is the lightest. Guyana is in Latin America but the largest ethnic group is actually Indians at 40%. The data for the ethnic groups in the country are:

So in this case, the lightest group is somehow the Amerindians who also have among the lowest knowledge score, thus giving the reversed correlation (Suriname has the same kind of ethnic groups and has a null relationship). In general, the test is too easy with a general pass rate close to 90%. Somewhat surprisingly, the Africans performed quite well on the test, almost as well as the small Chinese sample (n=50).

Concerning Belize, a tiny country in central America:

There is a European/Spanish group, which has the lightest skin, but the lowest cognitive scores. The most obvious explanation I could find was language bias, as the European groups appear to speak Spanish and thus may not read so much English news and thus score lower on the question regarding the US president. But fitting a linear model didn’t show this to be that true: the effect of Spanish language was -0.03 whereas the effect of White/Spanish was -0.10. Language bias cannot explain the lower European performance here. I wasn’t able to find any other data to cross-check this finding with, but the educational attainment proxy checks out, the Europeans there really are quite poorly performing. Perhaps the above average Europeans left a long time ago and this is whatever remains.

Honduras is right next door to Belize, and the plot shows it has a massive uncertainty. Why is that? Well because the correlations were -0.03 in 2010, -0.09 in 2012, but 0.18 in 2014 (!). These values are mutually incongruent, so what is going on? First, I thought it may be item related (since they used different items in 2014), so I fit logistic model for each item in each wave:

So no, even the same items flip between 2010-2012 and 2014. Mysterious. Maybe they reversed the scale by accident?:

No, the Whites are the lightest in every wave, but the scale itself is changing. The (self id) Whites got 0.55 darker, and the other groups all got lighter. Very strange stuff. It appears it got fashionable to report being something else. Or maybe the sampling methods changed. I don’t know what is happening here either.

I think the main take-away message from this is that using skin color as rated by an interviewer is not a very good way to study race in Latin America. It does show the overall negative correlation, but as these case studies show, the interpretation can be very difficult as any kind of proxy for consistent genetic ancestry, at least within countries.

• ENEM, 1998-2024, ages 17-18 (secondary school), 3-5M/year, 4 subjects (~180 items)

• ENADE, 2017-2023, ages 22-24 (undergrads), various subjects (rotating)

• SAEB, 2017-2023, ages 10/14/17, math and language

• ANA, 2014, age 8 (3rd grade), math and language

• Prova Brasil, ages 10/14, math and language

• ENCCEJA, ages 15/18, various subjects

The sample sizes are in the millions, so one can estimate the subnational divisions quite well. Brazil has 5 regions, 27 states (including federal district like DC in USA), and 5500+ municipalities. Given the sample sizes, it is possible to fairly accurately estimate the means of the municipalities. First, it is useful to start with an understanding of how Brazilians classify themselves using the usual race color terms:

The numbers indicate a mixed country leaving towards European ancestry. This is true from genetic studies, but there is a lot of ancestry variation within those categories. Also interesting is the East Asian presence. Many people don’t know that Brazil hosts quite a lot of Japanese migrants. The maps of these groups look like this, the Whites:

They live mainly in the southern part, part of the southern cone. They share this mostly with the Asians, the yellows:

Given that this is the land of the Amerindians pre-Columbus, a lot of people have Amerindian ancestry, but those that identify that way as their primary ancestry mainly live in the far northwest rainforests:

The Blacks, the descendants of slaves, are to be found on the eastern coast, closest to Africa where they came from:

I was surprised there were not more of them in the northeastern tip. The remaining brown-mixed group is found everywhere but in smaller proportions where there are many Whites and Amerindians:

The Brazilian government supplies us with a Human Development Index-like score for each municipality:

This is a bit dated because the 2020 cycle has not yet been released. We can however also estimate this socioeconomic status using the questionnaires given in the ENEM:

The maps look about the same, and the correlation is strong:

The nonlinearity arises because HDI itself is a suboptimal metric. It is not a true factor score based on 3 indicators (education, health, income) because it uses a non-standard kind of average, the geometric mean, and does nonlinear rescaling because they want to keep the metric on 0-1 scale for whatever reason. This aside, the correlation is about 0.9.

Regarding intelligence, or cognitive ability more broadly speaking, we can aggregate data from the various tests into municipalities. However, some of them are more fitting than others. The older ages are suboptimal because they involve selected students, who didn’t drop out of school, and sometimes moved from their hometown to pursue education. Here’s the IQ map of Brazil using the ENEM test:

I’ve set the scores in tentative international IQ (British norms) using Brazil’s mean IQ and the Brazilian Whites assumed to have SD = 15. This scaling may be inaccurate, so buyer beware. The results suggest that southern parts of the Brazil should be fairly similar to parts of Spain, Portugal, Greece and so on in their level of development. Are they? Using the 2010 HDI values, yes, they are reasonably close. The highest IQ most White Brazilian municipalities are about 0.82 HDI, which was also true for southern Europe in 2010, e.g. the motherland Portugal was at 0.83. But this is only true when looking at the top tier municipalities, none of the states reach this level except for the capital (0.82).

The correlations between these variables are:

White and Asian (yellow) population %’s are correlated with positive outcomes, while mixed% is negatively correlated, and Black% only slightly negatively so. However, correlations reflect the variation in variables and their intercorrelations. Better is a regression model:

I left the variables in their natural units and used the unstandardized betas. The values for the slopes thus represent the effect of going from 0% to 100% for a given population. For instance, going from 0% to 100% East Asian (from 100% White) predicts a gain of ... 162 IQ. Clearly, something is amiss with this kind of model. One could say maybe this is because it is extrapolating to 100% from a range of only 0 to 11%, but Black% also suggests +8 IQ, while mixed (with Black%) suggests -20 IQ.

OK, maybe spatial dependency issues is our problem. Here are the full models but using the spatial error model. This model allows neighboring areas to have correlated errors. What it really means is that if there are some unobserved causes of variation in these variables that is spatially autocorrelated (geographically clustered), we can indirectly control for them using the spatial data. Using this kind of model is usually a very good idea for such aggregate data which invariably shows spatial clustering. Results:

The results became more sensible, but not satisfactory. Hypothetically, going from 100% White to 100% East Asian now only predicts 66 IQ gain down from 162 IQ. On the other hand, the mixed% slope increased from -20 to -40 IQ. The Black% was also turned negative, as is expected. It was an improvement, but the results are not great.

Trying to figure out ethnic means using this way is fraught with issues, but we can also just use the direct approach since we have subject data. So here’s the ENEM means by self-id race and subject:

National mean set to 0, SD = 1. Thus we see the unexpected result that Asians perform below the Whites at the individual level by something like 0.25 national SD units. General gap sizes are not as large as those seen in other countries with nominally the same groups. One reason for this is that ENEM is for secondary school students who intend to go to university, so it is a selected sample. We can turn to the SAEB instead in which participation is mandatory and it is also given at younger ages:

Curiously, the Asian disadvantage is larger here. It seems very mysterious. I mean, it is possible that Japanese Brazilians are very negatively selected to the point where they cannot even outperform the Brazilian Whites, but there is actually something else going on that’s more mundane. The problem is that very few people are actually East Asian and should press the “yellow” category. But humans make mistakes, and children more mistakes. Given how few Asians there are in Brazil, it is possible that the majority of “yellows” are actually not Asians at all, but errors. We can see this by looking at the distribution by age and test:

The census shows 0.4% Asians but these tests show 2.2-2.9% Asians. Unless there’s a large amount of new Asian migration to Brazil or Asians have a surprisingly high fertility rate, these numbers can’t be right and must instead reflect errors. In a simple model, if X % of students click at random adding to the Asian%, then assuming the census data are correct, we have to posit that about 10-15% of students click at random. That’s a quite high error rate, but this is Brazil after all.

There is a way to test this error model. We can look at Asian performance in the areas where there are many actual Asians (which we can confirm with other sources) meaning that those self-identified Asians are much more likely to be real Asians, compared to plausibly falsely reported Asians in other areas:

The table bears out the model well. Something like 80% of those who clicked yellow are from areas the census shows there are fewer than 0.25% Asians, and their mean score is about 0.5 SD below Whites in the same area. As we change to areas with more known Asians, the gap quickly narrows and becomes positive and substantial, at least 0.5 SD for the 2%+ Asian areas. Thus, the Asians aren’t underperforming at all, rather it’s a sneaky measurement issue! 8 years ago, I summarized some studies that used children’s names to investigate ancestry and cognitive performance in Brazil. These also showed Asian performance was above par:

Not exactly obvious how to convert these coefficients to the values we obtained above, but at least we can be confident that more accurate measurement than our Asian% in the municipality proxy method also shows the Asian advantage, as well as for other groups. The reference is Iberian (Spanish/Portuguese) names, so their model suggests having Japanese surname predicted about 3.3 IQ higher score in math in grade 3, and 2.4 IQ for German last name. Suspiciously, they have left out any underperforming other groups, and in general the paper only talks about cultural effects, not genetics.

Anyway, this just about sums up the results. The aggregate regression results are somewhat messed up, possibly in part because of the incorrect race assignments of students. The spatial error model reduced the issues, but not entirely. The race gaps at the individual level were initially confusing for the Asians, but it was due to measurement issues. After that, things seem to work out about the same in Brazil as they do everywhere else.

Some leftover plots for those looking for things to post online. White% -> HDI:

It shows the same nonlinear form as before. White% -> S factor from ENEM:

The nonlinearity is now smaller.

White% -> ENEM g:

One could also show the others but generally single variable scatterplots work best with the largest categories. Since Brazil has 2 categories of about even size (White and Mixed/Brown), there is little reason to duplicate them here. The smaller fractions will not show anything sensible (refer back to the correlation matrix).

First, we have to understand the structure of France from an administrative perspective since the available datasets will reflect this structure. France has 13 regions (level 1, US state equivalent), 101 departments (level 2, US county equivalent) and X communes (level 5):

The communes are too numerous to usefully show but this map shows the regions of mainland France and their departments. Paris itself is split into 4 or 8 departments depending on how inclusive you are, which is good for us.

The next peculiar thing about France is that it has a law that makes it broadly illegal to collect ethnic/race and political/philosophical data. I know this sounds insane, and it is. It also sounds like a modern Woke invention but it is not, and also prevents them from complaining about inequality directly since they themselves cannot collect such data. Of course, when regulation is introduced, the market interprets this as cost of doing business and routes around it, and this is also true for the scientific market. Thus, a number of different approaches exist to counting the ongoing population replacement:

1. Foreign born % (also broken down by country or region of birth)

2. Foreign citizenship % (including categorization)

3. Sickle cell anemia testing of newborns

4. First name counting and classification

5. Counting mosques and Muslim businesses on the map

The government publishes data for 1-2 at various levels of granularity depending on the administrative level, that is, most fine-grained for the national situation and less precise for the lower levels. Sickle cell anemia is a clever workaround because the law stipulated that newborns should be offered genetic testing if at least one parent is from an at-risk ethnic background, and thus indirectly this tells us about which fraction of babies are born to such people (apparently not violating the law against ethnic data). More or less every culture has distinctive names, and while this is more true for last names, first names are also alright. Muslims really like Mohammed and very frequently give that name to their sons. Muslim names are much more clustered around a few popular names than other cultures which makes counting Muslims using first names easier. Finally, using various open map data or company listings, one can count the density of Muslim related organizations. The combination of these various methods thus give us a quite good idea about what is going on in France despite the direct ban on the data collection. The names% approach is how people post stuff like this on Reddit:

Here’s my replication of this map:

The correlation is about 0.88, but I wasn’t able to resolve the causes of the discrepancy. Notice that Muslims are heavily represented in the north and east of Paris. This is very helpful because population density or urbanization confounds many social metrics that we can look at, so having a city split into different parts with roughly equal urbanization/population density means we can control for this factor effectively. There are some names that are common among Muslims but also common among Europeans, like Sara(h) and Adam. One could include these, and thus count some Europeans, or not include them, and miss some Muslims. Either way gives some errors and it’s not clear which is more accurate. The stricter standard underestimates the Muslim/African% (MA) of newborns, but hopefully is not too biased. It is worth noting that newborns is a flow metric -- the new people entering the population at age 0 -- rather than a stock metric, of the existing population. Stock metrics are what we want since these are most relevant to the current socioeconomic performance of the people in some location, but we will have to use the flow metric as a proxy. The two metrics will eventually align with each other given infinite time without further changes, but at any given time may not, and does not in the west because Europeans are older on average and have lower fertility (usually). Thus the newborn names will both over- and underestimate the MA% of the total population. It seems pretty accurate, though, because this is the correlation with the sickle cell anemia data for the regions:

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1. Admixture regression: does % Jewish ancestry predict intelligence and achievement?

2. Polygenic scores: do Jews have higher polygenic scores for intelligence and its proxy, education?

There are a few studies using the 2nd method, all of which show that Ashkenazis have higher than European average polygenic scores. As far as I know, the first such study was the 2019 study by Dunkel et al (including myself). It used a relatively small sample of American Jews (53) inside a larger sample from 1950s Wisconsin (Wisconsin Longitudinal Study, WLS). Still, if the advantage is large enough, it can show up in such small samples and it did:

The same year some academics led by Jeremy Freese published a preprint criticizing it, but it appears it was never formally published (nothing wrong with that). Ultimately, the criticism was irrelevant because a much larger dataset of Jewish SNP frequencies became available in the GNOMAD dataset, and it shows the same advantage:

GNOMAD at the time had 145 Jews, so nearly triple the sample size as the WLS. Later, GNOMAD was updated and included 1,736 Jews and Piffer 2023 found these results for education GWAS 3 and 4:

Ashkenazis sit either above the other Europeans (with the East Asians) or at the upper end, depending on EA3 or EA4 being used.

As far as I know, these are all the genetic studies of Jewish intelligence. Honorable mention to the earlier but speculative study A natural history of Ashkenazi intelligence (2006) that started the modern debate.

Today we want to move the science forward a bit by presenting 2 admixture studies. The datasets are the ABCD and PNC, both large US samples. The first is nationally representative and the latter is from the Philadelphia area (east coast). Ancestry was estimated using the Privé 2022 pretrained models which provides estimates for 20 ancestries, including Ashkenazi. IQ was scored the simple way: first factor of good cognitive tests, scaled to 100/15 for Whites. Tests were age adjusted beforehand using splines. Parental education or socioeconomic status was also calculated as an alternative outcome. The main results for ancestries were, with British Whites as reference:

Some groups have very imprecise estimates because there are very few Americans with such ancestries (e.g. Bangladeshi in top left). Given the uncertainties, the results are reasonably consistent:

The correlation is not great because many estimates have large errors, but the weighted correlation is 0.85. Attempting an error-corrected estimate is somewhat foolhardy given n=20, but it is 1.21. (Error corrected estimates can exceed 1.00 due to sampling error).

The estimated slopes are similar to our published results using a simpler k=5 model (European, African, Amerindian, East Asian, South Asian) for those ancestries. The Jewish samples aren’t great. There are ~300 Jewish genomes in ABCD and 477 in PNC. These are sums of fractional ancestry, not counts of pure Jews. Of those with 50%+ Jewish ancestry, there are 117 in ABCD and 344 in PNC. This should be sufficient to estimate slopes with some precision. The bigger issue is that there are nonlinear effects:

Such nonlinearities can happen due to non-random mating. Among secular Jews, outbreeding has become very common (70% in US, 50% in Europe) and thus many people end up with 50% and later 25% Jewish ancestry. Since the secular Jews are smarter, this creates a nonlinear pattern with a steeper slope from 0 to 50% and weaker from 50 to 100%. The overall slope should be accurate as the average effect of the ancestry though. These two estimates are 11.4 and 5.3 IQ.

There is also a nonlinear effect for West African ancestry:

The cause of this is the recent migration of elite Africans from Africa, which boosts the right tail.

Combining the results from the datasets, we get these meta-analytic estimates:

The Ashkenazi slope is 7.5 for IQ, but the 95% range is 2.3 to 12.7 IQ. This is because the results from ABCD and PNC are not so consistent (I² = 73%, p = 5%). The general issue here is that the cognitive measures in PNC are worse in general (many memory tests with poor g-loadings). The IQ ancestry slopes are ~30% smaller in PNC than in ABCD (Deming regression slope). The PNC sample includes children of quite varying ages, whereas ABCD have nearly homogeneous ages (around 11). The age residualization introduces some noise due to sampling issues and differences in developmental speed. If we assume the Deming regression slope represents measurement issues in PNC, the Ashkenazi slope becomes about 7.5 IQ.

Zooming out, we can estimate the mean PGS, IQ, and parental SES combined across datasets. This gives a kind of group-level plot for genetic potential of ancestries vs. their estimated IQs:

The weighted correlation is an amazing 0.96. For parental SES:

A bit less, but 0.88 is pretty good.

Overall, the results show that cognitive and social inequality is not so mysterious.

Where does this leave us for Jewish intelligence? Well, clearly, there is genetic evidence from large samples pointing in the right direction. The specific values are hard to estimate for a number of reasons:

1. Ancestry estimates are probably not that accurate for many of the closely related European groups, including the Ashkenazis.

2. Intelligence was measured mostly in childhood, and in PNC at varying ages with a suboptimal battery of tests. In general, all the PNC results were weaker.

3. The usual caveats apply to the polygenic scores. These are trained on Europeans and have weaker correlations for the other groups. EA4 shows mean bias for Africans, which is also why I used the EA3 in the last 2 plots even though it’s a subset of EA4 (the correlations for EA4 are 0.81 and 0.69). One could apply Piffer’s filtering method here but I leave this for future research.

These results are somewhat affected by the usual GDP issues relating to tax haven (Ireland etc.). There are various ways to avoid this, but a simple one is using household consumption data:

The main change is that Ireland moves down to the other west block countries. Overall, though, it doesn’t matter so much, r = 0.89. From the plot, you can also probably spot that the effect is mainly the poorer countries on the list growing faster:

This kind of pattern is usually called the advantage of backwardness. The idea is that if your country is current poor, it is easier to copy working technology and policies from more successful countries, and since copying is easier than inventing, your growth will be faster than theirs, all else equal. We see this clearly in the OECD countries. Many of the countries are dealing with the legacy of communism which retarded their economic growth, so they are catching up to where ‘they should be’ (would otherwise have been).

This story is nice, but it is a gross simplification for the world at large:

You have to pay for baby food if you want to keep reading.

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Since I am Danish, I am familiar with our own atrocious law commonly called the racism paragraph (racismeparagraffen, 266b). The historical origin of the law is that Nazi propaganda about the Jews were spilling over from our aggressive southern neighbor and the Danish parliament tried to protect the local Jews (0.1% of population). As far as I can tell, the law was then mostly dormant until the benefits of mass migration from the 3rd world were felt. The prosecutor’s office provides case summaries of every case since the year 2000, so we can see who is being protected by the state in Denmark. In total, there were 142 guilty verdicts in the lower courts (byretten) from then till now. Some of these were appealed to the higher courts, but to avoid double counting, I am just using the lower court judgements here. The timeline looks like this:

The state is thus increasingly hostile to speech that involves insulting various groups. Some of the increases in persecution also comes from various super-national bodies that change legal practice by adding more protected groups.

But is the law fair? Which groups are being protected from hostile speech? I initially did my own classifications of each case and tabulated them. However, since the cases keep accumulating I’ve had Claude do it again now. It looks like this:

My own tabulations were materially the same. Thus, the large majority of cases concern statements or utterances about non-Danes. In fact, most of the verdicts about potentially Danish people were forced by opponents of the law that published parallel versions of statements to test the legal boundaries. Thus, because an Iranian immigrant had written something about Muslims (she’s anti-Islam) and was found guilty, in protest they decided to write her statements again but with the target group changed to various other groups such as the Catholics (a tiny minority of Danes), Eskimos and so on. Most of these did not lead to guilty verdicts, but a few of them did. The one case that involving protecting the native population was even incidental since it was a spillover of a deranged rant against Jews/Israel on a public bus that also involving threatening others (case 1.1.119):

[machine translation]

Judgment 1.1.119. – Judgment of the Court of Appeal of 14 March 2024
60 days in prison

Violation of section 266 of the Penal Code, cf. section 81 (6) and section 266b (2). 1, by May 11, 2023 during the period from approx. 17.00 to approx. at. 19.55 in a bus to have threatened to commit a criminal offense and publicly or intentionally to spread in a further opinion or national or ethnic origin or belief or his disability or because of the sexual orientation of the group concerned, gender identity, gender expression or gender characteristics were threatened, mocked or degraded, with the intention of the bus’s passengers to hear the opinions, i.a. stated: ”When I come to Aarhus, I skip the shit in the air ” [Name] 1> [Names] 1”I fucking throw you out of the bus and fucking stab you ”, ”Fucking Danes! You are all Jews and you must be blown up in the air – both women and children and family ”, ”Danish pigs, you should be killed ” Danish pigs, you should be shot ”, ” Danish pigs, you should bomb ”should I have the Jews ” everything suitable to cause serious fears about the lives, health or welfare of passengers.everything suitable to cause serious fears about the lives, health or welfare of passengers.

Clearly, this person should be punished but not in my opinion for insulting the Danes or Jews, but because such threatening behavior should not be tolerated on a bus.

The law is clearly not being used fairly, but benefits foreigners at the expense of Danes who are at legal risk for even making fairly accurate predictions of the outcomes of migration. Particularly bad was the case of a political advertisement from the Danish People’s Party:

[machine translation]

Judgment 1.1.9. - Judgment of the Court of Justice of 11 October 2002
5 day fines of DKK 500 for both defendants

Violation of section 27 (2) of the Media Liability Act 2, cf. section 266b (b) of the Penal Code. 1, and Media Liability Act section 27 (2). 1, by publishing an ad in a trade magazine printed in 40,000 copies and free of charge to higher education institutions. The ad had the following text: ”Mass rapes, harsh violence, insecurity, forced marriages, women’s repression, gang crime. That’s what a multi-ethnic community offers us ”. The text was accompanied by a picture of three young light-haired girls with the subtitle ”Denmark today ” as well as a picture of three hooded, blood-plated men who show the Qur’an, with the subtitle ”Denmark in 10 years ”. The district court found that the fact that the defendants, due to hustleness up to the magazine’s deadline, did not see the ad until it was printed, cannot lead to impunity due to lack of intent. However, the district court did not find either,that such a systematic, intensive or sustained dissemination of discriminatory communications in order to influence the formation of opinion that there had beencget propaganda business, cf. 2nd See also Østre Landsret’s judgment of 9 May 2003, section 2.2., (judgment 2.2.4.) concerning the same ad.

Anyone can look up the crime statistics and confirm that those predictions were accurate.

Danish version of the plots, by target group:

Antal domme:

• Hu, M.,& Kirkegaard, E. O. W.(2026). Left-wing ideology, mental health and body modifications. Journal of Open Inquiry in the Behavioral Sciences, 5(1).

Recent research has identified a recurring association between left-wing political ideology and poorer mental health. These findings show both reduced positive well-being (e.g., life satisfaction) and increased negative symptoms (e.g., depression, anxiety). We administered 76 mental health and 41 political ideology items to a sample of 978 fairly representative American adults recruited via the Prolific data platform. Overall, we found that every aspect of mental health correlated negatively with overall leftism (r’s for 18 diagnoses = -0.20, last 2 weeks symptoms = -0.14, MMPI-subset = -0.17, life satisfaction = -0.15, all p’s < .001). Diagnoses were the primary predictor of leftism in multivariate models. This relationship was not explained by measurement bias, as invariance testing revealed only minimal, counter-balancing item bias. Furthermore, we expanded this network by incorporating behavioral markers, finding that body modifications (e.g., unnatural hair color, tattoos) showed weak-to-modest associations with both left-wing ideology and mental health diagnoses.

The purpose of the study was mainly to check the measurement invariance of the relationship, since many people had doubted this. Perhaps leftists are just more likely to see therapy or maybe they fill out questionnaires differently. For this reason, we went a bit overboard with the mental health measurement having 76 questions, 18 concerning specific diagnoses and the remaining the more commonly used self-report questions about various aspects. Politics was measured using 41 questions concerning various current thing political questions for Americans, and scored just using the 1-factor model. (Yes, one can extract other dimensions but this one is dominant.) General results:

The various scales called “p” are mental health reversed (worse) based on different approaches. Symptoms is all the self-report scales items combined, diag = diagnoses count, MMPI = items from MMPI (yes/no format), last2weeks (typical format used in surveys), satisfaction (positively phrased questions about life satisfaction). The rightmost column shows that leftism correlates positively with every variable except for age. Given these demographic associations (age, female), one may want to try a regression model to see if leftism correlates with mental problems merely because it is correlated with age and femaleness:

The answer is no, not only, but maybe in part. Diagnoses correlates 0.20 with leftism but 0.16 controlled for age, sex, US-born, and race (though the CI overlaps with 0.20). More interesting is that the models that include both self-report measures and diagnoses counts, the diagnoses have the signal and the others turn non-significant (but stay positive). With ~1000 people, we can’t say whether diagnoses count mediates the entire effect but possibly. One could even try controlling for self-reported mental problems and see if leftism still predicts diagnoses:

And yes, diagnoses still predict but at about half the strength as the raw link (0.10 vs. 0.20). As a first step into measurement invariance testing, we can check whether the questions that better measure overall psychopathology predict leftism better as well (Jensen’s method):

This was also found to be the case, thus showing that the link is via the general factor (p). One can also try from the opposite side, do the questions that better measure overall leftism correlate more with mental illness?:

The answer is also yes, though the correlations aren’t that impressive. This kind of analysis has a sample size related toward-0 bias, so it is not so easy to say what the hypothetical infinite sample size correlation would be, but it would be higher. Fun fact was that the best political question for predicting mental illness was “Western civilization is uniquely evil”, a combined self-hatred and leftism question for Whites.

Next up we also used the more standard DIF (differential item functioning) approach:

We didn’t find much evidence of directional bias in the measurement, no matter how the mental health questions were scored (separately by scale, mixed). There were many biased items but they were roughly evenly balanced, as is typical.

From the perspective of stereotype accuracy, one can also check whether the various bodily modifications have independent signal for predicting either leftism or mental illness:

It turns out that controlling for age, sex, and race, tattoos and piercings don’t predict leftism, but unnatural hair color does, as does diagnoses. However, for predicting mental diagnoses, tattoos work while piercings and unnatural hair color does not, with or without including leftism as a predictor. Thus, the adept stereotyper would have to remember that unnatural hair color is particularly indicative of leftism, while tattoos are particularly indicative of poor mental health.

One issue with the piercing variable is that women have a lot of earrings compared to men, and this doesn’t relate much to anything aside from being a woman:

We also see the usual far-left effect of political ideology, as opposed to a clean linear trend:

Though given the sample size and sex interaction, it was strangely only seen in men.

Leftism by piercing type was amusing:

It is particularly genital and septum (ugly nose) piercings that associate with leftism, the latter which is in line with popular memes. An entire standard deviation difference between those with and without! The tattoos that predict diagnoses were in particular places on the body: arms (hard to hide?), mouth (over 1 SD effect) and “other”. These results hold when controlling for the other piercings and tattoo locations, as well as demographics.

The data are public if you want to try some other ideas. From an academic-political question, I guess this publication also provides another study to cite if one doesn’t want to cite our now retracted Finnish study. The findings are about the same.

The areas are too broad to really show what is going on in detail except for Copenhagen, where it is quite clear. All the communes with larger cities (Aarhus, Odense, Aalborg, København) have low ratings of safety, which of course could be due to many factors. Nevertheless, given the known crime rate differences, the most obvious idea to check is this one:

It’s a strikingly strong correlation. Compare with the others:

So MENAPTA% is the strongest correlate of feelings of safety, aside from the other measures given in the same survey. Some of the stranger correlations are probably due to aggregation issues. Aside from the Copenhagen splits, the other large cities are in a single commune unit that is thus composed of migrants, university students, rich Danes, working class Danes and so on, which may create strange patterns.

For those wondering about regressions, maybe it is population density in some sense that causes safety concerns. So let’s try that:

Using either urbanization (% of population living in settlements of 200+ people) or population density does not materially change the results for MENAPTA% as a predictor. They are weaker using the Realdania dataset, perhaps because they asked a different safety question:

• MOJ: “Now a question about fear of crime. On a scale from 1–7 [...], how safe or unsafe do you feel? By ‘neighbourhood’ we mean the area immediately surrounding your residence.”.

• Realdania: “Are there places in your local area where you avoid going after nightfall because you feel unsafe?” % answering “No, I feel safe in the whole local area”.

The MOJ variable is more reliable because it is based on 4 years of data versus a single year for Realdania. These two measures are very strongly correlated:

Using regression models assumes a simple causal structure of the data in the form of effect <- cause1 + cause2 + cause3 + cause.... In real life we know that a more plausible causal model is like this:

In this way, we can see that given this plausible causal model, the effect of MENAPTA on subjective safety is ~90% direct, not mediated by the crime rate. This may be somewhat puzzling. If people’s feelings of safety relate to reality, they should also mainly be a function of antisocial behavior as proxied by the crime rate. This could be because 1) some crime or antisocial behavior is not captured by the crime rate e.g. under-reporting, ‘new normal’, or behavioral adaptation (you don’t feel unsafe because you no longer think about walking home alone at 2 am), or 2) these peoples just feel less safe in general and the effect we see is mainly a composition effect. Prior research has frequently found that such compositional effects are large. Whites in USA report higher interpersonal trust levels no matter where they live. One review included this summary:

Studies of trends reveal significant ethnoracial gaps in trust (Smith 1997, Patterson 1999, Alesina & La Ferrara 2002, Uslaner 2002). For instance, Smith (1997) finds that members of minority groups report substantially more misanthropy (less trust) than members of the majority. Among the 40 ethnic groups studied, misanthropy was highest among blacks. In descending order, they were followed by Asians, Amerindians, Hispanics from Spanish-speaking countries, more recent European immigrants from Southern and Eastern Europe, and middle European immigrants from countries such as France, French Canada, Germany, and Ireland. Misanthropy was lowest among descendants of early European immigrants from Scandinavia and Great Britain.

...

Here again, Uslaner (2002) illustrates the point well. Among those who have attended high school, 41% of whites report trusting others, compared with just 13% of blacks. Among those who attended or graduated college, 55% of whites compared with just 22% of blacks reported trusting others. Inconceivably, trust among the wealthiest blacks was similar to levels of trust expressed by the poorest whites (also see Patterson 1999).

The blue-eyed and naive Nord stereotype.

(R notebook, OSF repo.)

• Charge More: Price remains a powerful lever. However, it should be noted that by default estimated revenue is a function of price. So this correlation may exist regardless.

• Post Often: Reducing the average time between posts (posting more frequently) still shows a strong positive association with revenue.

• Paid Percentage: The positive correlation holds – more paid posts generally link to higher revenue in the model, though the visual plots (below) still suggest a potential curve peaking around 50-60%.

• Word Count: Longer posts (both free and paid, after log transformations) still show a statistically significant positive correlation with revenue, but the effect sizes are smaller than before. Frequency likely remains more impactful than length alone.

• Consistency? Maybe Not: The slight positive correlation for more variance in posting intervals persists. Frequency seems to matter more than rigid timing.

Today I wanted to tackle a different question. Substacks relate to each other in various ways. They can link to each other in posts, say, because they are having a debate, or because they just feature link collection posts. One could collect of all these by scraping the HTML code and finding all the cross-links. Another option is using Substack’s recommendation list. A given Substack can recommend other Substacks. I scraped this data initially for all the top 100 science Substacks, but it turns out that many people don’t use the feature:

So 35% of these popular Substacks don’t recommend anyone, which is poor manners, but also gives the authors an easy way out in case someone asks them “Can you please add me to your recommendation list?”. Additionally, it protects the authors against 6 degrees of Kevin Bacon guilt by association recommendation. Whatever the reason, this dataset is not great for analysis. Regarding the network data, Substack itself provides the crude overlap metric. Mine are:

I think this is some variant of the crude overlap from my Substack’s perspective, which is to say that 33% of subscribers also subscribe to Aporia, 26% to Cremieux and so on. The problem with this metric is that larger Substacks will always have more overlap in general, regardless of whether they have any particular shared topics or not. One solution to this is to use the PMI metric. This is based on the relative rate of overlap given a neutral prior. So if one Substack has 10% of all users and another has 5%, their expected overlap by chance is just the product, that is, 0.5%. If we find that the actual value is 2%, then the relative rate is 4x, and PMI is log2(RR). The related NPMI metric normalizes this value to -1 to 1 range. Anyway, the Substack-level recommendations are unsuitable given the 35% of the data is missing. But we can go further. I scraped all the posts for the top 100 science Substacks to find all the users (~31k posts). Then I scraped all the users’ pages to see which Substacks they subscribed to (~62k users). Their distributions of subscriptions look like this:

It’s a beautiful power law distribution. Using these subscriptions, we can build an overall network of Substacks using NPMI:

Yes, it is very small and hard to read. The labels are given by Claude based on largest blogs in each cluster. For the paying subscribers, there is an interactive version available so you can zoom in on whatever you want.

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