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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• I used country level data with total fertility rate (TFR) as the outcome. I used time series data so that we can include country fixed effects (FEs) which by design removes all between country variation and only uses the within country variation (fixest). This avoids most confounding factors that are stable between countries (language, culture, neighbors, geography).

• I used raw TFR and log(TFR) as outcome in parallel models. The latter model approach will estimate percentage changes instead of absolute. In raw units, the change from 4 to 2 TFR is the same as 2 to 0, but the latter is 100% and the former is 50% change. It’s not obvious that causal factors affect TFR in raw or percentage units.

• I examined results for core OECD (core, not Turkey etc.) and the world at large, since it is possible that causal effects are different for developed countries and those in the world at large.

• Since it wasn’t clear how to control for the effects of time, I used 3 approaches: no control, linear, and FE. The main models used yearly FEs, the most strict standard.

• One cannot strictly prove causality even using country FEs, since it is possible something else is covarying across time with TFR within units. If something is truly a causal factor, we would expect it to have a consistent sign and effect size (in raw units) across model specifications and countries (the latter done using a mixed effects model via lme4). This gives us two metrics for such variation (coefficient of variation).

• A variable may be consistent across countries and model specifications but have trivial effect size. Since they are all on different scales because different units (e.g. female employment rate % vs. GDPpc $), I used the 2000 cross sectional world sample to scale all variables to SD metrics. Thus, the effect size here means that when the predictor increased 1 year 2000 country standard deviation, the TFR/log(TFR) changed by X. Alternatively, I used the within-countries R2, which is a model fit metric. A variable that is important should have a non-trivial R2, but a trivial variable may have a large R2.

I could start with the main results and maybe you wouldn’t read the rest, so I will start with the details and you can skip ahead if you want the main findings. First, should we use raw or log(TFR) as outcome? Do predictors predict raw changes in TFR or percentage changes? The models are difficult to compare directly, but we can backtransform the log-TFR predictions to TFR scale and see which parallel models predict more accurately:

Overall, there is some edge to the log-TFR models which is mainly seen for the global dataset. The reason for this is that among OECD countries, the TFR variation is already small, so the difference between TFR and log-TFR would be hard to see. Thus in general we should prefer the log-TFR models in the model specifications.

Regarding the standardized effect sizes, they look like this:

When the full and empty circles in matching color are not near each other, it means we get different estimates from the OECD subset and world at large. This could be consistent with a causal factor having a nonlinear effect, or it may be because of confounding that is reduced or enhanced in one of the datasets. For the variables with non-trivial effect sizes, though, we see that they consistent in direction except for one: GDP per capita ppp. This variable has opposite signed effects whether we study OECD or the world. This is impossible given a linear causal effect, but perhaps possible with a nonlinear one. The same pattern is seen for poverty rate, which seemingly has opposite effects in OECD and the world. We can also just compare the model fits between linear and nonlinear models in general:

So it turns out that most variables benefit from nonlinear forms (splines), which is not reassuring for any causal explanation. Who can believe, for instance, that child mortality has this kind of causal effect:

The checkmark pattern in OECD is clearly impossible and reflects some kind of confounding that somehow evades the dual fixed effects (country + year). These non-monotonic checkmark curves gained some fame years ago when researchers found the same thing for HDI:

This result provided a lot of hopium for some years but now it looks like this:

Gone is the hopium result but I still see it posted from time to time. One can in fact get an even less credible version of it even using the dual fixed effects:

I think what happens is that despite the country FEs, the spline function has flexibility to capture the Arab oil states having high fertility at increasing wealth. A strange case of linear models being more appropriate than splines despite large detectable nonlinearity.

Overall, the final summary table for results is this:

The most likely causal effects are those that 1) have a sizable standardized effect, 2) small variation between model specifications, 3+4) a decent r² within countries on average for both OECD and the world, 5) small variation among countries. The plot ranks these metrics taken together. Thus, years of formal education for adults is the single most promising variable. This is strange because if so, we expect it to chiefly relate to women in higher education, which is the years of schooling that primarily block/postpone fertility. However, female tertiary education % we have as a separate variable and it found nothing. This is the same result I found before using different methods. This result is also not in line with individual level results (UK results):

Fertility is here measured as number of children a woman has at age 40, which is almost the completed fertility value. There’s a clear educational gradient by educational attainment related to post primary education, which is the exact one we don’t find in the country level data.

OK, so the education results are strange, what about the next finding? Contraception. It passes with flying colors and has an obvious causal mechanism. Next we have 3 health measures -- child/infant mortality rate and life expectancy -- which show consistent results. There isn’t an immediate causal mechanism here, but there is a large literature on how mortality salience supposedly has effects on desired and realized fertility. The evidence consists of various priming studies (dubious) and some observational (women in Africa having more children as a function of how many funerals they attended). Nothing is entirely convincing, but maybe.

Median age is a bad variable, but I’ve kept it for inclusiveness. Why is it bad? Well, having more children decreases the median age, so it is caused by the outcome itself. It’s also affected by general health and development, which makes it about the same as the ones above, just measured in a different way.

Urbanization is an interesting variable. Aside from contraception, it is the only one that governments can realistically do something about. It shows a much larger R2 inside the OECD than outside, which is probably because among the world’s countries, other factors are much more important, but among rich countries, urbanization is important. More Births has compiled tons of indirect evidence of urbanization measured in various ways, such as housing size and density. Every map of cities and TFR show something like this:

These kinds of map are of course not conclusive evidence because people don’t live in random places. When people want to start making family, they usually leave inner cities for a house further out, which in part causes this pattern by concentrating the voluntarily childless in cities. What we need is an experiment where people were moved around at random, some to better/larger housing. It would appear this is possible using the Moving to Opportunity dataset, but it is not publicly available. If you have access, please send it to me so I can check. I couldn’t find any published study looking at the fertility of the people receiving the grant for moving, as everybody is busy p-hacking the outcomes for the children (4000+ citations already).

All the remaining predictors did not produce patterns consistent with a simple causal model. This includes GDP/GNI and their variants, government size/social spending, house to income ratio, inflation, inequality, female employment. Maybe some of these things matter, but we can’t detect it here.

I think the general conclusion of this exercise is that if one is willing to try many model specifications and data subsets, one can surely find some cool looking plot and write it up with some exciting but speculative story and then submit that to one’s favorite journal of p-hacked results. However, a systematic search of variables just found that various measures of overall health all negatively predict fertility (infant/child mortality/life expectancy/median age), which isn’t very useful. Even if this is causal, I don’t think governments will be telling their voters soon that their plan to boost the fertility rate is to kill 20% of newborns at random. The only potentially tractable variables were years of schooling, contraception, and urbanization. Regarding the years of schooling, we find the awkward result that the effect seems primarily related to primary schooling, not tertiary schooling. For contraception, I mean, governments could ban it or discourage it, but citizens would just buy it elsewhere since demand is so strong. There is no realistic way to severely limit access to contraception in this day and age. We’ve also seen that banning abortion has only marginal effects. This leaves us with urbanization as a plausible actionable cause. The problem here is that the modern economy works by division of labor and this is much easier when there is a lot of people around, that is, with cities. To reverse this urbanization trend would require ability to do highly productive labor from home, or substantially improving commuting travel times or discomfort. Both of these are possible. A more general conclusion is that using country-level data does not seem to afford us ability to find stuff of interest, aside from ruling out large effects of certain things. We must turn to randomized experiments, if governments were interested in doing them, and if not, then at least ‘natural experiments’ exploiting legal changes.

Given this stark over-representation, there is of course the question of why they are so successful. The mainstream explanation is vague hand-waving about Talmudic traditions or cultures of learning. The HBD blogger position is that it is mainly due to higher than average intelligence. There are some small meta-analyses of Jewish IQ, which look like this:

You can find more studies. The ones with very high means are usually small select samples from NYC. The general problem with the estimates from the studies above is that the identification of Jews is usually by self-report of religious stance. Since the secular Jews are the smartest, the use of the religion=Judaism proxy for identification leads to an underestimate. Similarly, modern self-described Jews are admixed with mainly Europeans (and increasingly East Asians), which results in half and quarter Jews with somewhat lower mean IQs on average (racial assortative mating for intelligence does not completely eliminate this outbreeding effect). Using the large Project Talent data and Jensen’s method, one can estimate that a perfectly g-loaded test would get about 110 IQ.

But maybe this amount of intelligence isn’t enough, so we need something more to explain. You are no doubt familiar with the various anti-Jewish takes which center on ethnocentrism, parasitism and so on. These kinds of accounts also usually claim the IQ advantage is not real (normal academics also sometimes deny the intelligence advantage). Their main mistake is not understanding Israel’s demographic composition and thinking that Israel’s national intelligence average of 92-94 IQ is inconsistent with high Ashkenazi intelligence. These points are all dealt with in Seb’s post. Nevertheless, even a 10 IQ advantage may not be enough to explain the over-representation. Seb tried estimating some models, and I’ve previously suggested that mental instability explains some other part of their creative output. It’s not clear we need something more to explain Jewish achievement with, but I decided to look in the OKCupid data to see what differences exist between non-Jewish Whites and Jews. In my dog and cat people study, I had made a variety of scales out of the questions on OKCupid, so we can reuse them here for quick results:

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§44
(1) No alien shall be naturalized except by
statute.
(2) The extent of the right of aliens to become
owners of real property shall be laid down by
statute

So there are two ways to be a Danish citizen. You are either granted it by virtue of birth to a Danish citizen, or parliament specifically makes a law to grant it to you. Since all laws are public, everybody who has been ‘naturalized’ this way has their name written in a law somewhere. This fact means that we can track all such conversions for the purpose of seeing who is ‘becoming Danish’ in this legal sense. Using Claude, I scraped all these laws and built a database. It turns out that the information available about the people also changes by year:

For the pre-2000 laws, the text stated their birth country. Here’s a snippet from a 1995 law:

1) Samir Toufik Abbas, København, født i Libanon.

2) Abdel Haq Abdel Razzag Abbas-Al-Awsi, Frederiksberg, født i Irak.

3) Farah-Legha Abdalkhani, Odense, født i Iran.

“født i” = born in. For the 2000-2020 laws, no information is given, 2010 example:

1) Manuelito Sy Abalos, Albertslund.

2) Gulalay Abbassi, Århus.

3) Farrokh Abdolkarimi Koohbanani, Aalborg.

Only their current residence commune is given. From 2021 to present, broader regions are given:

§ 2. Indfødsret meddeles til følgende personer, som er statsborgere i andre vestlige lande end lande i Norden:

2) Maiken Ellen Baird, bosiddende i Amerikas Forenede Stater.

3) Bente Beckmann, bosiddende i Forbundsrepublikken Tyskland.

4) Ian-Alexandru Aakmann Businschi, bosiddende i Silkeborg Kommune.

But these concern now citizenship not birth country. As such, we have no data aside from names 2000-2020 and citizenship for 2021-present. In total, there are ~31k people with complete information which we can train on. There are laws before 2000 but they follow a different database format, are harder to get, and won’t have many people.

Before going further, it is reasonable to look at the counts of names. First names:

There’s a variety of versions of Mohammad, and it is in fact the most common naturalized name. Merging the spelling variants:

The last names are less conspicuously foreign:

There are a lot of Danish ones, which presumably reflect foreign spouses taking a Danish name and eventually acquiring citizenship. The most common is the Vietnamese Nguyen.

Using the names of people, we can attempt to infer their ethnicity for the years we have no birth country data. There are a variety of such name-to-ethnicity prediction models available. A commonly used one is ethnicolr. It produces these results:

There’s a surprising number of Nordic and British names. However, checking these we see that they are often wrong:

• Nicolette King - ethnicolr: British, actual: born in Denmark (likely Anglo parent)

• Seyd Ahmad Maasoumivishget - ethnicolr: British, actual: Iranian

• Jason Mikaeli - ethnicolr: British, actual: Iranian (Western first name, Iranian surname)

• Marie Noelle Tranemose - ethnicolr: British, actual: French

• Cathrine Falck - ethnicolr: British, actual: Norwegian

Of particular concern is that this prediction model has no Turkish group, but Turks are the largest foreigner group in Denmark. Of course, for people with mixed origin names, we cannot determine for sure what ethnicity they belong to, but we can at least make a reasonable guess. So I decided to build my own prediction model using the pre-2000 names and origin countries. This gives us this result:

There are too many small groups though, so if we simplify it to 10 broader groups:

There are remaining issues. Ehiopia, for instance, as an origin group is mixed of Christian, Muslim, and African names, so they follow 3 different linguistic patterns, and the model obviously has issues with this. We don’t have enough of them to split them into these 3 groups. Similar issue for South Africa, which is mainly Anglo names with some Dutch (Afrikaans), and a few African ones. Nevertheless, it is an improvement. In terms of model accuracy:

Accuracy tells you whether the model predicted most likely origin was the same as the one the data says (origin). AUC is the better metric in general, and it was extremely high. AUC measures how far part the probability distributions are for true cases and true negatives (in 2-way comparison) and the one above is a multi-class generation of this idea. We can understand that when we look at the predicted probabilities:

The larger groups have very distinctive probability distributions. Almost all the Vietnamese names are assigned with high probabilities and the non-Vietnamese names are not assigned high probabilities often. For smaller groups, it doesn’t work out so well. Latin American names are Spanish, so they get confused with the south European Spanish ones. Better is to look at the 10-group version:

Most of them are now looking good, but some are not. Sub-Saharan African names can be Christian or Muslim and thus get confused with the European or MENAP clusters. The confusion matrix shows this:

They are row-normalized (percentage), so you start with a row and read the values to see how each ‘true’ origin (birth country) is classified according to the model. For the main Muslim group MENAP, 98% are classified that way. For SS African, 34% are classified as MENAP due to Muslim names. The various European groups can’t get pulled apart cleanly, e.g. 16% of Romance origin names are classified into Germanic, presumably due to shared cultural origins, and the usual Frankish-Germanic mixture in France. Note that while some East Asian names are very distinctive, say, Japanese, there are only 34 Japan-born people in this dataset:

• Kenichi Nakashima

• Toshio Aoyagi

• Miyako Jensen

• Atsuko Kjær

• Taeko Møller

And only some of them have full Japanese names, the others took Danish last names from spouses, confusing the model.

Autistic model details aside, this is the final best guess distribution of the people naturalizing in Denmark:

About half of them are Muslims (MENAP + Turkey), and the rest are a scattering mix of others. The most surprising is the number of East Europeans. There are 1600+ Poles alone. I guess this is the Danish version of the Poles in the UK pattern.

One could take this project further using other countries. Norway and Sweden don’t appear to do this by law, but France does. Applying our 10-cluster model to France and Denmark for comparison:

France is getting more Muslims than Denmark in % terms. I only used one law from June 2025 because they are in PDF format and behind anti-scraping measures, so getting all the files may be a hassle. If some French person can get these for me, I can apply the prediction model.

Anyway, that’s it for now. R notebook is here. Code is here.

The content of the questions doesn’t matter too much, and most of these tests use trivia questions, but you can in principle use anything. There’s one based on US trivia/geography here, and another US trivia one here. There’s 2 main formats, the one using true/false and input confidence level format, and the one where you input your numerical range that it is supposed to have a certain coverage. An example of that is this test:

This format is harder for the users as it is not a typical format used, and it requires a lot of typing of numbers leading to data entry issues. I would think in general this therefore leads to less reliable estimates.

The test was made with Claude, by just asking it to generate a website with 120 true/false questions. I took the test myself and then told it to fix a number of questions. The ones I replaced or fixed were:

• Q1: “Sahara is the largest desert” → “Sahara is the largest hot desert” (answer flipped to true)

  • It was a trick question based on a definition of desert that includes Antarctica.

• Q6: “Dead Sea is the lowest point on Earth’s land surface” → “Lake Baikal is the deepest lake”

  • The Dead Sea is not a land surface.

• Q13: “Mount Everest is in Nepal” → “Mount Everest is in Tibet”

  • Originally, it was coded as false because mount Everest peak sits at the border, and AI doesn’t think this means it is “in Nepal”. Honestly, it is still a bad question.

• Q41: “Bananas are berries” → “China produces more rice than India”

  • Trick question based on unusual fruit/berry definitions used in botany that are opposite of ordinary language. The new question turns out to be very bad too because China and India actually produce the same amount of rice, within 1%.

• Q68: “Dracula was written by an Irish author” → “War and Peace was written by Dostoevsky”

  • He was half English by descent, and some might interpret Irish as referring to the ethnic group.

• Q93: “Java was developed at Sun Microsystems” → “Python is named after Monty Python”

  • Too obscure.

• Q98: “Internet and WWW are the same thing” → “Russia spans 11 time zones”

  • Original concerns obscure technical difference. In normal language use, they mean the same thing.

• Q100: “Linux created by a Finnish computer scientist” → “The human stomach produces a new lining every few days.”

  • Linus is a Swedish Finn, so same issue with nationality vs. ethnicity as above.

• Q104: “White chocolate contains no cocoa solids” → “Iceland has no standing army”

  • Question was about the exact form of cocoa, butter vs. solid.

• Q106: “Coffee is made from a bean” → “Coffee beans grow on trees”

  • Another botany akshualy vs. everyday speech. The second version is also a botany trick question.

• Q109: “A banana is an herb” → “The Moon is slowly moving away from Earth”

  • Another botany trick question.

• Q110: “The dot over i and j is called a tittle” → “More people in Bangladesh than Russia”

  • Too obscure.

• Q114: “Polar bear fur is transparent” → “An octopus has blue blood”

  • Autistic distinction between ‘transparent’ and ‘white’.

As you can see, I didn’t do a great job of fixing all the questions and more remain quite suboptimal as we will see. Nevertheless, users should take this ‘potentially bad question’ uncertainty into account, and if such questions are a small % of all questions, the test will work fine.

Regarding the data, the test now has complete data from 559 people taking the test for the first time (some people take the tests multiple times), so let’s have a look at it. We have data on 2 levels: 1) we have subjects, and their various scores, and 2) we have items and their statistics. Let’s start with the person level. When you take the test, you will get a few scores:

• % correct is the % of questions you got correct, the site will also show the absolute count. There are 120 questions, so these are close to the same value.

• Mean confidence is the average confidence given for the chosen answer. For perfectly calibrated people, this value is the same as their % correct.

• Overconfidence is the difference between the two above, that is, if your confidence levels implied you got 100 correct but you only got 90, the score is 100-90 = 10. You were overconfident by 10 questions in aggregate.

• MAE = mean absolute error is the distance between the confidences given and the truth, so if you give 90% to A being true and it is true, the deviation is 0.1. If you thought it was false with 90%, the deviation is 0.9. The Brier score is conceptually the same but nonlinear and has some nice mathematical features at the cost of being less intuitive.

• AUC = Area Under Curve, commonly used accuracy metric in machine learning. 0.5 is random and 1.0 is perfect. The name comes from plotting values on a plot and finding the area under the line. It also has a connection to Cohen’s d, as in it is based on the distance between the probability distributions you gave for true and false statements. Thus, if you gave 100% confidence in all true statements, and 0% confidence in all false statements (100% in them being false), then the Cohen’s d between these distributions is infinite and the value becomes 1. You don’t need to care about the mathematics of it except to know that 0.5 is chance and 1.0 is perfect. The main advantage of AUC is that it is relatively independent of the ratio of cases to controls, which affects many other metrics of binary classification.

These are the correlations for the subjects between these metrics:

Most of them have at least decent correlations with each other but have different meanings. For instance, you could answer every question correctly with 50% confidence, and you will get 100% correct, but a bad score on the others. For interpretation, overconfidence is tricky because 0 is the best value, so in theory it should have nonlinear U shaped relationships to others, but it doesn’t. It is also mathematically impossible to be overconfident if you get everything correct, which necessitates a negative overconfidence score unless you answered 100% confidence to every question.

Regarding the questions, we can treat this as just another general knowledge test and analyze it using a simplified 1 factor model with IRT. If we do this, we get this:

Since these are true or false questions, the guessing rate is just 50%, and any question with below 50% suggests users misinterpret the question, it is scored incorrectly, or there is some trick to it. Usually, when you make a scale/test, such questions are dropped. Similarly, the loadings distribution show that 9 questions have negative factor loadings and most have loadings below 0.30, a typically used cutoff for bad items. The items are not working very well in general as a measure of general knowledge. Still, because it has 120 items, it still achieves a reliability of 0.85, which is decent. Item pass rates and loadings are theoretically unrelated, but empirically may be related. We see a decent positive correlation, with a subset of items having below 50% pass rates and low loadings. These are the items with less than 40% pass rate:

• Q76. Edvard Munch’s The Scream depicts a person screaming (15.6%, False)

  • This is a bad question since this is indeterminate.

• Q34. Magellan completed the first circumnavigation of the globe (27.2%, False)

  • It’s somewhat of a trick because he died on the journey and thus didn’t complete it.

• Q117. A bolt of lightning contains enough energy to power a house for a month (33.2%, False)

  • There’s a lot of popular articles about this, but getting a determinate answer is hard since obviously measurement is difficult. The best I could find is that for cloud-to-ground strikes, they contain about 0.8 GJ, which is 222 kWh, which covers electricity use for a US house for 7 days, EU one for 11-15 days, and 3rd world for much longer. It could be taken as true if one interprets as only electricity and uses a world median house, it could power for about a month. It’s not a great question.

• Q77. The first feature-length animated film was made by Disney (36.6%, False)

  • Most people think of Snow White, the first US one, but there were others before, most of which are now lost. Not a trick just hard.

• Q84. The human nose can detect over one trillion scents (37.6%, True)

  • Based on a contested study that got popular. Bad question.

These are the questions with very bad loadings, < 0.10:

• Q59. Vincent van Gogh sold only one painting during his lifetime (loading: -0.06, 51.8%)

• Q65. Charlie Chaplin once lost a Charlie Chaplin lookalike contest (-0.05, 86.3%)

• Q13. Mount Everest is in Tibet (-0.05, 50.1%)

• Q41. China produces more rice than India (-0.05, 72.9%)

• Q45. Glass is a liquid that flows very slowly (-0.03, 58.2%)

  • Akshually definition question between liquid and “amorphous solid”.

• Q76. Edvard Munch’s The Scream depicts a person screaming (-0.01, 15.6%)

• Q87. Most of the dust in your house is dead skin (0.00, 41.5%)

• Q106. Coffee beans grow on trees (0.01, 57.3%)

• Q108. Coca-Cola originally contained cocaine (0.01, 89.1%)

• Q60. Beethoven was completely deaf when he composed his 9th Symphony (0.01, 73.1%)

• Q8. Tokyo is further north than New York City (0.01, 55.5%)

• Q61. The Mona Lisa has no eyebrows (0.04, 42.0%)

• Q117. A bolt of lightning contains enough energy to power a house for a month (0.05, 33.2%)

• Q70. Michelangelo painted the ceiling of the Sistine Chapel (0.06, 95.4%)

• Q33. The Titanic sank on its maiden voyage (0.06, 89.8%)

• Q69. Tchaikovsky composed The Four Seasons (0.06, 73.1%)

  • Vivaldi.

• Q74. Moby-Dick was a commercial success when first published (0.07, 66.6%)

• Q83. Babies are born with about 270 bones (0.08, 64.3%)

• Q17. Sweden and Norway share the longest land border in Europe (0.08, 80.0%)

  • Claude originally rated this as false for some reason. It narrowly beats the Russia-Ukraine border, but it is true.

• Q34. Magellan completed the first circumnavigation of the globe (0.08, 27.2%)

• Q39. Oxygen was discovered before hydrogen (0.09, 67.0%)

  • Comes down to what “discovered” means, whether being isolated counts or also had to be recognized as an element in some proto-chemistry sense.

Many of these we have seen before, most of the others seem OK, but perform poorly for some reason.

In terms of the overall level of calibration seen, we can group responses by confidence level and the actual correct %:

This is the aggregated item version of the usual Dunning-Kruger pattern. On average, when subjects said they were 100% confident, they were right about 87% of the time. On the other end, when they said 50%, they were right 55% of the time. By the size of the points you can also see that people rarely used the intermediate probabilities, using far too many 50%’s and 100%’s. Here’s the person-level version:

The people getting 75+ questions right were somewhat underconfident, and everybody else was overconfident. It is a common finding that people are in general bit overconfident. Here’s the distribution of overconfidence as seen in a study from the UK “nudge” unit:

Why do we care about overconfidence? Well, it has some practical consequences. A study of eye witnesses found that they too were overconfident, more so than for general knowledge questions:

Sorry, the source quality is low.

OK, so how do these scores that people are given correlate with other cognitive test results? The new correlations page on taketest allow you to see these:

The sample sizes for people having taken the calibration test and some of the cognitive tests are not great, but they are OK for getting a general impression. It looks like it doesn’t matter too much which calibration test metric is used insofar as correlations with intelligence tests are concerned, except perhaps that overconfidence and MAE are worse. This is interesting, but the central claim of the LessWrong/rationalist idea of debiasing is that rationality has independent positive causal effects from general intelligence (g) itself. We unfortunately cannot test this here and there is little research on this question to my knowledge. The fact that we observe about the same correlations between the simple sum scoring of the answers and the other metrics with other cognitive tests does not bode well for the prospect of having incremental validity.

Overall, I would say the test works despite some bad items. I could replace the bad questions with others but this would make comparison with the earlier results difficult. The best I can do is shorten the test by removing the bad items from consideration, and I might do that, in which case it may become a 70-item test (dropping 50 worst items). This kind of pruning step is in fact common for the creation of scales, though usually it is done in several stages which we can’t easily do here. The main lesson is that I should have given AI more clear instructions: 1) avoid trick questions involving technical vs. ordinary language definitions, 2) only use facts that have definitive answers that are not a close call or which might change soon.

Regarding the alternative format, the numerical range input, I’ve created a new test for trying out this version. Once enough people have taken this variant, we can compare the person-level metrics to see how well the formats agree. Note that many versions use 95%, 90% or even 50% intervals. The latter is statistically optimal since it allows one to clearly detect under- and overconfident people, which is not possible with 95%. 50% intervals are psychologically unusual though. As a reasonable compromise between statistical utility and psychological sensibility, I’ve chosen 75% confidence intervals. Thus, input ranges that you think give you 3 out of 4 chances of containing the true value.

By the way, here are my scores on the old test:

It regularly goes viral on X with the usual abortion debate to follow. The source is this site, where we can also learn that this plot is 15 years old. Here’s the newest one they have from 2022:

The newer map shows Portugal now has a higher rate, and Poland is still the big outlier together with Austria (in their data). I think these rates are based on abortions in that country, so does not include medical tourism, which is now very easy to do. Poland’s effective rate is thus much higher than the <2% seen here. Naturally, abortions lower the fertility rate, so you would expect that if we plot these together, we get a decent negative correlation:

But that’s not what we see, instead it is positive for European countries, and worldwide it is:

In neither case is the relationship stronger than chance level, despite we knowing that it has a causal effect. It tells us that abortion rates per pregnancy is not the cause of national differences taken as a snapshot (cross-sectional). Clearly, what matters must be the other part of the equation, the pregnancy rate:

Countries above the regression line are those with few failed pregnancies, whether from abortion or miscarriage. If you look closely you can see that Poland is a bit above the line. And in general, Poland does not have higher TFR than its neighbors:

The issue with the focus on abortion is that it is not the only way women can control fertility. If you ban abortion, they will just take more care to not get pregnant in the first place and not rely on abortion as a backup solution This is what Polish women do:

Only Ukraine has a lower pregnancy rate.

We have time series data, so we can also try the country fixed effect model, which controls for anything that doesn’t change for a given country (geography, neighbors). Using this, can we show that changing the abortion rate per pregnancy boosts fertility? No, within country variation in TFR is not much linked to %aborted either, 1.4% variance explained, and with the wrong sign. Fitting the more correct model -- TFR = pregnancy rate * (1 - abortion_rate_pp) -- explains 90% of the variance and change is almost entire due to changes in the pregnancy rate, not the aborted%. Abortions are a distraction, communist Romania aside. The model doesn’t fit perfectly because the pregnancy rate is given in per 1000 women, and the TFR is a metric that attempts to predict the lifetime fertility of a woman using the current age specific birth rates. This forecasting model implicitly assumes that these rates do not change, which of course we know they do. There is also a minor effect of the age and sex composition of countries, but these are minor compared to the main cause, the pregnancy rate. To boost fertility rates, countries must focus on this variable, not having religious or quasi-religious arguments about abortion. You must make women want to have children. Make Motherhood Great Again.

Some more maps for those interested. Aborted% by country:

Pregnancy rate map:

TFR map:

Cross-sectional fit of TFR ~ pregnancy_rate * (1-aborted%):

Notes on the data (Claude)

1. World Bank World Development Indicators (WDI)

• Variables: Total Fertility Rate (SP.DYN.TFRT.IN), crude birth rate (SP.DYN.CBRT.IN), total population (SP.POP.TOTL), female population 15-64 (SP.POP.1564.FE.IN), female population total (SP.POP.TOTL.FE.IN)

• Coverage: 215 countries, 1960-2024 (annual)

• Download: Bulk CSV from https://databank.worldbank.org/data/download/WDI_CSV.zip (the API was down at time of download)

• Quality: High. Originates from UN World Population Prospects. Interpolated/modeled for years without census data.

• File: data/raw/wdi_panel.csv

2. Guttmacher Global Abortion Incidence Dataset (GAID)

• Reference: Popinchalk, Beavin & Kwok, hosted at https://osf.io/5k7fp/

• Variables: Number of abortions, abortion rate (per 1,000 women 15-44), % of pregnancies ending in abortion, data source type, completeness classification

• Coverage: 108 countries, 1989-2018 (annual where available, gaps common)

• Quality: Variable. Compiles official statistics, surveys, and study estimates. This is the input data for the Bearak et al. modeled estimates.

• File: data/raw/guttmacher_abortion_incidence.csv

3. Eurostat - Legally Induced Abortions (demo_fabort)

• Variables: Number of legally induced abortions, by age of mother

• Coverage: 41 European countries, 1960-2024 (varying by country)

• Quality: Official statistics from national agencies. Used to gap-fill countries missing from GAID (added 30 country-year series not in GAID).

• File: data/raw/eurostat_abortions.csv

4. WHO Global Health Observatory - Modeled Abortion Rate

• Reference: Based on Bearak et al. (2020, 2022)

• Variables: Abortion rate per 1,000 women 15-49, with 80% and 95% uncertainty intervals

• Coverage: 144 countries, single period (2015-2019 average)

• Quality: Modeled estimates (Bayesian hierarchical model). Wide uncertainty intervals for countries without official statistics. Cross-sectional only - not usable for panel analysis.

• File: data/raw/who_abortion_rate.csv

5. Bearak et al. 2022 (BMJ Global Health) - Supplementary Data

• Reference: Bearak et al., “Country-specific estimates of unintended pregnancy and abortion incidence”

• Variables: Country-level modeled abortion rates, % of pregnancies aborted, with uncertainty intervals

• Coverage: ~150 countries, 2015-2019 average

• Quality: Modeled estimates. Cross-sectional only.

• File: data/raw/bmjgh-2021-007151supp001.xlsx

Constructed Variables

In data/panel.csv, the following are computed from the raw sources:

• live_births = (birth_rate / 1000) * pop_total

• abort_rate = (n_abortions / female_pop_15_64) * 1000 — abortions per 1,000 women 15-64

• abort_per_birth = (n_abortions / live_births) * 1000 — abortions per 1,000 live births

• pregnancies = live_births + n_abortions — does NOT include miscarriages/stillbirths

• preg_rate = (pregnancies / female_pop_15_64) * 1000 — pregnancies per 1,000 women 15-64

• pct_abort = n_abortions / pregnancies * 100 — % of (known) pregnancies ending in abortion

Known Issues

Systematic undercount of abortions

Official statistics systematically undercount abortions, especially where abortion is legally restricted. Countries with restrictive laws (most of Latin America, Africa, Middle East) either don’t report or report implausibly low numbers. Of the 97 countries in our cross-section, only 12 are classified as “Complete” in the GAID; 31 are “Incomplete” and 54 have no completeness rating (mostly Eurostat-sourced, which reports only legal abortions).

Poland’s reported numbers are almost certainly too low

Poland reports ~1,100 legal abortions per year. Estimates of actual abortions (including travel to neighboring countries and underground pill use) range from 80,000-150,000. This means Poland’s pct_abort of 0.3% is a massive underestimate; the true figure may be 10-15%.

Stale data for some countries

14 countries in the cross-section have their most recent abortion data from before 2010. Austria’s data is from 1988 (the last year Eurostat has Austrian abortion statistics — Austria stopped reporting). Other notably old: Turkmenistan (1990), Brazil (1991), South Korea (2005). Median year of most recent observation is 2017.

“Study” estimates vs official statistics

23 of 97 countries in the cross-section use abortion counts from academic studies or surveys rather than official government statistics. These are often one-off estimates with different methodologies, making cross-country comparison difficult. Countries relying on study data are predominantly in Latin America, Africa, and Asia — precisely the places where official reporting is weakest.

Pregnancy rate denominator mismatch

Our pregnancy rate uses women aged 15-64 as the denominator (from WDI), while TFR sums age-specific fertility rates over ages 15-49. This creates a systematic wedge: countries with older/younger age structures will have different ratios of TFR to our computed pregnancy rate. The multiplicative model TFR ~ preg_rate * (1 - pct_abort) achieves R² = 0.98 cross-sectionally and within-R² = 0.90 in the panel, with the residual largely attributable to this age-structure mismatch.

Pregnancies exclude miscarriages and stillbirths

Our pregnancies variable = births + abortions, omitting spontaneous pregnancy losses (miscarriage, stillbirth), estimated at ~10-20% of recognized pregnancies. This doesn’t bias the pct_abort calculation much (it affects both numerator composition and denominator equally), but it means our “pregnancy rate” is better described as “recognized pregnancy rate resulting in birth or induced abortion.”

Eurostat gap-filling

For 30 European countries, GAID had no data but Eurostat did. We filled these gaps with Eurostat counts. Eurostat reports only legally induced abortions, which may undercount where clandestine abortion exists (though this is minimal in most of the EU).

Generally, the correlations are positive as expected -- countries that have more top players per capita in one game also have more in other games -- but not entirely so. There are some clear clusters in the data related to game type and platform (PC vs. mobile). The top left cluster are mobile games. Chess.com is also there as the only non-esport of sorts, even though it is played on a computer. It’s mostly uncorrelated with the others. These are the top 30 games, which is an arbitrary number I chose, and one could pick a larger number. Since I wanted to do factor analysis on these variables with ~150 countries, I cannot have too many games as it makes the results potentially unstable.

I need to pay for baby food 👶, so if you want to read this, you will have to help pay for the baby food.

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The reader is left to interpret that guns cause homicides. It’s correct if we include suicides but it’s not true for homicides as a whole:

But then again, we know that homicide rate is mostly related to which % of the state is Black. The leftists are trapped. To show that gun ownership causes homicides -- how could they not? it’s an effective and easy to use method -- they need to control for the confounders. But that would mean doing regressions and seeing that Black% is the main variable, a big no-no. So I don’t know what they do, I guess just nothing except to post gun ownership vs. gun deaths. Anyway, we can still examine this question. We can do the analysis at the state level, but with n = 50/51, this isn’t statistically great. We want the county-level data for more precision and to avoid whatever aggregation biases exist for state-level analysis. The problem is that there are no reliable data of gun ownership % by US counties. There is no national registry of guns so there is no government data to rely on. There are some very large surveys from 20 years ago that asked people about gun ownership in the home (BRFSS), but then they stopped including that question in the survey for ? reasons. So researchers found a clever proxy to use: firearm suicide % of all suicides. The idea being that the more firearms are around, the more people will kill themselves with them as opposed to some other method. It makes sense, even if the scaling may be nonlinear. Still, even the large surveys are not sufficiently large to have enough people from all 3100+ US counties. One can accept this and use data from the largest counties, or one could impute the missing data using data we can precisely measure even in small counties. Such data are things like % of people below 18, median age, White%, Asian%, % with bachelor’s or more degree, and Republican vote %. If we train a model on the counties where we have enough data (city areas merged from multiple counties), and validate this model, then we can impute the values for the counties where we don’t have enough survey data. And we can also validate this against the firearms suicide method as an independent validation.

The task is extra difficult here because we must predict potentially out of range from the training data. The training data does not have any data for rural counties with small populations and high gun ownership rates, but we must somehow predict these correctly. We don’t care about model interpretability here, just predictive validity, so we can use fancy machine learning algorithms that can capture nonlinear and interaction effects. I tried a few different models from the simplest (ridge regression) to the more flexible (xgboost, SVMs). Still, we have to recall that we only have 118 large counties to train on (MMSAs), so we have to be rigorous about overfitting issues.

First, though, let’s look at the state-level regressions for predicting homicide rates:

We see that in model 2, firearm ownership does not predict beyond chance alone, but when combined with demographics, it does predict positively as expected. Leftists and hereditarians are both correct: Black% explains most homicide rate variation, and gun ownership explains some net of this. It’s coefficient is p < 1%, and not that small. Going from 0% to 100% gun ownership predicts 7.2/100k homicides more, which is a lot because the US average is 5.3, so more than a doubling. In reality, the states range from 9% (Hawaii) to 64% (Wyoming), which suggests that in Wyoming the homicide rate is 7.2*0.59=4.2 higher than it would otherwise be. We can see that the model is not well-behaved because the actual rate in Wyoming is 3.4, and it can’t become -1.2.

We repeat for the large counties with large enough samples in BRFSS survey:

Here gun ownership predicts in both models, but it’s a poor predictor (about 2% variance), and yet it retain p < 1% with the demographic controls. And finally for all the counties including the imputed ones:

Now it predicts... negatively alone, presumably because of high estimated ownership% in White rural countries with low homicide rates, and it predicts slightly positively net of demographics (p < 5%). This decline in slope is possibly related to our imputations being dodgy for these units, but note that Black% is also smaller. This relates to sampling errors in the outcome variable as well I think, which can also be seen in the R2 being lower.

The reason for writing this post was that someone asked me about a potential Black% * firearms interaction:

There’s nothing for the datasets where we have high quality estimates, but there’s a strong negative interaction for the imputed data. I am not sure what to make of this. Gun ownership protects against Black homicides? Dubious. The issue is that the small-n models cannot estimate these values precisely (SEs about 20), which is also why Black% is unstable (non-sig for states). We didn’t get much more wise with this interaction test analysis since the 2 datasets with reliable data are underpowered, and the one with sufficient power relies on questionable imputations.

So, how confident are we in these imputations? Here’s the model accuracies and calibrations:

There’s a few different metrics to be concerned with. LOOCV (leave one out cross validation) is out of sample R2 in the training sample, more is better. The state values are for the quasi out of sample test using the aggregate state data. Here it is important to have both high R2 and slope=1 and intercept=0. The SVM does best, but XGboost is about the same. The issue with XGboost is that it cannot predict values not seen in the training data (because it is a decision tree model). Thus, it cannot predict very high ownership % for rural counties because these aren’t in the training data to begin with. For this reason I went with the SVM, which can extrapolate beyond the observed range. The advantage of the SVM and XGboost is that they can capture nonlinear effects and interaction effects, which lasso/ridge don’t by default because they are just OLS models with penalization (one can manually specify interactions and splines, but then one has to do a lot of testing to find them). State level correlation matrix:

RAND is the RAND institution’s estimates of % of households with firearms, BRFSS is the one based on the large surveys. They correlate at 0.91. Firearms suicide % is the other method, which correlates at about 0.85 with the others. Pretty good.

Here’s the correlations at county level, split by large and all:

Bottom half has the full dataset, upper only the large counties used for training. There’s no BRFSS data for counties, only the aggregated city data, so those cells are empty. In the all data part, we see that the correlations for imputed values and the firearm suicide % are similar, except for the correlation with Black% which changes sign. May be a problem. We don’t have any ground truth for the counties, so we just kinda have to have faith that the imputations generalize to the small-n counties based on the city data. We know they generalize to the states, even the ones that weren’t used for training. Overall, though, it does seem like more guns means more homicides in general, net of demographics and our county-level analyses back this up, just not entirely convincingly so.

R notebook. OSF repo.

• Kirkegaard, E. & Jensen, S. (2025). Meta-Analysis of American Race Differences in Intelligence. Mankind Quarterly, 66(2), 290-300. https://doi.org/10.46469/mq.2025.66.2.5

We present a meta-analysis of 139 U.S. studies (1918–2017; N = 400,000) examining racial differences in intelligence averages and distributions. Studies were included if they used representative U.S. samples, IQ tests with at least 3 subtests, reported White reference groups, and provided sufficient statistics to compute Cohen’s d. Studies were excluded if samples were unrepresentative (e.g., elites, college-only, selective cities), duplicated, lacked general ability differences, lacked within-group SDs, lacked a White comparison group, or relied on scholastic achievement tests. Random- and mixed-effects meta-analytic models were used to estimate racial means. With the White mean set to 100, averages were 82 (Black), 89 (Hispanic/American Indian), 105 (Asian), and 109 (Jewish). Evidence indicates small study effects inflated Black mean IQs. Variances and distributions were similar across races, and there is strong evidence against convergence in intelligence between Blacks and Whites in cohorts born after 1960.

It’s been a long time since Roth et al 2001, the last comprehensive meta-analysis. After that there was only the Dickens and Flynn 2006 vs. Murray 2006 exchange. The issue with DF was that they extrapolated changes, and these extrapolations turned out to be very wrong. There are a newer of more recent studies all of which showed normal gap sizes for Black-White. However, the only way to show that was to do a new comprehensive meta-analysis. Finding someone willing to dig through 1000s of papers to build the database is difficult, but Jensen was up for the task. And so now we can present the newest meta-analysis of American race gaps in IQ. Main table:

Our results are about the same as the earlier studies, which is not surprising because we just added a few studies to an already existing large literature dating back over 100 years. The more interesting point was the funnel plot:

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So everybody knows that race predicts crime, that is, members of some races are more likely to be criminals than others. These rank-orders are mostly not but entirely consistent across time and place, which I reviewed previously. In the USA, Blacks (~80% African ancestry, ~20% European) have by far the highest crime rates with a homicide rate about 6-10x the White one, depending on time:

Given this strong association at the individual level, the geography of crime in the USA is to some extent a map of where Blacks live:

The other red spots are Amerindian places, mainly reservations, and these are very sparsely populated. This isn’t so obviously to people who haven’t been there, but it looks like this:

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So I decided I wanted to dig into these findings and conduct a large-scale comprehensive replication. I surveyed Americans on Prolific and only targeted those with completed fertility in ages 50-69. I wanted to try out the Multifactor General Knowledge Test on another sample. It has an odd response format, where it shows you 10 options and says “Pick the 5 things that are X and don’t pick any things that aren’t X”. You get 1 point for each correct thing you picked and 1 point for each incorrect thing you didn’t pick. There are 32 questions, and thus one can get 320 points at most. We shall see that this format presents severe psychometric issues that I didn’t previously see, and Seb Jensen didn’t note them in our paper on this test. In addition, I put together a few questions to measure overall religiousness, a standard US-style left-right scale, and a checklist for mental illness diagnoses. Thus, putting all of this together, we should be in a decent position to find those pesky effects. They are hard to find because the intelligence fertility correlation is weak to begin with, about 0.10, and we are looking for relatively week interactions with that, say, that changes it to 0.00 or 0.20. This require a lot of statistical precision.

This post is basically the preview of the academic write-up of this article, since I just finished the analyses after waiting some months for the data collection to finish.

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So you tell people that some treatment/policy was given to two groups of people/units. The trick is that these groups are of unequal size, instead of the intuitively expected 50-50% that we usually see in randomized controlled trials. As such, one cannot just look at the counts of units that improved with treatment, one must calculate the fractions and compare those. Doing those numbers in the head is a bit obnoxious, but clearly the 223/75 (2.97 OR) is smaller than 107/21 (5.09 OR). Depending on which labels are put on, then, the subject just has to 1) realize that fractions or odds ratios are to be used, not raw counts, 2) determine which number is higher, and 3) click the right option. In the top left table (A), thus, the hypothetical cream was effective against the rash since the proportion of people who got better is higher. The labels are just for distraction and it’s a relatively simple math question. To do the study, then, you survey some people and give them a random subset of these questions, with labels chosen at random, some political, some not. If you gave them all of them, they would figure out the trick and the study probably wouldn’t find too much of interest. Before giving them these questions, you measure their numeracy IQ and ask their political leanings. Now you are ready to fit some regression models to predict whether a given person solved the trick questions. The way motivated reasoning/Bayesian priors enters the picture is that if people already think the conclusion is true (guns prevent violence, say), then they are probably less likely to double check their math, and thus more likely to make mistakes. For the control condition of the cream and rash (non-political):

We see the expected effect of numeracy increasing the chances that people get that item right. But what about the political versions?:

Here they just split the sample in 2 by political leaning (left vs. right). For the gun ban vs. violence, their plot shows that numeracy seemingly does not predict getting the trick question right unless it aligns politically. Thus, it appears both sides have about equal motivated reasoning/Bayesian priors.

So what is the issue? Their sample size is fairly reasonable, 1100 Americans fairly balanced for politics (Yougov data). But there are some replication studies. First Kahan et al published their own n=800 people direct replication in reply to some critics:

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They then dutifully collected some survey data to see how this scale correlated with various other aspects of humanity. Their results are reported in a number of Pearson correlation matrices, but this doesn’t properly showcase their results. So I downloaded their data and had a closer look. First, the sex difference:

A non-trivial sex difference emerged, as you might expect. This is better than the paper’s report of a Pearson correlation of 0.19. The mental trick is to double the correlated to get the Cohen’s d. This works when 1) the correlation is relatively small, and 2) the groups are balanced. Both apply here so the quick and dirty method works, but it doesn’t work as well for race:

The Black-White difference is 0.56 d, whereas the paper reported a correlation between non-White of 0.10. The issue is that the sample is unbalanced, so the Pearson correlation is forced downwards and ended up hiding a quite substantial age. For age:

There is a weak negative correlation with age (-0.1), and women are higher at every age. The slope appears to be more negative for women, but it’s not beyond chance levels.

The study had a bunch of self-report mental health scales covering the usual stuff, anxiety, depression, emotional regulation, PTSD-like. I collapsed these to a single general psychopathology factor score (P). I included the neuroticism part of the Big Five/OCEAN for this. General factor from bifactor model was strong, omega_h = 0.86 fra CFA, and shows this correlation:

The correlation isn’t massive, r = 0.19, but it isn’t trivial either. Finally, politics:

Or by party choice:

Which replicated the stereotype about the insensitive libertarian, who is about 1 SD lower on this scale than the Democrat voters.

Some of the above may not be that independent, say, age could just be a proxy for leftism or non-White, since younger people are more leftist and less White. Some regressions to clarify:

The age effect was already marginal to begin with, and it disappears entirely when leftism is included in model 3. The mental health variables are approx. orthogonal due to the bifactor model, so the effect of anxiety is particularly strong since there is both an effect of high general mental pathology and an effect of anxiety separately. We can compare the effects more cleanly in another way by looking at the partial epsilon values:

These are akin to parital R2’s giving us independent variances explained by different variables. These are different than the standardized betas because standardized betas can be large and yet explain little variance if they are highly redundant with other variables. I have also taken the square root so they are on a correlation-like scale instead of the nonlinear variance scale. What it shows is that there are 5 variables of approximately equal importance in explaining the variation in belief in magic words in this dataset. These values depend on sample composition, so if the sample had fewer Blacks, the effect size would decline (you can’t explain a large proportion of variance in an outcome with a predictor that has little variance). In line with our work with the Finnish data, anxiety independent of general psychopathology seems to be particularly important for explaining some other variables. Still, the overall model only mustered to explain 20% of variance, so I don’t know what explains the remaining 80%. The scale seemed pretty reliable, so not too much of this can be ascribed to unreliability of the outcome variable.

That’s all I could think of. Thanks to Sam Pratt for making their data public. I hope this post can help their study get more attention. R notebook is here.

• James Burnham 1964 political quiz “Are you a liberal?“ that people were talking about on X some weeks ago

• Figure reasoning test (44 items), which is made using an algorithm I developed some years ago. Seems appropriately difficult since the mean score is 25.

• Fluid reasoning test (14 items, 2 minutes timed), from the UK Biobank. This is the one all those GWASs are based on.

• IPIP NEO Big 5 + facets test (300 items), for people who enjoy these

• SPI-135, an alternative factor structured scoring giving 27 smaller traits like trust, sociability, and impulsivity

• The Pew Research Science tests (years 2013, 2015, 2019) combined into a 35 item version. This one has US representative norms

• A 25 item science knowledge test I posted on the internet years ago (with some overlap with the Pew test for comparison purposes)

• I’ll add some more every day or so.

Taking a test gives you a results page, like this one for the UKBB fluid reasoning test:

Yes, I missed the last item. I checked the server logs and I had 50 seconds remaining but I didn’t see the timer (top right corner), so I thought I had used too much time and the timer was bugged. Oh well.

Or the 27 smaller personality traits:

I posted these on X, and this gave us quite a bit of data for that Burnham (Suicide of the West) test:

There is no login, but the site saves a cookie on your device, shown in the bottom of the page. You can just save that value and make all your devices use the same ‘account’. Eventually, this will enable us to correlate responses across tests. So far, the overlap isn’t amazing, but I guess with enough data it will eventually be:

If you know if some good stuff to include, post it in the comments.

The methods we consider here are:

1. Raw score: positive / total. Unbiased but noisy at small n.

2. SteamDB formula: score - (score - 0.5) * 2^(-log10(n + 1)). Shrinks toward 50% with an ad hoc decay function.

3. Wilson lower bound: Lower end of a 95% confidence interval for the proportion. Conservative — designed to answer “what’s the worst this game plausibly is?”

4. Laplace smoothing: (positive + 1) / (n + 2). Bayesian posterior mean with a uniform Beta(1,1) prior. Shrinks toward 50%.

5. Empirical Bayes: (positive + a) / (n + a + b) where the Beta(a, b) prior is estimated from the observed distribution of game ratings via method of moments. Shrinks toward the actual mean rating (~85%) with data-calibrated strength.

Results by method and game ranking:

Lower error is better, so we see that for the representative sample of games (2.2k games), the theoretically superior empirical Bayes is in fact also the best method, and the worst method is using the lower confidence interval. The high error of the lower CI is not surprising because it is not actually a shrinkage estimator at all, though it can sort of be used as a penalization method. All the methods converge after about 1k reviews are in anyway. For the top ranked games, both the Bayesian methods (informative and uninformative priors) and the raw mean are about the same except for small review counts. For the top ranked games, the situation is artificially easy because they were selected for analysis because of their final high ranking, so not much shrinkage is ever needed, and the prior can be very accurate anyway.

We can also look for bias in the estimates, that is, degree to which they are systematically too positive or too negative:

The raw mean cannot actually be biased as a method, but it appears biased because earlier votes for a game are slightly more positive than later reviews. Specifically, the first 10 ratings are 4%points more positive than the final average after at least 5k ratings, on average across the games. The two Bayesian methods show slightly smaller biases. The Laplace version has a negative bias because it uses a wrong prior (like the SteamDB formula). The two last methods are just generally bad and should not be used for this purpose. The SteamDB method is the worst because it still shows a significant negative bias even after 1000 ratings, which is to say, it penalizes smaller games. Literally doing nothing would have been better. The site might as well just limit their top list to games with at least 1000 votes and this would be better.

Some randomly chosen games for illustrative purposes:

Here we can see the insider/friend voting for 3 games that have uniformly positive votes (red line being at the top) for a while until they end up with shit averages after unrelated people start rating them. We also see another issue with these data: games may simply improve over time, giving rise to an apparent reversal effect. Assuming that games have a kind of stable long term, fixed rating is not really correct, but a statistical fantasy. Nevertheless, the Bayesian method with the informative prior is the best if one wants to be nerdy about it (and I do), but these sites might as well just use a hardcoded minimum of X ratings to considered for inclusion in their top lists.

Mea culpa

Speaking of the above decline effect, a few days ago I wrote a blogpost about there being no detectable recency effect in Steam game ratings. This was wrong because of data error. The issue is that Steam’s API returns newest reviews first, and I limited games to 50k reviews, which means that I had the latest 50k. For a subset of games, these reviews did not include the first ratings because the game had more than 50k ratings, and thus the votes were being incorrectly encoded as being e.g. number 1, 2, 3, whereas really they were perhaps number 99991, 99992, 99992 etc. Numerically, though, most of the data was correct and the decline effect is relatively weak. It’s about 4%points for a typical game across 5 years:

Or comparing earlier to later ratings:

0th centile is the first rating and 100th is the last. This across the rating history, the average game declines about 4%points on a 0-100% scale, which is fairly small. Much smaller than the IMDB recency effect.