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National Intelligence and Economic Growth: A Bayesian Update

  • Ulster Institute for Social Research


Since Lynn and Vanhanen's book IQ and the Wealth of Nations (2002), many publications have evidenced a relationship between national IQ and national prosperity. The strongest statistical case for this lies in Jones and Schneider's (2006) use of Bayesian model averaging to run thousands of regressions on GDP growth (1960-1996), using different combinations of explanatory variables. This generated a weighted average over many regressions to create estimates robust to the problem of model uncertainty. We replicate and extend Jones and Schneider's work with many new robustness tests, including new variables, different time periods, different priors and different estimates of average national intelligence. We find national IQ to be the "best predictor" of economic growth, with a higher average coefficient and average posterior inclusion probability than all other tested variables (over 67) in every test run. Our best estimates find a one point increase in IQ is associated with a 7.8% increase in GDP per capita, above Jones and Schneider's estimate of 6.1%. We tested the causality of national IQs using three different instrumental variables: cranial capacity, ancestry-adjusted UV radiation, and 19 th-century numeracy scores. We found little evidence for reverse causation, with only ancestry-adjusted UV radiation passing the Wu-Hausman test (p < .05) when the logarithm of GDP per capita in 1960 was used as the only control variable.
MANKIND QUARTERLY 2022 63.1 9-78
National Intelligence and Economic Growth: A Bayesian
George Francis*
Independent Researcher, United Kingdom
Emil O.W. Kirkegaard*
Independent Researcher, Denmark
* Addresses for contact: and
Since Lynn and Vanhanen’s book IQ and the Wealth of Nations (2002),
many publications have evidenced a relationship between national IQ and
national prosperity. The strongest statistical case for this lies in Jones and
Schneider’s (2006) use of Bayesian model averaging to run thousands of
regressions on GDP growth (1960-1996), using different combinations of
explanatory variables. This generated a weighted average over many
regressions to create estimates robust to the problem of model
uncertainty. We replicate and extend Jones and Schneider’s work with
many new robustness tests, including new variables, different time
periods, different priors and different estimates of average national
intelligence. We find national IQ to be the “best predictor” of economic
growth, with a higher average coefficient and average posterior inclusion
probability than all other tested variables (over 67) in every test run. Our
best estimates find a one point increase in IQ is associated with a 7.8%
increase in GDP per capita, above Jones and Schneider’s estimate of
6.1%. We tested the causality of national IQs using three different
instrumental variables: cranial capacity, ancestry-adjusted UV radiation,
and 19th-century numeracy scores. We found little evidence for reverse
causation, with only ancestry-adjusted UV radiation passing the Wu-
Hausman test (p < .05) when the logarithm of GDP per capita in 1960 was
used as the only control variable.
Key Words: Human capital, National IQ, Economic growth, Bayesian
model averaging, Intelligence, Smart fraction
Much research has found that national IQ is associated with per capita GDP
and economic growth, suggesting cognitive skills are important for prosperity.
However, it is unclear exactly how robust this relationship is and how important
this theory is compared to alternative theories. Merely reporting regression
models is not sufficient. Researchers can choose what variables to employ and
what models to report that best support their own theories. Moreover, only so
many variables can be included in a model, allowing for few comparisons
between national IQ and other explanatory variables.
Jones and Schneider (2006) came closest to addressing this problem. They
performed Bayesian model averaging of economic growth, running thousands of
regressions with different explanatory variables, including national IQ, and then
took a weighted average of these results. National IQ was in 96% of the models
after the models were weighted according to how well they fitted the data,
suggesting national IQ is very good at predicting economic growth. Unfortunately,
Jones and Schneider did not report results for other variables making any firm
comparisons between national IQ and other variables difficult. Furthermore,
recent literature on Bayesian model averaging and economic growth has found
the results to be very sensitive to minor changes in the data and priors used
(Bruns & Ioannidis, 2020; Ciccone & Jarociński, 2010; Rockey & Temple, 2016).
Just as with regression models, it is not sufficient to only present one or a few
Bayesian model averages, rather a large range should be used if we are to be
confident in the results.
In this paper, we replicate and extend Jones and Schneider’s (2006) work by
employing national IQ in Bayesian model averaging. We standardize our
variables and present the results for all variables possible to compare national IQ
to rival theories of economic growth. We use a long series of stress tests from the
Bayesian model averaging literature and others we have come up with. This
includes resampling, different datasets, different priors, and different time periods.
This is to see if national IQ is robust or whether Jones and Schneider’s results
were merely a fluke from the sensitivity of Bayesian model averaging.
We also review the prior literature on causality and use instrumental variables
to test this. GDP per capita at the start of the observation period is used as a
“fixed regressor” in all regressions, meaning it is not a variable we test in this
paper. We use the term fixed regressor not in the traditional way it is used in time
series econometrics, but rather to mean that it is forced into every regression that
is model averaged, ensuring its posterior inclusion probability (PIP) is always
equal to one.
Compared to all other tested explanatory variables, we find national IQ to be
the most important predictor of economic growth. In every set of stress tests, we
find national IQ to have the largest average coefficient and the largest posterior
inclusion probability. Our results suggest each IQ point increases GDP per capita
by 7.8% compared to Jones and Schneider’s 6.1% estimate. We extend the use
of Bayesian model averaging to re-evaluate many questions in the national IQ
literature. We test smart fraction theory whether the mean IQ or that of another
part of the IQ distribution best predicts economic growth, as well as rival
psychological explanations of economic growth, finding national IQ to dominate
them all. We also test whether national IQ affects economic growth through an
exogenous model, an endogenous one, or a Nelson-Phelps technology diffusion
In section 1 we summarize the literature on how national IQ can function as
a measure of human capital. In section 2 we review the issue of model uncertainty
and how Bayesian model averaging has tried to respond to this problem. In
section 3 we explain our Bayesian model averaging methodology. In section 4 we
explain what data we use in this paper. This includes which national IQ measures
are used, such as the World Bank’s Harmonised Learning Outcomes, what
measures of GDP we use, what datasets of control variables we employ, and the
additional variables we employ in stress tests. In section 5 we present our main
results using Bayesian model averaging to test the robustness of national IQ and
Smart Fraction theory. Section 6 discusses the problem of causality and tests this
with instrumental variables. In section 7 we review the general limitations of our
methodology. In section 8 we draw our conclusions and describe their
implications for policy and the future of the world economy. In an online
supplement we discuss our results in the context of endogenous and exogenous
models and test the Nelson-Phelps technology diffusion model.
Section 1: National IQ as a Measure of Human Capital
Economists have empirically tested the role of human capital in causing
economic growth since at least Mankiw, Romer and Weil (1992). Typically studies
have used years in education, such as Barro and Lee’s years in education
measure (1993), or enrollment rates in education as in Sala-i-Martin (1997) and
Sala-i-Martin, Doppelhofer and Miller (2004). However, despite the correlation
between the level of education and economic growth, increases in education have
sometimes been found to have no relationship with economic growth (Hamilton
& Monteagudo, 1998) or even a negative relationship (Pritchett, 2001), calling
into question whether variation in education is a satisfactory indicator of variation
in human capital.
An alternative approach to measuring human capital as a predictor of
economic growth has been to use measures of human intelligence or attained
academic ability rather than amount of schooling focusing on educational
‘output’ (Hanushek & Woessmann, 2015), rather than any supposed ‘inputs’. If
education is ineffective at improving ability (see Caplan, 2018 for a review), or is
heterogeneous in its quality, or simply only one of many causes of variation in
human ability, then a direct measurement of a people’s cognitive ability may
better measure their human capital. If more capable countries tend to have more
education, then it may be confounded with human ability explaining education’s
apparently spurious relationship with growth.
Although this output-based approach to human capital had been suggested
by Barbara Lerner (1983), its relationship with economic output was only tested
and supported in regression models by Hanushek and Kim (1995) and Lynn and
Vanhanen (2002). Lynn and Vanhanen created “national IQs” using samples of
psychometric IQ tests from countries around the world to create average national
IQs to test their effect on GDP. By contrast, Hanushek and Kim used the results
of recurrent international student assessments in mathematics and reading to
create measures of education quality to predict economic growth.
Many further studies have been published studying economic growth with
data from student assessments such as PIRLS, TIMMS and the OECD’s
Programme for International Student Assessment (PISA) (e.g. Angrist et al.,
2019, 2021; Hanushek & Woessmann, 2015; Lim et al., 2018) and IQ tests (e.g.
Christainsen, 2020; Meisenberg, 2012; Ram, 2007, Weede & Kämpf, 2002),
finding these variables to have positive and significant coefficients. Furthermore,
some studies have used both student assessments and national IQs or even
combined them (Rindermann, 2008, 2018). Both student assessments and
national IQs appear to measure the same construct, cognitive ability
(Rindermann, 2006, 2007), as they correlate at 0.8 or more at the national level
(Meisenberg & Lynn, 2011). For the sake of ease, we refer to all measures of
national average cognitive ability as ‘national IQ’, rather than just average IQ
scores from nationally representative samples.
There are strong theoretical reasons for supposing that IQ would make an
appropriate measure of human capital. For a start, intelligent people tend to be
more productive workers. Psychologists have found smarter workers are more
productive in their occupations (Gottfredson, 1986, 1997). One IQ point is
associated with approximately 1% higher wages (Behrman et al., 2004; Bishop,
IQ stands for intelligence quotient and was originally invented to measure cognitive
ability by dividing scores by the test taker’s age, hence the term ‘quotient’. The term is
somewhat of a misnomer when used in ‘national IQ’ because modern IQ tests do not
divide by the test taker’s age and they are designed for individuals rather than nations.
Nevertheless, it has become commonplace to refer to national cognitive ability as
national IQ, so we follow this practice.
1989; Cawley et al., 1997; Grosse et al., 2002; Neal & Johnson, 1996; Zax &
Rees, 2002).
It is clear that individual differences in intelligence could cause large
individual differences in income. However, the magnitude of differences in the
average intelligence of nations also implies large differences of wealth between
nations. For example, in Lynn’s original IQ dataset (Lynn & Vanhanen, 2002), the
UK has a national IQ of 100 whilst Brazil has an IQ of 82, more than a standard
deviation (15 points) lower than the UK.
Figure 1. A ‘level 3’ difficulty question asked on PISA.
The magnitude and importance of national IQ differences may be more
clearly intuited by looking at the national results from individual questions on
intelligence tests. Take the question in Figure 1 from the OECD’s 2012 maths
PISA test given to 15-year-olds (accessed from:
2012/). It involves reading a table providing details regarding different cars. The
test subject had to find the car with the smallest engine capacity. This question is
considered to be of ‘level 3 difficulty’ by the OECD. Despite the ease of this task,
only 55% of OECD students scored level 3 or above. 80% of Singaporeans
achieved level 3 or above compared to only 18% of Mexicans, 13% of Brazilians,
and 8% of Indonesians. Inability to read tables would make any sort of analytical
work impossible and would even make simple tasks, such as reading a train
timetable, difficult for the majority of people in many countries. Given the
extraordinary differences in average cognitive ability between countries, we ought
to consider whether it could affect gross domestic product.
IQ’s effect on individual productivity is not the only explanation for why it
predicts economic growth. Jones and Schneider (2010) calibrated an IQ-
augmented Cobb-Douglas production function to model log GDP per worker in
the year 2000, using the 1% estimate of IQ’s effect on earnings. They found this
estimate of IQ’s effect could only explain 16% of the variation in national earnings,
whilst in a simple correlation (Lynn & Vanhanen, 2006) IQ can explain 58% of the
variation and each additional national IQ point is associated with 6.7% higher per
capita earnings. This “IQ paradox” suggests substantial reverse causation or
externalities, with intelligent people not fully internalizing the benefits of their
intelligence. We discuss the issue of causality in the ‘Causality’ section of this
Potential causes of externalities arising from IQ include its association with
free-market opinions (Carl, 2014a, 2015), with greater knowledge of economics
(Caplan & Miller, 2010), with lower time preference and more saving (Jones &
Podemska-Midluch, 2010; Kirkegaard & Karlin, 2020; Shamosh & Gray, 2008;
Yeh et al., 2021), with higher levels of social trust (Carl, 2014b; Carl & Billari,
2014), with cooperation in public goods games (Al-Ubaydli et al., 2016; Putterman
et al., 2012) and the prisoner's dilemma (Proto et al., 2019), national IQ’s
association with institutional quality (Jones & Potrafke, 2014; Kanyama, 2014;
Potrafke, 2012) and the prevalence of O-ring production functions (Jones, 2013).
For an overview of the mechanisms by which IQ could create externalities see
Jones (2016) and Anomaly and Jones (2021).
Section 2: Modelling Uncertainty
In growth modelling with IQ, and regression modelling generally, researchers
are faced with the problem of model uncertainty. Model estimates are dependent
on what variables are included, meaning reported significant results from a subset
of all possible models may just be an artefact. For example, with 50 potential
explanatory variables, there are  possible models, which is greater than one
quadrillion. How can we be sure the few models presented in a paper, or even an
entire literature, are representative and that the results are not just the result of
data mining?
Model uncertainty implies that regression results could be coincidental, and
it also allows researchers to ‘p-hack’ their results with specification searching
only presenting the models which best support their theories. In addition, journals
may prefer only to publish statistically significant results rather than null findings.
The economics literature seems to have been affected by specification searching,
as p and t values in published findings are less likely to be marginally insignificant
than would be expected by chance (Brodeur et al., 2016; Bruns et al., 2019; Vivalt,
2019). This indicates that economists are biased, consciously or not, and slightly
change their methodology until their results are statistically significant. This
should make us skeptical of the reported results from merely a few models.
Bayesian model averaging can potentially provide more accurate results free
from biases arising from selective model reporting (Zeugner & Feldkircher, 2015).
This methodology was first employed to study economic growth by Fernandez et
al. (2001) and Sala-i-Martin et al. (2004), although previous papers had attempted
similar methods by creating summary statistics from running many (Levine &
Renelt, 1992) or millions of regressions (Sala-i-Martin, 1997a,b).
This method involves running a large sample of possible models with
different explanatory variables and fixing a prior probability of each model being
the ‘true model’ before looking at the data. Then using Bayes theorem, a posterior
model probability is calculated for each model based on their marginal likelihoods.
The coefficients of explanatory variables are then calculated by weighting
coefficients in individual models by the model’s posterior probability. Furthermore,
a posterior inclusion probability (PIP) is calculated for each explanatory variable
which represents the sum of the posterior model probabilities of the models in
which the covariate is included. As such the PIP represents the explanatory
power of a variable and can be crudely understood as the probability of a variable
being in the ‘true model’ or the probability that a variable’s true coefficient is non-
zero. Moreover, by comparing the posterior inclusion probability of a variable to
its prior inclusion probability we can see whether the data tends to increase or
decrease our impression of whether a variable is a robust predictor. Full details
of Bayesian model averaging are given in the Methodology section.
To test how robust national IQ is as a predictor of economic growth, Jones
and Schneider (2006) used this variable in Bayesian model averaging of the
growth rate in GDP per capita. In addition to national IQ, they employed the 21
variables considered robust in Sala-i-Martin’s (1997a,b) paper ‘I just ran two
million regressions’. Jones and Schneider found that national IQ had an extremely
high posterior-inclusion probability of 96%. By comparison, the top three
performing variables in Fernandez and Lay’s (2001) study using Sala-i-Martin’s
entire dataset had PIPs of 99.5% (fraction Confucian), 99.5% (life expectancy)
and 94% (equipment investment). A 1 point increase in national IQ was
associated with a 0.11% increase in the GDP growth rate.
The results of Jones and Schneider (2006) provide strong support for the
relationship between economic growth and national IQ and suggest the significant
results of other studies are not the result of poorly specified models, whether by
coincidence or various forms of bias. Unfortunately, Jones and Schneider do not
provide the results for all the control variables, meaning that fifteen years on we
still do not have a clear picture of how important national IQ is relative to other
variables both in the size of its coefficient and its posterior inclusion probability.
Does IQ have the largest effect size? Are there many or any variables as robust
as national IQ? We hope to answer these questions.
The Bayesian modelling literature
Since Fernandez et al. (2001), Bayesian model averaging has been widely
applied to the study of economic growth, with focus on things such as the
jointness of growth determinants (Doppelhofer & Weeks, 2009; Ley & Steel,
2007), growth in specific regions (Cuaresma et al., 2009, 2013; Masanjala &
Papageorgiou, 2008; Próchniak & Witkowski, 2013a) and testing particular
theories of economic growth (Durlauf et al., 2008; Égert, 2015; Eris & Ulasan,
2013; Horvarth, 2011; Próchniak & Witkowski, 2013b). However, despite the
strong results of Jones and Schneider (2006), no one has employed national IQ
with Bayesian model averaging since.
Despite the popular use of Bayesian modelling, some researchers have
found the results to be extremely fragile to minor differences in methodology and
data. If the results of Bayesian modelling are unstable or unreliable, we may not
have confidence that Jones and Schneider’s (2006) results on IQ will replicate.
Ciccone and Jarocinski (2010) in their paper Determinants of Economic Growth:
Will Data Tell? re-ran the Bayesian modelling of Sala-i-Martin et al. (2004) using
different updates of the Penn World Tables (PWT versions 6.0, 6.1 and 6.2),
which provides the national accounting data for variables such as GDP. They
found that minor changes in the national accounting data were enough to
substantially alter the results of Bayesian model averaging. An extreme example
of this was the ‘Investment Price’ variable, which moved from having a posterior
inclusion probability of 98% to 2% depending upon the PWT dataset used. Thus
variables that could appear to be robust predictors of economic growth may not
be robust to measurement error.
Bruns and Ioannidis (2020) tested the sensitivity of Bayesian modelling using
multiple time periods from 1960 to 2010. They found the inferences on growth
determinants were unstable across time periods. The posterior inclusion
probabilities of determinants were evenly distributed across early time periods
preventing identification of which control variables were important. However,
Ioannidis and Bruns find more recent time periods show less even distributions
of posterior inclusion probabilities suggesting improvements in measurement
could cause Bayesian modeling to find more stable results.
In response to concerns about the sensitivity of Bayesian model averaging
some researchers have suggested methods to improve BMA. Feldkircher and
Zeugner (2009) proposed the use of flexible priors on model coefficients that
allow for ‘data-adaptive shrinkage’. Feldkircher and Zeugner (2012) show that the
use of these priors makes Bayesian modelling more robust to changes in the
Penn World Tables. Likewise, Rockey and Temple (2016) recommend the use of
fixed regressors to improve the stability of results, particularly the use of GDP per
capita in the starting year and regional dummies. However the use of flexible
priors and fixed regressors leads to PIPs being more evenly distributed making it
difficult to determine which variables are important.
In overview, Bayesian model averaging appears to be either very sensitive,
or it fails to discriminate between variables (Bruns & Ioannidis, 2020; Rockey &
Temple, 2016), resulting in ‘robust ambiguity’ with failure to find support for growth
regressors, except for GDP per capita in the starting year. Given that national IQ
has only been tested with Bayesian modelling by Jones and Schneider (2006), it
is reasonable to question whether it will replicate given the apparent conclusion
of robust ambiguity. To see whether national IQ’s posterior inclusion probability
is too sensitive to be robust, we run many sets of Bayesian model averaging,
using different datasets, different time periods, different versions of the Penn
World Tables, different priors, different fixed regressors, new potential confounds
of IQ, different national IQs, and resampling methods such as bootstrapping and
Jackknife resampling. In applying all the robustness tests in the BMA growth
literature and more, we ensure that our research employs the most challenging
set of tests in the literature so far. If national IQ performs the best in all these
tests, with the highest average PIP and coefficient in each test, we will consider
it to be the most powerful predictor of economic growth in the literature.
Ciccone and Jarocinski (2010) asked in the title of their paper Determinants
of Economic Growth: Will Data Tell?. We question whether the right data, national
IQ, is being used.
Section 3: Methodology
To perform Bayesian modelling averaging (BMA), we use the BMS package
in R. We draw heavily from the package’s tutorial (Zeugner & Feldkircher, 2015)
in explaining the methodology.
To model growth we can use a linear regression model of the following structure:
 
 󰇛󰇜
is our dependent variable, the average rate of growth in nations. is a
constant, the regression coefficients, and ε is the normal IID error term
variance . With many plausible control variables󰇝󰇞to employ as but with
a limited sample size, simply employing all variables would not be feasible.
BMA deals with the problem of model uncertainty by estimating models for
many possible combinations of 󰇝󰇞 and then taking a weighted average
over all of them. The models are weighted by their posterior model probability
󰇛󰇜 which can be derived from Bayes’ Rule:
󰇛󰇜 󰇛󰇜󰇛󰇜
󰇛󰇜 󰇛󰇜󰇛󰇜
󰇛󰇜 is the model prior and 󰇛󰇜 is the marginal likelihood of model
. 󰇛󰇜 denotes the integrated likelihood which is the same for all models.
The posterior model probability is thus proportional to the marginal likelihood of
the model times the prior model probability.
The marginal likelihood of model is given by
󰇛󰇜 󰇛󰇜󰇛󰇜
where 󰇛󰇜 is the likelihood of model and 󰇛󰇜 is the
prior density of the coefficients of model .
The key results we are interested in are the variable posterior inclusion
probabilities (PIPs) and the variable coefficients. The PIPs indicate what percent
of the posterior model mass is made up of models including regressor .
IID normality of error terms is certainly a strong assumption, nevertheless there has
been little discussion of its importance in the growth literature and the statistical
package we employ relies on this assumption. As such, we follow common practice by
keeping the assumption.
To be precise the PIP of is the sum of posterior model probabilities over
those models where is included.
󰇛 󰇜 󰇛󰇜
 󰇝   󰇞
is an indicator function that is 1 if regressor is included in model j and
0 otherwise. is the set of models that include .
How should we interpret PIPs? Sala-i-Martin et al. (2004) suggest comparing
the posterior inclusion probability to the prior inclusion probability. If the PIP is
larger than the prior inclusion probability, we can say that the data has updated
our priors in favor of variable . Sala-i-Martin suggests we use this as a
threshold for ‘significance’.
The model weighted density function for coefficients is represented above.
󰇛󰇜 represents the density function of coefficientgiven the data
in model , whilst󰇛󰇜 represents the marginal likelihood of model .
This explains the core mechanics of Bayesian modeling, but we need to elicit
what the model priors are to calculate the results. To perform BMA well we should
choose priors that are non-informative so that the priors have little impact on
posterior inference so we let the data come to its own conclusions rather than
forcing our own priors upon it. The standard method has been to follow Fernandez
et al. (2001) in assigning a ‘g-prior’ (Zellner, 1986) on and improper priors on
the constant term and the error variance. Improper priors are those that are
evenly distributed over their domain - complete prior uncertainty:
󰇛󰇜 
 󰇛󰇛
The key prior is the one on the regression coefficients. We assume a prior
mean of 0 on the coefficients. The variance structure is defined according to
Zellner’s g. This means we start with an expectation of all coefficients being equal
to 0 and our confidence in this prior is given by the term g. A small g represents
high certainty that the coefficients are near zero whilst a large one means we are
very uncertain that the coefficients are zero. A large g tends to concentrate
posterior model probabilities on a few best-fitting models, known as the
‘supermodel effect’ (Feldkircher & Zeugner, 2009), potentially making BMA
oversensitive to small changes in the data (Feldkircher & Zeugner, 2015), whilst
a small g can systematically underestimate all coefficients leading to ambiguous
Various values for g have been suggested. A brief explanation of popular g’s
are given in Table 1. Unfortunately there is no consensus about which value of g
is best. For a full review of different g-priors see Feldkircher and Zeugner (2009).
We take the Unit Information Prior as our standard in this paper, but use the rest
as a robustness test. The value of the Unit Information Prior is in its simplicity. It
sets g equal to the number of observations available, thus linking our confidence
in our regression results to the sample size the information available. The
Uniform Information Prior has been used widely in Bayesian model averaging
such as in the papers of Feldkircher and Zeugner (2012) and Rockey and Temple
Table 1. Descriptions of g-priors used.
Prior (UIP)
 , Sets g according to the amount of information available
which is the number of observations. This causes the Bayes factors
to behave according to the Bayesian Information Criterion (BIC)
(Kass & Wasserman, 1995).
Risk Inflation
Prior (RIC)
, Calibrates priors for model selection based upon the
Risk Inflation (Zeugner & Feldkircher, 2015)
Prior (BRIC)
 󰇛󰇜, Fernandez et al. (2001)
Criterion (HQ)
󰇛󰇜 (Zeugner & Feldkircher, 2015)
Local Empirical
Bayes (EBL)
Estimates a separate g for each model using its marginal
likelihood. (Zeugner & Feldkircher, 2015)
Hyper g prior
Uses a hyperprior distribution on g. Adjusts the posterior
distribution to reflect the data’s signal-to-noise ratio, reducing the
sensitivity of BMA (Feldkircher & Zeugner, 2009).
In addition to providing a g-prior, we need to choose a model prior. We use
binomial model priors, putting a fixed prior inclusion probability ofon each
variable which in turn determines the priors for each model. As such the prior
probability of a model size is
󰇛󰇜 󰇛 󰇜
represents the inclusion probability of each regressor and is the number
of regressors included in . In growth modeling, a model size of seven is
considered standard (Barro & Sala-i-Martin, 2003; Jones & Schneider, 2005;
Sala-i-Martin et al., 2004). As such we adjust in each set of regressions to
ensure the expected model size is 7. This means  where is the total
number of explanatory variables in our dataset. However, when fixed regressors
are used in addition to GDP per capita in the starting year, we increase the
expected model size to ensure our tested variables always have the same prior
probability of inclusion across tests of different fixed regressors.
Alternative model priors are possible. One approach is to make random as
done by Ley and Steel (2009) and Bruns and Ioannidis (2020). This is to reduce
the effect of possibly fixing the wrong model priors. Another approach is to set
equal to 0.5 resulting in uniform model priors. A problem with this approach is that
it centres the expected model size at , overweighting the more numerous
‘large’ models which can cause overfitting. Fernandez et al. (2001) and Jones
and Schneider (2006) use uniform model priors for example. Crucially, Jones and
Schneider only consider models of size 7 meaning there is no overweighting of
large models. Our approach of considering models of all sizes allows our results
to be influenced by the strongest models regardless of their size. Given the
simplicity of setting an expected model size of seven, we use this as standard
practice. Uniform model priors and random model priors are used as a robustness
There are two other important methodological differences between our
research and Jones and Schneider (2006). In their approach they use the
maximum possible sample size allowed in each regression. This means the
regression models are not being employed on the same observations making
them less comparable. In our approach we remove observations that cannot be
used in every possible regression model. Nevertheless, both approaches are
affected by selection bias into the sample.
Another difference is that Jones and Schneider (2006) enumerate all their
possible models and take a Bayesian average of them. They are able to do this
because they keep three regressors fixed, which Sala-i-Martin (1997) considered
to be particularly strong variables, ensuring there were fewer possible models.
We employ the same fixed variables only in our robustness test examining the
effect of different fixed variables. We avoid this approach to ensure we do
consider a wider population of possible models. To do this we only take a sample
of all possible models rather than enumerating all our possible models which
would take too long. To do this we use Markov Chain Monte Carlo sampler as is
standard practice in the prior literature (eg. Bruns & Ioannidis, 2020; Fernández,
Ley & Steel, 2001b). We use 200,000 iterations of models after a burn in phase
of 100,000 iterations of models. Due to time constraints, we used a tenth of the
iterations in each Bayesian model average within our bootstrapping approach
which involved 1,000 Bayesian model averages. We use 20,000 iterations of
models after a burn in phase of 10,000 iterations of models. By comparison, the
default settings for the BMS package, which is designed with the application to
economic growth in mind, uses 3,000 models after a burn in phase of 1,000
A final note regarding methodology is necessary. In every BMA run we
include the logarithm of GDP per capita in the starting year as a fixed regressor.
This is because prior literature has consistently found a strong negative effect of
the starting level of the logarithm of GDP per capita (eg. Barro & Sala-i-Martin,
2003, p. 496, p. 521) dubbed the advantage of backwardness. This has
theoretical roots in neoclassical growth models in which diminishing marginal
returns to investment allows poorer countries to grow faster. Given the high
correlation of IQ and other variables with GDP in the starting year, any models
that do not include GDP would bias national IQ’s coefficient downwards as it takes
on some of the effect of the advantage of backwardness. Given this potentially
large co-dependency of GDP per capita and other explanatory variables, we
follow common practice by including it as a fixed regressor.
Section 4: Data
National IQ
National intelligence can be measured in two ways. One way is the
psychometric method, administering IQ tests to more-or-less representative
samples within each country. These results were collected by Richard Lynn and
co-authors (Lynn & Vanhanen, 2002, 2012; Lynn & Becker, 2019). These scores
are adjusted for changes in IQ over time, the Flynn effect, assuming these
changes are linear and the same across countries. The UK’s score is then set to
100, and one standard deviation in IQ amongst British people is set to 15. This is
the ‘Greenwich mean IQ’.
The Lynn national IQ data derived from IQ tests have been criticized by
Wicherts et al. (2010a,b). The critics suggest that scores from Sub-Saharan
countries are implausibly low, do not use representative samples, and may be
unduly deflated by cultural factors, poor nutrition, and poor education. Lynn and
Meisenberg (2010a) have responded to these critiques defending the quality of
the national IQ scores. Lynn and Meisenberg argued many of the studies
Wicherts et al. used to show higher IQ for Sub-Saharan Africans are
unrepresentative because they are based on university students. David Becker
later went back to the sources and recalculated the national IQs with a more
rigorous set of conditions for inclusion (Lynn & Becker, 2019). These scores
correlated very well with Lynn and Vanhanen’s (2002) original IQ scores and
support many of the very low scores for the most underdeveloped nations.
Moreover, Lynn and Vanhanen’s (2002) IQ scores for Sub-Saharan Africans are
consistent with the results of the Southern and Eastern Africa Consortium for
Measuring Education Quality (SACMEQ) assessment (Sandefur, 2018;
Thompson, 2016).
Sample representativeness is a serious concern for using national IQs as a
measure of human capital. Other critiques are not necessarily so important for
economics research. Whilst psychologists may be concerned that culture,
nutrition and education quality may mask a nation’s ‘true’ or potential intelligence,
economists are interested in the actual, phenotypic ability that determines the
cognitive human capital of workers. These environmental factors may be
important for reverse causality, which we discuss in the Causality section of the
To avoid specific critiques based on the psychometric national IQ datasets,
we also repeat our analysis using a second set of cognitive measures: student
assessment tests. This includes the PISA, TIMSS and PIRLS tests which are
regularly given to students in a large range of countries testing proficiency in
mathematics, the native language, and science. As a measure of educational
output without pretensions of measuring ‘IQ’, these scores avoid criticism that
they do not in fact measure intelligence. Nonetheless, they appear to measure
the same cognitive human capital that IQ tests measure because their scores
correlate highly (r > .9) with different updates of Lynn’s national IQs (Lynn &
Meisenberg, 2010b; Meisenberg & Lynn, 2011). This strong relationship between
test scores collected by intergovernmental organizations and Lynn’s
psychometric national IQs strongly supports the validity of psychometric IQs.
Furthermore, student assessments have been popular amongst economists,
having been employed in various research (Hanushek & Woessmann, 2012,
2015) and used to create human capital measures for the World Bank (Angrist et
al., 2019, 2021; Lim et al., 2018).
Student assessment tests were available at the time Jones and Schneider
(2006) performed their Bayesian model averaging, but sample sizes were very
small. Since then, many more countries have had their school children take part
in these standardized assessments, allowing larger samples to be used in the
study of economic growth (e.g. Hanushek & Woessmann, 2015). Thus in our
replication of Jones and Schneider, we employ various measures of cognitive
human capital derived from student assessments to avoid criticism unique to
Lynn’s national IQ data. Furthermore, given the discussed sensitivity of Bayesian
model averaging, it is important to see whether minor variations in national IQ
data could alter the results.
Table 2. National IQ data.
Lynn &
Column ‘E’ of the ‘FAV’ tab, version 1.3.3 of the national IQ
dataset ( This variable recreates Lynn &
Vanhanen’s psychometric IQs, with different methodology
and selection criteria, weighting samples by their quality and
Lynn &
A simple average of Becker’s psychometric and student
assessment IQ scores.
Becker, SAS
Lynn &
Mean IQs calculated from PISA, TIMSS and PIRLS tests.
Hanushek &
Woessmann, SAS
Hanushek &
A ‘cognitive skills’ measure created from 12 different student
assessment tests from 1964-2003.
L&V 2002,
Lynn &
The original set of psychometric national IQs, standardized to
British IQ, adjusting for a constant Flynn effect
L&V 2012,
Lynn &
Updates Lynn & Vanhanen’s (2002) national IQ scores with
additional samples and countries.
Weighted average of psychometric scores and student
assessment scores, putting twice as much weight on SAS,
missing data extrapolated from International Mathematics
Rindermann, SAS
Student assessment scores from a range of tests
standardized across tests and time.
World Bank HLOs
Outcomes), SAS
Angrist et al.
Student assessment results standardized across different
tests. World Bank does not provide an average of these
scores across time so we only used HLOs from 2015.
For this study, we picked a wide range of publicly available popular
psychometric, student assessment (SAS) and mixed measures of national IQ. A
list and brief description of these variables are presented in Table 2. Our standard
national IQ is the mixed SAS and psychometric score of Rindermann (2018). This
measure has the largest sample size of all the national IQs because it uses a
wide range of student assessments and national IQs. This measure also ensures
a larger sample size for each country making IQ estimates more accurate. Finally,
the data puts a greater weight (3 to 1) on student assessment scores due to their
larger sample sizes, making it preferable to mixed national IQ scores from
Becker’s national IQ dataset. The rest of our selected national IQs are used as a
robustness test.
A correlation matrix for our national IQ variables is shown in Table 3. As in
the prior literature, cognitive skills whether measured via IQ tests, student
assessments or a mixture correlate extremely well. The lowest correlation seen
between any two measures is .83.
Table 3. National IQ correlation matrix; P = psychometric, S = school
achievement, H&W = Hanushek & Woessmann, L&V = Lynn & Vanhanen, R =
Rindermann, HLO = Harmonized Learning Outcomes (World Bank), mean r =
mean correlation with the other measures.
2002 P
2012 P
R, S
Becker, P
Becker, S
H&W, S
L&V 2002, P
L&V 2012, P
R, P&S
R, S
Control variables
We employ two different datasets of control variables in this paper. The first
is the dataset created by Sala-i-Martin, Doppelhofer and Miller (2004) used in
their Bayesian modeling, hereinafter named SDM. SDM first found variables that
predicted economic growth in the prior literature. From this group, only select
variables were included in the dataset if they had values sufficiently close to the
year 1960. Unfortunately, some variables start in 1965. This was to reduce the
problem of endogeneity. To ensure a large sample size, SDM then selected
variables that would maximize the product of the sample size and the number of
variables. This left SDM with 67 explanatory variables.
SDM studied the determinants of growth for the period 1960-1996. To
incorporate more recent GDP data, we employ the growth rate from 1960-2010
and use new figures for log GDP per capita. SDM’s GDP data came from version
6 of the Penn World Tables (PWT) whereas ours come from PWT 10 (Feenstra
et al., 2015), variable RGDPe, to provide log GDP per capita in the starting year
and the growth period. RGDPe is expenditure-side real GDP at chained PPPs, to
compare relative living standards across countries and over time.
The SDM dataset has two key advantages. The first is its large number of
control variables and large sample size. The second advantage is that it is a well-
tested and well-respected dataset having been used in many subsequent papers
using Bayesian modeling to study economic growth (eg. Ciccone et al., 2010;
Doppelhofer & Weeks, 2009). This limits criticism regarding our choice of control
variables and ensures we could not commit ‘data dredging’ specifically
designing a dataset to prove our hypotheses.
We could have used the dataset created by Sala-i-Martin (1997a,b) or the
subsection of it which was first used for Bayesian modeling by Fernandez et al.
(2001). The subsection takes only variables found to be ‘important’ and well-
performing in Sala-i-Martin’s (1997a,b) model averaging method and other
variables from the Sala-i-Martin data which did not reduce the sample size. This
subsection is also a popular dataset used in other papers on Bayesian modelling
(e.g. Horvarth, 2011; Ley & Steel, 2007). Jones and Schneider (2006) use a
subset of the Sala-i-Martin dataset, in a similar fashion to Fernandez et al. (2001),
but take only the significant variables.
We think the SDM dataset is superior to the Fernandez et al. and Jones and
Schneider dataset. Excluding plausible control variables, which model averaging
has previously found little support for, would undermine our goal of testing
national IQ against all plausible variables and theories. The rejection of the
excluded variables could represent a false negative, which may perform well
under different specifications.
The second dataset we use is the dataset used by Bruns and Ioannidis
(2020), which is itself intended to recreate a dataset similar to SDM. Hereafter the
modified Bruns and Ioannidis data is labelled the BI dataset. In their paper, Bruns
and Ioannidis test the stability of predictors across different time frames. This
restricts their variables to those that are available regularly for different periods.
This property of the dataset makes it easy for us to test the effect of national IQ
in different time periods from 1960 to 2010: 20-year time periods starting in years
divisible by 5. When we use this dataset, all control variables except national IQ
are taken from the starting year of the growth period. This is a substantial
limitation of our method which is discussed further in the Causality section.
Furthermore, Bruns and Ioannidis take many of their variables from recent
editions of the Penn World Tables. This allows us to easily perform a sensitivity
test using different editions of the Penn World Tables. Bruns and Ioannidis
attempt to further remove any endogeneity by removing variables describing
countries in the duration of the growth period, such as a socialist dummy, average
inflation rate, and proportion of time the country spends at war. Despite this, Bruns
and Ioannidis still employ a variable measuring growth in the terms of trade (that
is change in exports divided by imports), which we remove in our dataset.
Ioannidis and Bruns use time-invariant geographic variables used by SDM,
but which originally come from the Gallup et al. (2001) geography dataset.
Because the geographic variables contain the same missing variables, it would
not reduce our sample size to include additional ones. As such, to test national
IQ against a larger body of variables and thus plausible theories, we include
additional time-invariant geographic variables from the Gallup et al. (2001)
geography dataset.
A full list of all the variables employed in these datasets is given in Tables 11
and 12 of the Appendix.
Additional explanatory variables
To impose discipline on the estimation methodology, we have not added any
additional control variables to the SDM dataset, except NIQ. But we also do this
because these datasets have been optimized to maximize the sample size. If we
carelessly add additional variables, the efficiency of our Bayesian model
averaging could be severely affected. With Rindermann’s national IQ, the SDM
dataset has 82 observations and the BI dataset has 43 observations. These are
not sample sizes that should be decreased further unnecessarily. Thus to test the
effect of additional variables we use these as a single and separate test.
Additional variables included are given in Table 4.
The first type of variables we add are psychological ones. These are social
trust, time preference, and kinship intensity. Social trust is measured by how a
nation’s population responds to the following question from the World Values
Survey: “Generally speaking would you say that most people can be trusted or
that you can't be too careful in dealing with people?” Many economists have found
a positive relationship between a nation’s level of social trust and their GDP, see
Bjørnskov (2017) for a review of this literature. A trusting, or perhaps a
trustworthy, society can reduce the transaction costs of business and reduces the
risk of theft and rent-seeking in business (Algan & Cahuc, 2010, 2013). Intelligent
individuals (e.g. Carl & Billari, 2014) and intelligent societies (Rindermann, 2008)
tend to be more trusting. This suggests social trust might mediate national IQ’s
effect or that it might confound IQ’s effect on economic growth. Roth (2009) found
that with national fixed effects, social trust had a negative association with
economic growth. Later, Carl (2014) found social trust no longer predicted GDP
when IQ was controlled for. We replicate this test by including social trust as a
Table 4. Extra variables.
Variable name
Source and description
Social trust
Measure of self-reported social trust; from Carl (2014) and derived
from the World Values Survey.
Time preference
Time preference measure derived from surveys and correlated
variables such as credit risk; from Rieger et al. (2021).
Kinship Intensity
Measure of ‘kinship intensity’ from Schulz et al. (2019)
Fraser Institute’s Economic Freedom of the World index (Murphy
& Lawson, 2018)
UV radiation
Taken from Andersen et al. (2021)
Time preference or patience refers to how individuals value consumption
across different time periods. Less intelligent individuals tend to have a larger
time preference (Mischel et al., 1972, 1989; Watts et al., 2018), preferring smaller
rewards today over larger ones in the future. At the level of nations, time
preference has been estimated using the Global Preference Survey (Falk et al.,
2018) in which individuals are asked about how they would make trade-offs
between cash prizes given at different points in time. Time preference may
influence economic growth through higher savings and investment (Jones, 2010,
2012). Unsurprisingly, national IQ correlates with savings rates (Jones, 2010) and
time preference measures (Kirkegaard & Karlin, 2020) at the national level. When
Karlin and Kirkegaard tested national IQ and time preference as predictors of
national welfare, they found time preference was statistically insignificant when
IQ was included. Like social trust, time preference represents a potential mediator
or confound of national IQ so we include it as an additional variable.
Joseph Henrich (2020) has suggested that marriage patterns have played a
key role in determining the prosperity of the West. Rules created by the Catholic
Church discouraged Europeans from marrying their relatives, and therefore
exposure to the Catholic Church is associated with non-cognitive psychological
differences today (Schulz et al., 2019). This reduction of inbreeding is thought to
have reduced the intensity of kin-based institutions and allowed for individualism
which has driven innovation and capitalism. Henrich (2020) found individualism
to be associated with patents per capita. We employ the Kinship Intensity Index,
which measures the presence of cousin-marriage preferences, polygamy, co-
residence of extended families, clan organization, and community endogamy
(Schulz et al., 2019). As a novel variable to indicate psychological differences, it
is a natural rival to national IQ.
As mentioned in Section 2, smarter individuals tend to support a free market
(Carl, 2014a, 2015; Kirkegaard et al., 2017). Smarter nations tend to have a freer
economy which may mediate national IQ’s effect on GDP (Christainsen, 2020;
Rindermann & Thompson, 2011). The SDM dataset includes an old “Degree of
Capitalism” measure (Hall & Jones, 1999). However, the variable is not very
sophisticated (Christainsen, 2020) and is ordinal rather than continuous. To
improve upon this we employ the Economic Freedom Index created by the Fraser
Institute (Murphy & Lawson, 2018). In our test of additional variables, we add this
to the BI dataset and replace the Degree of Capitalism variable with the Economic
Freedom Index in the SDM dataset.
National variations in cognitive ability have often been explained as an
evolutionary adaptation to the challenges of cold winters (Frost, 2019; Lynn,
1987; Rushton, 1995). The theory fits the data with groups further from the
equator having larger cranial capacity (Kanazawa, 2008) and skin color having
the strongest relationship, of all variables, with national IQ (Templer & Arikawa,
2006). We discuss Cold Winters theory in greater depth in the Causality section.
If the theory is wrong, national IQ might only predict growth due to geographic
confounding. After all, many economists have found strong relationships
between absolute latitude (distance from the equator) and GDP per capita (e.g.
Nordhaus, 2006). Absolute latitude is already in the SDM and BI datasets, but to
better test IQ against possible climatic confounding, we also include UV radiation
as one of our extra variables.
Section 5: Results
Before using any of our robustness tests or additional variables, we ran
Bayesian model averaging with the BI and SDM datasets with Rindermann’s
national IQ scores. As expected, national IQ performs extremely well with a
posterior inclusion probability of 1. Its absolute coefficient is the largest of all
variables tested, not including log GDP per capita in 1960 because it is used as
a fixed regressor in all regressions. The SDM dataset has the larger number of
explanatory variables (81) and observations (69), whereas our BI dataset has 63
variables and 63 observations.
In the SDM dataset (Figure 2), national IQ has an absolute coefficient of 1.4,
implying a one standard deviation increase in national IQ is associated with a 1.4
percentage-point increase in the growth rate. In the BI dataset, national IQ has a
somewhat smaller coefficient of 1.2. Without standardizing our independent
variables, one national IQ point is associated with 0.09 percentage point higher
growth per year with the BI data and 0.11 percentage points in the SDM dataset.
If we interpret our results through the framework of an exogenous model, each
additional national IQ point is associated with a 6.5% larger GDP per capita in the
BI data and 7.8% in the SDM data. This compares with a previous estimate of
6.4% from Jones and Schneider (2006). Details of these calculations and
discussion of different growth models (exogenous, endogenous and the Nelson-
Phelps technology diffusion model) can be found in the online supplement.
Some other variables do perform well, with posterior inclusion probabilities
higher than their prior probabilities. In the SDM dataset there are five other
variables that pass this test: fraction of GDP in mining, primary school enrolment,
fraction of population living in the tropics, fraction of the country in the tropics,
trade openness. However, only the first three of these variables had posterior
inclusion probability greater than 0.5 indicating they are more likely to be included
in the best model than not. Moreover even of these variables the highest
coefficient is less than half of national IQ’s coefficient indicating IQ is substantially
more important than even best performing competitors.
MANKIND QUARTERLY 2022 63.1 9-78
Note: Dashed line denotes the prior inclusion probability
Figure 2. SDM data main results
The BI dataset has four other variables with higher PIPs than priors (Figure 3).
These are life expectancy, exports of primary goods as a percentage of GDP,
average distance to rivers, and average distance to the coast. The failure of
primary school enrolment to have a higher PIP than prior in the BI dataset should
make us skeptical of its robustness despite its good performance in the SDM
An important difference between our results and Sala-i-Martin et al.'s (2004)
results is that their East Asian dummy had the highest PIP, and fraction Confucian
was the 9th best variable. These variables do not perform well in our results. This
is likely due to the fact East Asian countries have high national IQs, and Sala-i-
Martin et al.’s variables were mostly proxies for high IQ. Likewise the Sub-
Saharan African dummy variable was the 10th best variable for Sala-i-Martin et al.
(2004). This suggests much of the regional effects found in prior studies might be
spurious due to being confounded with national IQ.
MANKIND QUARTERLY 2022 63.1 9-78
Note: Dashed line denotes the prior inclusion probability
Figure 3. BI data main results.
Results with additional variables
To test whether national IQ’s apparent success is due to omitted variable
bias, we ran the same Bayesian model averaging but with popular variables that
are related to or confounded with intelligence as represented in Table 4. National
IQ’s posterior inclusion probability falls from 1 to 0.96 in both datasets. The results
have barely changed indicating that national IQ’s predictive powers cannot be
explained by possible confounds.
UV radiation, time preference, social trust, and economic freedom did not
have a higher PIP than prior (Figures 4 & 5). This replicates the findings of Carl
(2014) and Kirkegaard and Karlin (2020) who respectively tested whether social
trust and time preference could explain national IQ’s relationship with economic
growth. The failure of UV radiation and latitude to robustly predict economic
growth suggests that IQ’s relationship with growth is not due to spatial
autocorrelation. The Fraser Institute’s Economic Freedom Index’s PIP is lower
than its prior in both datasets. This contrasts with Christainsen (2020) and Weede
and Kämpf (2002), who find that economic freedom is statistically significant in
their growth regressions which use national IQ. Nonetheless, this result is not
unexpected because degree of capitalism has shown inconsistent results in
studies using rigorous model averaging methods. For example, Sala-i-Martin
(1997) found that the variable was robust whilst Sala-i-Martin et al. (2004) found
the degree of capitalism to have the third lowest PIP out of 67 tested variables.
Note: Dashed line denotes the prior inclusion probability
Figure 4. SDM results with extra variables.
Only one of our extra variables, the Kinship Intensity Index, has a higher
posterior than prior probability. Moreover this result only occurs in the BI dataset.
It has a posterior inclusion probability of 0.20 which is not large but double the
prior inclusion probability. Given that we have added four extra variables into two
different datasets, we should probably expect at least one of the variables to
perform well once by chance. Nonetheless, the result is consistent with Joseph
Henrich’s hypothesis that societies with lower kinship intensity tend to become
more prosperous (Henrich, 2020).
Note: Dashed line denotes the prior inclusion probability
Figure 5. BI results with extra variables
Smart fraction theory
So far we have only considered the effect of average national IQ on economic
growth, however national populations do not just differ in the means but in their
entire distributions. An important question is whether the smartest fraction of a
country’s IQ distribution plays a more important role than the mean.
This is a plausible theory on many grounds. Psychologists such as Terman
(1916) and Jensen (1980, p. 114) have argued that because exceptional
achievement is created by the brightest, they will have the largest effect on
societies. Many previous studies looking at economic development and economic
growth have found larger effects of the 95th percentile IQ than the 5th percentile
or the mean level (Rindermann, 2012, 2018; Rindermann, Kodila-Tedika &
Christainsen, 2015).
A particular problem with this research is that the mean IQ and IQ of the top
5% correlate highly, even at r = .98 in Rindermann, Kodila-Tedika and
Christainsen (2015). With such multicollinearity it is difficult to differentiate the
effect of the average IQ and that of the cognitive elite. Kirkegaard (forthcoming)
responds to this issue by regressing the top 5% IQ on the mean IQ and taking the
residuals as a measure of how smart the brightest in the nation are compared to
what one would expect based on the mean ability. In regressions both the mean
and residualized elite IQs were statistically significant predictors of national
welfare across many variables.
Note: Dashed line denotes the prior inclusion probability
Figure 6. Smart fraction results using BI data.
We test Kirkegaard’s smart fraction measure in the SDM and BI datasets
(Figures 6 & 7). In this test we use Rindermann’s (2018) student assessment IQ
scores rather than his combined psychometric and student assessment scores
because the measurement of the nation’s smartest 5% of students comes only
from the results of student assessments.
Note: Dashed line denotes the prior inclusion probability
Figure 7. Smart fraction results using SDM data.
In general the Smart Fraction variable performed poorly, with a PIP of 0.18
in the BI dataset and 0.08 in the SDM dataset. The result for the BI dataset was
marginally above the prior inclusion probability of 0.14. Moreover, the estimated
coefficient in the BI dataset was 0.03, implying a standard deviation increase in
the elite IQ, over and above what is expected from the mean IQ, only increases
economic growth by 0.03% a year. Despite performing well in a few regression
models of the general socioeconomic factor for nations (Kirkegaard and Carl, in
review), we find smart fraction theory has little explanatory power for economic
growth. Kirkegaard and Carl (in review) note that measurement error is largest in
the tails of a distribution, suggesting our measure of the smart fraction may be
weak. Use of residuals to test smart fraction theory should be re-evaluated in the
future when further samples allow better estimations.
A more general problem for smart fraction theory is that it is not clear how
the smart fraction should be defined. In the work of Rindermann (2018) the smart
fraction is defined as how smart the smartest 5% of a country is. However, in one
formulation of smart fraction theory (La Griffe du Leon, 2002) the variable of
concern is the fraction of the population of a ‘smart’ IQ of 105 necessary for
complex work. Our residualized approach compounds this problem. If the IQ of
the top 5% is higher than what would be expected of the mean IQ, then our
measure also tells us that the median IQ is lower than the mean. In other words,
our residualized approach to measuring Rindermann’s conception of the smart
fraction may be negatively related to La Griffe du Lion’s measure of the smart
fraction. An alternative operationalization of smart fraction theory may be
Alternate national IQs
So far we have used Rindermann’s (2018) national IQs as our standard. This
was because by combining student assessment scores with national IQs we
attain data on more countries and have larger samples for the countries included.
Here we try different national IQs. Given the sensitivity of Bayesian model
averaging it is possible that even slight changes in national IQ scores due to
measurement issues could create substantial differences in results.
In the SDM dataset, the posterior inclusion probability is greater than the prior
probability for every national IQ score employed, with two thirds performing
extremely well with a PIP equal to one (Figure 8).
There is no obvious difference in the PIPs between student assessment
scores such as Hanushek and Woessmann’s (2012) and the World Bank’s
Harmonised Learning Outcomes, and the psychometric IQ scores such as Lynn
and Vanhannen’s (2002, 2012). Nonetheless the coefficients for the student
assessment scores tend to be lower, although the situation is reversed in David
Becker’s data with student assessments outperforming psychometric IQ. It should
be noted that the observations available were different for each IQ score meaning
the coefficients are not perfectly comparable. In the BI dataset, national IQ’s
coefficients and PIPs are smaller, but still robust (Figure 9). This should be
expected given that even with the use of Rindermann’s psychometric and SAS
national IQs, the sample size is only 43.
MANKIND QUARTERLY 2022 63.1 9-78
Note: Dashed line denotes the prior inclusion probability
Figure 8. Results of different NIQs using SDM data.
Note: Dashed line denotes the prior inclusion probability
Figure 9. Results of different NIQs using BI data
MANKIND QUARTERLY 2022 63.1 9-78
The IQ data with the largest coefficient on growth is also the oldest Lynn
and Vanhanen’s (2002) dataset. This is perhaps particularly surprising given the
scale of criticism this data has been given methodologically. In particular critics
suggested the scores could be biased against Sub-Saharan African countries
because their scores were so low. However, in our results Sub-Saharan Africa
has a negative coefficient on growth. The complete results are available in the
online supplement. If Sub-Saharan Africa was not inherently bad for growth and
Richard Lynn’s national IQ scores underestimated the human capital of Sub-
Saharan Africans, then the Sub-Saharan African binary variable should have a
positive coefficient. However, the estimated coefficient is negative. These results
support Garett Jones’s (2012) comments on Lynn’s national IQ scores “If national
average IQ estimates are indeed ’biased’, they appear to be biased in favor of
productivity growth.”
Penn World Tables
Ciccone and Jarociński (2010) found that using different editions of the Penn
World Tables leads to radically different results, suggesting the relevant economic
data is simply not good enough to reliably find the best explanatory variables.
Using national IQ as an explanatory variable with the BI dataset we replicate their
test. The BI dataset is used because a substantial number of its variables come
from recent editions of the Penn World Table allowing us to easily use different
versions of the same variables.
Across the five most recent editions of the Penn World Tables (PWT) we find
remarkably similar results. National IQ has a PIP of 1 regardless of what Penn
World Table is used. National IQ’s coefficient ranges from 1.1 to 1.3 (Figures 10
& 11). The coefficient is typically larger in older versions of the Penn World
Tables. This is consistent with prior research finding that older editions of the
Penn World Tables tend to provide more accurate measures of GDP, with
stronger correlations to proxies such as light intensity (Johnson et al., 2013;
Pinkovskiy & Sala-i-Martin, 2016). This may imply that better measures of GDP
would further increase our estimate of national IQ’s effect.
The consistency of national IQ in the face of measurement error and different
observations from different editions of the Penn World Tables further supports the
idea that national IQ is an extremely robust predictor of economic growth.
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Note: Dashed line denotes the prior inclusion probability
Figure 10. Results of different PWTs using BI data.
Figure 11. National IQ’s coefficient on economic growth using different PWT
MANKIND QUARTERLY 2022 63.1 9-78
Fixed regressors
Employing regional dummies as fixed regressors has been found to reduce
the sensitivity of Bayesian model averaging to measurement error in the Penn
World Tables (Rockey & Temple, 2016). Many explanatory variables show
greater variation across regions than within them. This means that regressions
with or without different regional dummies can find radically different results for
many explanatory variables. Because of this, Rockey and Temple (2016)
recommend using regional dummy variables alongside the logarithm of GDP per
capita as fixed regressors. This may be particularly important to diminish omitted
variable bias for national IQ given there are large regional variations in IQ scores.
We reran our Bayesian model averaging with regional dummies in every
regression. We also tried the fixed regressors utilized by Sala-i-Martin (1997) and
Jones and Schneider (2006). These are primary school enrolment in 1960, life
expectancy in 1960, and the logarithm of GDP per capita in 1960. We do this not
only to allow our results to be comparable with Jones and Schneider’s, but also
to stress test national IQ in case it is confounded with life expectancy or
education, showing co-dependency with these variables. After all, better health
and education may increase national intelligence.
In all variations of fixed regressors, national IQ still has a posterior inclusion
probability of 1 (Figures 12 & 13). Although national IQ’s coefficient is larger when
regional dummies are used in the BI dataset, it is slightly smaller under this
scenario in the SDM dataset. For the use of Sala-i-Martin’s fixed regressors, the
situation is reversed with a larger coefficient in the SDM dataset and a lower one
in the BI dataset. We can conclude that fixed regressors do not substantially alter
our results. Moreover, the effect of IQ is not due to regional confounding.
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Note: Dashed line denotes the prior inclusion probability. LGDPpc fixed regressors
include log GDP per capita. Continental fixed regressors include log GDP per capita and
regional dummies. SDM fixed regressors include life expectancy, primary school
enrolment and log GDP per capita.
Figure 12. Results of different fixed regressors using BI data.
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Note: Dashed line denotes the prior inclusion probability. lGDPpc fixed regressors include
log GDP per capita. Continental fixed regressors include log GDP per capita and regional
dummies. SDM fixed regressors include life expectancy, primary school enrolment, and
log GDP per capita.
Figure 13. Results of different fixed regressors using SDM data.
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Different priors
In Bayesian model averaging we had to specify priors on model probabilities
and on the variance of coefficients the ‘g prior’. This means approaching the
data with different prior expectations can alter the posterior conclusions. If IQ
really is robustly associated with economic growth, it should perform well under
all reasonable priors. So far we have only used one set of priors. We created
model probabilities based on the number of variables they included, assuming a
fixed probability of the inclusion of any variable such that the expected model size
was 7. We let the g prior be equal to the number of observations, calibrating our
certainty in coefficient sizes to the amount of information we could supply with our
Bayesian model averaging.
To test whether our results are robust to different priors, we employ all
possible combinations of model priors and g-priors within the BMS package. In
our results presented in Figures 14 and 15, the first part of the legend indicates
what model priors were used, Random meaning model priors drawn from a beta
distribution, Uniform meaning all models have the same prior, and Fixed which
we have already employed. The second part of the legend provides the acronym
for the g-prior used. The names, acronyms and brief explanations for these g-
priors are provided in the Methodology section. Further details of these priors can
be found in Feldkircher and Zeugner (2009) and Zeugner and Feldkircher (2015).
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Note: Dashed line denotes the prior inclusion probability
Figure 14. Results of different priors using BI data.
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Note: Dashed line denotes the prior inclusion probability
Figure 15. Results of different priors using SDM data.
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In prior literature on the sensitivity of BMA in growth modelling, different data
has been found to substantially change the results due to both measurement error
and different sampling resulting from different datasets (Rockey & Temple, 2016).
So far we have only studied whether national IQ is robust to using different Penn
World Tables data and different national IQs, but we have not studied the issue
of sampling in isolation. With sampling bias our results so far may be inaccurate,
and even with random sampling our results may be coincidental due to outliers.
To pursue this issue further we use Bayesian model averaging again by
resampling our data with two methods: bootstrapping, and jackknife resampling.
Thus we are performing observation sampling and then model sampling
sequentially. Although resampling and weighting observations has been
recommended to improve the robustness of Bayesian model averaging with
economic growth (Doppelhofer & Weeks, 2011), no one has yet tried it. To
perform this resampling most effectively, we use the SDM dataset of controls
because its larger sample size allows us to present the results of a wider range
of possible combinations of observations.
In bootstrapping we randomly resample our observations. In this process the
same observation may be picked more than once for the new sample. We
resample our observations 1,000 times. We then perform Bayesian model
averaging upon each resample. Our initial attempt to do this ran into dummy
variable traps that had homogenous values for certain variables making the
regressions impossible. To solve this problem we sorted the variables by the
number of unique values they had and deleted the variables with fewest unique
values, one by one, until running all our regressions was feasible. This meant we
had to reduce the number of variables from 68 to 43. Although we could have
kept all variables and ignored failed regressions, that would be limiting the
resampling, ‘baking in’ sampling bias.
We use the box plot shown in Figure 16 to present the distribution of the PIPs
and coefficients estimated from this method.
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Note: Dashed line denotes the prior inclusion probability
Figure 16. Bootstrap sampling results using SDM data.
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Of our tested variables, GDP per capita in 1960 and national IQ had the
highest median PIP of 1. Primary school enrollment in 1960 was a close
competitor with a median PIP of 0.99. However, national IQ performed the best
with the first quartile of its PIPs being equal to 0.98, whilst primary education’s
lower quartile PIP was at 0.88. National IQ had the lowest interquartile range of
PIPs at 0.02. The next smallest interquartile range was for primary education at
0.12, six times larger than national IQ’s PIP interquartile range. National IQ’s
median coefficient was the largest for all variables tested at 1.07. primary school
enrolment had a coefficient of 0.69. This was the second largest coefficient, but
it was still only 64% the size of national IQ’s coefficient. Political Rights, a
democracy index with higher values indicating greater levels of democracy
(Barro, 1991), was the worst performing of all the variables with PIPs greater than
priors. It should be noted its coefficient on economic growth was negative,
suggesting the result may have been a fluke. Summary statistics for PIPs and
coefficients of variables with a median PIP higher than the prior inclusion
probability (0.14) are given in Tables 5 and 6.
Notably, PIPs range from at least 0.2 to 1 for all trialed variables. This is
testament to the sensitivity of Bayesian model averaging of economic growth to
sampling, suggesting that reporting one or a few BMAs with the same data or
variables is not sufficient to be confident in one’s results. Nonetheless, the fact
national IQ is the best performing in terms of its median coefficient, median PIPs,
first quartile PIP, and interquartile range of PIP in the face of this sensitivity,
suggests it is the most robust predictor of economic growth.
Table 5. Summary statistics of posterior inclusion probabilities.
Political rights
% tropical
GDP per capita
National IQ
Table 6. Summary statistics of variable coefficients.
Political rights
% tropical
GDP per capita
National IQ
Jackknife resampling, otherwise known as the leave-one-out cross
validation, involves removing each observation separately and then running BMA
on all the resulting subsamples. This method focuses on the effect of each one-
removed observation allowing us to check if there are any influential observations
skewing our estimates of national IQ’s PIP or coefficient. An advantage of this is
that it allows us to keep all variables from the SDM dataset employed without
running into rank deficient models. However, the subsamples are more similar to
the original dataset than the resamples from the bootstrapping method, making
the jackknife a less rigorous check on the effects of resampling.
We find the PIP of national IQ to be 1 in all jackknife samples (Figure 17),
meaning no individual observations are skewing the inclusion probability of
national IQ. We find the coefficient of national IQ ranges from 1.3 to 1.4 with a
median value of 1.4. Regardless of which observations are removed we find large
robust coefficients for national IQ.
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Note: Dashed line denotes the prior inclusion probability
Figure 17. Jackknife sampling results using SDM data.
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Time periods
As the BI dataset is set up for many different time periods, we re-ran our
analysis on 20-year periods from 1960 to 2010. All explanatory variables, except
national IQ and geographic variables, were given for the starting year of the
growth period studied. National IQ had a higher PIP than prior in every single time
period. Of the seven time periods studied we only found one, 1975-1995, where
national IQ had a posterior inclusion probability less than 0.50. This indicates that
national IQ consistently predicts economic growth, with its high performance not
being the coincidental result of any particular time period. It is the best performing
tested variable in all but two time periods, 1975-1995 and 1980-2000. In these
time periods fertility has a higher PIP than national IQ, with a negative coefficient.
This is surprising given that fertility has a lower PIP than prior in three of our
subperiods and in our main 1960-2010 period. We suggest this may be
coincidental due to fertility’s strong negative correlation with national IQ
(Meisenberg, 2009).
Bruns and Ioannidis (2020) were the first to test Bayesian model averaging
across different time periods. They found no tested variable was robust across all
time periods. They suggested this supported the view of ‘robust ambiguity’, that
statistical modeling of economic growth is unable to identify strong explanatory
variables with the exception of GDP per capita in the starting year. Their
conclusion was in the title of their paper Different Time Different Answer. Our
results contradict Bruns and Ioannidis because national IQ is supported in every
one of our time periods. It is not the case that Bayesian model averaging cannot
identify strong explanatory variables. Rather, economists have failed to use the
variable that matters the most.
In the shorter time periods national IQ’s coefficients are between 0.4 and 1.4,
typically smaller than our estimate in the SDM dataset of 1.4 for the 1960-2010
time period (Figures 18 and 19). GDP per capita’s coefficient is also smaller and
more variable, ranging from around -0.7 to -2.5 compared to our SDM result of -
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Note: Dashed line denotes the prior inclusion probability
Figure 18. NIQ’s PIPs and coefficients under different time periods using BI data.
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Note: Dashed line denotes the prior inclusion probability
Figure 19. Results under different time periods using BI Data.
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Section 6: Causality
Whilst we have found national IQ to be extremely robust in its relationship to
economic growth, the causality of this relationship can be questioned. This
problem has two parts: to what extent can economic growth cause increase in
national IQ scores, and to what extent do changes in national IQ scores represent
real changes in ‘intelligence’ with the same causal effect on GDP.
The scores from psychometric tests are compiled from many different time
periods mainly in the second half of the 20th century, and most of the student
assessment scores are even more recent. If there is much reverse causality from
growth to test scores, this could explain national IQ’s strong relationship with
Large increases in IQ scores in the 20th century, known as the Flynn effect,
support the possibility of reverse causality. For example, IQ scores in East Asia
have risen rapidly (e.g. te Nijenhuis et al., 2012). The national IQ scores we use
adjust for the Flynn effect by assuming it is the same in all countries, but if Flynn
effects are heterogeneous, our estimated coefficients could be upwards biased
due to reverse causality. On the other hand, if Flynn effect changes in national IQ
are in some way ‘hollow’ and have a smaller effect on GDP, then this could put a
downwards bias on estimates.
An important step in disentangling the problem of causality was the study of
Rindermann and Becker (2018) which found significant correlations between
some lags of the Flynn effects in countries and the rate of economic growth.
However, the paper only studied 27 countries and various biases could be driving
the results. For example, the Flynn effect and economic growth could be
confounded by a third factor, as national level fixed effects were not employed. If
the Flynn effect and economic growth move in parallel, then even with lags it may
be difficult to identify which factor is causing the other. This is because lagged
variables do not always avoid ‘simultaneity bias’ (Reed, 2015). Moreover, their
reported correlations do not provide us with an easily interpretable effect of Flynn
effects on economic growth because they use rates of change in national IQs to
predict economic growth with time periods of differing length for different
observations. Furthermore, it is not clear from the results that it is not genetic
changes rather than Flynn effects that are associated with economic growth.
A general problem for arguing that Flynn effects drive growth is the failure of
increases in education to predict growth in fixed effects analysis (e.g. Hamilton &
Monteagudo, 1998; Pritchett, 2001). A meta-analysis of quasi-experimental
studies suggests years in education do increase IQ test scores (Ritchie & Tucker-
Drob, 2018) meaning that if increases in IQ scores affect growth, so should
education. We suggest that Flynn effects may be a hollow ‘inflation’ in test scores
that do not affect growth. After all, whilst education increases test scores, it does
not appear to affect general intelligence (Ritchie et al., 2015) or processing speed
(Ritchie et al., 2013). General intelligence g refers to the latent factor which IQ
tests try to measure (Spearman, 1904). This interpretation of Flynn effects on
economic growth also concords with the Jensen effect (Rushton, 1998) whereby
correlations between outcomes and IQ are strongest on more ‘g-loaded’ IQ tests
which are also more heritable. Many studies also support this interpretation by
finding Flynn effects appear to only exist on specific IQ tests rather than on the
general factor of intelligence (e.g. Jensen, 1998; Must et al., 2003; Rushton,
1998; te Nijenhuis & van der Flier, 2013; Woodley & Madison, 2013). However,
some scientists have found Flynn effects represent a Jensen effect on fluid rather
than crystallized measures of IQ (Colom et al., 2001). An important caveat to this
line of thought is that whilst the gains from education may be hollow, other
hypothetical causes of IQ increases, such as nutrition, may have “real” effects on
An approach to remove possible reverse causality is to create national IQ
scores that were created before the period of economic growth studied or very
close to it, since future economic growth cannot plausibly alter past intelligence
scores. This approach has been used in a few studies such as Christainsen
(2020), Rindermann (2018) and Hanushek and Woessmann (2015). These
studies find past test scores have the same coefficient on future growth as
contemporary test scores have on past results. However, there are some
limitations to this approach. The sample sizes are often much smaller.
Christainsen (2020) had the largest sample size of 45 countries using this method
whilst the other papers have often had substantially smaller samples. The small
sample sizes may reduce the accuracy of modelling and possibly introduce bias
and range restriction from missing values.
Intelligence may have a causal effect despite Flynn effects if national levels
of intelligence are path dependent, which could be caused by genetics. Under
such a theory societies that start more intelligent grow more and continue to
perform more highly in measures of human capital, whether or not the increases
in human capital measures are actually determining economic growth. This path
dependence would allow us to estimate the effect of intelligence on economic
growth, regardless of when intelligence is measured. For example, although
Meisenberg and Woodley (2013) found the student assessment scores of low-IQ
countries were catching up with high-IQ countries between 1995 and 2009, the
rank order of different regions remained the same.
Strong path dependence in human capital has been shown by Baten and Juif
(2014). They use age heaping measures of numeracy from 1820 and compare
them with student assessment scores from the second half of the twentieth
century, as used by Hanushek and Woessmann (2012). Innumerate people are
less likely to be able to calculate or remember their age so they typically give
rounded figures for their age, leading to ages on gravestones, censuses, and
documents ‘heaping’ at ages that are multiples of five or ten. From the degree of
‘heaping’ an index for numeracy can be created. When Baten and Juif (2014)
found the age heaping scores had a statistically significant relation with more
recent student assessment scores, they did not report a simple correlation.
Kirkegaard (2015) found Lynn’s 2012 IQ scores had a correlation between 0.52
with an age heaping index in 1890 and 0.85 with an age heaping index from 1800.
This approach has a few limitations because the ceiling effect of numeracy is very
strong in later cohorts (i.e., there is almost no heaping), and because the set of
included countries varies across cohorts.
Path dependence can be found more generally in the ‘deep roots’ literature
on economic growth. Comin, Easterly and Gong (2010) in their paper Was the
Wealth of Nations Determined in 1000 BC find a strong relationship between
development throughout history, such as a correlation of r = .71 between
‘migration adjusted technology level’ in 1500 AD and log per capita income in
2002. Similar results have been found by Putterman and Weil (2010) and
Spolaore and Wacziarg (2013) who diplomatically state that “The evidence
suggests that economic development is affected by traits that have been
transmitted across generations over the very long run.”
Given strong path dependence in human capital and economic growth, it
should be no surprise that contemporary IQ scores can predict past prosperity far
further back than the twentieth century. For example, Lynn and Vanhanen (2012)
find national IQ has a Spearman correlation with GDP per capita greater than .70
for 2003, 1870, and 1700.
Strong path dependence in human capital and GDP and correlations
between them support the idea that human capital has played a large role in
determining prosperity throughout history, but it is still vulnerable to collider bias
with a confounding variable determining both GDP and human capital. We
suggest genetic differences between populations are what determines human
capital and thus GDP. Despite the controversy surrounding the issue of race and
intelligence, when intelligence researchers are surveyed anonymously, 85%
believe genetics plays a role in the Black-White IQ gap in the USA (Rindermann
et al., 2020). Although we do not have the space in this paper to discuss racial
differences in intelligence within America, if genes affect intelligence differences
within the United States it is likely that they have some effect across the globe.
Genetic differences could also explain variation in the Flynn effect, with
genetically smarter populations being faster to learn (eg. te Nijenhuis et al., 2012).
For example, African Americans score lower than East Asians in IQ tests in
America despite similar environments. As expected, East Asian countries have
seen large Flynn effects whilst sub-Saharan countries appear to have
experienced none (Wicherts et al., 2010c).
Various evidence suggests the national variation in intelligence may be
genetic in origin. Piffer (2015, 2019, 2020, 2021) finds educational polygenic
scores, trained on predicting educational attainment in white populations,
correlate with national IQs at r > .90. Nevertheless, there are concerns about the
transracial validity of these polygenic scores. Economists have found genetic
distance between countries is associated with various outcomes including
economic growth (eg. Saha & Mishra, 2020). Whilst this literature uses genetic
distance as proxy for cultural distance, assuming that ideas and technology
diffuse faster across similar groups, it also has obvious implications for the
possibility that genetic variation in intelligence could mediate differences in
economic growth. Moreover, genetic distance correlates with national IQ (Becker
& Rindermann, 2016; Kodila-Tedika & Asongu, 2016). IQs correlate with cranial
size (r = .26; Pietschnig et al., 2015), and national IQs have been found to
correlate with cranial size in a sample of ten countries (r = .91; Rushton, 2010),
supporting a biological origin for national differences in intelligence. Furthermore,
cranial capacity is substantially genetic with a heritability of around 90% in early
adulthood (Batouli et al., 2014).
Quasi-experimental evidence from variation in wealth and environment also
suggests genetics may be the cause of variation in national IQ. For example,
countries that are or become rich due to oil wealth attain no higher IQs than their
poorer genetically similar neighbors (Christainsen, 2013; Jones & Schneider,
2009). Christainsen (2013) set out to estimate environmental effects through
regressing national IQ on measures of environment such as education and
malnutrition. He found that regional dummy variables dominated the regression
relative to environmental variables, suggesting ancestry has a much larger effect
on IQ than socioeconomic environment.
A popular explanation for why nations and peoples differ in their intelligence
is Cold Winters Theory (Frost, 2019; Lynn, 1987; Rushton, 1995). This theory
supposes that the challenges of cold winters and the necessary preparation for
the seasons is cognitively demanding such that humans are selected for
intelligence further from the equator and in colder environments. The theory has
repeatedly been rediscovered by scholars throughout history such as Alfred
Russell Wallace (1864), Arthur Schopenhauer (2000, p. 159) and Sa’id al-
Andalusi who was born in the year 1029 (Lewis & Lewis 1990, pp. 47-48). The
theory fits the data as groups with higher intelligence and higher cranial capacity
tend to have evolved in colder environments further from the equator (Kanazawa,
2008). The strongest cold winter correlate of national IQ appears to be skin
reflectiveness suggesting UV radiation may best capture the cold winter effect
(Templer & Arikawa, 2006). Furthermore, behavioral ecologists have
independently found the same pattern within non-human primates (Navarrete et
al., 2016), birds (e.g. Roth et al., 2010; Sol et al., 2010) and other species (Gillooly
& McCoy, 2014; Jiang et al., 2015), giving the theory parsimony. In particular, the
evidence from birds shows that the relationship between absolute latitude or
winter temperature to brain size is only present in non-migrating birds, a
prediction of the cold winters theory that is difficult to explain otherwise.
To test whether genetic or path-dependent variation in intelligence causes
growth, rather than the reverse, we use instrumental variable estimation.
Appropriate instrumental variables are ones that should influence national
intelligence but have no other association with economic growth, allowing us to
isolate the direct effect of national IQ on economic growth. In the first stage the
instrumental variables model national IQ and predicted national IQs are taken. In
the second stage, growth regressions are run using predicted national IQs rather
than actual IQs. The predicted values of national IQ represent the effect of the
instrumental variables directly on national IQ and any possible indirect effect
through economic growth. Crucially, however, the predicted national IQs are
unaffected by exogenous changes in GDP during the growth period studied.
We employ two further statistical tests in this approach. Firstly we use the
Wu-Hausman endogeneity test. This is a test of whether the OLS and IV
coefficient estimates significantly differ, indicating the existence of endogeneity in
the OLS regression model. Because we expect our IV estimates to identify a
causal estimate of the effect of prior cognitive ability on economic growth, a
significantly different OLS estimate would indicate that endogeneity biases
estimates of IQ’s effect on economic growth. Furthermore, we employ the Weak
Instruments Test. This is an F test comparing the second stage regression with
and without the instrument. If the regression does not perform significantly better
with the instrument, this suggests it is weak. To perform instrumental variable
estimation we use the R package ivreg (Fox et al., 2021). Further details of our
statistical tests can be found in the textbook Econometric Analysis (Greene,
We are not the first to employ instrumental variables for measures of national
cognitive ability. Previously, measures of educational institutions and school
quality (Hanushek & Woessmann, 2015) have been used as instrumental
variables. For example, these instrumental variables include the level of private
school competition, the existence of exit exams, and relative teacher pay. They
found no evidence of reverse causation with the Wu-Hausman endogeneity test.
However, these instrumental variables are taken from times during the growth
period studied. This makes these variables unsuitable for identifying causality
because educational institutions may be influenced by changes in growth or
changes in intelligence. In our instrumental variable approach we only use
measures taken before the period of growth to represent the deep root causes of
intelligence. Christainsen (unpublished) has used regional dummies as
instruments for national IQ. Given it is unpublished, we refrain from discussing
the results.
We employ three instrumental variables separately. Firstly we use numeracy
measures created with age heaping, which was collected from a range of samples
by Joerg Baten (2015). We standardize age heaping scores across all time
periods in the 19th century and then take an average. This tests whether human
capital’s relationship with growth is path dependent, allowing us to predict
economic growth with national IQs from any time period. Our second instrumental
variable is cranial capacity. This is an estimate from Beals et al. (1984) which
uses a sample of skulls from 124 ethnic groups and then imputes estimated
cranial capacity for all areas of the planet. From these scores David Becker (2019)
estimated cranial capacities for countries, adjusting for population density and
migration (See column FW in the ‘NAT’ tab of version 1.3.3 of the national IQ
dataset at Given the prior support for Cold
Winters theory, we also use UV radiation by country adjusted for migration post-
1500. This measure is obtained from Andersen et al. (2021), who estimate the
average level of UV radiation nations’ ancestors had in 1500. The cranial capacity
and UV measures thus allow us to test whether biological factors determine the
wealth of nations. A correlation matrix of our instrumental variables with
Rindermann’s national IQ scores is provided in Table 7.
For control variables we use log GDP per capita in the starting year. We also
perform the same IV estimation with the control variables from the model with the
highest posterior model probability (15%) in our Bayesian model averaging with
the SDM dataset of controls. These variables are Tropical Population Percent,
Primary School Enrollment in 1960, and Fraction of GDP in Mining. Initial
regressions before employing IV estimation are in Table 8 and our IV estimates
are in Table 9.
Table 7. Correlation matrix of NIQ and instruments
Ancestry-adjusted UV
National IQ
Age heaping
Ancestry-adjusted UV
Table 8. OLS models of economic growth; * p < 0.05, ** p < 0.01, *** p < 0.001
Model 1
Model 2
national IQ
Log GDPpc 1960
Fraction of GDP in mining
Primary school enrolment
Tropical population percent
Table 9. Instrumental variable models of economic growth; * p < 0.05, ** p < 0.01,
*** p <0.001
Instrumental variable
Cranial capacity
UV radiation
Age heaping
(19th century
National IQ
Log GDPpc 1960
Fraction of GDP in
Primary school enrolment
Tropical population %
Weak instruments test
Wu-Hausman p-value
Our initial estimates find one IQ point increases economic growth by 0.14%
without controls and 0.11% with controls, which was the same estimate our
Bayesian model averaging produced. In our IV estimates all models pass the Wu-
Hausman test except when ancestry-adjusted UV is employed (p < .05) without
control variables in model 3. In model 3, national IQ’s coefficient is 0.17 which is
significantly larger than the OLS estimate of 0.11. If there is reverse causation, it
causes us to underestimate the effect of national IQ. In the other instrumental
variable estimations, national IQ’s coefficient is similar to the OLS estimate. A
likely explanation for model 3 is that ancestry-adjusted UV may not be exogenous
because its geographic or environmental confounds may have an independent
effect on growth. This problem might be solved by using control variables such
as Tropical Population. In all regressions our instrumental variables passed the
Weak Instruments test, meaning they have a robust relationship with national IQ.
The failure to reject the null in the Wu-Hausman test is suggestive of there
being little reciprocal causation, but it is not proof. It merely suggests OLS
estimates are close to the true causal effect size, assuming our instruments only
covary with GDP growth due to their effect on intelligence.
Overall our instrumental variable estimates found results consistent with the
OLS and BMA methods. We conclude that reverse causality does not play a
substantial role in distorting estimated coefficients of national IQ on GDP growth.
Section 7: Limitations
The Bayesian model averaging method attains more reliable estimates by
reducing researcher degrees of freedom in choosing explanatory variables.
Nonetheless many researcher degrees of freedom still existed in this study such
as the choice of dataset and the choice of time period. Furthermore, BMA creates
more researcher degrees of freedom by requiring the specification of prior
probabilities. In this study we have tried using a sample of plausible
methodologies as robustness tests to see whether the sensitivity of BMA is
distorting our results. We held our method constant whilst making one change to
our method at a time as a robustness test. It is possible that different combinations
could have produced different results. Nonetheless, given the breadth of tests
performed and the consistency of national IQ to have the highest average PIP
and coefficient in all the tests gives us strong reasons for supposing national IQ
is the best predictor of economic growth.
A more challenging problem would be if our results were systematically
biased. This could occur through sample bias and range restriction. Our data will
not be missing at random as it is likely that poorer countries are less likely to have
data available from the 1960s. This may undermine the power of variables
competing with national IQ. It is likely that the worst socialist and authoritarian
countries would not have sufficient economic statistics to be in our sample. For
example, North Korea was not an observation in any of our models. Were the
statistics available we might have found stronger results for economic and
political freedom indexes, when in fact their posterior inclusion probabilities were
systematically lower than their prior inclusion probabilities. As the world develops,
more data should be released from countries allowing national IQ to be tested
with large samples. However, regional levels of prosperity have consistently had
a strong relationship with regional IQs (Fuerst & Kirkegaard, 2016; Lynn et al.,
2018). Given that there are no sample biases for within-country studies, we
should be skeptical to think that sample bias plays any substantial role in the high
performance of national IQ to predict growth.
A related surprising result from Bayesian model averaging is how poorly
popular theories of economic growth perform. As mentioned, popular institutional
measures such as democracy and economic freedom appear to have negligible
or even negative effect sizes. A possible reason for this is that our variables may
be poor quality measures, for example there are various difficulties in measuring
institutions (see Glaeser et al., 2004). Furthermore, many of the variables tested
will change over time meaning economic growth might relate to their average
values over a time period rather than their initial values. This problem should be
reduced in the subperiod analysis we have performed. Yet many popular
variables, such as the Polity 2 democracy index, still perform poorly in the
subperiod analysis.
An important question for judging our control variables is how to interpret
posterior inclusion probabilities. The very low PIPs of rival explanatory variables
might suggest that only national IQ and few other variables matter. Alternatively,
the rival variables might have a small but real effect on economic growth which
we are unable to distinguish due to the low sample size. With only one planet of
nations, of which we only have a limited sample, regression methods only have
sufficient degrees of freedom to distinguish the largest effects on economic
growth. Whilst it is certainly plausible that variables apart from education, IQ and
natural resources do influence growth, their effects may be subtle and more
suited to historical rather than statistical analysis.
Section 8: Conclusion
Of our tested variables, national IQ consistently has the largest coefficient
and the largest posterior inclusion probability, suggesting it is the most robust
predictor of economic growth. This replicates the finding of Jones and Schneider
(2006) showing that national IQ has a high posterior inclusion probability in
Bayesian model averaging. We found that IQ’s effect was robust under many
tests such as the use of different data, different fixed regressors, different time
periods and resampling methods. Prior literature which did not use national IQ
found that growth modeling led to ‘robust ambiguity’ without clear indications of
which variables really matter. Our results contradict robust ambiguity findings
because there is strong consistent support for national IQ. The methods, sample
size and data quality were not insufficient to find powerful causes of the wealth of
nations, rather the best explanatory variable was not being used by economists.
We also applied Bayesian model averaging to study more niche issues in the
national IQ literature. We found potentially confounding variables and rival
psychometric variables, but these did not explain away national IQ’s relationship
with economic growth. Using updated measures of smart fractions we found that
only the average IQ of nations was robustly predictive of economic growth, rather
than the intelligence of the ‘elite’ section of the intelligence distribution.
In interpreting our results, we discussed the prior literature suggesting that
human capital differences between nations are deep-rooted and possibly of
biological origin. To support this hypothesis we used 19th-century numeracy
measures, cranial capacity, and ancestry-adjusted UV radiation as instrumental
variables for national IQ. Endogeneity was only found (p < .05) in one of the six
models. This was when ancestry-adjusted UV radiation was used as an
instrument with only the logarithm of GDP per capita as a control variable. This
result disappeared when additional controls were employed. We suggested the
endogeneity found in this regression represented UV radiation having geographic
confounds that could affect economic growth. Overall our IV methodology could
not find strong evidence for reciprocal causation.
Our findings have substantial implications for government policy and the
future of economic growth. The poor evidence for smart fraction theory suggests
only small effects from having an intelligent elite. This weakens the case for
policies, such as Paul Romer’s charter cities, ‘state building’ and imperialism,
which attempt to employ highly educated smart people from Western countries to
design or run key institutions in developing countries. The finding may also
suggest immigration can lower per capita GDP. If a high IQ country takes in lower
IQ immigrants the new average may determine the prosperity of the society, even
if the intelligence of the native elite remains the same. Moreover the finding makes
the ‘migration-ability paradox’ (Rindermann, 2018, p. 422) worrisome. When less
intelligent countries send their smartest people to intelligent countries, this can
lower the average IQ of both nations. Under Smart Fraction theory the less
intelligent nation might lose whilst the more intelligent nation may be relatively
unaffected. However, when the average national IQ is what matters, both senders
and receivers of migrants may be made worse off.
National IQ appears to be the most important factor in determining the GDP
of a nation, yet it is deeply path-dependent with 19th-century numeracy measures
having an effect on GDP similar to more recent student test scores. Moreover,
the strong correlates of national IQ with the genetic polygenic scores and cranial
capacity suggest biology determines which human capital paths nations are on.
The inequality of countries may be fatalistically determined in our genes.
To find policies that can increase economic growth, economists, scientists,
governments and the private sector should study and test the effectiveness of
policies to increase national intelligence. Our results provide new evidence
supporting Cattell’s (1937a,b) calls for nations to develop strategies to increase
their intelligence. For example, Cattell recommended an ‘intelligence department’
of the state devoted to measuring and improving national intelligence over time.
With embryo selection and gene editing, humanity now has powerful and
consensual tools to increase national intelligence genotypically. See Anomaly
and Jones (2020) and Anomaly (2020) for a discussion of the ethics and policy
implications of genetic engineering.
If genes determine GDP, we must expect future economic growth to fall.
Since Charles Darwin (1871), scientists have observed dysgenics the less
intelligent having more children and doing so faster than others. See Dutton and
Woodley (2018) for a review of this literature. More recently genetic data from the
United States (Beauchamp, 2016), United Kingdom (Hugh-Jones & Abdellaoui,
2021) and Iceland (Kong et al., 2017) show polygenic scores for educational
attainment to be declining. After accounting for unexplained variance in the
educational polygenic scores in the Icelandic data, Dutton and Woodley (2018)
estimated that IQ was falling by 0.8 points per decade. We can crudely
extrapolate our finding that each IQ point increases GDP per capita by 7.8% to
estimate the effect of dysgenics on GDP in one hundred years’ time. If we could
stop the current dysgenics of 0.8 points per decade, then GDP will be
  higher in 2122 than under our current dysgenic
trajectory. The power of genetics to determine prosperity paints a bleak picture of
our future.
Online Supplement: The appendix is available at, as are
Figures 1-19 from this paper.
Acknowledgements: We would like to thank the attendants of the London
Conference of Intelligence 2021 for their feedback on an early presentation of this
paper. We would particularly like to thank Gregory Christainsen for his
discussions with the authors. All errors and omissions are our own.
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