Introduction

The IQ - short for Intelligence Quotient - is an indicator meant to assess one’s intelligence. Created in the early 1900s, the IQ was, originally, a tool that the German psychologist William Stern designed to identify children in difficulty. Nowadays, the IQ is not quite the same as it used to be. It doesn’t define one’s intellect but his/her capacity to provide an intellectual performance or reasoning. Evaluated by a psychologist, the IQ is now built so that it follows a Gaussian distribution, whose mean is 100 and standard deviation is 15. Therefore, an IQ of 115 or more is considered abnormally high, while a score of 85 or less is considered particularly low, as 68.2% of the population are supposed to have an IQ between these two scores.

As the IQ test became widespread, we have been able to build average IQ statistics that evaluate countries’ average IQ ; and, even though the mean IQ is, by construction, meant to be 100, we can observe huge differences in these IQs. In the past, these gaps have been used to justify a country - or a race, in the sociological sense - superiority over others. Since then, it has been proven that neither race nor ethnicity determine the IQ. More than that, the wide use of the IQ has become controversial as it was created by occidental scientists, so it may be more adapted for occidental individuals. However, that does not mean that we cannot find variables that, at the scale of a country, impact the average score. That is why the question I am addressing here is : what makes the average IQ of a country ?

Literature review

There have been very few researchers or papers trying to assess to causal impact of aggregated variables on the average IQ of countries. Indeed, this area of research is a bit of a minefield as it is often associated to racialism and racism, either because the authors are writing from these perspectives or because their findings are misinterpreted in this way.

The main paper in this field study is probably IQ and the wealth of Nations of Richard Lynn and Tatu Vanhanen (2002). They aimed at establishing a relationship a country’s GDP and its average IQ, and they managed to evidence a positive correlation between them. They also formulated the hypothesis that other variables had to be taken into account, which Lynn and David Becker did with The intelligence of Nations in 2019, as they included temperatures and demographic data, among others, in their analysis. However, these papers’ findings tend to be questioned due to the methodology of the first one : Richard Lynn is a well-known white supremacist accused of adapting his ways of evaluating countries’ average IQ in order to lessen African ones. Not only did it tarnish his reputation, it also made his following studies less credible.

So, as I have not been able to find proper and morally acceptable studies that assess the impact of aggregate variables on the average IQ, I decided to do it myself.

Data

To do so, I relied on data I encountered in here. This website provides data about loads of variables, at scales going from US cities to the world. The main dataset I used displays the average IQ for 199 countries, alongside with a bunch of others variables, such as their total population, area, or even density. However, this dataset only was not sufficient, which is why I added three other ones, also coming from the same website. These datasets include the same variables, except for the fact that the IQ has been replaced by the GDP, the average temperature and the HDI. I merged all these sets into one, which was all the easier as all datasets came from the same source, so used the same country names.

However, I could not directly use them. Indeed, some editing was required since, in each dataset, there were rows that contained one or two more variables than the other (mostly another subregion), and some figures that were not readable correctly by R because of their number of decimal places.

I ended up with a dataset that describes 199 countries, although temperature data is missing for 15 countries and HDI data is missing for 14 countries (all are small countries or countries whose diplomatic situation is tense, such as Taïwan).

With my study, I also wanted to try and assess the impact of being a former colony on the average IQ. To do so, I identified all the countries that were colonies at the beginning of the XX° century and created the dummy variable colony that takes the value 1 if the country was a colony, and 0 if it was not.

I decided not to consider colonies the countries that were independent before the XX° century because I assumed that the (supposed) effects of colonization on their average IQ would have faded by now (and also, most countries that were counted as colonies gained their independence only 70 years ago, which is not so much).

So, here is what my final dataset looks like.

Descriptive statistics

Summary Statistics
Variable N Mean Std. Dev. Min Pctl. 25 Pctl. 75 Max
IQ 199 82.031 13.348 42.99 74.37 91.435 106.48

As shown by this table, the mean average IQ is not 100 - as it should have been theoretically as the mean IQ is supposed to be 100 - but 82.03, with a standard deviation of 13.35. Two countries can have drastically different average IQ, as the range of average IQ scores is no less than 63.49. The median average IQ is 83.13 : it’s Colombia’s IQ (as its IQ_rank is a 100). So, half of the average IQs are greater or equal than 83.13, and 75% of them are greater or equal than 74.37 : there is only a few countries whose IQ is “really” low.

All of the graphs and the map (except for the last ones) are interactive : click on countries/bars/bubbles or on the legend to display more information.

region Mean_region
Africa 68.25404
Asia 85.79820
Europe 94.93786
North America 78.45276
Oceania 86.94143
South America 83.78333

As shown by the map, most, if not all, countries with the lowest average IQ are located in South countries, especially in Africa and Central America (which are counted as North American countries in my data). These are also the regions where average IQs are the less regular and whose mean regional average IQ is the lowest, as shown by Plot 1 where each dashed line represent the mean average IQ in the region. Asian average IQs are also relatively irregular, as we can find among them the highest average IQ (Japan’s) and the lowest (Nepal’s). However, the mean in Asia is relatively high, as in the three other regions, whose countries have more similar average IQs.

Plot 2 displays the data from another perspective and allows to see that richer countries tend to have a higher average IQ (this positive relationship is represented by the increasing regression line). Also, each bubble represents a country and its size is proportional to its population. On the graph bigger bubbles tend to be on the right, meaning that the more populated the country the richer it is, but it is hard to make the same statement about the IQ, or at least the relationship between the average IQ and the population of country seems weaker than the other one. Finally, the doted line represents the mean of the average IQs, and once again, it is pretty clear that African countries are below except for Mauritius, whereas all European ones are above, except for Albania.

Plot 3 ranks the countries by ascending HDI and shows their average IQ. Clearly, a strong positive correlation is appearing, and, most importantly, it seems that the higher the HDI, the more countries have similar average IQs (they tend to come closer and closer to the regression line). As we’ll see in the next section, this relationship was to be expected given the previous one.

Plot 4 has to be understood as a simple bar chart, going all the way from Canada to Mali (both located at “twelve o’clock”). Countries are ranked from the coldest, Canada, to the hottest, Mali, and the height of the bar represents their average IQs. This plot allows to observe that the coldest countries are have the highest IQs, as the first quadrant of the circle is clearly the biggest, and bars kind of go decreasing as we move around to the hottest ones. Unsurprisingly, most European countries are among the coldest countries and, ergo, among those with the highest IQs.

So, as of now, we have been able to observe the differences in average IQs of the countries, and we identified more or less strong relationships with aggregated variables (being positive with the GDP, and in a lesser measure, with the population, and negative with the temperature).

Methodology

In order to truly understand these relationships and to establish whether or not the aggregate variables I chose do have a causal impact on average IQs, I will need to rely on mathematical tools, especially linear regressions. I already gave a sense of that with Plot 2 which includes a regression line. This line is the one that best represents the relationship between the log of the GDP and the average IQ of countries. By construction, its equation is equivalent to : \[IQ_{i} = b_{0} + b_{1} \times log(GDP_{i})\] IQi and GDPi and the IQ and GDP of country i, b0 is the intercept of the line, and b1 the regression coefficient. This last coefficient gives an idea of how much these two variables are associated, without being sufficient to establish clear causality between them.

Indeed, as we are about to see, even though the coefficient is positive and might come close to one, there has to be omitted variables that I won’t take into account in my analysis, preventing me from coming up with a model perfectly explaining and predicting the average IQ of a country. Moreover, I chose to include both GDP and HDI, but, we shall not forget that the HDI is partially constructed with the GDP. Indeed, the HDI is nothing more than the geometric mean of a country’s level of education, level of longevity and GNI per inhabitant (where the GNI includes the GDP and net receipts of primary income from abroad) ; we have : \[HDI_{i} = \sqrt[3]{I_{life}\times I_{education}\times I_{GNI}}\] I am going to use it to my advantage : by assessing the impact of these two variables on the average IQ, we will be able to have an idea of the impact that the education level and the life expectation have. I did have the idea to directly study the level of education, since going to school develops the ability to think and solve problems, but, this kind of data is hard to find, and when it is available, roughly half of the countries are accounted for and the reference year is not always the same, so I decided not to include it, at least not directly.

Results and analysis

Table 1 : Regressions based on the log of the GDP, the average temperature and the population
IQ
GDP Model Temperature Model Population Model
GDP (log) 2.736***
(0.387)
Temperature (in °C) -0.939***
(0.098)
Population (in 2022) 0.000
(0.000)
Constant 14.604 99.002*** 81.141***
(9.490) (2.001) (1.039)
N 179 179 179
R2 0.220 0.342 0.007
Adjusted R2 0.216 0.339 0.001
Residual Std. Error (df = 177) 11.849 10.883 13.374
F Statistic (df = 1; 177) 50.064*** 92.158*** 1.244
*p<0.1;**p<0.05;***p<0.01

Table 1 displays the results of the 3 first regressions : all of them are linear regressions meant to assess numerically the impact of GDP (1), temperature (2) and population (3) on the average IQ. It is pretty striking that population (3) and average IQ seem totally decorrelated, as the regression coefficient between them is 0. However, these models do provide evidence on the impact of the other variables.

As the GDP is expressed in logs, we cannot directly interpret the regression coefficient. Indeed, we have to use the level-log model conventions, according to which an increase in GDP of 1% results in an increase in the average IQ of 0.027. Simple calculations show that in order for the average IQ to increase by 1 point, the GDP has to increase by 44% according to this model, which looks statistically significant as the coefficient is associated with a small p-value, a decent \(R^2\) and a F-statistic factor relatively high. Moreover, the coefficient is more than twice the standard error (0.387) : everything points that a country’s GDP does have an impact on its average IQ.

It is even truer with the temperature model, which almost depicts a perfectly negative relationship between the average temperature and the average IQ, with an even higher significance level.

Table 2 : Regressions based on the log of the GDP and the HDI
Dependent variable : Average IQ
GDP Model HDI Model
GDP (log) 2.736***
(0.387)
HDI 52.816***
(4.388)
Constant 14.604 44.008***
(9.490) (3.230)
N 179 185
R2 0.220 0.442
Adjusted R2 0.216 0.439
Residual Std. Error 11.849 (df = 177) 9.961 (df = 183)
F Statistic 50.064*** (df = 1; 177) 144.877*** (df = 1; 183)
*p<0.1;**p<0.05;***p<0.01

Table 2 allows us to compare the GDP and HDI models. Both depict a positive relationship with the average IQ, though the one with the HDI is stronger : the regression coefficient, 52.816, implies that an increase in HDI by 0.01 is associated to an increase in the average IQ of 0.52 (the coefficient is greater than 1 because the HDI is expressed as an index included between 0 and 1). The \(R^2\) is also greater for the HDI than it is for the GDP. From that, we can assume that the education level (and also the life expectation) matter more than the GDP when it comes to the average IQ. Indeed, the HDI seems to be far more significant than the GDP to explain the average IQ of countries.

Table 3 : Regressions based on the colony variable
Dependent variable : Average IQ
Colony Model
Colony -11.724***
(1.737)
Constant 88.924***
(1.332)
N 199
R2 0.188
Adjusted R2 0.184
Residual Std. Error 12.059 (df = 197)
F Statistic 45.568*** (df = 1; 197)
*p<0.1;**p<0.05;***p<0.01

The Colony Model main takeaway is the following : all other things being equal, a country going from “hasn’t been a colony during the XX° century” to “has been a colony during the XX° century” loses 11.724 points in its average IQ score. In other terms, had we had an “average former colony country” and an “average never-colonized country”, the gap between their average IQs would have been 11.724. This model seems significant too, so we can state that colonization did have, and still has, a negative impact on the average IQ of former colonies.

Table 4 : Multiple regression
Dependent variable : Average IQ
HDI 37.208***
(4.913)
Temperature -0.537***
(0.103)
Colony -1.186
(1.784)
Constant 65.821***
(4.635)
N 181
R2 0.531
Adjusted R2 0.523
Residual Std. Error 9.123 (df = 177)
F Statistic 66.854*** (df = 3; 177)
*p<0.1;**p<0.05;***p<0.01

Finally, I performed a multiple regression that includes, as explanatory variables, HDI, averageTemperature and colony. I purposefully left out imfGDP and pop2022 because their coefficients were both 0, which I think is due to the presence of the HDI variable, that already takes them into account. As they do not bring any new information, it wasn’t necessary nor relevant to include them.

This last table puts the previous findings into perspective, as the effects of the three variables are lesser than they were before. The colony variable is not really significant anymore, as it is associated to a p-value greater than 0.1, and even though the two others still are, it appears that these three variables are linked and partially explain one another, which is what Table 4 expresses with its lesser coefficients. For instance, the temperature is the variable whose effect is the most important ; however, that doesn’t mean that warmer climates directly diminish the IQs of the populations that bear it. It’s more likely that high temperatures have had many consequences (differences in development that allowed the colonization of South countries, differences in life conditions, differences in school and legal systems…), which had a more direct impact on the average IQ.

Conclusion

I have therefore been able to shed light on meaningful relationships that help us better understand the differences in average IQs between countries. My main and most explanatory variables - the HDI, the temperature, and the “colony” factor - can look rather significant, even though it is pretty clear that they co-produce each other. More than that, even though we cannot talk about causality solely based on these findings, the question of reverse causality arises when it comes to the HDI. Indeed, I stated that countries with a high HDI more easily had a high average IQ, but it could also be the other way around : perhaps the countries with high average IQs have their average IQ precisely because of their high HDI, which would allow them to provide great education to most children.

With that being said, it is clear that we still have a lot of work to do in order to perfectly understand average IQs. This study explored what seemed like the more obvious leads and we’ve been able to reach promising results. But, what was the most striking to me, regardless of the results, were the average IQ scores. I expected them to be around 100, as they should be, but it turned out that most average IQs are around 85, which could mean that the IQ, in its construction, is no longer adapted to our societies.

Acknowledgement

With this study ends our semester in Introduction to econometrics with R. As innovative as interesting, this course was taught by Florian Oswald, to whom I wish to express my warm thanks : without him, this study would not have been as thorough.

Hugo Kpakpo.

Bibliography

Works

Websites