(I know some readers are curious about this – because they have told me so..)

I have been annoyed at myself for not gathering data, given that the question has come up a couple of times over the last few weeks. So here goes:

“Mensa Norge Resultat – Mensa Norges hjemmetest
Din IQ ble beregnet til 128 tilsvarende 96.9 prosentil
Besøk Mensa.no for å ta en kontrollert test.

This test was developed by Olav Hoel Dørum from august 2007 to march 2008.”

To people who don’t speak Norwegian, this is my result from Mensa Norway’s IQ test. IQ: 128 (96,9th percentile). I didn’t think it made any sense to try out the Danish Mensa test again – I took that one a few years ago and you’re not supposed to take the same test multiple times. So I looked around the web and I took 3 different tests, all of which were tests I’ve never taken before. The first one I never got to finish, because I got a severe case of hypoglycemia while taking it (this is not an IQ boosting condition, to say the least). I knew that no matter how I handled this, the results would have been unreliable; my blood glucose when I stopped the test was 2.2 mmol/L, which is pretty damn low – low enough to have had significant performance effects for a while before I realized something was wrong. Working hard with your brain for an extended period of time lowers blood sugar, which is part of the reason why I always have difficulties during exams. So in that case I never got a result – the test was timed, and starting over would bias the estimate upwards. The second test I took was frankly stupid, because I never felt I had to think very hard about the answers. It was too easy and it gave me an unrealistically high score of 139+ (99 point something percentile, which is just silly). But this last one was probably okay and I ended up with an estimate not completely outside what I consider a ‘realistic realm’. Before taking this test, I basically didn’t think that I had more than one ‘reasonable IQ estimate’; the result of the Danish online Mensa test, which yielded an IQ estimate of 123. I had taken a few other tests along the way, but I didn’t think much of any of them and none of them caused me to significatly alter the baseline Mensa estimate. So I’ve always – well, since I took the first test a few years ago – thought of myself as an IQ 120-125 kinda guy. Maybe I should revise my estimate upwards, just a bit.

Update: Heh, I just read this part of Gwern’s site. He took the same test I did – the one that got me the 123 estimate:

“In February 2009, for the purpose of a before-after dual n-back comparison, I took the Raven’s test at http://iqtest.dk/ and scored 115. (Others report they too received low scores.)”

If Gwern’s IQ is 115 then I’m a black guy. I guess I should update. I’ve not taken many tests (3? 4?) besides the original Mensa test over time, and I’ve never taken a test which was not taken online, but part of the reason was that they yielded higher estimates than Mensa’s test, which made me question the validity of online estimates more generally. I’m sure some questioning is merited, but perhaps I’ve been overly dismissive of some of those other results.

Reaching peak performance?

From this paper – Comparative longitudinal structural analyses of the growth and decline of multiple intellectual abilities over the life span.

On a related if tangential note; I tend to do better on some of the measures included than I do on others. I tend to do well on some of the kinds of measures of intellectual ability – and/or (depending on who you ask..) measures which correlate significantly with intellectual ability – that are relatively easily observable, and I think some people, including some of the readers of this blog, overestimate me for that reason. There are people out there who can calculate the inverses of 2 3×3 matrices, then proceed to calculate the Kronecker product of the matrices and then move on to finally calculate the determinant of the resulting 9×9 matrix in a ridiculously short amount of time, and/or perhaps even without writing anything down along the way. I’m not one of those people and there are a lot of people in between me and them. (Now, you might argue that such an ability is easily observable but the kind of observability I have in mind here is one which relates to the social context.)

Incidentally, I did not blog this back when I originally read it (via MR; Tabarrok posted another graph which sparked a lot of debate) and now’s as good a time as any to post it here:

Here’s another one from the same presentation:

Gordon – Everyday Life as an Intelligence Test

Here’s the link (pdf). Some excerpts:

“this article examines the issue of general intelligence in everyday life, where many tasks tend to be performed widely if not universally. The aim is to elucidate both the practical importance of intelligence within that sphere and some major obstacles to the full recognition of that importance. The effects of such obstacles often exist side by side with a keen, if sometimes reticent, awareness by many individuals of the role of intelligence in its more standard applications, such as schooling and certain occupations. [...]

It is often not apparent to persons that cognitive tasks are embedded in many of life’s everyday activities, as those activities (say, parenting) often exhibit other, perhaps more salient, facets of content (warmth) that seem to outweigh any cognitive component (judgment) until the latter comes forcibly to attention (as when a warm parent leaves small children unattended with matches in the house). Empirically, however, such noncognitive facets may individually contribute much less than g does to variance in overall or long-term task performance (child safety) and, especially, to the task-as-item covariance (i.e., what is common to all such tasks) upon which any test depends for its reliability. [...]

Underrecognition of the cognitive component is abetted by numerous other features of the phenomenology and organization of intelligence in everyday life. Not least among these is the fact that there certainly are everyday activities in which a cognitive component is thought crucial, but such activities are set somewhat apart by our culture in special categories. The result is that the residual activities may unthinkingly be consigned by laypersons to the noncognitive realm by virtue of the contrast. Education and learning have, of course, been the chief repositories of tasks viewed as essentially cognitive, and it is only in recent times that this view has been broadened among specialists to include performance within jobs and participation in crime.
Although Singaporean mothers were able, when specifically asked, to perceive the role of intelligence in a variety of children’s behaviors, such as “Shows common-sense” and “Sizes up a situation badly,” it was “Learns quickly,” a typically academic marker, that had the highest g loading in a factor analysis of 55 ranked items (Nevo & Khader, 1995). Between first, third, and sixth grades, academic skills increasingly come to dominate children’s attention as examples of what it means to be smart or intelligent (Yussen & Kane, 1985, Tables 2-3). It would appear that social perception of the role of intelligence is drawn toward outcomes with the highest g loadings, which is not surprising, but it may sometimes be tacitly misconcluded as a result that other outcomes have no g loadings at all when their loadings are simply not as high. Just as individuals may often be assigned too hastily to only two categories on the g continuum, say, qualified and unqualified, so may the g-loadedness of outcomes be falsely dichotomized.
A crucial final point is that, as in aggregate data, repetition of a single task or response by multiple persons can produce regularities in percentages and averages that are as reliable in life (and as indicative of the operation of g) as the results of multiple tasks presented to a single person on tests. If two populations differ in the average g that they bring to a repeated single task in everyday life, reliable group differences in average performance will emerge, just as group differences emerge in rates of passing an individual test item. Support for the role of intelligence from aggregate data, when uncovered, thus makes it possible to work backward to the inference that intelligence was very likely an influential component of the individual behavior so aggregated if that was not already an accepted view [...]

What I am arguing against here, and hope to overcome with data, is a double standard in agnosticism among many test defenders concerning the potential g-loadedness of items, depending on whether the items appear on tests or in everyday life. [...]

Although again deceptively commonplace to test experts, Jensen’s (1986b,p. 109) third provision, that in order to measure individual differences in a group of people, “item difficulty (i.e., percent ‘failing’ the item) must be greater than 0 and less than loo%,” is of profound significance for understanding why the role of g in life tasks tends to be underestimated. Many everyday behaviors, such as operating a car, prove so easy for most persons that they seem not to depend on what the layperson thinks of as intelligence at all, and performing them produces no subjective sense of the effort known as “thinking.” Recall the estimate quoted above that some errors occur as seldom as one in 10,000 opportunities. Many such tasks, of course, were overlearned in childhood, when effort would have been more apparent. Adults who commit inexplicable errors on such tasks are greeted with special epithets, suggestive of no intelligence at all. [...]

Research on elementary cognitive tasks (ECTs), although conducted in the laboratory rather than on everyday tasks, provides especially informative examples of performances misperceived as making no demand on intelligence. ECTs are often so easy (pressing the button beside the light that goes on) that virtually no one gets them wrong, and participants cannot tell the difference between their own better and poorer performances (Jensen, 1980a, p. 691). Sensitive monitoring of reaction times (defined as the interval, in milliseconds, between the light signal and release of one’s finger from a home button) reveals, however, that speed of such performances does vary and is reliably correlated with g (Jensen,1993b). Jensen (1980b, p. 109) remarked that the cognitive demands of one particular ECT “are so extremely simple that it seems almost implausible that the procedure could yield any measurements that would be correlated with IQ.” The indefinite linearity of performance with IQ upwards (e.g., Hawk, 1970) appears to apply in the downward direction as well when appropriately measured, to include performance on tasks even as easy as these. [...] In test parlance, mundane life lacks sufficient “top” or “ceiling,” that is, lacks items at a sufficiently high level of difficulty to reveal clearly the advantages of high intelligence over average intelligence [...]

Almost all research on intelligence has been focused upon the individual level of analysis. For studied outcomes, research usually takes the form of correlating a measure of g with the outcome. For several reasons, some made understandable by the previous discussion of the test analogy, the theoretical value of such correlations is often underestimated. First, behaviors are rarely observed at the lowest level of performance, which would make their dependence on intelligence more apparent, and the correlations more convincing, because society is usually structured to prevent such poor performances from occurring. Second, performance failures, when witnessed, are often attributed to superficial causes, for example, not planning ahead, that are formulated in a manner that conceals the role of intelligence behind noncognitive, often motivational, terminology. Third, modest correlations that do get reported between IQ and outcomes are often dismissed as too inconsequential to motivate theory”

…

From the first 13 pages (of 118). I haven’t read much more than that yet, maybe I’ll post more on this later. Here’s a related paper written around the same time.

Why g matters

The paper is here, here are some excerpts:

“personnel psychologists no longer dispute the conclusion that g helps to predict performance in most if not all jobs (Hartigan & Wigdor, 1989). Rather, their disputes concern how large the predictive validities are, often in the context of deciding the appropriate composition of a personnel selection battery. Estimates of the average validity of g across all jobs in the economy generally range between .3 and .5 (on a scale from 0 to 1.O), depending on how validities are corrected for unreliability in the criterion and restriction in range on the predictor (Hartigan & Wigdor, 1989).
These estimates are based primarily on studies that used supervisor ratings of job performance. Average validities are yet higher when performance is measured objectively.

Validities vary widely across different kinds of jobs, from a low of about .2 to a high of .8.” [...] An especially important observation is that predictive validities vary systematically according to the overall complexity of the work involved.”

[...]

g can be said to be the most powerful single predictor of overall job performance. First, no other measured trait, except perhaps conscientiousness (Landy et al., 1994, pp. 271, 273), has such general utility across the sweep of jobs in the U.S. economy. More specific personality traits and aptitudes, such as extraversion or spatial aptitude, sometimes seem essential above and beyond g, but across a more limited range of jobs (e.g., Bat-rick & Mount, 1991; Gottfredson, 1986a).
Second, no other single predictor measured to date (specific aptitude, personality, education, experience) seems to have such consistently high predictive validities for job performance. The clearest exceptions to the predictive superiority of g prove its relative importance.”

[...]

“there are striking differences in the IQ ranges from which occupations tend to draw the bulk of their workers. More specifically, there appear to be minimum IQ thresholds that rise steadily with job level. The median of an applicant pool is often recommended as a minimum passing score for further consideration of applicants to that job (Wonderlic Personnel Test, 1992, p. 14), so it can be viewed as a threshold for applicant competitiveness. By this measure, one needs an IQ of about 120 (the 91st percentile of the general population) to be competitive for the highest level jobs in Figure 1 (research analyst and advertising manager). The IQ levels required for competitiveness drop with job level: for example, IQ 112 (81st percentile of the general adult population) for accountant and teacher; IQ 100 (50th percentile) for cashier, meter reader, and teller; IQ 90 (25th percentile) for custodian and material handler. The medians of the highest and lowest of these applicant IQ distributions (IQ 120 vs. 90) differ by 2 SD, which means these distributions do not overlap much.
If the 25th WPT percentile of applicants is used to estimate the minimum threshold for employability in an occupation, it suggests that virtually all occupations accommodate individuals down to IQ 110, but virtually none routinely accommodates individuals below IQ 80 (WPT 10). Employment options drop dramatically with IQ-from virtually unlimited above IQ 120 to scant below IQ 80. Such options are virtually nonexistent today (except in sheltered settings) for individuals below IQ 70 to 75, the usual threshold for borderline mental retardation.
Lest IQ 80 seem an unreasonably high (i.e., exclusionary) threshold in hiring, it should be noted that the military is prohibited by law (except under a declaration of war) from enlisting recruits below that level (the 10th percentile). That law was enacted because of the extraordinarily high training costs and high rates of failure among such men during the mobilization of forces in World War II (Laurence & Ramsberger, 1991; Sticht et al., 1987; U.S. Department of the Army, 1965).”

[...]

why does g have such pervasive practical utility? For example, why is a higher level of g a substantial advantage in carpentry, managing people, and navigating vehicles of all kinds? And, very importantly, why do those advantages vary in the ways they do? Why is g more helpful in repairing trucks than in driving them for a living? Or more for doing well in school than staying out of trouble? For example, IQ correlates .5 to .7 with academic achievement (Jensen, 1980, p. 319), but only -.25 with delinquency (Gordon, 1986). What explains this pattern of results?
Also, can we presume that similar activities in other venues might be similarly affected by intelligence? For example, if differences in intelligence change the odds of effectively managing and motivating people on the job, do they also change the odds of successfully dealing with one’s own children? If so, why, and how much?
The heart of the argument I develop here is this: For practical purposes, g is the ability to deal with cognitive complexity – in particular, with complex information processing. All tasks in life involve some complexity, that is, some information processing. Life tasks, like job duties, vary greatly in their complexity (g loadedness). This means that the advantages of higher g are large in some situations and small in others, but probably never zero.”

[...]

“variance in performance levels among workers rises with job complexity. Hunter et al. (1990) found that the ratios of SD in performance to mean performance were 19%, 32%, and 48%, respectively, in low-, medium-, and high-complexity civilian jobs. This means that the same differences in g lead to bigger differences in performance in more complex jobs, because g variance counts more heavily in those jobs.”

[...]

“Perhaps the most important conclusion to be drawn from these people-related ratings, however, is that dealing with people is always fairly complex. This should not be surprising, because other individuals are among the most complex, novel, changing, active, demanding, and unpredictable objects in our environments, Living and working with others is a complicated business.”

[...]

Education, training, experience, and the job knowledge to which they lead are all important aids in performing jobs well. This fact is aptly captured by discussions of the “practical intelligence” and “tacit knowledge” that is gained through experience (Jensen, 1993; Schmidt & Hunter, 1993; Sternberg & Wagner, 1993; Sternberg, Wagner, Williams, & Horvath, 1995). Raw intelligence is not enough, as the path analyses of intelligence, knowledge, and performance discussed earlier suggest. However, knowledge is merely a tool that people apply with different degrees of competence to an unending array of new situations – some potentially critical (engine failure in flight, an injured or trapped child, plunging sales, corporate mergers) and others less so (novel questions or complaints from customers, comparison shopping, applying and interviewing for jobs, setting behavioral standards for one’s adolescent children). As discussed earlier, the facility with which individuals accumulate these tools (trainability) and the competence with which they apply them (task proficiency) often depend heavily on g, especially in the absence of close supervision.

Complex Job Duties Have Everyday Analogs
Many of the duties that correlate highly with overall job complexity suffuse our lives: advising, planning, negotiating, persuading, supervising others, to name just a few. The job analysis tools used to analyze paid work could readily be adapted to analyze the nature of unpaid roles in life, such as parenting. One might ponder, for example, whether the most important elements of good parenting involve the duties associated with low complexity work such as driver, custodian, nurse’s aide, messenger, and food service worker – or whether they are more like the duties of moderate to high complexity jobs such as teacher, counselor, dispatcher, police officer, and accountant.”

[...]

Table 8 shows the percentages of White adults who are proficient at each of the five levels on the three NALS scales. Generally about 4% reach the highest level. Level 5 (376-500) signals an 80% probability, for example, of being able to summarize two ways that lawyers challenge prospective jurors (based on a passage discussing such practices) and to use a calculator to determine the total cost of carpet to cover a room (see Figure 2). Roughly another 20% of White adults reach Level 4 (326-375), where individuals can perform such tasks as restating an argument made in a lengthy news article and calculating the money needed to raise a child based on information stated in a news article.
A total of about one third of White adults reach Level 3 (276-325), but no higher, which includes capabilities for writing a brief letter explaining an error in a credit card bill and using a flight schedule to plan travel arrangements. Level 2 proficiency (226-275) includes locating an intersection on a street map, entering background information on an application for a social security card, and determining the price difference between two show tickets. This level is reached but not exceeded by about 25% of Whites. Finally, one out of seven White adults functions routinely no higher than Level 1 (less than 225), which is limited to 80% proficiency in skills like locating an expiration date on a driver’s license and totaling a bank deposit. Individuals at Level 1 or 2 “are not likely to be able to perform the range of complex literacy tasks that the National Education Goals Panel considers important for competing successfully in a global economy and exercising fully the rights and responsibilities of citizenship” (Baldwin et al., 1995, p. 16).”

…

The paper has much more.

Garett Jones’ paper

Plamus linked to it in the comments section and I’ve seen it linked elsewhere as well, it’s an interesting paper.

Here’s the abstract:

“A recent line of research demonstrates that cognitive skills—IQ scores, math skills, and the like — have only a modest influence on individual wages, but are strongly correlated with national outcomes. Is this largely due to human capital spillovers? This paper argues that the answer is yes. It presents four different channels through which intelligence may matter more for nations than for individuals: 1. Intelligence is associated with patience and hence higher savings rates; 2. Intelligence causes cooperation; 3. Higher group intelligence opens the door to using fragile, high-value production technologies, and 4. Intelligence is associated with supporting market-oriented policies. Abundant evidence from across the ADB region demonstrating that environmental improvements can raise cognitive skills is reviewed.”

I don’t buy 4 at all unless/before much more work is done in that field. Now it mostly just reads ‘I read Caplan’s book and people I know talk about it so I should probably mention it in my study’ to me. The other parts I don’t have strong opinions about. Below’s some stuff from the study and my remarks. Here’s Figure 1 from the paper, you have log-GDP pr. capita up the y-axis:

The ‘PRC’ in the corner is China, and there are plenty of reasons (the name of the most significant one is Mao) why you’d think it makes good sense that they haven’t managed as well as the theory suggests. The IQ-effect is huge: “Jones and Schneider [...] found that across countries [...]: 15 IQ points is associated with a 150 percent increase in productivity.” If you think simply in terms of labour input, this finding would suggest that in a country with an average IQ of 115, 2 average workers can be expected to add the same value to a product as (‘do the work of’) 5 workers living in a country with an average IQ of 100. Yet the private returns related to that productivity difference is very small; in the paper they mention an estimated wage differential of just 13 percent.

There’s a lot of stuff in the paper, I’ll just go through a few interesting bits I found. Here’s some stuff on environmental factors and their influence on IQ:

“there is a vast public health literature on environmental correlates of intelligence, and many of these papers study nations in Asia. A study of excessive fluoride in Indian drinking water found a 13 IQ point-difference between children “residing in two [separate] village areas of India with similar educational and socioeconomic conditions” (Trivedi et al. 2007, 178). If even half of this relationship is genuinely causal, and if intelligence has some of the technological and political spillover effects discussed below, then public health matters are of first-order concern for economic development.”

The impact of just two environmental factors of that size could in theory reduce the mean intelligence of a population with Mensa-level average IQ to that of current-day Japan. These effect sizes are huge.

“Arsenic and fluoride exposures are also associated with low IQ in the People’s Republic of China’s (PRC) Shanxi province (Wang et al. 2007, 664), even when comparing “groups [who] lived in rural areas with similar geographic and cultural conditions and a comparable level of socioeconomic development.” High arsenic exposure was associated with a 10-point IQ gap, and high fluoride exposure with a 4-point gap. In both cases, the “normal” group had an IQ of 105, 5 points above the US mean.

In the Visayas region of the Philippines, Solon et al. (2008) found evidence that lead levels reduced the IQ of children. In their study, one microgram of lead per liter of blood was associated with a 2.5 point reduction in the verbal IQ of older children, and a 3.3 point reduction in the IQ of young children. In their sample of children, the levels of lead in the blood averaged 7.1 micrograms per liter, so lead exposure could be costing the average child in this sample 15 IQ points even under conservative estimates.”

The role of nutrition is mentioned in the paper, but they don’t go much into the specifics. I’m pretty sure that’s one of the main things holding India back on the IQ-scale of Figure 1.

I think both point V and VI are only/mainly there because of the agenda of the authors and I hate that kind of thing. V is almost pure speculation using an already (with respect to which conclusions can be drawn from the findings) speculative voter preferences model from the US to talk about East Asia. Smarter people will be more likely to support free market policies if they think they’ll gain from it and they get a say in the matter, which depends mainly on how the local government decides to split up the cake. Show me a group of American professors of theoretical physics pushing for more free market policies in education (fewer gov. subsidies). No, that’s not the relevant margin, but to take an extreme example in the opposite direction, in a standard median voter model you could have an IQ increase of 30 points of the 4 top deciles having no effect on policies whatsoever, if the intelligence of the median voter is unchanged. Yeah, you might argue the IQ effects are to be had on the other side of the distribution, but model symmetry means that you could make the same argument and apply the change to the 4 lowest IQ deciles. Conceptually they probably just take up this subject to encourage further research, but I’m one of those people thinking that Caplan is drawing way too strong conclusions from his findings already, and using IQ proxies to speculate about effects in countries looking nothing like the US, having wastly different political systems – well, that’s just not very smart. Point VI is of the same kind – it smells of ‘we want to push this idea, how can we include it in the paper’-motivation. It mentions one way to increase a country’s IQ – immigration. From the paper:

“Even if scientists and public health officials quickly reach their limits in raising a person’s IQ—again, not a foregone conclusion — we still have a reliable tool for raising a nation’s IQ. Encourage immigration by individuals with higher average intelligence. Many countries implicitly do this by permitting high-skilled immigrants to enter and work legally.”

Nowhere in the paper is it mentioned that this is most likely a zero-sum game. One country’s gain is another country’s loss. And the ‘many countries implicitly do this…’ part is correct but only half of the story, as many countries, especially Western countries, also implicitly do the opposite – import massive amounts of low-IQ immigrants (and also implicitly form/maintain policies which encourage these people to have a lot of children, lowering national IQ and future human capital even further).

Surprising fact(s) of the day

A comment on gnxp(/discover):

“Sorry, kinda OT: “standard deviation of I.Q. within the population is 15 points, and across full-siblings it is also 15 points”

Any references for this? I find this result very, very surprising. Using your analogy to height, this would be an equivalent of height distribution in families having the same variation as in general population. Anecdotally this sounds wrong.”

Razib in his response to the comment then pointed to this. Quote:

“But how similar are biological siblings? The typical sibling correlation for IQ test scores is about .45 when corrected for attenuation (Scarr & Weinberg, 1978). If the IQ correlation between biological siblings is .45 and the standard deviation of the IQ measure is 15 points, which is typical of such measures, then the average absolute difference between siblings is 13 IQ points, a difference of nearly one standard deviation.

[...]

Given that randomly paired people in the population have scores that are not correlated, their average IQ difference is 17 points, compared with the biological sibling difference of 13 points – not a very impressive increase for being a randomly chosen mate.
Adopted adolescent siblings, reared together since infancy, have negligible correlations in IQ (-.03 in our study and .02 in another large study) on the same intelligence scales, so that their average difference is close to that of the general population.”

…

So the standard deviation of siblings is a little lower than that of the general population – but not much. I had no idea the standard deviation of (biological) siblings was that high, though I probably should have had a suspicion about it given the stuff I do know about this area. I knew about regression towards the mean, but I’d always implicitly modelled the mean reversion process as though the stdvr. of siblings was significantly lower than that of the population in general. As noted the variance is smaller, so it depends on your definition of significantly, but still, I find this result very surprising and I now think that there are probably other things in this area I should consider myself less sure about. Of course the fact that this holds for siblings in general does not mean that it holds for all sibling pairs. I’d estimate that for ‘reasonable estimates’ of my brothers’ IQs and mine the stdvr. is about half of that (6-7). There’s just no way it’s above 10.

…

So I decided to add another point to this post which might seem surprising to a lot of people unfamiliar with statistics. The precise numbers matter less than the concepts I try to illustrate, not having looked at them closely I don’t know if the numbers are completely correct, but the concepts are. Say you have a large country, Egypt, with a population of 80.000.000 people and a much smaller country, say Switzerland, with a population of ~8.000.000 (1/10th of Egypt’s). Using the IQ estimates from IQ and the Wealth of Nations gives us corresponding national IQs of 83 (Egypt) and 101 (Switzerland). Now assume the two IQ-distributions follow normal distributions and have a sigma of 15. How many people with an IQ above 130 do the two countries have given our assumptions?

I was lazy so I just used this handy Java applet to calculate the probabilities and Excel to do the rest. The question I’m asking is: What is the probability that the IQ of an individual is between 0 and 130? How much does the difference in the means matter compared to the population difference? Well, in Egypt’s case, the resulting probability is 0,99914 (setting mu=83, sigma=15 and let 0 and 130 be the cutoffs). So ~0,08% have an IQ of 130 or more. In Switzerland’s case the probability is 0,973402. So 2,66% of the population has a mean of 130 or more. Now we figure out how many people those percentages correspond to:

Egypt: ~0,08% * 80.000.000 = 69.120 people.
Switzerland: ~2,66% * 8.000.000 = 212.784 people. This is more than three times as many as Egypt.

Given the difference in population size, what average IQ-level would Egypt have to have to achieve the same number of very smart people? The answer is that a population with an average IQ of 88 with stdvr. of 15 yields a 0,255% likelihood of an individual having an IQ higher than 130 (1/10th the likelihood of the Swiss, because there are 10 times as many people in Egypt), and approximately the same number of very smart people.

If a population has a quite low average IQ, there’ll be very few very smart people pretty much no matter how many people live there; likely even fewer than you’d think.

IQ and willingness to pay

Ok, here’s a few thoughts (I have been studying for exams for some days now, bear with me…):

Consider a situation where the following 3 assumptions are fulfilled:

1) Doctors have found a method to increase cognitive ability (~ IQ)

2) The treatment is uncomplicated (no risks involved) and will if undertaken cause a permanent boost in the cognitive ability.

3) IQ and income are uncorrelated, and an increase in IQ do not change your current or expected future income (this in order to disregard investment incentives and only focus on the “pure” marginal utility of cognitive ability).

4) Having made these assumptions, how much would you now be willing to pay in order to increase your IQ by 1 point? 5 points? How do your marginal wtp-function look like? Is it increasing or decreasing? Is it kinked? Why?

5) Do your answers depend on the population distribution?

To elaborate on this, consider first the case where you are the only one offered the treatment; that is, the population distribution is unaffected by the introduction of the procedure – meaning that by undertaking the treatment, you will move up in the intellectual hierarchy. Consider next the case where the treatment is publicly available. Now, by paying for the treatment, you get more intelligent, but many others do so too; such a scenario might result in an outcome where you still will not be able to understand what the smart-asses around you are talking about, but to understand Einstein’s points about general relativity will no longer be a problem. Stated in another way – in this case, by not undertaking the treatment, you will most likely move downwards in the intellectual hierarchy.

5b) Having considered the two scenarios above: How much of your wtp is related to the cognitive ability per se, and how much is related to the distributional effect?

6) Might IQ and wtp be correlated? How and why? What about income?

I have a fairly good idea about my own preferences and wtp-function, but I shall not share this with you. I don’t know about 6)