Mobility: Intelligence

What is Intelligence?

Intelligence and personality research actually share quite a bit of commonalities.

People tend to come to both with strong preconceived notions and feelings. Both are abstract and kind of ineffable by nature. Both are poorly defined in layperson use.

One other thing they share is the standard approach used by experts to resolve these issues: factor analysis Factor analysis. In Wikipedia.

"If I could only tell you N numbers about someone to help you predict what they're like, what N numbers would I give you?"

This is kind of abstract, so let's go through personality as an example.

Researchers basically came up with a bunch of quantitative questions that felt related to personality. Questions like "Rate how well the following sentence describes you from 1 to 5. I am always prepared."

Next, they sent out surveys with these questions to a bunch of people.

Then they did factor analysis to figure out how to compress peoples' answers into five numbers. They then slapped on some English labels and, voilà, the Big Five personality model was born Five personality traits.

IQ was derived in a mathematically similar way, but instead of personality questions, they gave people lots of cognitive tests.

It turns out there that performance on superficially completely different tests are, in fact, virtually always positive correlated. For instance, there is a positive correlation between the ability to tell musical pitches apart and scores on math tests. Because this correlation is strong and robust, when statisticians run factor analysis, they find that there is a single number (factor) that dominates the explanatory power: the "general intelligence factor" (or "g factor") G factor (psychometrics). In Wikipedia

This is how intelligence is rigorously and statistically defined in the mainstream literature: it is the abstract number that allows for the best prediction of your performance on a wide variety of cognitive tests.

A wrinkle this creates is that you can not measure someone's intelligence directly: you can only infer it statistically (e.g. with noise). In practice, this noise tends to be small and, so, simplistic analysis (and lay people) often conflate the score on an IQ test and someone's actual intelligence (g-factor), but this conflation causes issues.

The most important issue is that the correlation between IQ test score and X (some other variable) will almost always be lower than the (unmeasurable) correlation between g-factor and X. This is a manifestation of a more general statistical problem introduced by measurement error that is frequently ignored, even in academia.

Intelligence Heritability

From Haworth:

I'm going to focus on young adulthood.

While I think this paper is a good survey of the literature, I have a few issues with its analysis. The biggest is that they conflate measured intelligence with actual intelligence. Specifically:

1. The "0.90" test-retest correlation cited comes from Jensen, where the test-retest correlation is mentioned twice:

   The reliability coefficients for multiitem tests of more complex mental processes, such as measured by typical IQ tests, are generally about .90 to .95. This is higher than the reliability of people’s height and weight measured in a doctor’s office!

   For intervals of less than one year, the test-retest correlations are generally above .90.

   This is just a sloppy citation, but it impacts the next point...

2. The authors elide an important definitional/philosophical problem. The fact the test-retest correlation for g is only 0.90 is a result of conflating two different definitions of g: a score on a test to measure g and the platonic ideal of g itself. The latter must, by definition, have a test-retest validity of 1. This suggests the correlation between MZ twin's gs is actually more like 0.89 and that much of the "unshared environment" is, in fact, simply due to measurement error.

3. But, in fact, the problem is worse than that: this still assumes IQ tests are unbiased measure of g - e.g. it assumes your score on the Wechsler is just g plus some random noise. This is probably not the case. This can most easily be seen in the subtests: it doesn't matter how many questions you add to your math subtest, at some point the reason it doesn't perfectly measure g is that g is not just math. Each test has a test-specific factor that isn't g, and unless you take literally infinitely many tests these factors will introduce additional error that can't be estimated via simple retesting.

   For instance Raven's matrices and the WAIS have a correlation of about 0.84 Paul, 0.76 (when corrected for range-restriction) O'Leary, or 0.74 McLaurin, much lower than the ~0.925 you'd expect based on simple test-retest correlations.

   For this reason, it is entirely possible that the correlation between identical twins actual intelligence (as opposed to measured intelligence) is indistinguishable from 1.

   The sceptic will retort that maybe the test-specific factors are even more heritable than g, which would mean traditional analysis of twin studies will overstate g's heritability. To this there are two defenses: (a) even after only accounting for the within-test measurement error, estimates of g's h^2 rise to above ~0.89, which makes it one of the most heritable traits to be measured; it is, a priori, unlikely that the test-specific traits are even more heritable, and (b) more g-loaded tests tend to be more heritable Kan Pedersen Nijenhuis, which means test-specific traits must tend to be less heritable than g.

All the above points suggest the true correlation for MZ intelligence is approximately 1, 22% higher than the measured correlation. The same arguments apply to the DZ correlation: placing the true correlation at about r~0.59 rather than the measured r~0.49. Naively, this DZ correlation would suggest that common environment is still important, even in young adulthood. This brings us to assortative mating.

As the authors, themselves, note: they did not account for assortative mating, which they admit is probably a problem. The correlation between spouse IQs is typically reported to be in the 0.3-0.4 range, with some studies finding values as high as 0.6 Watkins Familial studies of intelligence: A review Mascie-Taylor Watson. Again, though, these correlations run into measurement error issues and, so, I think a conservative estimate of the correlation between spouse intelligence is r~0.4, which would explain away about 7pp of the DZ correlation. It is very much not a stretch to believe assortative mating also explains away the remaining 2pp and brings the DZ correlation down to 0.50, exactly where you'd expect a 100% heritable trait to be.

Moreover, most IQ studies assume non-zero common environment and zero genetic dominance effects: that is they use the ACE model rather than the ADE model. This means they are biased against finding genetic effects. We don't need to appeal to this bias, but it gives yet more evidence that traditional estimations are biased against genetic explanations.

In other words, I think bulk of the evidence suggests that true intelligence is 100% heritable, and that belief to the contrary stems from imperfect measurement and common ACE model assumptions.

That being said, in the name of full disclosure, here is all the evidence I've found against this conclusion:

• Some experts believe common environment can have significant effects on intelligence in adulthood Kaplan.
• Even within identical twins, IQ test scores correlate with income - albeit, they explain only about a quarter the variance Sandewall. This suggests that some of the facets of unshared environment that affect IQ scores also affect ability to earn money, which means such factors can't be mere measurement error. In my opinion, the most parsimonious explanation is that some test-specific factors help on both (imperfect) IQ tests and with earning money, while intelligence itself remains entirely genetic.

Correlation with Income

The correlation coefficient been IQ scores and income has been estimated at 0.40 Jensen, 0.15 Bowles, 0.27 Predictors of objective and subjective career success: A meta‐analysis, and 0.23 Strenze, and its typically higher for men than for women.

One significant problem with some of these meta-analyses is that they include studies that use different control variables (or none at all), which makes aggregating them in a meta-analysis dubious at best. The two meta-analyses I found that didn't do this simply used no control variables at all and found correlations of 0.27 Predictors of objective and subjective career success: A meta‐analysis and 0.23 Strenze.

However, I took a look at the study cited by Jensen. It had nearly 29,000 people and some odd things show up when we look at the details of the two meta-analyses above as they relate to this study.

The first meta-analysis didn't include this study at all for reasons I can't discern.

The second study did include it, but gave it less weight for no principled reason:

Moreover, the second study used the correlation found in the overall sample rather than at the highest age. This isn't a "mistake" per-se, but since the correlation between IQ scores and income increase with age, but it is a decision that affects the results. If the authors hadn't made these choices, the meta-estimated would likely have been about 0.27, matching the other meta-analysis.

Both meta-analyses find the correlation between IQ and income increases with age.

There are, however, several issues with taking these correlations at face value. More crucially, these correlations ignore measurement error (are you noticing a recurring theme?). For instance, if reported income correlates with measured income r~0.8 and IQ test score correlates with g-factor r~0.8, then the observed r~0.27 reflects a true correlation of r~0.42. This presumably rises further if we were to use lifetime income rather than one-year income, which is the most common measure in the above studies.

Given all the above, I'd guess the the correlation between g-factor and lifetime earnings is somewhere between 0.4 and 0.6.

How much of that effect is causal? I'm genuinely not sure whether that is a coherent question, and I'm definitely unaware at any attempt to establish a causal connection. I think the best we can say is that IQ significantly predicts earnings and that (genetic) variance in IQ accounts for roughly 40% of the genetic variance in income.

Outliers

It has been suggested by some that intelligence has decreasing returns - that, after a certain point, it doesn't pay to be smarter. As far as I know, no one has investigated this claim for earnings, specifically, but some studies have investigated this for other correlations and, as far as I've been able to discern, there isn't really any support for the hypothesis. Probably the most famous such study is the Study of Mathematically Precocious Youth Study of Mathematically Precocious Youth. In Wikipedia Lubinski, D., & Benbow, C. P. (2006) Robertson, but see also Preckel.

There's a weaker form of this hypothesis: that intelligence matters less at higher levels of intelligence. As far as I know, this hasn't been rigorously examined either, but I'm skeptical because of this figure from those "precocious" youth Robertson:

There is, however, a sense in which it is true, and that is Spearman's "law of diminishing returns", which is basically the finding that tests become less correlated at higher levels of ability. For instance, maybe the correlation between English and math test scores is r~0.7 for typical tests, but is only r~0.3 for tests taken by people at the 95th percentile. This general idea is true Blum.

Causation

Whether intelligence causes income is a tricky question - largely because it depends how we define intelligence. The literal number printed you representing your score on an IQ tests obviously doesn't causally affect how much money you earn.

Instead, for investigating whether intelligence causes income, it only really makes sense to refer the abstraction that is intelligence ("g-factor").

Suppose our discussion above is all 100% true and that adult intelligence is literally 100% heritable. In that case, it isn't meaningful to distinguish intelligence from the genes that cause it (at least in ethical studies), so the most we can say is that the correlation between genes and intelligence is an unbiased measure of the extent to which the same genes cause both.

Alright, but suppose the above discussion is only 90% true. Suppose intelligence has some non-genetic causes. Then, this question becomes equivalent to the questions of whether height and BMI cause income. To answer it, we can use the same methodology: looking at twins and siblings:

• A Danish study found the slope between IQ and earnings falls 23% once you include sibling FEs Hegelund.
• A Swedish study found a naive IQ~income correlation of 16% Sandewall, but that this fell to 7.8% after including twin FEs.

So, sibling FEs drop the slope by about 25%, and MZ twin FEs drop it by about twice as much. This is consistent with (a) minimal shared environmental confounding (b) half the correlation is due to the same genes causing both outcomes (c) half the correlation is because intelligence causes income.

It is also possible unshared environment acts as a confounder here, causing both income and intelligence, but given that paucity of shared environment's effects, that doesn't seem likely to me.