Mobility: Genes

Twin Studies

[ See this spreadsheet for a table of twin studies examining income. It is largely copied from Hyytinen. ]

The median twin study on the heritability of income finds ~45% of the variability is due to genetic causes while ~0% is due to common environment.

The two most important sources of heterogeneity are gender and measurement duration, both of which affect the strength of genes' influence while leaving common environment's influence at ~0.

Of the four studies that examined men and women separately, the median found genes' effect on men's incomes are roughly 11pp higher than their effect on women's.

A Swedish study found that using average earnings over 20 years raised the genetic component estimates by 23pp points relative to a single year Benjamin (see also here).

The four studies on both genders in the US found heritablity estimates of 28%, 38%, 40%, and 52% - all looked at only one year of income, which yields a median of 39%. There was also one study of American men that found slightly higher estimates than one would expected based on the other four studies, which bumps my best guess of one-year income heritability up to 40%.

If we then correct by assuming a similar decrease in noise as found in the Swedish study, we find an estimated heritability for 20-year income of about 63%. If we extrapolate this model to 40-year income, we find heritability rises just a tiny bit more to around 64%.

There's also the fact that assortative mating applies to income too Schwartz, which also biases the above heritability estimates downwards. Adjusting for this probably places heritability estimate at around ~72%.

Note, there are yet other sources of bias inherent in twin studies that we haven't accounted for. In particular, all but one of the American twin studies used self-reported earnings data Johnson Rouse Schnittker Taubman Roos. The correlation between self-reported earnings and actual earnings tends to be around 0.8 Rodgers. This means that if error in self-reported earnings were independent among twins/siblings, it would be likely that the heritability of lifetime earnings approaches unity. On the other hand, maybe that error tends to be in the direction of their true lifetime earnings or tends to be towards their twin's income. It is unclear how to correct for this issue, but it suggests our 72% estimate is on the low side.

Finally, estimated heritability in Sweden using government data and 20 years of earnings is only ~62% after adjusting for assortative mating.

The tl;dr here is that (a) lifetime income is likely more than 70% heritable in the US and (b) this heritability is probably 10 to 20 points higher for men than for women.

Cross-Generational Mobility

An easy way to cross-reference the conclusions above is to check what they predict parent-child income correlations should be and then check the actual parent-child income correlations.

Chetty et al use 5 years of parent income and 2 years of child income from millions of tax returns. They find a correlation of about 0.34 for log income Where is the land of opportunity? The geography of intergenerational mobility in the United States. Let's assume (a) this entire effect is genetic (which seems reasonable per the above twin studies) and (b) that there is no measurement error here since we are using tax returns. From these assumptions, let's infer what the heritability of income is.

First note, assortative mating doesn't affect the correlation between average-parent-phenotype and child-phenotype: it is always h^2/sqrt(2). Second, Chetty et al confirm that the parent-child income correlation stops increasing from the mid 30s, which is when they measure it. Together, all of this suggests (legal) income averaged over 3-ish years is about 48% heritable. If we add about 18pp to extrapolate to lifetime-income-heritability, we achieve an estimate of 66%.

If we measure income at older ages and over 9 years, that 0.34 correlation rises considerably to about 0.5 Mitnik, suggesting a heritability of 70%. Extrapolating to lifetime heritability increases it a little more.

All in all, these raw parent correlations suggest a heritability of around 70%, which is pretty consistent with the results from the twin studies.

Sibling Fixed Effect Models

Another interesting class of studies for inferring the causal contribution of genes compares the naive correlations between two traits - say height and income - and the correlation that remains after including siblings fixed effects. The naive correlation can be caused by any of

1. The same genes cause both height and income.
2. The same common environment factors cause both traits.
3. Height causes income (or vice-versa).
4. Assortative mating causes the two to be correlated.
5. Some unshared environment factor causing both

The within-siblings correlation, on the other hand, can only be caused by half of (1), all of (3), and all of (5). Because of this, the difference between the naive and within-siblings correlation can offer some insight into what is driving the naive correlation - especially when pair with supplemental measures of assortative mating.

In particular, if the slope with sibling FEs is equal to the naive slope, this represents (1) a causal relationship and/or (2) unshared environment factor causes both. This isn't perfect proof of a causal relationship, but it is quite suggestive in my opinion - after all if controlling for half of genes and all of common environment don't reduce the slope at all, what remaining confounder could worry was important than those two?

Let's get concrete. It is well known that height positive correlates with income. What is less well know is that a third of this correlation goes away after including sibling FEs. Given that neither income nor height have strong common environment factors, this suggests that fully controlling for genes would remove two-thirds of the slope. This leaves a third of the slope left - to be explained either by unshared environment or height causing income, at least up until the average height. Common environment factors and assortative mating, meanwhile, look relatively unimportant in explaining the relationship.

Contrast this with BMI and earnings, where about half of the naive slope disappears once sibling FEs are added. This suggests the main reason BMI correlates with income is due to (2) or (4): common environment or assortative mating. We've already talked about how the former appears to have a minimal effect on income, but it also has a minimal effect on BMI. So, really, what this suggests is that ~half of the association between BMI and income is driven by assortative mating, while the other half is the same genes causing both/

Conventional wisdom says women care about earnings and height, while men care about BMI. Assortative mating effectively means each sex trading something the other sex values for something they value. Hence, women "trade" BMI for their mate's earnings (and height). But there is no cross-sex trade by which earnings is traded for height (except insofar as men value shorter women, but that works in the opposite direction of the naive height-earnings correlation). In short, the empirical findings above are consistent with the conventional wisdom of how dating works.

I don't think it would be super productive to go through all the traits ever examined, but here are a few such studies:

• Personality The effects of personality traits on adult labor market outcomes: Evidence from siblings
• Early life health Early life health and adult earnings: evidence from a large sample of siblings and twins
• High school popularity Friends or family? Revisiting the effects of high school popularity on adult earnings

There are also interesting studies that involve time components in their sibling FE models. For instance, this study De Neve found a significant correlation between positive affect at age 16 and income at age 30, even after controlling for IQ and educational attainment. This relationships persists at a similar magnitude even accounting for sibling FEs. This suggests that happiness likely causes people to earn more (though the relationship is fairly small: r~0.06) and, because earnings is measured 14 years after positive affect, it rules out reverse-causation.

Finally, identical twins make this even more powerful. A correlation between two variables within a pair of identical twins can only be caused by (3) and (5), which makes causal interpretations even more plausible. Such studies have examined education and earnings, which we'll look at in a future post.

Multi-Generational Mobility

Adjacent to the literature on income mobility is a fascinating literature on status mobility, which attempts to less myopically focused on money. While the main focus of this sequence of posts is on the former, I'm going to touch on the latter for a moment here.

Suppose social status is normally distributed with mean 0 and variance 1. Suppose people with an "elite" surname follow a normal distribution with mean $\mu$ and variance $\sigma^2$. Finally, suppose we say that the top 2% of people have a prestigious job. These assumptions let us model the disproportionate number of elite people with prestigious jobs:

And if we assume $\mu$ reverts towards 0 by a certain percent per generation, we can model what should happen to the proportion of prestigious-job-havers who have an elite last name (after accounting for different birth rates).

This study Clark does exactly that, using official lists of attorneys and doctors. They generally find $\mu$ is multiplied by about 0.75 per generation in Sweden.

It's important to note that if we assume (a) social status is entirely genetic and (b) there is no assortative mating, then $\mu$ should be multiplied by 0.5 per generation. The fact that it decays so slowly strongly suggests that one of those assumptions is violated: that the rich perpetuate their social status via environmental means and/or that there is assortative mating.

Mild shock.

As mentioned above, shared environment seems to explain minimal variance in income. It would, therefore, be a little strange if it explained significant variance in social status. Indeed, the only story I can think of is that maybe kids from wealthier families feel less incentive to earn more since they can rely on familial wealth. I can believe this might be true in edge cases (e.g. the top 0.1%), but it seems generally false (see Figure VI from Race and economic opportunity in the United States: An intergenerational perspective). I'm not saying childhood environment has no effect on a child's eventual social status, but the effect is probably relatively small.

This leaves assortative mating. Like I mentioned above, there is definitely noticeable assortative mating by income, and I'd guess the assortative mating by social status is even higher. I don't know how one would go about estimating the true degree of assortative mating in social status, but if r~0.38, then this plus the "100% genetic" assumption would be consistent with these results. Given the assortative mating numbers I've seen regarding income Schwartz, this seems plausible.

I think this is an interesting line of inquery that I'd like to do more with, but, for now I'm gonna call it quits - after all this is off the main trail of this post sequence.