# The non-linear effect of ability on earnings in the computer age

A reader/watcher/listener has brought to my attention another paper, which shows that, for college-educated individuals, earnings are a non-linear function of cognitive ability or *g* — at least in the National Longitudinal Survey of Youth from 1979-1994. The paper is a 2003 article by Justin Tobias in the *Oxford Bulletin of Economics and Statistics*.

There may be other studies on this question, but a selling point of this article is that it tries to use the least restrictive assumptions possible. Namely, allowing for non-linearities. In the social sciences, there is a huge bias toward finding linear effects, because most of the workhorse models everyone learns in grad school are linear models. Non-linear models are trickier and harder to interpret and so they're just used much less, even in contexts where non-linearities are very plausible.

A common motif in "accelerationist" social/political theories is the exponential curve. Many of us have priors suggesting that, at least for most of the non-trivial tendenices characterizing modern polities, there are likely to be non-linear processes at work. If the contemporary social scientist using workhorse regression models is biased toward finding linear effects, accelerationists tend to go looking for non-linear processes at the individual, group, nation, or global level. So for those of us who think the accelerationist frame is the one best fit to parsing the politics of modernity, studies allowing for non-linearity can be especially revealing.

The first main finding of Tobias is visually summarized in the figure below. Tobias has more complicated arguments about the relationship between ability, education, and earnings, but we'll ignore those here. Considering college-educated individuals only, the graph below plots on the y-axis the percentage change in wages associated with a one-standard-deviation increase in ability, across a range of abilities. Note that whereas many graphs will show you how some change in X is associated with some change in Y, this plot is different: It shows the marginal effect of X on Y, but for different values of X.

The implication of the above graph is pretty clear. It just means that the earnings gain from any unit increase in *g* is greater at higher levels of *g.* An easy way to summarize this is to say that the effect of X on Y is exponential or multiplicative. Note also there's nothing obvious about this effect; contrast this graph to the diminishing marginal utility of money. Gaining $1000 when you're a millionaire has less of an effect on your happiness than if you're at the median wealth level. But when it comes to earnings, gaining a little bit of extra ability when you're already able is worth even more than if you were starting at a low level of ability.

The paper has a lot of nuances, which I'm blithely steamrolling. My last paragraph is only true for the college educated, and there are a few other interesting wrinkles. But this is a blog, and so I mostly collect what is of interest to me personally. Thus I'll skip to the end of the paper, where Tobias estimates separate models for each year. The graph below shows the size of the wage gap between the college-educated and the non-college-educated, for three different ability types, in each year. The solid line is one standard deviation above the mean ability, the solid line with dots is mean ability, and the dotted line is one standard deviation below the mean ability.

An obvious implication is that the wage gap increases over this period, more or less for each ability level. But what's interesting is that the slope looks a bit steeper, and is less volatile, for high-ability than for average and low-ability. There is a lot of temporal volatility for the class of low-ability individuals. In fact, for low-ability individuals there is not even a consistent wage premium enjoyed by the college-educated until 1990.

Anyway, file under runaway intelligence takeoff...