I suggested in the previous post that America’s elite reproduces itself through privileged access to higher education. Digging deeper into it, I realize that that is not quite what’s up. Parental income is *not* in fact a strong correlate of the kid’s income. See Figure 1. (We are using the same spreadsheet as the previous post.)

Something quite different is going on. Figure 2 reproduces the graph in Figure 1, but with the school tier identified. What I really like about this graph is that it makes abundantly clear precisely what is going on. The prestige of the university you attend largely determines your earnings. This is the big sort.

Figure 3 displays the mean earnings for different college tiers. The prestige university premium is the difference in earnings between graduates of prestige schools and those of non-prestige schools. Taking non-selective schools as the baseline, the premium ranges from $13,334 for selective schools, $28,278 for highly selective schools, $45,371 for other elite schools, and $84,803 for Ivy Plus. On the other side of the great divide, taking never attenders as the baseline, attending late adds $3,299, attending for less than two years adds $4,515, attending a two-year program adds $12,772, and attending a non-selective 4-year college adds $12,867. The prestige school premium is dramatically larger than the college premium.

My previous post suggested that rich households enjoy privileged access to elite schools. Yet the evidence for that is thin. Figure 4 shows that while school tier is an excellent predictor of income, parental income is a poor predictor of school tier.

Just to be sure, I tried fitting a multinomial model. Specifically, I fit an ordinal probit model that posits that the probability that you end up in one of *n* boxes depends on a unobserved latent variable as follows.

Figure 5 displays the *fitted* probabilities of getting into prestige schools for selected parental income percentiles.

The probit model has very poor fit; meaning that parental income is indeed a poor predictor of the odds. The basic reason is that the odds decay really fast; especially for the top tiers. Because the model is looking for the gradient across the parental income distribution, the relatively high rates at the very top end get barely picked up. Even so, the coefficients are what you’d expect and they are significant. (There is indeed nothing wrong with the probit model itself. See postscript below.)

Our interpretation is that for the bulk of population parental income has little effect on the kids’ odds of getting into prestige schools. Whence the posited channel of class reproduction—parental income increases the odds of the kid getting into a prestige school—is empirically indefensible.

This of course does not mean that parents do not pass on their advantages to their children. They do. But not through the channel we posited. Specifically, parental income becomes a good predictor of kids’ income *after* we control for school tier. Figure 6 shows that this effect is significant for all school tiers. And that it is much more significant for lower tier than for higher tiers.

We also run a full model for kids’ income with parental income, dummies for school tiers and percent unemployed, we find all variables to be significant and obtain an excellent fit. Figure 7 displays the scatter plot.

To sum up: There are two basic channels through which parental advantages can be passed on to their children. (1) Children of richer parents can get into prestige schools at higher rates. (2) Parental privilege can help children achieve higher earnings at the margin given their school tier. Somewhat counter-intuitively, the empirical evidence is very weak for (1) and very strong for (2). But neither of these is decisive. In the big picture, the university you went to trumps everything else. In other words, what we are seeing is consistent with the big sort, *not* neofeudalism.

The evidence can be read as supporting a triumphalist narrative of America as a great meritocracy. Or it can be read as suggesting an intensification of the neoliberal condition. For what it suggests above all is the picture of 18-year-olds engaged in brutal market-like competition—a fight to the death.

*Postscript.* Petey Bee’s comment got me worry about the probit model. I realized that there was an easy way to check that I wasn’t missing something: Replace parental income with kids’ earnings. If the results look reasonable, we are alright. The following figure display the fitted probabilities by earnings percentile for all school tiers. They all look kosher. Really stunning how you are more or less guaranteed to have gone to an Ivy Plus school if you are in the top 5 percent of earners.

*Post-postscript*. Ron and Jaime, personal friends and smart scientists both, pointed out the incredible separability of Figure 2. It does look “fishy”. Why? There are two reasons I think for the incredible separability of the data. The first is, I think, that the data is coarse. “There is one row for each parent percentile [101] and college tier [15]” for a total of 1,515 observations. So there has already been averaging within percentile-tiers. The raw underlying data would no doubt look messier. The second, I think, is my fault. I merged some nearby tiers to gain clarity. Here is the offending graph for the original tiers.

I apologize. I should’ve been clearer. That being said, there is nothing nefarious involved in either Chetty et al.’s decision to average the data at the percentile-tier resolution or my decision to merge certain categories. If one were to use raw data and the original tiers, it would look considerably messier, but the systematic differential would not disappear and the results above would no doubt still hold.

Very cool data!

Question:

Is figure 4 (top graph) in this article the same as the data of the previous post?

IOW, If the “probability of getting into” Ivy+ is nearly equal for 25%ile vs 90%ile, why does previous post’s graph show that “portion of” Ivy+ students at 90%ile is 10 times that of 25%ile?

Is the distribution of “parental-income-for-all-18-21y-year-olds” skewed? Does that make a difference in “probability of a getting into” vs “probability of having come from”? (i.e., absurd example, if a school has 2 students, one always a 10%ile, one always a 90%ile, would it be accurate to say the odds favor the 90%ile kids since there are fewer of them in the general population?

oops, the last paragraph should refer to actual income, not %ile

Hey man. Sorry I should’ve been clearer. The probit model has very poor fit. I displayed the graph to show that parental income is a poor predictor of the odds. The basic reason is that the odds decay really fast; especially for the top tiers. Because the model is looking for the gradient across the parental income distribution, the relatively high rates at the very top end get barely picked up. I bet if we restricted the sample to the top 10 or top 5 percent of families by income, we would get a more significant gradient. Even so, the coefficients are what you’d expect and they are significant. But the fact remains that for the bulk of population parental income has little effect on the kids’ odds of getting into prestige schools.

I updated the text to address this issue. Hope its clearer now.

Thanks! I think completely misunderstood this at first.

I also found the answer to my question about getting in.

A graph of “count / totcount” vs “par_pctile” vs “tier” tells the getting-in story.

It is indeed more flat than I would’ve guessed.

Pingback: Parental Income vs College Enrollment vs College Prestige Level [Policy Tensor] | Pete's Politics and Variety

Got the “getting in” part to look like this:

Splendid work! If you are playing with the numbers as well, let me know if I got something wrong!

I think you are light years ahead of me in that department. Is it ok if I repost a copy of your final graph?

Absolutely.