Elite universities and social mobility

Social mobility has decreased over the past two decades. Overall, there was some divergence between countries: the US, the UK and France for instance experienced a decrease in social mobility, while the trends were rather flat in e.g. the Nordic countries.

One dimension along which these countries differ is their tertiary education system: the US, the UK and France have two-tier systems with standard and elite universities. In this post I’m asking what effect such a stratification of college education can have on social mobility.

This question is studied by Brezis and Hellier (2013). Let us start with some stylized facts, and then move on to their model and results.

Standard and elite universities differ on two dimensions: selectivity and budget. For instance, in the US standard colleges increased enrollment by 525% between 1959 and 2008, whereas elite college did so only by 250%. As for budget differences, note that Ivies have about a three times higher budget than other schools, and their budgets increased by about 20% between 1999 and 2009, while the increase was less than 8% in other schools.

We see similar trends in France for instance. Selectivity increased over time at top grandes écoles, and the budgetary differences are clearly visible in the chart below (made by me, based on a source cited by the authors). Note: GE stands for grande école, which are basically the elite universities of France.

Figures are for 2001/2002 (source: Observatoire Boivigny)

Figures are for 2001/2002 (source: Observatoire Boivigny)

One concern that may arise after one reads these stylized facts is that selectivity is actually a good thing: if elite schools are meritocratic, then selectivity per se does not hamper social mobility. This is not entirely true because human capital (e.g. IQ, SAT scores, GPAs) is partially transferred from one generation to the next. Therefore, those whose parents attended an elite institution will on average be more likely to be smart/prepared enough to get admitted to an elite school themselves. And therefore, selectivity can also drive stratification.

Now, let’s move on to the model of Brezis and Hellier. The main idea is quite simple. Suppose there are families whose children receive a basic (pre-college) education. The human capital of the children after this education will depend on: (i) their innate ability and (ii) their parents’ transferred human capital. Here, we’re implicitly assuming that basic education is the same in all social groups (i.e. no elite high schools). If we were to assume otherwise, the results of the authors would only be strengthened. It is also assumed that (i) is randomly distributed and doesn’t depend on social class. Note that (ii) is just the intergenerational transfer of human capital discussed in the previous paragraph.

Children then have some level of human capital after basic education. If this is larger than a threshold they have access to higher education. Furthermore, there is a second (even higher) threshold which if they surpass, they get to go to an elite institution. The size of elite institutions is fixed and exogenous, they always admit the top x% of students.

Higher education also contributes to the human capital of children. After all education is taken in to account, we will have three groups of people:

  1. Those with basic education only. Their human capital depends on their random innate ability and their parents’ human capital. It is also lower than the threshold required to enter college.
  2. Those with standard tertiary education. Their human capital is equal to what they accumulated from basic education plus some bonus they receive from attending college. The bonus depends on the expenditures per student at their institution.
  3. Those with elite tertiary education. This is the same as the previous group except that the “bonus” is higher because expenditures per student are higher at elite institutions. This group thus has a higher human capital than the previous one.

This is the simple setup of the authors. They derive several interesting results from it. Note that we’re going to focus on the mobility between groups (2) and (3), because that’s the main interest of the paper.

Because ability is random and not social class-dependent, there can be mobility between the middle class and the top. Nevertheless, there are also levels of parental human capital such that the child of a parent with such human capital will be bound to stay in the same social class as their parent (because they won’t be able to surpass (or drop below) the elite school threshold). This is true even if the child has the highest (or lowest) possible ability. This is illustrated in the figure below.

Social mobility and stratification: steady segments

The S-steady segment is the the range of human capital levels that if your parent is in, you will also be bound to stay within that segment and thus within the middle class. The E-steady segment is the same for the elite class. There is also a mobility segment that is located in-between these two segments.

The authors show that the mobile segment shown in the picture above exists if the difference between elite and standard university expenditures is not too big. If it is too big, then elite kids will have much higher human capital than middle class kids, and since this is partially transferred to their offspring so will their children. If this difference is too large, no mobility will take place.

Similarly, a larger range of abilities (i.e. a bigger difference between the highest and lowest possible ability) fosters mobility. This is because with a larger range, the probability that there will be a large ability difference between any two kids will be higher. Consequently, ability then has a more important effect on human capital overall, simply because it can vary more.

If elite institutions become less selective (i.e. they admit a larger percentage of the population), then two things happen: (i) more middle class children join the elite class (trivially), but also (ii) more elite kids can stay within the elite system. There is thus more upward mobility (i), but also a higher self-reproduction rate among the elite (ii). The effect on social mobility is ambiguous.

If the size of the middle class increases (i.e. the cutoff to enter standard colleges is decreased), then the opposite of the previous situation happens: (i) lower middle class upward mobility, and (ii) lower elite self-reproduction. The first effect comes from the fact that the middle class becomes larger in absolute numbers, and thus mobility measured in percentage terms drops. The second effect is a result of the same fact: a larger number of middle class children have a higher chance of attaining a high enough ability to join the elite group.

It must be noted that these are the long-term effects. For the first generation impacted by the change, the results are different. The middle class is expanded at the bottom in terms of abilities (because the standard university cutoff score is decreased). So the people who join the middle class and leave the lower classes are better off. But since the middle class is expanded from the bottom, the first generation of the upper part of the middle class (and the elite) is not affected by this.

Finally, the authors also run some simulations of their model to get a feel of what the model implies numerically.

  • They show that if there is a one-tier education system (i.e. no difference in elite/standard budgets), then the elite self-reproduction rate (% of elite kids that stays elite) is 17.7%, and the middle class upward mobility rate (% of middle class kids that becomes elite) is 4.3%. This is quite good, given that it is assumed that elite colleges admit 5% of the population.
  • If we move to a slightly elitist scenario (elite budgets twice as high as standard), elite self-reproduction sky-rockets to 66.9%, and the middle class upward mobility rate drops to 1.7%.
  • If we move to a heavily elitist system (elite budgets four times higher than standard), then elite self-reproduction is at 96.6%, middle class upward mobility is at 0.2%.

According to the authors, elite budgets are 3-4 times higher than standard budgets in France, the UK and the US. The “heavily elitist” scenario described above is thus an upper bound of this. The “slightly elitist” scenario, on the other hand, is somewhat more egalitarian than what we observe in reality.

Of course, do not take these numbers at face value. We’re talking about a simple model whose main purpose was not to do quantitative modeling, i.e. not to come up with exact numbers but to give a good qualitative gist of how a two-tier system can affect mobility. The calibration is very simple/somewhat ad-hoc and there are no sensitivity analyses. Still, this paper is quite interesting, especially for its qualitative predictions.

Let me close with three remarks. First, the authors note that in the post-World War 2 period, tertiary education experienced democratization. The size of the middle class increased, which initially allowed the lower classes to be upwardly mobile, and the size of the elite increased, which allowed more middle class kids to access the elite. These were the short-term changes, and mobility increased post-WW2. But then it started decreasing again, because a larger middle class size hampers upward mobility in the long run, and a larger elite size increases elite self-reproduction. All these short-term and long-term effects are implied by the model and are discussed above.

Second, note that this whole elite self-reproduction is also the result of assortative mating: that is, elite people marrying other elite people, middle class people marrying other middle class people, etc. It must be noted that assortative mating was much lower post-WW2 than it is today (as consistent with the mobility figures). Why is this? Two interesting reasons are as follows:

  1. In the 1950s, there were lots of frictions in the dating market (the college population was mostly male, there was no internet dating or similar things). So – as standard matching models would predict – people in such a situation (high frictions) were much more likely to settle for an inferior match, then wait around for the off-chance that they meet a good match. In the 2000s, there are much fewer frictions in the dating market, people can meet potential mates much more often and thus are less willing to settle.
  2. Another theory is that in the 1950s, substitutability was much more important within a marriage: traditionally, the husband would make money and the wife would do chores around the house. So the husband needed to be a high ability, high earner type, while the wife someone who’s good at housework. By the 2000s, this disappeared. Now, complementarity is more important. Both spouses being highly educated is more advantageous because there are higher returns to education (for both genders), and household chores have become much less time consuming (with all the machines invented).

Third, there is evidence (ungated) that low-income high-achieving students avoid selective elite colleges because they perceive them as too expensive. They are uninformed about the possibilities of financial aid at these institutions and thus are more likely to go to cheaper, standard colleges. This is a mechanism that can further exacerbate the kind of social immobility discussed in this post.

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