Human Capital Contracts Could Increase Dropouts

I’ve received pushback from Andrew P. Kelly and others on the right on twitter arguing that human capital contracts (ISAs) would help increase graduation rates, and that my arguments and evidence doesn’t capture this. Schools have varying completion rates, and reducing dropouts is an important priority. ISA creditors would have an incentive to make sure college students graduate, so they can receive more upside income. How can ISAs help? By offering better terms for colleges that have lower dropout rates, aligning the profit motive of financial capital with the goals of a better, more just, education system.

Why would we assume they do this? I want to post a toy model showing there’s a reasonable story where they won’t. (This is how the quants would approach it. The big difference is that we are taking the future salaries for granted, but that’s what would need to be modeled.)

There’s Mike. He’s 18 and could attend one of two colleges that costs the same, School A and School B. Let’s say he signs an ISA promising 10% of his income until he hits 30 in order to attend either one. He doesn’t make any money while in college, and the ISA has a discount rate of 8% (probably low given the downside adverse selection risk it has to hold).

In one world, Mike attends School A and drops out after two years because it’s a poor quality school. He make $30,000 a year after dropping out with some college. Alternatively, in another world, Mike attends School B, finishing after four years and gets to make 30% more, for a yearly income of $39,000. That’s a big premium! Obviously the ISA would prefer the world where Mike attends School B and he graduates, right?

No. The ISA would prefer he drops out and start paying out earlier to maximize profits. Excel:

When it comes to the present value (PV) of the ISA, two extra years of payments earlier more than compensate for higher earnings later.

This difference is increasing in the discount rate, dropout income and equity rate, decreasing in the length of payments and education premium. It’s not juked – if anything that discount rate feels low, and this is robust to different ways of setting up the terms. Even if it was just 10 payments each, a higher discount rate and lower premium does the same thing. (Again, it’s tough to model an imaginary market that won’t exist without extensive government intervention because of profound adverse selection problems.)

Here’s the kicker: since the present value of the ISA when Mike attends the bad school and drops out is higher, the quants would be able to offer him better terms to attend that school. (Better terms here is a lower rate of equity payments.) You would receive a better rate to attend the worse school. The price mechanism of the ISA could easily, as demonstrated in this toy model, lead to a world where people are encouraged to attend a worse school option. This contradicts the idea that the ISA would necessarily, through the profit motive, offer better terms to better schools, especially ones with higher completion rates.

Will this happen? I don’t know. Neither does anyone else. But this shows the problem with assuming that this ISA financial instrument seeks to maximize school quality, rather than the actual goal of maximizing expected earnings. We should take the profit-motive as what it is – designed to extract profits ruthlessly and completely. We shouldn’t assume it lines up with the social outcomes that we want.