Ask HN: Present Value of Knowing Math Well?

The present value of math skills is not just Q-N, because there are confounding factors. For example, do smarter people gravitate to quantitative careers? Do more ambitious people select quantitative careers? Do people with a better starting environment in life receive the necessary encouragement and guidance to pursue a quantitative career versus those with worse starting environments?

I have no answer to those questions, but they are all at least credible concerns. To fairly answer the OP's question, we'd have to observe people who exhibit all the qualities of a person selecting a quantitative career, but who have not actually done so.

This is similar to the problem of measuring the returns on attending elite colleges versus standard colleges. Measured by comparing the earnings of elite graduates versus standard graduates, it appears that there is a high return. But measured by tracking earnings of those who earned admission to elite colleges, but instead chose standard colleges, the difference disappears: there is no incremental return, for a person qualified to attend an elite college, for doing so.

We may have a similar problem here. Any ideas on the best way to measure this?

Do people with a better starting environment in life receive the necessary encouragement and guidance to pursue a quantitative career versus those with worse starting environments?

The known fact (well known to economists of education) that advantaged young people are more likely to pursue and complete college degrees is indeed a confound here.

http://www.jkcf.org/assets/files/0000/0084/Achievement_Trap....

So, yes, when any of the helpful links that have been submitted in replies in this thread report that college graduates, or college graduates of a particular kind, have higher incomes than other college graduates, or than people who didn't graduate from college at all, it may be that college didn't cause the difference. Maybe the environmental advantages that PRECEDED college caused the difference in lifetime outcomes.

But as OP I am indeed asking what a parent should think about how much to spend to ensure precollege advantages. It looks like HUGE expenditures in childhood to ensure children's success in college preparation and especially in math preparation are well warranted.

measured by tracking earnings of those who earned admission to elite colleges, but instead chose standard colleges, the difference disappears: there is no incremental return, for a person qualified to attend an elite college, for doing so.

This is the generally announced result of the Krueger-Dale study, but I agree with the critics of the study

http://www.overcomingbias.com/2009/03/college-prestige-matte...

(previously submitted to HN)

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=379801

(a footnote in this study criticizes the Dale-Krueger study methodology and data analysis)

that the correct conclusion is that attending the best available college is plainly beneficial for students from low-income families, and perhaps beneficial for all students.

I read through your notes on the Dale-Krueger study and found them educational. I was not aware that their study's results indicated the opposite of the general conclusion it's often cited to support -- particularly when measured against tuition costs or Barron's rankings.

Your revised question (is it worth investing in pre-college advantages?) is slightly different than the original question (what is the value of a quantitative career?). I would agree with you that pre-college advantages tend to have very high returns.

http://www.prospects.ac.uk/cms/ShowPage/Home_page/What_do_gr...

From the above page, in the UK:

Financial returns

Back in 2001, the government reported that graduates' lifetime earnings would be £400,000 greater than those who ended their full-time education with A-levels. Recent estimates have been more conservative. According to a study from the University of Wales Swansea, after taking into accounts the costs of acquiring a degree (foregone earnings and tuition costs), male graduates can expect to see their lifetime earnings (net of taxes) increased by £141,539 over similar men who finished their education with two or more A-levels. The corresponding figure for women is £157,982, reinforcing the findings from other studies that women benefit even more than their male counterpart from a university education.

...

The financial benefits of a degree are, perhaps unsurprisingly, subject dependent. Maths and computing degrees were found to offer the greatest increase in lifetime earnings for male graduates, whilst a degree in education represents the highest returns for women. The Swansea report concluded that the cost of gaining a degree is far less than the potential increase in lifetime earnings for the majority of graduates.

Unattributed - you can Google:

"Both graduates and non graduates who took Maths A-level ended up earning on average 10 percent more than those of similar ability and background who did not"

There's lots more if you look for it. The consensus is that having a qualification in mathematics has a measurable impact on your earnings.

If you really want to compute this, I think you'll need to use marginal benefits of math skills, which varies a lot by person and environment. It depends on not just other aptitudes, but also preferences and circumstances surrounding that person. Britney Spears or Tiger Woods probably wouldn't benefit much from Calculus.

Even for an 'average' salary person, it depends a lot on other skills s/he has. A top salesperson/marketing wizard does not need calculus and can earn several times the salary of the best engineer who does not pursue business or get involved in a startup.

The premise that Q-N is positive could be flawed from the start. See, e.g. "A Whole New Mind" http://www.amazon.com/Whole-New-Mind-Information-Conceptual/...

The premise that Q-N is positive could be flawed from the start.

That's an important caution, and thanks for posting the link to the book description. Whether Q-N is positive in general is, of course, an empirical question. (I'm pretty sure the general answer to that question is yes, quantitative careers outearn nonquantitative careers in the aggregate.) You make some very good points about individual preferences and particular skills that trump math skills. If I had a child who played soccer like Freddy Adu

http://en.wikipedia.org/wiki/Freddy_Adu

and who enjoyed playing soccer, I'd only bother him about enough math homework to make sure his agent wasn't cheating him.

A reassuring chart:

http://blogs.payscale.com/salary_report_kris_cowan/2008/07/l...

Computer Science and engineering students seem to get about $20,000 more in starting salary on average.

Using the data on median salaries (http://www.payscale.com/best-colleges/degrees.asp), the top 10 majors were all quantitative topics, with the possible exception of economics. The top majors, all quantitative, averaged between 90 and 100 thousand per year, with the non quantitative vocational majors averaging about 60-80, and the bottom tier (Sociology, Drama, ect.) averaging about 50-60. The information does not include people who attend grad school.

The 'quant premium' seems to be about $25,000 per year over other useful majors, and $40,000 per year over generic college degree.

Just to tug sideways a little bit, math skills can be a form of marketing in almost every profession, even if the skills are only superficial. A person who can offer brief explanations for math concepts to lay audiences, or can compute in his head quickly, can use those abilities at the right moments to gain an incredible (albeit somewhat undeserved) level of credibility.

Between my partner and I, I often play the "technical guy" role during sales meetings, and simply multiplying fairly large numbers in my head before the client has a chance to fumble for a calculator really puts me in a position of "credible expert" by way of the Halo Effect.

It's a subtle effect, and it can easily become obnoxious, but it's worth considering.

Do you really think that multiplying large numbers in your head is knowing math well? Seriously.

Knowing math well, i.e., knowing stuff like Differential Geometry or Algebraic Topology, is anything but a form of marketing...

Clearly not. I was just using an example, and I did say it was a superficial one. My point was that signaling credibility through shows of raw math talent can be effective.

This question exposes the flaws of quantitative economic analysis. How can you price future assets in todays dollars with unstable economic growth? inflation could be 3% a year or 30% a year depending on what the government does.

How is inflation relevant to this calculation? Both career paths will presumably be paid with the same currency.

Depends on the country, the industry, and what happens to the industry in the future.

How can you price future assets in todays dollars with unstable economic growth?

The same discount rate applies in general to both income streams in the usual calculation. It is enough to figure out how different the income streams are likely to be (very different, according to some of the links already submitted as replies here) and then get a ballpark estimate of the present value of that difference. By hypothesis, most parents substantially underinvest in ensuring their children's college readiness and math ability.

you're assuming homogenous growth rates between economic sectors. the labor market is determined by supply and demand. who knows what the proportion of CS grads:CS jobs there will be in 25 years for instance.