

Ask HN: Present Value of Knowing Math Well? - tokenadult

A comment in another thread reminds of a question I've wanted to ask for a while. How might one calculate the present value of knowing math well as contrasted with not knowing math well? If "quantitative" careers pay better over the course of life than "nonquantitative" careers (and that seems to be the generally reported fact, how much money is worth spending during a child's education to make sure the child has enough developed math ability to pursue a quantitative career if the child so chooses?<p>An example calculation:<p>average salary of all college graduates with "quantitative" careers times number of years those graduates are in the workforce (call this term "Q")<p>compared to<p>average salary of all college graduates with "nonquantitative" careers times number of years those graduates are in the workforce (call this term "N")<p>and then the usual financial calculation of "present value" showing how much money today is worth as much as that difference (Q-N) in lifetime earnings. I think most parents and most young people would be surprised at how much it is worthwhile investing in learning math well.<p>Perhaps "quantitative" careers can be defined as careers that involve taking and passing a calculus course at the college level, and "nonquantitative" as all other careers. Or perhaps you'd like to propose a different definition.<p>P.S. A similar calculation could compare knowing or not knowing how to program computers.
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RiderOfGiraffes
[http://www.prospects.ac.uk/cms/ShowPage/Home_page/What_do_gr...](http://www.prospects.ac.uk/cms/ShowPage/Home_page/What_do_graduates_do__2006/The_graduate_market_and_salaries/p!eLaXeij)

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.

------
mediaman
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?

~~~
tokenadult
_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....](http://www.jkcf.org/assets/files/0000/0084/Achievement_Trap.pdf)

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...](http://www.overcomingbias.com/2009/03/college-prestige-matters.html)

(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.

~~~
mediaman
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.

------
nopinsight
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/...](http://www.amazon.com/Whole-New-Mind-Information-
Conceptual/dp/1573223085)

~~~
tokenadult
_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.

------
Dilpil
A reassuring chart:

[http://blogs.payscale.com/salary_report_kris_cowan/2008/07/l...](http://blogs.payscale.com/salary_report_kris_cowan/2008/07/list-
of-best-co.html)

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.

------
pmichaud
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.

~~~
TriinT
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...

~~~
pmichaud
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.

------
nazgulnarsil
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.

~~~
tokenadult
_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.

~~~
nazgulnarsil
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.

