Ambitious high school students are typically heavily constrained in the sense that maximizing their college admissions prospects comes at the cost of spending a lot of time on coursework. See for example our page on College statements on the importance of grades and coursework. Outside of improving college admissions prospects, this is often a waste of time. In What You'll Wish You Had Known, Y Combinator founder Paul Graham wrote:

Right now most of you feel your job in life is to be a promising college applicant. But that means you're designing your life to satisfy a process so mindless that there's a whole industry devoted to subverting it. [...] So what do you do? What you should not do is rebel. [...] By putting you in this situation, society has fouled you. Yes, as you suspect, a lot of the stuff you learn in your classes is crap. And yes, as you suspect, the college admissions process is largely a charade. But like many fouls, this one was unintentional. So just keep playing.

However, colleges grant students considerable latitude with respect to how they spend their time on extracurricular activities. In What colleges look for in extracurricular activities I reported on conversations with admissions officers in which they said that it doesn't matter what extracurricular activities a student is involved in as long as he/she demonstrates characteristics such as passion and commitment. My post got a lot of pushback (in part because I framed the finding suboptimally), but based on these conversations and on reading writings by college admissions consultants, even if college admissions officers have some preferences, it's unlikely that they're sufficiently strong and narrow so that there's not considerable variability in the value of the activities that students can engage in and still look good to colleges. This raises the possibility that there's considerable potential for high school students to benefit more from their extracurricular activities and to contribute more social value through them (whether directly or indirectly).

This post focuses on social value, with the background context that social value contributed is often aligned with a person's interests, whether they be altruistic or financial. In some places below, I use income as a proxy to social value, though it's an imperfect one. The arguments below don't depend on the use of this proxy, it's just convenient for giving rough quantitative estimates. The calculations below are very rough and should not be taken literally. The significance of the results of the calculations is seen in their order of magnitude and so small fractional errors in estimation don't affect the bottom line.

A baseline

It seems reasonable to assume that on average, motivated students spend at least 10 hours of time on extracurricular activities a week, with the number much higher during summer months. Thus, one gets a plausible lower bound of 500 hours/year/person.

A lower bound for the economic value that could in principle be generated with this time comes from the assumption that these hours be spent on minimum wage paying jobs. If one assumes average wages of $10/hour, one gets a figure of $5k/year/student.

How many students are there? There are about 4 million students of a given age in America, so 16 million people of high school age, which corresponds to roughly 50 million in the developed world. Attaching the $5k/year/person figure to these people gives $250 billion/year. (The figure would be smaller if one excluded high school dropouts, but not substantially.) Those in Cognito Mentoring's target audience constitute a subset of about 1% of the size, so the figure is $2.5 billion/year for high school students in our target audience.

(This may be higher than the status quo – it's just a lower bound in principle.) 

How much potential for improvement relative to the baseline is there through changed habits? For habits to change, some causal pathway would have to exist to facilitate the change. But for the moment, consider a high school student in the top ~1% academically who's willing to consider all possible options, and choose the ones that best meet her goals. How much better more economic value would she generate than $5k/year?

Hypothetical routes toward productivity boosts

One possible path is to build human capital so as to enter the workforce as a higher skilled worker at an earlier stage.

For a rough quantitative estimate, consider the following hypothetical. The student could supplement high school courses with college courses (taking at night or during summers) and graduate from college and enter the workforce a year earlier. She could plausibly do this by spending an extra 500 hours/year (over the course of 4 years, that would be enough to take a full year's worth of college courses). Assuming that after college she takes a job with starting salary of $25/hr and a 40 hour work week, the payoff is then $12.5k/year of high school "extracurricular" time, within the first year (not counting the returns coming from being able to get higher paying jobs earlier in subsequent years). This is roughly 2x as high as working a minimum wage paying job.

Extracurricular activities often serve as a change of pace from academic activities, so it's not clear that people would be able to do this without worsened overall academic performance, or that they'd want to. Moreover, doing academic activities exclusively would plausibly send a negative signal to colleges, reducing expected starting salary. But students can still move in this direction to some extent, for example, a student considering becoming a programmer might consider contributing to StackOverflow and building her skills in the process.

Another is to spend the time learning about different careers. By doing research on careers, and internships, the student could better evaluate what she would like to do. In expectation, aside from increasing personal satisfaction, this would also increase productivity on the job, and reduce sunk cost associated with training for a career path that one ends up leaving. The potential gains here are hard to quantify, but plausibly spending 10 hours / week for 4 years (the equivalent of one full time year) learning about careers is better than working a minimum wage paying job, and has returns on the same order as those of entering the workforce as a college graduate one year early.

Those who wish to work during high school and who are also interested in charity can donate earnings to help those in the developing world. This doesn't create outsized economic value when measured in dollars, but if one instead measures economic value in percent increase in earnings per person, the impact can be outsized. In particular, donating $5k/year earnings from a $10/hr job to GiveDirectly could generate the equivalent of $150k/year in economic value. I doubt that GiveDirectly is this cost-effective, as historically favorable cost-effectiveness estimates have turned out to be overly optimistic, but there's at least a reasonable chance that one can contribute economic value many times greater than one's salary through such donations.

Those who are interested in contributing social value and who have specialized skills (or the capacity to develop them quickly) can leverage their specialized skills to do socially valuable projects. For example, somebody with high intellectual curiosity and good writing skills can contribute to Wikipedia, writing articles that thousands of people can benefit from. Here too, the benefits are difficult to quantify, but based on an aggregation of numerous case studies, it seems possible for people with specialized skills to contribute economic value several times greater than their earning power through working on well-chosen socially valuable projects.

The collection of paths listed above is probably not exhaustive. For example, it neglects the consumptive experience of the student in extracurricular activities, which probably varies substantially across activities.

What are students doing now, and what would they do if better informed?

Some extracurricular activities that are popular amongst high school students such as sports, music and drama have consumptive benefits that can't easily be substituted for by activities that produce greater economic value, and plausibly many high schoolers would be unwilling to give them up in favor of activities that produce more economic value. [Edit: After writing this post I realized that these lines carry the connotation that sports, music and drama have low social value. As ChristianKI points out, sports can improve productivity through exercise, and drama could improve social skills, on top of their consumptive value. The point here is just that there's probably not much room for change here, not that the status quo is bad.]

In other cases, there are more holistically rewarding activities that high schoolers might plausibly shift toward. For example, one may prefer to write an article online over one in a school newspaper, on the grounds that the former will reach a broader audience. One may prefer to learn computer programming over doing math contest problems, on the grounds that the former confers an employable skill.

The baseline figure of $250 billion/year coming from how people of high school age spend their time outside of school sufficiently high so that it's clear that the issue of how productively high school students spend their time is a major one, with small fractional increases yielding huge returns.