Your Time Might Be More Valuable Than You Think

by Mark Xu9 min read18th Oct 202112 comments

53

Time (value of)Practical
Frontpage
This is a linkpost for https://markxu.com/value-time

Summary

  • People often seem to implicitly value their time at the amount they can convert hours to dollars given their current skills.
  • However, the value of saving the marginal hour today is to increase the total number of one's working hours by one, resulting in a new hour at the end of one's career, not a new hour at their current skill level.
  • This suggests that people who expect their time to become valuable in the future must think their time is approximately just as valuable now, because saving time now gets them to the point where their time is valuable faster and gives them more of such time.
  • This analysis is complicated by various temporal dependencies (e.g. time discounting) that push the value of the current hour up or down compared to the value of the marginal hour at the end of one's career.
  • Under such a view, finding promising young altruists and speeding up their careers represents a significant value add.

Intro

Many people in my social circles have an amount they "value their time." Roughly speaking, if someone values their time at $50/hr, they should be willing to pay $50 to save an hour of time, or be paid $50 to do work that has negligible non-monetary value. Knowing this value can provide a simple decision rule for deciding which opportunities to trade money for time it's efficient for you to take. I will argue that a naive perspective on time evaluations generally results in an underestimate. This analysis suggests that altruistic actors with large amounts of money giving or lending money to young, resource-poor altruists might produce large amounts of altruistic good per dollar. I will analyze the situation mostly in terms of wages as expressed in dollars; however, readers might want to substitute "altruistic impact" instead. I will begin by analyzing a simplified situation, adding more nuance later.

The value of your time is the value of the marginal hour at the end of your career

If I currently have a job that lets me convert one hour of time into $50 dollars, then it's clear that I should take all time-saving opportunities at less than $50 dollars. (Note that this doesn't mean that I should pay $50 to save an hour of furniture assembly. Furniture assembly might be enjoyable, teach me valuable skills, etc.) However, this assumes that the benefits I receive from my job are entirely monetary. For most jobs, this will not be the case. If one is a software engineer, then much of the benefit of 1 hour of working as a software engineer will be the skills and experience gained during that hour. To be more specific, the hourly rate that a software engineer commands depends on their skill, which depends on training/experience in turn. Thus an hour of software engineering might increase expected future compensation by more than $50 (in fact, under plausible assumptions, this will be the primary benefit of the early part of most careers.)

To be more quantitative, let be the wage an employee with hours of experience can earn per hour. Suppose that you currently have hours of experience and your career in total will be hours long. The amount of dollars you expect to earn in the future is . (Note that a more precise analysis would have included a discount rate. Money now is worth more than money later because of investment possibilities.) A naive model of saving an hour of present time calculates the total earnings of your career as , meaning you should take an opportunity to save an hour at cost if and only if .

However, as stated above, this suggests that the marginal hour at the present is worth , your current wage. This is not what actually happens when you save one hour at the present. What actually happens is that your total earnings of your career will now be for a difference of instead of . Since one's expected wage at the end of a career is likely substantially higher than ones current wage (especially for people at the beginning of their careers), treating the value of one's time as instead of leads to an underestimate by .

For example, suppose that one is a quantitative trader. They currently earn $100/hr. However, with 20,000 hours (10 years, assuming 2000 working hours a year) of experience, they expect to earn $1000/hr. If they have no time-discount rate on money, then they should be willing to pay up to $1000 to save an hour of time presently, despite the fact that they will be net down $900 if they use that time to do work. Another way of seeing this is that saving an hour of time for your present self is in some sense the same thing as saving an hour of time for your future self, because it causes the future to arrive one hour earlier and be one hour longer. Thus, if you would be willing to trade an hour for $1000 in the future, you should also be willing to do so now.

This also suggests that the returns to working twice as much results in much more than twice the value produced. Naively, a 160,000 hour career produces the same value as two 80,000 hour careers. However, in reality, one of those careers is going to start with 80,000 hours of experience! This doesn't account for a lot of relative factors (being faster than competitors can produce much higher amounts of value) or aging-out effects like getting worse at working as you work more.

A corollary is that burning out for a year is a disaster, because it's equivalent to losing a final career year. Similarly, vacations and other such leisure activities have larger costs than one might have naively expected, since they delay career growth and shorten careers. For example, if someone who could have had a 40 year career burns out for a year, their career is now 39 years and is missing the year where they would have had 39 years of experience.

Temporal Dependence

One key factor missing in the above analysis is a temporal dependence on the value of wages. (The substitution of wages for altruistic impact is going to break down slightly and depend on complicated factors like the flow-through effects of altruism and whether standard investment returns are higher than altruistic flow-through effects. See Flow-Through Effects of Innovation Through the Ages and Giving Now vs. Later for a more nuanced discussion.) The most obvious form of temporal dependence is a monetary discount rate controlled by the ability to turn money now into more money later via standard investments. Such a discount rate suggests that our theoretical quantitative trader discussed above should not be willing to spend $1000 to save an hour of time at the present day, but rather spend an amount that would be equivalent to $1000 after 10 years of investment (approximately $500 at 7% yearly returns). I could write an equation expressing this, but I don't think it would lend much clarity.

Less standard but more accurate analyses would incorporate the relative differences in the value of money over time for your particular goals. For instance, it might be that the altruistic discount rate on dollars is much higher than the standard discount rate because there are altruistic opportunities available now that won't be available later, even if you had double the money. Another salient example is effective altruism movement building (meta-EA), which might get most of its value early on. One way to model this is that instead of producing value directly, people in meta-EA save other people's time (by getting them into the movement earlier), enabling them to produce more value later. If you think, for example, that this century is particularly important, then saving an early career altruistic professional 1 year of time in 2090 is going to get you the marginal year of someone with ~10 years of experience, compared to saving such a person 1 year in 2080, which gets the marginal year with ~20 years of experience. Depending on how quickly you think the value of someone's work goes up with respect to experience, then this might suggest large discount rates.

As another example, people working in AI Alignment (like me) might think that most valuable alignment work is going to be done in the ~10 years preceding transformative AI (TAI). If you think this date is about 2055 (see Holden's summary of Ajeya's Forecasting TAI from Biological Anchors), then the most important thing is to maximize your abilities as a researcher from 2045-2055. (It's possible that you should be making different bets, e.g. if you think you have more influence in worlds where TAI is sooner.) Since I'll probably still be working in 2055, saving a marginal year of time today gives me one extra year of research experience during the decade preceding TAI, but not any extra marginal years during that decade. (This does suggest that saving time during that decade is very valuable, though.) Of course, I am not modeling various effects that current research has on things like field building, which potentially dominates the value of my current work.

Actionables

This analysis suggests that people with the potential to earn high salaries/have high altruistic impact have high time value, not because they can produce useful work currently, but because it will get them to where they eventually will end up faster. Provided this holds qualitatively, it suggests a couple of things:

  • Care about the value of your time more and try to aggressively take opportunities to save it or spend it more effectively, even if this doesn't make that much sense in terms of the value you think you can currently generate.
    • This might mean that you should take out loans and such, so you have resources. If your expected future earnings are high, then things like hiring tutors to graduate school faster are likely worth the interest on the loan.
  • What you spend your free time doing actually kind of matters. Developing some skill one year faster increases the amount of value you produce on the margin by quite a bit.
  • Standard advice saying that young people have time to explore potential career options should be balanced against the cost of becoming less awesome in that particular career option because too much time was spent exploring.
    • For example, if someone is potentially a promising AI Aligner, and they take a year off college to travel the world and see the sights, this decreases the amount of research experience they have during the period around TAI by a year.
    • Exploration is still probably a good idea, but it should be traded off not against the value one would have produced directly, but rather the marginal increase in value that would have resulted from the increased growth/experience if that time wasn't spent exploring.
  • Finding promising young people and using large amounts of resources to speed up their careers probably has pretty good altruistic returns.
    • (If you think you're such a person and could benefit from additional resources, feel free to send me an email and I'll see what I can do.)

53

12 comments, sorted by Highlighting new comments since Today at 11:08 PM
New Comment

I do think most people are undervaluing their time, but I currently believe that my time now is much more valuable than my time in 10 years, and that i also believe this to be true about your time (like, specifically you, Mark Xu). 

I think this is mostly because I think that in worlds where we have any chance of solving the AI Alignment problem, we are currently setting in place a field and network of people who will eventually solve the problem, and the founder effects here seem much larger than the experience effects. As a concrete example, I would value an hour of Larry Page's time from 20 years ago, much higher than an hour now, because the marginal hour at the time had a decent chance of making the difference between Google succeeding vs. not, whereas his time now doesn't really seem as high-leverage, even though he theoretically has access to billions of dollars and lots of people to direct. Most of the variance of what Google is working on was determined 20 years ago, and Larry's ability to affect the world now seems much lower than it was 20 years ago (in hindsight, of course. At the time, it was likely really hard to tell Larry apart from any of the other founders of technology companies, and I wouldn't have valued his time as highly, with the knowledge of the time, but I think I would gladly trade 5 hours of Larry's time now, to send them back 20 years)

"his time doesn't seem as high leverage" because he chooses not to work on high leverage stuff or because he is incapable of it? For instance, if he provides advice and resources to 10 new startups (or 10 new exploratory divisions in his company), could that be equivalent to him doing a startup himself? Plus he has a ton of experience now.

I don't have a strong opinion on it but maybe his ability to direct fledgling new divisions working on AI or self-driving cars or whatever could be higher impact than building a search engine 20 years, if he commits sufficient time to it. (And maybe he does, for all I know)

I find all these sorts of analyses deeply frustrating because they seem to take place in spherical-cow world and never to take account of the actual experience of virtually everyone who participates in the labor market -- you can't just choose how many of your hours you convert into dollars at an arbitrary level!

For hourly employees, one's employer usually determines the schedule with limited input from workers.

For salaried employees, the marginal hour worked results in essentially zero wage gain. It may result in being marginally more likely to receive a bonus or promotion down the line but these effects are highly uncertain and may have all sorts of slopes and plateaus in the hours/$$ curve.

For self-employed, if you do anything other than daytrade, then you likely have to interact with suppliers, customers, etc, and there's often pretty legit exogenous limits on your ability to translate hours in to $$.

 

Additionally, the experience benefits seem dubious to me for a similar reason, which is that to the extent you are selling your labor in any capacity (vast majority of workers), the potential buyers of your labor often have limited view into your experience or productivity, and to the extent they estimate these based on your experience, it's usually going to be measured in years not in hours.

 

So its very unclear to me the mechanism by which most people could decide to turn their time into money at anything approaching something that looks like a marginal wage, and additionally unclear to me how, even if so, working harder now will actually increase the returns 20 years from now in the way this post proposes.

Yes, there are whole constellations of frictionless, spherical cows in here.

I think at best you could say that accepting an offer of employment for $X/hr implies that you value your time less than $X/hr, but even this best-case interpretation is only true for the first few hours per week or whatever. Having enough income to avoid being homeless and worried about food is likely very much more valuable than whatever income comes in on top of that. What's more, employment turns non-employment time into a scarcer resource.

Someone could work for $15/hr, but quite consistently value their remaining time at $100/hr due to a combination of decreasing utility of money and value of an increasingly scarce resource.

Likewise someone could work for $100/hr and it could still be consistent for them to value an hour of their time at $15/hr.

Real life is messy.

Athletes that try to get good at a activity don't do the activity 24/7. I have seen even the case made of intentional practise where a 4 hours per day vs 8 hours a day would favour 4 hours. Doing twice the time doesn't mean you are doing twice the exp curve.

I would think that if the goal is just to get good at the end then doing research/practise would have a decent chance upping future capability more than doing it more. That is it seem plausible to me that doing full time research of a field for half a year could have similar expertise building as doing a year of that activity as a day job. I think they are likely to have different gains and might be ackwardly cross-dependent, ie some research is inaccessible or inefficient unless one has 3 years of experience practising. But it might make sense to study wider/more rather than make your studies short. It can also be akward to start studies again once one is "done" with them.

There are lots of assumptions in even assigning a monetary value to time-spent-now. However, I think you're doing your analysis a huge disservice by explicitly ignoring discounting and investment. Over timescales of multiple decades, these dominate most other things!

I'm not even referring expressly to financial investment and capital production, but also to things like time investment in family, discounting due to compounding uncertainty and risks over time, and other factors. If an hour spent now is only worth as much as an hour at the end of someone's career, they've pretty much failed in all of these things, because an hour at the end of someone's career really shouldn't be worth as much to them as an hour now.

An end-of-career hour may be worth more to somebody else, but that's highly variable across professions.

Genuine question I have: is 30 years of experience really worth much more than 20 years of experience? Would be keen on knowing from people who actually have that kind of experience.

Cause my gut is inclined towards no cause a) finite memory to retain insights b) finite max depth at which you can explore one field c) too much depth might have diminishing returns. But definitely not a strong opinion, happy to be 100% wrong.

I heard a quote recently which might link:

"Do they have 30 years of experience? or one year, repeated 30 times?".

If it's the former, then 30 years of experience is undoubtedly worth much more than 20 years of experience.
E.g. a surgeon who is dealing with new cases all the time will benefit from the 10 years of additional experience.

If the latter, then there's a very limited benefit to having an additional 10 years of experience — if you've been washing dishes for 20 years, sure you'll get better with an additional 10 years experience but not that much better.

Yup true, I'm assuming it's something like a surgeon or researcher where more years does in fact expose you to more useful data. I'm wondering if that translates into more useful insights or discoveries though. Can the surgeon remember 10 years of new insights without forgetting anything from the previous 20?

I mostly agree. Two thoughts:

  • Rather than thinking in terms of wages, w(t), I think we should just think in terms of time-value or marginal utility, u(t). Clearly everything you say applies to all value-we-can-get-from-time, not just wages.
  • Some of your conclusions (e.g., "if you would be willing to trade an hour for $1000 in the future [i.e., and gain the hour], you should also be willing to do so now") only apply when the following is true: for the rest of the person's life, their value-from-time is a (nondecreasing) function of their time spent working in the past. This is a plausible approximation in many cases. But both of the following are plausible:
    • working/experience will have a greater effect on u in the future, after I'm better-credentialed (I'm currently an undergraduate; the same number of hours experience counts for more if it's done in a higher-status position at a higher-status organization; first working in a lower-status way has some career benefits but its not like the next t hours of my work experience will have the same effect on my long-term prospects regardless of whether I get a low-status job now or a high-status job after college)
    • I will have higher direct time-value in the future due to reasons that are nearly independent of how I spend my marginal time now.

More generally, it seems sometimes true that e.g. doing 60 hrs/wk for 1 year is less valuable for u than 30 hrs/wk for 2 years (because value from work is generally a function not just of experience/productivity but also legibility-of-experience). If I could save up marginal time now to spend later, I would (not just because I expect some future time to be higher-leverage because of TAI, but also because I expect to have higher direct time-value in the future in a way that I largely can't affect by spending more time productively now); I'm not sure where I'd draw the line, but I'm pretty sure I'd save up time even if it cost 2 hours to give a single hour to future me.

(I'm not great at Markdown; please let me know if there's a way to make the above paragraph part of the second bullet point)

I have mixed thoughts about this post.

On one hand: it seems Scott covered this in his post, Ars Longa Vita Brevis.
It seems obvious there that saving one hour of time at the start of the Teacher-of-Teachers life is equivalent to saving one hour of time at the end of their life.

However, in this post, and in the example of quantitative trading, these areas have several important elements:

  • The scope of the area is effectively infinite. You can always learn to be a better teacher, and you will always be adapting to changing market conditions when quantitative trading.
  • You can work in these areas continually (24/7). They aren't limited by closing times, weekends, public holidays, etc. Learning to be a better teacher doesn't stop at 5pm, and honing the tools of your quantitative trading trade doesn't need to stop when the market closes.
  • Value is immediately available, for your time to be compensated as you go. In the case of a Teacher-of-Teachers, the person is supported lifelong in their task. In the case of quantitative trading, the market rewards you immediately.
  • Increasing your skills quickly increases the value you receive in exchange. Learning a better teaching technique = your student makes more progress. Learning a better quantitative trading technique = you make more money the next day.

However, consider the case of a someone who works at a restaurant during the week, washing dishes by hand. They love their job, and want to keep doing it. They start out at $5/hour, and at the end of their career, they do such an excellent job that they are paid $50/hour.

  • The scope is very limited. Once they've been washing dishes for 20 years, an extra 30 won't make a massive improvement.
  • The work is limited. If the restaurant is closed, they can't wash dishes.
  • Spending time in the weekend improving their dish-washing skills has very little benefit, and doesn't pay them anything.
  • Getting 2% faster at washing dishes won't improve their wage by 2%. It might not improve it at all. If it does, the payrise will be very much delayed — often until the annual performance review, or as an increase when changing jobs.

In this case, for this person, saving two hours in the weekend isn't worth $100 (future wage) to them. It probably isn't even worth $10 to them (their current wage).
Going off earnings only, their time during the weekend is valued at $0.

I feel the same is true of most jobs.
I get paid a salary for working certain hours. Outside of those hours, I get paid nothing.
Should I pay someone $20 to wash my car in the weekend, or should I spend an hour doing it myself?

The above could be summarised as: Are you rewarded for results? or for time?

If you're rewarded for results: The value of your time is the value of the marginal hour at the end of your career.

If you're rewarded for time: The value of your time is the value of whatever you're currently being paid.