Valuing Leisure Time

(Eventually this will be folded into my Welfare Estimation sequence, but feeling like I had to do things in the proper order was causing them to not get done, and this post is general-interest enough that people who are not interested in the full sequence might want to read it.)

Introduction

The standard methodology of cost-benefit analysis, as typified and explained in HHS Guidelines (pages 32-33 of the pdf), is to value a person’s leisure time at their post-tax wage:

The fourth default assumption is that the opportunity cost of unpaid time can be best approximated by post-tax wages. Consistent with the standard economic model, this approach assumes that individuals decide whether to engage in paid work depending on whether the incremental income exceeds the value they place on unpaid time, a decision generally described as the labor-leisure trade-off. Taxes and benefits are usually excluded from this calculation, assuming that individuals focus on their take-home pay in making related decisions.

Before going any further, I would like to applaud and congratulate the community of cost-benefit economists for placing a positive value on people’s leisure time, and for doing the work to force governments to (sometimes) do the same. We must give credit where credit is due, and this was a hard-fought victory. The typical “Seeing Like a State” approach taken by government bureaucrats is to implicitly (and sometimes explicitly) place a zero (or sometimes negative) value on the leisure time of citizens.

However, we can do better. In this post, I will argue that the following procedure is the proper way to value the leisure time of everyone in the world, including children and the unemployed, for the purposes of EA impact evaluations. It is also a good way of determining the value of your own leisure time for the purposes of life optimization.

The Method and its Results

Figure out how many leisure-equivalent hours people have in a year. Divide the developed-world Value of a Statistical Life Year (currently about $250k) by that number.

If work and chores all had zero experience-value, such that people would prefer not to be conscious while doing them, then all value in a life would come from people’s average of 5.2 hours a day of leisure, and leisure time would be valued at about $130 an hour. With numbers for the experience-value of work and chores that I intuitively feel are right (three hours of work or two hours of chores give as much utility as one hour of leisure), the average person has about 9.5 leisure-equivalent hours per day, and leisure time should be valued at about $70 an hour. Assuming economic rationality and frictionless contracting, and that the average values of leisure and work are the same as the marginal values, the average person has 11 leisure-equivalent hours per day, and leisure time should be valued at about $60 an hour.

Note that this is the value of leisure vs nonexistence. Most things that take away people’s leisure are not as bad as nonexistence (although some of them are, or are even worse). In the special case where the thing that replaces a person’s leisure has exactly as much disutility as their job, and the person is earning the average wage, then the value of preventing that harm will be the same as a person’s post-tax wage.

Also note that this gives the average value of leisure time, not the marginal value of a person’s least valuable hour of leisure time. I think that this is defensible, and possibly optimal, because people are limited in their ability to reschedule things, especially in the short run. If an unexpected shock like a government mandate or medical emergency takes an hour away from someone, it might randomly take away a very valuable hour.

Problems with the Wage-Based Approach

The standard wage-based approach is simple, uses easily available data, and has a fairly good theoretical justification. So why should we change it to this new method?

First, and most important, it assumes that time spent working generates zero utility, as does the thing that leisure is replaced with. This means that it can only work as an estimate of the cost of replacing leisure with something that feels exactly like the person’s paid job. We would like to have more flexibility in our analysis. The cost of an action that takes away leisure will depend on how bad the thing that replaces leisure is, and we should not assume all such things are equally as bad as work or each other. Some of them, like an unnecessary medical procedure, might even be worse than nonexistence.

Second, it means we have no good way to value the time of children, as this recent paper discusses. Most papers value childrens’ time only by the expected future wage gains from their time spent in formal education, which is...less than ideal.

Third, it is inaccurate. The standard economic model it is based on assumes perfect information and rationality, frictionless contracting (the ability to freely choose any length of workweek), and no budget constraints. Normally these assumptions cause less problems than you might think, but here, they plausibly introduce significant distortions. For the rest of this post, I will use the ‘rational actor and equilibrium’ model as a suggestion, or one model specification, one that is informative and useful but not definitively true.

Finally, the wage-based method is unfair. It values the time of a rich person more than a poor person, and, if used as the basis of analysis, will preferentially direct more resources to rich people. This is wrong, for reasons I discussed at length in my post on Life-Valuation Variability.

Does Consumption Increase Utility?

It is true that people report enjoying their leisure time more when they have more and nicer stuff, and that standard economic theory states that utility increases as consumption increases.

However, I approach public policy from a contractualist viewpoint, which takes as a foundational axiom the equal moral status of all people. I think that most people share these intuitions, and that a society based around social contracts and equal rights will be more stable and prosperous than a society based around pure utility maximization. I believe that ‘utility maximization’ should be a much bigger part of our social contract than it currently is, because it is a very valuable coordination mechanism. But if it violates one of the other core clauses of the social contract, then I will overrule it.

In an ultimate physical sense, utility is a myth. It is a tool we create to allow us to coordinate. And so, we can give it the properties we need to give it, in order to do its job better. So we can simply assert that, for the purpose of public policy or EA cause prioritization, utility is independent of consumption, and that we will not value the time of people more because they are consuming more.

This assertion is less of a violation of ‘the real world’ than you might think. In fact, it might actually be true. All consumption can be assigned to one of three categories of health, positional, and hedonic; and it is not proven that any of these actually increase the utility that an hour of leisure gives people. (In the previous sentence and for the rest of this section, I use the word ‘utility’ as a utilitarian would use it, not the definition I have previously asserted.)

The first category of consumption is things that lengthen one’s lifespan and health-related quality of life, by purchasing health and safety. All value from this consumption is captured in a measurement of the total Quality-Adjusted Life Years the person lives; it does not increase utility in the time that it is spent.

The second category is positional goods, which provide no value to humanity on net because the utility to the purchaser is offset by the disutility it imposes on everyone else. I do not consider it proper for any social planner or charity to value a person’s life or time more because they have purchased positional goods. If anything, this should be seen as a hostile and antisocial action, and heavily taxed.

Even in standard economic theory, is is not known whether purchasing positional goods increases the utility of leisure time. Does a person who owns a lot of jewelry get more utility from spending time with their family? If not, then even a utilitarian would not value their leisure time more, and if so, you have admitted the real-world existence of a utility monster and discredited utilitarianism as a guide to public policy.

The final category of consumption is hedonic goods, those that give pleasure through some sensory mechanism independent of social status. (The mind is a sense, and reading a good book is a pleasure similar to the more physical pleasures.) This is what most people think of when they think of consumption, and standard economic theory assumes that more expensive things give more pleasure and utility.

However, standard economic theory has not taken the hedonic treadmill into account. People seem to adapt to most physical pleasures pretty quickly. We know that a drug addict isn’t actually any happier than a non-addict. And we know that drug addiction works by hijacking the same reward mechanisms in the brain that are responsible for ordinary physical pleasures. So it may be that case that a rich person who goes to an expensive spa every weekend is basically a kind of drug addict, and that their consumption only serves to prevent withdrawal rather than to actually give more utility per hour of leisure.

Leisure-Equivalent Hours

So, given that we have made a choice to ignore consumption and value the time of all people the same regardless of how much they are spending, how do we measure the experience-value of that time?

By revealed preference, time spent in leisure is more valuable to people than time spent in work or chores. (I have carefully considered and respectfully disagree with the Puritan assertion that work and chores are actually better than leisure, but that people are addicted to leisure because they are confused about what ultimately good for them.) However, I believe that for most people, most of the time, work and chores are better than nonexistence. A life with these things, plus some amount of leisure, is better than a life that only contains that amount of leisure. It has as much utility as a life with some larger amount of leisure. I am using the term ‘leisure-equivalent hours’ to mean the amount of pure leisure that would give as much utility as the lives we observe, with their mix of leisure and work and chores.

For the purpose of valuing leisure time, I assume that the Value of Statistical Life Year ultimately derives from the the number of leisure-equivalent hours in that year. This will be larger than the number of leisure hours, but smaller than the total number hours that a person is awake. We can then use this number to find the value of an hour of pure leisure.

Estimation Approaches

The American Time Use Survey collects data on how people in the US spend their time. (I am using American data for this, because I am using the American VSLY. When we are taking money from people, or asking them to donate, we use their VSL, which means using their value of a leisure hour. For the full explanation, see Life-Valuation Variability.) In the average American’s average day (not the average worker’s workday) there are 8.8 hours of sleep, 3.6 hours of work, and 5.2 hours of leisure. I will collectively call the other 6.4 hours ‘chores’ although they include many things that people might classify as leisure, like eating, shopping, playing with pets, and attending religious services.

The question is what value to assign to work and chores. There are lots of ways to do this, like surveys, and you could spend a lot of time fussing over the details. But for the purpose of illustration, I will show two approaches. First, I will use my intuitions for what the numbers should be, and second, I will go with the standard economic model. Then, for both of them, I use a simple spreadsheet to calculate the value of a leisure hour. Feel free to make a copy of the sheet and play around with different values. (If you want to assign a positive value to time spent sleeping, on the assumption that dreams have experience-value and moral worth even if they are not remembered, then go for it. I will set the value at 0 for must specifications.)

For most people, work really sucks. A significant fraction of the population would probably choose to take a pill that turned them into a p-zombie during their work hours, so they would not have to experience it at all. They would prefer to go unconscious and then wake up after their shift. But other people don’t mind it so much, and/or have opportunities to do things during their workday that give them utility. So, on average, I would place a value of 0.3 on the utility of work, relative to leisure. This means that the average disutility of work is 70% as much as the disutility of not existing. This is worse than the DALY adjustments of some really nasty diseases and disabilities. With that value, and with a 0.5 value for chores, the average leisure hour would be valued at $72.

This means that, for the average person, the average work hour has a value of $22. But this does not mean that, at the margin, they would get $50 of value by working an hour less. It is plausible that the value of leisure goes down as you get more of it, so the value of the last hour of leisure exceeds the value of work by about people’s take-home pay. It is also plausible that labor market distortions keep people working more than they would prefer to.

However, as a sanity check, I will do the standard economist thing: use revealed preference, and assume that people are optimizing in a well-functioning market. Yes, this assumes many inaccurate things that could introduce distortions. It will also assume that the average value of leisure is exactly the same as the last hour. But I’m fairly sure that the distortions cause people to work more than they prefer, and to prefer to work more than their coherent extrapolated volition says they should prefer to. So this should be seen as an upper bound on the experience-value of working, and a lower bound on the value of leisure.

I used the very scientific technique of changing the utility of work and chores in the spreadsheet in increments of 0.1 until the marginal value of leisure vs work was closest to the average after-tax wage. This happened at 0.6. With this value, an hour of leisure is worth $61, an hour of work is worth $37, and the difference is $24, which is about the average after-tax wage.

If we instead set the experience-value of chores at 0.9 and sleep at 0.1, then a work value of 0.5 causes the marginal value of leisure to equal take-home wages. In this case, the value of a leisure hour is $50, again assuming that the average value equals the marginal value. This is the lowest you could possibly go for the value of an hour of free time, even under extreme assumptions.

Conversely, if I have underestimated the disutility of work and/or chores, then the value of an hour of free time will be higher. If they are both set to zero, then it is $130. If work is 0.1 and chores are 0.3, then it is about $90.

So, given all this, my point estimate for the value of an hour of leisure is $70, and my 90% confidence interval is $60-$90. (This is based on a point estimate of a $250k VSLY; uncertainty in that number will carry through and increase the confidence interval.) This is the value we should use for anyone in the world, regardless of their consumption, assuming that we are spending donor money raised in the developed world, for the same reasons that we should value all life-years equally and use them as the unit of analysis.

Of course, people in poor countries can purchase an hour of leisure very cheaply if they have their own cash, so any intervention that saves them time must still beat direct cash transfers to them in order to be considered. But for policies that directly impose time costs on them, we should use this number. This is, obviously, conditional on also valuing their lives and health using donor-country VSLYs. Basically, if we pay for a medical intervention that reduces the mortality risk of a population but also consumes hours of their time, we should value their time at the same donor-country rate that we value their lives.