Time is money. But, how much?


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Valuing people's time is a key challenge in a lot of applied micro development work. Farmers, micro-entrepreneurs, informal traders and caregivers, etc. All work on their own account, without a pay slip. Given all these applications, it is easy to motivate valuing people's time as an important research question. And yet, there has been surprisingly little attention devoted to the ``how'’ of valuing people's time in settings where we do not observe a wage.


Enters a new NBER working paper by Agness, Baseler, Chassang, Dupas, and Snowberg (ungated version). In this paper, the authors leverage individual choice data they generate on farmers in western Kenya to solve a general problem: do behavioral phenomena drive individual choices when trading off cash for time, or cash and time for goods? Their results have direct, practical implications when trying to value time spent in self employment: they measure the size of the bias individuals apply when considering the monetary value of the time they spend working on their own farm, such that it can be removed from the market wage to provide a more accurate measure of time spent on a job of one's own. 


Some key features of the paper before we dig into it. First, it involves lottery tickets to win an irrigation pump — hitting someone's soft spot right there… Second, it is a great reference guide on approaches to elicit individual preferences in an experiment—I learned a lot reading through their exposition. Finally, and certainly of great use to our readers, it delivers an actual rule of thumb to value the time people spend in self-employed tasks! SPOILER ALERT: 60% of the market wage in contexts similar to western Kenya! Since their estimates account for behavioral biases that are likely context-specific, they discuss external validity and how to apply their rule in other contexts… More on this at the end of the blog. 


Wait, why is this an issue? Don't we know how to value stuff?

One of the central contributions of the paper is to recognize that, while we have a toolbox to value stuff, the assumptions needed to place a monetary value on people's time in a simple willingness to accept exercise may not hold. In fact, the authors propose that these violations of standard theory when trading off time for money may be at the very origin of labor market frictions documented in the literature (examples of these here and there). E.g., imagine that farmers actually prefer to work on their farm vs. working on someone else's farm, even holding the task and other transaction costs constant. In this example, carrying out a revealed preference experiment in which we would elicit a farmer's willingness to accept farming work in exchange for money may not return a reliable measure of the value of time spent on one's own farm.


To figure out how to value people's time we first need to figure out how they value it!

This is Agness et al's next step. Their goal is to capture and contrast two measures of a farmer's time: a direct measure, by eliciting each respondent's willingness to access to perform an agricultural task for money (reservation wage); and, an indirect measure, by 1/ eliciting each respondent's willingness to pay for a good (lottery ticket to win a pump), 2/ eliciting willingness to work for the same good, and 3/ relating the two.


Armed with data from their choice experiment, they are able to show that direct and indirect values of time do not line up, and that the benchmark model cannot explain patterns in data. Their next 2 steps to figure out a value of time in their context are 1/ identify a source of wedge between direct and indirect value of time; and 2/ remove it to back out a value of time net of this bias. 


Behavioral respondents.

They consider behavioral models that can help explain the wedge between direct and indirect value of time in their data. They retain two types of behavioral biases, and for each they consider a special case that only applies to monetary transactions: 

  • Symmetric self-serving bias: self-serving people prefer not to transact with others → wedge between their valuation and the actual value of these transactions
    • Money-specific self-serving bias: people are self-serving about money transactions.
  • Symmetric loss aversion: the cost of losing something is greater than the value of winning that same thing.
    • Money-specific loss aversion: the cost of losing money is great than the value of winning that same amount.


[NB: they also consider a host of alternative explanations in their tonic Appendix E: effort costs of casual work, risk aversion, order effects, anchoring, non-compliance, censoring, stigma surrounding low wages. They also test for ``shading'' in the casual labor task, and find it only when the wage is set below the wage farmers reported they could earn for the task, and only when the payment was made in cash (Appendix F).]


Considering these behavioral phenomena in a simple model and solving the indifference conditions over the three different transactions yields an expression that links direct and indirect values of time with the wedge under each of these four different behavioral models. Solving for the wedge in these four systems implies that the value of a self-employed farmer's time is lies between 40 and 100% of the market wage. While Agness et al show that this range of estimates of value of time returns appreciable levels of precision to reject negative profits from devoting time to self-employed activities across a range of studies, they take one last step to add precision. 


To keep things tractable, they structurally estimate a model that nests these behavioral models. They start by noting that, while all four behavioral biases can explain the wedge they observed between direct and indirect value of time in their data, they predict different correlations between choices: they use that as a source of identification in the structural estimation part of the paper. Namely, comparing simulated data and data from their experiment to show that a weighted average of money-specific self-serving bias and money-specific loss aversion is needed to reproduce the correlations between choices and behavioral discount rates observed in their experimental data. They formalize this intuition with some math, but this is the main insight: participants are behavioral when the choice involves cash, but trading off time and a good is not affected.


They proceed to estimating a model that allows for both money-specific self-serving bias and money-specific loss aversion, and the size of the wedge they estimate implies a value of time in self employment of 60% of the market wage in their context. 


A job of one's own.

So thanks to Agness et al we now have a reliable rule of thumb to value time devoted to self-employed activities in western Kenya: 60%! (Okay, let's admit, this has a nice HHGTTG feel to it and, at some level, weren't we all rooting for 42?) 


They of course discuss external validity and how to export their findings to other contexts. While they argue we should all spend more time figuring out the right value of time in our own study contexts (e.g., replicate their choice experiment), we can still hope to lean on their work as follows:


  • Use 40-100% of the market wage, since this doesn't require figuring out the correct behavioral phenomena at play, and is informative in many of the contexts they review;
  • Use 60% of the market wage when working in similar context to theirs. They do caution that, even within a context, there is evidence of stark heterogeneity across people and time.


As a proof of concept, they apply this rule of thumb to a bunch of recent papers in which self-employment meaningfully enters in the estimation of profitability and for which sufficient data was reported to apply their estimates. So, are all these self-employed people operating under negative profits? Unlikely! Instead, we just tend to underestimate the value of a job of one's own .

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