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And no, I am not going to dissect the situation with Game Theory. For today I am interested in understanding the timing of when parents attempt to potty train their children. My mom claims that I was potty trained at one (how is that possible when I am not all that well trained now!) and stories abound from friends and relatives about how rapidly they were able to have their kids trained.

I frankly have no clue whether these stories are apocryphal. Let’s assume they are not. And let’s also leave the analysis of the readiness and behavior of children for another day (YOU try to effectively appeal to a 12 month old with incentives, for example). What does the economic way of thinking tell us about when parents decide to potty train their children?

It all comes down to costs and benefits (marginal) of course. The major benefit of having a potty trained child is not having to actually change diapers many times a day. Even if you can pull off a pitstop in just 2 minutes, that is still about 15 minutes per day spent changing diapers. Part of this benefit is not just in the time savings, but rather dramatically in the reduction in “yuckiness” factor. A second major benefit of having a potty trained child is the reduction in cost of purchasing and disposing of diapers – a savings of at least a quarter per diaper (believe me, this adds up). Perhaps there are other benefits, but I think they pale in comparison to these two. Two that I can think of are that potty training is a way of teaching and disciplining a child, and the second is that it confers some sort of status, or gratification, to the parents. I might subscribe to the former myself, as for the latter … let’s leave that discussion for another day.

What are the costs of potty training? Aside from the week of misery that you and your child go through during the training process, the major cost is that rather than changing diapers, you need to tend to a child in the bathroom. This certainly takes more time than it does to change diapers, but the yuckiness factor is clearly lower than having to change diapers. A related cost is that it makes going out with your child, at least in the early stages, much more difficult. You have to find clean bathrooms, you need to carry around a portable potty seat, etc. There might be some other smaller costs, such as the occassional accident, but leave those aside for now.

As with any (rational) action taken by individuals, parents will attempt to potty train their children when the incremental benefits from doing so exceed the incremental costs from doing so. The changes to benefits and costs above are obviously wildly heterogeneous (i.e. they vary widely across families) and depend on the intelligence of the child, the patience of the parents, the income of the parents, the type of diapers that are being used, how much families travel, what type of travel families like, how many bathrooms are in the house, and much more. There is neither time nor interest in analyzing each of those factors right now, but I welcome your insights on them, or I will post more on it later.

In the meantime, we should see potty training accelerated when the relative benefits of doing so occur earlier in a child’s life and we should see potty training taking a longer time when the relative benefits of doing so are not realized as soon. I tend to think of this in the way that labor economists think about the “demand for leisure” in the presence of wage changes. It is a priori indeterminate whether an increase in a wage rate will result in an individual working more or less hours (though in the aggregate there is a fairly strong positive relationship). This is because a wage change has two effects on individuals. The first effect can be thought of as a “wealth effect” (more commonly referred to as an income effect). When wages go up, even if a worker works the same number of hours, they will be wealthier. With increased wealth, people tend to purchase more of all goods and services, and among these goods is leisure time. Thus, the income effect of a wage increase suggests that individuals will work less. On the other hand there is a second effect at play too. When wages go up, every hour that an individual chooses to be away from his job is now costing him more. For example if you work one hour less when your wage is $10 per hour, that hour of free time “cost” you only $10, but if you had a wage of $30 per hour, leaving work one hour early now cost you three times as much. This effect suggests that when wages go up, individuals tend to consume less leisure, because the price of leisure has increased. This effect is known as the “substitution effect.” Whether a wage increase will tend to make an individual work more or less is therefore an empirical question.

Now, what does this have to do with potty training? The analogy is not perfect, but I still see both an income and substitution effect at play here. Incomes have risen dramatically in the U.S. over the past 100 years (7-fold increase in per-capita terms). With this improved standard of living and higher wages, the value of the typical individual’s time has increased dramatically. To the extent that taking care of a potty trained child is more time consuming than simply changing diapers, an increase in income is predicted to result in families delaying the time until a child is potty trained, at least until the point where the yuckiness factor, and social embarrassment at having an untrained toddler, are too much to bear. At the same time, disposable diapers did not come into use until the 1940s and was not until much later that they were more than a luxury that few could afford. So while time has become more valuable, the cost of diapering a child has been falling – leading to an increase in the benefits of keeping a child in diapers, all else equal. A lot of the related improvements in US living standards over time (e.g. we travel more) seem to also point in the direction of leaving infants and toddlers in diapers for a longer period of time.

Alternately, as standards of living improve, there are two things that make it easier for parents to get their kids trained faster. The obvious one is that with the rise of two earner families, and the rise in incomes, many parents can pay to have someone else do the dirty work for them. Second is that our increased wealth has made traveling with potty-needy children much easier today than it was decades ago. I think of these as countervailing “substitution effects.”

Which of these effects dominates seems to me to be an empirical question – and yes there are dozens and dozens of other factors we can consider. My casual observation is that families are taking longer to train their kids today than they have in the past. We are currently working with our 29 month old daughter in earnest (we tried many months ago and failed miserably). Before we had her, I would have bet we would have succeeded a long time ago – how wrong I was.

Finally, the answer to this question will be different for different groups of people. But addressing the question is simple. For what groups have the benefits of training increased/decreased the most over time? For what groups have the costs of training increased/decreased the most over time? How have the benefits and costs changed? Do different people place different weights on each of the above factors (surely they do)? And have factors influencing these weights changed over time?

I wonder if there is a data set some clever empiricist could examine to address this question. Is it an important enough question for someone to spend real research time on? Perhaps only for folks with tenure.

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