My Forecast for Japan — Population and Fertility

[This is part of my series on Thomas Malthus’ “Essay on the Principle of Population,” first published in 1798. You can find an overview of all my posts here that I will keep updated: “Synopsis: What’s Wrong with the Malthusian Argument?”]

In my last post, I made an argument that the population in Japan is pursuing a population target of about 113 million. I also proposed two bets, but there was some handwaving in my argument. I would like to make the bets now more precise, much more precise. To show you what you are up against, I lay my cards on the table.

What I have done is set up a little model where I can do simulations. It was a good choice to use Java here and not Scilab or even Excel. This gets too complicated without object-orientation. But with it, it is actually pretty easy. Strictly speaking I do not need to do simulation because I can calculate everything directly. But then this is only a first step to a much larger project.

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Here is what I do:

I simulate a population that starts out at a size of 10,000. They are all born at the same time. That means initially you have population momentum when they have children and grandchildren (for an explanation of the concept, see here). To avoid this artifcat, I let the dynamics run for 200 years with replacement fertility, to get close to a steady state. That yields somewhat more than 25,000 people.

I use similar assumptions as in my post on population momentum. The propensity to have children depending on age, ie. fertility, is a hat function that runs from 15 to 45 years and peaks at 30 years. As for mortality, I have built also a little in before age 50, 5% until age 30. After age 50, mortality picks up somewhat, and after age 80 even further. All in all, this leads to life expectancy of somewhat more than 75 years, which is slightly too low, but not by much. Replacement fertility works out to 2.13, which is minimally too high.

After the initial phase, I suddenly raise the population target to a level two thirds above what it was before. I use the formula that drops out of my analysis for South Korea to calculate actual fertility for the population. Notabene that this is not a fit for Japan. I assume we are dealing with something that is a part of human nature.

The level of actual fertility that the population pursues can be calculated via the simple formula:

ln(actual fertility) = ln(replacement level) + ln(target size/actual size)/0.3.

All you have to do then to get the level for actual fertility is exponentiate the result. I use this for the whole population at a time.

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Here is now what I get over three hundred years for population size (visualization with Scilab). I set the target size to 113 million, a value that I have derived in my previous post.

Note that the ramp-up is somewhat uneven because I suddenly change the target size. In reality, Japan experienced population growth since the 19th century. My choice leads hence to a somewhat spurious oscillation on top of the general increase. This results from population momentum because of the sharp switch. In reality there was a somewhat similar effect because of depressed fertility during World War II. But then I do not want photorealism here.

The size of the population of Japan in 1935 was about 70 million and 73 million in 1940. I have set the starting point to 1935 in the chart, you have to give or take a few years here. From this initial value, the population grows to slightly less than 130 million. The dynamics are impressively close to reality. A peak is reached shortly after 2000, and indeed that happened around 2005.

My prediction now is that the population of Japan will decrease to slightly more than 100 million somewhat after the middle of the century. However, the dynamics will lead to rising fertility, and that stops the decline. Note that that also means shrinkage will be by less than 20% from the peak, and not by 50% as a quasi-official forecast wants to have it that I have seen only a few days back. And then the population of Japan will grow again to about 120 million. With ever smaller oscillations it will converge to the target size of 113 million. That will also be about the level at the end of the century.

I assume there will also be some immigration. The interaction with fertility is somewhat complicated. But on the whole that should lead to more population than under my assumptions. Hence, I think my hunch that I could bet against less than 100 million until the end of the century seems pretty safe from my vantage point. But then this is only so if my analysis is warranted.

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Here is how this development looks for realized fertility. In my model, I have all the information in retrospect because I actually simulate over 500 years. Realized fertility is how many children there really were per woman. This is a better measure than “total fertility rates,” which may suffer from a “tempo effect” (I will explain the concept in another post).

Due to the rather small population size of about 40,000 in my simulation most of the time, the randomness comes through. There are only about 500 women per cohort on average, and that may vary. For a much larger population results should be practically smooth. I shift realized fertility forward by 30 years. It makes no sense to plot it at the time when the cohort was born, only when it had its peak fertility. So the value for 1935 is actually for the cohort of 1905. Since that is in the initial phase where I have replacement fertility, you can see a build-up. But that is an artifact.

The results are pretty perfect apart from slight quibbles. Actual fertility in 1930 was 4.7 and 4.11 in 1940 (total fertility rates), but I assume that the latter was depressed because of the contempory situation. In the later 1940s, it jumped back to about 4.5 (all data come from here). Fertility then fell to below the replacement level after the early 1970s. My model is more sluggish in the 1950s, but crosses below the replacement at about the same time. And then fertility bottomed out around 2005. I get almost the same result, also that fertility starts to rise from the low as has been the case for a decade now. The low value of about 1.3 is eerily close to reality.

Here is now my prediction: To everybody’s surprise, fertility in Japan will keep rising and will probably hit the replacement level in the 2030s. It will be even worse for the doomsayers: Fertility will rise to well above the replacement level, and Japan will have a “baby boom” on a par, for example, with the German “baby boom” in the 1960s. However, that will not go on, and fertility will fall again, but not to the lows a decade ago. This is the same pattern as for population size only in the other direction.

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Let me now specify my two bets for Japan. The first one does not change from my last post:

• The population of Japan will not fall below 100 million until the end of the century. As you can see, this is a close call on my part even assuming the model is correct. If you take any other forecast for Japan, you will win easily. But then I will win.

The other bet was somewhat vague and turned around fertility. Here is my call:

• Over the next twenty-five years, fertility in Japan will go above 1.9. Again, if you believe the “official forecasts,” you can only win. But I will win that bet, too.

So, any takers? As I have already remarked, I do not want to bet anyone. This is not to chicken out after proposing the bets. But I would like to have some public control on both sides. Preferrably it should be someone with a reputation to lose, some Paul Ehrlich so to say. There are so many people around who pose as experts on demographics and are super-confident about what will happen in Japan.

I am surprised that noone wants to put their money where their mouth is. Small sums, this is about showing your confidence in your own expertise. The downside is not the money, but that everybody sees you were wrong. I am willing to take that risk although my analysis is still pretty a work in progress.