Actual Populations Are Not Malthusian

[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?”]

Someone has criticized me because I only make a “philosophical” argument. I don’t know whether that is really a critique or rather a compliment. What he probably meant is that I take Malthus’ original argument seriously and dissect it to show why and how it doesn’t work. I make also some derivations from first principles, eg. what you should expect for beings that essentially live in two dimensions, and why that implies that quadratic and not exponential growth is the go-to functional form. And I allude to a non-Malthusian model for population dynamics that I have in the background. Of course, all this cannot prove that it is so, and I understand why this is not satisfactory.

To make things concrete and less “philosophical,” I would like to flesh a few central claims out with actual data. Maybe that helps to get over a view where “philosophical” perhaps means “not grounded on empirical evidence.” What I want to show in this post is that human populations clearly do not behave as Malthus and his followers think they do. It is actually so in your face that I find it hard to understand how you could miss this.

I will interpret the data in light of my model and show why it can explain a host of phenomena that are incomprehensible for Malthusians at least on a qualitative level. I will work the details of a non-Malthusian model out in further posts. But to explain the thrust of my argument, here is a rundown of the main contentions:

• Human populations regularly have the power to stabilize their numbers at some target size. They not just have this power, but have regularly done this since time immemorial. It is a part of our human nature.
• What happens when a population grows from a lower to a higher target size and then stabilizes there is just a “demographic transition.” This is no new phenomenon in modernity. It has happened many times before, and is probably older even than humankind. It is plausible that also many other species behave in this way.
• Population growth, and also sometimes population shrinkage, have been the exception historically. They occur when conditions improve, respectively when they deteriorate. Target sizes are adjusted accordingly: upwards in the first, downwards in the second case. The crucial point here is that conditions change first, and then a population grows or shrinks into more or less opportunity. It is not so that we scramble to produce adequate food because the size of the population can just not stop growing as Malthusians think. There is no “population pressure.”
• In preindustrial socities, mortality was more or less a constant although it could vary slowly over time. There were also extreme events, but those were the exception. The conclusion from this is that mortality cannot be the explanation for population dynamics although it has, of course, an effect over the short run. It can also have an impact over the longer run, but in a more indirect way.
• A species has to have maximum fertility high enough so it can raise its actual fertility and absorb shocks from rising and especially extraordinary mortality. That implies that most of the time fertility has to be well below the maximum. Otherwise there would be no leeway on the upside, and any lasting increase for mortality would force the species into extinction. That’s why the Malthusian idée fixe is wrong that humans almost always have very highfertility. The normal level is replacement fertility corresponding to the current level of mortality, and population hovered around it, mostly with only small deviations.
• Only under dramatic circumstances were populations sometimes forced down to a lower size by mortality. The “positive checks” that Malthus is so fond of exploring only played a role over the short term, and over the longer run only indirectly. Fertility — and that is fertility that reverts to the replacement level for prevailing mortality — is the driver of population dynamics, not mortality. The only thing new in modern times is that mortality fell to a much lower level, not that there was a demographic transition.
• Target sizes are set by a population depending on its level of distress where this mostly turns around nutritional distress: how often, for how long, and how severely we have to starve. The problem here is that it is difficult to ascertain the current level of distress if you are successful at keeping starvation away. You have few data, but need many for an estimation in the background. (BTW, “data” is a plural.)
• That’s why humans not only use their own personal experience of nutritional distress, but also many proxies that may be imperfect, but add information long before you suffer yourself. We empathize with those who starve, we form opinions about the situation on a social level, and we track how much of a buffer we have. We are already distressed when it becomes harder to get food on the table although starvation may be far away.
• There are further proxies we use: Diseases can be the result of a deteriorating nutritional situation and can also make it worse. There need not be a connection, but we treat distress from disease as a proxy for nutritional distress. We also empathize with those who suffer in this way and form opinions on the social level. Similarly, we use information for other types of distress, which may, but need not be connected with nutritonal distress, eg. distress from violence, social strife, or just deaths around us.
• The estimate for the level of distress is updated with information that comes in and accumulates. This underlying statistical procedure leads to an asymmetrical outcome. Negative events immediately ramp the estimate up, while improvements have an impact only over time.
• There is a longer-run memory here that may be passed on over generations although it may not be on a conscious level.
• The target size a population aims for is mostly determined by its level of distress. When it goes down, the target size increases. When it goes up, the target size decreases. That can then induce demographic transitions or their a mirror image, which might be called a reverse demographic transition. The properties of the estimation in the background, especially the asymmetry, lead to corresponding phenomena for target sizes.

There are plenty of further details that I leave out here. Yet, I hope you get the drift of where I am going. The concrete examples below are no proof, but may perhaps convince you that the phenomena in my explanation are real. I interpret them in light of my model to show it can explain what actual populations do, at least on a qualitative level. These observations stomp Malthusians, and rightly so because they amount to a refutation of the Malthusian argument.

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Below I focus on the development for England over the longer run, which is particularly well-researched. There is also another reason for this. I would like to criticize a few things that Gregory Clark gets wrong in his “A Farewell to Alms.” This is a warm-up for even further posts.

The points I am about to make may seem perhaps a little disjointed, but as will become clear that is not the case. It just takes a little to tie the different strands together.

The Population of England

In the following I use data for England from 1210 on that Gregory Clark has thankfully made available on his homepage. Here is how the population grew from 1210 to 1860:

I have stretched the Y-axis a lot, which is for millions of people. Since there is a strong increase from the mid 18th century on, the danger is that everything before that just looks flat because of the scale. However, developments were actually quite similar to what happened at the end. The same percentage changes look more impressive from a higher level than from a lower one.

An important point to note here is what happened before 1210. As far as I can see, there are only scant data. One comparably reliable source is the ”Domesday Book”, which was compiled until 1086 on the order of William the Conqueror. That was not really a census in a modern sense, but it is possible to get a rough idea for how many people lived in England at the time.

Apparently the population of England in 1086 stood at only 1.5 million. Compare this to France where the population could have been as high as 13 million, or to Italy with perhaps 10 to 13 million inhabitants (source is this Wikipedia page). There are also other estimates for England in the 11th century that I have seen, with a low value of 1.25 million and a high value of 2 million people. You should add huge error bars mentally here. Angus Maddison puts the size of the population on the territory of the current UK at 2 million in the year 1000 AD, which is roughly in line with the above estimate.

Gregory Clark’s framing in his book is one of eternal stagnation. I fully understand why the population size for the late 11th century does not figure prominently in his account. (I am unsure: Or is not mentioned at all?) It shows that there was massive population growth from 1.5 million in 1086 to 5.8 million in 1310, almost a quadrupling.

However, if you break it down and calculate annual growth, it is less impressive, only about 0.6% per year. To understand what that means, we can rewrite it in this way:

With mortality until fertile age of 50%, which is roughly what it was in preindustrial societies, replacement fertility is four children per two persons (half of them die and so you have two people in the next generation, ie. a stable population). With a generation length of 30 years, annual growth of 0.6% corresponds to about 20% growth per generation. That means people had an average fertility of about 4 * 120% = 4.8 during this growth spurt. In other words, although they had higher ferility than the replacement level, it cannot have strayed from it a lot on average. And it was clearly below a maximum of eight or even more.

Hence you can immediately conclude that also the people from the 11th to the 14th had rather good control over their fertility. If they could keep it at 4.8 on average instead of eight or more, it is not clear why they could not also have had replacement fertility of 4. They had the power to tune fertility down by 80% in that direction, why not also by 100% or even more?

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The typical story, informed by a Malthusian worldview, is that the population of England grew too large because it just could not stop, and hence suffered from “overpopulation” at the beginning of the 14th century. However, that cannot be true. The population size was above 5 million for half a century, and above 4 million for a century. If there had been too little food for so many people in England, the population would have been pushed below these levels within perhaps a year. Instead it hovers above 4 and even 5 million for decades. To put it differently: England was able to produce enough food for such a population and on a regular basis.

Surely, it is possible that extreme events could hit the population. But it is not obvious why that could not have happened also at any other population size. The problem with extreme events is exactly that they are extreme and hence also unexpected. Now, a population will regularly produce enough food to feed it in normal times and perhaps some more as a reserve, but only so much. It makes no sense to always grow five times as much food than you need and let 80% of it rot away, just in case something disastrous happens. That holds at any population level. If then an extremely bad year arrives that goes beyond what could be reasonably expected, there will be too little food and a famine. But that does not show that there was “overpopulation,” whatever that is supposed to mean. Famine could have struck a population at any other size, too.

And unfortunately that was what happened to the poor people in the 14th century with the Great Famine from 1315 to 1317 (note the Malthusian explanations with “population pressures” in the Wikipedia entry). The cause is unclear, but it is not unreasonable to think that it was the eruption of a volcano in New Zealand, Mount Tarawera. That probably led to a cooling around the world. Maybe there was also another unrelated climatic change because temperatures remained depressed for a long time afterwards following an exceptionally warm phase. And of course, noone could foresee the eruption of a volcano on the other side of the world and its repercussions.

It began with unexpectedly heavy rain in 1315. Straw and hay could not be cured for the animals, and grain could not ripen under these conditions. People tried to dry it indoors, which did not work well because of high humidity. Depots were drawn down, and I assume at first people could make up somewhat for the shortfall from their reserves. However, then also the crops in 1316 and in 1317 failed again. Seed grain was eaten up and draft animals were slaughtered, which made things even worse. At one point, even the King of England found it hard to buy bread, something that has never happened again. England was a literal hell at the time. It took until about 1325 before conditions had returned to normal.

You can see this also in the graph above where the size of the population suddenly jumps down. However, the dent is remarkably small. One explanation for this is population momentum. Population growth also leads to further population growth one and even two generations down the line because the extra people then have children and grandchildren. The population structure is geared towards younger people after a ramp-up.

Despite of this, though, the population of England does not recover to its former size after the Great Famine, but keeps shrinking although only moderately. The only explanation in my view for this is not mortality, but lower fertility. Plausibly this was a reaction to the horrible events that the people had had to go through.

In my model, that is to be expected: The population felt at ease with a population size of 5 million or even more before the Great Famine. But it then lowered its target size and pursued that with lower fertility when it got very negative feedback. Such a behavior makes perfect sense in general: The population gets new information about its long-run situation, namely that its size might be too large. And it responds with a lower population size to stay away from extreme distress.

— — —

The poor people in the 14th century had no luck after they had made it through the Great Famine. Just a quarter century later, another scourge swept across Europe: the Black Death. It came from the South and reached England around 1350. A common explanation is that the Great Famine made things worse because the population was already weakened. However, that does not seem plausible with two decades between the events. That would be more than enough time to get back to normal. But then the memory of the horrors must have been still vivid, and there was more to come now.

The Black Death killed a lot of people off as you can see in the marked decline in population size around 1350. Still, there was apparently already a downward trend because of lowered fertility. If that was driven by the memory from the Great Famine, it would now be exacerbated by the experience of the Black Death. The population of England should then yank its population target down even more drastically. And that is what apparently happened. The plague did also not go away right away, but stuck around with outbreaks, though not on the same scale, as late as the 17th century. That should have kept the memory alive, the estimate for the level of distress high, and the target size low.

If that is correct the further decrease in population was caused by lower fertility to reach a now much lower population target, not because of higher mortality directly. A population that runs at a fertility of about four has a lot of leeway on the upside to counteract even major increases in mortality. With fertility of eight, the population could double in just one generation. Obviously, the population of England did not do that.

Why lower the population target because of a disease? The Black Death was in principle unrelated to the food supply. Yersinia pestis spreads through flees that live on rats. All classes in society suffered huge losses no matter how well-fed they were. And the plague struck all over Europe, also in a rather thinly populated country like England. You could argue that a higher population density made epidemics more devastating. Maybe so, but then half the population would not make such a difference perhaps. As noted above, my explanation is that humans lump all kinds of suffering together because they might contain information on the nutriotional situation over the longer run, not because they always do.

If the estimate for the level of distress is passed down the generations, maybe not even on a conscious level and only embedded in a target size that feels adequate, you can have long-run persistence. The population of England keeps shrinking until the 15th century where it apparently reaches its new and much lower population target of less than 2.5 million and levels off.

The problem for Malthusians here is that this is not how it is supposed to work. With a shrinking population, demand for labor began to rise and with it also real wages. However, people did not use this to have more children as Malthusians will tell you against all the evidence. Instead they treated higher real incomes as a buffer against potential problems that they perceived with a high level of distress. Luxury goods cannot feed you, but you have leeway to ramp up food production if things indeed get as bad as you expect.

Note also that the development means that people had fertility below the replacement level for decades on end. If they could do this, also replacement fertility itself was in the range they could achieve, ie. the population had the power to stabilize, contrary to the Malthusian argument.

Only after one and a half centuries, around 1500, did the population start to grow again although that actually went along with falling real incomes. In my explanation, the population should slowly raise its population target when the memories of the Great Famine and the Black Death fade away. If it had been possible to feed a population of 5 million and more people before the calamities of the 14th century, the target size should probably go back to that level once people get more relaxed. Since you perceive less of a need to have a huge buffer, you might even do this while real income is falling somewhat.

There is then rapid growth again until about 1650 when the size of the population levels off for a century again at about the level in the early 14th century. Population growth from 1500 to 1600 runs at 0.54% annually on average. That works out to average fertility over time of about 4.71 if the replacement level is set to four (=50% mortality until fertile age). So, the development was actually quite similar to the one from the 11th to the 14th century, even a bit slower.

— — —

After a century of stagnation, ie. fertility at the replacement level (or even somewhat below to counter population momentum from the increase before), the population of England starts to grow again from about 1750 on. The increase until 1860 seems more dramatic than the one in the 16th century. But that is the scale that misleads you somewhat. Increases just look bigger on a higher level, and here growth also continues for a longer time.

Average annual population growth from 1600 until 1860 is only marginally higher at 0.56% than in the 16th century. However, it is indeed higher with about 1.1% from 1750 to 1850. With a reference level for replacement fertility of four again, this works out to average fertility of 4.7, and 5.6, respectively. However, that is only for comparison, the actual level for fertility must have been lower in the later phase because mortality began to fall from the mid 18th century on. I will address that part in a moment. Note that fertility was higher than from 1750 to 1850 than with earlier growth spurts, but still way below a maximum on average.

All in all, my admittedly rather qualitative explanation can account for the general pattern we see here. The population of England starts out at a low level in the 11th century. I don’t know what exactly happened then, but I assume that the Normans brought better agricultural techniques from the Continent with them (note that France and Italy could have far larger populations at the time, much larger than even at the peak in England, while their populations are now roughly on a par). Also climatic conditions were fortunate with relatively high temperatures. The population took advantage of this, and grew into the opportunity with a target size of perhaps 5 million instead of only 1.5 million before.

Not “overpopulation,” but a string of extremely horrible events in the 14th century made the population lower their target size to about 2.5 million. That was mostly achieved via lower fertility. Mortality played a role in the short run, but had an impact only indirectly. Once the memory of the 14th century faded away, the target size began to rise again. And so the population went into a growth regime similar to the one before 1300. It apparently set itself even a similar target size. That happened in the 16th century. Afterwards there was stabilization until about 1750.

Sometimes you are also lucky, and that’s what happened next. With further improvements and a level of distress that now began to fall to historically unprecedented levels, the population of England raised its target size by a lot. That led to comparably fast population growth, which lasted into the 20th century because it was just so good.

Fertility and Mortality Over the Long Run

To understand how this worked out, it is necessary to look not only at population growth, which lumps fertility and mortality together, but at the two inputs separately. Unfortunately, I do not have the data for England over time, which are probably hard to estimate for the Middle Ages with scarce data. Instead I illustrate the development with birth rates and death rates. As I have explained in another post, those are potentially poor stand-ins for fertility and mortality, though.

Birth and death rates are defined as the number of births and deaths for a reference population, usually 1,000 people strong. There are many pitfalls here. The most serious one is that birth and death rates not only depend on fertility and mortality, but also on the population structure. Especially, during times of growth or shinkage there can be major shifts here. It may seem as if fertility and mortality had changed, but the effect might come from how the population evolves.

Another problem is population momentum: After a rise in population, there will be further increases one and even two generations afterwards when the extra children have children and grandchildren of their own. Basically, this works out through the population structure, which is geared towards younger cohorts. That means birth rates can remain high after a ramp-up although fertility is already decreasing.

In a way, the pattern for birth rates is the pattern for fertility with an overlay of itself one and even two generations before. You have echoes for about half a century where there can be a high birth rate while fertility is falling. The opposite effect occurs after a population shrinks. In this case, further decreases follow over half a century although fertility may be rising. Similar remarks also apply for mortality. In addition, falling mortality can lead to distortions. It means that the population is now older and the share of those of fertile age is shrinking. That then leads to lower birth rates even with fixed fertility.

The implication of all this is that you have to treat arguments based on birth and death rates with extreme caution. I am baffled how many people treat them as an obvious choice anyway, and even confound them with fertility and mortality. Nonetheless, birth and death rates can give you an idea of how things are working out. You should just not overinterpret the finer developments.

Here is now development for death rates in England over time:

The blue line are data that originally come from Wrigley and Schofield (I get them via OurWorld in Data). I smooth them with a median filter, the red line. It works like this: I take a few values around a data point and then calculate their median. That cuts spikes away and makes the curve more stable. Below I want to avoid spurious effects where it looks like fertility goes down, while indeed it is mortality that goes up over the short run. Note that the data behind the graph are first for five-year intervals, but from 1861 on, they are on an annual basis. That explains the piecewise linear appearance on the left, which is just a meaningless interpolation.

As a general observation: Volatility for death rates was much higher before the 19th century. But it begins to fall already from about 1750 on, then goes down further over the 19th century, and even more so over the 20th century, apart from spikes for the two World Wars. If you think of this as an imperfect proxy for the level of distress, then there was a major improvement, which should increase the target size for the population a lot.

All in all, what we see in the graph are broadly stable death rates before 1750 on a high level (roughly also for mortality). There are some slow fluctations around a mean, and an overlay with high volatility on a short time-scale. Afterwards, death rates fall steeply, with plateaus in the middle of the 19th and then in the middle of the 20th century.

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Now as for fertility, it means different things for different mortalities. With mortality of 50% until fertile age, a fertility of four is just the replacement level where a population stabilizes. For mortality of only 5% as nowadays in developed countries, fertility of four means very fast population growth, almost a doubling per generation. The same holds roughly also for birth rates with the above caveats.

To correct for this decreasing replacement level, I subtract the death rate from the birth rate. You could view this as a fixed death rate of zero, or as how many more births there were than for a stable population. This is not entirely correct for the above reasons, but gives you an idea of what happened with fertility. Please keep especially in mind that there are echos for birth rates from previously high fertility one and two generations down the line. Fertility moves faster than birth rates may indicate, and might already be falling while birth rates are still high.

I plot to lines here: The red line is the birth rate minus the death rate (sorry, colors are now the other way around, I messed it up). And the blue line is the birth rate minus the median-smoothed death rate, which removes short-term spikes. You can also see why I wanted to have both: The red line dips lower at the time of the two World Wars because there is extraordinary mortality. But that does not tell you anything about fertility which should move more like the blue line.

Another way to look at the graph is this: The difference between the birth rate and the death rate is just population growth (without immigration and emigration, where the former should have some effect in the 20th and the latter in the 19th century). The rates are per 1,000, so you have to divide by ten to get percentage changes.

In this way, you can directly see average annual growth for the population in the 16th century (I only have data for the second half unfortunately). It is really an average: The population grows at about 1% a year at the peak, but then growth falls to practically 0% when the population stabilizes around 1650. And you can also see the higher growth rate from 1750 to 1860 with a rise from about about 0.5% to 1.5%.

— — —

Broadly, you can see long waves here for birth rates with some fluctuations. As for fertility, it peaks already earlier on before birth rates begin to fall. There must be a ramp-up from 1750 on, but fertility should begin to fall already in the second half of the 19th century. This development then goes on into the 20th century.

But you can see also the down-swing of a similar wave at the beginning that started around 1500 and comes to an end in the mid-17th century. Although population growth is somewhat stronger into the 19th century than at the peak of the previous growth spurt in about 1600, the difference is not that large. What leads to a huge boost is that population growth goes on for much longer and stabilization comes much later.

In other words: Although it may seem so, and most people treat it like that: Demographic transitions are nothing new. They follow a very regular pattern. There was also one from the 16th to the 17th century. And that was not the first one either. In the Middle Ages there must have been even an reverse demographic transition when the population stabilized on a lower level around 1500: Fertility had to run below the replacement level for decades and then grew to it from below. And if there had not been the catastrophes in the 14th century, there would probably have been a demographic transition also then.

What was indeed new over the past 250 years was neither the pattern of a demographic transition nor its amplitude, it was only that all this happened on top of falling mortality. That had never happened in human history before, at least not to such an extent, because mortality was more or less on a constant level as you can seen in the graph for the time before 1750. There were some fluctuations around this level, but not some major move to mortality as low as in our times.

If you take mortality and perhaps even more so the volatility of mortality as an imperfect proxy for the level of distress, then this extraordinary development since 1750 should have led to a massive increase for the target size in my model. This would then induce a strong increase for fertility that could also be prolonged. But when the population then reaches the eventual target size with almost a minimum for distress, this should also come to an end. Fertility would go down again and approach the replacement level, now lower also because of lower mortality. Unlike with a Malthusian explanation, none of what happened should be surprising.

Fertility and Mortality Over the Short Run

The previous graph has even more interesting details. So far, I have only focused on the long-term pattern. Let me now zoom in on the 20th century:

We come from still high population growth of more than 1% in the 19th century. Yet, as for fertility, it had been falling already before that, this is more of an echo from previously high fertility. After one or two generations, the momentum effect comes to an end, and then also birth rates fall. That happens throughout the 20th century with a long movement downwards, ie. towards stabilization.

However, there are also sharp swings here. The first comes with World War I. The red line includes excess mortality at the time and hence dips deeper than the blue with median-smoothing in the background. It is rather easy to understand why birth rates dropped during World War I. Probably many men were at the front. But there should also have been another component: People should raise their estimate for the level of distress with such a bad environment. They would hence lower their population target. However, there is an even faster reaction where people probably postpone having children for the time being.

But then after World War I, the birth rate bounces back almost as if the population wants to make up for the loss in the years before. That is not difficult to understand: People now have the children they wanted. This lasts only for a very short time, though, the peak is already in 1920. You can see that the aftermath of World War I lasts longer, however. I would interpret this as driven by a correction downwards for the population target. So birth rates in the 1920s are below what you would expect from the long-run trend over the 20th century, even after the short “baby boom.”

Then from the late 1920s on, there is the Great Depression, which apparently leads to a further downward correction for the target size and falling birth rates also because people postpone births for the time being. World War II hits the population of England already at a low level for the birth rate. There is again a further decrease, presumably for the same reasons as during World War I: Men are at the front, more postponement, and a correction downwards for the population target.

But already from 1942 on, when victory becomes palpable, birth rates begin to tick up. The first small peak is in 1944. And then the birth rate seriously bounces back after the war, with a peak in 1947. However, the further development is different from that in the 1920s and 1930s. Whereas the situation after World War I kept pushing in the downward direction, things start to look up materially after World War II.

The birth rate goes down after postponed births are through. Yet, as the population feels better, they raise their target size again, and that leads to an extended baby boom that peaks in 1964. From there it goes down again, with a low during the difficult times in the 1970, and then birth rates go up again, but part of this may only be an echo from the “baby boom.” All in all, though, these are fluctuations around a longer-run trend downwards, which means towards a stabilization of the population at a target size.

— — —

You had similar developments also in other countries. As for Germany, the general pattern was like that for England, but still slightly different. You also had the same bounce back after World War I. Then the situation got worse than in the UK with the hyperinflation in 1923, so the target size was depressed already earlier on. The Great Depression hit Germany particularly hard, with unemployment of more than 30% around 1930. However, from this extreme low, the economy improved rather swiftly in the 1930s. That then led to a first “baby boom” in the 1930s, for which the Nazis took credit, in my view for no reason.

The devastation of World War II was worse for Germany and that last into the later 1940s. But then economic recovery went very fast, and there was now a second “baby boom” that got going during the 1950s and peaked exactly in the same year as in England, namely in 1964. Interestingly, West and East Germany moved in lockstep until the 1970s despite a relatively lacklustre development under the Communist regime. The main point here was probably not the absolute level, but that the population went from really stressful times to feeling at ease again.

As for the US, there was also a similar pattern as in England with only one “baby boom.” It began during World War II and then peaked already in the 1950s. I guess people in England are as confused as I am when Americans speak about “baby boomers” because the respective age group born in the later 1940s and 1950s are not associated with a “baby booms” on this side of the Atlantic. In German, they also go by the rather bureaucratic term “geburtenstarke Jahrgänge” (cohorts with strong births).

— — —

There are here two different phenomena that are intertwined. When there is a crisis, birth rates are yanked down immediately. However, people apparently only postpone having children at first. If things go back to normal fast, birth rates bounce back almost as fast. That should be so if the target level is adjusted only slowly. In a way, this makes sense: You should not change your long-run behavior a lot just because of a one-off event. After the down and up, the population goes on almost as if nothing had happened.

However, when conditions remain bad for a long time, the population lowers its target size seriously. That should be so if there is an estimation in the background where cumulatively many bad years can lead to more of an effect than only a few. People who thought they would just postpone having more children might then give up. But that is not all that’s to it, there is also a longer-run depression as the example of England from the 14th century on shows. Again, that makes sense: If you get consistent negative feedback, it perhaps appropriate to think your long-run target size over.

As noted above, the result is asymmetric: Bad news has an immediate effect on the target level, while good news only works out more slowly. That should be so with a sluggish estimation in the background that is driven by negative news. Good news are only the absence of bad news and do not lead to a major correction, only cumulatively. This then leads to a “baby boom” that basically makes up for the depressed target size before.

We can now plug this together with the interpretation for England in the Middle Ages: However bad the two World Wars were for England — and they really were bad as you can see in the disruption they also caused for fertility — they were perhaps not as bad as what the people in the 14th century had to go through. The Great Famine was so horrible that even cannibalism was not unheard of. People at the time were understandably full of despair.

While the two World Wars lasted for only a few years, the people in the 14th century were first shaken by a huge famine from 1315 to 1317, but with an aftermath until 1325. And before there could be any “baby boom,” there was an even heavier blow with the Black Death. The plague also lingered on for decades and that should have kept the feeling alive that the level of distress was very high.

Under these conditions, you would expect a major correction for the target size downwards in my model that persists for a long time. It took one and half a centuries before the population slowly began to see there was perhaps also an upside. When the memory faded away, the population grew back to its old level at the beginning of the 14th century by about 1700. And then the pleasant surprise was that things got better and better from 1750 on.

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My explanation is only qualitative here. I retell events also with the assumption that my model provides the correct interpretation. That is a bit circular, and I don’t mean this as a proof, only as a demonstration that actual events are rather easy to understand within the framework.

And this explanation makes sense of a lot of things that are baffling for Malthusians:

• Populations stabilize at a target level. When they go from a lower to a higher one, then there is a demographic transition. When they go from a higher to a lower one, then there is a reverse demographic transition.
• There is an asymmetric response to deteriorations and improvements. The former have an immediate effect, the latter work out over the longer run.
• If bad news turn out to be a one-off, there are short-term moves downwards and upwards for birth rates, though with a small net effect. That works through postponed births.
• If bad news are persistent, the population lowers its target size, and then pursues it with a reverse demographic transition. That works out over decades.
• If good news are persistent, the opposite occurs: The population raises its target and then pursues a demographic transition. “Baby booms” are a mini-version of this. If good news come in over a longer run, there can be a major boost for population. But also that will come to an end when the higher target level is reached.
• Fertility fluctuates around the replacement level. Deviations are usually rather modest. Only rarely is maximum fertility reached, which Malthus thinks is the normal behavior of humans.

All in all, I find this pretty clever. Humans are not the dumb beings that Malthus imagines they are, who just have children because there is food at the moment. Populations only grow when there are improvements first that make more population possible. And when they sense problems approaching, they react already early on.

I will develop all this more in detail in further posts. But I think you can see already why an explanation along these lines can explain a host of phenomena that are incomprehensible for Malthusians.