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A MODEST REVIEW OF MALTHUSIANISM

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Author: Carles Magrinyà Torrell

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INTRODUCTION

Thomas Robert Malthus (1766-1834) was an Anglican clergyman. Born into a wealthy family, he grew up surrounded by the elites of his time and would go on to become a leading thinker himself.
His most famous work “An Essay on the Principle of Population” was published in 1798 and it was his answer to positivist theorists like William Godwin or Nicolas de Condorcet. In it he maintained that prosperity was not possible due to demographic pressures on the available resources. The book, reaching seven editions, was a success at the time and it has influenced thinkers since. At the time Mill and Ricardo accepted his theory of population while Marx and Engels criticized him for not considering the role of classist institutions played in the persistence of poverty. He would even inspire Darwin’s theory of evolution. Malthus was also part of the political discourse of his time, opposing the English poor laws (which were intended to provide relief to the poor and unemployed) and defending the Corn Laws (trade laws intended to protect English agriculture).

Although his prediction was wrong, as we eventually broke out of the vicious cycle he described, many argue that his theory is great at explaining most of our history. A good way to see why is with figure 1, in which we see how the global average GDP takes the shape of a hockey stick, showing a long period of stagnation up until a point in which there’s an abrupt transition into rapid growth. The goal of this article is to understand this famous theory and to see if it really has the explanatory power some claim it has.

Figure 1: World GDP per capita over the long run. Source: Our World in Data

THE THEORY

The intuition of the model is fairly simple but there are several things that are important to have in mind: population growth vs. food growth, land as a fixed factor of production and diminishing returns. According to Malthus the population grew exponentially (or geometrically) while food production grew arithmetically. This, combined with limited and fixed space for production and that returns are diminishing, creates the framework for stagnation in a world in which eating and reproduction are facts of life. Considering this, the model has two basic assumptions. First, an increase in resources allows for an increase in the population (with abundance people can have more children which can be better fed and thus survive plus, because everyone else also eats better, less people die). And secondly, an increase in the population worsens the standard of living when space is limited (when there’s more people resources are consumed faster, therefore the excess quickly disappears, and people go back to subsistence). This meant that although population could increase, real wages and the standard of living didn’t.

This balance between creation and destruction is called the Malthusian trap and it can take place through two different channels. One is through “positive checks” which happen when population (at that moment exceeding available resources) decreases due to wars, famines or epidemics. The other are “preventive checks”, which take place when through conscious decisions people reduce the fertility rate, either delaying marriage or with contraceptive methods. To get a better image of this let’s look at these mechanisms graphically:

Figures 2 and 3: Malthusian model. Source: Caplan’s critique of Clark’s Malthusian model.

In the left hand-side diagrams (figure 2) we see the starting point of the model, in the upper diagram we see the birth and death rates as a function of income per person (the first one is increasing, i.e. more money more children while the second one is decreasing, i.e. more money less dead). In the lower diagram we see reflected the assumption that as population increases resources decrease with the technology schedule.

So, what happens if a positive check, like a harvest failure, takes place? That is reflected on the right hand-side diagrams (figure 3). Harvest failure means there is less food, which causes people to die of famine shifting the death right curve upwards. With this shift the economy will reach a new equilibrium with higher income but less population.

This graphical representation is useful but for his class materials, professor Jón Steinsson takes it a little bit further and provides a mathematical outline of the model accompanied by its graphical representation (figure 4) which can be helpful to further understand this topic:

Figure 4: Graphical solution to Steinsson’s model. Source: Steinsson’s public lecture notes.

In this graph we can see the simplified population growth equation plotted, which has a concave shape due to the population at time t being raised to a power between 0 and 1. The 45º line simply gives all the points where the population in time period t is equal to t+1. This is useful because the point at which the two lines cross is the steady state population level and if the population starts here it will remain at this level. However, for all the values lower than 𝑁¯ 𝑁t+1 will be higher than 𝑁t which means that the population will increase until it reaches that steady state. For higher values, the opposite happens, i.e. the population will decrease until the equilibrium point.

Figure 5: labor Demand in the Malthus Model by Steinsson. Source: Steinsson’s public lecture notes.

Another important graph we can plot is the one for the labor demand (figure 5), which tells us the number of workers employers are willing to hire at a certain wage rate and will show how real wages change with shifts in population. The fact that the curve is downward sloping is very revealing. That happens because the marginal product of labor has diminishing returns (meaning that the extra production added by a new worker decreases as more workers are hired) which also means that as the population rises the real wage will decrease. At the steady state 𝑁¯ real wages are at the subsistence level. However, if population starts at a higher level, wages will be below subsistence which will cause the corresponding decrease in population predicted by the theory. The decrease will stop when equilibrium is reached again (and in the opposite case wages will increase up to that point). This rule, that implies that no matter the starting point real wages will reach the same equilibrium point is called the Iron Law of Wages (it was first outlined by Ricardo but it’s very present in Malthus’s work).

MALTHUS’ VIEWS

Now, with a clearer understanding of the theory, Malthus’ position on key policy topics of his time can be examined more deeply. Beginning with the poor laws, they can be thought of as a monetary transfer, so what happens when people in need receive it? According to Malthus it would ultimately deteriorate their living standards because they would get the impression that they could maintain a bigger family, this means that the preventive check doesn’t take place and that a positive check will happen instead. So, because these kinds of checks are unavoidable, he believed it was better that the preventive check prevailed and that families didn’t get the false impression that they could expand, therefore avoiding diseases and infant mortality. A second dimension of this problem can be seen through wages: because families would have more money thanks to this policy, they would buy more food which would in turn increase its prices, decreasing real wages for all workers, especially the poorest.

The other big policy is the Corn Laws. They appeared in the aftermath of the Napoleonic wars when agricultural prices decreased across Europe and in response British landowners demanded protection. This created an important debate between advocates of protectionism and of free trade. As mentioned, Malthus was on the side of the former. To understand why, let’s look at the economic thinking of the time: economists believed that agricultural and mining activities had diminishing returns while manufacturing had constant returns. The implication this has in Malthus’s theory is quite important as it means that agricultural production won’t be able to catch up to demand if population increases because more people will be employed in the manufacturing sector than in agriculture. This means there will be more supply of manufactured goods than agricultural ones, increasing the relative price of food worsening factory workers’ standard of living. If the Corn Laws were repelled manufacturing would increase, so that is one of the reasons. The other reason for his stance is that he believed that there was a systematically low demand that jeopardized the emergence and establishment of entrepreneurs. The solution to this problem was provided by rich landowners, which were the ones that bought luxury products and therefore kept aggregate demand afloat. That is why opening the country to trade, harming landowners’ wealth, would reduce demand and impact negatively on the economy as a whole.

THE BLACK DEATH

As was mentioned before, one of the forms positive checks can take is that of epidemics and between the 14th and 17th century Europe was prey to several plagues that shattered its population. These tragic events had a tremendous impact on the population and the economy, this effects can be seen in the grpah below (figure 6) where real wages and populationof England are ploted tagether for this period:

Figure 6-Evolution of real rural wages (grey line and y axis on the left) and population (black line and y axis on the right) during the Black Death period in England. Source: El viatge de la humanitat (Catalan translation of The Journey of Humanity by Oded Galor).

What this graph shows is that despite the tragedy people had to keep working, and because there were less workers, wages increased a lot. And although plagues kept destroying the population these higher wages also meant that people could expand their family and so birth rates increased until the population level recovered and real wages fell to their original point. Let’s see this in more detail with Steinsson’s model:

Figure 7-Impact of a plague according to Steinsson’s Malthusian model. Source: Steinsson’s public lecture notes.

Imagine the plague strikes in period 0, in this period the population experiences a negative shock, and it’s reduced setting the level to the left of 𝑁1. But, in the next period population growth is again dictated by the regular function and so it will keep increasing as long as the population is below the equilibrium level, and it is reached in the same manner as it was described before (figure on the left). The big difference is the plague, in period 0 a fraction of the population is killed and although it will eventually grow to equilibrium again it provides an example of why population would even deviate from this point. Regarding the labor demand (figure on the right), it shows how wages change because of this shock. The change in population doesn’t cause a shift but rather a move upwards. That’s because when there are fewer people the marginal product of their work increases (there are less people so what an additional worker brings to the table is higher than before) and in this model this equals the wage. However, as was just mentioned, the population bounces back, which means that wages will also go back to equilibrium.

Finally, these last graphs (figure 8) show the effects of the plague on the population and the wages over a long period of time. They reflect what was just explained, the initial shock will cause a sudden decrease in population with a simultaneous increase in wages and over time these levels will eventually converge to the steady state.

Figure 8-Long-run response of wages according to Steinsson’s model. Source: Steinsson’s public lecture notes.

THE EUROPEAN MARRIAGE PATTERN

Having talked about the impact of a positive check, what about that of a preventive one? A great example of that would be the European Marriage Pattern. During most of history couples married early, which meant that fertility was quite high (although it never reached the biological maximum) because people couldn’t use contraceptive methods (plus, childbirth outside marriage wasn’t common), and it made economic sense for families to have as many children as possible. Because most families worked in agriculture and the jobs that had to be done didn’t require formal education, children were seen as an asset. They provided labor and security when the parents became older, softening the bad times in a family life cycle characterized by deficit and surplus periods that in the end didn’t leave much room for saving.

However, around the time after the Black Death, a new pattern became prominent in Northwestern Europe characterized by a delay in the age of marriage (this meant that women married in their mid- twenties) which implied a reduction in fertility. This is what’s called the European Marriage Pattern (EMP). Other characteristics were low levels of illegitimacy, a relatively high proportion of unmarried people (around 10% never married), a partible inheritance system and nuclear families (meaning a family was formed by the parents and their children). The last two points are particularly important because that meant that to get married the couple had to save before, which caused the delayed marriages that reduce fertility rates.

In the rest of Europe, the picture was quite different as there were joint households and women received their inheritance through dowries when they married. This reduced considerably the burden of marriage and incentivized fertility. So, at least the EMP acted as a constrain to fertility therefore sustaining the standard of living and at most it played a key role in the change towards prosperity (as some scholars believe that the lower fertility brought by this was vital to escape the Malthusian trap, lowered death rates and encouraged investment in human capital).

WHAT ABOUT THE REST OF HISTORY?

As was shown in the beginning GDP per capita (although these estimates are not great) was stagnant while population growth, plotted in the long run (figure 9) follows a very similar shape to that of GDP per capita.

Figure 9-Population growth over the long run. Source: Our world in data.

Real wages of laborers in England, estimated by Clark (figure 10), although covering a smaller time period a similar yet more detailed picture (they cover the fluctuations caused by the several plagues that Europe suffered).

Figure 10-Real Wages of Laborers in England from 1250 to 2000, plotted on a logarithmic scale of base 2 and scaled to be equal to 100 in the 1860s. Source: Steinsson’s public lecture notes but constructed from Gregory Clark’s data (2005 and 2010).

Furthermore, Ashraf and Galor (2011) tested the Malthusian hypothesis that technology might temporarily improve income per capita but over the long run this improvement will be offset by population growth, and their analysis confirmed it. However, this view is not shared by everyone.

CRITIQUES

Having examined the mainstream consensus, let’s look at some of the arguments that question the previous affirmations. Starting with the long period of stagnation the graph below paints a very different picture (figure 11). According to this growth would have begun much earlier than previously thought. So how can the difference between figure 1 and this one be explained? The reason is probably the data and estimations made for each. Historical data is far from perfect and research must adapt to what’s available to paint the best picture possible. In this case Maddison’s estimations (which are used for figure 1) are known to be far from perfect but they were a breakthrough and so, despite their weaknesses, they are still used today to paint a general picture of what the world looked like for most of our history. The real GDP per person estimates by Broadberry et al. besides being more recent, they are just for England (which is probably the country with the best data) and for a shorter period. This combined with the work that had already been done allowed for a more detailed and descriptive estimation.

But what about the difference between Clark’s (real wages of laborers) estimation and Broadberry et al.’s? It can be explained on the one hand, by the fact that the share of output isn’t split equally and changes through time (so for example during the industrial revolution capitalists are the ones that keep the most benefits). And on the other, that difference could be taking place because in the 17th and 18th centuries more people might have been working more hours. Yet, it’s still important to mention that Clark’s estimation might also suffer from estimation problems, in his case the series probably doesn’t capture the impact of new goods and improvements in existing ones which impact the standard of living. Despite all these discrepancies looking at the big picture, Malthusianism is still a good theory as neither income per capita, nor life expectancy show any sign of progress during most of history.

Figure 11-Real Wages of Laborers (figure 10) vs. Real GDP per Person (data from Broadberry et al. 2015, and Clark, 2010). Source: Steinsson’s public lecture notes.

On the more theoretical side Ester Boserup made strong arguments against Malthus. First, she argued that it was population that affected agricultural productivity, not the other way around. Furthermore, she opposed the assumption of diminishing returns as higher population may lead to better ideas that improve efficiency (i.e. more people imply more ingenious people that can come up with great solutions to existing problems). For similar reasons she believed that soil fertility shouldn’t be taken as given as it can always be improved by technology. Julian L. Simon argued in a similar line, that although in the short run an increase in population might be harmful in the long run it can have a positive effect due to better ideas and economies of scale. Another type of criticism focusses on fertility decisions, arguing that the original theory didn’t account well for the fact that parents could decide the number of children and the quality of life they received, thus omitting the importance of education and costs of child rearing, which were especially important at the dawn and during the Industrial Revolution. When that is considered Malthus’ prediction doesn’t hold.

Going back to the simple graphs designed by Clark to explain the basic mechanisms of the Malthusian model there’s an important punctuation to be made which is pointed out by Caplan (figure 12):

Figure 12-Caplan’s critique to Clark’s model. Source: Caplan’s critique of Clark’s Malthusian model.

The problem that Caplan has is that, in most cases of positive checks, people do not die immediately (like in a harvest failure which is the case of this example). Rather death is brought upon by a decrease in productivity which is not properly reflected in the model and brings Clark to the conclusion that a phenomenon like a harvest failure is good. However, in this example that is not the case at all. The best way to represent that is with a downward shift in the technology schedule, which means that, because they are less productive people earn much less (income goes from Y* to Y’) moving horizontally to the new curve. As more people die of starvation, the population decreases, moving down the curve until Y* is reached again. So according to Caplan, the only silver lining of these destructive phenomena is that some people survive and can get back to the original level. Although this contrasts with some empirical observations, like during the plagues in which wages went up (instead of worsening like he predicts), he is right that some thinkers might be too quick to celebrate this silver lining when in fact, higher wages implies that many people have lost their loved ones causing harrowing pain.

Another flaw in the theory can be found in comparative study by Weir of the demography of France (a high-pressure system ruled by positive checks) and England (which was characterized by the preventive check) testing for Malthusian effects. Therefore, due to these structural differences the impact of a price shock should be different: it’s expected that in England birth rates have a higher response and that in France mortality rates have a bigger reaction. However, he finds that the hypothesis does not hold true. However, this is mostly focused on the short and medium term, which does not mean that in the long term the Malthusian model is inconsistent.

Finally, regarding the EMP, some research has argued that it is more complex than it might seem, especially when it comes to its ties to sustained economic growth. Arguing that the Central European countries, in which it was more evident, experienced more stagnation and that in fact in England the marrying age wasn’t as high. Furthermore, fertility restrictions were also applied in East Asian societies, which also didn’t experience growth until much later. However, this might be due to a too narrow understanding of the EMP, as measuring it by age at first marriage is too simplistic. Plus, accounting for institutions provides much needed context to the analysis.

CONCLUSION

In conclusion, although the model is far from perfect, it does provide a useful framework for the long. Furthermore, it is still in use today, especially in Unified Growth Theory, which aims to understand how we were able to escape the Malthusian trap. Yet, as many researchers note, the population dynamics described in this article were not the only factor in action. What’s more, this model doesn’t work particularly well for the short and medium term. Plus, due to its simplifying nature, it omits important changes and overlooks key nuances that, when added up, give a much better picture of the past. Which is why it is vital to clearly understand the purpose of the model, as overly relying on it will only lead to a flawed analysis of the reasons why we have been able to prosper so much in such little time.

REFERENCES

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