There is a need for the Malthusian Model?

Perhaps not really.

Introduction

The Malthusian model is a vestigial remnant of classical economics that still survives in modern economics to explain pre-modern economic history. Still, when analyzed carefully, it fails to be a necessary model for understanding the past.

The Malthusian model

The concept of a Malthusian economy is the notion that in such an economy, there is no economic growth in the sense of a sustained rise in living standards; instead, any temporary improvement in productivity (due to factors such as technological progress) produces an increase in population which presses against the finite material resources and results in a return to the long-run steady-state level of productivity.

This model is based on the assumption that the population growth rate increases when real incomes increase and this increased population produces decreasing returns to labor due to the scarcity of natural resources. Malthusian economic historians believe that this model is a mostly accurate representation of world economic history until 1800. For thousands of years of history up to 1800, they believed that fluctuations in living standards were not sustainable but results of temporary shocks. Only after 1800 that technological change become fast enough to increase productivity to a degree large enough so that the population growth could not erase the gain in productivity.

Evidence of economic growth before 1800, such as the improvement in living standards in Ancient Greece over a period of five centuries (see Ober 2015, the Rise and Fall of Classical Greece) is often interpreted as a temporary improvement due to the result of random shocks. According to those who defend the Malthusian model, this growth over 500 years just was not real sustained economic growth: it was unlike the real growth that is observed in our modern economies in the past 200 years. Another, more plausible interpretation in my view, of the Ancient Greek growth experience is that it was exceptional like modern growth, still leaving the vast majority of the world’s economic history as Malthusian anyway (this is the impression one gets from reading Ober 2015).

Problems with the model

I see three main issues with the Malthusian model:

1. Living standards, over the long run, cannot be described by a unidimensional variable.

As explained by Tyler Cowen in Eternal economic growth and Effective Altruism - Marginal Revolution:

Real gdp comparisons give you good information locally, when comparing relatively similar societies or states of affairs.  The numbers have much less meaning across very different world states, or very long spans of time with ongoing growth.  Comparing say Beverly Hills gdp per capita to Stone Age gdp per capita just isn’t an accurate numerical exercise period.  It is fair to say that the Beverly Hills number is “a whole lot more,” and much better, but I wouldn’t go too much further than that.  They are very different situations, rather than one being a mere exponential version of the other.  The economics literature on real income comparisons supports this take.

It is a good approximation to use unidimensional GDP figures for the short run when the composition of goods and the relative prices in the economy does not change much so that an increase in purchasing power in terms of a fixed basket of goods is a good representation of changes in living standards over time.

But over the very long run, the concept of GDP breaks down: for example, according to official national accounts and the PPPs from the World Bank, Mexico today has about the same level of real GDP per capita as the United States had in 1960. Can we conclude that living standards in 2023 in Mexico are really the same as in the US from 1960? Of course not.

In 1960 the US produced 8.34 million motor vehicles, and almost all were sold domestically; in a country of 180 million people, its domestic consumption of motor vehicles per capita was about the same as today: in 2021-2022, sales were of ca. 15 million vehicles for a population of nearly 340 million. For comparison, in Mexico in 2022, motor vehicle sales were 1.13 million vehicles for a population of 130 million: Mexican per capita sales are about five times smaller than in the US today and the US of 1960.

The reason for this discrepancy in per capita motor vehicle sales between the 1960 US and 2023 Mexico is that the 1960 US was a developed middle-class society like today, but operating with 1960’s technology, while Mexico today is an underdeveloped country where the majority of the population lives in poverty and so only households among a small elite in Mexico can afford to purchase a car.

While Mexicans today have access to the vastly superior 2023 technology compared to the 1960 technology that Americans had access to in 1960, life expectancy in Mexico today is higher than in the 1960 US (74 years for 2019 Mexico, 70 years for 1960 US). Overall, living standards in Mexico today compared to the US in 1960 are just two very different situations and in my view, it is not possible to say which one was “better” than the other: one was a rich middle-class society operating with 1960 technology, another is an underdeveloped society operating with 2023 technology. For longer periods, the concept of GDP gets even more distorted, so it is just ludicrous to claim that an estimate of the GDP of medieval England in current US dollars is a meaningful figure.

This also means that as real income is not unidimensional, then there cannot be a simple relationship between real income and demographics, fertility, and mortality. As there is really no such thing as a “real income y” variable.

2. Population growth does not follow the Malthusian assumptions

In the modern world, it is obvious that the population growth rate does not follow the assumption of the Malthusian model: it is preposterous to think that the vegetative population growth rate of rich countries like Switzerland and Norway is greater than in poor countries like Afghanistan and Nigeria. In fact, today, the correlation between living standards and population growth rate is negative.

For the more distant past, we lack high-quality data to make claims that cannot be disputed, but evidence from past societies also suggests that population growth and living standards were not intimately connected. In Ancient Greece from 800 BC to 300 BC, living standards improved while the population grew, but the rate of population growth was already zero around 400-350 BC, while living standards were much better than in previous centuries. Greece’s population began to contract after 350 BC and the decision of households to reduce fertility is to blame according to contemporary accounts, while there is no evidence of economic calamity in the centuries from 350 BC to the beginning of the Roman period.

Archeological field surveys suggest that population densities in Ancient Greece peaked around 400-350 BC while living standards were improving (for example, the ancient houses dug by archeologists increased in size by 50% from the 5th to the 4th centuries BC).

Polybius, writing in 150 BC, blames the fall in population due to a conscious decision by households to not have many kids, just like modern households in developed countries are doing:

“In our own time the whole of Greece has been subject to a low birth rate and a general decrease of the population, owing to which cities have become deserted and the land has ceased to yield fruit, although there have neither been continuous wars nor epidemics... For as men had fallen into such a state of pretentiousness, avarice, and indolence that they did not wish to marry, or if they married to rear the children born to them, or at most as a rule but one or two of them, so as to leave these in affluence and bring them up to waste their substance….”
― Polybius, The Histories, Vol 6: Bks.XXVIII-XXXIX

France also enjoyed low fertility rates before it became a modern industrialized economy, so its population growth in the 19th century was much slower than in other parts of Europe like the UK or Germany.

However, estimates of GDP per capita show France had approximately the same macroeconomic trajectory as the rest of Western Europe during the last 250 years, this is because economic growth in advanced economies is mainly determined by the advance of the so-called technological frontier which is the same for all countries:

3. Natural resources are not exogenous to the economy.

Malthusians often think in terms of societies enjoying a fixed endowment of “land,” which means that as population increases, the assumption that the stock of land is fixed implies that productivity of labor decreases (assuming contra 1, there is such a thing as a unidimensional variable that describes the productivity of labor) as the size of the population increases. But the capacity of humans to harness nature is determined by the number of ideas that humans have which is increasing in the population: that is why today when the world has 8 billion people, natural resources are more plentiful than ever.

What about the increase in real wages following the Black Death?

It is often argued as the “proof” of the historical existence of a Malthusian economy that European wages rose substantially following the Black Death. This is interpreted as the notion that an exogenous shock (the Black Death) reduced the population while the quantity of land was fixed, which increased the supply of land to the population, increasing labor productivity which resulted in higher wages. Eventually, the population grew back, and labor productivity fell substantially and wages decreased. Therefore, they conclude that Europe was a Malthusian economy in the 14th, 15th, and 16th centuries.

However, it is not hard to construct a non-Malthusian model that generates the exact same pattern: consider a simple endogenous growth model where productivity is determined by the stock of knowledge and physical capital. Suppose that knowledge is generated by the population at a fixed rate and is highly durable, with a depreciation rate of 0.5% per year.

Physical capital depreciates much more quickly at 5% per year, so in the very long run the capital-labor ratio only varies as a function of the stock of knowledge (more knowledge increases productivity, which increases capital accumulation), so output per worker can be written as the geometric mean of the stock of knowledge and the capital/labor ratio.

Suppose the population of workers grows at 0.2% per year and 10% of output is reinvested into capital. Suppose there is a Black Death shock that kills 40% of the population in the year 1340, what happens to labor productivity? This graph shows what happens:

This simple exercise shows a sharp increase in labor productivity following the Black Death shock, which takes 300 years to recover.

It is also not hard to write down a non-Malthusian model that produces stagnant living standards over many centuries: very slow population growth and a very durable stock of knowledge will automatically generate that effect. When one considers that the population density of many regions of the former Roman Empire, such as Greece and Egypt, was lower in the mid-19th century than it was in the 1st century (the Greek region of Boeotia had 200,000 to 250,000 inhabitants around the time of Aristotle, by the late 19th century it had only 40,000), this apparently millennial stagnation is not hard to explain.

Conclusion

Overall, I do not see a need to use Malthusian models to explain economic history, as well as the important point that economic development is multi-dimensional, not unidimensional, which is often forgotten by our GDP-obsessed economics profession.

Instead, the Malthusian model should be regarded as a vestigial element of classical economics that has survived the marginal revolution (which showed that economic value is subjective and hence not accurately represented by unidimensional variables when there is more than one agent) and survives on the idea that human being is a kind of bacteria that just replicates to fill its external environment until there is no extra-food left, instead of rational agents with subjective preferences that can modify their environment.