The Earth’s population has been growing steadily over the last century, and agricultural production could keep up with it. This means that there were no Malthusian constraints on population. The question in such a situation is for how long population can keep growing.
To answer this question, one has to make several assumptions. For instance, the UN’s calculations assuming a mid-level of fertility (meaning all countries converge to the replacement level of 2.1 births per woman) would imply that world population plateaus off around 11 billion by 2100. But how accurate is this prediction?
To investigate this and to give an alternative prediction for future population dynamics, Lanz, Dietz and Swanson (2014) build an economic growth model with endogenous fertility. They then calibrate it to real-world data to analyze its predictions. The point of the model is not to assume that population dynamics will take any specific direction or magnitude (i.e. they do not assume any particular fertility rate). On the contrary, population dynamics will be the outcome of the model.
First, I briefly describe the four main features of the model: production, technological progress, land resources, and fertility.
The model in question is a two-sector model including a manufacturing and an agricultural sector. Agriculture produces food, which is necessary to maintain the population. Manufacturing produces a consumption good that delivers utility directly to households. Both sectors utilize labor and capital in their production. Agriculture also uses land resources, which are assumed to be imperfect substitutes to the other inputs (labor and capital) in agricultural production.
Total factor productivity (i.e. technology) increases if innovations are made. The number of innovations made per period depends on the fraction of the labor force allocated towards R&D activities. It is important that it is the share and not the absolute size of R&D labor that counts. The latter would imply a positive relationship between population and technology, which is not observed in the data.
Land is finite, and initially it is “natural” land. This needs to be converted into agricultural land by using labor. There is, however, diminishing returns to labor devoted to land conversion. This captures the effect that the more land is already converted, the more costly it is to convert new land. Equivalently, this says that most productive and easy-to-convert lands are converted first, whereas the rougher areas are left to be converted last. Obviously, total agricultural land cannot exceed the finite land endowment of the world. The model will therefore also be able to make predictions about how much land will be in used for agricultural purposes over the forecast horizon.
On to fertility, households care about their consumption (of the manufactured good), the number of children they have and the utility of their children. Raising and educating children costs time, and thus competes with other labor market activities. Furthermore, the (time and human capital) cost of raising a child increases with the level of technology. This means that in more technologically advanced economies, you need to invest more in each child. Of course, this will lead to a convergence to a low fertility regime as technology develops. A final constraint on population is agricultural production, which needs to cover total food expenditures. It must be noted that food expenditure per capita is increasing in per capita income (but at a decreasing rate). This captures the effect of changing diets as people become richer.
Thus these 4 factors (household’s desire to have happy children, time costs of raising children, technological progress, and agricultural production) along with a constant mortality rate determine population dynamics in the model.
Now, let’s move on to the results of the model. After calibration the model is simulated to make projections for the 2010-2100 period. Some of the results are summarized in the following figures.
World population is projected to reach 9.85 billion by 2050, largely in line with UN predictions, and 12 billion by 2100, which is above the mid-level UN predictions but below the highest ones. Population growth doesn’t entirely disappear, it still remains around 0.1% in 2150.
There is a 67% increase in agricultural output by 2050 (in line with other evidence), and a further 31% increase by 2100. Despite this, the area of agricultural lands mostly stops growing by 2050 and levels off around 1.77 billion hectares. This would mean an additional patch of land the size of Mongolia (or Alaska, or three times Spain) being converted into agricultural land by 2050.
But how will population keep growing when we don’t convert more natural land into agricultural land anymore? Technological growth in the model is relatively low (1% per year), so that’s not the main driving force. Instead, we see that agriculture will become more and more capital-intensive. Actually, the capital stock used in agriculture will double between 2010 and 2050 whereas the labor employed in agriculture (both in absolute numbers and in percentage) will decline.
As for economic indicators, world GDP growth will decline from around 2% in 2010 to below 1% in 2100. This still means that output will double by 2050 and triple by 2100. Furthermore, per capita consumption will also more than double by 2100.
To sum up, this model mainly differs from existing population projections in that it does not explicitly assume any particular fertility rate. The main difference vis-a-vis other projections is that this model does not forecast the demise of global population growth. Global population is only expected to level off in the very long run (i.e. way beyond 2100).
In my opinion, the framework used by Lanz, Dietz and Swanson (2014) is more robust than existing forecasts, which are based on strong assumptions on future fertility. The main uncertainty about the model is that all of its parameters and variables (of which there are a lot) need to be calibrated to make projections. And there is an inherent uncertainty in that. Sensitivity analyses on a couple key variables, however, reveal that the projections are quite robust to changes in the subsitutability between land and capital/labor in agricultural production, altruism towards children, the discount factor, and the mortality rate.