Adjusting population density to account for land quality

Vernon Henderson, Adam Storeygard, David Weil 19 December 2020

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Scholars have thought about population density and how it affects economic outcomes for far longer than there have been economists. Writing around the year 200, the Christian church father Tertullian complained that there were so many people that “we are burdensome to the world, the resources are scarcely adequate to us; and our needs straiten us and complaints are everywhere while already nature does not sustain us.” The negative effect of a mismatch between population and the availability of land was at the centre of Malthus’ analysis. More recently, the one child policy in China resulted from a fear that growing population would soon outstrip the country’s natural resources, and similar fears motivated less draconian policies in India and several other countries. The issue even plays a central role in the 2018 film “Avengers: Infinity War,” in which the chief bad guy, Thanos, pursues a plan to kill half of the population in order to stave off the ruin brought on by overpopulation. And in 2019, Donald Trump tweeted “Our country is FULL.” 

The simplest way to think about the adequacy of local geophysical resources to support human habitation or economic development is in terms of population density. But a moment’s consideration suggests that this is far from ideal. Land differs enormously in many characteristics that are relevant for economic activity, and thus 100 km2 in, say, the Île-de-France, can support a far larger population than a similar area in the Tibetan Plateau.

Previous literature has made ad hoc adjustments for variations in land characteristics, for example by calculating population per million calories of agricultural production potential (Galor and Özak 2016). However, the set of geographic characteristics that affect suitability of land for habitation or for economic activity extends far beyond agricultural productivity. The fact that land near coastlines and ocean-navigable waterways is more densely populated than land without access to the sea suggests that such access makes land more useful (Mellinger et al. 2000). Similarly, terrain roughness, the presence of disease vectors such as malaria mosquitoes, and other dimensions of the climate are all likely factors in determining land quality. 

In our recent paper (Henderson et al. 2020), we take a systematic approach to assessing land quality and adjust population density according to differences in this measure of land quality. We term this quality-adjusted population density and compute it for various countries, but similar analyses would be possible both at larger or smaller scales. The first step in this process is deriving weights on geographic and climatological characteristics that can be measured on a consistent and fine scale (quarter degree longitude-latitude grid squares, of which there are approximately 250,000 on land worldwide). The characteristics we examine include agricultural productivity, biomes, proximity to the sea, navigable rivers, large lakes, and natural harbours, as well as terrain roughness and elevation. We derive weights for each of these characteristics by studying their influence on the distribution of the population within a country. Hence, we base our analysis on within rather than between country variation and are thus able to avoid any bias that might result from a potential correlation of a country’s climate or geography and its institutions, income per capita, or overall population density. 

Using our estimates of the weights on geographic characteristics, we assign a quality measure to each grid square in the world. The bottom panel of Figure 1 presents the result of this exercise, aggregated to country level. In this map, each country’s area is adjusted by our measure of quality explained above. For comparison, the top panel of the figure shows each country’s actual land area but in both cases, countries are shrunk slightly for legibility. Several comparisons are striking. Quality adjustment expands the US, since its average land quality is higher than the world average, while it shrinks neighbouring Canada substantially. Western European countries get much bigger, while those in sub-Saharan Africa shrink. Denmark, Ireland, the Netherlands, Croatia, and the United Kingdom expand the most, as they have the five highest estimated values of average land quality.

Figure 1 Country-level quality-adjusted area

A. Countries by land area

B. Countries by quality-adjusted area

The second stage of our analysis compares the actual population of a country to what we would expect if the current population of the world were redistributed according to land quality – that is, if population per quality-adjusted area was the same everywhere. The results are shown in Figure 2, where the blue dots represent the fitted population, while the red dots represent the actual population. Note that the figure only covers the 80 countries with the largest fitted populations. Countries where the red dot is to the right of the blue one have a quality-adjusted population density that is higher than the world average, with the distance between the dots showing the degree of the mismatch as a proportion (log scale). Similarly, countries where the red dot is to the left of the blue have quality-adjusted population densities below the world average. The figure shows that while both China and India have populations in excess of what would be assigned based on land quality, the mismatch is far higher in India. Australia, New Zealand, Ireland, and Uruguay all stand out for having populations far below what would be assigned based on land quality. The Netherlands, often noted as an unusually densely populated country, is actually slightly below the world average in terms of quality-adjusted population density. Were the world population to be reassigned on the basis of Figure 2, the largest absolute gainers would be Australia (adding 631 million), the US (478 million), and Argentina (338 million), while the largest losers would be India (subtracting 1.06 billion), China (834 million), and Pakistan (167 million).

Figure 2 Top 80 countries by fitted population

Finally, we look at the relationship between our measure of quality-adjusted population density and income per capita where we find surprising results. Figure 3A plots the relationship between the logs of conventionally measured population density and income per capita in a scatterplot. If we fit a line to this data, it is flat, with a slope insignificantly different from zero. By contrast, as shown in Figure 3B, there is a strongly negative and statistically significant relationship between the logs of quality-adjusted population density and income per capita. For a fixed quantity and quality of land, a country being twice as rich is associated with having a 30% lower population. This is a new finding that only comes to light once one adjusts population density for land quality.

Figure 3 Density and GDP per capita

A. Conventional population density and GDP per capita

B. Quality-adjusted population density and GDP per capita

In Henderson et al. (2020) we further probe this finding. We start by asking whether it could be taken as evidence for a simple Malthusian mechanism: countries where there are a lot of people relative to quality-adjusted land are poor simply because of resource congestion. However, we find that even with a generous estimate of the role that resources play in production, such a channel is insufficient to explain the magnitude of the negative relationship observed in the data. 

As an alternative to the resource-congestion story, we focus on different population histories of the currently rich versus poor countries. We show that the correlation between income and quality-adjusted population that we observe in modern data is primarily the result of population growth over the last 200 years, rather than being due to poor countries always having had high ratios of population to quality-adjusted land. Put another way, currently poor countries have on average seen much faster population growth since the start of modern economic growth than currently rich countries. This is particularly true in Old World countries where the native populations were not displaced over the last 500 years. This is in turn attributable to the rapid transfer of health technologies from rich to poor countries, primarily in the period after World War II (see Acemoglu and Johnson 2007). Health miracles – that is, episodes of rapid increases in life expectancy – were far more frequent than income growth miracles. This was a humanitarian triumph, but it led to late-developing countries seeing their populations expand by a larger multiple over the course of their demographic transitions than those countries that developed early, which make up the bulk of rich countries today.  

References 

Acemoglu, D and S Johnson (2007), "Disease and development: the effect of life expectancy on economic growth", Journal of Political Economy 115(6 ): 925-985.

Galor, O and Ö Özak (2016), “The Agricultural Origins of Time Preference", American Economic Review 106(10): 3064-3103.

Henderson, J V, A Storeygard and D N Weil (2020), “Quality-adjusted Population Density”, NBER Working Paper 28070.

Mellinger, A, J D Sachs and J L Gallup (2000), "Climate, Coastal Proximity, and Development", in Clark, G L, M P Feldman and M S Gertler (eds.), The Oxford Handbook of Economic Geography: 169-194.

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Topics:  Development

Tags:  population density, income per capita, land quality

School Professor of Economic Geography, London School of Economics

Associate Professor of Economics, Tufts University

Professor of Economics at Brown University

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