Our paper in Communications Earth & Environment reports multiple lines of evidence suggesting that economic growth and income convergence might be slow compared to the range of economic scenarios widely used by the international scientific community, including the Intergovernmental Panel on Climate Change (IPCC). The paper came about as a synergy between three previously independent lines of research from our group at the University of Colorado Boulder, from our co-author David Tilman’s group at the University of Minnesota, and from the Frederick S. Pardee Center for International Futures at the University of Denver, which was founded by Barry Hughes and is currently directed by Jonathan Moyer, both co-authors. The paper also sheds light on a fascinating parallel between the growth of economies and the growth of animal and plant populations.

It is an axiom of ecology that a population’s growth rate depends on its size. Resource scarcity and competition limit the growth of very large populations. Difficulty finding mates and lack of genetic diversity can limit the growth of very small populations. The fastest-growing populations typically have abundances between these extremes.

In the 1980s, famed macroeconomist William Baumol noticed a similar pattern in the growth rates of countries’ gross domestic product (GDP) per capita—a measure of affluence. Very poor countries often have slow GDP per capita growth rates, for reasons such as civil conflict, poor governance, and lack of capital. Very rich countries also can have slow GDP per capita growth rates, largely due to aging populations caused by low birth rates, and shifts from manufacturing-based economies to service-based economies. Middle-income countries—rich enough to have the physical and human capital for industry and to have a growing middle class of consumers, poor enough to be cost competitive in export industries—tend to have the fastest growth.

David Tilman is a renowned ecologist, who has published several high-profile papers since 2011 quantifying environmental tradeoffs associated with meeting future food demands. A country’s food demand depends on its affluence, in addition to its population size. Richer countries consume more food per person, and they especially consume more meat per person, which creates more greenhouse gas (GHG) emissions than plant-based diets. Therefore, Tilman and his colleagues needed to forecast GDP per capita into the future in order to forecast food demands.

To do this, they used a simple differential-equation model (DEM) based on Baumol’s insight, whose parallels to ecology Tilman recognized. Following a 1994 study by Thomas Selden and Daqing Song, Tilman and colleagues fit a quadratic logarithmic function to the relationship between GDP per capita and its growth rate, aggregating countries to income groups. The quality of this fit is striking, as Fig. 1a in our new paper highlights. The function specifies a differential equation, which Tilman and colleagues used to project GDP per capita forward.

Independently, our group has been studying the GHG emissions scenarios used by the IPCC, trying to understand which emissions futures—and therefore climate futures—are most plausible. In a paper published in November 2020, we reported that IPCC scenarios have tended to over-project GHG emissions compared to recent history, and one of the key reasons for this positive bias is a positive bias in the scenarios’ GDP per capita projections. It turns out that the International Monetary Fund (IMF) and national governments have similarly tended to be positively biased in their GDP per capita forecasts.

Also in November 2020, Tilman and colleagues published a paper in Science, led by Michael Clark of the University of Oxford, which projected that food demands alone could prevent the world from limiting warming to 1.5ºC above pre-industrial temperatures—the aspirational target of the Paris Agreement. We wondered if their projection of food demands might be positively biased, knowing that they were based on a model of GDP per capita growth (the DEM, described above). So, we dug into their paper’s Supplementary Material, and, to our surprise, their GDP per capita forecast bias seemed smaller than what we had seen in the IPCC scenarios and IMF forecasts. We quickly got in touch with Tilman (who had been Burgess’ PhD co-advisor years earlier), and the three of us, along with our colleague Ashley Dancer, decided to work together to understand the reasons for the DEM's historical forecast accuracy and to explore its projections of future economic growth.

Then, in September 2021, one of us (Burgess) attended a workshop at the University of Denver, where he met Jonathan Moyer. Burgess presented our work on the DEM and Moyer presented economic forecasts from his center’s International Futures (IFs) model, initially developed by Barry Hughes. IFs is a highly complex integrated assessment model—containing dozens of modules fit to thousands of data series—that projects economic growth and a number of other quantities related to development and sustainability. At the workshop, we were struck by the fact that the simple DEM and the complex IFs model produced nearly identical forecasts of 2100 GDP per capita for World Bank income groups, and we decided to work together to understand why this was the case. Upon further inspection, both the hump-shaped relationship between GDP per capita and its growth rate, and the underlying drivers of this relationship such as the income-dependence of fertility and manufacturing, were emergent properties of the IFs model.

Our paper, which uses these contrasting models to project economic development, has two major implications. First, economic growth and income convergence may both be slower than previously expected. Historically, our DEM would have been positively biased in in the low-income group of countries, and yet it still projects an economic future with slow growth and income convergence compared to the range of widely used economic scenarios. This suggests that what we currently think of as worst-case economic scenarios for growth and inequality might actually be best-case scenarios, if past trends continue. 

Second, it is remarkable that a simple model (the DEM has three estimated parameters) is able to produce consistent and relatively accurate economic growth forecasts for income groups. The DEM’s projections of 2100 world GDP per capita would have been consistent to within 30%, projecting forward from 1980, 2020, or years in between. In all income groups except the low-income group, the DEM, projecting from 1980, would have more accurately projected 2010s GDP per capita than the IMF’s short-term (2-5-year) forecasts. This suggests that, although the dynamics of economies are highly complex, growth rates of GDP per capita seems to have a strong and consistent (at least for the past several decades) dependence on GDP per capita levels, analogous to the way plant and animal population growth rates strongly depend on their population sizes. This parallel between ecosystems and economies is fascinating and we plan to study it further.