GLOBAL POPULATION GROWTH, TECHNOLOGY, AND MALTHUSIAN CONSTRAINTS: A QUANTITATIVE GROWTH THEORETIC PERSPECTIVE

• Author: Simon Dietz,Bruno Lanz,Timothy Swanson
• Date: 01 August 2017
• Published date: 01 August 2017
• DOI: http://doi.org/10.1111/iere.12242

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 3, August 2017

GLOBAL POPULATION GROWTH, TECHNOLOGY, AND MALTHUSIAN

CONSTRAINTS: A QUANTITATIVE GROWTH THEORETIC PERSPECTIVE∗

BYBRUNO LANZ,SIMON DIETZ,AND TIMOTHY SWANSON1

University of Neuchˆ

atel, Switzerland;London School of Economics and Political Science, U.K.;

Graduate Institute, Switzerland

We structurally estimate a two-sector Schumpeterian growth model with endogenous population and finite

land reserves to study the long-run evolution of global population, technological progress, and the demand

for food. The estimated model closely replicates trajectories for world population, GDP, sectoral productivity

growth, and crop land area from 1960 to 2010. Projections from 2010 onward show a slowdown of technological

progress, and, because it is a key determinant of fertility costs, significant population growth. By 2100, global

population reaches 12.4 billion and agricultural production doubles, but the land constraint does not bind because

of capital investment and technological progress.

1. INTRODUCTION

World population has doubled over the last 50 years and quadrupled over the past century

(United Nations, 1999). During this period and in most parts of the world, productivity gains

in agriculture have confounded Malthusian predictions that population growth would outstrip

food supply. Population and income have determined the demand for food and thus agricultural

production, instead of food availability determining population. However, recent evidence

suggests a widespread slowdown of growth in agricultural output per unit of land area (i.e.,

agricultural yields; see Alston et al., 2009), and the amount of land that can be brought into the

agricultural system is physically finite. For reasons such as these, several prominent contributions

from the natural sciences have recently raised the concern that a much larger world population

cannot be fed (e.g., Godfray et al., 2010; Tilman et al., 2011). Our aim in this article is to study

how population and the demand for land interacted with technological progress over the past

50 years and derive some quantitative implications for the years to come.

Despite the importance of these issues, few economists have contributed to the debate about

the role of Malthusian constraints in future population growth. This is especially surprising given

the success of economic theories in explaining the (past) demographic transition in developed

countries in the context of their wider development paths (e.g., Galor and Weil, 2000; Jones,

2001; Bar and Leukhina, 2010; Jones and Schoonbroodt, 2010, and other contributions reviewed

below). Empirical evidence emphasizes the role of technology, education, and per-capita income

in long-run fertility development (e.g., Rosenzweig, 1990; Herzer et al., 2012), and it documents

a complementarity between technological progress and the demand for human capital (Goldin

and Katz, 1998). Furthermore, per-capita income is an important determinant of the demand

∗Manuscript received June 2015; revised January 2016.

1We thank Alex Bowen, Julien Daubanes, Derek Eaton, Sam Fankhauser, Timo Goeschl, David Laborde, Guy

Meunier, Antony Millner, Pietro Peretto, John Reilly, Emilson Silva, David Simpson, Simone Valente, and Marty

Weitzman as well as seminar participants at ETH Z¨

urich, INRA-ALISS, LSE, the University of Cape Town, IUCN,

SURED 2014, and Bioecon 2013 for comments and discussions. We are also particularly grateful for the comments and

suggestions made by the associate editor and three anonymous referees. Excellent research assistance was provided

by Ozgun Haznedar and Arun Jacob. The GAMS code for the model is available from Bruno Lanz’s we site. Funding

from the MAVA foundation is gratefully acknowledged. Any remaining errors are ours.

Please address correspondence to: Bruno Lanz, Department of Economics and Business, University of Neuchˆ

atel,

A.-L. Breguet 2, CH-2000 Neuchˆ

atel, Switzerland. E-mail: bruno.lanz@unine.ch.

973

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(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

974 LANZ,DIETZ,AND SWANSON

for food (e.g., Subramanian and Deaton, 1996; Thomas and Strauss, 1997), just as technological

progress is of food production and associated demand for land (Alston and Pardey, 2014).

The role of economic incentives and technology in the long-run evolution of population and

per capita income and the associated demand for food and land is, however, absent from leading

international assessments of population growth and agricultural production. In addition, while

the evolution of population and agriculture is inherently interconnected, they are considered

separately. On the one hand, the de facto standard source of demographic projections is the

United Nations’ series of World Population Prospects. The UN works from the basic demo-

graphic identity that the change in population, at the global level, is equal to the number of

births less the number of deaths, with exogenous trajectories assumed for fertility and mortality.

Implications for food demand and supply are not explicitly considered, although it is implic-

itly assumed that the projected population can be supported by agricultural production. On

the other hand, agricultural projections by the Food and Agriculture Organisation of the UN

(FAO) use exogenous trajectories for population, per-capita income, and agricultural yields

(see Alexandratos and Bruinsma, 2012). Clearly, considering outcomes separately makes the

assessment of potential Malthusian constraints difficult.

In this article, we propose to use an integrated, quantitative approach to study the interactions

between global population, technological progress, per-capita income, demand for food, and

agricultural land expansion. More specifically, we formulate a model of endogenous growth with

an explicit behavioral representation linking child-rearing decisions to technology, per-capita

income, and availability of food. In the tradition of Barro and Becker (1989), households in

the model have preferences over own consumption, the number of children they have, and

the utility of their children. Child rearing is time intensive, and fertility competes with other

labor-market activities. As in Galor and Weil (2000), technological advances are associated with

a higher demand for human capital, capturing the aforementioned complementarity between

human capital and the level of technology, so that the cost of educating children increases with

technological progress. It follows that, over time, technological process gradually increases the

cost of population increments (or additions to the stock of effective labor units) both directly

(as human capital requirements and education costs increase) and indirectly (as wages and the

opportunity cost of time increases), which induces a gradual transition to a low-fertility regime.

Besides the cost of rearing and educating children, the other key driver of population growth

in our model is food requirements. As in Strulik and Weisdorf (2008), Vollrath (2011), and Sharp

et al. (2012), we make agricultural output a necessary condition to sustain the contemporaneous

level of population. In addition, the demand for food is increasing in per-capita income (albeit at

a declining rate; see Subramanian and Deaton, 1996), reflecting empirical evidence on how diet

changes as affluence rises. An agricultural sector, which meets the demand for food, requires

land as an input, and agricultural land has to be converted from a stock of natural land.

Therefore, as population and income grow, the demand for food increases, raising the demand

for agricultural land. In the model, land is treated as a scarce form of capital, which has to be

converted from a finite together resource stock of natural land. The cost of land conversion

and the fact that it is physically finite together generate a potential Malthusian constraint to

long-run economic development.

In our model, technology plays a central role in both fertility and land conversion decisions.

On the one hand, technological progress raises the opportunity and human-capital cost of

children. On the other hand, whether land conversion acts as a constraint on population growth

mainly depends on technological progress. We model the process of knowledge accumulation

in the Schumpeterian framework of Aghion and Howitt (1992), where the growth rate of total

factor productivity (TFP) increases with labor hired for research and development (R&D)

activities. A well-known drawback of such a representation of technological progress is the

population-scale effect (see Jones, 1995a).2This is important in a setting with endogenous

2The population scale effect, or positive equilibrium relationship between the size of the labor force and aggregate

productivity growth, can be used to explain the take-off phase that followed stagnation in the preindustrial era (e.g.,

GLOBAL POPULATION GROWTH 975

population, as it would imply that accumulating population would increase long-run technology

and income growth. By contrast, our representation of technological progress falls in the class

of Schumpeterian growth models that dispose of the scale effect by considering that innovation

applies to a growing number of differentiated products (“product lines”; see Dinopoulos and

Thompson, 1998; Peretto, 1998; Young, 1998), so that long-run growth is not proportional to

the level or growth rate of population.3

To fix ideas, we start with a simple theoretical illustration of the mechanism underlying fertility

and land conversion decisions in our model. However, the main contribution of our work is

to structurally estimate the model and use it to study the quantitative behavior of the system.

More specifically, most of the parameters of the model are either imposed or calibrated from

external sources, but those determining the marginal cost of population, labor productivity in

sectoral R&D, and labor productivity in agricultural land conversion are structurally estimated

with simulation methods. We use 1960–2010 data on world population, GDP, sectoral TFP

growth, and crop land area to define a minimum distance estimator, which compares observed

trajectories with those simulated from the model. We show that trajectories simulated with

the estimated vector of parameters closely replicate observed data for 1960–2010, and that the

estimated model also provides a good account of nontargeted moments over the estimation

period, notably agricultural output and its share of total output. We then employ the estimated

model to jointly project outcomes up to 2100.

The key results are as follows: Trajectories from the estimated model suggest a population of

9.85 billion by 2050, further growing to 12.4 billion by 2100. Moreover, although the population

growth rate declines over time, population does not reach a steady state over the period we

consider. This is mainly due to the fact that the pace of technological progress, which is the

main driver of the demographic transition in our model, declines over time, so that population

growth remains positive over the horizon we consider. Despite a doubling of agricultural output

associated with growth in population and per-capita income, agricultural land expansion stops

by 2050 at around 1.8 billion hectares, a 10% increase over 2010.4A direct implication of our

work is that the land constraint does not bind, even though (i) our population projections are

higher than UN’s latest (2012) estimates; and (ii) our projections are rather conservative in

terms of technological progress (agricultural TFP growth in both sectors is below 1% per year

and declining from 2010 onward).

One important feature of these dynamics is that they derive entirely from the structure of

the model, instead of changes in the underlying parameters. We also consider the sensitivity

and robustness of our results to a number of assumptions, notably substitution possibilities in

agriculture and the income elasticity of food demand. Overall, we find that projections from

the model are fairly robust to plausible changes in the structure of the model. Some variations

suggest an optimal population path that is higher than our baseline case, although the evolution

of agricultural land is only marginally affected. The robustness of our results essentially derives

from estimating the model with 50 years of data, tying down trajectories over a long time

horizon.

1.1. Related Literature. Our work relates to at least three strands of economic research.

First, there is unified growth theory, which studies economic development and population over

Boserup, 1965; Kremer, 1993). However, empirical evidence from growth in recent history is difficult to reconcile with

the scale effect (e.g., Jones, 1995b; Laincz and Peretto, 2006). See Strulik et al. (2013) on how the transition between

the two growth regimes can be explained endogenously through accumulation of human capital.

3In a product-line representation of technological progress, R&D takes place at the firm (or product) level, and new

firms are allowed to enter the market. An implication is that the number of products grows over time, thereby diluting

R&D inputs, so that growth does not necessarily rely on an increasing labor force assigned to R&D activities, but rather

on the share of labor in the R&D sector (Laincz and Peretto, 2006).

4This corresponds to the conversion of a further 150 million hectares of natural land into agriculture, roughly the area

of Mongolia or three times that of Spain. Because developed countries will likely experience a decline in agricultural

land area (Alexandratos and Bruinsma, 2012), land conversion in developing countries will need to be more than that.