ISSN (Print) 0473-453X

Discussion Paper No. 1190

ISSN (Online) 2435-0982

THE SLOW DEMOGRAPHIC TRANSITION
IN REGIONS VULNERABLE
TO CLIMATE CHANGE
Thang Dao
Matthias Kalkuhl
Chrysovalantis Vasilakis

September 2022

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

The slow demographic transition in regions
vulnerable to climate change∗
Thang Dao†

Matthias Kalkuhl‡

Chrysovalantis Vasilakis§

September 21, 2022

Abstract

This paper considers the persistent effects of climate change on the speed of demographic transition, and hence on the size of the population in regions that are the least developed and the mostvulnerable to climate change, such as Sub-Saharan Africa. These effects are transmitted throughinteractions between the education gender gap within families, fertility, and the local environment,
through which the demographic transition is delayed. Environmental conditions affect intra-household
labor allocation because of the impacts on local resources under the poor infrastructural system. Examples include the collection of essential resources, e.g. clean water and firewood, by women for theirfamilies’ daily lives. Climate change causes damage to local resources, offsetting (partially) the roleof technological progress and infrastructure investment in saving time that women spend on theirhousework duties. Hence, the gender inequality in education/income is upheld, delaying declines in
fertility and creating population momentum. The bigger population, in turn, degrades local resources
and the environment through expanded production. The interplay between local resources, genderinequality, and population, under the persistent effect of climate change, may thus generate a slow
demographic transition and stagnation of the least developed regions. We provide empirical confirmation for our theoretical predictions using data from 44 African countries in the period from 1960
to 2017.
Keywords: Climate change, local resources, fertility, gender inequality in education, slow demographic transition.
JEL: J11, J16, Q01, Q20, Q54, Q56.
∗ We would like to thank Gregory Casey and Klaus Prettner for very instructive comments and suggestions. We are grateful toOttmar Edenhofer and Rick van der Ploeg for helpful discussions and encouragement. The financial support from the KAKENHI
Startup Grant-in-Aid for Research Activity, Japan Society for the Promotion of Science (20K22121), from the Joint Usage/ResearchCenter at ISER, Osaka University, and from the German Ministry of Education and Research for funding of the marEEshift project(01LC1826A) are fully acknowledged. We also thank the participants from numerous conferences, workshops, and seminars for theirhelpful comments. The first author is indebted to Kimiyo Moriuchi and Yoshie Tachikawa for their excellent administrative support.
† Institute of Social and Economic Research, Osaka University, 6 - 1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan (email:daonguyen@iser.osaka-u.ac.jp); Leibniz Institute for Freshwater Ecology and Inland Fisheries, Berlin, Germany (email: dao@igbberlin.de); and Business School, University of Roehampton, London, the United Kingdom.
‡ Mercator Research Institute on Global Commons and Climate Change, Torgauer Str. 12 - 15, 10829 Berlin, Germany; andUniversity of Potsdam. Email: kalkulh@mcc-berlin.net.
§ Bangor Business School and IZA. Email: c.vasilakis@bangor.ac.uk

1

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1

INTRODUCTION

Introduction

Our paper contributes to the literature by incorporating climate and local resource factors intoa unified growth framework to study the persistent effects of climate change on fertility andthe feedback loop between population growth, availability of local resources, gender inequality
in education investment, and technological progress. We provide a new mechanism to explain
the persistent stagnation of Sub-Saharan Africa along with the fast population growth and thedepletion of its ecological system in the context of climate change. We also characterize theconditions and dynamic interactions between population and local resources through which an
economy may fall into an environmental crisis within a finite time. The climate change economics
literature for the most part considers the impact of climate change on economies through theadverse effects it has on the total factor productivity at aggregate production.
To gain a more accurate picture of the latter impact, we conduct an empirical investigationof the impact of climate on the basic local resources. Based on Dell et al. (2012), we proxy theclimate variable with temperature. Our study uses a rich set of controls, including demographic
and economic variables covering 44 African countries in the period from 1960 to 2017. Our
results point to a negative link between the temperature and basic local resources. Moreover, we
also explore the interplay between temperature, education gap, and fertility in our data. Firstof all, we find that there is a positive and significant effect exerted by temperature on fertility.
Second, we highlight that the temperature has a negative and significant impact on education
gap. However, the above results are contrary for other developing countries, which are more
likely to see their fertility negatively affected by temperature. Our paper is the first to study
the direct effects of climate change on the microstructure of the economy, and its subsequenteffects on the macro level and long-run development of the economy.
The demographic transitions are differential across countries and regions. While developed
countries have completed their demographic transitions and most developing countries haveexperienced fast demographic transition throughout the second half of the 20th century, theleast developed ones in the regions most vulnerable to climate change, such as those in SubSaharan Africa, have been experiencing persistently high fertility rates and slow demographictransitions. Figure 1 illustrates such a distinctive difference in total fertility rates and speedsof decline in fertility between some developing countries and some Sub-Saharan African ones.
Indeed, around the 1960s, the fertility rates between developing and least developed countries
were almost the same. However, the fertility rates in developing countries in Asia and Latin
America fell quickly from above six children per woman in the 1960s to below three children
per woman after three decades, while the least developed countries in Sub-Saharan Africa havebeen exhibiting a slow decline in fertility rates. Their current fertility rates are more than fivechildren per woman, and the figure is even higher in some countries.1
1 The fertility rate in Niger is even at around seven children per woman, and the fertility dynamics of the country shows thispersistent high level.

2

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INTRODUCTION

Figure 1: Total Fertility rate (births per woman, 1960–2020) among developing and least developed countries. Source:
World Bank (2021).

Along with the difference in the speeds of demographic transition mentioned above, there areconsiderable differences in housework allocation across genders between Sub-Saharan countries
and others. The figure 2 below shows the distribution of households by persons responsible forwater collection, in which women in Sub-Saharan countries play a particularly predominant role.
This figure also reflects the much poorer infrastructure of clean water systems in Sub-SaharanAfrica, particularly in rural areas, compared with other developing regions. Indeed, the water
infrastructure in Sub-Saharan Africa does not provide adequate freshwater to its inhabitants(Lutz 2011). As a result, there is an over reliance on freshwater resources such as local rivers
and the local groundwater system, from which women need to spend an inordinate amount oftime collecting water.
The key stylized facts depicted in Figures 1 and 2 indicate to us the merit of proposing atheoretical mechanism linking the persistent effects of climate change in terms of damaging local
resources and the interplay between local resources, gender inequality, fertility, and population
to explain the slow demographic transition and the stagnation of Sub-Saharan Africa. Our
mechanism starts from the current scientific consensus that climate change has been likely resulting in widespread alterations to hydrologic conditions that very adversely affect the surface
and groundwater systems, forest conservation, and biodiversity of Sub-Saharan Africa. These3

1

INTRODUCTION

Figure 2: Distribution of households by gender responsible for water collection. Figure borrowed from World’s Women,
Trends and Statistics, UNDESA (2015)

adverse effects make it necessary for a woman in a household to spend more time collecting
local resources, i.e. water from rivers and/or groundwater systems, firewood from forests, etc.,
for her family’s daily life, instead of supplying labor to the formal labor markets. In a family,
when the parents anticipate that their daughter(s) will spend more time on such housework,
they rationally invest less in education for their daughter(s) and more for their son(s), creating a significant gap in education, and hence a significant gap in income, across genders. The
lower income of women implies lower opportunity cost of child-rearing by which the householdincreases the fertility rate, generating a population momentum in the medium and long run.
The bigger population, in turn, contributes to local resource depletion through the expansionof production. This reinforcing feedback loop has generated a slow demographic transition andstagnant economic growth in Sub-Saharan Africa.
Population growth is documented as one of key driving forces of global emissions (IPCC2014) and is one of the main causes of natural resource depletion and environmental degradation(Ehrlich and Holden 1971, Meadow et al. 1972, Cleaver and Schreiber 1994, Kates 1996, Foster
et al. 2002). The observation of differential fertility rates across regions suggests that several
related research questions need to be answered. Why have the least developed regions, which
are the most vulnerable to climate change and the most at risk of local environmental disasters,
experienced persistently high fertility rates and a slow demographic transition? Does climatechange have any effect on fertility decisions? If yes, through which mechanism? Answering thesequestions analytically and understanding the mechanisms in explaining the slow demographictransition, in our point of view, are key to combating global climate change through policies
enabling management of population growth in relation to environmental protection in the least

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INTRODUCTION

developed regions vulnerable to climate change.
While the effects of population growth on climate change are included in many numerical
works (O’Neill et al. 2010, Wheeler and Hammer 2010, Lutz and Striessnig 2015, Scovronick et
al. 2017, among others), investigations into the effects of climate change and natural resource
depletion on population growth are surprisingly rare in the related economic literature. Thereis a small empirical body of literature studying the effects of environmental and local resource
conditions on fertility at the micro level in developing countries (e.g. Grace et al. 2016, Aggarwal
et al. 2001, Filmer and Pritchett 2002, Nankhuni and Findeis 2004, Biddlecom et al. 2005).
These studies show that environmental conditions affect households’ fertility decisions throughthe channels of health and the intra-household division of labor. In addition, historians such as
Diamond (2005) emphasize how overpopulation and excessive environmental degradation, e.g.
due to deforestation, were responsible for the collapse of some past societies such as the Easter
Island civilization and the Maya of Central America. While precise explanations for the collapseof the population of Easter Island remain controversial, environmental feedback mechanisms
feature a prominent role in many studies (Brander and Tayler 1998, Reuveny and Decker 2000,
de la Croix and Dottori 2008, among others). That is to say, fundamentally theoretical researchon the interplay between population and environmental change should be developed in thecontext of climate change in the 21st century in the least developed regions. The present study
attempts to develop such an analytical framework for this task.
Modern demographic transition theories focus on non-environmental factors in explaining
the demographic transitions that were mostly experienced in developed countries. The firstprominent theory, which is linked to the rise in income per capita, was proposed by Becker(1960). Becker argues that the rise in per capita income leads to a decline in fertility becauseof the associated increase in the opportunity cost of raising children. In a refined model, Becker
and Lewis (1973) suggest that when the income elasticity with respect to investments in childquality is high and the income elasticity for child quantity is low, then fertility declines whenincome increases. The second theory links fertility to the decline in infant and child mortality.
Developed by demographers, this theory incorporates the empirical observation that in many
countries, a decline in child mortality preceded a decline in fertility (Montgomery and Cohen
1998). O’Hara (1975) argues that the decline in infant and child mortality reduces gross fertility,
but not necessarily net fertility (i.e. the demand for surviving children). Moreover, O’Hara points
out that demographic transition only occurs if parents substitute child quality for child quantity.
The third theory is the old-age security hypothesis (Neher 1971, Caldwell 1976, Boldrin and Jones
2002). This theory suggests that when capital markets or public safety nets are absent, children
are treated as an asset that permits parents to transfer income to old age. The development of
capital markets reduces the demand for children, which, in turn, leads to demographic transition.
The fourth theory, proposed by Galor and Weil (2000) and Galor and Moav (2002), highlights
the rise in demand for human capital. They argue that technological change increases the5

2

THE MODEL

demand for human capital and returns to educational investments. This, in turn, changes thetrade-off between quantity and quality of children, thus generating demographic transition. The
fifth theory is related to the decline in the gender gap with respect to income and employment
during the development process. The decline in the gender gap is reflected by the rise in women’s
relative income and the associated increase in women’s bargaining power. This theory, developed
by Galor and Weil (1996), Doepke and Tertilt (2009), Diebolt and Perrin (2013), Prettner andStrulik (2017), Bloom et al. (2020), and recently Dao et al. (2021), proposes that the rise in
women’s relative income increases the opportunity cost of child-rearing and, thereby reduces
fertility.
While the modern demographic transition theories neglect environmental and resource factors, the natural environment and resources play a dominant role in early works on population
dynamics. Particularly, in the influential treatise “An Essay on the Principle of Population”,
Thomas R. Malthus (1798) argued that as population growth is limited by natural resources,
the population will eventually converge to a stable level. Despite Malthus’s warning, the past
two centuries experienced high rates of population growth along with climate change and environmental degradation. The fertility rates in the regions most vulnerable to climate change havebeen persistently high in spite of the climate-related damage on production and local natural
resources. This stylized fact suggests the existence of an alternative pattern of demographictransition for these least developed regions in which climate change may play a crucial role.
Unified growth theory (Galor and Weil 1996, Galor and Weil 2000, Galor and Moav 2002, andGalor 2011) generates a mechanism whereby economies escape Malthusian stagnation to enter
the modern sustained growth regime along with the demographic transition. Differing fromours, this theory, however, so far does not aim at explaining the current stagnation in Africa in
relation to climate change.
The rest of this paper is organized as follows. The next section introduces the model andderives the competitive equilibrium dynamics. Section 3 defines equilibria and the dynamic
system of the economy. Section 4 analyzes the evolution of population and local resources, andthe convergence to conditional steady states. Section 5 analyzes the impact of extreme climatechange and the mechanisms that lead to environmental disasters. The global evolution of theeconomy is discussed in section 6. Section 7 tests empirically the hypotheses developed fromthe theoretical framework. Section 8 concludes the paper and discusses further works for thisresearch agenda.

2

The model

We extend the model in Dao et al. (2021) by incorporating the role of local resources on
women’s time for doing housework and the dynamics of local resources under the persistenteffects of climate change. By “local resources” we mean the entire geographical environment and6

2

THE MODEL

natural resources of the economy that support the daily lives of people, such as water resources,
firewood, air quality, etc. We consider an economy consisting of Lt identical households at any
period t ∈ N. For simplicity, we assume that each household consists of two persons, as a couple,
with gender male and female. Each member of a household lives for two periods—childhood andadulthood—and is endowed with one unit of time as an adult. Adult members of the household(i) allocate their total time between supplying labor, doing housework such as collecting essential
resources for daily life (e.g. firewood and clean water), and child-rearing; (ii) decide how muchto invest in their offspring’s human capital, and (iii) consume the remainder of their income. As
in Becker (1985, p. 52), we assume that within a household the child-rearing and housework
is taken care of by only the woman, which is in accordance with cross-cultural evidence. The
time for doing housework in any period t, ϕt = ϕ(Rt , at ) ∈ [0, 1], depends on the availability of
local resources, Rt , and the level of technology, at , of the economy. In particular, the following
assumption describes the properties of function ϕ(R, a).
Assumption 1. ϕi (R, a) < 0 with i ∈ {R, a}, ϕRR (R, a) > 0, andlim

lim ϕ(R, a) = 0.

R →+∞ a →+∞Assumption 1 implies the fact that the availability of local resources, such as water andfirewood, saves time for women in the least developed regions in terms of collecting them for theirfamily’s daily lives. In addition, a higher level of technology of the economy not only improves
productivity but also saves women time on housework. Indeed, the level of technology of theeconomy could be reflected by infrastructure development, such as the diffusion of electricity andclean water supply, which strongly affect the time women allocate for housework. Greenwood
et al. (2005) argue that technological progress plays a crucial role in a household’s allocationof time. Indeed, the appearance and the generalization of appliances such as washing machines,
vacuum cleaners, and refrigerators (mid-20th century), as well as frozen foods and ready-mademeals (mid- to late 20th century) has freed a considerable amount of time from housework, andwhich can thus be used otherwise.
Regarding child-rearing, the offspring of each household’s offspring—consisting of two-person,
multi-gender households as well, for the sake of simplicity—requires devoting an amount of timeρt > 0, while the human capital of each member of the “child” household is assumed to bea power θ ∈ [ 21 , 1) of the parent household’s educational investment in each of them, et for amale child and ẽt for a female child respectively.2 We assume that the time for raising children
depends positively on the population density Lt /X, i.e. ρt = ρ(Lt /X), where X is the size ofland, which is fixed, of the economy. For simplicity, we normalize X = 1, hence ρt = ρ(Lt ). We
introduce the following assumption on the functional form of ρ(L).
Assumption 2. ρ′ (L) > 0 and ρ′′ (L) < 0 for all L ≥ 0.

This assumption implies that the cost in time of raising children is increasing concave in
2 The condition θ ≥ 1 implies plausibly that the returns on education do not decrease so quickly.
2

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2.1

Households

2

THE MODEL

population density.3
2.1

Households

Adult households at t have preferences, and make choices regarding their consumption, numberof children, and potential income that the children could earn as adults —as a function of thehuman capital they are endowed with by their parents’ educational investment. Specifically,
households maximize their utility (1) under their budget constraint (2) and the time constraintof the women (3),max (1 − γ) ln ct + γ ln nt wt+1 [eθt + (1 − ϕt+1 )ẽθt ]ct ,nt >0(1)

et ,ẽt ≥0

subject to
ct + nt (et + ẽt ) ≤ wt eθt−1 + (1 − ϕt − ρt nt )ẽθt−1(2)

ϕt + ρt nt ≤ 1(3)given the wage rate wt+1 per efficient unit of labor at t+1; the fractions of household time ϕt , ϕt+1
needed for housework at t, t+1;4 and past choices of educational investments et−1 and ẽt−1 madeby the household’s parents —where, at each period t, ct is adult household consumption, nt is thenumber of (household-)children per household.5 The parameter γ ∈ (0, 1) captures the weightof the household’s offspring in its utility.
This paper focuses on the current least developed economies with fertility rates that havebeen falling slowly—i.e. those that are beyond a peak fertility rate—along with the increasing
participation of female labor supply. Based on this, we introduce the following assumption
guaranteeing that the time constraint of women is not binding.
hi1−θγ(1−θ)
Assumption 3. ϕ(0, 0) ≤ 1 − 1−γ(1−θ).
The following lemma characterizes the optimal choice of a representative household.
Lemma 1. Under assumption 3, the optimal choice of a representative household, which is theinterior solution to (1) subject to (2) and (3), is
ct = (1 − γ)wt [eθt−1 + (1 − ϕt )ẽθt−1 ],

(4)

θ
ρt
θ
1 wt ẽt−1 ,1 − θ 1 + (1 − ϕt+1 ) 1−θ

(5)

et =

3 This idea is introduced in Goodsell (1937) and Thompson (1938), and was recently cited by De la Croix and Gosseries (2012)and Dao and DÃ¡vila (2013) to take into account that when households have small dwellings, child production is more costly andhouseholds have fewer children. More recently, De la Croix and Gobbi (2017) provide empirical evidence that confirms this idea.
4 We assume that, when assessing the children’s potential income, the household perfectly foresees ϕ
t+1 , which is a consequenceof its own choices —because of the technological progress induced by its educational investments—but not what is the result of its
children’s choices (hence the absence of ρt+1 nt+1 in the household’s objective).
5 We assume that the gender ratio at birth (male to female) is 1 : 1, which is close to the natural gender ratio 1.05 : 1.

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2.2

Production, technology, and locally natural resources

ẽt =

ρt
θ
θ
1 wt ẽt−1 ,1 − θ 1 + (1 − ϕt+1 ) θ−1γ(1 − θ) eθt−1nt =+ 1 − ϕt .
ρtẽθt−1

2

THE MODEL

(6)

(7)

Proof. The proof is available upon request.

From (4) to (7), we have: (i) consumption is proportional to the household’s potential income—i.e. net of housework costs; (ii) educational investments are proportional to the woman’s
potential income; and (iii) fertility is increasing in the human capital gender gap—resulting
from differentiated educational investment— between the man and the woman of the household.
Specifically, equations (5) and (6) show the different educational investment across genders
due to the asymmetric time allocation for housework. These equations tell us that increasing
the expected time for housework, which will be spent by daughter(s), leads parents to reduce
education investment for their daughter(s). They instead increase the education investment
for their son(s). Any exogenous effect on time for housework thus creates an impact on the
education gender gap. Equation (7) suggests that the relative education gender gap among
male and female parental members within a household determines the household’s fertility rate.
Indeed, the education gender gap generates an income gender gap that reflects the income effectand substitution effect on fertility decisions of the household such that the former raises fertility,
whereas the latter, which reflects an increase in the opportunity cost of childrearing, reduces it.
An increase in the relative education gender gap, et−1 /ẽt−1 , makes the income effect dominant
over the substitution effect, thereby fostering fertility.
2.2

Production, technology, and locally natural resources

We assume that the final good production in each period t is linear in the effective units of labor
supplied in-elastically by the household adults
Yt = A(at , Et )Ht = A(at , Et )Lt ht ,where Ht = Lt ht is aggregate human capital in final good production, and ht = eθt−1 + (1 −ϕt − ρt nt )ẽθt is the average human capital that the representative household devotes to the
production.6 The marginal return to human capital is
wt = A(at , Et ),6 For sake of simplicity, we abstract from physical capital. The physical capital, indeed, can be introduced without changing thequalitative results of the model if we consider a small and open economy with perfect physical capital mobility. In this case, we
define the constant returns scale technology-augmented labor production function as Yt = F (Kt , A(at , Et )Ht ), and we extend thehouseholds to live for three periods with saving motives.

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2.2

Production, technology, and locally natural resources

2

THE MODEL

where A(at , Et ) > 0 is the total factor productivity of the economy in period t that depends onthe contemporary level of technology at and exogenous global climate index Et ∈ [0, +∞). We
can read Et as the index of global carbon concentration. An increase in Et reflects the moreclimate change to be. We assume plausibly
Aa (at , Et ) > 0 and AE (at , Et ) < 0,which tell us that technological progress enhances total factor productivity, whereas climatechange damages it.
The technology evolves according to
at+1 = (1 + gt )at ,where gt = g
that

 θ

et−1 +ẽθt−1
at

is the rate of technological progress between t and t + 1. We assume

g (x) , g ′ (x)


 >0

if

x > x̄

 =0if

x ∈ [0, x̄].

That is to say, the rate of technological progress is non-decreasing in average human capital and non-increasing in level of technology; and the higher level of technology at requires asufficiently high average human capital ht in production to guarantee a strictly positive rate oftechnological progress.
The locally natural resources or locally environmental quality index, Rt+1 , evolves according
to the following dynamic equation
Rt+1 = Rt + Ω(Rt , Et ) − ξt Yt ,where ξt Yt is the damage to local natural resources coming from the production activity, andξt > 0 measures the damage level of production in period t. We assume that ξt = atξht , which
captures the idea that higher level of technology and average human capital go hand in hand withcleaner production.7 Without loss of generality, we normalize ξ = 1. The function Ω(Rt , Et ) is
the regeneration capacity of local resources, which depends on the quality of the local resources
themselves, Rt , and on the exogenous global climate index Et . An increase in Et has an impact
on the regeneration capacity of the local natural environment and resources.8
7 Swinton and Quiroz (2003) pointed out, in a study on Peru, that higher human capital favors the choice of more sustainable
practices.
8 We follow the laws of thermodynamics as mentioned in Georgescu-Rogen (1971) in order to set up the general form of functionΩ(R, E). Indeed, the state of the environment is constrained by biophysical principles, specifically through two processes: (i) the
entropic process and (ii) the preservation process. The economy is basically a closed system with respect to material. According
to the law of material or energy conservation, material is neither lost nor created in any transformation process. The entropic
process transforms the availability of material or energy in a closed system in the sense that the available energy is continuously

10

2.3

Some static analyses

2

THE MODEL

Assumption 4. The function Ω(R, E) is continuous in its variables and satisfies the following

properties(i) ΩE (R, E) < 0, Ω(0, E) = Ω(R̄(E), E) = 0 for all E ≥ 0(ii) ΩR (R, E) > (<)(=) 0 if R < (>)(=) R̂(E) ∈ (0, R̄(E))(iii) ΩR (R, E) > −1 and Ω(R, +∞) = 0 for all R.

Figure 3: The regeneration capacity of local resources

2.3

Some static analyses

In this section, we carry out some important static analyses that help us understand the effects
of technological progress and availability of local resources on education gender gap and fertility.
Definition 1. (Education gender gap) The education gender gap in any t is the relative gap

in education investments between the man and the woman in a representative household. That
is,
ζt =

et−1
.
ẽt−1

By definition 1, from equations (5) and (6), with one period lagged, we have1

ζt = [1 − ϕ(Rt , at )] θ−1 ≡ ζ(Rt , at )(8)and hence, the fertility rate is determined bytransformed into unavailable energy until it disappears completely. Fortunately, the economy is an open system with respect toenergy. The preservation process refers to the constant receiving of solar radiation, which provides energy to compensate for theentropic process, thus making resources renewable. That is to say, while natural and human transformation processes destroy theavailability of material, new energy inflows provide energy to recollect material and energy and to offset such destruction. This
explains the equilibrium in our ecology systems and the renewable nature of natural resources (Smulders 1995a,b).

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2.3

Some static analyses2o1γ(1 − θ) n
θ−1
[1 − ϕ(Rt , at )]+ 1 − ϕ(Rt , at ) ≡ n(Lt , Rt , at )nt =ρ(Lt )THE MODEL(9)

Proposition 1 states some important effects of local resources and technology on gender equality in education and fertility.
Proposition 1. The following properties hold:(i) ζ(Rt , at ) > 1 ∀(Rt , at ) ≥ (0, 0), and ζi (Rt , at ) < 0 with i ∈ {R, a};(ii) nj (Lt , Rt , at ) < 0 with j ∈ {L, R, a}.
Proof. The proofs for these statements are obtained from equations (8), (9), and properties offunctions ρ(L) and ϕ(R, a).
The statement (i) in Proposition 1 tells us that males always receive more education investment than females. This is because of the asymmetric time allocation across gender withinhouseholds, as reflected in equation (8). As time on housework is unpaid and taken by womenwhile the potential income of a child-household also constitutes the utility for their parents, aparent-household chooses optimally to invest more in education for their son(s) than for theirdaughter(s). The relative education gender gap ζt , however, decreases in both the availability of
local resources Rt and level of technology at . That is because both the increase in availabilityof local resources and technological progress save women time on housework. When the time
women spend on housework, ϕ(Rt , at ), is expected to be reduced, a parent-household will have
incentive to invest more in education for their daughter(s)—because the initial imbalance makes
the marginal return to female education higher—while the total education investment for one
couple of children (one son and one daughter), derived from equations (5) and (6) with one
period lagged, iset−1 + ẽt−1 =θρt−1 wt−1 ẽθt−2 ,1−θwhich is given, independent on at and Rt , and determined by past (predetermined) variables.
Therefore, to increase education investment for the daughter(s), a parent-household has to reduce
education investment for the son(s). As a result, the relative education gender gap is reduced.
Statement (ii) says that the fertility rate nt decreases in the size of population Lt , the availability of local resources Rt , and the level of technology at . That is rather intuitive. A larger
population Lt , i.e. higher population density, increases the cost in time of raising children, resulting in a decline in demand for children. Higher availability of local resources Rt and/or higher
level of technology at save the women time on housework, resulting in women being endowedwith more education investment, which increases the opportunity cost of childrearing, making
the substitution effect dominate the income effect. Hence, the fertility rate is reduced.

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3

EQUILIBRIA AND DYNAMICS

Equilibria and dynamics

The competitive equilibria of the economy are characterized by: (i) the household’s utility maximization under its constraints, (ii) the aggregate output equating the total return to humancapital, (iii) the dynamics of population size, (iv) the dynamics of technology, and (v) the dynamics of the local natural environment and resources. That is to say a competitive equilibrium(ct , et , ẽt , nt , at+1 , Lt+1 , Rt+1 , wt ) is determined by the following system of equations
ct = (1 − γ)wt (eθt−1 + [1 − ϕ(Rt , at )]ẽθt−1 ),

(10)

et =

θ
ρ(Lt )
θ
1 wt ẽt−1 ,1 − θ 1 + [1 − ϕ(Rt+1 , at+1 )] 1−θ

(11)

ẽt =

θ
ρ(Lt )
θ
1 wt ẽt−1 ,1 − θ 1 + [1 − ϕ(Rt+1 , at+1 )] θ−1

(12)

o
θ
γ(1 − θ) n
[1 − ϕ(Rt , at )] θ−1 + 1 − ϕ(Rt , at ) ,ρ(Lt )

(13)

nt =



 θ
et−1 + ẽθt−1
at ,at+1 = 1 + g
at

(14)

Lt+1 = nt Lt ,(15)

Rt+1 = Rt + Ω(Rt , Et ) − ξt Yt ,(16)

wt = A(at , Et ),(17)given an exogenous global climate change index Et ≥ 0.
The competitive equilibria are fully characterized by the following reduced system describing
the equilibrium dynamics of the educational investments for male and female children et and ẽt ,the level of technology at+1 , the population size Lt+1 , and the local natural environment andresources Rt+1 .
et =θρ(Lt )θ
1 A(at , Et )ẽt−1
1 − θ 1 + [1 − ϕ(Rt+1 , at+1 )] 1−θ

ẽt =

θ
ρ(Lt )θ
1 A(at , Et )ẽt−1
1 − θ 1 + [1 − ϕ(Rt+1 , at+1 )] θ−1

13

4

EVOLUTION OF LOCAL RESOURCES AND POPULATION


 θ

et−1 + ẽθt−1
at+1 = 1 + g
at
at
o
θ
γ(1 − θ) n
θ−1
[1 − ϕ(Rt , at )]+ 1 − ϕ(Rt , at ) Lt
Lt+1 =
ρ(Lt )
Rt+1 = Rt + Ω(Rt , Et ) − Ltgiven initial conditions e−1 , ẽ−1 , a0 , L0 , R0 > 0, and a sequence of exogenous climate changeindexes (Et )+∞
t=0 .

4

Evolution of local resources and population

In this section, we study the evolution of the economy conditionally on a given level of technology
a and a given climate change index E.
4.1

Conditional steady states

The conditional dynamics of the economy is characterised by the following dynamic system of
equationsoθγ(1 − θ) n
θ−1
Lt+1 =[1 − ϕ(Rt , a)]+ 1 − ϕ(Rt , a) Lt(18)
ρ(Lt )
Rt+1 = Rt + Ω(Rt , E) − Lt

(19)

Given any level of technology a and global climate change index E, we define the loci LL(a)and RR(E) as follows

LL(a) ≡ (Lt , Rt ) ∈ ℜ2+ : Lt+1 = Ltihθi.e. Lt = ρ−1 γ(1 − θ) [1 − ϕ(Rt , a)] θ−1 + 1 − ϕ(Rt , a) ≡ ψ(Rt ; a)

(20)

and

RR(E) ≡ (Lt , Rt ) ∈ ℜ2+ : Rt+1 = Rt
i.e. Lt = Ω(Rt ; E)

(21)

Lemma 2. ψa (R; a) < 0, and ψR (R; a) < 0, ψRR (R; a) > 0.
Proof. By applying the implicit function theorem for equation (20) with respects to Lt , Rt , a,and noting that θ ∈ [ 21 , 1), we have
14

4.1

Conditional steady states

4

EVOLUTION OF LOCAL RESOURCES AND POPULATION


1
γ 
θ−1
θ[1 − ϕ(R, a)]− 1 + θ ϕi (R, a) < 0,
ψi (R; a) = ′ρ (L)i ∈ {R, a}andγ
ψRR (R; a) = ′
ρ (L)





2−θ
1
θ
[1 − ϕ] θ−1 ϕ2R + θ[1 − ϕ] θ−1 − 1 + θ ϕRR
1−θ


−

ρ′′ (L) 2
ψ >0
ρ′ (L) R

The properties of the function ψ(R; a), as stated in lemma 2, and those of the functionΩ(R; E) are very important in determining the number of conditional steady states as pointed
out in proposition 2. In addition, as will be apparent in the subsequent subsections, they allow us
to study the impacts of technological progress and climate change on the size of the populationand the availability of local resources at the conditional steady states.
Lemma 3. For the dynamic system characterized by equations (18) and (19), then
 > 0 if Lt < ψ(Rt ; a)(i) Lt+1 − Lt
= 0 if Lt = ψ(Rt ; a)
 < 0 if Lt > ψ(Rt ; a)
 > 0 if Lt < Ω(Rt ; E)and (ii) Rt+1 − Rt
= 0 if Lt = Ω(Rt ; E)
 < 0 if Lt > Ω(Rt ; E)

Proof. The proofs are fairly straightforward.

Given a level of technology, a, and a global climate change index, E, the conditional steadystates of the economy are determined by the intersections between the loci LL(a) and RR(E).
Analytically, they are the solutions, R, to the following equationΩ(R; E) = ψ(R; a)(22)

The following proposition states the existence of conditional steady states and their properties.
Proposition 2. Given a level of technology a and a global environmental quality index E,(i) There exists at most two distinct conditional steady states;(ii) If there exists a steady state(s), then there is at least a steady state at which it holds that
R > R̂(E);(iii) If there exists two distinct conditional steady states characterized by R > R̃, then:(iii.a) the one with higher availability of local resource R is a locally stable node;(iii.b) if ψR (R̃; a) ≥ −1, the steady state with R∗ = R̃ is a saddle node.

15

4.1

Conditional steady states

4

EVOLUTION OF LOCAL RESOURCES AND POPULATION

Proof. See Appendix

Proposition 2 characterizes the number of conditional steady states and their properties, particularly their stability. In the case that two distinct conditional steady states prevails, thecondition ψR (R̃; a) ≥ −1 is just a sufficient condition under which the steady state (R̃, L̃) is astable node.9 We will focus on this most interesting case (the case of two distinct conditional
steady states). The diagram in figure 4 depicts the existence of and the convergences to conditional steady states. In this case, there is a unique saddle path (stable arm) leading to theconditional steady state (R̃, L̃). This saddle path can be represented by a monotonically increasing function L(R; E, a), and there exists an availability level of local resources, which depends
on the level of technology and the global environmental index, R(a, E) ∈ [0, R̃).

Figure 4: Dynamics and convergence to conditional steady states

Definition 2. (Environmental disaster ) The economy is called falling in an environmental

disaster in some period t if Rt ≤ 0.
9 Indeed, we have room to introduce the following condition on parameters and functional forms under which ψ (R; a) ≥ −1
R
always holds. It is1γ θ[1 − ϕ(0, 0)] θ−1 − 1 + θ ϕR (0, 0) + ρ′ (sup Ω(R; E)) ≥ 0

16

4.2

Impact of technological progress

4

EVOLUTION OF LOCAL RESOURCES AND POPULATION

Proposition 3. If, in some period t, the state of economy is characterized by (Rt , Lt ) such that

Lt > L(Rt ; a, E)

or Rt < R(a, E)

then an environmental disaster will occur.
Proposition 3 characterizes a dangerous area that is located on the left side of the saddle path,as depicted graphically by the diagram in Figure 4. Proposition 3 tells us that, if the economy
falls into this dangerous area, then in the long run an environmental disaster will occur. This
result implies an important implication that, as will be more apparent in the later analyses,
if there is a sufficiently strong environmental shock that puts the economy into the dangerous
area, without sufficient technological progress, then, in the long run, the economy will fall into
an environmental disaster.
4.2

Impact of technological progress

In this subsection, we consider the impact of technological progress on the availability of local
resources and the size of population over the long term. Let us focus on the case where theeconomy converges to a conditional stable steady state. We know from lemma 2 that ψa (Rt ; a) <0. That is to say, the increase in the level of technology, a, makes the locus LL(a) move
downward as depicted in figure 5. The downward shift of LL locus from LL(a) to LL(a′ ) makes
the economy tend to converge to a conditional steady state with higher availability of local
resources, R(a′ , E) > R(a, E), and smaller population size, L(a′ , E) < L(a, E).
The economic intuitions for the convergence to the conditional steady state with higher availability of local resources and smaller population size, under the impact of increasing technology,
is as follows. As analyzed in section 2.3, technological progress reduces the fertility rate because it makes the substitution effect dominate the income effect through increasing education
investment for daughters relatively more compared with sons. The lower fertility rate leads
to the smaller population size, which will be associated with better human capital and higher
female labor force participation, in the future. The smaller population size, in turn, as reflectedin equation (19), results in less damages to local resources, increasing the availability of local
resources. The higher availability of local resources, in turn, saves women time on housework
for their families’ daily lives, thereby reinforcing the convergence to the conditional steady state(R(a′ , E), L(a′ , E)).
4.3

Impact of climate change

We study in this subsection the impact of climate change on the availability of local resources
and the population size over the long term. As in the previous subsection, we also focus on
the case where the economy converges to a conditional stable steady state. We have from
17

4.3

Impact of climate change

4

EVOLUTION OF LOCAL RESOURCES AND POPULATION

Figure 5: Dynamics and convergence to conditional steady statesassumption 4 that ΩE (R, E) < 0. That is to say, the increase in climate change makes the
RR locus shift downward from RR(E) to RR(E ′ ), as illustrated in Figure 6. This downward
shift of the locus RR makes the conditional stable steady state move from (R(a, E), L(a, E)) to(R(a, E ′ ), L(a, E ′ )) with R(a, E ′ ) < R(a, E) and L(a, E) > L(a, E ′ ).
The mechanism associated with the persistent impact of climate change is as follows. The
increase in climate change reduces the regeneration capacity of the local resources, thereby
making the local resources scarcer, requiring women to spend more time collecting essential
resources for their families’ daily lives. Through this channel, the education gender gap isenlarged because households tend to reduce education investment for their daughter(s) andinstead invest more in education for their son(s). As a result, the fertility will be increased,creating a bigger population in the future associated with low average human capital. The
bigger population and lower average human capital, in turn, damage local resources through(more polluted) production activity. The feedback loop between local resources, population,and gender inequality in education, under the persistent effects of increased climate change,leads to the convergence to the conditional stable steady state (R(a, E ′ ), L(a, E ′ )).
Compared with the effects of technological progress, increased climate change has the opposite
effect over the long term on local resources and population through the opposite mechanism
linking women’s time in doing housework, education investment across genders, and fertility.
18

5

CLIMATE CHANGE AND DISASTER

Figure 6: Dynamics and convergence to conditional steady states

5

Climate change and disaster

The analyses and phase diagrams in the previous section suggest that when climate change is too
extreme such that the RR(E) locus always lies below the LL(a) locus —i.e. RR(E)∩LL(a) = ∅—as depicted in figure 7, then an environmental disaster will occur. In this section, we will
characterize the precise conditions regarding climate change and level of technology under which
the interactions between population and local resources will lead to an environmental disasterregardless of the starting state (R0 , L0 ) ∈ ℜ2++ of the economy.
In order to characterize the condition under which climate change always leads to an environmental disaster, we study the economy under the following assumption.
Assumption 5. LL(0) ∩ RR(E) ̸= ∅ for some E < +∞.

To facilitate the analyses, in subsection 5.1, we consider the conditional convergence to an
environmental disaster in the sense that we fix the level of technology, a, when we study the
dynamics. In subsection 5.2 we instead study unconditional convergence by allowing the levelof technology to change over time.
5.1

Conditional convergence to an environmental disaster

Proposition 4 provides us the properties of conditional dynamics of population Lt and local
19

5.1

Conditional convergence to an environmental disaster5

CLIMATE CHANGE AND DISASTER

Figure 7: Extreme climate change

resources Rt , which, under certain conditions, generate a monotonic convergence to an environmental disaster.
Proposition 4. If LL(a) ∩ RR(E) = ∅ and in some T , the state of the economy (RT , LT ) ∈ ℜ2++

is characterized byLT ∈ (Ω(RT , E), ψ(RT , a))(23)then the economy converges monotonically in an environmental disaster, in which for all t ≥ T
until the environmental disaster occurs, the following properties hold
Rt+1 < Rt

and Lt < Lt+1 ∈ (Ω(Rt+1 , E), ψ(Rt+1 , a)) .

Proof. See Appendix.

Proposition 4 implies that, in the absence of technological progress10 , when the economy
falls into a certain area characterized by condition (23), the size of population will increase
monotonically, whereas the availability of local resources will decrease monotonically, making anenvironmental disaster occur within a finite time. The economic intuition for these dynamics
10 or if technology progresses too slowly

20

5.1

Conditional convergence to an environmental disaster5

CLIMATE CHANGE AND DISASTER

is rather obvious. Lt ∈ (Ω(Rt , E), ψ(Rt , a)) implies two aspects of the population size Lt in
relation to the availability of local resources, Rt . First, Lt > Ω(Rt , E) means that the size of
population Lt , and hence labor force, is relatively high compared with the regeneration capacityΩ(Rt , E) of contemporary local resources. Hence, the environmental damage from aggregate
production exceeds the regeneration of local resources, making the availability of local resources
decline. The decline in the availability of local resources, as pointed out in an earlier section,enhances the fertility rate by enlarging the gender gap in education—and hence the gender gap
in income—because it requires women to spend more time on housework duties, resulting inparents investing less in education on their daughter(s). Second, Lt < ψ(Rt , a) indicates thatthe size of population Lt , and hence population density, is not sufficiently high to make the costin time of raising children physically expensive enough such that the demand for children of
the representative household is nt ≤ 1. Thus, the size of the population becomes bigger overtime. The mechanism of interactions between population and local resources creates a monotonic
convergence to an environmental disaster.
The directions of motion of the population size and the availability of local resources, as
pointed out in lemma 3, tell us that when the economy starts from a state such that L0 ∈/(Ω(R0 , E), ψ(R0 , a)) then it will enter the area LT ∈ (Ω(RT , E), ψ(RT , a)) within some finite
time T , and, eventually, the economy will converge monotonically in an environmental disaster.

Figure 8: Extreme climate change

21

5.2

Unconditional convergence to an environmental disaster5

CLIMATE CHANGE AND DISASTER

The next proposition characterizes the level of climate change under which an environmental
disaster will occur.
Proposition 5. Given any level of technology a unchanged (more strictly, non-increasing) overtime, there exists a unique threshold E∗ (a) > 0 such that for all E > E∗ (a), an environmental
disaster will occur, regardless of the starting state of the economy (R0 , L0 ) ∈ ℜ2++ . Moreover,E∗′ (a) > 0.
Proof. See Appendix.

Proposition 5 provides an important condition under which an economy will fall into an
environmental disaster. It implies that if the level of climate change is too strong relatively
compared with the level of technology of the economy—i.e. when it holds that E > E∗ (a)—thenin the long run the availability of local resources is zero, R = 0, i.e. an environmental disasterwill occur, even if the economy starts from an initial state characterized by small population
size L0 and high availability of local resources R0 . In the absence of technological progress, theinterplay between population and local resources, under the persistent effects of climate change,
makes the population size increase along with the decrease in the availability of local resources
until the latter reaches zero.
5.2

Unconditional convergence to an environmental disasterIn this section, we relax the conditions whereby technological levels and global environmental

indexes are fixed. We allow these variables to change over time. Let us define AT = (aτ )+∞
τ =T

+∞
and ET = (Eτ )τ =T to be respectively the set of levels of technology and the set of global
climate change indexes from some period T ≥ 0 onward.
Proposition 6. If LL(sup AT ) ∩ RR(inf ET ) = ∅ and in some period T , the state of the economy(RT , LT ) ∈ ℜ2++ is characterized byLT ∈ (Ω(RT , inf ET ), ψ(RT , sup AT ))then the economy converges monotonically in an environmental disaster, in which for all t ≥ T
until an environmental disaster occurs, the following properties hold
Rt+1 < Rt

and Lt < Lt+1 ∈ (Ω(Rt+1 , inf Et+1 ), ψ(Rt+1 , sup At+1 )) .

Proof. The proof for this proposition is similar to that for proposition 4

The following theorem extends the result stated in proposition 5.

22

6

GLOBAL DYNAMICS AND DISCUSSION

Proposition 7. If in some period T ,inf ET > E∗ (sup AT )or equivalently

sup AT < E∗−1 (inf ET ) ,then an environmental disaster occurs within some finite time t ≥ T .
Proof. Under the condition stated in proposition 7, in any period t ≥ T , it holds that LL(at ) ∩RR(Et ) = ∅ —i.e. there is no conditional steady state. Hence, from the directions of motionsof Rt and Lt , as pointed out in lemma 3, the economy eventually falls into an environmental
disaster.

6

Global dynamics and discussion

The global dynamics of the economy is governed by the following system of equationset =θ
ρ(Lt )θ
1 A(at , Et )ẽt−1
1 − θ 1 + [1 − ϕ(Rt+1 , at+1 )] 1−θ

(24)

ẽt =

θ
ρ(Lt )θ
1 A(at , Et )ẽt−1
1 − θ 1 + [1 − ϕ(Rt+1 , at+1 )] θ−1

(25)


 θ

et−1 + ẽθt−1
at+1 = 1 + g
at
at
Lt+1 =oθγ(1 − θ) n
[1 − ϕ(Rt , at )] θ−1 + 1 − ϕ(Rt , at ) Lt
ρ(Lt )
Rt+1 = Rt + Ω(Rt , Et ) − Lt

(26)

(27)

(28)

given initial conditions e−1 > 0, ẽ−1 > 0, a0 > 0, L0 > 0, R0 > 0, and given an exogenous
sequence of global carbon concentration index (Et )+∞t=0 .
In addition to the previous section, we study in this section the impact of climate change ontechnological progress. We learn from the previous section that the level of technology has anegative impact on fertility by narrowing the gender gap in education investment. Hence, weshow in this section that by affecting technological progress, climate change has other reinforcing
effects on gender inequality in education and fertility in addition to the effects studied in theprevious section. The following proposition states the impact of climate change on technologicalprogress
Proposition 8. An increase in global climate change index Et in period t slows the rate of tech-

nological progress gt+1 between periods t + 1 and t + 2.
Proof. In effect, we come back with the education gender gap as defined in definition 1,
23

6

ζt+1 =GLOBAL DYNAMICS AND DISCUSSION1et= [1 − ϕ(Rt+1 , at+1 )] θ−1 ≡ ζ(Rt+1 , at+1 ),ẽtwhere in any period t + 1, variables at+1 and Rt+1 are predetermined by equations (26) and (28)respectively.
We have2−θ∂ζ(Rt+1 , at+1 )1=[1 − ϕ(Rt+1 , at+1 )] θ−1 ϕR (Rt+1 , at+1 )ΩE (Rt , Et ) > 0,∂Et
1−θ

which implies that the climate change enlarges the gender inequality in education investment,
while the total education investment for a couple of children isθρ(Lt )A(at , Et )ẽθt−11−θ
which decreases in the climate change index Et .
The decrease in total education investment for a couple of children, the reallocation in education investment being more biased toward the son, and the concavity of human capital formation
function together induce the decline in the rate of technological progress.
et + ẽt =The theoretical results so far may suggest a mechanism to explain the slow demographic transition in the least developed regions that are the most vulnerable to climate change, accompaniedby gender inequality in education. Climate change persistently plays a role in maintaining highrates of fertility in these regions through several channels. First, it causes damage to the local
resources that are essential for life, thereby making it necessary for women to spend more timecollecting resources for their families. When households anticipate that their daughters will
have less labor supply because of spending more time doing housework, they will invest lessin education for their daughters and more in education for their sons. Through this channel,
the gender inequality in education, which is biased toward the sons, is maintained. Hence, thehigh fertility rate is also upheld because the opportunity cost of child-rearing becomes relatively
inexpensive, making the substitution effect dominated by the income effect on fertility. Second,climate change directly decreases the return to human capital, reducing household income, andthus indirectly makes households invest less in education for their offspring. That is to say,climate change slows the rate of technological progress because it decreases the average humancapital of the economy. The low level of technology, in turn, inhibits the development of infrastructure, such as electricity and clean water supply, as well as the diffusion of appliances, whichsave women time on housework. Therefore, through this channel, climate change also upholds
gender inequality in education and thus maintains a high fertility rate.

24

7

7

EMPIRICAL ANALYSIS

Empirical Analysis

In this section, we test our theoretical predictions derived from our model for African countries.
In particular, our model suggests that climate change and population negatively affect the local
resources, which cause a reduction in the female labor force and female incomes given that the
women need to spend significant time at home. Because the women need to spend significant
time at home they will receive less investment in education. As a result, the gender gap in
education will increase and fertility will increase. More specifically, our model-based hypotheses
that will be tested in this section can be summarized as follows:• H1: Climate change positively affects fertility.
• H2: Climate change has a negative relationship with local resources.
• H3: Climate change increases the gender gap in education investment and reduces the female

labor force participation and female income.
7.1

Data

Our analysis is restricted to African countries (44 countries) from the period 1960 to 2017. We
corroborate the strategy of Dell et al. (2012) for constructing the climate variable, which is thethe temperature. More precisely, we collect the historical weather data from the Terrestrial Air
Temperature: 1900 - 2017 Gridded Monthly Time Series, Version 5.01 (Matsuura and Willmott2007). The dataset includes worldwide monthly mean temperature data at 0.5 Ã 0.5 degrees
resolution (approximately 56km Ã 56km at the equator). The values are interpolated for eachgrid node from an average of 20 different weather stations, with corrections for elevation. We use
the ArcGIS software to aggregate the weather data to the country-year level. In our specification,
we use population-weighted average temperature where the weights are constructed from 1990
population data at Gridded Population Count Data (GRUMP). We also consider averaging
based on geographic area, which produces broadly similar temperatures for most countries.
To proxy the local resources, we use two variables. The first one is the percentage of the
population that has access to basic hand washing facilities including soap and water. The othervariable is the percentage of the population with access to basic drinking water. Both variables
are collected from the World Bank’s World Development Indicators. Data on female formal
labor force participation and female incomes in agriculture also come from the World BankWorld Development Indicators, covering the period 1990-2015 (yearly observations). Data on
education comes from the Barro and Lee Database, and observations are available from 1950 on,
on a five-year basis (Barro and Lee 2013). The population, fertility rate, exports (expressed aspercentage of GDP), urban, income per capita, excess mortality, and age dependency ratio arecollected from the World Bank Indicators.

25

7.2

Model

7

EMPIRICAL ANALYSIS

We logarithm the variables population, income per capita, temperature, local resources andage dependency ratio in order to make them normal. For the robustness of our analysis, wereplicate our empirical specification using data for the rest of developing countries and the sametime span.
Table 1 illustrates the summary of statistics for all the variables for African countries in Panel
A and the summary of statistics of the rest of the developing countries in Panel B.
Table 1: Summary statistics
Panel A:African Countries
Mean
Water sources (in logs)
4.448
Temperature (in logs)
2.522
Gender Education Gap
0.727
Basic Water Sources (in logs)
4.102
Labour female participation
55.741
Exports (% GDP)28.134
Wage female in Agriculture
1.458
Urbanization (% GDP)
30.456
Population( in logs)
15.402
Total fertility rate
5.897
Under 5-mortality rate
154.43
Income per capita (in logs)
6.878
Panel B:Other Developing Countries Mean
Total fertility rate
3.718
Temperature (in logs)
2.504
Exports (% GDP)
32.613
Urbanization (% GDP)
45.691
Under 5-mortality rate
71.608
Income per capita (in logs)
7.836
Population( in logs)
15.126
Gender Education Gap
0.816
Female labor force participation
47.1477.2

Std. Dev.
0.287
0.149
0.5
0.298
21.65217.414
0.198
17.8741.444
1.405
78.261
0.982
Std. Dev.
1.831
0.144
20.291
21.19567.005
0.992
2.294
0.233
16.005

N
2534
2552
342
791
1233
1973
2303
2460
2460
2552
2232
2040
N
6100
4634
3286
4700
3967
3384
4718
660
2919

Model

Following Dell et al. (2012) and Dao et al. (2021), we use OLS fixed-effect estimation to
exploit the within-country variation of temperature to total fertility rates, female labor force
participation, local resources and the female wages.
Yit = ai + at + β1 ln(temperatureit ) + β2 Xit + ϵit(29)

The key coefficient is β1 , which shows the impact of temperature on the outcome variable
Yit . We include country fixed effects ( ai ) and year fixed effects (at ) to capture the unobserved
heterogeneity and eliminate all the co-founding factors so that they are not captured by theother control variables (Xit ), such as income per capita (in logs), population (in logs), excess
child mortality, urbanization (% GDP), and exports (% GDP) included in the regression. ϵit iserror term. We cluster heteroskedasticity adjusted standard errors at the bank-level to account
26

7.3

Results

7

EMPIRICAL ANALYSIS

for serial correlation and small standard errors (Bertrand, Mullainathan, and Duflo 2004).
7.3

Results

Table 1 illustrates the results related to the effects of climate change on local resources. As
mentioned in the data section, access to local resources is proxied by two variables: the percentage of the population that has access to drinking water and the percentage that has access tohandwashing water. Column 1 shows the estimates of Equation (29) having the percentage ofthe population with access to drinking water as a dependent variable, with the only independent
variable the temperature in logs. Column 2 presents similar estimates, with the percentage of
population having access to handwashing water as a dependent variable. Both columns showthat the temperature has a negative and significant impact on basic water sources.
More specifically, a percentage increase in the temperature decreases the local resources by
0.5 (see Column 1) and 0.1 (see Column 2) percentage. The results remain robust when we
include control variables for both of the different measures of basic water resources in columns
3 and 4. Notably, the only variables that are significant are income per capita in logs and the
population in logs. The population has a negative and significant coefficient at 5%, showingthat the larger the population, the less access to the local resources will be. On the other hand,
we observe that the estimated coefficient for income per capita is quite intuitive given that thewealthier the country is, the greater the population’s access to drinking water. To the end, we
note that the adjusted R-square is around 0.92 on average, indicating that the model has a good
fit with the independent variables. All the estimated models include country and year fixed
effects and the standard errors are clustered at country level.
Table 2 illustrates the impact of climate on fertility. Column 1 presents the effect of temperature
on fertility without including any control variables. In column 2, we introduce only the economic
variables as controls in addition to the temperature variable and in column 3, we add only the
demographic variables such as population and child mortality. To the end, column 4 includes
all the variables (economic and demographic variables). All the columns show a similar result,which is that the temperature has a positive and significant effect on fertility. In particular, wefind that a rise in temperature increases fertility by 0.5 children per woman on average. This
result is in line with Case et al. (2019). By contrast, studies by Chang et al. (1963), Mathew(1941), and Barreca et al. (2018) show that temperature has a negative effect on the birth rateor the health of infants. Consequently, we need to further examine our results to highlight themechanism of our current results.
Table 3 examines the effects of climate change on education and labor outcomes. Column
1 shows the impact of temperature in logs on education gap. Following Dao et al. (2021),
the gender gap in education is measured by the female-to-male ratio of average years of total
27

7.3

Results

7

EMPIRICAL ANALYSIS

Table 2: Local basic resources and Climate
VARIABLES
Temperature (in logs)

(1)
Model
Basic water sources

(2)
Model
Basic water sources

(3)
Model
Basic water sources

(4)
Model
Basic water sources-0.469***(0.092)-0.113**(0.043)5.630***(0.233)4.396***(0.111)-0.316***(0.076)-0.595***(0.161)0.000(0.001)0.005**(0.002)0.000(0.000)0.402*(0.228)0.028*(0.015)15.745***(2.450)-0.051**(0.020)-0.409***(0.157)-0.000(0.001)0.001(0.006)-0.000(0.001)0.785*(0.420)-0.039(0.025)-5.873(4.378)

2,534
0.815
Yes
Yes

791
0.931
Yes
Yes

1,784
0.878
Yes
Yes

627
0.963
Yes
Yes

Population( in logs)
Exports (% GDP)
Urbanization (% GDP)
Under 5-mortality rate
Income per capita (in logs)
Income per capita squ. (in logs)
Constant

Observations
Adjusted R-squaredYear fixed effects
Country fixed effects

Notes: ***, **, and * indicate statistical significance at the 1%, 5% and 10% levels respectively.

Table 3: Fertility and Climate
VARIABLES
Temperature (in logs)

(1)
Model
Total fertility rate

(2)
Model
Total fertility rate

(3)
Model
Total fertility rate

(4)
Model
Total fertility rate

0.683**(0.279)0.509**(0.187)0.007(0.005)-0.013(0.019)-1.021*(0.623)0.052(0.088)0.566**(0.256)0.444**(0.220)0.004(0.005)-0.035**(0.016)-0.353*(0.530)0.010(0.095)0.475(1.025)0.000(0.003)
0.124(16.481)
1,796
0.880
Yes
Yes
.

Exports (% GDP)
Urbanization (% GDP)
Income per capita (in logs)
Income per capita sq. (in logs)
Population (in logs)

4.175***(0.704)9.286*(4.702)0.424(0.776)-0.000(0.003)-2.035(12.480)

2,552
0.806
Yes
Yes
.

1,886
0.854
Yes
Yes
.

2,228
0.828
Yes
Yes
.

Under 5-mortality rate
Constant

Observations
R-squared
Year fixed effects
Country fixed effects
widstatNotes: ***, **, and * indicate statistical significance at the 1%, 5% and 10% levels respectively.

28

7.3

Results

7

EMPIRICAL ANALYSIS

schooling for ages 20â24. Column 1 shows the impact of temperature in logs on education
gap. We find that the temperature (in logs) has a negative and significant impact on education
gap. This result shows that climate change decreases the number of females that attend school,
instead remaining at home. The latter result is supported by the other two columns in Table 3.
Columns 2 and 3 show the effects of climate change on the percentage of the women that are in
the labor force and female wages in the agriculture (in logs).
Both regression models show that there is a significant negative effect of temperature on
the female labor participation and female wages in agriculture. In particular, we find that one
percentage point increase in temperature results in a decrease of 2.1 percentage points in female
wages. The adjusted R-square of all the models is above 80%, which shows that there is a good
fit of the model with the included variables. In all the models, we include control variables suchas income per capita, income per capita squared, child mortality, population (in logs), exports,
urbanization, and country and year fixed effects.

Table 4: Education, labor, and climate
VARIABLES
Temperature (in logs)
Exports (% GDP)
Urbanization (% GDP)
Under 5-mortality rate
Income per capita (in logs)
Income per capita sq. (in logs)
Population( in logs)
Constant

Observations
R-squared
Year fixed effects
Country fixed effects

(1)
Model
Gender Education Gap

(2)
Model
Female labor force participation

(3)
Model
Female wages in Agriculture-0.612**(0.290)0.000(0.007)-0.002(0.011)0.000(0.001)0.476(0.720)-0.040(0.054)0.303(0.484)-3.815(7.107)-9.403**(4.121)-0.111(0.087)0.381(0.399)0.076(0.054)2.080(17.512)-0.072(1.109)16.641(26.963)-214.615(459.158)-2.281***(0.479)-0.002(0.001)0.009**(0.004)0.001**(0.000)-0.082(0.277)0.011(0.019)0.004(0.117)9.596***(2.005)

278
0.542
Yes
Yes

1,004
0.810
Yes
Yes

1,591
0.908
Yes
Yes

Notes: ***, **, and * indicate statistical significance at the 1%, 5% and 10% levels respectively.

29

7.3

Results

7

EMPIRICAL ANALYSIS

So far, our analysis has been focused on African countries. Our stylized facts indicate that our
hypotheses hold only for the African countries but not for the rest of the developing countries.
In Table 4, we estimate Equation (29) with the variables of interest as dependent variables forthe rest of the developing countries (120 countries). We define developing countries based on
the World Bank income classification. Columns 1, 2, 3, and 4 show the impact of climate on
basic access to water resources, total fertility rate, female labor force participation and gendereducation gap, respectively. All the columns include control variables such as the income percapita, income per capita squared, child mortality, population (in logs), exports, urbanization,and country and year fixed effects.
We find that temperature as a proxy of climate does not have any impact on local resources
and female labor force participation. This result could be explained by the fact that otherdeveloping countries could have better infrastructure for access to the basic local resources
compared to African countries. Consequently, there is no need for women to remain at home.
We reach this outcome based on the fact that we find that the temperature has a negative andsignificant impact at 10% on the total fertility rate. This outcome is consistent with empiricalliterature that shows that the climate is responsible for the drop in all pregnancy outcomes inseveral countries (Cachon et al. 2012). The mechanism of the latter result could be that the hottemperatures might reduce sexual activity or does not affect certain sectors.

Table 5: Other developing countries and climate
VARIABLES
Temperature (in logs)
Exports (% GDP)
Urbanization (% GDP)
Under 5-mortality rate
Income per capita (in logs)
Income per capita sq. (in logs)
Population(in logs)
Constant

Observations
R-squared
Day fixed effects
Sector fixed effects

(1)
Model
Basic Water Sources

(2)
Model
Total fertility rate

(3)
Model
Labour(4)
Model
Gender Education Gap

0.003(0.015)-0.000(0.000)0.001(0.001)0.001*(0.000)-0.065(0.159)0.008(0.010)-0.018(0.030)4.746***(0.806)-0.138*(0.075)-0.004*(0.002)-0.024**(0.010)0.004(0.003)-2.530***(0.849)0.176***(0.054)-1.401***(0.377)36.636***(7.066)0.236(0.596)-0.012(0.017)0.094(0.106)0.021(0.039)-27.061*(14.667)
1.574(0.951)8.964**(3.775)9.947(80.184)-0.047*(0.024)0.001(0.000)-0.001(0.002)-0.001**(0.000)0.397**(0.156)-0.027**(0.011)0.155**(0.073)-2.916**(1.165)

2,283
0.764
Yes
Yes

2,362
0.950
Yes
Yes

1,436
0.965
Yes
Yes

399
0.941
Yes
Yes

Notes: *** p<0.01, ** p<0.05, * p<0.1.
Notes: ***, **, and * indicate statistical significance at the 1%, 5% and 10% levels respectively.

30

9

8

APPENDIX

Conclusion and further researchThis paper advances a theory integrating two emerging and important topics in the literature,demography and climate change, in order to explain the slow demographic transition in the least
developed regions of Africa. It provides a novel mechanism to explain the slow demographictransition and stagnation of the least developed regions. It also characterizes the conditions on
population size, availability of local resources, and extreme of climate change through which anenvironmental disaster will occur within some finite time.
On empirical grounds, we use a database covering 44 African countries over the period 1960
- 2017 to identify the role of temperature on basic local resources and fertility. We find that as
the temperature increases, basic water resources go down. By contrast, we show that there is apositive relationship between temperature and fertility. However, the latter result does not holdfor the other developing countries.
The global dynamics of the model needs numerical exercises to illustrate the mechanism that
leads to slow demographic transition along with the slow technological progress and the persistent gender inequality in education, as well as the mechanism that leads to an environmental
disaster. Several hypotheses, further research questions, and policy implications should be addressed based on the theoretical results of the model. These include, but are not limited to, thefollowing: (i) Damage caused by climate change to local resources increases gender inequality
in education/income (and hence fertility) through its asymmetric effects on the time allocations
between genders; (ii) Is only public investment in education sufficient for triggering developmentin the least developed regions?; (iii) Using carbon tax revenue to invest in essential infrastructure(e.g. clean water supply and electricity) may trigger development in the least developed regions.
These further directions of research are ongoing in our research agenda.

9

Appendix

Proof of Proposition 2
Proof. (i) From equation (22), the strict concavity of Ω(R; E) in R and the strict convexity of

ψ(R; a) in R guarantees that at most two distinct conditional steady states exist.
(ii) We consider first the case where there is only one conditional steady state. Since ψ(0; a) >Ω(0; E) = 0, ψ(R̄(E); a) > Ω(R̄(E); E) = 0, and the strict concavity of Ω(R; E) in R andthe strict convexity ofψ(R; a) in R, this case occurs when the curves Ω(R; E) and ψ(R; a) aretangent to each other at such a steady state (R, L). That is to say, at a steady state it holds
that ΩR (R; E) = ψR (R; a). From lemma 2 we have ΩR (R; E) < 0, and hence from assumption
4 and equation (21) we have R > R̂(E).
In the case that there are two distinct conditional steady states characterized by 0 < R̃ <R < R̄(E), let us suppose a negation that R ≤ R̂(E). Hence, Ω(R; E) > Ω(R̃; E) while

31

9

APPENDIX

ψ(R; a) < ψ(R̃; a). In addition, we have Ω(R̃; E) = ψ(R̃; a). Therefore, Ω(R; E) > ψ(R; a),which contradicts the property that Ω(R; E) = ψ(R; a). That is to say, R > R̂(E).
(iii) In order to examine the local stability of steady states, we linearize the dynamic system,
which is characterized by two equations (18) and (19), around the steady states. The associatedJacobian matrix appears as

1 − ηL∗


J =
−1
∗ ′

η ∗ ψR (R∗ ; a)1 + ΩR (R∗ ; E)





∗

ρ (L )
is the elasticity of cost of raising children with respect to the population
where η ∗ = L ρ(L∗)
density evaluated at a steady state (R∗ , L∗ ). By assumption 2 we have η ∗ ∈ (0, 1).
The trace and determinant of the Jacobian matrix J are respectively

Tr(J) = 1 − η ∗ + 1 + ΩR (R∗ ; E) > 0det(J) = (1 − η ∗ ) [1 + ΩR (R∗ ; E)] + ηL∗ ψR (R∗ ; a)Since ψR (R∗ ; a) < 0, it is straightforward that Tr(J)2 > 4 det(J). That is to say the characteristic polynomial
C(λ) ≡ λ2 − Tr(J)λ + det(J) = 0
has two real distinct eigenvalues λ1 < λ2 , which satisfy the following properties
λ1 + λ2 = Tr(J) and λ1 λ2 = det(J)It is fairly straightforward to prove that ψR (R; a) > ΩR (R; E) and ψR (R̃; a) < ΩR (R̃; E). So,
we have
C(1) = ηL∗ [ψR (R∗ ; a) − ΩR (R∗ ; E)]


 >0

if

R∗ = R <0ifR∗ = R̃

(30)(iii.a) For the steady state with R∗ = R : We have −1 < ΩR (R; E) < ψR (R; a) < 0, thenλ1 + λ2 = Tr(J) ∈ (0, 2) and λ1 λ2 = det(J) ∈ (−1, 1). We know that −1 < λ1 < λ2 < 1. Indeed,since λ1 + λ2 < 2 then λ1 < 1. Let us now suppose a negation that λ1 ≤ −1. In this case λ2 > 1
because λ1 + λ2 > 0. Hence, λ1 λ2 < −1 which contradicts the property det(J) > −1. Therefore,−1 < λ1 < 1. Since, at R∗ = R, C(1) > 0, then λ2 < 1. In summary, it holds −1 < λ1 < λ2 < 1.
That is to say, the steady state with R∗ = R is a stable node.
(iii.b) For the steady state with R∗ = R̃ : From (30) we have C(1) < 0 then λ1 < 1 < λ2 .

32

9APPENDIX

Since ψR (R̃; a) ≥ −1 then det(J) > −1, thereforehiC(−1) = 4 + 2ΩR (R̃; E) − 2η̃ − ΩR (R̃; E) − ψR (R̃; a) η̃ > 2 + ΩR (R̃; E) + ψR (R̃; a) > 0
where η̃L ∈ (0, 1) is the elasticity of cost raising children with respect to the population density
evaluated at the steady state (R̃, L̃). Hence, λ1 ∈ (−1, 1) while λ2 > 1. That is to say, thesteady state (R̃, L̃) is a stable node.

Proof of Proposition 4
Proof. We have for

RT +1 = RT + Ω(RT , E) − LT < RT

(31)

and, as in (18),
n
o L
θ
LT
T
= ρ(ψ(RT , a))LT +1 = γ(1 − θ) [1 − ϕ(RT , a)] θ−1 + 1 − ϕ(RT , a)ρ(LT )
ρ(LT )

n
o
θ
−1
θ−1
γ(1 − θ) [1 − ϕ(RT , a)]because, as defined in (20), ψ(RT , a) = ρ+ 1 − ϕ(RT , a) .
Hence, by assumption 2, equation (31), and ψR (R, a) < 0, we obtain
LT = ρ(LT )LTψ(RT , a)< LT +1 < ρ(ψ(RT , a))= ψ(RT , a) < ψ(RT +1 , a)ρ(LT )
ρ(ψ(RT , a))(32)

We prove next that LT +1 > Ω(RT +1 , E). Indeed, it is trivially true for RT , RT +1 ∈ (0, R̂(E)].
For the case RT , RT +1 ∈ (R̂(E), R̄(E)), since ΩR (R, E) < 0 for RT +1 ∈ (R̂(E), R̄(E)) andLT +1 > LT , we haveΩ(RT +1 , E) = Ω(RT + Ω(RT ) − LT , E) < Ω(RT + Ω(RT ) − LT +1 , E)

(33)

Let us define the following function
G(LT +1 , RT ) = LT +1 − Ω(RT + Ω(RT ) − LT +1 , E)

(34)

We have
GL (LT +1 , RT ) = 1 + ΩR (RT + Ω(RT ) − LT +1 , E) > 0
since , by assumption 4, ΩR (RT , E) > −1.
Note from (32) that LT +1 > LT > Ω(RT , E), hence we haveG(LT +1 , RT ) > G(Ω(RT , E), RT ) = 0
33

(35)

9

APPENDIX

Combining (33), (34), (35), (32), and (31), we have
LT < LT +1 ∈ (Ω(RT +1 , E), ψ(RT +1 , a))and RT +1 < RT .

Thus, by inducing for all t > T , we obtain the results stated in proposition 4.

Proof of Proposition 5
Proof. We need to prove that for all given a, there exists a unique pair (R∗ , E∗ ) ∈ ℜ2++ such thatthe following system of equations (36) and (37) holdsΩ(R∗ , E∗ ) − ψ(R∗ , a) = 0(36)ΩR (R∗ , E∗ ) − ψR (R∗ , a) = 0(37)This system of equations tells us that the loci LL(a) and RR(E) are tangent to each otherat (R∗ , E∗ ). Thus, by the strict concavity of Ω(R, E) in R and the strict convexity of ψ(R, a) in
R when R ∈ (0, R̄(E)), the system above implies that
LL(a) ∩ RR(E∗ ) = {(R∗ , ψ(R∗ , a))}By assumptions 4 and 5, there always exists E∗ > 0 such that the equation (36) has at leasta solution R∗ . By applying the implicit function theorem for the equation (36) with respect toE∗ and a, we have E∗ to be a function of a,E∗ = E∗ (a) with E∗′ (a) =ψa (R∗ , a)>0
ΩE (R∗ , E∗ )We now complete the proof by showing that, for all a, there exists a unique R∗ making
equation (37) holds. Indeed, let us define△(R; a) = ΩR (R, E∗ (a)) − ψR (R, a)
We have, for all R ∈ (0, R̄(E∗ (a))),△R (R; a) = ΩRR (R, E∗ (a)) − ψRR (R, a) < 0;△(R̂(E∗ (a)); a) > 0 and △(R̄(E∗ (a)); a) < 0.

Thus, there exists a unique R∗ ∈ (R̂(E∗ (a)), R̄(E∗ (a))) to be the solution to △(R; a) = 0.
Hence, there exists a unique pair (R∗ , E∗ ) ∈ (0, R̄(E∗ )) × ℜ++ solving the system of equations(36) and (37).

34

9APPENDIX

That is to say, for a given a there exists a unique E∗ = E∗ (a) such that the loci LL(a)and RR(E) are tangent to each other. For any E > E∗ (a), LL(0) ∩ RR(E) = ∅. Hence, theevolutionary processes of Rt and Lt , as depicted by the directions of motions in figure 7, willlead the economy to fall into an environmental disaster.

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