Economic and Demographic Transition,Mortality, and Comparative Development
Matteo Cervellati Uwe Sunde
DESA UN New YorkNovember 2008
Economic and Demographic Development: Main Patterns
Economic Transition:
I GDP per capita take-off after stagnation;
I Human capital formation: drastic change in the “educationcomposition” of the population (from below 20 percent ofindividuals with some education to about 90 percent in fewgenerations);
I (Structural Change: Agriculture-Industry)
Demographic Transition:
I Increase in adult longevity (50-70 in few generations)
I Reduction in infant mortality (250 to 4 per thousand in fewgenerations)
I Gross and net fertility (eventually) drop(from 6 child per woman to 2)
I Population growth despite decreases in fertility
Economic and Demographic Development: Main Patterns
Economic Transition:
I GDP per capita take-off after stagnation;
I Human capital formation: drastic change in the “educationcomposition” of the population (from below 20 percent ofindividuals with some education to about 90 percent in fewgenerations);
I (Structural Change: Agriculture-Industry)
Demographic Transition:
I Increase in adult longevity (50-70 in few generations)
I Reduction in infant mortality (250 to 4 per thousand in fewgenerations)
I Gross and net fertility (eventually) drop(from 6 child per woman to 2)
I Population growth despite decreases in fertility
Economic and Demographic Development: Main Patterns
Economic Transition:
I GDP per capita take-off after stagnation;
I Human capital formation: drastic change in the “educationcomposition” of the population (from below 20 percent ofindividuals with some education to about 90 percent in fewgenerations);
I (Structural Change: Agriculture-Industry)
Demographic Transition:
I Increase in adult longevity (50-70 in few generations)
I Reduction in infant mortality (250 to 4 per thousand in fewgenerations)
I Gross and net fertility (eventually) drop(from 6 child per woman to 2)
I Population growth despite decreases in fertility
Some Facts
I In 1970 half of the countries had:
1. Life expectancy at birth below 55 years;2. Average total fertility around 6 children per woman;3. Share of population with at least completed secondary
education below 20 percent.
I In 2000 40 percent of these countries had not exited thedevelopment trap yet.
I Most of these are countries in regions with large extrinsic mortality(due to e.g. tropical diseases, high density of pathogen species etc.)
Some Facts
I In 1970 half of the countries had:
1. Life expectancy at birth below 55 years;2. Average total fertility around 6 children per woman;3. Share of population with at least completed secondary
education below 20 percent.
I In 2000 40 percent of these countries had not exited thedevelopment trap yet.
I Most of these are countries in regions with large extrinsic mortality(due to e.g. tropical diseases, high density of pathogen species etc.)
Some Facts
I In 1970 half of the countries had:
1. Life expectancy at birth below 55 years;2. Average total fertility around 6 children per woman;3. Share of population with at least completed secondary
education below 20 percent.
I In 2000 40 percent of these countries had not exited thedevelopment trap yet.
I Most of these are countries in regions with large extrinsic mortality(due to e.g. tropical diseases, high density of pathogen species etc.)
Research Questions
I What are the underlying forces behind transitions out of thedevelopment trap in these different dimensions?
I No available theory allows to analyze the economic anddemographic dimensions in a unified framework delivering anendogenous transition.
I Why do some developing countries remain trapped in poor livingconditions?
I Since 1970 only a bit more than half of the developingcountries have undergone the transition
I What is the role of mortality?
I Ongoing empirical debate: we separately consider theimplications of exogenous improvements (shocks) andstructural differences in extrinsic mortality environment;
Research Questions
I What are the underlying forces behind transitions out of thedevelopment trap in these different dimensions?
I No available theory allows to analyze the economic anddemographic dimensions in a unified framework delivering anendogenous transition.
I Why do some developing countries remain trapped in poor livingconditions?
I Since 1970 only a bit more than half of the developingcountries have undergone the transition
I What is the role of mortality?
I Ongoing empirical debate: we separately consider theimplications of exogenous improvements (shocks) andstructural differences in extrinsic mortality environment;
Research Questions
I What are the underlying forces behind transitions out of thedevelopment trap in these different dimensions?
I No available theory allows to analyze the economic anddemographic dimensions in a unified framework delivering anendogenous transition.
I Why do some developing countries remain trapped in poor livingconditions?
I Since 1970 only a bit more than half of the developingcountries have undergone the transition
I What is the role of mortality?
I Ongoing empirical debate: we separately consider theimplications of exogenous improvements (shocks) andstructural differences in extrinsic mortality environment;
Contribution of this Paper
I Theory of Economic and Demographic Transition:
I Endogenous change in mortality, fertility, education structurein population, gdp.
I rationalize “difficult evidence”: e.g. role of longevity forfertility, dynamic change in fertility and net fertility drop.
I Theoretical investigation of the role of mortality for comparativedevelopment:
I exogenous “shocks” to mortality (e.g. introduction ofpenicillin)
I permanent differences in the mortality environment (e.g.tropical diseases)
I Compare theoretical implications with evidence from time series andcross-country panel data
Contribution of this Paper
I Theory of Economic and Demographic Transition:
I Endogenous change in mortality, fertility, education structurein population, gdp.
I rationalize “difficult evidence”: e.g. role of longevity forfertility, dynamic change in fertility and net fertility drop.
I Theoretical investigation of the role of mortality for comparativedevelopment:
I exogenous “shocks” to mortality (e.g. introduction ofpenicillin)
I permanent differences in the mortality environment (e.g.tropical diseases)
I Compare theoretical implications with evidence from time series andcross-country panel data
Contribution of this Paper
I Theory of Economic and Demographic Transition:
I Endogenous change in mortality, fertility, education structurein population, gdp.
I rationalize “difficult evidence”: e.g. role of longevity forfertility, dynamic change in fertility and net fertility drop.
I Theoretical investigation of the role of mortality for comparativedevelopment:
I exogenous “shocks” to mortality (e.g. introduction ofpenicillin)
I permanent differences in the mortality environment (e.g.tropical diseases)
I Compare theoretical implications with evidence from time series andcross-country panel data
Related Literature
Unified Growth Theories
I Change in fertility with quantity-quality trade-off [Galor and Weil,aer 2000, Galor and Moav, qje 2002] (technical problems inincluding mortality)
I Exogenous mortality decline [Boldrin and Jones red 2002,Boucekkine, de la Croix and Licandro, jet 2002, Soares, aer 2005]
I Endogenous mortality decline [Lagerlof, ier 2003, Cervellati andSunde, aer 2005, de la Croix and Licandro, mimeo 2007].
I Differential fertility and heterogenous human capital [de la Croixand Doepke, aer 2003, jde 2004]
Related Literature (2)
Underdevelopment Traps and Comparative Development
I Poverty Traps [Azariadis and Stachurski, handbook eg 2005],Mortality Traps [Bloom and Canning, pnas 2007]
I Role of Mortality for development [Shastry and Weil, jeea 2003,Soares, aer 2005, Weil, qje 2007, Lorentzen et al., jeg 2008,Acemoglu and Johnson, jpe 2007];
I Debate “Geography vs. Institutions” [Acemoglu, Johnson andRobinson, aer 2001, Glaeser et al., jeg 2004, Rodrick et al., jeg2004, Sachs, nber 2003, (..)]
Related Literature (2)
Underdevelopment Traps and Comparative Development
I Poverty Traps [Azariadis and Stachurski, handbook eg 2005],Mortality Traps [Bloom and Canning, pnas 2007]
I Role of Mortality for development [Shastry and Weil, jeea 2003,Soares, aer 2005, Weil, qje 2007, Lorentzen et al., jeg 2008,Acemoglu and Johnson, jpe 2007];
I Debate “Geography vs. Institutions” [Acemoglu, Johnson andRobinson, aer 2001, Glaeser et al., jeg 2004, Rodrick et al., jeg2004, Sachs, nber 2003, (..)]
Set up
I Time is continuous, τ ∈ R+
I Overlapping Generations of individuals t ∈ N+
I Frequency of Births kt .
I Individual - generation specific - life expectancy Tt of adults, andchild mortality (1− πt)
I Heterogeneous agents i with uniform ex ante distribution of abilitieswith ai ∈ [0, 1]
Timing of Events
- ττ0 (τ0 + k) (τ0 + 2k) (τ0 + 3k) (τ0 + 4k)
t� �� �Tt
(τ0 + Tt )
t + 1� �� �Tt+1
(τ0 + k + Tt+1)
t + 2� �� �Tt+2
(τ0 + 2k + Tt+2)
t + 3
Preferences and Production Function
I Utility from own lifetime consumption c it and well-being (potential
income) of offspring y it+1
I Preferences
u(c it , y
it+1πtn
it) =
(c it
)(1−γ) (y it+1πtn
it
)γwith γ ∈ (0, 1) (1)
I Unique consumption good produced with (vintage) aggregateproduction function.
I Aggregate production function:
Yt = At [xt (Hut )η + (1− xt) (Hs
t )η]
1η (2)
with η ∈ (0, 1) and the relative production share xt ∈ (0, 1) ∀t.
Preferences and Production Function
I Utility from own lifetime consumption c it and well-being (potential
income) of offspring y it+1
I Preferences
u(c it , y
it+1πtn
it) =
(c it
)(1−γ) (y it+1πtn
it
)γwith γ ∈ (0, 1) (1)
I Unique consumption good produced with (vintage) aggregateproduction function.
I Aggregate production function:
Yt = At [xt (Hut )η + (1− xt) (Hs
t )η]
1η (2)
with η ∈ (0, 1) and the relative production share xt ∈ (0, 1) ∀t.
Production of human capital
hj(ai , rt−1, et
)= αj
(et − e j
)f (rt−1, ·) mj(ai ) (3)
with hj = 0 ∀e < e j and es > eu ≥ 0, αj > 0, j = u, s.
I Education time (intensive margin) et ;
I Investment of parents:f (rt−1, ·) (4)
with fr (.) > 0 and frr (.) < 0.
I Ability:mj
(ai
)(5)
with mjr
(ai
)≥ 0 [simplify: ms (a) = a and mu (a) = 1].
Individual Decision Problem
I Total lifetime income of individual i with ability a choosinghuman capital type j
y i,jt
(ai
)= y j
t
(ai , r i
t−1, ei,jt
)= w j
t hj(ai , r i
t−1, ei,jt
) (Tt − e i,j
t
)(6)
I Individual Problem: Choose type j = u, s and time of owneducation e i,j
t , gross fertility ni , and time spent in raising children rt :
{j∗, e i,j∗t , ni,j∗
t , r i∗t } = arg max
{nt ,rt ,,ejt ,j=u,s}
ut
(c it , πtn
i,jt y j
t+1
(ai , r i
t , ei,jt+1
))(P1)
subject to:
c it = w j
t hjt
(ai , r i
t−1, ei,jt
) (Tt
(1− r i
tπtni,jt
)− e j
t
)and to (6) for j = u, s.
Individual Decision Problem
I Total lifetime income of individual i with ability a choosinghuman capital type j
y i,jt
(ai
)= y j
t
(ai , r i
t−1, ei,jt
)= w j
t hj(ai , r i
t−1, ei,jt
) (Tt − e i,j
t
)(6)
I Individual Problem: Choose type j = u, s and time of owneducation e i,j
t , gross fertility ni , and time spent in raising children rt :
{j∗, e i,j∗t , ni,j∗
t , r i∗t } = arg max
{nt ,rt ,,ejt ,j=u,s}
ut
(c it , πtn
i,jt y j
t+1
(ai , r i
t , ei,jt+1
))(P1)
subject to:
c it = w j
t hjt
(ai , r i
t−1, ei,jt
) (Tt
(1− r i
tπtni,jt
)− e j
t
)and to (6) for j = u, s.
Partial Equilibrium: Individual Education and Fertility
Proposition
[Individual Education and Fertility] For any{
w jt ,Tt , πt
}, the
vector of an individual’s optimal education, fertility and time devoted to
his children,{
e j∗t , nj∗
t , r∗t
}, given that the individual acquires human
capital of type j = {u, s}, is given by,
e i,j∗t = e j∗
t =Tt (1− γ) + e j
(2− γ), (7)
ni,j∗t = nj∗
t =γ
2− γ
Tt − e j
Ttr∗t πtand (8)
with r∗t solving,
εf ,r ≡∂f
(r it , ·
)∂r i
t
r it
f(r it , ·
) = 1 (9)
General Equilibrium (Intra-generational)
=⇒ Wages?
I Aggregate levels of human capital supplied by generation t:
Hut (at) =
∫eat
0
hut (a)d(a)da and Hs
t (at) =
∫ 1
eat
hst (a)d(a)da
(10)
I Wage rates are determined on competitive labor markets:
w st =
∂Yt
∂Hst
and wut =
∂Yt
∂Hut
with,
wut
w st
=xt
1− xt
(Hs
t (at)
Hut (at)
)1−η
(11)
General Equilibrium (Intra-generational)
Proposition
[Human Capital Investment in Equilibrium] For any generationt, and for any given {Tt , πt ,At , xt} there exists a unique
λt ≡ 1− a∗t
and accordingly a unique vector,{
H j∗t ,w j∗
t , r∗t , e j∗t , nj∗
t , hj∗(a)}
for each
a ∈ [0, 1] and i = u, s, which solves the individual problem (P1) for eachindividual, consistent with wages given in (11), where
λt = Λ(Tt , xt) , (12)
is an increasing, S-shaped function of expected lifetime duration Tt , withzero slope for T −→ 0 and T −→∞.
Dynamics: Mortality
I Child Survival Rate (Child Mortality)
πt = Π
(+
Hst−1,
+yt−1
)(13)
with Π (0,Hs0) = π.
I Adult Longevity
Tt = Υ
(+
Hst−1,
+yt−1
)(14)
with Υ(0) > 0 and Υ(1) < ∞ and limyt→∞ ∂Tt/∂yt−1 = 0 whereyt−1 = Yt−1/Nt−1.
Dynamics: Technological Progress
Skill-biased technical change
gt =At − At−1
At−1= F (a∗t ,At−1) = δHs
t−1(Hst−1)At−1 (15)
where δ > 0, and
xt = X (At) with∂X (At)
∂At< 0 (16)
−→ instrumental assumption!
Development Dynamics of the Economy
Evolution of the non linear dynamic system:
λt = Λ(Tt , xt)Tt = Υ(λt−1)πt = Π(λt−1,Tt−1, xt−1)xt = X (λt−1,Tt−1, xt−1)
(17)
Evolution of Conditional Dynamic System
6
- T
1
0
λ
es
ΥΛ(x)
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T
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-?
�6
(a)
6
- T
1
0
λ
es
Υ
Λ(x)
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(b)
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- T
1
0
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Υ
Λ(x)
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(c)
Figure 3: The Process of Development
model. The main results would be reinforced by the presence of a change in r∗ as in the models
in the spirit of Galor and Weil (2000), while leaving the qualitative dynamics of the system
unchanged. In particular, r∗ would be low before the take-off but would accelerate during
and after the transition due to the larger technological change. This would imply a further
reduction of gross fertility for all individuals (irrespective of the education they acquire) after
the transition.
The proposed mechanism does not rely on scale effects or non-convexities like, e.g. subsistence
consumption levels. Extending the model by adding a subsistence thresholds for consumption
as in Galor and Weil (2000), Strulik (2008) and Dalgaard and Strulik (2008), would introduce
additional Malthusian features by including a corner solution in the dynamics of development.
Also, as shown by de la Croix and Doepke (2003) and de la Croix and Licandro (2007), the
consideration of corner regimes increases the likelihood of observing a temporary increase in
fertility at the onset of the transition before observing a drop after the transition.
The level of technology increases monotonically and deterministically over the course of
generations. But this instrumental prediction is obviously not necessary for the main argument
as long as productivity eventually increases enough to trigger the transition, i.e., to induce a
sufficiently large fraction of the population to acquire skilled human capital.41
In the characterization of the transition dynamics we concentrated exclusively on techno-
logical change. There are a number of other variables which can trigger the transition, with
potentially important implications for development policies. For example, the incentives for the
acquisition of skilled human capital also depend on the relative productivity of the time invested
in acquiring education. In fact, x and α are isomorphic in inducing a larger fraction of skilled
individuals λ for any T . Hence endogenous improvements in the production technologies of41Aiyar et al. (2006) propose a micro-foundation of the interactions between population dynamics and techno-
logical progress and regress in pre-industrial societies.
27
6
- T
1
0
λ
es
ΥΛ(x)
���������
T
�?
-?
�6
(a)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(b)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(c)
Figure 3: The Process of Development
model. The main results would be reinforced by the presence of a change in r∗ as in the models
in the spirit of Galor and Weil (2000), while leaving the qualitative dynamics of the system
unchanged. In particular, r∗ would be low before the take-off but would accelerate during
and after the transition due to the larger technological change. This would imply a further
reduction of gross fertility for all individuals (irrespective of the education they acquire) after
the transition.
The proposed mechanism does not rely on scale effects or non-convexities like, e.g. subsistence
consumption levels. Extending the model by adding a subsistence thresholds for consumption
as in Galor and Weil (2000), Strulik (2008) and Dalgaard and Strulik (2008), would introduce
additional Malthusian features by including a corner solution in the dynamics of development.
Also, as shown by de la Croix and Doepke (2003) and de la Croix and Licandro (2007), the
consideration of corner regimes increases the likelihood of observing a temporary increase in
fertility at the onset of the transition before observing a drop after the transition.
The level of technology increases monotonically and deterministically over the course of
generations. But this instrumental prediction is obviously not necessary for the main argument
as long as productivity eventually increases enough to trigger the transition, i.e., to induce a
sufficiently large fraction of the population to acquire skilled human capital.41
In the characterization of the transition dynamics we concentrated exclusively on techno-
logical change. There are a number of other variables which can trigger the transition, with
potentially important implications for development policies. For example, the incentives for the
acquisition of skilled human capital also depend on the relative productivity of the time invested
in acquiring education. In fact, x and α are isomorphic in inducing a larger fraction of skilled
individuals λ for any T . Hence endogenous improvements in the production technologies of41Aiyar et al. (2006) propose a micro-foundation of the interactions between population dynamics and techno-
logical progress and regress in pre-industrial societies.
27
6
- T
1
0
λ
es
ΥΛ(x)
���������
T
�?
-?
�6
(a)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(b)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(c)
Figure 3: The Process of Development
model. The main results would be reinforced by the presence of a change in r∗ as in the models
in the spirit of Galor and Weil (2000), while leaving the qualitative dynamics of the system
unchanged. In particular, r∗ would be low before the take-off but would accelerate during
and after the transition due to the larger technological change. This would imply a further
reduction of gross fertility for all individuals (irrespective of the education they acquire) after
the transition.
The proposed mechanism does not rely on scale effects or non-convexities like, e.g. subsistence
consumption levels. Extending the model by adding a subsistence thresholds for consumption
as in Galor and Weil (2000), Strulik (2008) and Dalgaard and Strulik (2008), would introduce
additional Malthusian features by including a corner solution in the dynamics of development.
Also, as shown by de la Croix and Doepke (2003) and de la Croix and Licandro (2007), the
consideration of corner regimes increases the likelihood of observing a temporary increase in
fertility at the onset of the transition before observing a drop after the transition.
The level of technology increases monotonically and deterministically over the course of
generations. But this instrumental prediction is obviously not necessary for the main argument
as long as productivity eventually increases enough to trigger the transition, i.e., to induce a
sufficiently large fraction of the population to acquire skilled human capital.41
In the characterization of the transition dynamics we concentrated exclusively on techno-
logical change. There are a number of other variables which can trigger the transition, with
potentially important implications for development policies. For example, the incentives for the
acquisition of skilled human capital also depend on the relative productivity of the time invested
in acquiring education. In fact, x and α are isomorphic in inducing a larger fraction of skilled
individuals λ for any T . Hence endogenous improvements in the production technologies of41Aiyar et al. (2006) propose a micro-foundation of the interactions between population dynamics and techno-
logical progress and regress in pre-industrial societies.
27
Evolution of Conditional Dynamic System
6
- T
1
0
λ
es
ΥΛ(x)
���������
T
�?
-?
�6
(a)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(b)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(c)
Figure 3: The Process of Development
model. The main results would be reinforced by the presence of a change in r∗ as in the models
in the spirit of Galor and Weil (2000), while leaving the qualitative dynamics of the system
unchanged. In particular, r∗ would be low before the take-off but would accelerate during
and after the transition due to the larger technological change. This would imply a further
reduction of gross fertility for all individuals (irrespective of the education they acquire) after
the transition.
The proposed mechanism does not rely on scale effects or non-convexities like, e.g. subsistence
consumption levels. Extending the model by adding a subsistence thresholds for consumption
as in Galor and Weil (2000), Strulik (2008) and Dalgaard and Strulik (2008), would introduce
additional Malthusian features by including a corner solution in the dynamics of development.
Also, as shown by de la Croix and Doepke (2003) and de la Croix and Licandro (2007), the
consideration of corner regimes increases the likelihood of observing a temporary increase in
fertility at the onset of the transition before observing a drop after the transition.
The level of technology increases monotonically and deterministically over the course of
generations. But this instrumental prediction is obviously not necessary for the main argument
as long as productivity eventually increases enough to trigger the transition, i.e., to induce a
sufficiently large fraction of the population to acquire skilled human capital.41
In the characterization of the transition dynamics we concentrated exclusively on techno-
logical change. There are a number of other variables which can trigger the transition, with
potentially important implications for development policies. For example, the incentives for the
acquisition of skilled human capital also depend on the relative productivity of the time invested
in acquiring education. In fact, x and α are isomorphic in inducing a larger fraction of skilled
individuals λ for any T . Hence endogenous improvements in the production technologies of41Aiyar et al. (2006) propose a micro-foundation of the interactions between population dynamics and techno-
logical progress and regress in pre-industrial societies.
27
6
- T
1
0
λ
es
ΥΛ(x)
���������
T
�?
-?
�6
(a)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(b)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(c)
Figure 3: The Process of Development
model. The main results would be reinforced by the presence of a change in r∗ as in the models
in the spirit of Galor and Weil (2000), while leaving the qualitative dynamics of the system
unchanged. In particular, r∗ would be low before the take-off but would accelerate during
and after the transition due to the larger technological change. This would imply a further
reduction of gross fertility for all individuals (irrespective of the education they acquire) after
the transition.
The proposed mechanism does not rely on scale effects or non-convexities like, e.g. subsistence
consumption levels. Extending the model by adding a subsistence thresholds for consumption
as in Galor and Weil (2000), Strulik (2008) and Dalgaard and Strulik (2008), would introduce
additional Malthusian features by including a corner solution in the dynamics of development.
Also, as shown by de la Croix and Doepke (2003) and de la Croix and Licandro (2007), the
consideration of corner regimes increases the likelihood of observing a temporary increase in
fertility at the onset of the transition before observing a drop after the transition.
The level of technology increases monotonically and deterministically over the course of
generations. But this instrumental prediction is obviously not necessary for the main argument
as long as productivity eventually increases enough to trigger the transition, i.e., to induce a
sufficiently large fraction of the population to acquire skilled human capital.41
In the characterization of the transition dynamics we concentrated exclusively on techno-
logical change. There are a number of other variables which can trigger the transition, with
potentially important implications for development policies. For example, the incentives for the
acquisition of skilled human capital also depend on the relative productivity of the time invested
in acquiring education. In fact, x and α are isomorphic in inducing a larger fraction of skilled
individuals λ for any T . Hence endogenous improvements in the production technologies of41Aiyar et al. (2006) propose a micro-foundation of the interactions between population dynamics and techno-
logical progress and regress in pre-industrial societies.
27
6
- T
1
0
λ
es
ΥΛ(x)
���������
T
�?
-?
�6
(a)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(b)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(c)
Figure 3: The Process of Development
model. The main results would be reinforced by the presence of a change in r∗ as in the models
in the spirit of Galor and Weil (2000), while leaving the qualitative dynamics of the system
unchanged. In particular, r∗ would be low before the take-off but would accelerate during
and after the transition due to the larger technological change. This would imply a further
reduction of gross fertility for all individuals (irrespective of the education they acquire) after
the transition.
The proposed mechanism does not rely on scale effects or non-convexities like, e.g. subsistence
consumption levels. Extending the model by adding a subsistence thresholds for consumption
as in Galor and Weil (2000), Strulik (2008) and Dalgaard and Strulik (2008), would introduce
additional Malthusian features by including a corner solution in the dynamics of development.
Also, as shown by de la Croix and Doepke (2003) and de la Croix and Licandro (2007), the
consideration of corner regimes increases the likelihood of observing a temporary increase in
fertility at the onset of the transition before observing a drop after the transition.
The level of technology increases monotonically and deterministically over the course of
generations. But this instrumental prediction is obviously not necessary for the main argument
as long as productivity eventually increases enough to trigger the transition, i.e., to induce a
sufficiently large fraction of the population to acquire skilled human capital.41
In the characterization of the transition dynamics we concentrated exclusively on techno-
logical change. There are a number of other variables which can trigger the transition, with
potentially important implications for development policies. For example, the incentives for the
acquisition of skilled human capital also depend on the relative productivity of the time invested
in acquiring education. In fact, x and α are isomorphic in inducing a larger fraction of skilled
individuals λ for any T . Hence endogenous improvements in the production technologies of41Aiyar et al. (2006) propose a micro-foundation of the interactions between population dynamics and techno-
logical progress and regress in pre-industrial societies.
27
Evolution of Conditional Dynamic System
6
- T
1
0
λ
es
ΥΛ(x)
���������
T
�?
-?
�6
(a)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(b)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(c)
Figure 3: The Process of Development
model. The main results would be reinforced by the presence of a change in r∗ as in the models
in the spirit of Galor and Weil (2000), while leaving the qualitative dynamics of the system
unchanged. In particular, r∗ would be low before the take-off but would accelerate during
and after the transition due to the larger technological change. This would imply a further
reduction of gross fertility for all individuals (irrespective of the education they acquire) after
the transition.
The proposed mechanism does not rely on scale effects or non-convexities like, e.g. subsistence
consumption levels. Extending the model by adding a subsistence thresholds for consumption
as in Galor and Weil (2000), Strulik (2008) and Dalgaard and Strulik (2008), would introduce
additional Malthusian features by including a corner solution in the dynamics of development.
Also, as shown by de la Croix and Doepke (2003) and de la Croix and Licandro (2007), the
consideration of corner regimes increases the likelihood of observing a temporary increase in
fertility at the onset of the transition before observing a drop after the transition.
The level of technology increases monotonically and deterministically over the course of
generations. But this instrumental prediction is obviously not necessary for the main argument
as long as productivity eventually increases enough to trigger the transition, i.e., to induce a
sufficiently large fraction of the population to acquire skilled human capital.41
In the characterization of the transition dynamics we concentrated exclusively on techno-
logical change. There are a number of other variables which can trigger the transition, with
potentially important implications for development policies. For example, the incentives for the
acquisition of skilled human capital also depend on the relative productivity of the time invested
in acquiring education. In fact, x and α are isomorphic in inducing a larger fraction of skilled
individuals λ for any T . Hence endogenous improvements in the production technologies of41Aiyar et al. (2006) propose a micro-foundation of the interactions between population dynamics and techno-
logical progress and regress in pre-industrial societies.
27
6
- T
1
0
λ
es
ΥΛ(x)
���������
T
�?
-?
�6
(a)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(b)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(c)
Figure 3: The Process of Development
model. The main results would be reinforced by the presence of a change in r∗ as in the models
in the spirit of Galor and Weil (2000), while leaving the qualitative dynamics of the system
unchanged. In particular, r∗ would be low before the take-off but would accelerate during
and after the transition due to the larger technological change. This would imply a further
reduction of gross fertility for all individuals (irrespective of the education they acquire) after
the transition.
The proposed mechanism does not rely on scale effects or non-convexities like, e.g. subsistence
consumption levels. Extending the model by adding a subsistence thresholds for consumption
as in Galor and Weil (2000), Strulik (2008) and Dalgaard and Strulik (2008), would introduce
additional Malthusian features by including a corner solution in the dynamics of development.
Also, as shown by de la Croix and Doepke (2003) and de la Croix and Licandro (2007), the
consideration of corner regimes increases the likelihood of observing a temporary increase in
fertility at the onset of the transition before observing a drop after the transition.
The level of technology increases monotonically and deterministically over the course of
generations. But this instrumental prediction is obviously not necessary for the main argument
as long as productivity eventually increases enough to trigger the transition, i.e., to induce a
sufficiently large fraction of the population to acquire skilled human capital.41
In the characterization of the transition dynamics we concentrated exclusively on techno-
logical change. There are a number of other variables which can trigger the transition, with
potentially important implications for development policies. For example, the incentives for the
acquisition of skilled human capital also depend on the relative productivity of the time invested
in acquiring education. In fact, x and α are isomorphic in inducing a larger fraction of skilled
individuals λ for any T . Hence endogenous improvements in the production technologies of41Aiyar et al. (2006) propose a micro-foundation of the interactions between population dynamics and techno-
logical progress and regress in pre-industrial societies.
27
6
- T
1
0
λ
es
ΥΛ(x)
���������
T
�?
-?
�6
(a)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(b)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(c)
Figure 3: The Process of Development
model. The main results would be reinforced by the presence of a change in r∗ as in the models
in the spirit of Galor and Weil (2000), while leaving the qualitative dynamics of the system
unchanged. In particular, r∗ would be low before the take-off but would accelerate during
and after the transition due to the larger technological change. This would imply a further
reduction of gross fertility for all individuals (irrespective of the education they acquire) after
the transition.
The proposed mechanism does not rely on scale effects or non-convexities like, e.g. subsistence
consumption levels. Extending the model by adding a subsistence thresholds for consumption
as in Galor and Weil (2000), Strulik (2008) and Dalgaard and Strulik (2008), would introduce
additional Malthusian features by including a corner solution in the dynamics of development.
Also, as shown by de la Croix and Doepke (2003) and de la Croix and Licandro (2007), the
consideration of corner regimes increases the likelihood of observing a temporary increase in
fertility at the onset of the transition before observing a drop after the transition.
The level of technology increases monotonically and deterministically over the course of
generations. But this instrumental prediction is obviously not necessary for the main argument
as long as productivity eventually increases enough to trigger the transition, i.e., to induce a
sufficiently large fraction of the population to acquire skilled human capital.41
In the characterization of the transition dynamics we concentrated exclusively on techno-
logical change. There are a number of other variables which can trigger the transition, with
potentially important implications for development policies. For example, the incentives for the
acquisition of skilled human capital also depend on the relative productivity of the time invested
in acquiring education. In fact, x and α are isomorphic in inducing a larger fraction of skilled
individuals λ for any T . Hence endogenous improvements in the production technologies of41Aiyar et al. (2006) propose a micro-foundation of the interactions between population dynamics and techno-
logical progress and regress in pre-industrial societies.
27
Evolution of Conditional Dynamic System
6
- T
1
0
λ
es
ΥΛ(x)
���������
T
�?
-?
�6
(a)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(b)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(c)
Figure 3: The Process of Development
model. The main results would be reinforced by the presence of a change in r∗ as in the models
in the spirit of Galor and Weil (2000), while leaving the qualitative dynamics of the system
unchanged. In particular, r∗ would be low before the take-off but would accelerate during
and after the transition due to the larger technological change. This would imply a further
reduction of gross fertility for all individuals (irrespective of the education they acquire) after
the transition.
The proposed mechanism does not rely on scale effects or non-convexities like, e.g. subsistence
consumption levels. Extending the model by adding a subsistence thresholds for consumption
as in Galor and Weil (2000), Strulik (2008) and Dalgaard and Strulik (2008), would introduce
additional Malthusian features by including a corner solution in the dynamics of development.
Also, as shown by de la Croix and Doepke (2003) and de la Croix and Licandro (2007), the
consideration of corner regimes increases the likelihood of observing a temporary increase in
fertility at the onset of the transition before observing a drop after the transition.
The level of technology increases monotonically and deterministically over the course of
generations. But this instrumental prediction is obviously not necessary for the main argument
as long as productivity eventually increases enough to trigger the transition, i.e., to induce a
sufficiently large fraction of the population to acquire skilled human capital.41
In the characterization of the transition dynamics we concentrated exclusively on techno-
logical change. There are a number of other variables which can trigger the transition, with
potentially important implications for development policies. For example, the incentives for the
acquisition of skilled human capital also depend on the relative productivity of the time invested
in acquiring education. In fact, x and α are isomorphic in inducing a larger fraction of skilled
individuals λ for any T . Hence endogenous improvements in the production technologies of41Aiyar et al. (2006) propose a micro-foundation of the interactions between population dynamics and techno-
logical progress and regress in pre-industrial societies.
27
6
- T
1
0
λ
es
ΥΛ(x)
���������
T
�?
-?
�6
(a)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(b)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(c)
Figure 3: The Process of Development
model. The main results would be reinforced by the presence of a change in r∗ as in the models
in the spirit of Galor and Weil (2000), while leaving the qualitative dynamics of the system
unchanged. In particular, r∗ would be low before the take-off but would accelerate during
and after the transition due to the larger technological change. This would imply a further
reduction of gross fertility for all individuals (irrespective of the education they acquire) after
the transition.
The proposed mechanism does not rely on scale effects or non-convexities like, e.g. subsistence
consumption levels. Extending the model by adding a subsistence thresholds for consumption
as in Galor and Weil (2000), Strulik (2008) and Dalgaard and Strulik (2008), would introduce
additional Malthusian features by including a corner solution in the dynamics of development.
Also, as shown by de la Croix and Doepke (2003) and de la Croix and Licandro (2007), the
consideration of corner regimes increases the likelihood of observing a temporary increase in
fertility at the onset of the transition before observing a drop after the transition.
The level of technology increases monotonically and deterministically over the course of
generations. But this instrumental prediction is obviously not necessary for the main argument
as long as productivity eventually increases enough to trigger the transition, i.e., to induce a
sufficiently large fraction of the population to acquire skilled human capital.41
In the characterization of the transition dynamics we concentrated exclusively on techno-
logical change. There are a number of other variables which can trigger the transition, with
potentially important implications for development policies. For example, the incentives for the
acquisition of skilled human capital also depend on the relative productivity of the time invested
in acquiring education. In fact, x and α are isomorphic in inducing a larger fraction of skilled
individuals λ for any T . Hence endogenous improvements in the production technologies of41Aiyar et al. (2006) propose a micro-foundation of the interactions between population dynamics and techno-
logical progress and regress in pre-industrial societies.
27
6
- T
1
0
λ
es
ΥΛ(x)
���������
T
�?
-?
�6
(a)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(b)
6
- T
1
0
λ
es
Υ
Λ(x)
���������
T
-6
-?
�6
(c)
Figure 3: The Process of Development
model. The main results would be reinforced by the presence of a change in r∗ as in the models
in the spirit of Galor and Weil (2000), while leaving the qualitative dynamics of the system
unchanged. In particular, r∗ would be low before the take-off but would accelerate during
and after the transition due to the larger technological change. This would imply a further
reduction of gross fertility for all individuals (irrespective of the education they acquire) after
the transition.
The proposed mechanism does not rely on scale effects or non-convexities like, e.g. subsistence
consumption levels. Extending the model by adding a subsistence thresholds for consumption
as in Galor and Weil (2000), Strulik (2008) and Dalgaard and Strulik (2008), would introduce
additional Malthusian features by including a corner solution in the dynamics of development.
Also, as shown by de la Croix and Doepke (2003) and de la Croix and Licandro (2007), the
consideration of corner regimes increases the likelihood of observing a temporary increase in
fertility at the onset of the transition before observing a drop after the transition.
The level of technology increases monotonically and deterministically over the course of
generations. But this instrumental prediction is obviously not necessary for the main argument
as long as productivity eventually increases enough to trigger the transition, i.e., to induce a
sufficiently large fraction of the population to acquire skilled human capital.41
In the characterization of the transition dynamics we concentrated exclusively on techno-
logical change. There are a number of other variables which can trigger the transition, with
potentially important implications for development policies. For example, the incentives for the
acquisition of skilled human capital also depend on the relative productivity of the time invested
in acquiring education. In fact, x and α are isomorphic in inducing a larger fraction of skilled
individuals λ for any T . Hence endogenous improvements in the production technologies of41Aiyar et al. (2006) propose a micro-foundation of the interactions between population dynamics and techno-
logical progress and regress in pre-industrial societies.
27
Time Series Predictions
Proposition
[Economic and Demographic Transitions] The economy ischaracterized by the following phases in the process of development:
(i) A (potentially very long) phase of stagnant development with littletechnological change, low longevity, T0 ' T, large child mortalityπ0 = π, very few individuals acquiring human capital hs , λ0 ' 0 andlarge gross and net fertility rates;
(ii) A rapid transition involving rapid increase in Tt , πt , λt income percapita yt and technological level At and a reduction in net fertility(possibly following an initial temporary increase);
(iii) A phase of significant permanent growth in technology and incomewith large life expectancy T∞ ' T + ρ, negligible child mortality π∞ ' 1all population acquiring hs human capital λ∞ ' 1 and low gross and netfertility rates.
Time Series Predictions
Proposition
[Economic and Demographic Transitions] The economy ischaracterized by the following phases in the process of development:
(i) A (potentially very long) phase of stagnant development with littletechnological change, low longevity, T0 ' T, large child mortalityπ0 = π, very few individuals acquiring human capital hs , λ0 ' 0 andlarge gross and net fertility rates;
(ii) A rapid transition involving rapid increase in Tt , πt , λt income percapita yt and technological level At and a reduction in net fertility(possibly following an initial temporary increase);
(iii) A phase of significant permanent growth in technology and incomewith large life expectancy T∞ ' T + ρ, negligible child mortality π∞ ' 1all population acquiring hs human capital λ∞ ' 1 and low gross and netfertility rates.
Time Series Predictions
Proposition
[Economic and Demographic Transitions] The economy ischaracterized by the following phases in the process of development:
(i) A (potentially very long) phase of stagnant development with littletechnological change, low longevity, T0 ' T, large child mortalityπ0 = π, very few individuals acquiring human capital hs , λ0 ' 0 andlarge gross and net fertility rates;
(ii) A rapid transition involving rapid increase in Tt , πt , λt income percapita yt and technological level At and a reduction in net fertility(possibly following an initial temporary increase);
(iii) A phase of significant permanent growth in technology and incomewith large life expectancy T∞ ' T + ρ, negligible child mortality π∞ ' 1all population acquiring hs human capital λ∞ ' 1 and low gross and netfertility rates.
Time Series Predictions: A Simulation of the Development Process
010
020
030
0lo
g In
com
e pe
r ca
pita
(19
00=1
00)
1600 1700 1800 1900 2000Year
(a) log GDP per capita (ln y)50
5560
6570
75A
dult
Long
evity
1600 1700 1800 1900 2000Year
(b) Adult Life Expectancy (T )
0.2
.4.6
.81
Sha
re S
kille
d
1600 1700 1800 1900 2000Year
(c) Share Skilled (λ)
0.1
.2.3
.4C
hild
Mor
talit
y
1600 1700 1800 1900 2000Year
(d) Child Mortality
11.
21.
41.
6
1600 1700 1800 1900 2000Year
Gross Fertility Net Fertility
(e) Gross and Net Reproduction
Rates (n, πn)1
1.2
1.4
1.6
1600 1700 1800 1900 2000Year
Fertility Skilled Fertility Unskilled
(f) Differential Fertility (nH , nL)
Time Series Data: Long-Run Development for Sweden
9010
011
012
0lo
g G
DP
per
cap
ita (
1900
=100
)
1750 1800 1850 1900 1950 2000year
(a) log GDP per capita
2530
3540
45Li
fe E
xpec
tanc
y at
Age
30
3040
5060
70Li
fe E
xpec
tanc
y at
Birt
h
1750 1800 1850 1900 1950 2000year
Life Expectancy at Birth Life Expectancy at Age 30
(b) Life Expectancy at Birth and at
Age 30
0.2
.4.6
.81
1750 1800 1850 1900 1950 2000year
Primary School Enrolment Secondary School Enrolment
(c) Primary and Secondary School
Enrolment
050
100
150
200
250
Infa
nt M
orta
lity
(/10
00)
1750 1800 1850 1900 1950 2000year
(d) Infant Mortality Rate
.51
1.5
22.
5
1750 1800 1850 1900 1950 2000year
Gross Replacement Rate Net Replacement Rate
(e) Gross and Net Reproduction
Rates
Time Series Data: Long-Run Development for England
4060
8010
012
014
0lo
g G
DP
(19
00=1
00)
1600 1700 1800 1900 2000Year
(g) log GDP per capita (U.K.)
5560
6570
Life
Exp
ecta
ncy
at A
ge 3
0
3040
5060
7080
Life
Exp
ecta
ncy
at B
irth
1600 1700 1800 1900 2000Year
Life Expectancy at Birth Life Expectancy at Age 30
(h) Life Expectancy at Birth and at
Age 30
2040
6080
100
Lite
racy
1600 1700 1800 1900 2000Year
(i) Literacy Levels (England and
Wales)
050
100
150
Infa
nt M
orta
lity
(/10
00)
1600 1700 1800 1900 2000Year
(j) Infant Mortality Rate
.51
1.5
22.
53
1600 1700 1800 1900 2000Year
Gross Replacement Rate Net Replacement Rate
(k) Gross and Net Reproduction
Rates (England and Wales)
Cross-Sectional Predictions
I The transition is driven by, and leads to, a change in “educationcomposition” in the population;
Corollary
There is a positive contemporaneous correlation between λt and lifeexpectancy (Tt and πt) over the course of development, and overall anegative contemporaneous correlation of λ with gross and net fertility.
Cross-Sectional Predictions:
Simulated data (reinterpreted cross-sectionally) and Data30
40
50
60
70
80
0 .2 .4 .6 .8 1Share Skilled
Life Expectancy at Birth Adult Longevity
(a) Adult Longevity (x),
LEB (o), λ
0.1
.2.3
.4C
hild M
ort
ality
0 .2 .4 .6 .8 1Share Skilled
(b) Child Mortality, λ
.95
11.0
51.1
Gro
ss F
ert
ility
0 .2 .4 .6 .8 1Share Skilled
(c) Av. Fertility, λ
0.2
.4.6
.81
Share
Skille
d
0 .2 .4 .6 .8 1Share Skilled 30 years earlier
(d) λt , λt−n (n=30 yrs.)
30
40
50
60
70
80
Life E
xpecta
ncy a
t B
irth
0 .2 .4 .6 .8 1Population share with some formal education (Barro−Lee)
Life Expectancy at Birth Life Expectancy at Birth
(e) LEB, λ , 1970 (o) and
2000 (x)
050
100
150
200
250
Infa
nt M
ort
ality
0 .2 .4 .6 .8 1Population share with some formal education (Barro−Lee)
Infant Mortality Infant Mortality
(f) Child Mortality, λ ,
1970 (o) and 2000 (x)
02
46
8T
ota
l F
ert
ility R
ate
0 .2 .4 .6 .8 1Population share with some formal education (Barro−Lee)
Total Fertility Rate Total Fertility Rate
(g) TFR, λ , 1970 (o) and
2000 (x)
.2.4
.6.8
1P
opula
tion s
hare
with s
om
e form
al education (
Barr
o−
Lee)
0 .2 .4 .6 .8 1Population share with some formal education in 1970 (Barro−Lee)
(h) λ 1970 and 2000
Cross-Sectional Predictions:
Simulated data (reinterpreted cross-sectionally) and Data30
40
50
60
70
80
0 .2 .4 .6 .8 1Share Skilled
Life Expectancy at Birth Adult Longevity
(a) Adult Longevity (x),
LEB (o), λ
0.1
.2.3
.4C
hild M
ort
ality
0 .2 .4 .6 .8 1Share Skilled
(b) Child Mortality, λ
.95
11.0
51.1
Gro
ss F
ert
ility
0 .2 .4 .6 .8 1Share Skilled
(c) Av. Fertility, λ
0.2
.4.6
.81
Share
Skille
d
0 .2 .4 .6 .8 1Share Skilled 30 years earlier
(d) λt , λt−n (n=30 yrs.)
30
40
50
60
70
80
Life E
xpecta
ncy a
t B
irth
0 .2 .4 .6 .8 1Population share with some formal education (Barro−Lee)
Life Expectancy at Birth Life Expectancy at Birth
(e) LEB, λ , 1970 (o) and
2000 (x)
050
100
150
200
250
Infa
nt M
ort
ality
0 .2 .4 .6 .8 1Population share with some formal education (Barro−Lee)
Infant Mortality Infant Mortality
(f) Child Mortality, λ ,
1970 (o) and 2000 (x)
02
46
8T
ota
l F
ert
ility R
ate
0 .2 .4 .6 .8 1Population share with some formal education (Barro−Lee)
Total Fertility Rate Total Fertility Rate
(g) TFR, λ , 1970 (o) and
2000 (x)
.2.4
.6.8
1P
opula
tion s
hare
with s
om
e form
al education (
Barr
o−
Lee)
0 .2 .4 .6 .8 1Population share with some formal education in 1970 (Barro−Lee)
(h) λ 1970 and 2000
Role of Mortality:
Adult Longevity and Changes in Education Composition
I The change in education composition depends on the “initiallevel” of longevity:
Corollary
I Along the development path, the correlation betweenlongevity and the subsequent change in the educationcomposition is hump-shaped.
I The longer the time horizon for subsequent changes in theeducation composition, the more pronounced is the hump andthe lower is the longevity associated with the largestsubsequent changes (the peak in the hump).
Role of Mortality:
Adult Longevity and Changes in Education Composition−
.10
.1.2
.3.4
.5.6
Cha
nge
in S
hare
Ski
lled
(ove
r 5
year
s)
50 55 60 65 70 75Adult Longevity (5 yrs. lagged)
(a) Change in λ over 5 years−
.10
.1.2
.3.4
.5.6
Cha
nge
in S
hare
Ski
lled
(ove
r 20
yea
rs)
50 55 60 65 70 75Adult Longevity (20 yrs. lagged)
(b) Change in λ over 20 years
−.1
0.1
.2.3
.4.5
.6C
hang
e in
Sha
re S
kille
d (o
ver
40 y
ears
)
50 55 60 65 70 75Adult Longevity (40 yr. lagged)
(c) Change in λ over 40 years
−.1
0.1
.2.3
.4.5
.6
30 40 50 60 70Life Expectancy at Birth in 1960
Change in population share with some formal education (Barro−Lee) (5 yrs. laggedFitted values
(d) Change in λ over 5 years(1960-
1965)
−.1
0.1
.2.3
.4.5
.6
30 40 50 60 70Life Expectancy at Birth in 1960
Change in population share with some formal education (Barro−Lee) (20 yrs. laggeFitted values
(e) Change in λ over 20 years
(1960-1980)
−.1
0.1
.2.3
.4.5
.6
30 40 50 60 70Life Expectancy at Birth in 1960
delta8_lambda Fitted values
(f) Change in λ over 40 years (1960-
2000)
Role of Mortality:
Adult Longevity and Changes in Education Composition−
.10
.1.2
.3.4
.5.6
Cha
nge
in S
hare
Ski
lled
(ove
r 5
year
s)
50 55 60 65 70 75Adult Longevity (5 yrs. lagged)
(a) Change in λ over 5 years−
.10
.1.2
.3.4
.5.6
Cha
nge
in S
hare
Ski
lled
(ove
r 20
yea
rs)
50 55 60 65 70 75Adult Longevity (20 yrs. lagged)
(b) Change in λ over 20 years
−.1
0.1
.2.3
.4.5
.6C
hang
e in
Sha
re S
kille
d (o
ver
40 y
ears
)
50 55 60 65 70 75Adult Longevity (40 yr. lagged)
(c) Change in λ over 40 years
−.1
0.1
.2.3
.4.5
.6
30 40 50 60 70Life Expectancy at Birth in 1960
Change in population share with some formal education (Barro−Lee) (5 yrs. laggedFitted values
(d) Change in λ over 5 years(1960-
1965)
−.1
0.1
.2.3
.4.5
.6
30 40 50 60 70Life Expectancy at Birth in 1960
Change in population share with some formal education (Barro−Lee) (20 yrs. laggeFitted values
(e) Change in λ over 20 years
(1960-1980)−
.10
.1.2
.3.4
.5.6
30 40 50 60 70Life Expectancy at Birth in 1960
delta8_lambda Fitted values
(f) Change in λ over 40 years (1960-
2000)
Role of Mortality:
Exogenous Improvements and Shocks
Corollary
The effect on education of an exogenous increase in longevity hasan inverse U-shape.
I Data from Acemoglu and Johnson (2007) on predictedmortality changes following the “epidemiological” revolutionin the 1940’s.
Role of Mortality:
Exogenous Improvements and Shocks−
.10
.1.2
.3.4
.5.6
30 40 50 60 70Life expectancy at Birth 1940
Change in population share with some formal education (Barro−Lee) (20 yrs. laggeFitted values(a) LEB (1940) andchange in λ (1960-1980)
−.1
0.1
.2.3
.4.5
.6
−1.2 −1 −.8 −.6 −.4 −.2Predicted Mortality Change 1940−1980
Change in population share with some formal education (Barro−Lee) (20 yrs. laggeFitted values(b) Pred Mortality change 1940-1980 and
change in λ (1960-1980)
Role of Mortality:
Permanent differences in Extrinsic Mortality Environment
I “Extrinsic” Mortality varies substantially across countries andis related to geographical characteristics [Brownmacroecology(1995), Gallup et al. irsr (1999), Guernieret al plos Biology (2004)]
Corollary
A lower baseline adult longevity, T implies (ceteris paribus:
I a later onset of the transition;
I a higher level of economic development in terms of income orproductivity at the onset of the transition.
Role of Mortality:
Permanent differences in Extrinsic Mortality Environment
Cross-sectional implications (T ∈ {46, 47, 48, 49, 50})
3040
5060
7080
Life
Exp
ecta
ncy
at B
irth
0 .2 .4 .6 .8 1Share Skilled
(a) Adult Life Expectancy and λ
0.1
.2.3
.4C
hild
Mor
talit
y
0 .2 .4 .6 .8 1Share Skilled
(b) Child Mortality and λ
11.
21.
41.
6G
ross
Fer
tility
0 .2 .4 .6 .8 1Share Skilled
(c) Average Fertility and λ
0.2
.4.6
.81
Sha
re S
kille
d
0 .2 .4 .6 .8 1Share Skilled 30 years earlier
(d) λt and λt−n (n=30 yrs.)
Role of Mortality:
Permanent differences in Extrinsic Mortality Environment
Timing of Transition (T ∈ {46, 47, 48, 49, 50})
40
50
60
70
80
Adult L
ongevity
1700 1800 1900 2000 2100 2200Year
Adult Longevity Adult Longevity Adult Longevity Adult Longevity Adult Longevity
Delay in onset of transition due to differences in baseline longevity.
Geography and Mortality: Latitude
3040
5060
7080
Life
Exp
ecta
ncy
at B
irth
1960
0 .2 .4 .6 .8Absolute Latitude
(a) LEB and latitude (1960)30
4050
6070
80Li
fe E
xpec
tanc
y at
Birt
h 20
00
0 .2 .4 .6 .8Absolute Latitude
(b) LEB and latitude (2000)
Geography and Mortality: Infectious Disease Richness
Multi-host vector-transmitted infectious agents are very localized andlittle affected by globalization and development(Smith et al., Ecology 2007).
02
46
81
0
0 .2 .4 .6 .8Absolute Latitude
Infectious Agents: Multi−host with Vector−bound Transmission Fitted values
(a) Infectious Disease Richness and latitude
[Multi-Host Vector Transmitted Diseases: Angiomatosis, Relapsing Fever, Typhus-epidemic, Trypanosomiasis(sleeping sickness), Filariasis, Leishmaniasis, Yellow Fever, Dengue, Onchocerciasis, (...)]
Geography and Mortality: Infectious Disease Richness
Multi-host vector-transmitted infectious agents are very localized andlittle affected by globalization and development(Smith et al., Ecology 2007).
02
46
81
0
0 .2 .4 .6 .8Absolute Latitude
Infectious Agents: Multi−host with Vector−bound Transmission Fitted values
(a) Infectious Disease Richness and latitude
[Multi-Host Vector Transmitted Diseases: Angiomatosis, Relapsing Fever, Typhus-epidemic, Trypanosomiasis(sleeping sickness), Filariasis, Leishmaniasis, Yellow Fever, Dengue, Onchocerciasis, (...)]
Geography and Mortality: Infectious Disease Richness
Multi-host vector-transmitted infectious agentsand Life Expectancy at Birth 1960-2000
30
40
50
60
70
0 2 4 6 8 10Infectious Agents: Multi−host with Vector−bound Transmission
Life Expectancy at Birth Fitted values
(a) Infectious Disease Richness and LEB (1960)
40
50
60
70
80
0 2 4 6 8 10Infectious Agents: Multi−host with Vector−bound Transmission
Life Expectancy at Birth Fitted values
(b) Infectious Disease Richness and LEB (2000)
Cross-Sectional Predictions over Time:
Bi-modal world distributions of mortality, fertility and education
Corollary
The cross-sectional distributions of adult longevity, child mortality,fertility and education are bi-modal, unless all countries are trapped orhave completed the transition.
Cross-Sectional Predictions over Time:
Share of agents with Some Education (81 countries, T ∈ [46, 50]).4
.6.8
11.
2De
nsity
0 .5 1Share Skilled
kernel = epanechnikov, bandwidth = 0.1373
Kernel density estimate
(a) Share Skilled (λ) (1950)
0.5
11.
5De
nsity
0 .5 1Share Skilled
kernel = epanechnikov, bandwidth = 0.1252
Kernel density estimate
(b) Share Skilled (λ) (2050)
0.5
11.
5D
ensi
ty
0 .5 1Share of 20−24 age cohort with at least secondary education
kernel = epanechnikov, bandwidth = 0.1134
Kernel density estimate
(c) Share with at least some schooling 1970
0.5
11.
5D
ensi
ty
0 .5 1Share of 20−24 age cohort with at least secondary education
kernel = epanechnikov, bandwidth = 0.0972
Kernel density estimate
(d) Share with at least some schooling 2000
Cross-Sectional Predictions over Time:
Share of agents with Some Education (81 countries, T ∈ [46, 50]).4
.6.8
11.
2De
nsity
0 .5 1Share Skilled
kernel = epanechnikov, bandwidth = 0.1373
Kernel density estimate
(a) Share Skilled (λ) (1950)
0.5
11.
5De
nsity
0 .5 1Share Skilled
kernel = epanechnikov, bandwidth = 0.1252
Kernel density estimate
(b) Share Skilled (λ) (2050)
0.5
11.
5D
ensi
ty
0 .5 1Share of 20−24 age cohort with at least secondary education
kernel = epanechnikov, bandwidth = 0.1134
Kernel density estimate
(c) Share with at least some schooling 1970
0.5
11.
5D
ensi
ty
0 .5 1Share of 20−24 age cohort with at least secondary education
kernel = epanechnikov, bandwidth = 0.0972
Kernel density estimate
(d) Share with at least some schooling 2000
Cross-Sectional Implications:
Life Expectancy at Birth (81 countries, T ∈ [46, 50]).0
05.0
1.0
15.0
2.0
25.0
3De
nsity
20 40 60 80Life Expectancy at Birth
kernel = epanechnikov, bandwidth = 6.0025
Kernel density estimate
(a) Life Expectancy at Birth (1950)
.005
.01
.015
.02
.025
.03
Dens
ity
20 40 60 80Life Expectancy at Birth
kernel = epanechnikov, bandwidth = 6.2874
Kernel density estimate
(b) Life Expectancy at Birth (2050)
0.0
1.0
2.0
3.0
4D
ensi
ty
30 40 50 60 70 801965−1970
kernel = epanechnikov, bandwidth = 3.5101
Kernel density estimate
(c) Life Expectancy at Birth 1965-1970
0.0
1.0
2.0
3.0
4.0
5D
ensi
ty
40 50 60 70 80 90Life Expectancy at Birth
kernel = epanechnikov, bandwidth = 3.4473
Kernel density estimate
(d) Life Expectancy at Birth 2000-2005
Cross-Sectional Implications:
Life Expectancy at Birth (81 countries, T ∈ [46, 50]).0
05.0
1.0
15.0
2.0
25.0
3De
nsity
20 40 60 80Life Expectancy at Birth
kernel = epanechnikov, bandwidth = 6.0025
Kernel density estimate
(a) Life Expectancy at Birth (1950)
.005
.01
.015
.02
.025
.03
Dens
ity
20 40 60 80Life Expectancy at Birth
kernel = epanechnikov, bandwidth = 6.2874
Kernel density estimate
(b) Life Expectancy at Birth (2050)
0.0
1.0
2.0
3.0
4D
ensi
ty
30 40 50 60 70 801965−1970
kernel = epanechnikov, bandwidth = 3.5101
Kernel density estimate
(c) Life Expectancy at Birth 1965-1970
0.0
1.0
2.0
3.0
4.0
5D
ensi
ty
40 50 60 70 80 90Life Expectancy at Birth
kernel = epanechnikov, bandwidth = 3.4473
Kernel density estimate
(d) Life Expectancy at Birth 2000-2005
Cross-Sectional Implications:
Child Mortality (81 countries, T ∈ [46, 50])1
23
4De
nsity
−.1 0 .1 .2 .3 .4Child Mortality
kernel = epanechnikov, bandwidth = 0.0491
Kernel density estimate
(a) Child Mortality (1 − π) (1950)
11.
52
2.5
33.
5De
nsity
−.1 0 .1 .2 .3 .4Child Mortality
kernel = epanechnikov, bandwidth = 0.0527
Kernel density estimate
(b) Child Mortality (1 − π) (2050)
0.0
02.0
04.0
06.0
08kd
ensi
ty in
fant
_mor
talit
y
0 50 100 150 200 250x
(c) Infant Mortality 1970
0.0
05.0
1.0
15kd
ensi
ty in
fant
_mor
talit
y
0 50 100 150 200x
(d) Infant Mortality 2000
Cross-Sectional Implications:
Child Mortality (81 countries, T ∈ [46, 50])1
23
4De
nsity
−.1 0 .1 .2 .3 .4Child Mortality
kernel = epanechnikov, bandwidth = 0.0491
Kernel density estimate
(a) Child Mortality (1 − π) (1950)
11.
52
2.5
33.
5De
nsity
−.1 0 .1 .2 .3 .4Child Mortality
kernel = epanechnikov, bandwidth = 0.0527
Kernel density estimate
(b) Child Mortality (1 − π) (2050)
0.0
02.0
04.0
06.0
08kd
ensi
ty in
fant
_mor
talit
y
0 50 100 150 200 250x
(c) Infant Mortality 1970
0.0
05.0
1.0
15kd
ensi
ty in
fant
_mor
talit
y
0 50 100 150 200x
(d) Infant Mortality 2000
Cross-Sectional Implications:
Gross Fertility (81 countries, T ∈ [46, 50]).5
11.
52
Dens
ity
.8 1 1.2 1.4 1.6 1.8Gross Fertility
kernel = epanechnikov, bandwidth = 0.0963
Kernel density estimate
(a) Gross Fertility (1950)
.51
1.5
22.
5De
nsity
.8 1 1.2 1.4 1.6 1.8Gross Fertility
kernel = epanechnikov, bandwidth = 0.0931
Kernel density estimate
(b) Gross Fertility (2050)
0.0
5.1
.15
.2.2
5D
ensi
ty
2 4 6 8 10Total Fertility Rate
kernel = epanechnikov, bandwidth = 0.6087
Kernel density estimate
(c) Total Fertility Rate 1970
0.1
.2.3
Den
sity
0 2 4 6 8Total Fertility Rate
kernel = epanechnikov, bandwidth = 0.5308
Kernel density estimate
(d) Total Fertility Rate 2000
Cross-Sectional Implications:
Net Fertility (81 countries, T ∈ [46, 50])4
68
10De
nsity
.95 1 1.05 1.1Net Fertility
kernel = epanechnikov, bandwidth = 0.0160
Kernel density estimate
(a) Net Fertility (1950)
05
1015
20De
nsity
.95 1 1.05 1.1Net Fertility
kernel = epanechnikov, bandwidth = 0.0122
Kernel density estimate
(b) Net Fertility (2050)
0.2
.4.6
.8D
ensi
ty
.5 1 1.5 2 2.5 3 3.5Net Replacement Rate
kernel = epanechnikov, bandwidth = 0.1837
Kernel density estimate
(c) Net Replacement Rate 1970
0.2
.4.6
Den
sity
.5 1 1.5 2 2.5 3Net Replacement Rate
kernel = epanechnikov, bandwidth = 0.1850
Kernel density estimate
(d) Net Replacement Rate 2000
Simulation and Data
Timing of transition
I Child Mortality improvements are more rapid than in simulation;
I Exit from trap is “quicker in the data” compared to the simulation(acceleration of development);
I Controlled experiment: Only variation in T leading to a constantspeed of exit from trap;
I Cross-country spillovers in medical knowledge and technologyI Public policiesI Institutional change
Simulation and Data
Timing of transition
I Child Mortality improvements are more rapid than in simulation;
I Exit from trap is “quicker in the data” compared to the simulation(acceleration of development);
I Controlled experiment: Only variation in T leading to a constantspeed of exit from trap;
I Cross-country spillovers in medical knowledge and technologyI Public policiesI Institutional change
Summary
I Unified theory of the economic and demographic transition in linewith historical and cross-country patterns of development thataccounts for changes in education composition and differentialfertility;
I Endogenous transition (exit from development trap)
I requires joint improvements in T , π, AI highlights different roles of adult longevity (composition) and
child mortality (fertility):I Take-off: iff change in λ
I Predictions on both time series and cross country dimension
I Study the distinct role of mortality: shocks and extrinsic differences.