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)

���������

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

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.