From Duty to Right:
The Role of Public Education inthe Transition to Aging Societies

By
Yoshiaki Sugimoto
Masao Nakagawa
1Objective
Develop a growth theory to analyze:- changing role of public education in theprocess of economic development;- allocation of government resources between
generations (i.e., endogenous policy);- population aging and economic-growth
slowdown in the long-run.
2

Key Elements
1. The notion of public education
Duty: poor households rely on child labor
Right: education investment is desirable
2. Generational Conflict
Old: Pensions and Social Securities
Young: Education and Child Care
Note: Relative political power changes with theage structure3Ratio%1.2

201
150.80.6

100.4

Old Share (%)

Public Service Ratio

Political Bias in Japan: 1973-2004

50.2

OLD AGE / UNIVERSITY
OLD SHARE (%)
00
1973

1976

1979

1982

1985

1988

1991

1994

1997

2000

2003

4

Political Bias in the UK: 1960-2002
170.90.8

16% of 65+

0.7

150.6
140.5
130.4
120.3
0.2

110.1

101960

1965

1970

1975

1980

1985

1990

1995

2000

Old Share (%)

Public Service Ratio

Pensions / UniversityPolitical Bias in OECDCountries 2000
4.03.53.0
2.5
2.0
1.5
1.0
0.5
0.0051015

Percentage of Age 65 and over206

Central Argument
Education and Population in the Growth
Process:
Stage of Public Education as a Duty-- Compulsory schooling prohibits child labor
and retards population growthStage of Public Education as a Right-- Vicious cycle between undersupply of public
education and population ageing
7

Economic Development
Education as aDuty

Compulsory
Education

Education as aRight

Fertility

PrivateEducation

PoliticalPower of theOld

PublicEducation

Child Labor

Fertility8Literature Review
1. Galor and Moav (2006)
Birth of public schooling on the course of industrialization→ No population growth
2. Doepke and Zilibotti (2005)
Legislation of child labor laws and fertility decline→ Child labor laws ≈ Education as a duty
→ No transition of public education from duty toright
3. Holtz-Eakin et al. (2004)
Educational policy determined through generational conflict→ Exogenous population growth9

By contrast, this Paper…
• Analyzes the interaction between educational
policy and population growth;• Reveals the changing effects of educational
policy on fertility;• Demonstrates the rise and fall of educational
policy.
10

The Features of the Model
1. Quantity-Quality trade-off
2. Substitutability b/w Public and Private Education
3. Public education as a Child Labor Regulation
4. Skill (Age)-biased Tech Progress
5. Generational Conflict

11

The Evolution of the Economy
Stage I:-- No HC Investment-- Tech progress driven by population growthStage II:-- Legislation of public rducation, which isa duty for the poor-- Fertility Decline

Stage III:-- Public education as a right for the young-->Political Conflict with the Elderly
12

The Evolution of Fertility inStage III13

Economic Growth Slowdown
The size of population may shrink toward zeroin the long run.

The growth rate of technology converges tozero in the long run:

14

Policy Implication
Education Policy works as a means to:- support child care;- prevent population aging andeconomic-growth slowdown;
only if the productivity of public education ishigh.
15

Economic Development
Education as a
Duty

Compulsory
Education

Education as a
RightFertility

PrivateEducation

Political
Power of theOld

PublicEducation

Child LaborFertility

16

Implication
Get : the quantity of public educationi Ghe
Therefore, 12 ( t ,et ) is sufficiently large
when…

public education has high quality
competitive with private education
17

Technological Progress

A − A = g(H ),At +1tt +1t

whereg (0 ) = 0g′( H ) > 0∀H ≥ 018

Economic Development
Education as a
Duty

Compulsory
Education

Education as a
Right

Fertility

PrivateEducation

PoliticalPower of theOld

PublicEducation

Child Labor

Fertility

19

Skill Acquisition
ht+1 = a h (et ,et )iiiGwhereie t : Private Education
Ge t : Public Educationh j > 0, h j < 0 and h < 0j12i.e., Private and public edu are substitute.
20

Aggregate Human Capital

Ht +1()= ∑ ht+1 N t +1T t +1iiii= R,PNote: Agg HC depends on fertility rates as well
as skill levels
21

Production• Closed OLG Economy• Single final good
• Two independent production sectors• Employ only labor(children, adults, and the elderly)
22Sector A
Employ only adult workers

Y =AHAtttwhereA … Technology Levelt

H t … Efficiency units of labor
23Sector B• Less advanced technology• Employ child and old workers

Y =wLBtt

w …stationary level of technology

L … number of workers
t24Households- Live and work for 3 periods- Born in period t-1- Belong to group i
1st period (t-1): work and education
2nd period (t): work and child-rearing
3rd period (t+1): work and consume public good x25

1st period (childhood)-- Work in Sector A to earn ωit-- Receive public and/or private education-- Consume a time fraction δ of her parent26

2nd period (adulthood)-- Acquire ht units of efficiency labor-- Work in Sector A to obtain wt ht-- Choose the quantity and quality of children---> determines the work time of children
27Income in the 2nd Period[It = zt 1− (δ + et − ωt ) nt
iwhereziiii]

it : her potential incomeite : private education for childrenω : child labor income
itit

n : number of children
28

3rd period (elderhood)-- Work in Sector B-- Spend income on consumption-- Enjoy the public service for the elderly, xt +129

Income in the 3rd Period=w=cIt
33t +1wherew : stationary wage rate in Sector B
3t +1 : consumption in elderhoodc30

Lifetime Utility Function
U =u +ρ ui
titi 3t t +1whereρuui
t : income-dependent discount ratei
:instantaneousutilityin
2ndperiodt

3: instantaneous utility in 3rd periodt +131

Utility in Adulthoodut = α ln ct + (1 − α ) ln nt
iii

whereict : consumptionint : number of children
32Utility in Elderhood()u t +1 = (1 − β ) ln min γ ct +1 , xt +1 + β ln ht +133i

where
3ct +1 : consumption

xt +1 : public good for the elderlyiht +1 : human capital of her child (whois adult in period t+1)

33

Supply of Child Labor(lt = l et + etiiG)ie t : Private Education
Ge t : Public Educationl (0 ) = 1; l (e ) = 0∀ e ≥ eˆ-> Public Education restricts child labor 34

Child Labor Wage()w ⋅ l et + etiGiωt =≡ ω et , et , ztiztii

G()

wherew : Wage rate in sector Bi
ωt : Child labor wageizt : Potential income of her parent
35

Human Capital(ht +1 = a h et , etiiiG)

whereai: ability of group i

h j > 0, h j < 0 and h < 0j12i.e. private and public edu are substitute36

Optimization (Adulthood)Price takers with perfect foresight
Maximize the objective function:v t = {(1 − α ) ln [1 − (δ + et − ω (et , et , z t ))nt ]+ α ln n + ρ (z )β ln h (e , e )}ii(iiiGtttt≡ v n t , et , et , z tiiiGiGii)
37

Private Education
if0⎧
eti = e etG , zti ≡ ⎨ G⎩φ et ≥ 0 if()( )w / δ < zti < z ∗zti ≥ z ∗whereφ (et ) + et > eˆ and φ ′(et ) < 0 ∀ et < eˆ
GG

GG

38

Fertility
1−α
⎧i
∗
1>
if
Giw
/
δ<z<z⎪δ − ω 0, e , zt⎪ttnti = n etG , zti ≡ ⎨i∗
⎪ 1−α > 0
ifz
≥
zt
G
⎪⎩δ + φ et()

()

( )

Note: The effect of public education changes
qualitatively
39The Government
Tax on adult individuals every period->obtains ατN t units of time
Allocate the tax revenues between- Public education for children- Public service for the elderly40Supply of Public Education
et =Gεtατε tnt: budget share of public educationnt ≡ N t +1 / N t : growth rate of population
41

Public Service for the Elderly
xt =(1 − ε t )ατ N tN()= ατ − etG nt nt −1t −1≡ x (etG , nt , nt −1 )nt −1 : adult/old ratio

nt : child/adult ratio
42Technological Progress−AA= g (H )g≡
At +1tt +1ttg (0 ) = 0g′( H ) > 0∀H ≥ 043

Aggregate Human Capital

Ht +1()= ∑ ht+1 N t +1T t +1iiii= R,P= α N [qt nt ht +1 + (1 − qt )nt ht +1 ] ≥ α N
RRPPtt +1qt : share of group R among adults
Note: Agg HC depends on fertility rates as well
as skill levels
44Class Structures
Group R … high ability when adultGroup P … low ability when adulta >aR

Recall that:P(ht +1 = a h et , etiiiG)

Note: Individuals are identical in 1st and 3rd period.
45

Initial Conditions
h =α > h =1R0RP0N =q N >0R000w / δ < (1 − τ ) A0 < z ∗ / a R

q0 : fraction of group R among adults
46

The Political System
et = λt [θet + (1−θ)et ]+ (1− λt )et
GWhereGRGP

G3λt ∈ (0,1)λt : political power of the adult generationθ : political power of group R among theadult generation

λt = λ (nt −1 )∀nt −1 ≥ 047

Policy Preferences
Adult Individuals’ desirable edu policies:(et = arg max v nt , et , et , ztiGiforzt < z∗forzt ≥ z∗Gi

⎧0= ⎨⎩τiiii)

48

Policy Preferences
The Elderly’s Objective Function[(v = min γw , x e , nt , nt −13tGt)]
49

Policy Preferences
The Elderly’s Desirable Policy
if et ≤ et⎧eG3t
et = ⎨G2ife>e()emax,0ttt⎩
G2G2e is such that γ w = x ( et , nt , nt −1 )50

Stage I: Economic Growth
Driven by Pop Expansion∗zt < zt < zPR∀t < t∗

It follows thatρt = ρt = 0RP

51

Education and CL in Stage Iet = et = et = 0i

GiGzt = (1 − τ )a Atii

[ ]∀t ∈ 0, t∗lt = lt = l (0) = 1RP

All children work and receive no education
52

Fertility in Stage I
1−α1−αP
1 < nt =< nt =Rδ − w / zt
δ − w / ztPR+NNNnt ≡=NNt +1tNote:

RPt +1t +1= qt ntR + (1 − qt )ntPtqt +1 ≤ qt--> the group R is decreasing its share over time
Note: the trend of nt is ambiguous
53

Stage II: Education Reformwith Class Conflictzt < z < zt ∀t ∈[t ,t′)∗PR∗

It follows thatρt = ρ > ρt = 0
R

Pi.e., only group R cares about HC of their children
54

Educational Policy in Stage II
et = τ > et = 0 ∀t ∈ [t , t ′)
GR

GP

∗

i.e., Education is undesirable for the pooret = θτ < eˆG∀t ∈ [t , t ′)∗55

Private Edu and CL in Stage IIet = φ (θτ ) > et = 0∀t ∈ [t , t ′)lt = l (φ (θτ ) + θτ ) = 0;

ltP = l (θτ ) > 0RRP∗∀t ∈ [t , t ′)∗56

Potential Income in Stage IIzt = (1 − τ )At a h(φ (θτ ),θτ )⎫⎪∗
′tt,t∀∈⎬P⎪⎭
zt = (1 − τ )At h(0,θτ )Ri( ]reflecting between-group inequality inprivate education.
57

Public Education as a Dutyi

GR

Given nt , education level et would
reduce consumption of group P, which is[ (()) ]ct = zt 1− δ − w 0, et , zt nt
PPGPP∀ t ∈ [t , t ′ )∗58Fertility in Stage II1−αnt =;δ + φ (θτ )R

1−αnt =>1P
δ − ω 0, θτ , ztP()

59

Population Growth in Stage II
nt = qt nt + (1 − qt )nt
RP

Proposition: If the initial share of group R,q , is sufficiently small under (A1)-(A4),0education policy in period t ∈[t ,t′)decreases the average fertility nt∗60

Stage III: Social Ageing &Generational Conflict∗z < zt < ztPR∀t ≥ t ′It follows thatρt = ρt = ρ > 0R

Pi.e., All individuals care about HC of their children
61

Private Edu and CLin Stage III( )l = l = l (φ (e ) + e ) = 0et = et = φ et > 0∀t ≥ t ′

RPG

Gtttt

∀t ≥ t ′R

P

Gi.e.,No CL regardless of educational policy
62

Educational Policy in Stage IIIet = λ (nt −1 )τ + [1 − λ (nt −1 )]e (nt , nt −1 )G

≡ e (nt , nt −1 )G∀ t ≥ t′63

Fertility in Stage III1−αnt = nt = nt =G
δ + φ etRP( )∀t ≥ t ′The fertility rate of group P above is lower
than that in the previous stages, as they nolonger use child labor64

Proposition 5
The growth rate of technology, g t ,converges to zero in the long run under(A1)-(A5) with the following conditions(a) Public education is sufficiently productive;i.e., h (et , et ) is sufficiently large for all (e , e ) ≥ 0i2

Git

Gt65

Assumptions• (A1)• (A2)• (A3)D (eˆ, eˆ) = ρβh(eˆ, eˆ)(δ + eˆ) − αh(eˆ, eˆ) > 0h*~z<z

⎧ h0R = α R > h0P = 1⎪⎪ R⎨ N 0 = q0 N 0⎪∗R()
w/
δ
1
τz/
a<−<⎪⎩A066

Assumptions• (A4)

θτ < e• (A5)

maxe

min

< eˆ

< τ < eˆ67

Proposition 5
The growth rate of technology, g t ,converges to zero in the long run under(A1)-(A5) with the following conditions:(b) The substitutability between public andprivate education is sufficiently strong;i.e., h (et , et ) is sufficiently small for all (et , et ) ≥ 0iGiG

1268

Implication
Get ; the quantity of education
Therefore, those conditions on the h function aresatisfied when…
public education has high quality
competitive with private education69

Implication
Educational Policy works as a means to:- support child care;- prevent population ageing andeconomic-growth slowdown;
only if the quality of public education is high.
70