the effects of education subsidies and child-labour laws on … · 2007-05-11 · introduction and...

Introduction and MotivationModel Setup

EquilibriumIntuition and Results

The Effects of Education Subsidies andChild-Labour Laws on Fertility and Education

ChoiceLecture 5

Based on Doepke (2005)

Economic Policy in Development 2, Part 2

May 4, 2007

Lecture 5, Human Capital and Fertility 1/49 Economic Policy in Development 2, Part 2



Outline

Introduction and MotivationReviewMotivationMalthus vs. SolowStylized facts

Model SetupTechnologies (Hansen and Prescott (2000)Preferences, policies and budget constraint

EquilibriumProposition 1Proposition 2Proposition 3Proposition 4

Intuition and ResultsBehavior of the ModelCalibration and computational experiments




Some correlations 3

Total Fertility Rate in Year t :

number of children a typical woman would have if the currentage specific fertility rates were to prevail in the future

◮ with Gross Domestic Product (-)

◮ with Infant Mortality Rate (+)

◮ with Life Expectancy (-)

◮ with Years of Schooling (-)

◮ with Labour Income Tax Rate (-)

(see Figures from X&Y, BJ, BDJ)




ReviewMotivationMalthus vs. SolowStylized facts

Intro 4

Accounting for fertility behaviour

→ important challenge for theories of development

→ demographic change affects economic performance

1. High population growth dilutes the stock of physical capital→ negative effect on income per capita

2. High fertility rates tend to be associated with low education→ high fertility countries accumulate less human capital





Intro 5

Third channel from the demog. transition to growth:

→ Changes in the age structure of the population

Rapid fertility decline lowers the dependency ratio since initiallyboth the old-age and child-age cohorts are small relative to theworking-age population.

Hence, fast fertility transition

⇒ size of the labour force increases faster than total population

⇒ sizable, if temporary, boost to level of output per capita,





Recall 6

Recall the simple models of fertility choice. We have studiedthe qualitative and quantitative properties of the Becker Barroand Barro Becker (hereafter B&B) models of fertility along withone based on the ideas of Caldwell (1978) on the demand forchildren as a source of old age support, see Boldrin Jones(B&J henceforth) for the model formalization.





The US and UK experience 1800-1990 7

From BJ (2002), we see that mortality decline andimprovements in financial market technologies seem to be oneof the major determinants of fertility decline (example of UK) –BJ model success

From JS (2007), we see that both productivity growth (before1850) and mortality (after 1850) decline seem to be the majordeterminants of fertility decline (example of US) – BB modelsuccess

The quantitative success of such simple models makes usoptimistic about the power of this class of models as potentialpositive models of fertility.





Policy in the BB and BJ Models 8

◮ Cross-country Income Tax differences

→ higher taxes, lower fertility

◮ Pensions

→ larger social security system, lower fertility?

◮ Child-labour laws and compulsory schooling

→ quantity-quality trade-off





Last week: 2 steps, Today: 1 big one 9

1. Determinants of educational choice

2. Think about reasons for and alternatives to child labour

3. Today: Incorporate these into B&B model of fertility choice(Doepke (2005))

Explore the ability of differences in educational and childlabor policies, to explain cross-country variations in theSPEED of fertility decline.





Motivation 10

Explore the ability of differences in educational and child laborpolicies, to explain cross-country variations in the SPEED offertility decline.

Motivation:

◮ Many economic models of fertility choice

→ quantity-quality tradeoff between the number andeducation per child

⇒ If fertility and education joint decisions, governmentpolicies that affect opportunity cost of education→ first-order effect on fertility.





Motivation 11

Explore the ability of differences in educational and child laborpolicies, to explain cross-country variations in the SPEED offertility decline.

Motivation:

◮ Observe large variations in educational and child laborpolicies

→ across countries during the transition to growth

→ extent and timing of these reforms varies widely

Brazil and Korea are drastic examples.





Intro ) 12

Here we will examine how people decide on the number ofchildren they have and how much education to provide.

Growth and industrialization are closely connected to fallingfertility rates.

→ 19th century England

→ same way for Asian countries that only recently began togrow at high rates and catch up with Western countries

Understanding these changes in fertility should help explainwhy some economies start to grow, while others remain poor.





Malthus vs. Solow (from Doepke (2005)) 13

First economist to think in a systematic way about growth andfertility: Thomas Malthus.

“Essay on Population” (1798), basic thesis:

◮ Fertility checked only by the food supply

◮ As long as enough to eat, people produce children

◮ Leads to population growth rates in excess of the growth inthe food supply

◮ People would be pushed back down to the subsistencelevel

According to Malthus’s theory, sustained growth in per capitaincomes was not possible.





Intro 14

Of course, today we know that Malthus was wrong, at least asfar as the now industrialized countries are concerned.

His theory was an accurate description of population dynamicsbefore the industrial revolution, and in many countries it seemsto apply even today.

Stated in modern terms, Malthus thought that children were anormal good. When income went up, more children would be“consumed” by parents.





Production functions 15

Malthusian production function:

One fixed factor of production (land) ⇒ decreasing returns topopulation

Optimal Ratio Fixed, stagnation at steady state(if no exogenous technological progress)

Endogenous growth (AKH model, Lecture 1):

Two accumulable factors of production (physical and humancapital) ⇒ constant returns to human capital

Optimal Ratio Fixed, both grow at constant rate in the long-run





Stylized facts 16

1. All economies start out with a long phase of stagnatingliving standards.Reason: population and output grow at the same rates ⇒GDP per capita is constant

2. Countries ultimately arrive to a growth regime in whichthere is sustained growth in output per capita with a fall infertility.

3. Speed and timing of the fertility decline differ widely acrosscountries.





Stylized facts 17

Examples: Bazil (B) and South Korea (SK)

◮ 1960: total fertility rate is 6.0 in both countries (TFR)◮ later 1960s and 1970s: B and SK grew; real GDP per

capita grew at 6% per year.◮ fertility started falling; however it fell below the replacement

level (level at which population growth becomes zero iffertility atys constant) in SK, but stayed above thereplacement level in B.

◮ SK had strict child-labor laws, B did not




Technologies (Hansen and Prescott (2000)Preferences, policies and budget constraint

Technologies (Hansen and Prescott (2000)) 18

1. Agricultural technologyAggregate: YF = AF (LFS)θs (LFU)θu Z 1−θs−θu

Individual: yF = AF (lFS)θs

θs+θu (lFS)θu

θs+θu

where AF = AF

((LFS)θs (LFU)θu

)−

1−θs−θuθs+θu Z 1−θs−θu

whith θs + θu < 1

2. Industrial technologyAggregate: YI = AI (LIS)1−α (LIU)α

Individual: yI = AI (lIS)1−α (lIU)α





Stylized facts 19

3. Assumptions:◮ (1 − α) > θs i.e. industrial technology is more skill intensive

◮ A′

F = γF AF and A′

I = γIA

4. State vector: x = {AF , AI , Ns, Nu}

State space: X = ℜ4+





Preferences (Barro and Becker (1988)) 20

1. Utility function:

ui = cσi + β (nis + niu)−ǫ [nisV ′

s + niuV ′

u]

whereV ′

s is children’s utility is skilled,V ′

u is children’s utility if unskilled,σ ∈ (0, 1) elasticity of utility w.r.t. consumption,β ∈ (0, 1) general level of altruism,ǫ ∈ (0, 1) elasticity of altruism w.r.t. number of children.





Policies 21

2. Policies

◮ Child labor restriction: lower φu .The government chooses a function φu(.) such that0 ≤ φu(x) ≤ φu for all x .

◮ (determines how much time children work)

◮ Education subsidy : subsidize a fixed amount δ of theschooling cost for all children at school.

◮ The government chooses a function δ(.) such that0 ≤ δ(x) ≤ 1 for all x .





Budget constraint 22

3. Budget constraint:

ci + ρ (nis + niu) + (1 − δ (x))φsws (x) nis

≤ (1 − τ(x)) [1 − φ(nis + niu)] wi(x) + φu(x)wu(x)niu




Proposition 1Proposition 2Proposition 3Proposition 4

Maximization problems 23

1. Problem of the Adult of Type i, where i denotes skilled orunskilled:

Vi(x) = max{cσ + β (nis + niu)−ǫ [nisV ′

s + niuV ′

u]}

subject to the budget constraint and the equilibrium law ofmotion x

′

= g(x)





Maximization Problems 24

2.a Firms Problem:

Agriculture sector :

ws(x) = AFθS

θS+θu

LFU(x)θu

LFS(x)1−θSZ 1−θu−θS

wu(x) = AFθu

θS+θu

LFS(x)θS

LFU(x)1−θUZ 1−θu−θS





Maximization Problems 25

2.b Firms Problem:

Industrial sector :

ws(x) = AI(1 − α)( LIU(x)LI S(x))

α if LIU(x), LIs(x) > 0

wu(x) = AIα( LIs(x)LI u(x))

1−α if LIU(x), LIs(x) > 0





Market Clearing 26

1. Define:

λi→j(x) fraction of adults of type i who have children oftype j ,if state is x

ηj(i , x) number of children of type j for type i parents

2. Labor supply:

Ls(x) = [1− (φ+ φs)λs→s(x)ηs(s, x)−φλs→u(x)ηu(s, x)]Ns

−φsλu→s(x)ηs(u, x)Nu

Lu(x) = [1 − φλu→s(x)ηs(u, x) − φλu→u(x)ηu(u, x)]Nu

+φu [λs→u(x)ηu(s, x)Ns + λu→u(x)ηu(u, x)Nu ]





Market Clearing 27

3. Assume:

Skilled adult can perform both skilled and unskilled work,so that ws(x) ≥ wu(x)

4. Market clearing conditions for labor market:

LFS(x) + LIS(x) ≤ LS(x) = if ws(x) > wu(x)

LFU(x) + LIU(x) = LU(x) + [LU(x) − LFS(x) − LIS(x)]





Government balances its budget 28

Budget Balance

τ(x) =δ(x)φsN

′

sws(x)

LS(x)ws(x)+LU (x)wu(x)+φsN′

sws(x)





Laws of Motion 29

N′

s = λs→s(x)ns(S, x)Ns + λu→s(x)ns(U, x)Nu

N′

u = λs→u(x)nu(S, x)Ns + λu→u(x)nu(U, x)Nu





Definition: Recursive Competitive Equilibrium 30

Given a government policy {φu , δ} , a RCE consists of a taxfunction,τ value functions , labor supply functions LS , LU , labordemand functions LFS, LFU , LIS , LIU , wage functions ws, wu ,mobility functions, policy functions ηs, ηu which map{SxR}xR+ → R+ and a law of motion g mapping X into itselfsuch that· consumers’ problem is solved· firms’ problem is solved· tax function satisfies balances government’s budget· markets clear· laws of motion satisfy equations given above





Proposition 1 31

Proposition 1:

Firms will be operating in the industrial sector only if the skilledand unskilled wages wS(x) and wU(x) satisfy the condition:ws(x)1−αwu(x)α ≤ AI(1 − α)1−ααα

Agriculture sector will operate under all wages.





Proposition 2 32

Proposition 2:

Let ε 6= 0. Then either f = 0 or f = 1.

Intuition:

Let ε = 0. Now if Vsρs

= Vuρu

,then the adult is indifferent between

having skilled & unskilled child. If ε 6= 0,then [ fρs

+ 1−fρu

]−ǫis aconvex function of ε,hence we only have corner solutions.





Proposition 3 33

Proposition 3:

An adult is indifferent between skilled and unskilled child iffcost and utilities satisfy:

Vs(ρs )1−ǫ = Vu

(ρu )1−ǫ





Proposition 4 34

Proposition 4:

In equilibrium, for any x ∈ X such that ws(x) > wu(x), thefollowing must be true:

◮ A positive fraction of skilled adults has skilled children, anda positive fraction of unskilled adults has unskilled children:

λS→S(X ), λU→U(X ) > 0

◮ Just one type of adult can be indifferent between the twotypes of children:

λS→U(X ) > 0 ⇒ λU→S(X ) = 0λU→S(X ) > 0 ⇒ λS→U(X ) = 0





Intuition 35

Intuition

Unskilled children are relatively more ’expensive’ for skilledparents and vice versa.

φwu(x)+φsws(x)+ρ

φwu(x)−φuwu(x)+ρ> φws(x)+φsws(x)+ρ

φws(x)−φuwu(x)+ρ

which after some algebra gives:

φwu(ws − wu) + φsws(ws − wu) > 0

This results from the particular cost structure and is a crucialassumption to get the desired results.




Behavior of the ModelCalibration and computational experiments

I. Malthusian regime 36

Assume at t = 0,

ws(x)1−αwu(x)α > AI(1 − α)1−ααα

Malthusian regime: wages stagnate, population growth offsetsimprovements in productivity

Key features that generate this:◮ children are a normal good, w ↑⇒ n ↑◮ agricultural technology exhibits decreasing returns to the

size of the labor force, n ↑⇒ w ↓◮ there is a goods cost ρ for each child (otherwise population

growth > productivity growth, and w would tend to 0)

Note: in steady state, fertility rate is higher for unskilled adultsLecture 5, Human Capital and Fertility 36/49 Economic Policy in Development 2, Part 2




II. Transition 37

Assume AI increasing over time (even if only YF operated)

Transition: At some point ws(x)1−αwu(x)α ≤ AI(1 − α)1−ααα

Now both technologies are used.

Changes:

◮ population growth does not depress wages in sectorI ⇒ w ↑↑⇒ Y/L ↑ at the same rate as AI

◮ YI more skill-intensive ⇒ ws/wu ↑⇒ returns to educationincrease ⇒ more unskilled parents choose skilled kids

Overall effect on fertility is ambiguous

◮ IE ⇒ more children◮ SE ⇒ less children but skilled





III. Policy introduction 38

Policy introduction:

◮ subsidy: tends to increase fertility, because the cost ofeducation is reduced

◮ child labor restrictions: tends to decrease fertility andincrease incentive to have skilled children, because thecost of having (unskilled) children increases





IV. Growth regime 39

Growth regime:

YI ↑↑ until YF negligible ⇒ BGP

Here fertility is lower because YI more skill intensive.

Average fertility is lower for skilled than unskilled adults.

The state variable is reduced to (NS/Nu, AI) .





How MUCH does it matter? 40

1. Calibration

2. Malthusian regime: data for England, relatively high quality

3. Growth regime: U.S. data

4. Transition: to test the model





Table 41

Insert Table





Computational experiments 42

Computational experiments

1. All economies start from identical conditions. AF , Ls, Lu sothat economies start in Malthusian steady state.

2. AI chosen such that transition starts 2 periods after thestart of the simulation (i.e. t = 2).

3. Apart from different timing of policy reforms, all simulationsare identical.





Policy reforms 43

Policy reforms:

◮ ”Brasilian” policy: no reform

◮ ”Korean” policy: immediate reformφu(x) = 0, δ = 0.5 end of t = 2

◮ ”English” policy: delayed reformφu(x) = 0, δ = 0.5 end of t = 5

Start of transition:

1950 for Brazil and South Korea

1800 for EnglandLecture 5, Human Capital and Fertility 43/49 Economic Policy in Development 2, Part 2




Effect on Growth Rates 44

1. Growth rate:

Policies have only temporary effect on growth rate becauseproductivity growth is exogenous.

Highest growth rate achieved for ”Korean” policy.





Effect on Total Fertility Rate 45

2. Total Fertility Rate:

Increases slightly before the start of transition and declinesin all simulations.

Speed and timing different:◮ ”Brasilian” policy: fertility decreases slowly to TFR of 3.

◮ ”Korean” policy: TFR drops below 3 at start of transition,replacement fertility reached in less than 2 generationsafter take-off

◮ ”English” policy: TFR falls right at outset, but gains speedafter policies introduced





TFR skilled vs. unskilled 46

3. Relative Total Fertility Ratebetween unskilled and skilled parents

◮ ”Brasilian” policy: stays large

◮ ”Korean” policy: declines rapidly

◮ ”English” policy: declines later

Data seems to confirm this pattern





new 47

4. Income distribution:

Initial increase due to increased demand for skilled (needskilled in sector I and as teachers), then decrease becauseof increased supply

◮ ”Brasilian” policy: inequality high and increases duringtransition.data: Gini coefficient between 0.5 and 0.6.

◮ ”Korean” policy: inequality generally low and decreasesslightly during transition, because increase in skill supplyfaster.data: Gini coefficient between 0.3 and 0.4.

◮ ”English” policy: Kuznets curve (U-shaped relationshipbetween income and inequality)





Effects of Individual Policies 48

5. Each policy individually:

It turns out that the child labor restriction alone has a muchbigger impact than the education subsidy.

Question: Which one is more easily enforced?





Concluding remarks 49

1. One calibration, 3 qualitative results.Quantitatively there are many issues.

2. Main criticisms:

◮ no capital◮ no mortality rate◮ particular cost structure (to which the model is sensitive)◮ implications for magnitudes of child labor not confronted

with data


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