Relation between education and economic growth

1. The conflict
Growth & Inequality
The role of education sector:
sub-Saharan Africa
Akash asija
Arhit ghosh
Aritra chakrabarty
Debanjan biswas
Naveen kumar

2. The models of endogenous growth theory focus on
productivity improvements through the creation
and implementation of new ideas.
Economists analyze the incentives for R&D as the
input to production process, thus endogenizing
the rate of technological progress. Theoretical
models assume R&D activities to depend on the
availability of skilled labour. These models allow
to analyze to what extent skilled individuals will
be involved in research, given the presence of
other activities.

3. In the context of „new growth theory‟, education is
important because certain educated will create new
ideas in the private sector; fuelling R&D investments
and the creation of ideas. State funding can also be
considered as complementary to private R&D
expenditure, both which tend to raise long-run growth
rates.
Paul Romer, one of the pioneers of endogenous growth
theory, discussed how these models might inform
education policy. Input to R&D, determined by the
quantity of education, is the engine of growth, as
noted by Romer.

4. The Lucas model
In the Lucas model, human capital is regarded as a
factor of production and knowledge takes a central
position which accelerates economic growth. It is a
two-sector model-goods sector and the education
sector. The former produces output with physical and
human capital.
Once we define an education sector, three immediate
questions arise-
 What are the inputs to education and how do we
gauge them
 What is the output from this sector and how is
quantified
 How should the inputs be combined

5. u: proportion of total labour time spent
working
h: stock of human capital.
Rewriting in per-capital terms, we have-
Which is shows constant returns to scale to
both inputs
Mankiw (1995) draws a distinction between „knowledge‟ and „human
capital‟. His insight shows that since lifetimes are finite, there‟s a maximum
limit to which human capital can be accumulated. Thus, it alone cant
guarantee perpetual growth. Knowledge, defined as the sum total of technical
and scientific discoveries, can be accumulated indefinitely and can be looked
as the source of long-run growth. Thus as Mankiw defines it, endogenous
growth models should focus on the process of research and technological
development than on human capital accumulation.
This makes interpretation from this model difficult and economists consider
this model as a tool of normative rather than for positive analysis.

6. The Ramsey-Cass-Koopmans version
According to the R-C-K version of social optimiser
situation, Lucas examined his model of endogenous
growth under this wherein a social planner seeks to
optimize to the value of k & h, i.e. solve for their
steady state.
At the steady state, all the macro-variables grow at a
constant rate given by:
This along with the differential equation of h, gives
the steady state growth path of human
capital, consumption and output. The key
parameter is φ, which corresponds to the interest
rate and also to the efficiency of human capital.

7. Carrying the R-C-K version forward, Lucas sought to
gauge the influence of external factors on human
capital. The basic idea here is that humans tend to be
more productive when surrounded by productive and
active human capital.
h̄: average wealth of human capital in the population.
ψ: coefficient measuring the response of ith individual to
external factor; i.e. high level of human capital.
Working with this model, Lucas showed that the under
decentralized setup, the steady-state rate of growth of
human capital for an individual economic agent is given
by-

8. Lucas also shows that the decentralised solution obtained is
suboptimal because individual consumers do not receive the full
benefits accruing to the society due to accumulation of own
stock of knowledge. Devoting more time to increasing hi will
add to the stock of h̄, which benefits all others in the society
including themselves who accumulate.
Moreover, the social optimal solution talks of greater
investment requirement in human capital than under the case of
decentralised solution. This is not surprising since individual
consumers will try to maximise own utility and hence add to
stock of individual knowledge base. Whereas a social planner
would need to invest more to add to the stock of knowledge of
the society to benefit all.

9. Sub-Saharan Africa-the reality
For decades, sub-Saharan Africa has been counted
among the most knowledge-handicapped regions
in the world. This region can be characterized as
one with high income inequalities, high cost of
education expenditure relative to income, scarce
employment opportunities for the educated and
low government expenditure on pupils.
We could say that there‟s a situation of a steady-
state „trap‟- a stagnant steady state of growth with
poor economic outcome. Empirics have also
suggested a decline in the last two-three decades
and no signs of improvement have been noticed.

10.  International aid organizations have restricted their
focus on primary and to a certain extent, secondary
education. Donor institutions have neglected the
importance of tertiary education in channeling
funds to African governments. Hence even the
governments have remained oblivious of the
emphasis needed on tertiary level.
 It has been cited that higher education leads to both
private and social benefits(knowledge-based
economy)and reduces poverty. The idea has
developed that enhancing tertiary education
improves economic output and accelerates the
speed of technological catch up.

11. A Proposed model
Apart from the original Lucas model with two
sectors, in which the production of human capital
involves no physical capital; here we propose two
additional econometric models-
=α1 +α2ye +β1qe +β2Ge +β3I
Where, I is the institutional factor represented as dummy
variable, i.e. I=0,1
The intercept term represents the structure of the labour
market in the economy
The term on the r.h.s; we call it as utilisation of human
capital

12. In the Lucas model, the production of
human capital is made to depend entirely
on human capital; in our equation, we
discuss the factors determining the
utilization of an individual’s skill.
The next equation follows from the previous
as we next look at government
expenditure on education-
=α1 +α2GDPn –β1Ce –β2hx +β3P
Where the term on the r.h.s indicates the
level of govt. expenditure. The intercept is
the minimum exp. from government
revenue. The last term is a dummy
variable of Policy openness taking into
account the rule of law factor.

13. This set of equations along with the fundamental
Lucas set-up determines the long-run growth rate of
C,H,K and Y.
 At the steady-state, K/H ratio determines the growth
rate of the economy. Growth occurs due to high MP
of human capital in goods sector.
 From our model, we put forth the idea that along with
the production of human capital, its utilization is also
an important factor. This is because whether skilled
labor takes up growth-enhancing activity or rent-
seeking activity is the end result of the production
process.

14. Theoretical literature has viewed the role of
government policy in enhancing growth. Knowledge-
based growth can see a higher steady state level
through government expenditure on education.
 The idea presented here is that public expenditure is
also a function of cost of education(crucial) which
has been confirmed by empirics. A high individual
cost of schooling deters enrollment.
 Human capital also includes physical health. In these
growth models we focus only on education. But a
higher social cost of providing health facility reduces
expenditure on education.

15. Model with an education trap
 The economy is inhabited by two two-period lived
agents.
 If child is not enrolled or is a dropout in the present
period, becomes an uneducated worker in the next
generation and chances are that he might have an
uneducated child and the economy is stagnated, thus
remaining in the trap.
 Let the ability with which a child completes
education is denoted by π (a), then, the dropouts are
denoted by (1 − π (α)) ∀ α ∈ (0, 1).
 The quality of education in an economy is denoted by
π, where, πrich> πpoor.

16. Parent’s decision to enroll or to not enroll
 Total cost to the economy if child is not
enrolled= e ≡ ed + (1 − ϕ) w.
 ed = education cost borne by parents,
 Φw= child can contribute by not goin to
school,
 Now, let-
 ne= fraction of educated workers enterin
the workforce,
 wj(ne) =Total earnings of a household of
type j(=e,u), where
‘e’=educated, ‘u’=uneducated.

17.  Cost borne by a parent for enrolling his
child= wj(ne) − e;
 So, a child having the ability= α, then, the
value of the parent for enrolling his child
to increase his optimality is denoted by
Bellman equation:
 Vj(a; ne)= max {enroll, don’t enroll)
= max {u(wj(ne) − e) + β [π(a)EVe(a’; ne’)
+ (1 − π(a))EVu(a’; ne’)] , u(wj(ne)) +
βEVu(a’; ne’) }.

18.  Where, EV=expected value of the child
during next genertaion;
 β = intergenerational discount
 a’= ability in the next generation;
 ne’= fraction of workforce in next
generation.
 The decision of the parents is an
important factor to pull the economy out
of the trap

19.  Low enrollments, high dropouts, “significant
expenditure” in comparison to low income .
So, employment after education is low.
 Redistribution of resources (tax and subsidies)
from poor households(HH) with lower ability
children to HH with higher ability children helps
the economy to come out of the “trap”.
 It‟s a cyclical process when it comes to two
period model with lower educated workforce in
second period and getting out of the trp gets
intensified.

20.  Better education can attain better health increasing
the knowledge of diseases.
 As compared to Latin America, East Asia and the
Caribbean, the Sub-Saharan African(sSA) countries
have a lower enrollment rate.
 In Zambia 70% and in Uganda 66% of the school
expenses are borne by parents.
 Mostly children engage in “looking after cattle”.
 Opportunity cost of studying is 20hr/ week.
So, attending school is thought to be expensive.

21.  The average GDP growth rate from 1965-98 was -
0.15 in sSA. Per capita annual growth decreased to -
1.3%.
 High dropouts and those who attend are subjected to
repetition.
 The student-teacher ratio increased from „90-‟98 and
is the highest in the world.
 The Government expenditure in 1990 (WDI 2000)
was 2.8%. However, the healthy fig is not of absolute
form since the GNP is low.
 The “real” Govt. Exp decreased from $135.6 in „60 to
$79.8 in „90.

22.  Apart from generating revenue from tax, internal
borrowing and monetary financing, the Govt.
borrows from other countries which increases Govt.
debt. However, the IMF and WB approved 29 sSA
countries debt reduction packages by end of „09.

23.  In 2003-06 survey the male-female education ratio is
very high except Lesotho where the male-female ratio
is approx 2:3.
 In Burkina, Faso and Niger, less than one quarter of
the population between 15 and 19 years can read and
write. Benin will catch up in 10yrs.

24.  Gender parity increased from 0.85 („99) to 0.89
(„06). 15 out of 41 sSA countries achieved gender
parity in primary education.
 Weak education governance leads to leakages in
the system, increasing the cost. exceptions:
Mauritius, Botswana and Rwanda.
 The definition of primary and secondary are
different for different sSA countries (increasing
the cost).
 Though the enrolment % grew over time but it
didn‟t grow according to the population rate.

25. Public Financing of Education
 Public education exp as a %age of total Govt. Exp
and as a % of GDP, which is the chief resource of
funding edu can be expressed as:
 Though the sSA countries invest a large proportion of
the Govt. exp on education, but their low GDP
contributes less to take them out of the trap.

26.  The real pub exp on education grew
annually by 6.1% on average since
2000.
 The largest increase was observed in
Burundi 3.2% (2000) to 8.3% (‘09).
Lesotho having the highest edu
spending with 12.4% in ‘09.

27.  A general trend follows where pub exp per
primary pupil increasing to around 20% of GDP
per capita as country income level rises.
 As income increases, gaps in primary education
exp per pupil across countries also shrinks.
 On average, sSA countries allocate 18.3% of
public resources to the education sector.
 The govt. exp on teachers also varies across
countries in sSA.
 A civil servant teacher teaching in a primary
school earns more than a contract or community
teacher.

28.  As the income rises in a country, private exp on education
also increases.
 The private-public partnership helps in diversification of the
Govt. burden.
 The private players include businessmen, NGO and others
(including parents) who carry out the task either by sub-
contracting or outsourcing.

29. Change of Workforce
 The primary workforce is still in agriculture.
However, the contribution to GDP shrank from
18.8% in ‟90 to 12.7% in „09. (Source: World
Bank ‘04)
 Rise in informal sector has increased the estimate
of urban migration to be 50% by 2030. (Source:
UNHABITAT 2010)

30.  In general, a positive relationship between human
capital investment and economic growth has been
confirmed but its robustness varies.
 For many countries there exists a casual relationship.
OECD countries data reveal that human capital
investment offsets the negative effect of logGDP on
growth. Higher education drives knowledge creation.
 for sSA, there exists a steady-state trap; stagnant
incomes, low employment opportunities have shunted
growth and increased disparity. But there‟s a success
story which we hope to be replicated elsewhere in the
region.
The road ahead: conclusion

31. Home bound!
Thank you