The conflictGrowth & Inequality

The role of education sector: sub-Saharan Africa

Akash asijaArhit ghosh

Aritra chakrabartyDebanjan biswas

Naveen kumar

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.

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.

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

u: proportion of total labour time spent workingh: 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.

The Ramsey-Cass-Koopmans versionAccording 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.

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.

h> : 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-

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 h> , 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.

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.

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.

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 +β3IWhere, I is the institutional factor

represented as dummy variable, i.e. I=0,1The intercept term represents the structure

of the labour market in the economyThe term on the r.h.s; we call it as utilisation

of human capital

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 +β3PWhere 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.

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.

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.

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.

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.

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’) }.

Where, EV=expected value of the child during next genertaion;

β = intergenerational discounta’= 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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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)

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

Home bound!Thank you