Different theories of growth and development

What are the different theories of growth and development that have been proposed? How do the modern growth theory based models differ from these?

There are many growth and development theories explaining how countries grow, why they grow and how growth can be encouraged. These theories can be split into two distinct categories, classical or traditional theories and modern theories. When we talk about growth or development here, we mean the economic growth in a country’s GDP, and not just developing countries but also how highly developed countries can maintain growth at a sustainable rate. This essay will discuss the four classical areas of growth and development theories that exist, how they differ, and how they have been improved in contrast to new growth theory.

The first area of classical theory is the linear stages-of-growth model, pioneered by Rostow who observed a pattern of growth from which he developed a five stage theory, throughout which capital, savings and investment are essential for growth. Rostow. His five stages were as follows, focusing on developing countries with large agricultural sectors:

The traditional society: characterised by pre-Newtonian science and technology, labour intensive agricultural methods. A ceiling to growth exists as there is no technological innovation.

The preconditions for take-off, is the transitional stage of development characterized by an intrusion by more advanced economies and movement towards a centralized state and specialisation techniques.

The take-off: the beginning of steady growth, in the UK this was born out of continued technological innovation. Savings and investment are very important to ensure technological progression, new industries expand and agricultural methods are developed, the structure of the economy is completely altered, and changes in productivity are highly influential.

The drive to maturity is reached after around sixty years; characterized by an ‘ability to move beyond the original industries which powered its take-off’ (Rostow: 1960) and investment runs at around 10-20

Stage of high mass consumption: industries focus on durable consumer goods and services; there is a considerable degree of urban migration, and living standards rise as the welfare state takes shape.

Sir Roy Harrod and Evsey Domar built on Rostow’s assumption that savings and investment are essential for a country to experience sustained growth. In the Harrod-Domar model they stated that some revenue is needed to replace old capital, but this doesn’t allow for growth, as production will be at the same level. In order to grow, further investment is needed to add to the capital stock. Firstly, it is assumed that total capital stock, K, is directly related to GDP, Y, via the capital-output-ratio (k) [i] . Secondly, the net savings ratio (s) is assumed to be a fixed percentage of GDP. We can now mathematically construct the model:

Net savings = net savings ratio x GDP

S=sY

Net investment (I) = change in capital stock

I=∆K

Due to the capital output ratio:

K/Y=k or ∆K/∆Y=k

This rearranges to:

∆K=k∆Y

Assuming a closed economy and ignoring the government:

Y=C+S [ii] 

Or alternatively:

Y=C+I

This means:

S=I

Now we can put all these elements together:

I=∆K=k∆Y

And

S=sY= k∆Y=∆K=I

sY= k∆Y

Dividing by Y and then through by K, we can rearrange,

∆Y/Y=s/k

Which states that the rate of growth in GDP is determined by both the capital-output ratio and the net savings ratio, the higher the savings rate, the more GDP will grow. If we now take the depreciation of capital into account:

s/k = g + δ

This final equation shows that, as the depreciation of capital (δ) is negative, not all revenue can be reinvested. It is unlikely that workers receiving low incomes in developing countries will save enough to ensure economic development, therefore foreign aid or private foreign investment may be necessary. For example, if an open economy was now assumed, and k is 3:1, if a country wishes to grow at a rate of 7% a year a savings rate of 21% would be needed, which is inconceivable. Foreign aid or investment could replace savings, and help the country to develop.

Secondly, structural change theory, as developed by W. Arthur Lewis in his Dual Sector theory of development, explained that there are two sectors in any underdeveloped economy, a traditional, predominantly rural subsistence sector and a modern industrial sector. In the traditional sector there is zero marginal labour productivity, which Lewis called ‘surplus labour’, deducing that labour could be transferred from the traditional to the modern sector without a loss of output. The high-productivity modern sector creates profits over the cost of wages, to reinvest which induces growth and development of the industrial sector. Lewis believed that employment expansion in the modern sector would continue until all the surplus labour was used, and the marginal product of agricultural labour was no longer zero.

Thirdly, the international dependence theory discusses the damaging effects of dominating rich countries, on which developing countries are dependent. The theory can be split into three subcategories:

Neo-colonial dependence model: developed out of Marxist theory which blamed the capitalist system of exploitation for the existence of underdeveloped countries (periphery), which cannot be self-reliant due to exploitation by developed countries (centre) which are interested in maintaining inequality.

False paradigm model: the advice from developed countries is biased, ethnocentric, uninformed and over-complicated. As many politically influential figures are educated in the developed countries, they absorb these inappropriate models and therefore problems cannot be dealt with properly.

Dualistic-Development Thesis: This model shows the continually diverging dual societies of rich and poor nations and can be further split into four arguments:

There are superior and inferior conditions, meaning highly educated and illiterate people coexist in the international economy,

This coexistence is persistent, it cannot just solve itself,

Inequalities are growing,

The superior elements do nothing to help the inferior elements catch up; they may even make the inequality worse.

Finally, the last area of classical theory is the more modern Neoclassical Counterrevolution which called for freer markets and expanding the private sector, it condemned developing country governments for poor resource allocation leading to inefficiencies and a lack of economic incentives for development. There are three approaches of neoclassical theory which vary in their opinion of the government and its usefulness:

Free market approach; argued that the markets alone are efficient and induce effective resource allocation, and government interference is distortionary.

Public-choice theory further condemns the government, insisting all agents act out of selfish motives, which restricts growth, resource allocation and individual freedom.

Finally the market-friendly approach recognises the importance of the government’s role, as the product and factor markets in developing countries are generally underdeveloped, and market failures are more apparent.

Furthermore the famous Solow neoclassical growth theory fits into this category, and is transitional into modern theories of development. The theory builds on the Harrod-Domar model discussed earlier, by adding labour as a second factor, which can be substituted for capital, and allowing for technological change. The Solow model implies that economies will converge to the same level of income [iii] , and that technological progress is an exogenous factor which explains long-term growth; the model is therefore referred to as an exogenous growth model.

Y=F (K, L) [iv] 

(Where Y is output (GDP),

K is capital and L is labour)

And due to constant returns to scale:

γY=F (γK,γL)

(Where γ is a positive constant)

Using the Cobb-Douglas production function:

Y=Kα(AL1-α)

(Where A is the productivity

of labour)

If γ=1/L then generally speaking, we can write:

Y/L=f (K/L,1) or y=f(k)

(Where k is K/L and lower-

case means per worker)

Or specifically:

y=Akα

This shows that output per worker is dependent on the amount of capital per worker, so the more capital per worker, the more output that worker can produce. If we now consider the rate of growth of the labour force per year (n) and of labour productivity, i.e. the rate at which A increases (λ). Providing savings are greater than depreciation (δ), the total capital stock grows, but capital per worker only grows when total capital stock is greater than the amount needed to equip new workers with the previous level of capital per worker.The full Solow equation:

∆k=sf(k) – (δ+n)k

Shows that the growth of the capital labour ratio (k) depends on savings (sf(k)) after depreciation and the amount of capital per new worker is taken into account. If we assume that A is constant, output and capital per worker are no longer growing, to show this ∆k=0 and k* is the level of capital per worker:

sf(k*)= (δ+n)k*

If A is increasing then capital per worker is not changing, but workers become more productive and produce output as if there were extra workers. The model can also be shown graphically:

The above graph [v] shows the movement towards a stable equilibrium, if k is above or below k*, as capital per worker increases or decreases towards the equilibrium, k*. To compare this model to the Harrod-Domar model, we can see what happens if the rate of savings, s, is raised. A temporary increase in the rate of output growth is realised, returning to the steady state of growth later on, which separates it from the Harrod-Domar mode. In the Solow model, an increase in the savings rate does not ensure long term growth, it only increases the equilibrium, meaning both the capital-labour ratio and output-labour ratio rise, but not the rate of growth. Shown graphically below, savings increase to s’:

As this happens the equilibrium output per person also increases, so despite the fact that the increase in the rate of growth is temporary, it still will be a very beneficial to the developing economy.

In juxtaposition to the Solow model, another modern growth theory, namely the Endogenous growth theory regards technology as endogenous: technological change is an outcome of public and private investments in human capital and knowledge intensive industries, such as ICT and telecommunications. Endogenous growth theories can be explained using a basic equation from the Harrod-Domar model: Y=AK, where A is any factor which affects technology and K now includes physical and human capital, taking investments in education into account. Investments in human and physical capital can produce positive externalities for external economies and improve labour productivity which in turn will offset any diminishing returns, resulting in sustained long-term growth. This simplification is similar to traditional theories as it still emphasises the importance of savings and investments for economic growth, but also different as it refutes that there is convergence of growth rates across closed economies, due to savings rates and levels of technology differing from country to country. Unlike the Solow model, there is no natural convergence of per capita incomes catching up to those of developing countries even with similar savings and population growth rates. Furthermore the ‘high’ rates of return offered to foreign private investors by developing countries with low capital-labour ratios are broken down as there little or no complementary investment in human capital such as education, without human capital investments the positive externalities of such investments cannot be realised, and so a level of complementary capital which is less than socially optimal is reached.

Romer’s model illustrates endogenous growth theory, by assuming that growth is stimulated at the firm or industry level as it is positively affected by the country’s total capital stock (K’) which could lead to increasing returns at the overall, despite constant returns being assumed in each industry. In this model human capital is included (A) which is a positive externality and benefits the other firms in the economy. Algebraically:

Y=AKαL1-αK’β

Assuming each industry uses the same level of capital and labour:

Y=AKα+βL1-α

If we assume A=0, the resulting growth rate for per capita income is:

g-n=βn/1-α-β

Where g and n are output and population growth rates respectively. Without allowing for spill-overs like in the Solow model and with constant returns to scale, β=0 and per capita growth would consequently be zero. But if, like Romer, we assume a positive capital externality (β>0) then g-n>0 and Y/L grows, if we also allowed for technological progress growth would be increased to the extent of the technological advancement, denoted by λ in Solow’s model.

Here we have shown that modern models such as the endogenous growth theory and possibly even Solow’s growth model, hold some very different assumptions to those of the traditional theories, which is natural as time progresses and more is learned about what methods are effective and what really motivates economic growth. No one theory is conclusive, and some are only explanatory, such as the structural change models. What is clear is that one factor such as technology or the savings rate, alone cannot explain why developed countries are developed and developing countries are not, or how to reach a happy medium. A number of factors must be taken into consideration, and as we moved into the more modern models, this became clear, as the old models were not discarded, but added to and built on.