The endogenous growth theory was developed as a reaction to omissions and deficiencies in the Solow- Swan neoclassical growth model. It is a new theory which explains the long-run growth rate of an economy on the basis of endogenous factors as against exogenous factors of the neoclassical growth theory.
As the long-run growth rate depended on exogenous factors, the neoclassical theory had few policy implications. As pointed out by Romer, “In models with exogenous technical change and exogenous population growth, it never really mattered what the government did.”
The new growth theory does not simply criticise the neoclassical growth theory. Rather, it extends the latter by introducing endogenous technical progress in growth models. The endogenous growth models have been developed by Arrow, Romer and Lucas, among other economists. We briefly study their main features, criticisms and policy implications.
The Endogenous Growth Models:
The endogenous growth models emphasise technical progress resulting from the rate of investment, the size of the capital stock, and the stock of human capital.
1. There are many firms in a market.
2. Knowledge or technological advance is a non-rival good.
3. There are increasing returns to scale to all factors taken together and constant returns to a single factor, at least for one.
4. Technological advance comes from things people do. This means that technological advance is based on the creation of new ideas.
5. Many individuals and firms have market power and earn profits from their discoveries. This assumption arises from increasing returns to scale in production that leads to imperfect competition.
As a matter of fact, these are the requirements of an endogenous growth theory. Given these assumptions, we explain the three main models of endogenous growth.
1. Arrow’s Learning by Doing and Other Models:
The Arrow Model:
Arrow was the first economist to introduce the concept of learning by doing in 1962 by regarding it as endogenous in the growth process. His hypothesis was that at any moment of time new capital goods incorporate all the knowledge then available based on accumulated experience, but once built, their productive deficiencies cannot be changed by subsequent learning. Arrow’s model in a simplified form can be written as
Yi= A (K) F (Ki,Li)
Where Yi denotes output of firm i, Kidonates its stock of capital, Li, denotes its stock of labour, K without a subscript denotes the aggregated stock of capital and A is the technology factor. He showed that if the stock of labour is held constant, growth ultimately comes to a halt because socially very little is invested and produced. Therefore, Arrow did not explain that his model could lead to sustained endogenous growth.
The Levhari-Sheshinski Model:
Arrow’s model has been generalised and extended by Levhari and Sheshinski. They emphasise the spillover effects of increased knowledge as the source of knowledge. They assume that the source of knowledge or learning by doing is each firm’s investment.
An increase in a firm’s investment leads to a parallel increase in its level of knowledge. Another assumption is that the knowledge of a firm is a public good which other firms can have at zero cost. Thus knowledge has a non-rival character which spills-over across all the firms in the economy. This stems from the fact that each firm operates under constant returns to scale and the economy as a whole is operating under increasing returns to scale.
In the Levhari-Sheshinski Model, endogenous technical progress in terms of knowledge or learning by doing is reflected in an upward raising of the production function and economic growth is explained “in the context of aggregate increasing returns being consistent with competitive equilibrium.”
The King-Robson Model:
King and Robson emphasise learning by watching in their technical progress function. Investment by a firm represents innovation to solve the problems it faces. If it is successful, the other firms will adapt the innovation to their own needs. Thus externalities resulting from learning by watching are a key to economic growth.
The King and Robson study shows that innovation in one sector of the economy has the contagion or demonstration effect on the productivity of other sectors, thereby leading to economic growth. They conclude that multiple steady state growth paths exist, even for economies having similar initial endowments, and policies that increase investment should be pursued.
The Romer Model:
Romer in his first paper on endogenous growth in 1986 presented a variant on Arrow’s model which is known as learning by investment. He assumes creation of knowledge as a side product of investment. He takes knowledge as an input in the production function of the following form
Y = A(R) F (Ri,Ki,Li)
Where Y is aggregate output; A is the public stock of knowledge from research and development R; Ri is the stock of results from expenditure on research and development by firm i; and Ki and Li are capital stock and labour stock of firm i respectively. He assumes the function F homogeneous of degree one in all its inputs Ri, Ki, and Li, and treats Ri as a rival good.
Romer took three key elements in his model, namely externalities, increasing returns in the production of output and diminishing returns in the production of new knowledge. According to Romer, it is spillovers from research efforts by a firm that leads to the creation of new knowledge by other firms. In other words, new research technology by a firm spills-over instantly across the entire economy.
In his model, new knowledge is the ultimate determinant of long-run growth which is determined by investment in research technology. Research technology exhibits diminishing returns which means that investments in research technology will not double knowledge.
Moreover, the firm investing in research technology will not be the exclusive beneficiary of the increase in knowledge. The other firms also make use of the new knowledge due to the inadequacy of patent protection and increase their production.
Thus the production of goods from increased knowledge displays increasing returns and competitive equilibrium is consistent with increasing aggregate returns owing to externalities. Thus Romer takes investment in research technology as endogenous factor in terms of the acquisition of new knowledge by rational profit maximisation firms.
2. The Lucas Model:
Uzawa developed an endogenous growth model based on investment in human capital which was used by Lucas. Lucas assumes that investment on education leads to the production of human capital which is the crucial determinant in the growth process.
He makes a distinction between the internal effects of human capital where the individual worker undergoing training becomes more productive, and external effects which spillover and increase the productivity of capital and of other workers in the economy. It is investment in human capital rather than physical capital that have spillover effects that increase the level of technology. Thus the output for firm i take the form
Yi = A(Ki).(Hi).He
Where A is the technical coefficient, Ki and Hi are the inputs of physical and human capital used by firms to produce goods Yi. The variable H is the economy’s average level of human capital. The parameter e represents the strength of the external effects from human capital to each firm’s productivity.
In the Lucas model, each firm faces constant returns to scale, while there are increasing returns for the whole economy. Further, learning by doing or on-the-job training and spillover effects involve human capital.
Each firm benefits from the average level of human capital in the economy, rather than from the aggregate of human capital. Thus it is not the accumulated knowledge or experience of other firms but the average level of skills and knowledge in the economy that are crucial for economic growth.
In the model, technology is endogenously provided as a side effect of investment decisions by firms. Technology is treated as a public good from the point of view of its users. As a result, firms can be treated as price takers and there can be equilibrium with many firms as under perfect competition.
3. Romer’s Model of Technological Change:
Romer’s model of Endogenous Technical Change of 1990 identifies a research sector specialising in the production of ideas. This sector invokes human capital alongwith the existing stock of knowledge to produce ideas or new knowledge. To Romer, ideas are more important than natural resources. He cites the example of Japan which has very few natural resources but it was open to new western ideas and technology.
It imported machines from the United States during the Meija era, dismantled them to see how they worked and manufactured their better prototypes. Therefore, ideas are essential for the growth of an economy. These ideas relate to improved designs for the production of producer durable goods for final production.
In the Romer model, new knowledge enters into the production process in three ways. First, a new design is used in the intermediate goods sector for the production of a new intermediate input. Second, in the final sector, labour, human capital and available producer durables produce the final product. Third, and a new design increases the total stock of knowledge which increases the productivity of human capital employed in the research sector.
The Romer model is based on the following assumptions:
1. Economic growth comes from technological change.
2. Technological change is endogenous.
3. Market incentives play an important role in making technological changes available to the economy.
4. Invention of a new design requires a specified amount of human capital.
5. The aggregate supply of human capital is fixed.
6. Knowledge or a new design is assumed to be partially excludable and retainable by the firm which invented the new design. It means that if an inventor has a patented design for a machine, no one can make or sell it without the agreement of the inventor.
On the other hand, other inventors are free to spend time to study the patented design for the machine and acquire knowledge that helps in the design of such a machine. Thus patents provide incentives to firms to engage in research and development, and other firms can also benefit from such knowledge. When there is partial excludability, investment in research and development leading to an invention by a firm can only bring in quasi-rent.
7. Technology is a non-rival input. Its use by one firm does not prevent its use by another.
8. The new design can be used by firms and in different periods without additional costs and without reducing the value of the input.
9. It is also assumed that the low cost of using an existing design reduces the cost of creating new designs.
10. When firms make investments on research and development and invent a new design, there are externalities that are internalised by private agreements.
Given these assumptions, the Romer model can be explained in terms of the following technological production function.
∆A = F (KA,HA,A)
Where AA is the increasing technology, KA is the amount of capital invested in producing the new design (or technology), HA is the amount of human capital (labour) employed in research and development of the new design, A is the existing technology of designs, and F is the production function for technology.
The production function shows that technology is endogenous when more human capital is employed for research and development of new designs, then technology increases by a larger amount, i.e., A is greater. If more capital is invested in research laboratories and equipment to invent the new design, then technology also increases by a larger amount i.e., ∆A is more. Further, the existing technology, A, also leads to the production of new technology, ∆A.
Since it is assumed that technology is a non-rival input and partially excludable, there are positive spillover effects of technology which can be used by other firms. Thus the production of new technology (knowledge or idea) can be increased through the use of physical capital, human capital and existing technology.
Criticisms of Endogenous Growth Theory:
Despite the fact that the new growth theory has been regarded as an improvement over the new classical growth theory, still it has many critics:
1. According to Scott and Auerbach, the main ideas of the new growth theory can be traced to Adam Smith and increasing returns to Marx’s analysis.
2. Srinivasan does not find anything new in the new growth theory because increasing returns and endogeneity of variables have been taken from the neoclassical and Kaldor’s models.
3. Fisher criticises the new growth theory for depending only on the production function and the steady state.
4. To Olson, the new growth theory lays too much emphasis on the role of human capital and neglects the role of institutions.
5. In the various models of new growth theory, the difference between physical capital and human capital is not clear. For instance, in Romer’s model, capital goods are the key to economic growth. He assumes that human capital accumulates and when it is embodied in physical capital then it becomes a driving force. But he does not clarify which is the driving force.
6. By using secondary school enrollment as a proxy for human capital in their model, Mankiw, Romer and Weil find that physical and human capital accumulation cannot lead to perpetual economic growth.
Policy Implications of Endogenous Growth Theory:
The endogenous growth theory has important policy implications for both developed and developing economies:
1. This theory suggests that convergence of growth rates per capita of developing and developed countries can no longer be expected to occur. The increasing returns to both physical and human capital imply that the rate of return to investment will not fall in developed countries relative to developing countries.
In fact, the rate of return to capital in developed countries is likely to be higher than that in developing countries. Therefore, capital need not flow from the developed to the developing countries and actually the reverse may happen.
2. Another implication is that the measured contribution of both physical and human capital to growth may be larger than suggested by the Solow residual model. Investment on education or research and development of a firm has not only a positive effect on the firm itself but also spillover effects on other firms and hence on the economy as a whole. This suggests that the residual attributed to technical change in the Solow growth accounting may be actually much smaller.
3. One of the important implications is that it is not necessary that economies having increasing returns to scale must reach a steady state level of income growth, as suggested by the Solow-Swan model.
When there are large positive externalities from new investment on research and development, it is not necessary for diminishing returns to start. So the growth rate of income does not slow down and the economy does not reach steady state. But an increase in the saving rate can lead to a permanent increase in the growth rate of the economy.
4. This further implies that countries having greater stocks of human capital and investing more on research and development will enjoy a faster rate of economic growth. This may be one of the reasons for the slow growth rate of certain developing countries.