______Subject BUSINESS ECONOMICS
Paper No and Title 5: MACROECONOMIC ANALYSIS AND POLICY
Module No and Title 26: THEORIES OF ECONOMIC GROWTH PART – 3
Module Tag BSE_P5_M26
BUSINESS PAPER NO. 5: MACROECONOMIC ANALYSIS AND POLICY ECONOMICS MODULE NO.26: THEORIES OF ECONOMIC GROWTH PART – 3
______TABLE OF CONTENTS
1. Learning Outcomes
2. Introduction
3. Consumption in Steady State and Golden Rule
4. Endogenous Growth Models
4.1 Factors Affecting Technological Change
4.2 The AK Model: The Assumption of Constant Returns to Capital
4.3 Economic Growth in the AK Model
4.4 The Lucas Model
4.5 Implications of Endogenous Growth Models
5. Conclusion
6. Summary
BUSINESS PAPER NO. 5: MACROECONOMIC ANALYSIS AND POLICY ECONOMICS MODULE NO.26: THEORIES OF ECONOMIC GROWTH PART – 3
______1. Learning Outcomes
After studying this module, you shall be able to
Learn about an important implication of the Solow model, viz., about consumption, optimal savings rate or ‘golden rule savings ratio’ in the long run steady state Learn about the basic principles underlying endogenous growth models Understand the role of human capital in the economic growth process Appreciate the importance of savings and capital accumulation for technological progress and economic growth in the long run Understand the differences between the Neoclassical (Solow) growth model and the new (endogenous) growth models Know more about the implications of the endogenous growth framework
2. Introduction
In this module, first we shall discuss an important implication of the Solow model regarding the optimal level of consumption and savings in the long run steady state equilibrium. Thereafter, we shall try to give an idea regarding the factors affecting technological progress in an economy and discuss the basic structure, assumptions and implications of the endogenous growth models.
In the two previous modules on economic growth we learnt about the Harrod-Domar and Solow growth models. Both these models and especially the Solow Model acknowledged the importance of technology as a determinant of long run economic growth, but neither had an explanation about the drivers of technological progress.
In the Harrod-Domar model the effect of technological change on growth was captured indirectly via the capital-output ratio that was assumed to be a constant. Technological change would raise the long run growth rate by lowering the capital output ratio, for any given savings rate in this model. However, the main insights from this model focused not on technology, but on the importance of savings for long run growth of output. An increase in the rate of savings would lead to a proportionate increase in the long run rate of growth output in this model.
The Solow Model introduced an aggregate production function with diminishing factor returns and constant returns to scale. Unlike in the Harrod-Domar model, the capital-output ratio was a variable determined within the Solow model. It highlighted the role of technological progress, primarily in two ways. First, in the Solow model without technical progress, there was no growth of per capita income in the long run steady state; second, once the role of technical progress was incorporated, the long run steady state rate of growth of per capita income was determined solely by the rate of technological progress. In sharp contrast to the Harrod-Domar result, an increase in the saving rate led to an increase in per capita income levels in the steady state but it did not influence the long run rate of growth in the Solow model.
BUSINESS PAPER NO. 5: MACROECONOMIC ANALYSIS AND POLICY ECONOMICS MODULE NO.26: THEORIES OF ECONOMIC GROWTH PART – 3
______The Solow model stressed on the limits to growth from factor accumulation (owing to diminishing returns to capital) and emphasized the importance of technological progress for long run growth. However, it offered no explanation for the determinants of technical change; the model had no inbuilt mechanism explaining why certain countries experienced a faster rate of technical progress than others. Rather technological progress was viewed as an exogenous factor, appearing much like ‘manna from heaven’.
The literature on endogenous growth (also known as ‘New Growth Theory’) that appeared in the 1980s addressed precisely this lacuna in the literature on economic growth and added insights on the possible factors determining the pace of technological progress. This literature emphasized that the process of technological progress and innovation occurred simultaneously as a country undertook savings, investment and capital accumulation. In this sense, the determinants of technological change were actually endogenous in the process capital accumulation. It also took a broader view of capital formation and emphasized that it included both physical as well as human capital formation. As we shall see below the endogenous growth models emphasized the role of savings and also role of the government in influencing the long run rate of growth in an economy. This contrasts with the results flowing from the Solow model, that essentially focused on the supply side (i.e., on the production of output, ignoring the role of demand) and had little role for the government.
3. Consumption in Steady State and Golden Rule
In the previous module we had discussed the role of savings in the neo-classical growth model. In the Solow model, a higher savings rate, did not affect the long run growth rate, but led to a higher level of capital per capita and income per capita at steady state.
However, an increase in savings comes at the expense of lower consumption, which implies a lower welfare and standard of living. Note that if the savings rate is too low, per capita income would also be low and so would consumption per heads. E.g., in the limit, if the saving rate is zero, there is no capital accumulation and hence output and consumption is almost zero. However, when the savings rate is very high, capital stock would be very high as would be depreciation and hence a large amount of investments would be required just to maintain existing levels of the capital stock in steady state; this would drive consumption to very low levels. E.g., if the saving rate is one, people would save all their income so capital and output would be very high but consumption would be zero!
Logically therefore there must exist a savings rate, s* between zero and one (i.e., 0 < s* < 1), where per capita consumption in steady state is maximized. It is called the ‘Golden Rule saving ratio’. For s < s*, consumption would be increasing, whereas for s > s* consumption would be decreasing. The level of capital associated with the optimal savings rate s*, that yields the highest level of consumption in steady state, is known as "Golden-Rule capital stock".
BUSINESS PAPER NO. 5: MACROECONOMIC ANALYSIS AND POLICY ECONOMICS MODULE NO.26: THEORIES OF ECONOMIC GROWTH PART – 3
______We can write, c = y – sy = (1 - s) f (k(s)),
where, c = steady state per capita consumption, s = savings rate, k = capital per capita and y = f (k) is the per capita production function, which is increasing in k (as discussed in the previous module). Note that the steady state k is an increasing function of s. As s changes, say increases from a low value, there are two opposing pulls on c. (1-s) falls but f (k(s)) rises. At the Golden Rule value of s the opposite forces are balanced and the product (i.e., c) is maximized.
4. Endogenous Growth Models
4.1 Factors Affecting Technological Change
The neoclassical growth theory of Solow assumed that the rate of technological progress was determined by exogenous forces outside the model and that these forces were independent of economic activities. Neoclassical theory thus implied that the long-run growth rate was given exogenously from outside the economic system.
Endogenous growth theory on the other hand proposed that the rate of technological progress, and hence the long-run rate of economic growth, can be influenced by economic factors. In particular, technological progress takes place through innovations, in the form of new products, processes and markets, many of which are the result of economic activities. A higher pace of economic activity can in turn raise the pace of innovation process by giving firms more exposure and more production experience. Most of the innovations are the result of research and development (R&D) expenditures, and various economic policies with respect to international trade, competition, education, taxes and intellectual property can further affect the rate of innovation by influencing private costs and benefits of doing R&D.
The assumption of diminishing marginal product of physical capital in the Solow model entailed that as more and more of capital was accumulated, its productivity or per unit contribution to output declined. An important contribution of the endogenous growth theory was that it explicitly recognized that the capital endowment of an economy comprised both physical and human capital. This led to central insight from these models, that as the economy's stock of human capital improved it mitigated the decline in marginal product of physical capital. Therefore as capital accumulation occurred, diminishing marginal returns to capital was not inevitable. Rather there might be constant or even increasing marginal returns to capital. That is, the slope of the aggregate production function need not diminish with an increase in per capita capital stock. Rather, the slope might remain constant throughout or even increase.
This may be further explained as follows. Human capital essentially refers to an educated or skilled labour force. An economy that invests in human capital by setting up schools, universities, research centres, laboratories etc. essentially creates an environment conducive for learning, innovation and technological progress. As a result of more training and learning programs human capital becomes more efficient and productive. Moreover as workers acquire skills and gain experience with BUSINESS PAPER NO. 5: MACROECONOMIC ANALYSIS AND POLICY ECONOMICS MODULE NO.26: THEORIES OF ECONOMIC GROWTH PART – 3
______machines, there is ‘learning by doing’, so they innovate, learn newer techniques, gain more knowledge and their productivity improves. Moreover, human capital formation can go hand in hand with physical capital accumulation. E.g., as new production facilities are constructed and new machines are produced and put into use, the gains from these investments can be then re-invested and used for in building more, schools, health care facilities, training and research and development facilities. Since physical capital accumulation itself can lead to technological progress, hence diminishing marginal product of capital need not set in.
The government can also play a role in improving the pace of capital formation and technological progress, via subsidies for education, research and development. It can also strengthen institutional mechanisms such as patent laws etc. that create incentives for innovation and creation of new technology.
4.2 The AK model: The Assumption of Constant Returns to Capital
We now introduce a simple version of an endogenous growth model, where it is assumed that the aggregate output is proportional to capital and there is absence of diminishing returns to capital. This model displays both constant returns to scale and constant returns to capital and referred to as the AK Model. An early version of AK theory was produced by Frankel (1962) who argued that aggregate production function can exhibit a constant or increasing marginal product of capital
This model deviates from the standard assumption of Neoclassical growth theory.It emphasizes the role of investment in physical capital which further enhances the development of human capital As firms accumulate more and more of capital , some of the increased capital will be intellectual capital that enhances technological progress . This technological progress prevents any reduction in the marginal product of capital.
The state of technology is introduced as a variable in the production function and it is represented by A. This technological parameter essentially tells us how much output can be produced using a given quantity of capital and labor. Therefore the production function for this model is defined as:
Y = AK ----- (1)
A: A constant that reflects a level of technology K: aggregate capital (both human and physical capital)
This model assumes that the production function is linear in the only input, capital. Thus K can be assumed to include not just physical and human capital but the stock of knowledge and even financial capital in the economy. The above production function reflects both constant returns to scale and constant marginal returns to capital.
Constant returns to scale implies that for a given technology, if we increase capital by some proportion m, then output also increases by same proportion.
i.e., A (m K) = m Y BUSINESS PAPER NO. 5: MACROECONOMIC ANALYSIS AND POLICY ECONOMICS MODULE NO.26: THEORIES OF ECONOMIC GROWTH PART – 3
______Further, constant marginal returns to capital implies that when capital increases by one unit, the amount by which output increases is a constant given by A.
This implies for the above production function (1) we have:
MPK = dY/dK = A
Constant marginal productivity of capital may be observed when technological progress occurs alongside accumulation of physical and human capital. Human and physical capital interact with each other to enhance the efficiency of resources. The greater the stock of human capital in a country, the higher would be the marginal product of physical capital; the more skilled the workforce, higher would be the productivity of machines. Also, the greater the stock of physical capital in an economy, the higher would be the marginal product of human capital; the more machines there are in an economy, the greater would be the returns from investing in skills and education.
4.3 Economic Growth in the AK Model
We can show that the rate of growth depends on the rate of savings and investment in an endogenous growth framework1.
We assume that the economy is closed and that population is given and there is no population growth. So the rate of growth of per capita output is determined entirely by the rate of growth of output. Given the production function, the rate of growth of output in turn is determined by the rate of growth of capital.
Since the production function is given by Yt = A Kt, ------(1) so, (Yt+1 – Yt) / Yt = [A (Kt+1 – Kt)] / AKt or, gy = (Yt+1 – Yt) / Yt = [(Kt+1 – Kt)] / Kt------(2)
It is assumed that the savings rate is a constant (i.e., a constant fraction of income s is saved), so that total aggregate savings St = s.Yt ---- (3). Also in a simple closed economy without government the equilibrium condition is given by equality of investment and aggregate savings, i.e., It = St = s.Yt ------(4). In each period a fraction δ of the total capital stock depreciates, so the total amount of depreciated capital at each time period is given by δKt.
In this model, the process of capital accumulation may be denoted as follows:
Kt+1 – Kt = It - δKt ------(5)
There is capital accumulation or addition to the total capital stock (i.e., the l.h.s of (5) is positive) as long as new investments (It) exceed depreciated capital stock (δKt).
1 The discussion in this section is based on Chapter 10 in Sikdar, S. (2011), Principles of Macroeconomics, 2nd Edn, Oxford University Press : New Delhi. BUSINESS PAPER NO. 5: MACROECONOMIC ANALYSIS AND POLICY ECONOMICS MODULE NO.26: THEORIES OF ECONOMIC GROWTH PART – 3
______We can also write (5) as follows:
Kt+1 – Kt= sYt - δKt (using (4) above) or, Kt+1 – Kt= sAKt - δKt (using (1) above)
Now dividing both sides by Kt we get:
(Kt+1 – Kt) / Kt=sA – δ ------(6)
So, gy= (Kt+1 – Kt) / Kt= sA – δ
From this it can be seen that in an endogenous growth framework, the growth rate of the economy depends positively on the savings rate s. This is in contrast to the neo-classical model where the long-run rate of growth of per capita output was independent of s. In fact this simple model demonstrates that even without any exogenous technical progress (the technological parameter A is a constant), aggregate output can keep growing indefinitely as long as sA> δ. This result is in sharp contrast to that in the Solow model which showed without technological progress, there was no growth in per capita output in the long run equilibrium. In the Solow model, rather than faster capital accumulation, it was the pace of technological progress that determined countries’ long run rates of growth.
In the AK model, higher savings leads to higher growth by leading to higher investments and physical capital accumulation. As explained above, accumulation of physical capital further enhances human capital formation, which further raises the productivity of physical capital, so that there is no tendency for diminishing marginal returns to capital.
4.4 Skill formation as Foundation of Growth
Another approach to human capital (introduced by Robert Lucas) uses the production function Y = Kα (hL) 1-α where h is human capital per person. It is assumed that human capital evolves according to ∆h/h = 1-u where u is time spent working and (1-u) is time spent acquiring skill. The variable h is exactly similar to labour augmenting technical progress in the Solow model. The new element is that the growth of this factor depends on (1-u). Any policy that leads to a permanent increase in the time people spend to obtain skills generates a permanent increase in the growth of output per worker.
4.5 Implications of Endogenous Growth Models
The endogenous models have several interesting implications. First of all, as explained above, they emphasize the importance of savings and physical capital accumulation for long run growth in the economy. This is in contrast with one of the central results in the Solow model, where long-run growth was independent of the savings rate.
BUSINESS PAPER NO. 5: MACROECONOMIC ANALYSIS AND POLICY ECONOMICS MODULE NO.26: THEORIES OF ECONOMIC GROWTH PART – 3
______Second, these models underscore the link between physical and human capital formation. In doing so, they bring out the critical contribution of human capital in fostering technological progress that can prevent the setting in of diminishing marginal returns to capital. The Solow model had no explanation for the determinants of the pace of technological progress and did not differentiate between physical and human capital. In contrast, in the endogenous growth framework, growth of productivity is not accidental or exogenous rather, it is brought about by greater savings and investment in physical and human capital.
Third, these models also highlight the important role of governments in influencing the process of growth. Government policy can play a crucial role by fostering growth of human capital and creating an institutional framework (e.g., patent regime) that is conducive to innovation and generic research. This creates a case for specific policies e.g., public funding of education and knowledge creation (e.g., funding public schools, colleges, universities and fundamental research initiatives); policies promoting savings; policies of openness to international trade and investment flows, that can enhance domestic productivity and innovation by providing access to cutting edge imported technology etc.
Finally, an important implication of the Solow model is the notion of convergence. The concepts of unconditional and conditional convergence were discussed in detail in the previous module. However, convergence in growth rates is not inevitable in the endogenous growth framework. In practice, much of the observed cross-country variation in growth rates is attributable to differences in productivity growth. This suggests, differences with respect to human capital formation, capital accumulation and role of government may hold the key to understanding differences in productivity growth, as per the implications of the endogenous growth models.
5. Conclusion
In this module we saw that endogenous growth models try to provide explanations for the factors that affect technological progress. It is shown that these factors are inherent in the very process of factor accumulation. Endogenous growth theory also suggests that if government policies can boost investment, it not only increases the steady state capital stock but permanently affects the growth rate.
Theories of endogenous growth have been criticized on the grounds that they are inappropriate for developing economies where economic growth is mostly impeded by inefficiencies arising from poor infrastructure, inadequate institutional structures, imperfect capital and goods markets. However, the endogenous growth framework does not incorporate structural rigidities and as a consequence its applicability to cross country development comparison is limited. Further it has also been argued that the models fail to allow for adequate transitional dynamics, with the growth rate changing instantaneously with changes in parameter values.
BUSINESS PAPER NO. 5: MACROECONOMIC ANALYSIS AND POLICY ECONOMICS MODULE NO.26: THEORIES OF ECONOMIC GROWTH PART – 3
______6. Summary
The main insights from our discussion in this module can be summarized as follows: The ‘Golden Rule capital stock’ refers to the level of capital stock, associated with the optimal ‘Golden rule savings rate’, for which per capita consumption is maximized in the Solow steady state. The neo-classical Solow growth model emphasizes the importance of technology for long run growth but has no explanation for what drives technological change. Endogenous growth models emphasize that human capital formation, that accompanies physical capital accumulation is an important driver of technological progress. Unlike the Solow model, endogenous growth models are based on the assumption of constant or increasing marginal returns to capital. Endogenous growth models highlight the importance of savings and capital (both human and physical) accumulation for economic growth.
BUSINESS PAPER NO. 5: MACROECONOMIC ANALYSIS AND POLICY ECONOMICS MODULE NO.26: THEORIES OF ECONOMIC GROWTH PART – 3