Endogenous growth theory
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Endogenous growth theory holds that economic growth is primarily the result of endogenous and not external forces. Endogenous growth theory holds that investment in human capital, innovation, and knowledge are significant contributors to economic growth. The theory also focuses on positive externalities and spillover effects of a knowledge-based economy which will lead to economic development. There are classical, neo-classical and Keynesian theories of growth (see especially the book by Neri Salvodori and Carlo Panico, Classical, Neo-Classical and Keynesian Views on Growth and Distribution). The endogenous growth theory primarily holds that the long run growth rate of an economy depends on policy measures. For example, subsidies for research and development or education increase the growth rate in some endogenous growth models by increasing the incentive for innovation.
Models in Endogenous Growth 
In the mid-1980s, a group of growth theorists became increasingly dissatisfied with common accounts of exogenous factors determining long-run growth. They favored a model that replaced the exogenous growth variable (unexplained technical progress) with a model in which the key determinants of growth were explicit in the model. The initial research was based on the work of Kenneth Arrow (1962), Hirofumi Uzawa (1965), and Miguel Sidrauski (1967). Paul Romer (1986), Lucas (1988), and Rebelo (1991) omitted technological change. Instead, growth in these models was due to indefinite investment in human capital which had spillover effect on economy and reduces the diminishing return to capital accumulation.
The AK model, which is the simplest endogenous model, gives a constant-saving-rate of endogenous growth. It assumes a constant, exogenous, saving rate. It models technological progress with a single parameter (usually A). It uses the assumption that the production function does not exhibit diminishing returns to scale to lead to endogenous growth. Various rationales for this assumption have been given, such as positive spillovers from capital investment to the economy as a whole or improvements in technology leading to further improvements (i.e. learning-by-doing). However, the endogenous growth theory is further supported with models in which agents optimally determined the consumption and saving, optimizing the resources allocation to research and development leading to technological progress. Romer (1987, 1990) and signiﬁcant contributions by Aghion and Howitt (1992) and Grossman and Helpman (1991), incorporated imperfect markets and R&D to the growth model.
The AK Model 
The model works on the property of absence of diminishing returns to capital. The simplest form of production function with diminishing return is:
- , is a positive constant that reflects the level of the technology.
- capital (broad sense to include human capital)
- , output per capita and the average and marginal product are constant at the level
If we substitute in equation of transitional Dynamics of Solow-Swan model (Exogenous growth model) which shows how an economy’s per capita incomes converges toward its own steady-state value and to the per capita incomes of other nations.
Transitional Dynamics equation, where Growth rate on is given by,
on substituting , we get,
We return here to the case of zero technological progress, , because we want to show that per capita growth can now occur in the long-run even without exogenous technological change. The figure 1.1 explains the perpetual growth, with exogenous technical progress. The vertical distance between the two line, and n+δ gives the
As, n+δ, so that. Since the two line are parallel, is constant; in particular, it is independent of . In other words, always grows at steady states rate,.
- , equals
at every point of time. In addition, since
the growth rate of
- equals .
Hence, the entire per capita variable in the model grows at same rate, given by
However, we can observe that technology displays a positive long-run per capita growth without any exogenous technological development. The per capita growth depends on behavioural factors of the model as the saving rate and population. It is unlike neoclassical model, which is higher saving, s, promotes higher long-run per capita growth .
Endogenous versus exogenous growth theory 
In neo-classical growth models, the long-run rate of growth is exogenously determined by either the savings rate (the Harrod–Domar model) or the rate of technical progress (Solow model). However, the savings rate and rate of technological progress remain unexplained. Endogenous growth theory tries to overcome this shortcoming by building macroeconomic models out of microeconomic foundations. Households are assumed to maximize utility subject to budget constraints while firms maximize profits. Crucial importance is usually given to the production of new technologies and human capital. The engine for growth can be as simple as a constant return to scale production function (the AK model) or more complicated set ups with spillover effects (spillovers are positive externalities, benefits that are attributed to costs from other firms), increasing numbers of goods, increasing qualities, etc.
Often endogenous growth theory assumes constant marginal product of capital at the aggregate level, or at least that the limit of the marginal product of capital does not tend towards zero. This does not imply that larger firms will be more productive than small ones, because at the firm level the marginal product of capital is still diminishing. Therefore, it is possible to construct endogenous growth models with perfect competition. However, in many endogenous growth models the assumption of perfect competition is relaxed, and some degree of monopoly power is thought to exist. Generally monopoly power in these models comes from the holding of patents. These are models with two sectors, producers of final output and an R&D sector. The R&D sector develops ideas that they are granted a monopoly power. R&D firms are assumed to be able to make monopoly profits selling ideas to production firms, but the free entry condition means that these profits are dissipated on R&D spending.
An Endogenous growth theory implication is that policies which embrace openness, competition, change and innovation will promote growth. Conversely, policies which have the effect of restricting or slowing change by protecting or favouring particular existing industries or firms are likely over time to slow growth to the disadvantage of the community. Peter Howitt has written:
Sustained economic growth is everywhere and always a process of continual transformation. The sort of economic progress that has been enjoyed by the richest nations since the Industrial Revolution would not have been possible if people had not undergone wrenching changes. Economies that cease to transform themselves are destined to fall off the path of economic growth. The countries that most deserve the title of “developing” are not the poorest countries of the world, but the richest. [They] need to engage in the never-ending process of economic development if they are to enjoy continued prosperity. (Conclusion, "Growth and development: a Schumpeterian perspective", 2006 ).
One of the main failings of endogenous growth theories is the collective failure to explain conditional convergence reported in the empirical literature. Another frequent critique concerns the cornerstone assumption of diminishing returns to capital. Some[who?] contend that new growth theory has proven no more successful than exogenous growth theory in explaining the income divergence between the developing and developed worlds (despite usually being more complex).
See also 
- Economic growth
- Human capital
- Mahalanobis model
- Exogenous growth model
- Paul Romer
- Ramsey–Cass–Koopmans model
- Romer, P. M. (1994). "The Origins of Endogenous Growth". The Journal of Economic Perspectives 8 (1): 3.
- "Monetary Growth Theory". newschool.edu. 2011 [last update]. Retrieved 11 October 2011.
- Lucas, R. E. (1988). "On the mechanics of Economic Development". Journal of Monetary Economics 22.
- Rebelo, Sergio (1991). "Long-Run Policy Analysis and Long-Run Growth". Journal of Political Economy 99 (3): 500.
- Carroll, C. (2011 [last update]). "The Rebelo AK Growth Model". econ2.jhu.edu. Retrieved 11 October 2011. "the steady-state growth rate in a Rebelo economy is directly proportional to the saving rate."
- Barro, R. J.; Sala-i-Martin, Xavier (1998-11-20). Economic Growth. ISBN 978-0-262-02459-4.
- Economic Growth, 2nd Edition Robert J. Barro and Xavier Sala-i-Martin
- Fadare, Samuel O. "Recent Banking Sector Reforms and Economic Growth in Nigeria". Middle Eastern Finance and Economics (Issue 8 (2010)).
- See Sachs, Jeffrey D.; Warner, Andrew M. (1997). "Fundamental Sources of Long-Run Growth". American Economic Review 87 (2): 184–188. JSTOR 2950910.
- See for instance, Professor Stephen Parente's 2001 review, The Failure of Endogenous Growth (Online at the University of Illinois at Urbana-Champaign). (Published in Knowledge Technology & Policy Volume XIII, Number 4.)
- Economic Growth by Paul Romer.
- New Growth Theory, Technology and Learning: A Practitioner's Guide, U.S. Economic Development Administration.
- Technological Implications of New Growth Theory for the South, United Nations Development Programme.
- The AK Model by Economic Growth, 2nd Edition Robert J. Barro and Xavier Sala-i-Martin[dead link]
- The Origins of Endogenous Growth, Romer.M Paul,The Journal of Economic Perspectives, Vol. 8, No. 1. (Winter, 1994), pp. 3-22.