Endogenous growth theory
This article may be too technical for most readers to understand. (August 2011) 
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Endogenous growth theory holds that economic growth is primarily the result of endogenous and not external forces.^{[1]} 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 knowledgebased economy which will lead to economic development. 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.
Contents
Models
In the mid1980s, a group of growth theorists became increasingly dissatisfied with common accounts of exogenous factors determining longrun 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 work of Kenneth Arrow (1962), Hirofumi Uzawa (1965), and Miguel Sidrauski (1967) formed the basis for this research.^{[2]} Paul Romer (1986), Robert Lucas (1988),^{[3]} Sergio Rebelo (1991)^{[4]}^{[5]} and Ortigueira and Santos (1997)^{[6]} omitted technological change; instead, growth in these models is due to indefinite investment in human capital which had spillover effect on economy and reduces the diminishing return to capital accumulation.^{[7]}
The AK model, which is the simplest endogenous model, gives a constantsavings rate of endogenous growth and 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 (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.^{[7]}
AK model
The AK model works on the property of absence of diminishing returns to capital. The simplest form of production function with nondiminishing return is:
where
 , is a positive constant that reflects the level of the technology.
 capital (broad sense to include human capital)
Now, assume output per capita be determined by the constant
 ,
= capital per worker
= output/income per worker
If is substituted in the equation of transitional Dynamics of SolowSwan model (exogenous growth model), and f(k) is the output function per worker, how an economy’s per capita incomes converges toward its own steadystate value, to the per capita incomes of other nations, can be seen.
The transitional dynamics equation, in which the growth rate on is given by
on substituting , this is gotten:
The case of zero technological progress, , is returned to because per capita growth can now occur in the longrun 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,.
Since
 , 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, technology displays a positive longrun 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 longrun per capita growth .^{[7]}
Endogenous versus exogenous growth theory
In neoclassical growth models, the longrun 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.
Implications
An endogenous growth theory implication is that policies that embrace openness, competition, change and innovation will promote growth.^{[8]} Conversely, policies that 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 neverending process of economic development if they are to enjoy continued prosperity. (Conclusion, "Growth and development: a Schumpeterian perspective", 2006 [1]).
Criticisms
One of the main failings of endogenous growth theories is the collective failure to explain conditional convergence reported in empirical literature.^{[9]}
Another frequent critique concerns the cornerstone assumption of diminishing returns to capital. Stephen Parente contends that new growth theory has proved to be no more successful than exogenous growth theory in explaining the income divergence between the developing and developed worlds (despite usually being more complex).^{[10]}
Paul Krugman criticized endogenous growth theory as nearly impossible to check by empirical evidence; “too much of it involved making assumptions about how unmeasurable things affected other unmeasurable things.”^{[11]}
See also
 Economic growth
 Human capital
 Feldman–Mahalanobis model
 Solow–Swan model, “the” exogenous growth model
 Ramsey–Cass–Koopmans model, a microfounded growth model with infinite horizon
Notes
 ↑ Romer, P. M. (1994). "The Origins of Endogenous Growth". The Journal of Economic Perspectives. 8 (1): 3–22. JSTOR 2138148. doi:10.1257/jep.8.1.3.
 ↑ "Monetary Growth Theory". newschool.edu. 2011. Retrieved 11 October 2011.
 ↑ Lucas, R. E. (1988). "On the mechanics of Economic Development" (PDF). Journal of Monetary Economics. 22.
 ↑ Rebelo, Sergio (1991). "LongRun Policy Analysis and LongRun Growth". Journal of Political Economy. 99 (3): 500. doi:10.1086/261764.
 ↑ Carroll, C. (2011). "The Rebelo AK Growth Model" (PDF). econ2.jhu.edu. Retrieved 11 October 2011.
the steadystate growth rate in a Rebelo economy is directly proportional to the saving rate.
 ↑ Ortigueira, Salvador and Manuel S. Santos, (1997). "On the Speed of Convergence in Endogenous Growth Models, American Economic Review, Vol. 87, No. 3, pp. 383399.
 ↑ ^{7.0} ^{7.1} ^{7.2} Barro, R. J.; SalaiMartin, Xavier (2004). Economic Growth (2nd ed.). New York: McGrawHill. ISBN 0262025531.
 ↑ Fadare, Samuel O. "Recent Banking Sector Reforms and Economic Growth in Nigeria" (PDF). Middle Eastern Finance and Economics (8 (2010)).
 ↑ See Sachs, Jeffrey D.; Warner, Andrew M. (1997). "Fundamental Sources of LongRun Growth". American Economic Review. 87 (2): 184–188. JSTOR 2950910.
 ↑ Parente, Stephen (2001). "The Failure of Endogenous Growth". Knowledge, Technology & Policy. 13 (4): 49–58. doi:10.1007/BF02693989.
 ↑ Krugman, Paul (August 18, 2013). "The New Growth Fizzle". New York Times.
Further reading
 Acemoglu, Daron (2009). "Endogenous Technological Change". Introduction to Modern Economic Growth. Princeton University Press. pp. 411–533. ISBN 9780691132921.
 Barro, Robert J.; SalaiMartin, Xavier (2004). "OneSector Models of Endogenous Growth". Economic Growth (Second ed.). New York: McGrawHill. pp. 205–237. ISBN 0262025531.
 Farmer, Roger E. A. (1999). "Endogenous Growth Theory". Macroeconomics (Second ed.). Cincinnati: SouthWestern. pp. 357–380. ISBN 0324120583.
 Romer, David (2011). "Endogenous Growth". Advanced Macroeconomics (Fourth ed.). New York: McGrawHill. pp. 101–149. ISBN 9780073511375.