# Endogenous growth theory

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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 knowledge-based 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.

Economic growth is the increase in the inflation-adjusted market value of the goods and services produced by an economy over time. It is conventionally measured as the percent rate of increase in real gross domestic product, or real GDP.

In econometrics, endogeneity broadly refers to situations in which an explanatory variable is correlated with the error term. The distinction between endogenous and exogenous variables originated in simultaneous equations models, where one separates variables whose values are determined by the model from variables which are predetermined; ignoring simultaneity in the estimation leads to biased estimates as it violates the exogeneity assumption of the Gauss–Markov theorem. The problem of endogeneity is unfortunately, oftentimes ignored by researchers conducting non-experimental research and doing so precludes making policy recommendations. Instrumental variable techniques are commonly used to address this problem.

Human capital is the stock of habits, knowledge, social and personality attributes embodied in the ability to perform labour so as to produce economic value.

## Models

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 work of Kenneth Arrow (1962), HirofumiUzawa  ( 1965 ), and Miguel Sidrauski (1967) formed the basis for this research. [2] Paul Romer (1986), RobertLucas  ( 1988 ), SergioRebelo  ( 1991 ) [3] and OrtigueiraandSantos ( 1997 ) omitted technological change; instead, growth in these models is due to indefinite investment in human capital which had a spillover effect on the economy and reduces the diminishing return to capital accumulation. [4]

Kenneth Joseph Arrow was an American economist, mathematician, writer, and political theorist. He was the joint winner of the Nobel Memorial Prize in Economic Sciences with John Hicks in 1972.

Hirofumi Uzawa was a Japanese economist.

Miguel Sidrauski was an Argentine economist who made important contributions to the theory of economic growth by developing a modified version of the Ramsey–Cass–Koopmans model to describe the effects of money on long-run growth. He also published an article on exchange rate determination. Sidrauski taught economics at Massachusetts Institute of Technology.

The AK model, which is the simplest endogenous model, gives a constant-savings 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. 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. [4]

The AK model of economic growth is an endogenous growth model used in the theory of economic growth, a subfield of modern macroeconomics. In the 1980s it became progressively clearer that the standard neoclassical exogenous growth models were theoretically unsatisfactory as tools to explore long run growth, as these models predicted economies without technological change and thus they would eventually converge to a steady state, with zero per capita growth. A fundamental reason for this is the diminishing return of capital; the key property of AK endogenous-growth model is the absence of diminishing returns to capital. In lieu of the diminishing returns of capital implied by the usual parameterizations of a Cobb–Douglas production function, the AK model uses a linear model where output is a linear function of capital. Its appearance in most textbooks is to introduce endogenous growth theory.

### AK model

The AK model production function is a special case of a Cobb–Douglas production function:

In economics and econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs and the amount of output that can be produced by those inputs. The Cobb–Douglas form was developed and tested against statistical evidence by Charles Cobb and Paul Douglas during 1927–1947.

${\displaystyle Y=AK^{a}L^{1-a}\,}$

This equation shows a Cobb–Douglas function where Y represents the total production in an economy. A represents total factor productivity, K is capital, L is labor, and the parameter ${\displaystyle a}$ measures the output elasticity of capital. For the special case in which ${\displaystyle a=1}$, the production function becomes linear in capital thereby giving constant returns to scale: [4]

In economics, total-factor productivity (TFP), also called multi-factor productivity, is usually measured as the ratio of aggregate output to aggregate inputs. Under some simplifications about the production technology, growth in TFP becomes the portion of growth in output not explained by growth in traditionally measured inputs of labour and capital used in production. TFP is calculated by dividing output by the weighted average of labour and capital input, with the standard weighting of 0.7 for labour and 0.3 for capital. Total factor productivity is a measure of economic efficiency and accounts for part of the differences in cross-country per-capita income. The rate of TFP growth is calculated by subtracting growth rates of labor and capital inputs from the growth rate of output.

In economics, output elasticity is the percentage change of output divided by the percentage change of an input. It is sometimes called partial output elasticity to clarify that it refers to the change of only one input.

${\displaystyle Y=AK.}$

## 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.

The Harrod–Domar model is a classical Keynesian model of economic growth. It is used in development economics to explain an economy's growth rate in terms of the level of saving and productivity of capital. It suggests that there is no natural reason for an economy to have balanced growth. The model was developed independently by Roy F. Harrod in 1939, and Evsey Domar in 1946, although a similar model had been proposed by Gustav Cassel in 1924. The Harrod–Domar model was the precursor to the exogenous growth model.

In economics, the microfoundations are the microeconomic behavior of individual agents, such as households or firms, that underpins a macroeconomic theory.

Knowledge spillover is an exchange of ideas among individuals. In knowledge management economics, knowledge spillovers are non-rival knowledge market costs incurred by a party not agreeing to assume the costs that has a spillover effect of stimulating technological improvements in a neighbor through one's own innovation. Such innovations often come from specialization within an industry.

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. [5] 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 never-ending process of economic development if they are to enjoy continued prosperity. [6]

## Criticisms

One of the main failings of endogenous growth theories is the collective failure to explain conditional convergence reported in empirical literature. [7]

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). [8]

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.” [9]

## Notes

1. Romer, P. M. (1994). "The Origins of Endogenous Growth". The Journal of Economic Perspectives . 8 (1): 3–22. doi:10.1257/jep.8.1.3. JSTOR   2138148.
2. "Monetary Growth Theory". newschool.edu. 2011. Archived from the original on 21 October 2015. Retrieved 11 October 2011.
3. Carroll, C. (2011). "The Rebelo AK Growth Model" (PDF). econ2.jhu.edu. Retrieved 11 October 2011. the steady-state growth rate in a Rebelo economy is directly proportional to the saving rate.
4. Barro, R. J.; Sala-i-Martin, Xavier (2004). Economic Growth (2nd ed.). New York: McGraw-Hill. ISBN   978-0-262-02553-9.
5. Fadare, Samuel O. (2010). "Recent Banking Sector Reforms and Economic Growth in Nigeria" (PDF). Middle Eastern Finance and Economics (8). Archived from the original (PDF) on 2012-03-24.
6. Howitt, Peter (April 2007). Growth and development: a Schumpeterian perspective (PDF). C. D. Howe Institute Commentary. C. D. Howe Institute. ISBN   978-0888067098. ISSN   0824-8001. Archived from the original (PDF) on July 17, 2011. Retrieved August 16, 2018.
7. Sachs, Jeffrey D.; Warner, Andrew M. (1997). "Fundamental Sources of Long-Run Growth". American Economic Review . 87 (2): 184–188. JSTOR   2950910.
8. Parente, Stephen (2001). "The Failure of Endogenous Growth". Knowledge, Technology & Policy. 13 (4): 49–58. CiteSeerX  . doi:10.1007/BF02693989.
9. Krugman, Paul (August 18, 2013). "The New Growth Fizzle". New York Times.

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