Growth and Accumulation

Posted on March 13, 2015

The production function provides a qualitative link between the inputs and outputs. As a simplification, we can assume that \(K\), capital and \(N\), labor are the only inputs. Then the output \(Y\) depends on the inputs and the level of technology \(A\) (sometimes \(A\) is called productivity).

\[Y = A\, F(K,N)\]

Natural resources. For example, oil, fertile land (fertile land is the reason for US’s growth in 1800’s).
Human capital. Investment in human capital refers to schooling, on-the-job training. In poor countries, investment in health can be regarded as investment in human capital. In even poorer countries, rise in calorie intake of labourers can be regarded as investment in human capital. Including human capital, we can regard the production function \(Y\) as

\[Y = AF(K,H,N)\]

Studies claim that income share of human capital is large in industrialized countries.
Other factors such as arrival of monsoon, immigration of skilled workers, war refugees can also affect the short term growth.

Growth theory: The Neoclassical model

Work on growth theory can be divided according to the time at which it happened. The first in late 1950s and the 1960s and the second in the late 1980s and early 1990s. The research in the first period is created neoclassical growth theory. Neoclassical growth theory focuses on capital accumulation and link to savings decisions and the like. Best known contributor is Robert Solow.

The growth rate of output in steady state is exogenous (?); in this case this is equal to the population growth rate, \(n\). It is therefore independent of the saving rate \(s\).
Although, an increase in the saving rate does not affect the steady-state growth rate (?), it does increase the steady-state level of income by increasing the capital-output ratio.
Then, when we allow for productivity growth, we can show that if there is a steady state, the steady-state growth rate of output remains exogenous. The steady-state rate growth rate of aggregate output is the sum of the rate of technical progress and the rate of population growth.
The final prediction in this theory is convergence: If two countries have the same rate of population growth, the same saving rate, and access to the same production function, they will eventually reach the same level of income. In this framework, poor countries are poor because they have less capital, but they save at the same rate as rich countries and have access to the same technology, they will eventually catch up.

Neoclassical growth theory accounts for growth in output as a function of growth in inputs, particularly, the capital and labor. The relative importance of each input depends upon its factor share (?).
Labor is the most important input.
Long-run growth results from improvements in technology.
Absent technological improvement, output per person, will eventually converge to a steady-state value. Steady-state output per person depends positively on the saving rate and negatively on the rate of population growth.
The long run growth does not depend on the saving rate.

Neoclassical theory does a good job at explaining much of what we observe int the world and is also mathematically elegant. Nonetheless, in late 1980’s dissatisfaction in the theory arose both on empirical and theoretical basis. Mainly, the fact that Neoclassical growth theory attributes long-run growth to the technological progress, but leaves unexplained the economic determinants of the technological progress.
Empirical dissatisfaction developed over the prediction that growth and savings should be uncorrelated at the steady state. Some data indicates that the growth and savings rate are positively correlated across countries.

Endogenous growth theory emphasizes different growth opportunities in physical capital and knowledge capital. There are diminishing marginal returns on the former, but not on the latter.
Increased investment in knowledge increases growth is the key idea to linking higher savings rates to higher equilibrium growth rates.
Conditional convergence. The neoclassical growth theory predicts absolute convergence for economics with equal rates of saving and population growth and with access to same technology. Conditional convergence is predicted for economies with different rates of saving or population growth; that is, steady-state income will differ as predicted by Solow growth diagram, but growth rates will eventually equalize.
Robert Barro has shown that while countries that invest more tend to grow faster, the impact of higher investment seems to be transitory (i.e., continuing only for a short period of time or not enduring). Countries with higher investment will end in a steady state with higher per capita income but not with higher growth rate. This suggests that countries do converge conditionally, and thus endogenous growth theory is not very important for explaining international differences in growth rates, although it may be quite important for explaining growth in countries on the leading edge of technology.

Summary

Economic growth of most developed countries depends on the rate of technological progress. According to Endogenous growth model, the technological progress depends on saving, particularly investment directed toward human capital.
There are extraordinarily different growth experiences in different countries.

Endogenous growth theory relies on constant returns to scale to accumulable factors to generate ongoing growth.
Current empirical evidences suggest that endogenous growth theory is not very important for explaining international differences in growth rates.

Steady state equilibrium: for the economy is the combination of per capita GDP and per capita capital where the economy will remain at rest, that is, when the economic variables are no longer changing, \(\Delta y = 0\) and \(\Delta k = 0\).
Steady state occurs where the saving and investment requirement lines cross. Anywhere the saving line is above the investment requirement line, the economy is growing because capital is being added.
Production function: The production function \(y= f(k)\) is the relationship between per capita output and the capital-labor ratio.