Economic Growth

Economic growth is an increase in aggregate economic activities. More precisely, it is the rate of an increase in gross domestic product (GDP). Alternatively, economic growth can also be defined as the rate of an increase in real GDP per capita.

The Harrod-Domar model is of great importance in neoclassical exogenous growth models as it marks the first attempt to explain an economy’s long-run growth rate within the Keynesian framework.

This model has several limitations. First, it is assumed that an economy operates at full employment. Second, capital-output and capital-labor ratios are both assumed to be constant. Third, there is a lack of factor substitution; in other words, there is no substitution of capital for labor or the other way around. Last, despite its important role in long-run growth, technological progress is not considered in the model.

Solow (1956) is the first study that developed an exogenous model of long-run growth and it is considered to be the basis of all the subsequent growth models in the literature.

There are several assumptions of this model. First, there are two factors to be considered: labor and capital. Second, the production function has constant returns to scale. Third, output increases as labor and capital increase but there are diminishing returns to each factor. Last, technological change is exogenously given.

First, an increase in capital relative to labor may create economic growth because more capital is believed to enhance labor productivity. Second, due to the diminishing returns to capital, poor countries with less per capita capital will grow faster. This is because each investment in capital in these countries will produce a higher return when compared to rich countries. Third, again due to the diminishing returns to capital, economies will eventually reach a point where an increase in capital may not generate any growth. This point is called “steady-state”, which is a long-run equilibrium growth rate in the Solow model. Also, in the long run, output per capita depends on the saving rate; however, the output growth rate is not determined by the saving rate. Finally, long-run growth can be achieved only if countries improve their level of technology. However, given that technology is exogenous in this model, any technological change does not make any contribution to economic growth.

Convergence is the hypothesis suggesting that poor countries grow faster than rich countries. There are two important types of convergence in the neoclassical model: conditional and unconditional (absolute) convergence. Conditional convergence suggests that countries converge to their own steady-state level of income. However, according to unconditional convergence, all countries converge to the same steady-state level.

Assumption 1: There are diminishing returns to each factor, K (capital) and L (labor).

Assumption 2: The production function has constant returns to scale.

Assumption 3: Although the Solow model is one of the first models that address the importance of technological change in the long-run growth rate of output, technological progress is assumed to be exogenous in the model.

The golden rule level of capital accumulation was first articulated by Edmund Phelps and it is the level of capital that maximizes the level of consumption in the steady state. In other words, the economy moves to a new steady-state at which consumption is maximized.

• The steady-state levels of output and capital stock per worker are positively related with the saving rate (s) and technological progress (g), whereas they are negatively related with population growth (n) and depreciation rate (δ).
• The steady-state levels of output and capital stock per effective worker are positively related with the saving rate (s), whereas they are negatively related with technological progress (g), population growth (n), and depreciation rate (δ).
• The steady-state levels of aggregate output and capital stock are positively related with the saving rate (s), technological progress (g), and population growth (n), whereas they are negatively related with the depreciation rate (δ).
• With positive population growth (n) and technological progress (g), in the steadystate, it is assumed that economy’s aggregate capital stock (K *) and output (Y *) grow at the rate n+g, and that capital stock and output per worker increase at the rate g; however, capital stock and output per effective worker do not grow.
• Anincreaseinthesaving ratehas a temporary effect on the growth rates of capital stock and output, implying that it has no effect on their growth rates in the steady state. However, it has a permanent (increasing) effect on the steady-state levels of aggregate capital stock and output, capital stock per worker and output per worker, and capital stock per effective worker and output per effective worker.

• Although the growth rate in the model is determined by the rate of technological progress, the model cannot account for long-run growth because technological progress is assumed to be exogenous in the model.
• The Solow model cannot explain per capita income differences across countries.
• In the model, the absolute (unconditional) convergence hypothesis is assumed, implying that poor countries grow faster than rich countries until they reach their steady state. However, there is no empirical evidence supporting this hypothesis.

The Solow model fails to explain growth rates of per capita income or differences in living standards. Therefore, Mankiw et al. (1992) developed the augmented Solow model by introducing human capital into the basic Solow model.

Model implies that although human capital allows us to explain cross-country differences in income levels, the model still cannot account for long-run growth because technological progress is constant.

Although the Solow model was the first attempt to model long-run growth analytically, it has failed to provide compelling evidence about why some countries grow faster than others because it has several shortcomings. Most importantly, productivity growth, that is, technological progress, is the only determinant of an increase in the long-run per capita income but the Solow model cannot explain how technological progress is determined because it is assumed to be exogenous in the model.

Romer (1986)’s study is crucial to our wider understanding of endogenous growth models. In his study, he suggested that long-run growth is determined by the saving and investment rate of a country, rather than technological progress which is exogenously determined in the model.

Lucas (1988) suggested that technological progress is endogenous and that human capital is a contributing factor for economic growth.

In reviewing the literature, there are two strands of research on these types of models. Firstly, Romer (1990) developed a product-variety model where innovation can create new varieties of products, which in turn leads to productivity growth. Secondly, Aghion and Howitt (1992) developed the Schumpeterian version of endogenous growth theory, commonly referred to as “Schumpeterian growth theory” this is because Schumpeter’s (1942) idea of “creative destruction” is a key term in their model, suggesting that qualityimproving innovations make old products obsolete.

The AK model is one of the first endogenous growth models.

There are several assumptions of this model. First, the production function is linear in capital stock. Second, there is no labor in the production function. Third, capital exhibits constant returns. Fourth, a constant, exogenous saving rate is assumed. Also, there is a fixed level of technology. Finally, population growth is assumed to be constant so the growth rate of aggregate output, Y, is equal to the growth rate of per capita output, y.

In the AK model:

• Capital exhibits constant returns.
• Even without technological progress and population growth, growth of per capita income can be achieved.
• There is no convergence of per capita income levels across countries.
• The growth rate of per capita income is an increasing function of the saving rate.
• An increase in the saving rate has a permanent effect on the growth rate of per capita income.

However, in the Solow model:
• Capital exhibits diminishing returns.
• Growth of per capita income can only be achieved with technological progress.
• In line with the absolute (unconditional) convergence hypothesis, it is assumed that poor countries grow faster than rich countries until they reach their steady state. This is also the case with the human capital-augmented Solow model.
• The growth rate of per capita income is not dependent on the saving rate due to the diminishing returns to capital.
• An increase in the saving rate has no permanent effect on the growth rate of per capita income.