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Solow Growth Model Essay

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ESSAY TOPIC: Using your compiled dataset and basic statistical analysis based on a scatter plot (with a linear fit)[1] answer the following two questions:

  1. Discuss whether your data supports the predictions of the Solow type model in relation to the effects of the savings rate (or investment rate) and population growth on GDP per capita.
  2. Is there any evidence of convergence among the countries in your sample? Discuss.



Economic growth is a phenomenon desired by most countries because of the many benefits associated with it such as increased standard of living, favourable balance of payments etc. Sustained economic growth is even more desirous as it leads to development (Felipe, Kumar, Abdon, 2010).Although sustained economic growth is considered a necessity for development, ‘there are large differences in income per capita and output per worker across countries today’; industrialised countries are over 30 times as rich as bottom developing countries (Acemoglu, 2007).

These differences in growth rates amongst countries has led to many scholars’ publications all in a bid to explain why countries have different growth rates, to determine if the growth rates amongst countries converge i.e do poorer countries eventually catch up with richer countries and to suggest ways through which economic growth can be increased. Earlier economists made efforts to explain these differences. However, the birth of modern inquiry into explaining different growth rates amongst countries can be attributed to the publications of economist, Robert Solow.

This next section will look at the Solow model, its predictions and the findings of other scholars on Solow’s predictions, the third section contains data analysis using data from 24 developed countries and 15 developing countries (Sub-saharan Africa, Asia, Latin America and the Carribbean), the fourth section comprises of discussion of results and this essay will conclude in secton 5

The Solow Growth model

The Solow- Swan model popularly known as the Solow model led to a revolution in economic thoughts on economic growth. In 1956, Robert Solow published his work, ‘A contribution to the Theory of Economic Growth’ for which he won the Nobel prize in economics in 1987. Acemoglu (2007) describes the solow model as superior to the Harrod- Domer model due its simplicity and its introduction of the neo-classical production function.

The Assumptions of the Solow model

  • Only a single good is produced with a constant technology growth rate
  • All factors of production (labour and capital) are fully employed
  • Diminishing returns to the factors of production
  • Constant returns to scale
  • Technological progress, savings rate and population growth rate are exogenous
  • Two factors of production; labour and capital which are paid their marginal products

Solow adopts the cobb- douglas production function in his work:


Where A is technology growth rate

K is Capital stock

L is amount of labour

α and 1-α are capital’s and labour’s share of income respectively.

His predictions

The Solow model predicts that an increase in investment rate will shift the steady state (where change in capital is zero) to a higher level thereby increasing output (Y), an increase in population growth rate not matched by an increase in technology growth rate will shift the steady state downwards, reducing output (Y). Solow’s model also predicts convergence amongst countries with similar savings rate, population growth rate and depreciation rate, in output per capita and standard of living, in the long run based on his assumption of diminishing returns to capital for countries approaching or in their steady state (Solow, 1956). Based on his convergence principle, developing countries should be expected to catch up more quickly with the developed countries. As is usually done in the field of economics, several authors have carried out tests on Solow’s predictions, here are their findings, Mankiw, Romer and Weil (1992) using a large set of data for 1960-1985 found that savings rate and population growth rate affect output in the way Solow predicted.They argue that the solow model is better when human capital variable is included.They found no unconditional convergence amongst 98 countries in the world and unconditional convergence amongst 22 OECD countries. Barro, Salai-i-Martin, et al (1991) found there to be convergence among similar regions. Also Barossi-Filho et al (2005) found from data of 53 countries that savings and population growth have the Solow theoretically predicted signs and that on average, countries will converge at 7.2% in the long run. On the other hand, Lee et al (1997) suggest that countries are diverging rather than converging. The succeeding chapters of this work will test Solow’s predictions using data on 39 countries.

Data analysis

Data sources and Description

This work makes use of data on investment rate (Investment Share of real GDP Per Capita at 2005 constant prices [rgdpl]), population growth rate (computed from population (in thousands), Real GDP per capita and Real GDP per capita growth rate (real GDP per capita (Laspeyres), derived from growth rates of c, g, i, at 2005 constant prices) for 39 counties sourced from the penn world table spanning over a period of 1960 to 2000. Penn world table 7.1(2012)


Using STATA, scatter plots were generated for various combinations of the variables. A single value per variable for each country was computed by calculating the average over 41 years. Below are the scatter plots (results) generated by STATA

FIG 1: Scatter plot of population growth and GDP per capita

FIG 2: Scatter plot of investment rate and Real GDP per capita

FIG 3: Convergence amongst all 39 countries (initial rgdp is rgdp of 1960)

FIG 4: Convergence amongst the 24 developed countries

FIG 5: Convergence among the 15 developing countries

Discussion of results

Figure 1 and 2 support Solow’s prediction that increase in population growth rate is linked to a decrease in levels of per capita output while increase in investment rate is linked with higher levels of per capita output. These relationships are evident in the negative and positive sloped graphs respectively in the above diagrams. Figure 3 does not support his prediction that developing countries catch up quickly with their developed counterparts, in the graph developing countries are lagging behind the developing countries. There is no convergence. Figure 4 which represents convergence among the developed nations shows evidence of convergence just like Mankiw, Romer and Weil (1992) found, it shows that countries that started out with higher levels of intial rgdp such as Switzerland and Australia grew slower than countries like Japan and Portugal that had lower intial rgdp. Figure 4 does a good job of explaining differences in growth rates in developed countries.However, Figure 5 shows evidence of no convergence amongst developing nations, this may be as a result of differences in the various regions from which these countries were selected. Figure 5 gives credence to Barro and Salai-i-martin et al (1991) findings that there is regional convergence ie countries from dissimilar regions show no evidence of convergence.

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