Solow Growth Model

Solow model – how well it holds in the real world? Prepared by:- Amol Rattan (75013) Introduction Prior to Solow Model, Harrod Domar model had shown how the savings rate could play a crucial role in determining the Long run rate of Growth. Solow model however proved a result that was contrary to what Harrod Domar model had predicted. It showed that savings has only level effect on income and the growth rate of income depends upon the rate of efficiency or technical progress in the country. Solow Model relies on certain assumptions 1. There are constant returns to Scale(CRS) 2.The production function is standard neoclassical production function with diminishing returns to factor 3. The markets are perfectly competitive 4. Households save at a constant savings rate ‘s’ Equilibrium in Solow Model is defined as the steady state level of capital where the economy grows at a constant rate. By assuming that the two factors of production are capital and labour per efficie ncy unit, it can be shown that savings only affects the level of per capita income. It is only the rate of growth of efficiency which determines the rate of growth of per capita output.For production function: Y= K? L1-? Steady state values are: y†¢=[s/? +? +n]? /1-? k†¢ =[s/? +? +n]1/1-? Objective i) To find how true the result of convergence of Solow model holds for a sample of countries of the world ii) Test Solow model for India for the period 1990-2008 Methodology i) To find how true the result of convergence of Solow model holds for a sample of countries of the world †¢ To prove: Convergence result Solow model predicts that all nations with same parameter of savings rate, population growth rate and depreciation rate will all grow at the same rate in long run.This implies A) The rich countries (defined as those at high level of income) will grow at a lower rate B) The poor countries will grow at a faster rate These conditions mean that the poor countries are able to catch up with the rich countries in the long run. †¢ Test of convergence Regression We test the relation ln(rate of growth of y) = ? + ? ln(initial value of y) Conditions A and B imply that the coefficient ? should be negative Result: For a sample of 23 countries for period 1990-2008 we find: 1) the value of ? = -0. 377451859 ) I t is highly significant as the probability value(pvalue) is close to zero 3) The correlation of ln rate of growth of per capita income over the period with initial income is negative 4) % of data growth of rate of growth is explained by the initial level of income. It makes sense also as rate of growth depends not only on the initial level of income but other factors like education, R&D, etc Standard deviation We test how standard deviation of relative incomes (relative to US) of the countries changes over time. Convergence implies that income of countries become more and more equal.So we expect standard deviations to decrease over time. Result: St andard deviation falls over time for the sample of countries implying convergence Caveats The results that we get are consistent with the theoretical results. However most of the empirical work that has been done on Solow Model has shown the opposite result i. e. unconditional convergence is not seen to hold. The reason for this could the sampling error. We need to take a larger data set to test it again before accepting. ii) Test Solow model for India for the period 1990-2008Solow model gives us the steady state value of per capita income as y†¢=[s/? +? +n]? /1-? Taking log on both sides ln y†¢= (? /1-? )ln(s) – (? /1-? )ln(? +? +n) We estimate this equation for India for the period 1990-2008 A priori theory tells us that o The signs of ln s and ln (n+ ? +? ) should be opposite o The sign of ln s should be positive implying a positive impact of savings on level of per capita income o The sign of population growth increase in efficiency and depreciation should be ne gative as they lead to erosion of capital stock per capita.Result: 1. The signs are as per the expectations. Savings have indeed had a positive impact on the level of per capita income. The coefficient of saving is significant at 5 % level of significance 2. The sign of n +? +? is negative as expected. Though the value of the coefficient is very small. It is hard to believe that 1 % increase in population growth rate or depreciation rate or efficiency decreases per capita level of output by just 0. 3 %. Moreover, this term is not significant. 3.The reason could again be due to the fact that increase in expenditure on education has been taken a proxy for increasing efficiency. Perhaps growth rate of expenditure is not a good proxy and therefore we get such results. Conclusion Thus the two tests that we have taken prove some of the results of the Solow model but not all. Savings do have a positive effect on per capita level of income and convergence seems to exist for the set of count ries that we have taken. SOURCE 1. http://data. un. org/ 2. http://databank. worldbank. org/ 3. http://www. oecd. org/