The Solow Swan model of economic growth 1.0 Purpose Examine aspects of the Solow-Swan model of economic growth and identify whether capital accumulation has been the cause for growth in the cases of South Korea and Australia. 2.0 The Solow-Swan Model in brief The model shows how growth in capital stock (KM) and labour (L) affect economic growth (Y). It assumes that there is diminishing marginal returns for labour and capital considered separately as inputs and constant returns to scale when taken together. Mathematically, this is expressed as: Y = AK Î± L 1-Î± (from Cobb-Douglas Production function, where Y= National Income, K=Capital, L= Labour, A= Total Factor Productivity and 0<Î±<1) y = Y/L = AKÎ± L 1-Î±/L = AKÎ±/LÎ±= AkÎ± i.e y = AkÎ± (GDP per worker is a function of Capital accumulation per worker) A is the Total Factor Productivity function often interpreted as technology or knowledge. The above production function is combined with a constant savings rate to predict that long term growth occurs through capital accumulation. Since there are diminishing returns to capital, then economies would hit a steady state where the rate of depreciation of old capital is just equal to the rate of replacement of capital stock. All economies tend to approach this steady state in the long run. (Solow 1956) 3.0 Key predictions of the Solow-Swan model for empirical verification: 1. Is there a positive co-relation between the indicators of capital accumulation and economic growth as the model predicts? 2. If growth is indeed due to capital accumulation, then growth will be strongest when the countries have begun accumulation of capital and will slow down as capital accumulation progresses. Is this empirically observed? 3. The rate of interest i.e rate of return on capital should be highest in countries with lower labour productivity (seen from equation above) hence capital should flow from higher labour productive countries to lower. This would in turn cause faster development of the underdeveloped nations, and ultimately convergence. Has this been observed? 4.0 Empirical test of the Solow-Swan Model 4.1 Choice of Indicators: The predictions of the model are tested by comparing Y/L with first, capital accumulation and then, human capital accumulation. For Capital accumulation, the following indicators are chosen: CO2 emissions (kt) : As the level of industrial activity over the years has increased, the CO2 emissions would have also increased proportionately. Therefore the level of CO2 emissions each year can be a fair indicator of the amount of capital stock accumulated. GDP per capita (constant LCU): The increase in capital stock accumulated will eventually translate into higher GDP, thereby increasing the per capita GDP. So GDP per capita can be a fair indicator of the capital stock accumulated. Gross Fixed Capital Formation (constant LCU): this measure directly indicates the extent of capital stock accumulated. In the Solow-Swan model itself, investment is considered a direct determinant of growth. For Human Capital accumulation, the following indicators are chosen: Labor Participation rate, female (% of female population 15+) : an increased presence of women in the labor force indicates that the status of women has improved. Therefore a higher participation can be said to be a fair indicator that the human capital has grown. Age dependency ratio (% of working-age population): a higher dependency ratio reflects lower human capital development and vice versa. This is because, a population with high dependency rates in working population indicates high unemployment as well as lower labor productivity. Scientific and technical journal articles: the number of articles reflects the educational level and the skill levels of the general population. The higher the human capital, more will be the demand and supply of scientific articles. 4.2 Results of Regression: R2 Value/coefficient for Indicators and Y/L Indicators Australia S Korea Capital Accumulation (R2) 0.866 0.997 CO2 Emission 1.750 1.921 GDP per capita -4.273 6.384 K*-K (point estimates) 0.0091 +0.0004 Gross Fixed Capital Formation -2.059 -2.20 Indicators Australia S Korea Human Capital Accumulation (R2) 0.798 0.997 Labor Participation rate -0.003 0.147 Age Dependency Ratio -4.85 -0.774 No. of Scientific Articles published +3.91 0.00002 4.3 Analysis of Results: (Refer enclosed excel sheet) The graphs for K*-K for South Korea shows that initially there was little difference between the steady state and the current state of economic growth. Gradually this gap widened, and in the past decade this gap has reduced once again. This shows that South Korea has attained its level of steady state through capital accumulation The graph for K*-K for Australia does not show any regular pattern. Instead there is a zig-zag pattern along the horizontal axis, with the growth rate having surpassed the ideal state in some years and having fallen below in others. This reflects that capital accumulation alone perhaps cannot explain the differences in K*-K. the shifts in steady state are perhaps caused by some other factor. Overall, for South Korea there is a very strong correlation between Capital accumulation and productivity of labour. Australia also exhibits this relationship, albeit to a slightly lesser degree. For Australia, it is seen that the regression coefficient for GDP per capita and Y/L is negative. One of the reasons for this could be that the capital per worker rate in the Australian economy has been considerably below the long run equilibrium steady state, therefore there would have been higher returns to capital and hence a lower Y/L value during these periods Also, there is a very strong correlation between the indicators of Human Capital Accumulation and productivity of labour for both Australia and South Korea. 4.4 Discrepancies of empirical findings with Solow Model : 1. For both countries, the GDP growth does not appear to be slowing down with increase in capital stock accumulation. The following two charts depict this fact : GDP .v. Capital Stock (AUSTRALIA) GDP .v. Capital Stock (SOUTH KOREA) 2. Also, regression results between Y/L and Population Growth rate and Gross savings rate of Australia and South Korea, are not consistent with the expected findings from Solow model. SUMMARY OUTPUT of Regression of Y/L with Gross savings Rate and Population Growth for South Korea Regression Statistics Multiple R 0.927465 R Square 0.860192 Adjusted R Square 0.840219 Standard Error 2.026248 Observations 17 ANOVA df SS MS F Significance F Regression 2 353.6524 176.8262 43.06869 1.04E-06 Residual 14 57.47951 4.105679 Total 16 411.1319 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 69.17444 8.986995 7.697172 2.14E-06 49.89926 88.44963 49.89926 88.44963 Gross Savings rate -1.01206 0.29757 -3.40108 0.004304 -1.65028 -0.37384 -1.65028 -0.37384 Population Growth -8.23341 2.262968 -3.63832 0.002686 -13.087 -3.37983 -13.087 -3.37983 SUMMARY OUTPUT of Regression of Y/L with Population growth and Savings Rate of Australia Regression Statistics Multiple R 0.83054 R Square 0.689797 Adjusted R Square 0.645482 Standard Error 0.003653 Observations 17 ANOVA df SS MS F Significance F Regression 2 0.000415 0.000208 15.56583 0.000276 Residual 14 0.000187 1.33E-05 Total 16 0.000602 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -0.00894 0.018525 -0.48261 0.636832 -0.04867 0.030792 -0.04867 0.030792 Population Growth rate 0.001384 0.005547 0.249464 0.806625 -0.01051 0.01328 -0.01051 0.01328 Gross savings rate 0.00467 0.001148 4.066277 0.001156 0.002207 0.007133 0.002207 0.007133 (All Data from WDI,2009) From the Solow model, it would be expected that Y/L is positively correlated with savings rate and negatively correlated population growth rate. However, this is not entirely observed above. 5.0 Theoretical explanation for empirical observations Role of Technology So, there appears some other factors at work apart from capital accumulation that is increasing GDP growth in spite of increase in capital accumulation, and causing distortions in relation of Y/L with population growth rate and savings rate. Solow himself has offered an exogenous factor, i.e technology. As technological developments and innovations begin to appear in the economy, this moves the steady state up enabling the economy to keep experiencing economic growth without the effects of diminishing returns on capital setting in. Role of Human Capital Mankiw, Romer and Weil (Mankiw 1992) offered another improvement over the Solow model. Through their study, they found that as Solow predicted Y/L was positively correlated with rate of savings and negatively correlated with population growth. However, they found that the share of physical capital in the total factor income was very high compared to what was empirically observed in the U.S economy. This led them to propose an augmented Solow model wherein human capital accumulation is also considered as a factor of production along with capital and labour. From our regression data above, it is already seen that indicators of human capital accumulation and Y/L show a very strong correlation. Openness of Economy The Solow-Swan model assumes that it is a closed economy. However in reality, much of South Koreas growth was export driven. Sachs and Warner (Sachs 1997) have argued that countries with a liberal trade policy will experience higher growth. They have defined openness as the absence of non tariff barrier, more than 40% tariff rate, and a significant black exchange rate market, socialist economic system, and state monopoly of major export. (Sachs 1997) Role of Institutions and Government policies J. Schumpeter has shown the importance of institutions in savings decisions and economic development. They have a direct bearing on the capital accumulation in a country. (Schumpeter 1912) Further the regulatory climate in the country and institutional norms also influence growth. Data Deficiencies It is also possible that the above results are empirically incorrect due to the following errors: Regression has been limited to only 16 years Inaccuracy of historical data compared to current data Incorrect choice of Indicators.
Biodiversity Essay Biodiversity presents occurrence of variety of species and their natural community in which they live. By the definition it is â€œThe degree of variation of life forms within a given species, ecosystem, biome, or an entire planet. It is a measure of the health of ecosystems and is in part a function of climate.â€ (Rutherford) Ecosystem is on the other hand, â€œ community and its abiotic environmentâ€( Rutherford). Biodiversity exists in every ecosystem, weather it is big one, or just ecosystem of one garden, it has the same importance because without it nature loses its ability to perform major functions needed for life on Earth, as it is oxygen production. Trough this investigation, two different ecosystems will be explored and the level of their biodiversity on certain area. Research question â€œTo what extend is one ecosystem more diverse than other one?â€ Hypothesis If ecosystem has more number of species and organisms within those species, it will have higher biodiversity. Justification of hypothesis According to formula for Simpson`s diversity index, D = N (N-1) / Î£ n (n-1), where N is total number of organisms, while n is sum of individuals within a specie, we can see that sum of all individuals and total number of organisms of particular species affect the biodiversity index. Variables Dependent variable Biodiversity of ecosystem. Dependent variable is key of the study and it will be tested on independent and controllable ones. It will be derived from sufficient collection of data and using Simpson`s index. Finally it is going to be presented as number of species in two different ecosystems. Independent variable Size of area of ecosystem tested, which is going to be presented in m2. This variable does not depend on other ones, and I decided to calculate biodiversity on 3 m2 in both ecosystems, making sure that conditions are same for both. Controllable variables: Time, weather conditions. These variables control the biodiversity index which is going to be derived and will be controlled as I will decide at which time am I going to measure number of species in ecosystem. In my case, it will be beginning of June. As well as I am going to make sure that I measure it on optimal temperature, without rain or strong sun. PROCEDURE Material: * Meter * Paper * Pen * Calculator * Thermometer Procedure Plan is the key point of each procedure. As I already found material needed for beginning of my investigation, I have to decide on two different location for measuring. It is going to be meadow and garden around family house. In both locations, area of measurement is going to be 3 m2 and I am going to make sure that during the measurement in both locations, conditions of temperature are approximately the same. As I labeled the area of 3 m2 in meadow, I will count the number of different species living there. In addition, I will count number of organisms of each specie. While doing that, I will see the temperature on the thermometer. The same procedure is going to be repeated in garden. After collecting all the raw data, it is going to be presented through value of biodiversity index.