A Strong Negative Relationship between the Growth of per Capita - Term Paper Example

Analysis of Per Capita Income Convergence across Countries This research paper carries analysis based on a simple idea of regional convergence, which asserts that underdeveloped countries are likely to exhibit a faster growth than rich regions on the basis of income per capita comparison. Two approaches used in the process of confirming convergence thesis are “beta” and “sigma” convergence. The results accepted the null hypothesis which stated that there is a strong negative relationship between growth of per capita to the benchmark level of income across countries. The result concludes that underdeveloped economies have the affinity of growing faster, in terms of per capita incomes than the already richer economies. Introduction In exploring economies across the world, a great interest arises for establishing disparities between the individual individual countries and between regions. This is especially important in cases where there is need to establish monetary and economic union whereby there are both the developed and underdeveloped economies in play. As a result, two distinct positions that have been associated with this are regional divergence and regional convergence. For divergence, the theory asserts that there is foreseen increase in factor mobility for the developed regions in the event of an integration towards a single currency. For convergence, the argument is that higher integration will harmonize the regional disparities thereby making the underdeveloped regions to catch up with the developed nations. The view of convergence is based on the view of the difference in strength of diminishing returns, to capital, between the rich nations and the poorer nations (Roberto & Antonello, 2000, 463). Consequently, this study provides analysis of data to test the thesis of real convergence between countries. In which case, the paper tests the hypothesis that underdeveloped economies have the affinity of growing faster, in terms of per capita incomes than the already richer economies. The analysis is carried on real convergence between various countries for a period of between 1950 to 2010. This period gives a clear picture for the study since all the countries listed had all exhibited strong efforts to achieving nominal convergence. The results from this analysis are important for the future of regional policy across continents especially for the United Nations. The model of convergence is estimated for 94 countries over a period of 1950 to 2010. Hypothesis Ho - There is a strong negative relationship between growth of per capita to the benchmark level of income across countries H1 – There is a positive relationship between growth of per capita income to initial level of income across countries Overview of the convergence theory In understanding the convergence theory, two approaches used are “sigma” convergence and “beta” convergence. The “sigma” convergence uses the measure of dispersion of income per capita between countries on the cross-section series on the basis of standard deviation. In an event the standard deviation is found to be fall with time, the hypothesis of convergence is confirmed (Gil-Alana, 2002, 338). On the other hand, “beta” convergence makes use of regression analysis that estimates the income per capita income growth for a particular period on the benchmark level of income per capita. In a case of results showing regression coefficient “beta” having a negative sign is an indication that poorer nations grow more faster than the richer nations (Lee & Michael, 2004, 138). Methodology To calculate the arithmetic growth rate between 1950 and 2010, the following formula was used: where refers to country To calculate an annual growth rate over this period, the following formula should be used: For this study, there was exploration of recent GDP per capita data on a sample of countries from the Maddison Project. It was feasible to construct a sample of total 94 countries given in the sample data. Sigma convergence was then calculated with help of coefficient of variation and the results were recorded in table 1. The following equation was used to reach evidence of convergence, through non-linear regression analysis. The equation relates per-capita income growth to the base year while assuming a non-linear form. log(Yit/Yi0) = α+ (1-exp-βT)logYi0+ uit Whereby, Y represents the per capita income, i represents a country, 0 is initial year used as base while t is the final year; T is the whole period of time t, α is the constant representing a scenario of autonomous growth, β is the convergence rate. This equation was used three cases: whole period between 1950 and 2010; sub-period between 1975 and 1984; and final sub-period 1985 to 1995. Results The results shows that there is “sigma” convergence for two different periods: the period between 1950-2010 was accompanied by a higher decrease in dispersion of income per capita while for period 1975-1984 experiencing the lowest fall. However, divergence was observed for the period between 1986 and 1996 as shown in the table. Generally, the results indicates that for that period between 1950 to 2010 the witnessed divergence was moderate bringing the analysis to the conclusion that the dispersion of per capita income for the countries, based on absolute terms, is observed to increase. Figure 1, indicates a graph of coefficient of variation for income per capita against the period of time. Further, annualized growth rates were plotted against the bechnmark level of per-capita income. The methodology followed for this is plotting the graph for the whole period (1950-2010) and other for 1975-1984 and 1985-1996. The plot shows vertical axis measuring log of the annualized growth against period (T) for the horizontal axis. The figures give a clear view showing a negative relationship observed between annual growth rates from 1950. This proves the convergence idea across countries for this particular period of time. Further, the second period that is 1985-1995 exhibits a stronger negative relation thereby hinting on rapid cross-country convergence for the period as compared to the first, 1975-1984. A linear regression analysis was also carried and resulted to a negative coefficient of “beta” with a convergence rate of 1.33% for 1950-2010. The first sub-period had 1.68% of convergence rate while the second period had relatively higher convergence rate of 1.76%. The same evidence was obtained through nonlinear regression analysis comparing the growth per capita income to the base year. The following are the estimated results for the most significant statistics summary: Period 1950 – 2010 Log(Y1950/Y2010) = 4.01 – 0.01175 log Y1950 R2 = 0.348 (4.15) (-2.16) DW = 2.2 Sub period 2 Log(Y1950/Y2010) = 2.469 – 0.01558 log Y1950 R2 = 0.234 (3.21) (-1.89) DW = 1.96 Sub period 3 Log(Y1950/Y2010) = 2.348 – 0.01609 log Y2010 R2 = 0.221 (2.23) (-1.84) DW = 1.96 The above results obtained from regression analysis prove the convergence theory for all the periods. This is shown by negative beta and through confirming the statistical significance at 10%. Looking at the results obtained, a convergence rate of 1.18% each year is evident for the whole period/ while the first sub-period had 1.55% , the second having relatively higher speed than the former at the 1.61% each year. These results reveals consistency with the “sigma” convergence that also yielded a pattern where there was a fall in dispersion for both sub-periods even though the fall was relatively lower in second sub period than in first sub-period. In figure 6, a graph was plotted for the annualized growth per capita income versus the base level of income for the different countries, to confirm “beta” convergence for the case. The results depicted by the graphs indicates a negative relation thereby confirming the hypothesis about poor countries growing rapidly than rich countries, on the basis of per capita income. The pattern is depicted for the whole period of 1950-2010. Non-linear regression analysis was carried out to further confirm beta convergence. The following is a summary of statics from the results obtained. Log(Y1950/Y2010) = 1.653 – 0.0139 log Y2010 R2 = 0.155 (7.49) (-6.00) DW = 1.04 From the results, it is shown that “beta” convergence rate was 1.39% for the whole period. The statistical significance is high with low explanatory power. This insinuates that other additional variables come in play to influence the performance of the regions, for instance, industrialization and education. Conclusion The study successfully made use of both “sigma” and “beta” convergence to confirm convergence thesis between countries. The results accepted the null hypothesis, which stated that there is a strong negative relationship between growth of per capita to the benchmark level of income across countries. The results showing regression coefficient “beta” having a negative sign is an indication that poorer nations grow more faster than the richer nations The result conclude that underdeveloped economies have the affinity of growing faster, in terms of per capita incomes than the already richer economies. This is because of continued quest for integration, which harmonizes the regional disparities thereby making the underdeveloped regions to catch up with the developed nations. However, the results show that in the long run convergence is not ensured as shown in the uncertainties of this process. This is obvious in the 1990s which raises the problem of the efficiency of regional policies exercised by the individual member states and by the European Union. Bibliography Roberto Cellini & Antonello E. Scorcu, 2000. Segmented stochastic convergence across the G-7 countries, Empirical Economics, Springer, vol. 25(3), pages 463-474. Gil-Alana, Luis A., 2002. Seasonal long memory in the aggregate output. Economics Letters, Elsevier, vol. 74(3), pages 333-337, February. Lee Kian Lim & Michael McAleer, 2004. Convergence and catching up in ASEAN: a comparative analysis. Applied Economics, Taylor & Francis Journals, vol. 36(2), pages 137-153. Appendix Figure 1: coefficient of variation vs time 1975-2005 Figure 2: Coefficient of variation vs number of years 1986-1996 Figure 3: Country convergence between 1975-1984 Figure 4: Country convergence 1985-2000 Figure 5: Country convergence between 1950-2010 Figure 6: annualized growth rate againt log of per capita income Read More