After conducting a thorough theoretical research, we come to the point where we have to look at empirical evidence which would corroborate the said theoretical research. Therefore, our main aim in this part of the assignment is establish how appraisals of poverty can be calculates from a beta distribution which is fitted and is based on the values of either income or expenditure. Vis-à-vis this area of research, The World is conducting a large one at this point in time which they have well-documented on their website and publications.
These computations made by the World band are formulated on the basis of a Lorenz curve and which is approximately on the basis the overall percentages of consumption and population, who themselves are compiled on the basis of the information provided by quantitative primary research conducted on a large number of households. The work of Chen and Ravallion (2004, 2007) provide a solid analysis and holistic synopsis of the fitted beta distribution for the variables of total population and the percentages of consumption with respect to a specific comparison base demarcated by the researcher.
However, our angle of analysis will more geared towards the method that has been determined by Chotikapanich, Griffiths and Rao (2007) where they drop the usage of the fitted Lorenz curves in favour of this method of employing fitted beta distributions. Now, a major point of note is that both these approaches which we have described are frequently used in literature vis-as-vis this area of research on the notion of inequality and the other major factors that determine income disparities. The work of Kleiber and Katz (2003) analyses the large number of income disparities that have been previously approximated and the specific traits and they also provide a brief synopsis on the parametric Lorenz curves that have been approximated for specific cases.
Now, the Lorenz curves that are estimated and used by the World Bank are generally quadratic in nature (Villasenor and Arnold, 1989) and the Lorenz curves are usually described as beta. Now, our rational behind our decision to employ the beta distribution as a descriptive swap vis-à-vis Lorenz curve estimation for the calculation of poverty appraisals as: Employing a distribution rather than a Lorenz curve is based on the fact that there is a palpable divergence between the theoretical literatures on this topic that is present today. Previous researches conducted on these topics have provided ample evidence of the notion that the beta distributions vis-à-vis the available information of the target variables was pertinent and pragmatically applicable. The fitted distributions of the variables of income and mass expenditure are pertinent variants for the calculations of a diverse range of traits vis-s-vis these distributions.
They also include the Lorenz curve, however, it must be noted that the recovery of implicit distribution with regards to any variables and the specific traits of these variables and their specific distribution from a Lorenz curve is very difficult and usually is left incomplete.