Browsing by Author "Neethling, Willem Francois"

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    Comparison of methods to calculate measures of inequality based on interval data
    (Stellenbosch : Stellenbosch University, 2015-12) Neethling, Willem Francois; De Wet, Tertius; Neethling, Ariane; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science
    ENGLISH ABSTRACT: In recent decades, economists and sociologists have taken an increasing interest in the study of income attainment and income inequality. Many of these studies have used census data, but social surveys have also increasingly been utilised as sources for these analyses. In these surveys, respondents’ incomes are most often not measured in true amounts, but in categories of which the last category is open-ended. The reason is that income is seen as sensitive data and/or is sometimes difficult to reveal. Continuous data divided into categories is often more difficult to work with than ungrouped data. In this study, we compare different methods to convert grouped data to data where each observation has a specific value or point. For some methods, all the observations in an interval receive the same value; an example is the midpoint method, where all the observations in an interval are assigned the midpoint. Other methods include random methods, where each observation receives a random point between the lower and upper bound of the interval. For some methods, random and non-random, a distribution is fitted to the data and a value is calculated according to the distribution. The non-random methods that we use are the midpoint-, Pareto means- and lognormal means methods; the random methods are the random midpoint-, random Pareto- and random lognormal methods. Since our focus falls on income data, which usually follows a heavy-tailed distribution, we use the Pareto and lognormal distributions in our methods. The above-mentioned methods are applied to simulated and real datasets. The raw values of these datasets are known, and are categorised into intervals. These methods are then applied to the interval data to reconvert the interval data to point data. To test the effectiveness of these methods, we calculate some measures of inequality. The measures considered are the Gini coefficient, quintile share ratio (QSR), the Theil measure and the Atkinson measure. The estimated measures of inequality, calculated from each dataset obtained through these methods, are then compared to the true measures of inequality.