Comparison of methods to calculate measuresof inequality based on interval data

[摘要] ENGLISH ABSTRACT: In recent decades, economists and sociologists have taken an increasing interest in the study ofincome attainment and income inequality. Many of these studies have used census data, butsocial surveys have also increasingly been utilised as sources for these analyses. In thesesurveys, respondents' incomes are most often not measured in true amounts, but in categoriesof which the last category is open-ended. The reason is that income is seen as sensitive dataand/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 eachobservation has a specific value or point. For some methods, all the observations in an intervalreceive the same value; an example is the midpoint method, where all the observations in aninterval are assigned the midpoint. Other methods include random methods, where eachobservation receives a random point between the lower and upper bound of the interval. Forsome methods, random and non-random, a distribution is fitted to the data and a value iscalculated according to the distribution.The non-random methods that we use are the midpoint-, Pareto means- and lognormal meansmethods; the random methods are the random midpoint-, random Pareto- and randomlognormal methods. Since our focus falls on income data, which usually follows a heavy-taileddistribution, we use the Pareto and lognormal distributions in our methods.The above-mentioned methods are applied to simulated and real datasets. The raw values ofthese datasets are known, and are categorised into intervals. These methods are then appliedto the interval data to reconvert the interval data to point data. To test the effectiveness of thesemethods, we calculate some measures of inequality. The measures considered are the Ginicoefficient, quintile share ratio (QSR), the Theil measure and the Atkinson measure. Theestimated measures of inequality, calculated from each dataset obtained through thesemethods, are then compared to the true measures of inequality.

[发布机构] Stellenbosch University