Confidence intervals for estimators of welfare indices under complex sampling

ENGLISH ABSTRACT: The aim of this study is to obtain estimates and confidence intervals for welfareindices under complex sampling. It begins by looking at sampling in general withspecific focus on complex sampling and weighting. For the estimation of the welfareindices, two resampling techniques, viz. jackknife and bootstrap, are discussed.They are used for the estimation of bias and standard error under simple randomsampling and complex sampling. Three con dence intervals are discussed, viz. standard(asymptotic), percentile and bootstrap-t. An overview of welfare indices andtheir estimation is given. The indices are categorized into measures of poverty andmeasures of inequality. Two Laeken indices, viz. at-risk-of-poverty and quintileshare ratio, are included in the discussion. The study considers two poverty lines,namely an absolute poverty line based on percy (ratio of total household incometo household size) and a relative poverty line based on equivalized income (ratio oftotal household income to equivalized household size). The data set used as surrogatepopulation for the study is the Income and Expenditure survey 2005/2006conducted by Statistics South Africa and details of it are provided and discussed.An analysis of simulation data from the surrogate population was carried out usingtechniques mentioned above and the results were graphed, tabulated and discussed.Two issues were considered, namely whether the design of the survey should be consideredand whether resampling techniques provide reliable results, especially forcon dence intervals. The results were a mixed bag . Overall, however, it was foundthat weighting showed promise in many cases, especially in the improvement of thecoverage probabilities of the con dence intervals. It was also found that the bootstrapresampling technique was reliable (by looking at standard errors). Furtherresearch options are mentioned as possible solutions towards the mixed results.