Effectiveness of weighting and bootstrap in the estimation of welfare indices under complex sampling
Most poverty and inequality analysis rely on household-based surveys, such as income and expenditure surveys. Since multistage stratified sampling is used for these surveys, and coverage errors and non-response are generally part of surveys, it is essential that the data be weighted in order to obtain improved accuracy of the estimates of the measures. The first part of this paper considers the use of weighting, especially calibration/integrated weighting, in order to improve the estimation of welfare measures such as the Headcount index, Gini coefficient and Theil's index in complex surveys. The second part considers whether the bootstrap resampling technique provides reliable estimation results for poverty and inequality measures, especially for the construction of confidence intervals. Application of the bootstrap in complex sampling designs is discussed and used to estimate the bias and MSE of estimators of the welfare indices under consideration, over the different weighting techniques. Four confidence intervals for the welfare indices that are discussed under complex sampling, are the standard (asymptotic) interval, percentile interval, bootstrap-i interval and BCa interval. The latter confidence interval has not been applied previously in complex sampling. Results are given that assess the different weighting techniques as well as the performance of the bootstrap under complex sampling. These results are all obtained from a simulation study carried out on the Income and Expenditure Survey (IES) 2005/2006 of South Africa, using income as study variable.