Estimating some measures of income inequality from survey data: An application of the estimating equations approach

We summarize some salient aspects of the theory of estimation functions for finite populations. In particular, we discuss the problem of estimation of means and totals and extend this theory to estimating functions. We then apply this estimating functions framework to the problem of estimating measures of income inequality. The resulting statistics are nonlinear functions of the observations. Some of them depend on the order of observations or quantiles. Consequently, the mean squared errors of these estimates are inexpressible by simple formulae and cannot be estimated by conventional variance estimation methods. We show that within the estimating function framework this problem can be resolved using the Taylor linearization method. Finally, we illustrate the proposed methodology using income data from Canadian Survey of Consumer Finance and comparing it to the ‘delete-one-cluster’ jackknifing method.