On Statistical Inference for Inequality Measures Calculated from Complex Survey Data

We examine inference for Generalized Entropy and Atkinson inequality measures with complex survey data, using Wald statistics with variance-covariance matrices estimated from a linearization approximation rather than the d-method. Testing the equivalence of two or more inequality measures, including sub-group decomposition indices and group shares, are covered. We illustrate with Indian data from three surveys, examining children’s height-for-age, an anthropometric measure that can indicate long-term malnutrition. Sampling involved an urban/rural stratification with clustering before selection of households. We compare the linearization complex survey outcomes with those from an incorrect iid assumption and a bootstrap that accounts for the survey design. For our samples, the results from the easy to implement linearization method and more computationally burdensome bootstrap are in close agreement.