| Author/Presenter |
Judith Clarke (University of Victoria) |
| Co-author |
Nilanjana Roy (University of Victoria) |
| Title |
On statistical inference for inequality measures calculated with complex survey data |
| Abstract |
This paper examines inference using generalized entropy and Atkinson inequality measures with complex survey data. We show how to form Wald statistics to test hypotheses with variance-covariance matrices estimated nonparametrically using a linearization approximation. This approach avoids cumbersome covariance calculations that often arise with the -method. We cover testing the equivalence of two or more inequality measures that may be simple inequality indices, sub-group decomposition indices, and group shares of overall inequality. Modified statistics that account for small sampling design degrees of freedom are also given. We illustrate using the 2005/06 Indian National Family and Health Survey (NFHS-3) data on children's height-for-age, an anthropometric measure indicating growth retardation and cumulative growth deficits, suggestive of long-term malnutrition. The sampling design involved an urban/rural stratification with one or two stages of clustering prior to the final selection of households. In addition to providing variance estimates for simple inequality indices, sub-group decomposition measures and sub-group shares of overall inequality, with the decompositions based on gender and the urban/rural split, we undertake tests of equality of these measures. We also examine whether the NFHS-3 health inequality among children statistically differs from previous surveys: NFHS-1 (1992/93) and NFHS-2 (1998/99). India has experienced rapid economic growth over the 1990s along with poverty reduction. However, this has been accompanied by rising economic inequality within urban areas and also between urban and rural sectors. Testing across surveys allows us to answer what has been happening to inequality in another dimension of well-being: health inequality among children. For each testing scenario, we compare our outcomes with those from a (false) simple random sample assumption and from using a balanced half-sample replication procedure that accounts for the complex survey design. |
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