Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality
Article first published online: 10 DEC 2003
Econometric Society 2000
Volume 68, Issue 6, pages 1435–1464, November 2000
How to Cite
Davidson, R. and Duclos, J.-Y. (2000), Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality. Econometrica, 68: 1435–1464. doi: 10.1111/1468-0262.00167
- Issue published online: 10 DEC 2003
- Article first published online: 10 DEC 2003
- Stochastic dominance;
- distribution-free statistical inference;
- order-restricted inference.
We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare, and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance of any order. These curves can be used to determine whether poverty, inequality, or social welfare is greater in one distribution than in another for general classes of indices and for ranges of possible poverty lines. We also derive the sampling distribution of the maximal poverty lines up to which we may confidently assert that poverty is greater in one distribution than in another. The sampling distribution of convenient dual estimators for the measurement of poverty is also established. The statistical results are established for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes. Our results are briefly illustrated using data for four countries drawn from the Luxembourg Income Study data bases.