Bayesian inference for TIP curves: an application to child poverty in Germany
TIP curves are cumulative poverty gap curves used for representing the three different aspects of poverty: incidence, intensity and inequality. The paper provides Bayesian inference for TIP curves, linking their expression to a parametric representation of the income distribution using a mixture of log-normal densities. We treat specifically the question of zero-inflated income data and survey weights, which are two important issues in survey analysis. The advantage of the Bayesian approach is that it takes into account all the information contained in the sample and that it provides small sample credible intervals and tests for TIP dominance. We apply our methodology to evaluate the evolution of child poverty in Germany after 2002, providing thus an update the portrait of child poverty in Germany given in Corak et al. (Rev. Income Wealth 54(4), 547–571, 2008).
KeywordsBayesian inference Mixture model Survey weights Zero-inflated model Child poverty
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A first version of this paper was presented in May 2016 at the 10th Annual RCEA Bayesian Econometric Workshop in Rimini. Useful comments by participants are gratefully acknowledged. We are especially grateful to Denis de Crombrugghe, Christian Schluter, Luc Bauwens, the editor and an anonymous referee for a careful reading of a previous version of the paper and for their insightful suggestions. Of course usual disclaimers apply. This work has been carried out thanks to the support of the A*MIDEX project (No ANR-11-IDEX-0001-02) funded by the “Investissements d’Avenir” French Government program, managed by the French National Research Agency (ANR).
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