Bayesian Inference for Parametric Growth Incidence Curves

The growth incidence curve of Ravallion and Chen (2003) is based on the quantile function. Its distribution-free estimator behaves erratically with usual sample sizes leading to problems in the tails. We propose a series of parametric models in a Bayesian framework. A first solution consists in modelling the underlying income distribution using simple densities for which the quantile function has a closed analytical form. This solution is extended by considering a mixture model for the underlying income distribution. However in this case, the quantile function is semi-explicit and has to be evaluated numerically. The alternative solution consists in adjusting directly a functional form for the Lorenz curve and deriving its first order derivative to find the corresponding quantile function. We compare these models first by Monte Carlo simulations and second by using UK data from the Family Expenditure Survey where we devote a particular attention to the analysis of subgroups.