Confidence sets for dynamic poverty indexes

In this study, we consider different poverty indexes in a dynamic framework where individuals change their rate of income randomly in time. The primary objective of this paper is to assess the accuracy of the approximation of the indexes that can be obtained by applying the strong law of large numbers to an economic system composed of an infinite number of agents. The main result is a multivariate central limit theorem for dynamic poverty measures, which is obtained applying the theory of U-statistics. We also show how to get the confidence sets for the considered dynamic indexes, which show the appropriateness of the model. An application to the Italian income data from 1998 to 2012 confirms the effectiveness of the considered approach and the possibility to determine the evolution of poverty and inequality in real economies.