Perturbation analysis for dynamic poverty indexes

• Published in: Communications in statistics. Theory and methods Vol. 52; no. 19; pp. 6820 - 6839
• Main Authors: D'Amico, Guglielmo, De Blasis, Riccardo, Gismondi, Fulvio
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.10.2023; Taylor & Francis Ltd
• Subjects: Dynamic poverty indexes; Income; Indexes (ratios); Markov chain; Markov processes; matrix norm; Parameters; Perturbation methods; Sensitivity analysis
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2022.2034018

Sensitivity analysis of random systems may convey important information on the dynamical properties of the system. In this paper, we determine the effects of parameters' perturbation on two dynamic poverty indexes: the headcount ratio and the income gap ratio. This is achieved by perturbing the generator of the Markov process governing the evolution in time of the economic agents among three classes of income, the initial distribution of individuals and the vector of mean income for poverty class. The paper presents two bounds on the aforementioned poverty indexes which show how the perturbations on the model parameters propagate on the poverty indexes. The paper contributes to the literature presenting for the first time effective bounds for dynamic poverty indicators and exploring the applicability of the perturbation approach to real data.