Revisiting poverty measures using quantile functions

TL;DR

The paper reframes poverty measurement by expressing indices through quantile functions $Q(u)$ rather than distribution functions, enabling new modeling flexibility and tractable analysis for complex income models. It develops quantile-based analogs for additively separable and rank-based poverty measures, establishing that the poverty gap ratio is captured by $A_1(u)$ and that, in principle, $A_1(u)$ determines the entire income distribution via $Q(u)$. A suite of flexible quantile-income models (e.g., Kappa, Wakeby, Generalized Lambda, Govindarajulu, Dagum) is proposed, with explicit expressions for poverty measures in terms of $Q(u)$. An empirical California data application demonstrates estimation of $\mu_Q(u)$ and related indices, revealing near-linear behavior that yields explicit $Q(u)$ forms and illustrating the method's practical relevance for poverty and inequality analysis.

Abstract

In this article we redefine various poverty measures in literature in terms of quantile functions instead of distribution functions in the prevailing approach. This enables provision for alternative methodology for poverty measurement and analysis along with some new results that are difficult to obtain in the existing framework. Several flexible quantile function models that can enrich the existing ones are proposed and their utility is demonstrated for real data.

Figures (4)

• Figure 1: $S(u)$ of power, Pareto, Govindarajulu and Dagum distribution with different parameter values.
• Figure 2: Mean income of the poor.
• Figure 3: Gini index plot for the poor
• Figure 4: Sen index for the poor

Theorems & Definitions (19)

• Theorem 2.1
• proof
• Theorem 2.2
• proof
• Remark 2.1
• Example 2.1
• Example 2.2
• Theorem 2.3
• proof
• Example 2.3