Empirical Likelihood Inference for Sen and Sen--Shorrocks--Thon Indices

TL;DR

This paper develops empirical likelihood and jackknife empirical likelihood methods to construct confidence intervals for the Sen and SST poverty indices, providing reliable inference and comparison across populations.

Contribution

It introduces a new estimator for the Sen index based on U-statistics and studies the properties of EL and JEL ratio statistics for these indices.

Findings

JEL-based confidence intervals have good coverage in simulations.

Methods are effective on US and Indian income data.

Proposed estimators improve inference accuracy.

Abstract

The Sen index and Sen-Shorrocks-Thon (SST) index are widely used measures of poverty indices. Developing reliable inference for these measures enables us to compare these measures in different populations of interest in an effective way. It is important to construct confidence intervals for the Sen index and SST index, which provide better coverage probability and shorter interval length. Motivated by this, we discuss empirical likelihood (EL) and jackknife empirical likelihood (JEL) based inference for the Sen index. To derive a JEL-based confidence interval for the Sen and SST indices, we propose a new estimator for the Sen index using the theory of U-statistics and examine its properties. The large sample properties of the EL and JEL ratio statistics are studied. We also discuss EL and JEL-based inference for the Sen-Shorrocks-Thon (SST) index. The finite sample performance of the EL and JEL-based confidence intervals of both Sen and SST indices is evaluated through a Monte Carlo simulation study. Finally, we illustrate our methods using individual-level data from the Panel Study of Income Dynamics (PSID) survey from the US as well as Indian household level income data for different states sourced from the Consumer Pyramids Household Survey (CPHS).