Gini Index Estimation within Pre-Specified Error Bound: Application to Indian Household Survey Data

Francis Bilson Darku,Bhargab Chattopadhyay,Frank Konietschke

doi:10.3390/econometrics8020026

Abstract

The Gini index, a widely used economic inequality measure, is computed using data whose designs involve clustering and stratification, generally known as complex household surveys. Under complex household survey, we develop two novel procedures for estimating Gini index with a pre-specified error bound and confidence level. The two proposed approaches are based on the concept of sequential analysis which is known to be economical in the sense of obtaining an optimal cluster size which reduces project cost (that is total sampling cost) thereby achieving the pre-specified error bound and the confidence level under reasonable assumptions. Some large sample properties of the proposed procedures are examined without assuming any specific distribution. Empirical illustrations of both procedures are provided using the consumption expenditure data obtained by National Sample Survey (NSS) Organization in India.

Highlights

Economic measures based on income levels of the residents of a specific region play an important role in social, economic and socio-economic sciences
We propose a two stage procedure and a purely sequential procedure to find an estimate of the minimum number of clusters which is required to find a sufficiently narrow confidence interval under a distribution-free scenario
We find that the coverage probability for the confidence intervals for both purely sequential procedure and the two-stage procedure are approximately close to the desired confidence level provided that the cluster size is large, which is a basic criterion while proving the asymptotic normality in (4)

Summary

Introduction

Economic measures based on income levels of the residents of a specific region play an important role in social, economic and socio-economic sciences. They are used to quantify both the actual balance of the economy as well as the wealthiness and poverty of the people. According to the Organization for Economic Cooperation and Development (2017), the Gini indices of the USA, Germany and South Africa were GF = 0.39, 0.29, 0.62 in 2017, respectively. These values suggest income inequality in these regions.

Methods

Discussion

Conclusion