Single Imputation Methods and Confidence Intervals for the Gini Index

Encarnación Álvarez-Verdejo, Pablo J. Moya-Fernández and Juan F. Muñoz-Rosas
Additional contact information
Encarnación Álvarez-Verdejo: Department of Quantitative Methods in Economics and Business, University of Granada, 18011 Granada, Spain
Pablo J. Moya-Fernández: Department of Quantitative Methods in Economics and Business, University of Granada, 18011 Granada, Spain
Juan F. Muñoz-Rosas: Department of Quantitative Methods in Economics and Business, University of Granada, 18011 Granada, Spain

Mathematics, 2021, vol. 9, issue 24, 1-20

Abstract: The problem of missing data is a common feature in any study, and a single imputation method is often applied to deal with this problem. The first contribution of this paper is to analyse the empirical performance of some traditional single imputation methods when they are applied to the estimation of the Gini index, a popular measure of inequality used in many studies. Various methods for constructing confidence intervals for the Gini index are also empirically evaluated. We consider several empirical measures to analyse the performance of estimators and confidence intervals, allowing us to quantify the magnitude of the non-response bias problem. We find extremely large biases under certain non-response mechanisms, and this problem gets noticeably worse as the proportion of missing data increases. For a large correlation coefficient between the target and auxiliary variables, the regression imputation method may notably mitigate this bias problem, yielding appropriate mean square errors. We also find that confidence intervals have poor coverage rates when the probability of data being missing is not uniform, and that the regression imputation method substantially improves the handling of this problem as the correlation coefficient increases.

Keywords: missing data; variance estimation; coverage; inequality; non-response mechanism (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/24/3252/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/24/3252/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:24:p:3252-:d:703440

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().