Parameter: Jurnal Matematika, Statistika dan Terapannya
Vol 5 No 2 (2026): Parameter: Jurnal Matematika, Statistika dan Terapannya

Bias Reduced Linearization for Cluster Robust Standard Errors: An Application to Panel Data Analysis of Indonesia's Human Development Index 2018–2022

A. Muthiah Nur Angriany (Departemen of Statistics, Hasanuddin University)
Andi Harismahyanti A (Departement of Physics and Mathematics, Faculty of Mathematics and Natural Science, Tadulako University)
Raupong Raupong (Departemen of Statistics, Hasanuddin University)
A. Miftah Nabila Muthiah (Departemen of Statistics, Hasanuddin University)



Article Info

Publish Date
21 Sep 2026

Abstract

AbstractThe Human Development Index (HDI) is a vital metric for evaluating the quality of life across the domains of health, education, and standard of living. Accurate estimation in this context necessitates a robust statistical approach, particularly when dealing with panel data characterized by limited clusters. This study employs the Cluster Robust Standard Error (CRSE) method, grounded in Bias-Reduced Linearization (BRL), to address bias in standard error estimations and facilitate more valid statistical inferences for modeling the HDI in Indonesia from 2018–2022. Utilizing secondary data from the Central Bureau of Statistics (BPS), the analysis compares common, fixed, and random effect models, with the final model selection informed by the Chow and Hausman tests. The findings reveal that the average years of schooling, Gross Regional Domestic Product (GRDP) at constant prices, and access to safe drinking water significantly enhance the HDI, while poverty and open unemployment rates exert a significantly negative effect. The application of the BRL estimator is demonstrated to be superior to conventional Ordinary Least Squares (OLS), as it effectively accounts for intra-cluster correlation, yielding stable and unbiased standard errors. This enhances the reliability of the t- and F-test results, thereby facilitating more accurate policy-making conclusions regarding human development.

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Journal Info

Abbrev

parameter

Publisher

Subject

Mathematics

Description

Parameter: Jurnal Matematika, Statistika dan Terapannya is an open access journal (e-journal) published since April 2022. Parameteris published by Department of Mathematics, Faculty of Science and Mathematics, Pattimura. Parameterpublished scientific articles on various aspects related to ...