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; Andi Harismahyanti A; Andi Harismahyanti A; Raupong Raupong; A. Miftah Nabila Muthiah; A. Miftah Nabila Muthiah

doi:10.30598/parameterv5i2pp301-318

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
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
A. Miftah Nabila Muthiah Departemen of Statistics, Hasanuddin University

DOI: https://doi.org/10.30598/parameterv5i2pp301-318

Keywords: Human Development Index, Panel Data, Fixed Effect, BRL, Cluster Robust Standard Error.

Abstract

Abstract
The 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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