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

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 BRL-adjusted cluster-robust standard errors improves the reliability of statistical inference by adjusting the variance-covariance matrix and standard errors to account for intra-cluster correlation. Importantly, the BRL adjustment does not alter the FEM coefficient estimates; rather, it provides bias-reduced standard errors and more cautious t- and F-test results. This enhances the reliability of the t- and F-test results, thereby facilitating more accurate policy-making conclusions regarding human development.