Panel Data Regression Modeling with Weighted Least Squares Method Using Fair Weights

Abstract

Panel data regression is a robust method for analyzing relationships between dependent and independent variables by combining time-series and cross-sectional data. Its reliability hinges on key assumptions, particularly homoscedasticity. Violations, known as heteroscedasticity, lead to inefficient estimates and biased inference, as estimators fail to meet the Best Linear Unbiased Estimator criteria. The Weighted Least Squares (WLS) method addresses heteroscedasticity by weighting observations based on the inverse of their variance. WLS assumes prior knowledge of the heteroscedasticity structure, which is often impractical, creating gap in evaluating its effectiveness compared to alternative methods. The purpose of this study is to examines life expectancy in South Sulawesi as the dependent variable, with expected years of schooling, per capita expenditure, and average years of schooling as independent variables. The research methode used WLS with reasonable weighting, successfully addressing heteroscedasticity. The fixed-effects model was identified as the most appropriate, with an R-squared of 99.45%. Life expectancy was explained by the model. Results shows all variables positively and significantly influence life expectancy. In conclusion, the WLS method effectively overcomes heteroscedasticity in panel data regression, providing reliable estimators. This study highlights the importance of method selection in panel data analysis and offers insights for policymakers aiming to improve life expectancy in South Sulawesi.