BREUSCH-PAGAN TEST: A COMPREHENSIVE EVALUATION OF ITS PERFORMANCE IN DETECTING HETEROSCEDASTICITY ACROSS LINEAR, EXPONENTIAL, QUADRATIC, AND SQUARE ROOT STRUCTURES USING MONTE CARLO SIMULATIONS

This study provides a comprehensive evaluation of the Breusch-Pagan test's performance in detecting heteroscedasticity across various structures and levels, addressing a significant gap in existing literature. Through Monte Carlo simulations, we investigate the test's power, Type II errors ( = 0), and Type I errors ( 0) in confirming homoscedasticity assumptions at different sample sizes (100, 250, and 500). Our objectives include assessing the test's ability to detect heteroscedasticity at various levels and structures, examining the impact of sample size on its performance, comparing its performance across different structures, and identifying its limitations and potential biases. Our findings reveal that the Breusch-Pagan test's performance varies across different heteroscedasticity structures and levels, with poor detection of low-level heteroscedasticity but improved performance at higher levels, particularly for exponential heteroscedasticity structures (EHS). While increased sample size enhances the test's performance, it remains inadequate for linear heteroscedasticity structures (LHS) and square root heteroscedasticity structures (SQRTHS). Based on our results, we recommend cautious use of the Breusch-Pagan test, especially when dealing with low-level heteroscedasticity or specific structures like LHS and SQRTHS. We suggest using the test with moderate to high sample sizes for improved performance, particularly for EHS and quadratic heteroscedasticity structures (QHS). For researchers with limited sample sizes or dealing with LHS and SQRTHS, alternative tests for heteroscedasticity may be considered. Finally, we emphasize the importance of assessing the underlying structure of heteroscedasticity in the dataset to choose the most suitable test and interpretation.