A monte carlo investigation of the power of white and breuschpagan tests on detecting regression heteroscedasticity

Abstract

White and Breusch-Pagan Tests were designed to test whether the data violate the assumption of homoscedasticity in a linear model or not. In this research, a Monte Carlo Simulation was used to investigate the power as well as the consequence of failure of both tests in detection of heteroscedasticity as measured with Relative Efficiency (RE) of estimators between OLS and WLS. This research was focused on simple linear regression case and the variance function used was g(z, a) = I +a1 z", and the z was assumed as x. In this experiment, three factors were tried, the sample size or the ma"imum value of x, the proportion of contamination of error and the power of variauce fuuction. The simulation reveals that both tests have a similar pattern in the power due to the effects of three factors tried. However, the Breusch-Pagan Test always shows better power. The maximum value of x has increasing effect in the power of both tests and has interaction with power of the variance function. The proportion of contamination has non-linear effect on the power and has little interaction effect witll tile other factors. In general, the consequence of failure as measured with RE was the increase of RE as the power of both tests increased due to the increased of variance ratio between tile smallest and the largest value of the error variance yielded by tile variance function.