Estimation of Parameters of Linear Econometric Model and the Power of Test in the Presence of Heteroscedasticity Using Monte-Carlo Approach

Abstract

This paper is concerned with the estimation of parameters of linear econometric model and the power of test in the presence of heteroscedasticity using Monte-Carlo approach. The Monte Carlo approach was used for the study in which random samples of sizes 20, 50 and 100, each replicated 50 times were generated. Since the linear econometric model was considered, a fixed X variable for the different sample sizes was generated to follow a uniform distribution while 50 replicates of the stochastic error term for different sample sizes followed a normal distribution. Two functional form of heteroscedasticity  were introduced into the econometric model with the aim of studying the behaviour of the parameters to be estimated. 50 replicates of the dependent variable for each sample size was generated from the model  where the parameters,  were assumes to be 0.5 and 2.0 respectively. The Ordinary Least Squares (OLS) and the Generalized Least Squares (GLS) estimators were studied to identify which is more efficient in the presence of the two functional forms of heteroscedasticity considered. Both estimators were unbiased and consistent but none was convincingly more efficient than the other. The power of test was used to examine which test of heteroscedasticity (i.e., Glejser, Breusch-Pagan and White) is most efficient in the detection of any of the two forms of heteroscedasticity using different sample sizes. Glejser test detects heteroscedasticity more efficiently even in small sample sizes while White test is not as efficient when sample size is small compared to when the sample size is large.

Keywords: Heteroscedasticity, Monte Carlo, Power of Test, Ordinary Least Squares Estimator, Generalized Least Squares Estimator, Breusch-Pagan test, Glejser test, White test, Bias, Variance, Root Mean Square Error