1. Consider a linear regression model of y on K regressors and an intercept. (i)

Question

1. Consider a linear regression model of y on K regressors and an intercept.

(i) Describe the Breusch-Pagan test of heteroskedasticity.

(ii) What are the consequences for OLS estimation and testing of rejecting the null hypothesis of the BP test?

(iii)What can you say about the form of Heteroskedasticity function implied by BP? What if it is wrong?

(iv) Describe the test of heteroskedasticity proposed by White.

(v) When there is only one regressor (K=1), give the expression for White’s Heteroskedasticity consistent (robust) variance estimator for the slope coefficient. How do you compute this? How do you use this variance estimator to test hypotheses?

(vi) There is an alternative way of computing a White-type test which is less demanding of degrees of freedom. Describe this method and explain how it saves on degrees of freedom.

Explanation / Answer

One of the ssumptions of OLS is that thevariancce of the error is constant, known as homoskedasticity, but if error don't have constant variance, they are called heteroskedastic. Berusch-Pagan test detects any linear form of heteroskedasticity. The test considers as null hypothesys that the error variances are equal, and as alternative hypothesis that the variance is there result of the multiplication of one or more variables.

If BP test show that theri is heteroskedasticity condition, the OLS could be perform using weighted least squares method. However, most of the times heteroskedasticity results from improper modelspecification, meaning that maybe some relevant variables haven't been taking into account when specifying the model. That's why before performing a different test it is recommended to reconsider the model and/or transform the variables.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.