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.

Answer 1

1) :- it is that test which is used to test heteroskedasticity in linear regression and assume error term are normally distributed. Test based on varience of error from a from a regression is dependent on the value of independent variables.

2) :-consequence for ols estimate is that

• breusch - pagan test is chi- squaded test.

• the statistic test is distributed nX2 with K degree of freedom.

• if test have p- value below an appropriate ththreshold then null hyphothesis of Homoskedasticity reject and assume.

3) :- the weakness of bp test give assumptions that heteroskedasticity linear function of Independent variables . Heteroskedasticity and BP doesn't not rule out a nonlinear relationship between independent variables and error variance.

• if is wrong it is not useful to determine or correct model of heteroskedasticity.

4) :- white test is statistical test that is used to establish varience of the error regression model is constant . It is for heteroskedasticity.