Heteroskedasticity

Question 1

What are the three main causes?

Answer 1

1) Size issues - large explanatory variable (value of x)
2) Use of aggregated data
3) Misspecification of functional form of the regression

Question 2

What are the consequences?

Answer 2

Does not bias the coefficients, however, they are inefficient. The standard errors are wrongly estimated, meaning the t/f-tests are invalid.

Question 3

How and when do we use the GQ test?

Answer 3

-We use the GQ test when you are confident about the source of heteroskedasticity
1) Divide SSR3/SSR1 = test statistic
2) Degrees of freedom are n3-k-1,n1-k-1

Question 4

How and when do you use the Breusch-Pagan test?

Answer 4

-We use this when we are not confident about the source and is a small sample
1) We assume the variance of the disturbance term is proportional to a linear function of a vector of explanatory variables
2) Run the original equation, obtain the residuals and square them, regressing these vs x variables
3) Test statistic is nR^2 from the supplementary regression
4) Has an X^2 distribution, degrees of freedom = number of x in the supplementary regression

Question 5

How and when do we use the White test?

Answer 5

-We use this when we are not confident about the source and is a large sample
1) Obtain the residuals, square them and regress vs explanatory variables, and square their cross-products
2) Use this R^2 for test statistics = nR^2
3) Same distribution and degrees of freedom

Question 6

How do we solve heteroskedasticity?

Answer 6

We use weighted least squares