Dummy Variables + Heteroscedasticity

Question 1

How can we incorporate qualitative info in our regression model?

Answer 1

Use dummy variables
- sometimes known as binary variables

Question 2

How does dummy variable work?

Answer 2

Dummy variable = 1 if particular observation has certain characteristic
Dummy variable = 0 of particular observation doesn’t have characteristic

Question 3

Golden rule when using dummy variables?

Answer 3

When using dummy variables one category must always be omitted

Question 4

What is dummy variable trap?

Answer 4

Occurs when all categories are included in regression
- results on perfect Collinearity
- MLR 3 violated
- model cannot be estimated

Question 5

How to interpret dummy variable?

Answer 5

Interpretation of dummy variables is relevant to omitted category- also knows as the base category

Question 6

What are the consequences of heteroscedasticity?

Answer 6

• OLS still unbiased and consistent as long as MLR 1-4 hold
• Intwepretation of R-Squared and Adj R-Squared unchanged, this is because these are estimates of the population and depend on unconditional variances
• OLS no longer BLUE - min variance property no longer holds (MLR 5)
• Ftests, t-tests and CI no longer valid-this is because the estimated variances of our coefficients are no longer unbiased estimators
• true standard errors often larger than OLS reports

Question 7

In the B-P test what is evidence against the null? I.e against homoscedasticity?

Answer 7

• a high R-squared from the regression of the squared residuals on all the explanatory variables

Question 8

What is downfall of B-P test?

Answer 8

Imposes a linear relationship between variance and explanatory variables
- relationship may not be linear

Question 9

Why is the white test better than the B-P test?

Answer 9

White test detects more general deviations from homoscedasticity than B-P test
- capture more than just linear relationships by including squares and interaction terms

Question 10

Downfall of white test?

Answer 10

Including all squares and interactions leads to a large number of estimated parameters

Question 11

What must hold for B-P and White test to hold?

Answer 11

MLR1-4:
- linear in parameters
- random sampling
- no perfect Collinearity
- zero conditional mean

Question 12

What is main concern when carrying out B-P and Whote test?

Answer 12

• misspecificatipn of model
• if wrong FF is used I.e we use level-level instead of correct log-log form can lead to wrong conclusions