SU6 - Heteroskedasticity, Binary Variables and Introduction to Maximum Likelihood Estimation

Question 1

What is homoskedastic? SU6CH1

Answer 1

When Var(e|Y) = σ2, i.e the variance of e is constant no matter the number of Y

Question 2

What is heteroskedasticity? SU6CH1

Answer 2

When the conditional variance of the error term e varies systematically with the regressors.

Question 3

What are the two consequences of heteroskedasticity? SU6CH1

Answer 3

1) if OLS estimators are computed under the assumption of homoskedasticity, the estimators of the variances will be biased and incorrect, which leads to hypothesis testing to be incorrect
2) if Var(e|X) is not constant, OLS is no longer BLUE

Question 4

What does heteroskedasticity not affect? SU6CH1

Answer 4

1) does not cause OLS estimators to be biased or inconsistent
2) R squared is unaffected

Question 5

What is Heteroskedastic Robust Standard Errors? SU6CH1

Answer 5

To find the variance under the assumption of heteroskedasticity.

However, this formula is applicable to both hetero and homo

Question 6

What are the tests used to test for heteroskedasticity? SU6CH1

Answer 6

Breusch-Pagan test and the white test (more efficient)

The test is 𝐸(𝑒2|𝑋1,𝑋2,…,𝑋𝑘)is constant (homoskedasticity), or depends on the regressors (heteroskedasticity)

Question 7

Limitation of the Breusch-Pagan test? SU6CH1

Answer 7

Can only detect if the regressors have linear effects on the error variance. Nonlinear effects cannot be detected

Question 8

Limitation of the White test? SU6CH1

Answer 8

Can detect nonlinear effects but when the regression model has many regressors, this approach becomes quickly infeasible because there will be squares and cross-products

Question 9

What is a binary variable also called?

Answer 9

dummy variable

Question 10

What is the dummy variable trap?

Answer 10

Perfect collinearity arises from adding all the dummy variables for each quality

Question 11

How to avoid the dummy variable trap?

Answer 11

1) drop one dummy variable

2) if both dummies are included, drop the intercept

Question 12

What is the multiple linear regression model called when the dependent variable is a binary variable?

Answer 12

Linear probability model

Question 13

What’s the issue with the linear probability model?

Answer 13

The model is unlikely to be linearly related to the independent variable for all their possible values.

eg. going from zero to four young children reduces the probability of working by > 1, which is impossible

Question 14

Is the linear probability model heteroskedastic or homoskedastic?

Answer 14

heteroskedastic, therefore, do use robust standard errors when conducting hypothesis testing

Question 15

What does including a dummy variable do to a regression model?

Answer 15

it shifts the intercept, thus each group indicated by the binary variable may have a different intercept

Question 16

What are the interactive dummy variables and their purpose?

Answer 16

If there are more than two qualities/categories, we may use interactive dummies.

When the dummy variables are used to interact with the regressors, this allows the partial effects of the regressors to vary with the categories.