10. Heteroscedasticity

Question 1

MLR5 homoscedasticity

Answer 1

The errors have the same variance irrespective of the values of the explanatory variables

Question 2

Consequences of heteroscedasticity

Answer 2

• As long as the other Gauss Markov assumptions are valid, OLS still yields unbiased estimators
• OLS estimators are no longer efficient
• our formula for SE’s isn’t correct so our t tests and f tests could be wrong

Question 3

How can you detect heteroscedasticity using graphs?

Answer 3

Plot a two way scatter between an explanatory variable and uhat. If the dispersion appears to change as the variable increases then this suggests heteroscedasticity

Question 4

What is the name of the heteroscedasticity test?

Answer 4

The Breusch- Pagan test

Question 5

How do you set up the Breusch Pagan test?

Answer 5

• Ho: errors are homoscedastic
• H1: there is heteroscedasticity of a specific form
• test statistic: the Breusch Pagan LM stat, which has a chi squared distribution with p degrees of freedom

Question 6

What are the steps to doing the Breusch pagan test?

Answer 6

1. Estimate model using OLS, compute the squared residuals
2. Decide on the variable(s) Z, which you suspect are responsible for heteroscedasticity, let p= number of variables in Z
3. Choose sig level, find CV in chi squared distribution
4. Using OLS, estimate a model with dependent variable ûi^2 and explanatory variables are z, include constant
5. Calculate Breusch pagan LM stat, LM=nR^2
6. Reject null if LM>CV

Question 7

How do you set up the white test?

Answer 7

• Ho: the errors are homoscedastic
• H1: there is heteroscedasticity of a general form
• test statistic: the white statistic which has chi squared distribution with p degrees of freedom

Question 8

What are the steps of the white test?

Answer 8

1. Estimate model using OLS, compute the squared residuals
2. Generate the squares and the cross products of all the regressors (EVs) in the model.
3. Choose sig level, find CV in chi squared distribution
4. Using OLS, estimate a model with dependent variable ûi^2 and explanatory variables are z, include constant
5. Calculate Breusch pagan LM stat, LM=nR^2
6. Reject null if white stat>CV

Question 9

How do you ask stata to conduct a white test

Answer 9

Run the regression you want to test. Type “estat imtest, white”

Question 10

How do we ask stata to adjust the standard errors to account for heteroscedasticity?

Answer 10

We tell stata “regress lnCEOpay lnassets profit, vce(hc3)”

Question 11

Why do we use OLS estimators even when there is heteroscedasticity if they aren’t efficient?

Answer 11

Weighted least squares estimation is more efficient but it’s complicated so is rarely used