Deck 9: Heteroskedasticity

Question 1

The second step in the Goldfeld-Quandt test is to

A)omit the middle c observations from the ordered data set.
B)omit the bottom c observations from the ordered data set.
C)regress the squared residuals on the independent variables from the original OLS regression.
D)regress the squared residuals on the predicted value of the dependent variable from the original OLS regression.

Answer 1

A

Question 2

A simple way to generate some idea whether data are likely to be heteroskedastic is to

A)examine the residual plot.
B)construct a histogram.
C)calculate the variance of the sample.
D)plot the data points from smallest to largest.

Answer 2

A

Question 3

Homoskedasticity occurs when

A)the error variance is constant.
B)the error variance is non-constant.
C)the dependent variable variance is constant.
D)the dependent variable variance is non-constant.

Answer 3

A

Question 4

The alternative hypothesis for the Goldfeld-Quandt test is

A)
B)
C)
D)

Question 5

Suppose that you plot the residuals for your sample against independent variable x and get
You should conclude that the data are

A)definitely heteroskedastic.
B)likely homoskedastic.
C)possibly heteroskedastic and you would perform a formal test for heteroskedasticity.
D)possibly homoskedastic and you would perform a correction for homoskedasticity.

Question 6

Heteroskedasticity occurs when

A)the error variance is constant.
B)the error variance is non-constant.
C)the dependent variable variance is constant.
D)the dependent variable variance is non-constant.

Question 7

The second step in the Modified White's test is to regress the

A)residuals on the predicted value of the dependent variable.
B)squared residuals on the predicted value of the dependent variable.
C)squared residuals on the predicted value of the dependent variable squared.
D)squared residuals on the predicted value of the dependent variable and the predicted value of the dependent variable squared.

Question 8

The third step in the Goldfeld-Quandt test is to calculate the estimated sample regression function for the

A)bottom c observations in the ordered data set.
B)middle c observations in the ordered data set.
C)top c observations in the ordered data set.
D)bottom c and the top c observations in the ordered data set.

Question 9

The first step in the Breusch-Pagan test is to estimate the model and

A)calculate the predicted values of the dependent variable.
B)calculate the estimated residuals.
C)plot the estimated residuals.
D)test whether the residuals are non-constant.

Question 10

Heteroskedasticity is a problem because it results in

A)biased parameter estimates.
B)estimated standard errors that are incorrect.
C)estimated standard errors that are always too small.
D)incorrect estimated slope coefficients.

Question 11

The first step in the Goldfeld-Quandt test is to

A)estimate the model and calculate the estimated residuals.
B)estimate the model and calculate the estimated residuals squared.
C)sort the data set from the lowest to the highest value of the dependent variable.
D)sort the data set from the lowest to the highest value of the suspect independent variable.

Question 12

The final step in the Breusch-Pagan test is to perform

A)an F-test of the overall significance of the squared residuals regression.
B)an F-test of the overall significance of the original OLS regression.
C)a t-test of the overall significance of the squared residuals regression.
D)an F-test of the individual significance of the suspect independent variable in the squared residuals regression.

Question 13

Heteroskedasticity violates assumption

A)M3.
B)M4.
C)M5.
D)M6.

Question 14

Suppose that you plot the residuals for your sample and get
You should conclude that

A)definitely heteroskedastic.
B)likely homoskedastic.
C)possibly heteroskedastic and you would perform a formal test for heteroskedasticity.
D)possibly homoskedastic and you would perform a correction for homoskedasticity.

Question 15

Suppose that while performing the Modified White's test,you estimate the model
The final step in the Modified White's test is to perform

A)an F-test of the overall significance of the squared residuals regression.
B)an F-test of the joint significance of δ₁ and δ₂.
C)a t-test of the individual significance of δ₁.
D)a t-test of the individual significance of δ₂.

Question 16

The null hypothesis for testing for the presence of heteroskedasticity is

A)H₀ : the error term has constant variance.
B)H₀ : the error term has non-constant variance.
C)H₀ : β₁ = 0.
D)H₀ : Ɛ₁ = 0.

Question 17

The first step in the Modified White's test is to estimate the model and

A)calculate the predicted values of the dependent variable.
B)calculate the estimated residuals.
C)calculate the estimated residuals and the predicted values of the dependent variable.
D)plot the estimated residuals.

Question 18

The null hypothesis for the Goldfeld-Quandt test is

A)
B)
C)
D)

Question 19

The second step in the Breusch-Pagan test is to regress the

A)residuals on the independent variables from the original OLS regression.
B)squared residuals on the residuals from the original OLS regression.
C)squared residuals on the independent variables from the original OLS regression.
D)residuals on the squared residuals from the original OLS regression.

Question 20

The final step in the Goldfeld-Quandt test is to

A)perform an F-test of the overall significance of the estimated sample regression functions.
B)calculate the Goldfeld-Quandt test statistic and compare it to the appropriate critical value.
C)compare the calculated R² values for the estimated sample regression functions.
D)a t-test of the individual significance of the suspect independent variable in the squared residuals regression.

Question 21

What is the intuition behind the modified White's test for heteroskedasticity? Explain.

Question 22

Suppose you wish to explain variation in body mass index (BMI)by variation in height (in inches)by estimating the model
And you suspect heteroskedasticity of the form
)You could perform Weighted Least Squares by estimating the model

A) .
B) .
C) .
D) .

Question 23

How do you perform the Goldfeld-Quandt test for heteroskedasticity? Explain.

Question 24

Suppose you are interested in explaining variation in Body Mass Index in a nationally-representative sample of 12,486 men and women and that you estimate the sample regression function (standard errors in parentheses)
a)Which variable do you suspect could be responsible for heteroskedasticity in this model? Why? Explain.
b)How would you use the Breusch-Pagan test to determine whether heteroskedasticity is present? Explain.
c)How would you use Weighted Least Squares to account for heteroskedasticity if it is present? Explain.

Question 25

What is heteroskedasticity? Why is it problematic? Explain.

Question 26

What is the intuition behind the Breusch-Pagan test for heteroskedasticity? Explain.

Question 27

Why are White's heteroskedastic consistent standard errors the preferred method for dealing with potential heteroskedasticity? Explain.

Question 28

How do you perform the modified White's test for heteroskedasticity? Explain.

Question 29

How do you perform Weighted Least Squares? Why should it work? Explain.

Question 30

Suppose you are interested in explaining variation in Mile Run Time in a sample of 22,359 individuals over the age of 18 and that you estimate the sample regression function (standard errors in parentheses)
a)Which variable do you suspect could be responsible for heteroskedasticity in this model? Why? Explain.
b)How would you use the modified White's test to determine whether heteroskedasticity is present? Explain.
c)What would be your most preferred method for correcting for the potential heteroskedasticity? Explain.

Question 31

Suppose you are interested in explaining variation in Vacation Spending in a sample of 12,486 men and women and that you estimate the sample regression function (standard errors in parentheses)
a)Which variable do you suspect could be responsible for heteroskedasticity in this model? Why? Explain.
b)How would you use the Goldfeld-Quandt test to determine whether heteroskedasticity is present? Explain.
c)Suppose you know that heteroskedasticity takes the form
.How would you use Weighted Least Squares to correct for the heteroskedasticity? Explain.

Question 32

The appropriate critical value for performing the Goldfeld-Quandt test at the 95% level is

A)
B)
C)
D)

Question 33

Weighted Least Squares is performed by

A)re-weighting the estimated standard errors from the OLS regression.
B)re-weighting the estimated slope coefficients from the OLS regression.
C)including the command ",robust" in the estimation.
D)re-weighting the original data so that OLS provides estimated standard errors with minimum variance.

Question 34

White's Heteroskedastic standard errors are

A)the preferred method for correcting for potential heteroskedasticity.
B)calculated through an iterative process.
C)automatically calculated in Excel.
D)the result of performing weighted least squares.

Question 35

How do you perform the Breusch-Pagan test for heteroskedasticity? Explain.

Question 36

The Goldfeld-Quandt test statistic is

A)
B)
C)
D)

Question 37

The rejection rule for the Goldfeld-Quandt test at the 95% level is reject H₀ if

A)
B)
C)
D)

Question 38

What is the intuition behind the Goldfeld-Quandt test for heteroskedasticity? Explain.

Question 39

What are the null and alternative hypothesis for testing for the presence of heteroskedasticity? Why? Explain.