Deck 8: Heteroskedasticity

Question 1

Which of the following tests is used to compare the Ordinary Least Squares (OLS) estimates and the Weighted Least Squares (WLS) estimates?

A)The White test
B)The Hausman test
C) The Durbin-Watson test
D) The Breusch-Godfrey test

Answer 1

B
Explanation: The Hausman test can be used to formally compare the OLS and WLS estimates to see if they differ by more than sampling error suggests they should.

Question 2

The population R-squared is affected when heteroskedasticity is present in Var(u|x₁, …, x_k).​

Answer 2

False
Explanation: The population R-squared is unaffected when heteroskedasticity is present in Var(u|x₁, …, x_k).​

Question 3

Consider the following regression equation: . Which of the following indicates a functional form misspecification in E(y|x)?

A)Ordinary Least Squares estimates equal Weighted Least Squares estimates.
B)Ordinary Least Squares estimates exceed Weighted Least Squares estimates by a small magnitude.
C) Weighted Least Squares estimates exceed Ordinary Least Squares estimates by a small magnitude.
D) Ordinary Least Square estimates are positive while Weighted Least Squares estimates are negative.

Answer 3

D
Explanation: If Ordinary Least Square estimates are positive while Weighted Least Squares estimates are negative, the functional form of a regression equation is said to be misspecified.

Question 4

The linear probability model contains heteroskedasticity unless _____.

A)the intercept parameter is zero
B)all the slope parameters are positive
C) all the slope parameters are zero
D) the independent variables are binary

Question 5

Which of the following is true of heteroskedasticity?

A)Heteroskedasticty causes inconsistency in the Ordinary Least Squares estimators.
B)Population R² is affected by the presence of heteroskedasticty.
C) The Ordinary Least Square estimators are not the best linear unbiased estimators if heteroskedasticity is present.
D) It is not possible to obtain F statistics that are robust to heteroskedasticity of an unknown form.

Question 6

The square root of the quantity ​is called the _____ for .

A)heteroskedasticity-robust t statistic​
B)​heteroskedasticity-robust standard error
C) ​heteroskedasticity-robust F statistic
D) ​heteroskedasticity-robust Wald statistic

Question 7

Weighted least squares estimation is used only when _____.

A)the dependent variable in a regression model is binary
B)the independent variables in a regression model are correlated
C) the error term in a regression model has a constant variance
D) the functional form of the error variances is known

Question 8

What will you conclude about a regression model if the Breusch-Pagan test results in a small p-value?

A)The model contains homoskedasticty.
B)The model contains heteroskedasticty.
C) The model contains dummy variables.
D) The model omits some important explanatory factors.

Question 9

A test for heteroskedasticty can be significant if _____.​

A)​the Breusch-Pagan test results in a large p-value
B)​the White test results in a large p-value
C) ​the functional form of the regression model is misspecified
D) the regression model includes too many independent variables

Question 10

The interpretation of goodness-of-fit measures changes in the presence of heteroskedasticity.

Question 11

Which of the following is true of the OLS t statistics?

A)The heteroskedasticity-robust t statistics are justified only if the sample size is large.
B)The heteroskedasticty-robust t statistics are justified only if the sample size is small.
C) The usual t statistics do not have exact t distributions if the sample size is large.
D) In the presence of homoskedasticity, the usual t statistics do not have exact t distributions if the sample size is small.

Question 12

Which of the following is true?

A)In ordinary least squares estimation, each observation is given a different weight.
B)In weighted least squares estimation, each observation is given an identical weight.
C) In weighted least squares estimation, less weight is given to observations with a higher error variance.
D) In ordinary least squares estimation, less weight is given to observations with a lower error variance.

Question 13

Consider the following regression model: y_i = ₀ + ₁x_i + u_i. If the first four Gauss-Markov assumptions hold true, and the error term contains heteroskedasticity, then _____.

A)Var(u_i|x_i) = 0
B)Var(u_i|x_i) = 1
C) Var(u_i|x_i) =
i²
D) Var(u_i|x_i) =

Question 14

The heteroskedasticity-robust _____ is also called the heteroskedastcity-robust Wald statistic.

A)t statistic
B)F statistic
C) LM statistic
D) z statistic

Question 15

Which of the following is a difference between the White test and the Breusch-Pagan test?

A)The White test is used for detecting heteroskedasticty in a linear regression model while the Breusch-Pagan test is used for detecting autocorrelation.
B)The White test is used for detecting autocorrelation in a linear regression model while the Breusch-Pagan test is used for detecting heteroskedasticity. .
C) The number of regressors used in the White test is larger than the number of regressors used in the Breusch-Pagan test.
D) The number of regressors used in the Breusch-Pagan test is larger than the number of regressors used in the White test.

Question 16

Which of the following tests helps in the detection of heteroskedasticity?

A)The Breusch-Pagan test
B)The Breusch-Godfrey test
C) The Durbin-Watson test
D) The Chow test

Question 17

The general form of the t statistic is _____.

A)
B)
C)

D)

Question 18

Which of the following is true?​

A)​If we can estimate h_i for each i, it means that we can proceed directly with WLS estimation.
B)​The WLS method fails if i is negative or zero for any observation.
C) ​The simplest way to deal with homoskedasticity in the linear probability model is to continue to use OLS estimation.
D) ​The probability p(x) depends on the error term.

Question 19

The generalized least square (GLS) is an efficient procedure that weights each squared residual by the:​

A)​conditional variance of u_i given x_i.
B)​expected value of u_i given x_i.
C) ​inverse of the conditional variance of u_i given x_i.
D) ​square root of the inverse of the conditional variance of u_i given x_i.

Question 20

Which of the following is true of the White test?

A)The White test is used to detect the presence of multicollinearity in a linear regression model.
B)The White test cannot detect forms of heteroskedasticity that invalidate the usual Ordinary Least Squares standard errors.
C) The White test can detect the presence of heteroskedasticty in a linear regression model even if the functional form is misspecified.
D) The White test assumes that the square of the error term in a regression model is uncorrelated with all the independent variables, their squares and cross products.

Question 21

Multicollinearity among the independent variables in a linear regression model causes the heteroskedasticity-robust standard errors to be large.

Question 22

When the error variance differs across the two groups, we can obtain a heteroskedasticity-robust Chow test by including a dummy variable distinguishing the two groups along with interactions between that dummy variable and all other explanatory variables.​

Question 23

The linear probability model always contains heteroskedasticity when the dependent variable is a binary variable unless all of the slope parameters are zero.

Question 24

The generalized least square estimators for correcting heteroskedasticity are called weighed least squares estimators.

Question 25

If the Breusch-Pagan Test for heteroskedasticity results in a large p-value, the null hypothesis of homoskedasticty is rejected.