Heteroskedasticity Chapter 8 Test Questions & Answers Hill

File: Chapter 8 – Heteroskedasticity

Multiple Choice

1. If heteroskedasticity exists, which of the following statements is TRUE?

a. The probability density function of e_i does not change for each i.

b. The variation of observed y_i around different values of x_i changes.

c. .

d. The OLS estimate of will be unbiased.

2. Heteroskedasticity is a violation of which assumption of the MR model?

a. The values of each x_ik are not random and are not exact linear functions of the other explanatory variables.

b. var(y_i.) = var(e_i) = ².

c. E(y_i) = ₁ + ₂x_i2 + ₃x_i3 + ……. + _kx_ik, ⟺E(e_i) = 0.

d. cov(y_i, y_j) = cov(e_i, e_j) = 0; (i≠j).

3. In the context of a standard multiple heteroskedastic regression model with K explanatory variables, the heteroskedasticity assumption is . The function is referred to as the _____ function.

a. weighted

b. mean-variance

c. skedastic

d. bias

4. What are the consequences of using least squares when heteroskedasticity is present?

a. No consequences, coefficient estimates are still unbiased.

b. Confidence intervals and hypothesis testing are inaccurate due to inflated standard errors.

c. All coefficient estimates are biased for variables correlated with the error term.

d. It requires very large sample sizes to get efficient estimates.

5. If you wish to estimate a multiple regression model with a large sample but you are not sure if heteroskedasticity is present, then you should run your estimate using _____.

a. robust standard errors

b. normal standard errors

c. normal OLS procedure

d. Jarque-Bera test

6. How should you estimate a model with heteroskedasticity when you are confident the error variance is a function of one continuous variable?

a. WLS or GLS

b. White Robust

c. FGLS

d. Quasi-Least Squares

7. When using WLS to correct for heteroskedasticity, what weight should be used?

a. Whatever weight scales all variables and creates a homoskedastic error variance

b. The inverse of the error variance at x̄

c. Whatever weight is determined by the Goldfeld-Quandt test

d. The residuals from the initial regression model

8. How are coefficient estimates from WLS (weighted least squares) interpreted?

a. They must be scaled up by the weight used in order to calculate marginal effects.

b. There is no difference in interpretation since each observation is scaled by the same divisor.

c. Take the inverse of the natural logarithm of the coefficient to find marginal effects.

d. They should only be used for hypothesis testing. Coefficient estimates from the un- weighted, original model should be used for prediction.

9. If you have heteroskedasticity such that the sample can be divided into groups with each group having a different error variance, what estimation technique should be used?

a. FGLS—Feasible Generalized Least Squares

b. WLS—Weighted Least Squares

c. White’s robust estimator

d. Log-linear least squares

10. (Use the above information.) Which model is LEAST likely to have violated the assumption var(y_i) = var(e_i) = ²?

a. Model A

b. Model B

c. Model C

d. Model D

11. (Use the above information.) Which model is MOST likely to have violated the assumption var(y_i) = var(e_i) = ²?

a. Model A

b. Model B

c. Model C

d. Model D

12. (Use the above information.) In which model is WLS LEAST likely to be an effective solution for the heteroskedasticity?

a. Model A

b. Model B

c. Model C

d. Model D

13. Which test for heteroskedasticity should you use if you suspect different variances of the error term for different groups of observations?

a. White test

b. Lagrange Multiplier test

c. Goldfeld-Quandt test

d. Chow test

14. If heteroskedasticity is suspected, all of the following could be used to test for it EXCEPT the _____ test.

a. Lagrange Multiplier

b. Jarque-Bera

c. Breusch-Pagan

d. White

15. The LM (Lagrange Multiplier) test generates a test statistic N * R² ~²_(S-1). Where is the R² in the test statistic measured?

a. The original econometric model when estimated using the White correction technique

b. The average from all the auxiliary regressions estimated with each explanatory variable as a function of the other explanatory variables

c. The original econometric model before any test of heteroskedasticity has been performed

d. The auxiliary regression of residuals as a function of the explanatory variables generating the heteroskedasticity

16. The LM (Lagrange Multiplier) test generates a test statistic N * R² ~²_(S-1). To what does the S in this distribution refer?

a. The number of explanatory variables in the auxiliary regression

b. The number of explanatory variables in the initial model

c. N-K—The degrees of freedom in econometric model of interest

d. The statistical significance level chosen for the LM test

17. If you run an LM test for heteroskedasiticity and reject the null hypothesis, what should you conclude?

a. At least one coefficient in the auxiliary regression is significantly different from zero, the assumption var(y_i.) = var(e_i) = ² is unlikely to be true.

b. There is no evidence of heteroskedasticity, the assumption var(y_i.) = var(e_i) = ² is most likely true.

c. There is heteroskedasticity present, and it is correctly specified as tested.

d. There is heteroskedasticity, but it is not linear in the explanatory variables.

18. What is the tradeoff that a researcher faces when deciding how to deal with heteroskedasticity?

a. Goldfeld-Quandt overstates heteroskedasticity, but LM leads to more Type I errors.

b. White’s robust estimator should be used for hypothesis testing, but GLS is better for interval estimation.

c. GLS gives minimum variance, but results are more difficult to interpret.

d. White’s robust estimator requires no assumptions about the structure of the variance, but it is not as efficient as GLS estimates when the right structure is imposed on the variance.

19. A linear probability model is likely to violate which assumption of MR most of the time?

a. The values of each x_ik are not random and are not exact linear functions of the other explanatory variables.

b. var(y_i.) = var(e_i) = ²

c. E(y_i) = ₁ + ₂x_i2 + ₃x_i3 + ……. + _kx_ik, ⟺E(e_i) = 0

d. cov(y_i, y_j) = cov(e_i, e_j) = 0; (i≠j)

20. If your initial econometric model has heteroskedastic error terms, which estimator allows unbiased coefficient estimates without imposing a structure on the heteroskedasticity?

21. Suppose a simple regression model where the errors are statistically independent from one another and that heteroskedasticity is present in the form , . Derive the transformed model into one with homoscedastic errors.

2. Define the transformed variables and transformed errors:

3. New model is

4. Errors are not homoscedastic:

Level: Hard – Evaluation

AACSB: Analytic

Section: 8.4

22. What test for heteroskedasticity should be used if you suspect the error terms have different variances by category?