Free Printable Heteroskedasticity

1.

What are the possible consequences of heteroscedasticity for OLS estimator?

a)

It becomes inconsistent

b)

It becomes biased

c)

It becomes inefficient

d)

It becomes not linear

2.

If you performed White's test and got the p-value of 0.02. At 5% significance level you would:

a)

reject the null hypothesis of heteroscedasticity

b)

reject the null hypothesis of homoscedasticity

c)

do not reject the null hypothesis of heteroscedasticity

d)

do not reject the null hypothesis of homoscedasticity

3.

In the presence of heteroscedasticity if White's robust standard errors are used, usually

a)

Coefficients change, the standard errors are the same.

b)

Coefficients change, the standard errors become smaller.

c)

Coefficients do not change, standard errors become greater.

d)

Coefficients do not change, standard errors become smaller.

4.

Heteroscedasticity is associated with:

a)

Time series data

b)

Cross-sectional data

c)

Panel Data

d)

Unbalanced Panel Data

5.

A formula to compute White Test statistics is:

a)

N*R

b)

N*R²

c)

N*2R

d)

N*adjusted R²

6.

White Test is used to detecting:

a)

Heteroscedasticity

b)

Autocorrelation

c)

Correlation

d)

Homoscedasticity

7.

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.

8.

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)

$var\left(y_i\right)=var\left(e_i\right)=\sigma^2$

c)

$cov\left(y_i,\ y_j\right)=cov\left(e_i,\ e_j\right)=0;\ i\ne j$

d)

$E\left(y_i\right)=\beta_1+\beta_2x_{i2}+...+\beta_kx_{ik},\Longleftrightarrow\ E\left(e_i\right)=0$

9.

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

a)

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

b)

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

c)

There is no evidence of heteroskedasticity, the assumption $var\left(y_i\right)=var\left(e_i\right)=\sigma^2$ is most likely true.

d)

At least one coefficient in the auxiliary regression is significantly different from zero, the assumption $var\left(y_i\right)=var\left(e_i\right)=\sigma^2$ is unlikely to be true

10.

The LM (Lagrange Multiplier) test generates a test statistic $N\cdot R^2\sim\chi^2\left(s-1\right)$ Where is the R²in 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

11.

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

(a)

12.

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

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.

Which model is LEAST likely to have violated the assumption $var\left(y_i\right)=var\left(e_i\right)=\sigma^2$ ?

a)

b)

c)

d)

15.

Which model is MOST likely to have violated the assumption $var\left(y_i\right)=var\left(e_i\right)=\sigma^2$ ?

a)

b)

c)

d)

16.

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

17.

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 unweighted, original model should be used for prediction.

18.

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

19.

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.

20.

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)

The OLS estimate of $\beta_1$ will be unbiased.

d)

$var\left(e_i\right)=\sigma^2$

21.

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)

$var\left(y_i\right)=var\left(e_i\right)=\sigma^2$

c)

$cov\left(y_i,\ y_j\right)=cov\left(e_i,\ e_j\right)=0;\ i\ne j$

d)

$E\left(y_i\right)=\beta_1+\beta_2x_{i2}+...+\beta_kx_{ik},\Longleftrightarrow\ E\left(e_i\right)=0$

Heteroskedasticity

Total questions: 21

Worksheet time: 2hrs 32mins

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