Question 1

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

Accepted Answer

A) The values of each xik are not random and are not exact linear functions of the other explanatory variables 
B) var(yi. )= var(ei)= $\sigma$2 
C) E(yi)= $\beta$1 + $\beta$2xi2 + $\beta$3xi3 + …….+ $\beta$kxik,⟺E(ei)= 0 
D) cov(yi,yj)= cov(ei,ej)= 0; (i≠j) 
A) The values of each xik are not random and are not exact linear functions of the other explanatory variables 
B) var(yi. )= var(ei)= $\sigma$2 
C) E(yi)= $\beta$1 + $\beta$2xi2 + $\beta$3xi3 + …….+ $\beta$kxik,⟺E(ei)= 0 
D) cov(yi,yj)= cov(ei,ej)= 0; (i≠j) B

Question 2

(See graphs of Model A - D)The scatterplots show the estimated residuals plotted against predicted values of the dependent variable.Which model is LEAST likely to have violated the assumption var(yi)= var(ei)= $\sigma$2?

Accepted Answer

A) Model A 
B) Model B 
C) Model C 
D) Model D 
A) Model A 
B) Model B 
C) Model C 
D) Model D C

Question 3

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

Accepted Answer

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 
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 C

Question 4

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

Accepted Answer

A) White test 
B) Lagrange Multiplier test 
C) Goldfeld-Quandt test 
D) Chow Test 
A) White test 
B) Lagrange Multiplier test 
C) Goldfeld-Quandt test 
D) Chow Test

Question 5

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

Accepted Answer

A) at least one coefficients in the auxiliary regression is significantly different from zero,the assumption var(yi. )= var(ei)= $\sigma$2 is unlikely to be true 
B) there is no evidence of heteroskedasticity,the assumption var(yi. )= var(ei)= $\sigma$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 
A) at least one coefficients in the auxiliary regression is significantly different from zero,the assumption var(yi. )= var(ei)= $\sigma$2 is unlikely to be true 
B) there is no evidence of heteroskedasticity,the assumption var(yi. )= var(ei)= $\sigma$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

Question 6

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

Accepted Answer

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 
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

Question 7

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

Accepted Answer

White's Ro

Question 8

If you model has heteroskedastic error terms,but you do not know the functional form of the variance equation,what should be done?

Accepted Answer

A) use White's Robust Estimator 
B) use weighted least squares 
C) try different functional forms for the variance until the Lagrange Multiplier falls 10% 
D) add observations to the dataset and estimate again 
A) use White's Robust Estimator 
B) use weighted least squares 
C) try different functional forms for the variance until the Lagrange Multiplier falls 10% 
D) add observations to the dataset and estimate again

Question 9

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

Accepted Answer

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. 
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.

Question 10

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

Accepted Answer

A) WLS or GLS 
B) White Robust 
C) FGLS 
D) Quasi-Least Squares 
A) WLS or GLS 
B) White Robust 
C) FGLS 
D) Quasi-Least Squares

Question 11

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?

Accepted Answer

A) FGLS-feasible generalized least squares 
B) WLS-Weighted least squares 
C) White's robust estimator 
D) log-linear least squares 
A) FGLS-feasible generalized least squares 
B) WLS-Weighted least squares 
C) White's robust estimator 
D) log-linear least squares

Question 12

(See graphs of Model A - D)The scatterplots show the estimated residuals plotted against predicted values of the dependent variable.Which model is MOST likely to have violated the assumption var(yi)= var(ei)= $\sigma$2?

Accepted Answer

A) Model A 
B) Model B 
C) Model C 
D) Model D 
A) Model A 
B) Model B 
C) Model C 
D) Model D

Question 13

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

Accepted Answer

A) The values of each xik are not random and are not exact linear functions of the other explanatory variables 
B) var(yi. )= var(ei)= $\sigma$2 
C) E(yi)= $\beta$1 + $\beta$2xi2 + $\beta$3xi3 + …….+ $\beta$kxik,⟺E(ei)= 0 
D) cov(yi,yj)= cov(ei,ej)= 0; (i≠j) 
A) The values of each xik are not random and are not exact linear functions of the other explanatory variables 
B) var(yi. )= var(ei)= $\sigma$2 
C) E(yi)= $\beta$1 + $\beta$2xi2 + $\beta$3xi3 + …….+ $\beta$kxik,⟺E(ei)= 0 
D) cov(yi,yj)= cov(ei,ej)= 0; (i≠j)

Question 14

What is the tradeoff researchers face when deciding how to deal with heteroskedasticity?

Accepted Answer

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 
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

Question 15

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

Accepted Answer

A) Lagrange Multiplier test 
B) Jarque-Bera test 
C) Breusch-Pagan test 
D) White test 
A) Lagrange Multiplier test 
B) Jarque-Bera test 
C) Breusch-Pagan test 
D) White test

Question 16

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

Accepted Answer

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 
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

Question 17

(See graphs of Model A - D)The scatterplots show the estimated residuals plotted against predicted values of the dependent variable.In which model is WLS LEAST likely to be an effective solution for the heteroskedasticity?

Accepted Answer

A) Model A 
B) Model B 
C) Model C 
D) Model D 
A) Model A 
B) Model B 
C) Model C 
D) Model D

Question 18

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

Accepted Answer

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 
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

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

(See graphs of Model A - D)The scatterplots show the estimated residuals plotted against predicted values of the dependent variable.Which model is LEAST likely to have violated the assumption var(y_i)= var(e_i)= $\sigma$ ²?

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

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

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

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

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

If you model has heteroskedastic error terms,but you do not know the functional form of the variance equation,what should be done?

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

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

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?

(See graphs of Model A - D)The scatterplots show the estimated residuals plotted against predicted values of the dependent variable.Which model is MOST likely to have violated the assumption var(y_i)= var(e_i)= $\sigma$ ²?

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

What is the tradeoff researchers face when deciding how to deal with heteroskedasticity?

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

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

(See graphs of Model A - D)The scatterplots show the estimated residuals plotted against predicted values of the dependent variable.In which model is WLS LEAST likely to be an effective solution for the heteroskedasticity?

The LM (Lagrange Multiplier)test generates a test statistic N * R² ~ $\chi$ ²_(S-1).Where is the R²in the test statistic measured?

An Introduction to Econometrics

Pp : Prob, Probability Primer, Probability Primer

The Simple Linear Regression Model

Interval Estimation and Hypothesis Testing

Prediction, Goodness-Of-Fit and Modeling Issues

The Multiple Regression Model

Further Inference in the Multiple Regression Model

Using Indicator Variables

Regression With Time Series Data: Stationary Variables

Random Regressors and Moment Based Estimation

Simultaneous Equations Models

Regression With Time Series Data: Nonstationary Variables

Vector Error Correction and Vector Autoregressive Models

Time-Varying Volatility and Arch Models

Panel Data Models

Qualitative and Limited Dependent Variable Models

Filters

Exam 9: Heteroskedasticity

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

(See graphs of Model A - D)The scatterplots show the estimated residuals plotted against predicted values of the dependent variable.Which model is LEAST likely to have violated the assumption var(yi)= var(ei)= σ\sigmaσ 2?

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

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

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

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

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

If you model has heteroskedastic error terms,but you do not know the functional form of the variance equation,what should be done?

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

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

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?

(See graphs of Model A - D)The scatterplots show the estimated residuals plotted against predicted values of the dependent variable.Which model is MOST likely to have violated the assumption var(yi)= var(ei)= σ\sigmaσ 2?

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

What is the tradeoff researchers face when deciding how to deal with heteroskedasticity?

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

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

(See graphs of Model A - D)The scatterplots show the estimated residuals plotted against predicted values of the dependent variable.In which model is WLS LEAST likely to be an effective solution for the heteroskedasticity?

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

An Introduction to Econometrics

Pp : Prob, Probability Primer, Probability Primer

The Simple Linear Regression Model

Interval Estimation and Hypothesis Testing

Prediction, Goodness-Of-Fit and Modeling Issues

The Multiple Regression Model

Further Inference in the Multiple Regression Model

Using Indicator Variables

Regression With Time Series Data: Stationary Variables

Random Regressors and Moment Based Estimation

Simultaneous Equations Models

Regression With Time Series Data: Nonstationary Variables

Vector Error Correction and Vector Autoregressive Models

Time-Varying Volatility and Arch Models

Panel Data Models

Qualitative and Limited Dependent Variable Models

Filters

(See graphs of Model A - D)The scatterplots show the estimated residuals plotted against predicted values of the dependent variable.Which model is LEAST likely to have violated the assumption var(y_i)= var(e_i)= $\sigma$ ²?

(See graphs of Model A - D)The scatterplots show the estimated residuals plotted against predicted values of the dependent variable.Which model is MOST likely to have violated the assumption var(y_i)= var(e_i)= $\sigma$ ²?

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

The LM (Lagrange Multiplier)test generates a test statistic N * R² ~ $\chi$ ²_(S-1).Where is the R²in the test statistic measured?