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#### Principles of Econometrics 4th Edition by R. Carter Hill -Test Bank

File: Ch06, Chapter 6, Further Inference in the Multiple Regression Model

Multiple Choice

- The following model has been estimated using a dataset with 4854 observations.

SS | df | MS | |||||||

Regression | 919587.543 | 4 | 229896.9 | ||||||

Error | 2590390.62 | 121 | 534.2113 | ||||||

Variable | b | Std. Error | t | P>|t| | |||||

x2 | -0.0126355 | 0.005519 | -2.28937 | 0.022 | |||||

x3 | 0.5957923 | 0.014482 | 41.13934 | 0.000 | |||||

x4 | 1.124589 | 0.877192 | 1.282032 | 0.200 | |||||

x5 | 0.3237421 | 0.060709 | 5.332661 | 0.000 | |||||

Constant | 8.86016 | 1.766116 | 5.016749 | 0.000 | |||||

Calculate the F-statistic to test **H _{0}: **

**b**

_{2}**=**

**b**

_{3}**=-**

**b**

_{4}**=**

**b**

_{5}**= 0**

a.) 430.35

b.) .2620

c.) 76.80

d.) 2.8169

Ans: a

Level: Difficult

Section: 6.1

- The critical value for a given p-value in the F-distribution depends on the degrees of freedom in the numerator and denominator. How do you find the degrees of freedom in the numerator?

a.) It is the number of observations minus the number of coefficients estimated (N-K)

b.) It is the number of hypotheses being tested simultaneously (J)

c.) It is the number of coefficients being estimated (K)

d.) It is the number of observations minus the number of hypotheses tested (N-J)

Ans: b

Level: Moderate

Section: 6.1

- The critical value for a given p-value in the F-distribution depends on the degrees of freedom in the numerator and denominator. How do you find the degrees of freedom in the denominator?

a.) It is the number of observations minus the number of coefficients estimated (N-K)

b.) It is the number of hypotheses being tested simultaneously (J)

c.) It is the number of coefficients being estimated (K)

d.) It is the number of observations minus the number of hypotheses tested (N-J)

Ans: a

Level: Moderate

Section: 6.1

- When performing an F-test, if the null hypothesis is
**H**_{0}:**b**_{2}**=****b**_{3}**= 0**what is the alternative hypothesis?

a.) b_{2} ≠0 and b_{3}≠0

b.) b_{2} ≠0 or b_{3}≠0

c.) (b_{2} ≠0 and b_{3}=0) or (b_{2} =0 and b_{3}≠0)

d.) (b_{2} <0 and b_{3}>0) or (b_{2} >0 and b_{3}<0)

Ans: b

Level: Moderate

Section: 6.1

- The F
_{(1,218)}distribution is equivalent to what distribution?

a.) N (1,218)

b.) F_{(2, 114)}

c.) t_{(218)}

d.) c^{2}_{(2,114)}

Ans: c

Level: Moderate

Section: 6.1

- What statistical test allows joint hypotheses to be tested?

a.) Breusch-Pagan Test

b.) t-test

c.) Gauss-Markov

d.) F-test

Ans: d

Level: Easy

Section: 6.1

- If your computer printout includes an F-statistic and p-value for the overall model, how should you interpret the p-value?

a.) the probability that all of the coefficients are actually equal to zero

b.) the probability that all of the coefficients other than the intercept are actually zero and we would observe the estimated results

c.) the probability that the model is completely invalid

d.) the probability that the model is incorrectly specified

Ans: b

Level: Moderate

Section: 6.1

- Why should
__good__non-sample information be incorporated into an econometric model via restricted least squares?

a.) it reduces the variance of estimated coefficients without introducing bias

b.) it allows more precise hypotheses testing to be done

c.) it reduces the degrees of freedom in the denominator of an F-test

d.) It reduces the probability of rejecting a true null hypothesis

Ans: a

Level: Moderate

Section: 6.2

- How does omitting a relevant variable from a regression model affect the estimated coefficient of other variables in the model?

a.) they are biased downward and have smaller standard errors

b.) they are biased upward and have larger standard errors

c.) they are biased and the bias can be negative or positive

d.) they are unbiased but have larger standard errors

Ans: c.

Level: Moderate

Section: 6.3

- How does including an irrelevant variable in a regression model affect the estimated coefficient of other variables in the model?

a.) they are biased downward and have smaller standard errors

b.) they are biased upward and have larger standard errors

c.) they are biased and the bias can be negative or positive

d.) they are unbiased but have larger standard errors

Ans: d

Level: Moderate

Section: 6.3

- Which of the following measures is NOT used to evaluate model specification?

a.) adj R^{2}

b.) Akiake Information Criterion (AIC)

c.) Bayesian Information Criterion (BIC)

d.) Jarque-Bera Test

Ans: d

Level: Easy

Section: 6.3

- When are R
^{2}and adjusted R^{2}equal?

a.) when the model is correctly specified

b.) when K = 1

c.) when the error terms are normally distributed

d.) when an unrestricted model is estimated

Ans: b

Level: Moderate

Section: 6.3

- You estimate 4 different specifications of an econometric model by adding a variable each time and get the following results

R^{2} |
adj R^{2} |
AIC | ||

Model A | 0.3458 | 0.3285 | 22.56 | |

Model B | 0.3689 | 0.3394 | 22.37 | |

Model C | 0.4256 | 0.3916 | 21.21 | |

Model D | 0.4299 | 0.3911 | 21.79 | |

Which model appears to be correctly specified?

a.)A

b.)B

c.)C

d.)D

Ans: C

Level: Moderate

Section: 6.3

- If you reject the null hypothesis when performing a RESET test, what should you conclude?

a.) at least one of the original coefficients is not equal to zero

b.) the original model is incorrectly specified and can be improved upon

c.) relevant variable are omitted and the coefficient estimates of included variables are biased

d.) an incorrect functional form was used

Ans: b (the misspecification does not have to be an omitted variable)

Level: Moderate/Difficult

Section: 6.3

- When collinear variables are included in an econometric model coefficient estimates are

a.) biased downward and have smaller standard errors

b.) biased upward and have larger standard errors

c.) biased and the bias can be negative or positive

d.) unbiased but have larger standard errors

Ans: d

Level: Moderate

Section: 6.4

- When a set of variables with exact collinearity is included in an econometric model coefficient estimates are

a.) undefined

b.) unbiased

c.) biased upward

d.) biased, but the direction is unclear

Ans: a

Level: Easy

Section: 6.4

- If your regression results show a high R
^{2}, adj R^{2}, and a significant F-test, but low t values for the coefficients, what is the most likely cause?

a.) omitted relevant variables

b.) irrelevant variables included

c.) collinearity

d.) heteroskedasiticity

Ans: c

Level: Easy

Section: 6.4

- Running auxillary regressions where each explanatory variable is estimated as a function of eth remaining explanatory variables can help detect

a.) omitted relevant variables

b.) irrelevant variables included

c.) collinearity

d.) heteroskedasiticity

Ans: c

Level: Moderate

Section: 6.4

- Why is the variance of the forecast y larger than the variance of the expected value of y?

a.) the estimated forecast variance includes an estimate of ŝ^{2}

b.) the estimated forecast variance includes weighted covariance terms of all paired variables

c.) the Gauss-Markov theorem does not apply to forecast of a single observation

d.) the expected value of confidence intervals rely on the standard normal distribution while forecast use a t distribution.

Ans: a

Level: Difficult

Section: 6.5

Short Answer

- For what does RESET test?

Ans: Model misspecification

Level: Moderate

Section: 6.3

- When two or more variables move together in systematic ways they are said to be ________________?

Ans: Collinear

Level: Easy

Section: 6.4

File: Ch07, Chapter 7, Using Indicator Variables

Multiple Choice

- Which of the following terms is NOT commonly used to refer to an indicator variable?

a.) dummy

b.) binary

c.) dichotomous

d.) digital

Ans; d

Level: Easy

Section: 7.1

- Which of the following wage premia is modeled with an indicator variable that shifts the intercept?

a.) height

b.) gender

c.) education

d.) weight

Ans: b

Level: Easy

Section: 7.1

- The following Mincer equation has been used to estimate wages:

ln (*Y*) = ln (*Y*_{o}) + b_{2}*EDU* + b_{3}*EXPER* + b_{4 }*EXPER*^{2} + *e*

where *Y* is income, *Y*_{0} is income of someone with no education or experience, *EDU* is years of education and *EXPER* is experience in the field. If you suspect males earn higher wages than females and that the wage difference increases with education how would you adjust the econometric model to estimate wages?

a.) include a binary variable for gender, *MALE*

b.) include an interaction term equal to *MALE* EXPER*

c.) include an indicator variable for *MALE* and one for *FEMALE*

d.) include a binary variable for *MALE* and an interaction term equal to *MALE * EXPER*

* *

Ans: d

Level: Moderate

Section: 7.1

- The Chow test is a specific application of a(n)

a.) z-test

b.) c^{2} test

c.) F-test

d.) t-test

Ans: c

Level: Easy

Section 7.2

- A large company is accused of gender discrimination in wages. The following model has been estimated from the company’s human resource information

**ln( WAGE) = 1.439 + .0834 EDU + .0512 EXPER + .1932 MALE**

* *

Where WAGE is hourly wage, EDU is years of education, EXPER is years of relevant experience, and MALE indicates the employee is male. How much more do men at the firm earn, on average?

a.) $1.21 per hour more than females

b.) 19.32% more than females

c.) $19.32 per hour

d.) $19,320 more per year than females

Ans: b

Level: Moderate

Section: 7.3

[highlighted term should have a “hat” over]

- . A large company is accused of gender discrimination in wages. The following model has been estimated from the company’s human resource information

**ln( WAGE) = 1.439 + .0834 EDU + .0512 EXPER + .1932 MALE**

* *

Where WAGE is hourly wage, EDU is years of education, EXPER is years of relevant experience, and MALE indicates the employee is male. What hypothesis would you test to determine if the discrimination claim is valid?

a.) H_{0}:b_{MALE} = 0 ; H_{1}: b_{MALE} ≥ 0

b.) H_{0}:b_{MALE} = b_{EDU} = b_{EXPER }= 0 ; H_{1}: b_{MALE} ≠ 0 and b_{EDU} ≠ 0 and b_{EXPER }≠ 0

c.) H_{0}:b_{MALE} = b_{EDU} = b_{EXPER }= 0 ; H_{1}: b_{MALE} ≠ 0 or b_{EDU} ≠ 0 or b_{EXPER }≠ 0

d.) H_{0}:b_{MALE} ≤ b_{EDU} or b_{MALE }≤ b_{EXPER } ; H_{1}: b_{MALE} > b_{EDU} or b_{MALE }> b_{EXPER}

Ans: a

Level: Moderate

Section: 7.3

[highlighted term should have a “hat” over]

- When you have a multiple regression model with a binary dependent variable it is a __________.

a.) dichotomous model

b.) Bernoulli model

c.) Linear Probability model

d.) prediction model

Ans: c

Level: Easy

Section: 7.4

- The following economic model predicts whether a voter will vote for an incumbent school board member

*INCUMBENT* = b_{1} + b_{2} *MALE* + b_{3 }*PARTY* + b_{4 }*MARRIED *+ b_{5 }*KIDS *

where

*INCUMBENT* = 1 if the voter votes for them, 0 otherwise,

*MALE* = 1 if the voter is a male,

*PARTY* indicates the voter is registered with the same political party as the incumbent,

*MARRIED *= 1 for married voters, 0 otherwise, and

*KIDS *is the number of school age kids living with the voter.

What is the probability that a married female without kids who is not registered with a political party will vote for the incumbent?

a.) b_{1} + b_{4}

b.) b_{1}

c.) b_{1 }+ b_{2} + b_{3 }+ b_{5}

d.) b_{2} + b_{3} + b_{5}

Ans: a

Level: Moderate

Section: 7.4

- The following economic model predicts whether a voter will vote for an incumbent school board member

*INCUMBENT* = b_{1} + b_{2} *MALE* + b_{3 }*PARTY* + b_{4 }*MARRIED *+ b_{5 }*KIDS *

where

*INCUMBENT* = 1 if the voter votes for them, 0 otherwise,

*MALE* = 1 if the voter is a male,

*PARTY* indicates the voter is registered with the same political party as the incumbent,

*MARRIED *= 1 for married voters, 0 otherwise, and

*KIDS *is the number of school age kids living in the voter’s house.

How should we interpret b_{4}?

a.) the likelihood the incumbent candidate is married

b.) the percentage of married voters who vote for the incumbent

c.) the probability a married person is registered to vote

d.) the difference in probability a married voter will vote for the incumbent as opposed to an unmarried voter

Ans: d

Level: Moderate

Section: 7.4

- Treatment effects are
*best*estimated using data from

a.) randomized, controlled experiments.

b.) subjects that have already undergone the risky treatment.

c.) people most in need of the treatments.

d.) natural or quasi-experiments.

Ans: a

Level: Easy

Section: 7.5

- Randomized, controlled experiments are needed to accurately measure treatment effects without

a.) the expense of having to treat everyone.

b.) the risk of discrimination bias.

c.) exposing everyone to untested treatments.

d.) selection bias.

Ans: d

Level: Moderate

Section: 7.5

- When certain characteristics cause a person to choose to be in a treatment group, selection bias can be overcome by using

a.) conditional randomization and fixed effects.

b.) difference in differences estimation.

c.) larger sample sizes.

d.) quasi-experiments.

Ans: a

Level: Difficult

Section: 7.5

- Treatment effects can be estimated from natural or quasi-experiments using which estimator?

a.) Restricted least squares

b.) Difference-in-differences estimator

c.) Fixed effects

d.) Quasi-Likelihood

Ans: b

Level: Moderate

Section: 7.5

- Which of the following variables is not necessary in order to estimate treatment effects using difference-in-differences?

a.) a treatment/control indicator

b.) pre-treatment / post-treatment indicator

c.) treatment group * treatment time interaction term

d.) post-treatment performance

Ans: c

Level: Moderate

Section: 7.5

- Estimating treatment effects using difference-in-differences requires what kind of data?

a.) aggregate measures over time

b.) time-series data spanning the treatment length

c.) paired, panel data

d.) cross-section spanning the treated population

Ans: c

Level: Easy

Section: 7.5

- What benefit is gained by estimating treatment effects with fixed effects using panel data?

a.) it controls for unobserved, individual characteristics

b.) it controls for changes in individuals over time

c.) it allows the treatment effect to vary with the length of treatment

d.) it “fixes” the treatment to the same time for each individual

Ans: a

Level: Moderate

Section: 7.5

- The following economic model predicts whether a voter will vote for an incumbent school board member

*INCUMBENT* = b_{1} + b_{2} *MALE* + b_{3 }*PARTY* + b_{4 }*MARRIED *+ b_{5 }*KIDS *

where

*INCUMBENT* = 1 if the voter votes for them, 0 otherwise,

*MALE* = 1 if the voter is a male,

*PARTY* indicates the voter is registered with the same political party as the incumbent,

*MARRIED *= 1 for married voters, 0 otherwise, and

*KIDS *is the number of school age kids living in the voter’s house.

If you hypothesize males and females might have a different willingness to vote for a candidate registered with a different political party, which variable should you add to the economic model to allow you to test the hypothesis?

a.) MALE * PARTY

b.) MALE * MARRIED

c.) MARRIED * KIDS

d.) MARRIED * PARTY

Ans: a

Level: Easy

Section: 7.2

- The following economic model predicts whether a voter will vote for an incumbent school board member

*INCUMBENT* = b_{1} + b_{2} *MALE* + b_{3 }*PARTY* + b_{4 }*MARRIED *+ b_{5 }*KIDS *

where

*INCUMBENT* = 1 if the voter votes for them, 0 otherwise.

*MALE* = 1 if the voter is a male.

*PARTY* indicates the voter is registered with the same political party as the incumbent.

*MARRIED *= 1 for married voters, 0 otherwise.

*KIDS *is the number of school age kids living in the voter’s house.

If you believe marriage affects male and female voters differently, which variable should you add to the economic model to allow you to test the hypothesis?

a.) MALE * PARTY

b.) MALE * MARRIED

c.) MARRIED * KIDS

d.) MARRIED * PARTY

Ans: b

Level: Easy

Section: 7.2

- If you perform a Chow test to compare two regressions and reject the null hypothesis, what should you conclude?

a.) there is not sufficient evidence that the regressions are significantly different

b.) the regression equations are statistically different

c.) the regression equations are equivalent

d.) it depends on how you set up the null hypothesis

Ans: a

Level: Moderate

Section: 7.2