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Take Home Assignment

There are 40 multiple choice questions, worth 2.5 points each.

Please fill out the scantron that has been uploaded separately in this assignment.

Note that #1 on the scantron begins midway down the first column

Just put your name on the scantron; ID not needed

You must show work for any problem that requires it.

You can do this next to or under a problem in this document or all together on a

separate sheet.

Either way, upload your work either by uploading this document or a separate sheet.

When finished, please upload the scantron and whatever document shows your work,

as one file.

You may work together. However, you must turn in your own scantron and your own

written work.

1

Use the following output for questions 1-4.

An econometrician performs the following regression:

lsalary = ? 0 + ?1 games + ? 2 runs + u

where lsalary

= natural log salary of major league baseball player

games

= career games played

runs

= career runs scored

Source |

SS

df

MS

————-+—————————–Model | 220.933197

2 110.466598

Residual | 271.242338

350

.77497811

————-+—————————–Total | 492.175535

352 1.39822595

Number of obs

F( 2,

350)

Prob > F

R-squared

Adj R-squared

Root MSE

=

=

=

=

=

=

353

142.54

0.0000

0.4489

0.4457

.88033

—————————————————————————–lsalary |

Coef.

Std. Err.

t

P>|t|

[95% Conf. Interval]

————-+—————————————————————games |

.0005747

.0002504

2.29

0.022

.0000822

.0010672

runs |

.0016433

.0004482

3.67

0.000

.0007619

.0025247

_cons |

12.64234

.0766381

164.96

0.000

12.49161

12.79307

——————————————————————————

1. All else equal, an increase of 100 games played in a career has what effect on salary?

A. Increases salary by about 0.057%.

B. Increases salary by about $5,700.

C. Has no effect on salary.

D. Increases salary by about 5.7%.

2. Since career games played is included in the regression, the estimated coefficient on career runs is really measuring

A. how an increase in games played increases salary

B. how an increase in average runs per game played increases salary

C. how an increase in games played and runs per game increases salary

D. how an increase in the correlation between games played and runs per game increases salary

3. If games played had been left out of the regression, then the coefficient on runs would likely

be _________

A. biased upward

B. biased downward

C. unbiased

D. statistically insignificant

4. Based on the p-value associated with games, we know that

A. ?2 is NOT significantly different from 0 at the 1% level

B. ?1 is significantly different from 0 at the 1% level

C. ?1 is NOT significantly different from 0 at the 5% level

D. ?1 is significantly different from 0 at the 5% level

2

5. Manager Mark wants to find baseball players that are undervalued by the market (not being

paid their true worth). He believes that walks (walks) and extra bases (xtrabases) determine

wins. Which of the following strategies will help him find the players he wants after estimating

salary =?0 + ?1 walks + ?2 xtrabases + u?

A. Use the estimated model to predict each players residual, uhat. Players with negative uhat are undervalued.

B. Use the estimated model to predict each players residual, uhat. Players with positive uhat are undervalued.

C. Use the estimated model to predict each players salary, yhat. Players with small

yhat are undervalued.

D. Use the estimated model to predict each players salary, yhat. Players with large

yhat are undervalued.

Use the following model for questions 6-7. We estimate the following model for average standardized test scores of 5th graders in California school districts:

testscr = ?0 + ?1 avginc + ?2 avgincsq + u

where avginc is average household income in the district and avgincsq is avginc2.

. reg testscr avginc avgincsq

Source |

SS

df

MS

————-+—————————–Model | 84599.2786

2 42299.6393

Residual | 67510.3151

417

161.89524

————-+—————————–Total | 152109.594

419 363.030056

Number of obs

F( 2,

417)

Prob > F

R-squared

Adj R-squared

Root MSE

=

=

=

=

=

=

420

261.28

0.0000

0.5562

0.5540

12.724

—————————————————————————–testscr |

Coef.

Std. Err.

t

P>|t|

[95% Conf. Interval]

————-+—————————————————————avginc |

3.850995

.3042617

12.66

0.000

3.252917

4.449073

avgincsq | -.0423085

.0062601

-6.76

0.000

-.0546137

-.0300033

_cons |

607.3017

3.046219

199.36

0.000

601.3139

613.2896

6. What is the marginal effect of average income on test scores?

A. 3.85

B. 3.85 – .0423avginc

C. 0

D. 3.85 – .0846avginc

7. At approximately what value of average income are test scores maximized?

A. 36

B. 45.5

C. 64

D. 85.5

E. none of the above

3

8. A researcher interested in studying whether women trade off between time at work and

time sleeping gets the following estimated equation:

predicted weekly hours of sleep = ?? – ????weekly hours of work – ????education

If education were not included in the model, the size of the change in the estimated coefficient on hours depends upon

A. the amount of heteroskedasticity in the model

B. the amount of correlation between hours of work and education

C. the statistical significance of education

D. the sample size

9. Using data on 4,137 college students at a midsize research university, the following equation was estimated using OLS:

where colgpa is measured on a four-point scale, hsperc is the percentile in the high school

graduating class (so that, for example, hsperc = 5 corresponds to the top 5% of the class), and

sat is the combined math and verbal scores on the student achievement test.

Suppose that two high school graduates, A and B, graduated in the same percentile from high

school, but student As SAT score was 180 points higher. What is the predicted difference in

college GPA for these two students?

A. Student As GPA will be .572 points higher

B. Student As GPA will be .2664 points higher

C. Student Bs GPA will be .424 points higher

D. Student Bs GPA will be .3522 points higher

E. none of the above

10. Based on the following estimated wage equation, how would you interpret the coefficient

on college? The possible educational categories are: less than high school, high school grad,

some college, college grad, and graduate school.

ln(w age) = 1.1 + . 09highscho ol + .24somecollege + . 54college + .72graduate

+ .07exp – . 004exp 2 + .10male

A. Those with a college degree earn about 54% more than those who did not graduate

high school.

B. Those with a college degree earn about 54% more than high school graduates.

C. Those with a college degree earn about $0.54 per hour more than those who did not

graduate high school.

D. Those with a college degree earn about $54,000 more than those who did not graduate high school.

4

Use the following output for questions 11-13.

Suppose a researcher estimates a wage model, and gets the following STATA results, where:

lwage

= log wages

educ

= years of education

exper

= years of experience

female

= 1 if individual is female, 0 otherwise.

Source |

SS

df

MS

————-+—————————–Model |

52.29391

3 17.4313033

Residual | 96.0358517

522 .183976727

————-+—————————–Total | 148.329762

525

.28253288

Number of obs

F( 3,

522)

Prob > F

R-squared

Adj R-squared

Root MSE

=

=

=

=

=

=

526

94.75

0.0000

.42893

—————————————————————————–lwage |

Coef.

Std. Err.

t

P>|t|

[95% Conf. Interval]

————-+—————————————————————educ |

.0912897

12.82

.0772962

.1052833

exper |

.0094139

.0014493

0.000

.0065667

.012261

female | -.3435967

.0376668

0.000

-.4175939

-.2695995

_cons |

.4808356

.1050163

4.58

.2745292

.6871421

——————————————————————————

11. How much of the variation in the log of wages is explained by the variables in the model?

A. 0.2488

B. 0.3526

C. 0.4554

D. 0.5446

E. 0.6475

12. Is the coefficient (true beta) on female significantly different from 0 at the 5% level?

A. yes

B. no

C. not enough information to tell

13. What is the standard error for the estimated coefficient on educ?

A. 0.0002

B. 0.0071

C. 0.0145

D. 0.273

E. none of the above

14. All else constant, which of the following factors would decrease the estimated variance of

a beta-hat?

A. multicollinearity

B. a decrease in sample size

C. an increase in sample size

D. removing relevant variables from the regression

5

Use the following scenario for questions 15-16.

A researcher is interested in the determinants of sentencing, and using a random sample of

people convicted of homicide obtains the following, where priyears is prison sentence in years,

prviolnu is the number of prior violent offenses, stranger = 1 if the victim was a stranger,

black=1 if the offender is black, and vblack=1 if the victim was black.

—————————————————————————–priyears

| Coef.

Std. Err.

t

P>|t|

[95% Conf. Interval]

————-+—————————————————————prviolnu

| .5323433

.1477347

3.60

0.000

.2426575

.822029

stranger

| 1.801506

.5583621

3.23

0.001

.7066412

2.896372

black

| 1.70609

.7505269

2.27

0.023

.234418

3.177762

vblack

| -3.392937 .7427198

-4.57 0.000

-4.8493

-1.936573

_cons

| 9.536065

.4526042

21.07 0.000

8.648575

10.42355

——————————————————————————

15. Which factor decreases the predicted length of a prison sentence?

A. more prior violent offenses

B. the victim being a stranger

C. the offender being black

D. the victim being black

16. All else equal, how is the sentence of a black person who kills a white stranger (criminal A)

expected to compare to that of a white person who kills a black stranger (criminal B)?

A. criminal A is expected to be sentenced to 5.1 years more than criminal B

B. criminal A is expected to be sentenced to 1.7 years less than criminal B

C. criminal A is expected to be sentenced to 3.4 years more than criminal B

D. criminal A is expected to be sentenced to 1.7 years more than criminal B

17. Suppose we are interested in measuring the direct impact of productivity (measured as

wage) on the amount of exercise done in a week. However, we also suspect that exercise affects productivity. We would be worried that the following problem is occurring:

A. Intervening variable

B. No correlation

C. Common response

D. Reverse causation

18. You are considering trying to estimate the effect of IQ on income using cross-sectional data on individuals. However, you realize that the variance in income might differ by IQ level.

Thus, unless you take action, your model is likely to suffer from

A. multicollinearity

B. bias

C. serial correlation

D. heteroskedasticity

6

19. All else equal, which model is more likely to be in need of robust standard errors?

Model A: price = ? 0 + ?1lotsize + ? 2 sqrft + ? 3bdrms + u

Model B: ln( price ) = ? 0 + ?1lotsize + ? 2 sqrft + ? 3bdrms + u

A. Model A.

B. Model B.

C. They are equally likely to need robust standard errors.

D. There is not enough information to make an educated guess.

20. Which of the following can cause OLS estimators to be biased?

A. Heteroskedasticity

B. Omitting an important variable that is correlated with an included independent variable

C. A correlation of .80 between two independent variables included in the model

D. Including an interaction term in the model

E. None of these will cause OLS to be biased.

21. Based on the following estimated model of touchdowns as a function of pass attempts and

completions, how will estimated touchdowns change if a quarterback makes 100 more pass

attempts, 40 of which are also completions?

TD s = .025 ? .031attempts + .116completions

A. Estimated touchdowns will not change

B. Estimated touchdowns will decrease by about 7.5

C. Estimated touchdowns will increase by about 8.32

D. Estimated touchdowns will increase by about 1.54

7

Use the following output for questions 22-24.

Suppose you are interested in estimating the probability that an individual smokes as a function of:

educ

=

years of schooling

age

=

age in years

restaurn

=

1 if state restaurant smoking restrictions exist

. reg smoke educ age restaurn

Source |

SS

df

MS

————-+—————————–Model |

7.2089102

3 2.40297007

Residual | 183.708066

803 .228777168

————-+—————————–Total | 190.916976

806 .236869698

Number of obs

F( 3,

803)

Prob > F

R-squared

Adj R-squared

Root MSE

=

=

=

=

=

=

807

10.50

0.0000

0.0378

0.0342

.47831

—————————————————————————–smoke |

Coef.

Std. Err.

t

P>|t|

[95% Conf. Interval]

————-+—————————————————————educ | -.0223266

.0056113

-3.98

0.000

-.0333411

-.0113121

age | -.0036405

.0010064

-3.62

0.000

-.005616

-.001665

restaurn | -.0990255

.0391505

-2.53

0.012

-.1758749

-.022176

_cons |

.8371168

.0893487

9.37

0.000

.6617322

1.012501

——————————————————————————

22. Based on the linear probability model, what is the estimated probability of smoking for a 30year old with 12 years of education in a state that DOES have smoking restrictions?

A. 0.2245

B. 0.3612

C. 0.4013

D. 0.5589

E. 0.6104

23. Based on the linear probability model, how would you interpret the estimated coefficient on

educ?

A. An additional year of education decreases smoking by 2.2%

B. A 1% increase in years of education increases the probability of smoking by 0.022.

C. A 1% increase in years of education decreases the probability of smoking by 0.22.

D. An additional year of education decreases the probability of smoking by 0.022.

24. Based on the linear probability model, how would you interpret the estimated coefficient on restaurn?

A. Living in a state with restaurant smoking restrictions decreases the probability of smoking by .099.

B. Living in a state with restaurant smoking restrictions decreases the probability of smoking by 9.9%.

C. An additional restaurant in a state decreases the probability of smoking by .099

D. An additional restaurant in a state decreases the probability of smoking by .099%

25. The process of Ordinary Least Squares (OLS) estimates the parameters of a linear regression

by

A. simultaneously minimizing the residual for each observation

B. maximizing the likelihood of observing the data we have given our model

C. minimizing the sum of squared residuals

D. minimizing the square root of the product of the residuals

8

26. When deciding whether or not to drop variables from a model,

A. the economic significance of the coefficients does not matter

B. the change in the R-squared should be considered

C. its important to know whether heteroskedasticity is present, even if robust standard errors are used

D. an F-test should be conducted if the variables are individually insignificant and possibly

correlated

E. all of the above

Use the following output for questions 27 29.

The below STATA output estimates the following model, with northeast being the region

base/excluded category.

log( wage) = ? 0 + ?1educ + ? 2 female + ? 3exper + ? 4 female * exper + ? 5 married +

? 6 northcen + ? 7 south + ? 8 west + u

. reg lwage educ female exper femexper married northcen south west

Source |

SS

df

MS

————-+—————————–Model | 58.4412743

8 7.30515929

Residual | 89.8884874

517 .173865546

————-+—————————–Total | 148.329762

525

.28253288

Number of obs

F( 8,

517)

Prob > F

R-squared

Adj R-squared

Root MSE

=

=

=

=

=

=

526

42.02

0.0000

0.3940

0.3846

.41697

—————————————————————————–lwage |

Coef.

Std. Err.

t

P>|t|

[95% Conf. Interval]

————-+—————————————————————educ |

.0888772

.0071271

12.47

0.000

.0748756

.1028788

female | -.1622576

.0592933

-2.74

0.006

-.2787431

-.0457721

exper |

.0127103

.0020453

6.21

0.000

.0086922

.0167283

femexper | -.0098447

.0027135

-3.63

0.000

-.0151755

-.0045139

married |

.1384326

.0405266

3.42

0.001

.0588155

.2180496

northcen | -.0917406

.0530091

-1.73

0.084

-.1958804

.0123992

south | -.0948155

.0494229

-1.92

0.056

-.1919099

.0022788

west |

.0648169

.058641

1.11

0.270

-.050387

.1800208

_cons |

.4072016

.1137366

3.58

0.000

.1837588

.6306444

——————————————————————————

27. Choose the correct interpretation of the variable west.

A. Someone living in the west makes 64% more than everyone else.

B. Someone living in the west makes 6.5% more than someone living in the northeast.

C. Someone living in the west makes $6,400 more than someone living in the northeast.

D. Someone living in the west makes $0.64 more than everyone else.

28. An expression for the return to experience (effect of experience on log(wages)) is:

A. .0127 – .0098female

B. .0127

C. .0127 – .0098exper

D. .003exper

29. What is true about the return to experience?

A. The return to experience is higher for women, compared to men.

B. The return to experience is lower for women, compared to men.

C. The return to experience is negative for women.

D. The return to experience does not depend upon gender.

9

30. Suppose we would like to estimate the impact of a cigarette tax on lung cancer incidence. Our

hypothesis is that cigarette taxes will reduce consumption of cigarettes, thereby reducing

secondhand smoke and eventually lung cancer. In a model with lung cancer incidence as the dependent variable, should we include the level of cigarette consumption in order to more accurately

estimate the effect of the tax on lung cancer incidence?

A. Yes

B. No

C. Only if it increases the R-squared.

D. Its impossible to say without conducting an F-test.

Suppose an econometrician wants to see how gender and marital status affect wages. Everyone

can be categorized into one of four groups (married male, single male, married female, single female).

wages = ?0 + ?1 femmar + ?2 malemar + ?3 malesing + u

where femmar = 1 if female and married, 0 otherwise

malemar = 1 if male and married, 0 otherwise

malesing = 1 if male and not married, 0 otherwise

31. ?1 measures:

A. how much a married female earns compared to everyone else in the sample.

B. how much a married female earns compared to a single female.

C. how much a married female earns compared to a single male.

D. how much a married female earns compared to a married male.

Use the following information to answer questions 32-34. As an alternative to the above model, I

estimate the following model.

wages = ?0 + ?1 female + ?2 married + ?3 femmar + u

where femmar = female * married

female = 1 if female, 0 otherwise

married = 1 if married, 0 otherwise

32. Which of the following represents the expected wages for a married female?

A. ?0 + ?1

B. ?0 +?1 + ?2

C. ?0 +?2 + ?3

D. ?0 +?1 + ?2 + ?3

33. Which of the following is equivalent to ?1 in the above model (#31)?

A. ?1

B. ?1 + ?2

C. ?2 + ?3

D. ?1 + ?2 + ?3

10

34. The null hypothesis to test whether or not the effect of being married varies by gender is

A. Ho: ?1 = 0, ?3 = 0

B. Ho: ?3 = 0

C. Ho: ?1 = ?2

D. Ho: ?2 = 0, ?3 = 0

Use the following information for questions 35-37. We estimate a model of the natural logarithm of

salary for baseball players as a function of years played in the league, average games played per

year, batting average, home runs per year, and runs batted in per year.

ln( salary ) = ? 0 + ?1 years + ? 2 gamesyr + ? 3bavg + ? 4 hrunsyr + ? 5 rbisyr + u

. reg

lsalary years gamesyr bavg hrunsyr rbisyr

Source |

SS

df

MS

————-+—————————–Model | 308.989208

5 61.7978416

Residual | 183.186327

347 .527914487

————-+—————————–Total | 492.175535

352 1.39822595

Number of obs

F( 5,

347)

Prob > F

R-squared

Adj R-squared

Root MSE

=

=

=

=

=

=

353

117.06

0.0000

0.6278

0.6224

.72658

—————————————————————————–lsalary |

Coef.

Std. Err.

t

P>|t|

[95% Conf. Interval]

————-+—————————————————————years |

.0688626

.0121145

5.68

0.000

.0450355

.0926898

gamesyr |

.0125521

.0026468

4.74

0.000

.0073464

.0177578

bavg |

.0009786

.0011035

0.89

0.376

-.0011918

.003149

hrunsyr |

.0144295

.016057

0.90

0.369

-.0171518

.0460107

rbisyr |

.0107657

.007175

1.50

0.134

-.0033462

.0248776

_cons |

11.19242

.2888229

38.75

0.000

10.62435

11.76048

—————————————————————————–. test bavg hrunsyr rbisyr

( 1)

( 2)

( 3)

bavg = 0

hrunsyr = 0

rbisyr = 0

F(

3,

347) =

Prob > F =

9.55

0.0000

35. Consider the following null and alternative hypothesis:

H 0 : ?5 = 0

H1 : ?5 ? 0

Would you reject the null at the 20% level of significance?_________

Would you reject the null at the 5% level of significance?___________

Would you reject the null at the 1% level of significance?__________

A. yes; yes; yes

B. no; no; no

C. yes; no; no

D. no; yes; yes

36. What is the estimated variance of ?5 ?

A. 0.007175

B. 0.0000515

C. 0.0121

D. 0.00265

E. none of the above

11

37. What do you conclude when you test the following null hypothesis?

H 0 : ?3 = 0, ? 4 = 0, ?5 = 0

A. The parameters are jointly significant at the 10% level, but not at a lower significance

level.

B. The parameters are individually significant at less than the 1% level.

C. The parameters are not jointly significant at any reasonable level.

D. The parameters are jointly significant at less than the 1% level.

38. A researcher is planning on estimating a simple model of per-pupil school spending as a function of the districts per capita income. He obtains the following, where lnexppup is ln(per pupil

spending) and lnpcy is ln(per capita income).

predicted lnexppup = 5.41 + 2.14lnpcy

These results imply that

A. increasing per capita income by $100 increases spending by $21.40

B. increasing per capita income by $100 increases spending by 21%

C. increasing per capita income by 100% increases spending by $21.40

D. increasing per capita income by 1% increases spending by 2.14%

Use this information for questions 39-40. An econometrician estimates the following model:

colgpa = ?0 + ?1sat + ?2tothrs + ?3sathours + ?4female + u

where colgpa is college GPA, sat is SAT score, tothrs is the number of credit hours accumulated prior to the semester, sathours is an interaction of sat and tothrs, and female is a dummy variable = 1 if

the student is female.

. reg colgpa sat tothrs sathours female

Source |

SS

df

MS

————-+—————————–Model | 398.539145

4 99.6347864

Residual | 1395.65653 4132 .337767795

————-+—————————–Total | 1794.19567 4136 .433799728

Number of obs

F( 4, 4132)

Prob > F

R-squared

Adj R-squared

Root MSE

=

=

=

=

=

=

4137

294.98

0.0000

0.2221

0.2214

.58118

—————————————————————————–colgpa |

Coef.

Std. Err.

t

P>|t|

[95% Conf. Interval]

————-+—————————————————————sat |

.0027439

.0001184

23.17

0.000

.0025117

.002976

tothrs |

.0155283

.0018969

8.19

0.000

.0118095

.0192472

sathours | -.0000128

1.83e-06

-7.00

0.000

-.0000164

-9.24e-06

female |

.2248177

.0184042

12.22

0.000

.1887355

.2608998

_cons | -.3971054

.1236172

-3.21

0.001

-.6394617

-.1547492

——————————————————————————

39. What is true about the effect of SAT score on college GPA?

A. An increase in SAT of one point increases college GPA by .0027439

B. SAT does not have a statistically significant impact on college GPA

C. For those who have more accumulated credit hours, the impact of SAT on GPA is smaller

D. For those who have more accumulated credit hours, the impact of SAT on GPA is larger

E. None of the above

12

40. If 90 hours are accumulated, the effect of SAT on GPA is approximately:

A. 0.0027

B. 0.0016

C. -0.0000128

D. 0.016

E. none of the above

13

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