Midterm Fall2011

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Department of Economics Econometrics W3412

Columbia University Fall 2011

Midterm Exam

Section 3 – Prof. Seyhan Erden Arkonac

Instructions

1. Do not turn this page until so instructed.

2. The exam has three questions. Please put your answers in the space provided under each

question.

3. You are permitted to use a simple calculator. No computers, wireless, or other electronic

devices without prior permission. You may not share resources with anyone else.

4. Some questions ask you to draw a real-world judgment in a problem of practical importance.

The quality of that judgment counts. For example, consider the question: “It is 10oF outside.

In your judgment, why are so many people wearing heavy coats?” The answer, “To stay

warm” would receive more points than the answer, “Because they are fashion-conscious.”

5. Put your name and Columbia UNI on the cover of the exam.

Name: ___________________________________________________

UNI: ____________________________________________________

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Question 1 [30 points] Suppose that a researcher, using fictitious data on sugar consumption (SC) and diabetes (D),

estimates the OLS regression. SC is in grams per day and D is in number of patients per 100,000

people.

D = 100.0 + 2.5 x SC, R² = 0.10, SER = 10.

(20.0) (0.5)

a) (6p) Construct a 95% confidence interval for β1, the regression slope coefficient.

b) (6p) Calculate the p-value for the one-sided test of the null hypothesis H0: β1 = 1.5. Do

you reject the null hypothesis at 1% significance level? At the 5% significance level?

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c) (6p) Calculate the p-value for the two-sided test of the null H0: β1 = 2.0. Without doing

any additional calculations, determine whether 2.0 is contained in the 99% confidence

interval for β1.

d) (6p) Construct a 90% confidence interval for β0, the intercept coefficient? Explain what

this confidence interval means.

e) (6p) Interpret R².

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Question 2 [33 points] In the dataset construction, the country is divided into four regions: Northeast, Midwest, South,

and West. For the purposes of this exercise let

AHE = average hourly earnings (in 1998 dollars)

College = binary variable (1 if college, 0 if high school)

Female = binary variable (1 if female, 0 if male)

Age = age (in years)

Northeast = binary variable (1 if Region = Northeast, 0 otherwise)

Midwest = binary variable (1 if Region = Midwest, 0 otherwise)

South = binary variable (1 if Region = South, 0 otherwise)

West = binary variable (1 if Region = West, 0 otherwise)

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a) (6p) Mark is a 25-year-old male college graduate. John is a 30-year-old male college

graduate. Using regression 2, construct a 95% confidence interval for the expected

difference between their earnings.

b) (6p) Write down the STATA command for column (1).

c) (6p) Using the table, find a test for the null that all coefficients on Northeast, Midwest,

and South are zero at 5% significance level.

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d) Mary is a 30-year-old female college graduate from the South. Danielle is a 30-year-old

female college graduate from the West. Jennifer is a 30-year-old female college graduate

from the Midwest.

i. (5p) Construct a 90% confidence interval for the difference in expected earnings

between Mary and Danielle.

ii. (5p) Explain how you would construct a 95% confidence interval for the difference

in expected earnings between Mary and Jennifer.

iii. (5p) What happens if we add the dummy variable West in column (3)?

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Question 3: [37 points]

The following regressions are utilizing the data set WAGE2.dta which is used in the article by M.

Blackburn and D. Neumark (1992), “Unobserved Ability, Efficiency Wages, and Interindustry

Wage Differentials,” Quarterly Journal of Economics 107, 1421-1436.

DATA DESCRIPTION, FILE: WAGE2.dta

Variable Definition

lwage Logarithm of hourly wage.

educ Number of years spend in education.

exper Number of years worked in the industry.

expersq Experience squared.

female = 1 if observation belongs to a female.

= 0 otherwise.

nonwhite = 1 if the observation belongs to a non-white person.

= 0 if the observation belongs to a White person.

femxnonw Female times non-white.

femxeduc Female times educ

Regression 1: Number of obs = 526 F( 5, 520) = 65.58

Prob > F = 0.0000

R-squared = 0.3997

Root MSE = .41379

------------------------------------------------------------------------------

| Robust

lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

educ | .0839129 .0077567 10.82 0.000 .0686746 .0991512

exper | .0389529 .0046919 8.30 0.000 .0297355 .0481704

expersq | -.0006872 .000101 -6.80 0.000 -.0008856 -.0004887

female | -.3374241 .0362149 -9.32 0.000 -.4085696 -.2662787

nonwhite | -.0213127 .0627157 -0.34 0.734 -.1445201 .1018947

_cons | .3954016 .1102126 3.59 0.000 .1788849 .6119182

------------------------------------------------------------------------------


Prob > F = 0.0000

R-squared = 0.4024

Root MSE = .41329

------------------------------------------------------------------------------

| Robust


-------------+----------------------------------------------------------------

educ | .0845539 .007733 10.93 0.000 .0693621 .0997458

exper | .0397467 .0046833 8.49 0.000 .0305462 .0489472

expersq | -.0007046 .000101 -6.97 0.000 -.0009031 -.0005061

female | -.3182875 .0380722 -8.36 0.000 -.3930822 -.2434929

nonwhite | .063234 .0886931 0.71 0.476 -.1110076 .2374756

femxnonw | -.1811952 .1226804 -1.48 0.140 -.4222063 .059816

_cons | .3728613 .110089 3.39 0.001 .1565864 .5891361

------------------------------------------------------------------------------

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a) (6p) Interpret the coefficient of exper in Regression 1. How many years of experience

optimizes wage?

b) (6p) Interpret the coefficient of nonwhite in Regression 1.

c) (6p) Compare the model specification in Regressions 1 and 2.

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d) (7p) Write the the null hypothesis to test if there is a significant wage difference between

white females and nonwhite females. (No need to carry the test just write the null

hypothesis)

e) (6p) Consider regression 3


Prob > F = 0.0000

R-squared = 0.3997

Root MSE = .41419

------------------------------------------------------------------------------

| Robust


-------------+----------------------------------------------------------------

educ | .0840344 .0091177 9.22 0.000 .0661223 .1019465

exper | .0389502 .0046922 8.30 0.000 .0297321 .0481683

expersq | -.0006871 .0001011 -6.80 0.000 -.0008856 -.0004886

female | -.3335919 .1888261 -1.77 0.078 -.7045494 .0373656

nonwhite | -.0212238 .0629173 -0.34 0.736 -.1448278 .1023801

femxeduc | -.0003064 .0151172 -0.02 0.984 -.0300047 .0293919

_cons | .39384 .1270193 3.10 0.002 .1443048 .6433752

------------------------------------------------------------------------------

Interpret the coefficient of female, does the wage gap between males and females narrow

or widen as both become more educated? Explain your answer.

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f) (6p) Consider regression 4:

Regression 4: Number of obs = 526

F( 5, 520) = 48.50

Prob > F = 0.0000

R-squared = 0.3527

Root MSE = .42969

------------------------------------------------------------------------------

| Robust


-------------+----------------------------------------------------------------

educ | .0877603 .012387 7.08 0.000 .0634256 .112095

exper | .00745 .0051422 1.45 0.148 -.0026521 .0175521

female | -.3450433 .0383246 -9.00 0.000 -.4203333 -.2697532

nonwhite | -.0080678 .0642541 -0.13 0.900 -.1342973 .1181617

educxexper | .001660 .0004391 0.38 0.706 -.0006967 .0010286

_cons | .5264981 .1677327 3.14 0.002 .196981 .8560151

------------------------------------------------------------------------------

What is the difference in the predicted effect of a 2-years master’s degree on someone with

no job experience and someone with 5 years of job experience. Explain your answer. (i.e.

If you are considering a Master’s degree after college, will your wage be significantly

higher if you work for 5 years first and then have the degree? As opposed to having your

degree right after college)

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Standard Normal Distribution Table (from Ulberg, 1987)

Midterm Fall2011

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