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Department of Economics
Econ 3120
Cornell University
Applied Econometrics
Spring 2022
Prelim 1 — Spring 2022
GENERAL INSTRUCTIONS:
•
Please write your name on the cover bubble sheet.
•
Please fill in your Cornell student id on the bubble sheet under Student ID.
•
Please answer the survey (Question 0) using the bubble sheet.
•
You can use any notes you have written (or printed) on a single sheet of paper.
•
You may use a calculator as long as you don’t use it to store additional notes
or connect to the Internet.
•
You may not use a cell phone, the internet, make phone calls, or send text
messages during the exam.
•
Show your work.
•
Please write as neatly as you can.
•
If you need to make assumptions, please clearly state them in your answer.
2
Question 0. Brief Survey on Studying
(2 points)
Your answers to these questions have absolutely no impact on your exam score,
and I will remove all your names before I analyze this data.
(1) How much of the material we’ve covered since the review module (i.e.,
experiments and bivariate regression) had you seen before?
(a) none
(b) some
(c) almost all or all
(2) We’ve had 8 classroom lectures so far. How many did you attend?
(a) none
(b) 1-3
(c) 4-5
(d) 6-7
(e) 8
(3) Not including attending lectures, how much time have you spent on this
class each week doing things like reading or working on problem sets?
(a) less than one hour
(b) 1-2 hours
(c) 3-4 hours
(d) 5-6 hours
(e) 7+ hours
(4) How much time did you spend studying for this prelim?
(a) less than one hour
(b) 1-4 hours
(c) 4-8 hours
(d) 9+ hours
(5) Did you mostly study for this prelim by yourself or with other students in
the class?
(a) mostly by yourself
(b) mostly with other students in the class
(c) about half by yourself and half with other students in the class
3
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(6) When did you do most of your studying for this prelim?
(a) the day before and day of the exam
(b) spread over multiple sessions over multiple days starting before the
night before the exam
To prepare for this prelim, did you
(7) Review the lecture slides and/or your notes?
(a) Yes
(b) No
(8) Read the book?
(a) Yes
(b) No
(9) Identify areas or topics you are struggling with and get help (e.g., in o
ffi
ce
hours or on the course discussion board)?
(a) Yes
(b) No
(10) Study the problem sets and solutions?
(a) Yes
(b) No
(11) Re-work problems from the problem sets?
(a) Yes
(b) No
(12) Work new sample problems?
(a) Yes
(b) No
(13) Explain or teach the material to someone else?
(a) Yes
(b) No
4
Question 1. Alcoholic Beverage Expenditures
(20 points)
Suppose you are interested in the relationship between age and consumption of
alcoholic beverages.
You decide to analyze all the single member households
in the 2020 Consumer Expenditure Survey, and run the following regression.
The dependent variable is the natural log of quarterly alcoholic beverage ex-
penditures and the independent variable is the age (in years) of the household
member. Age ranges from 16 to 87 in the sample.
. reg ln_alcbevpq age_ref
Source |
SS
df
MS
Number of obs
=
689
-------------+----------------------------------
F(1, 687)
=
38.11
Model |
49.9641117
1
49.9641117
Prob > F
=
0.0000
Residual |
900.674363
687
1.31102527
R-squared
=
-------------+----------------------------------
Adj R-squared
=
Total |
950.638475
688
1.38174197
Root MSE
=
1.145
------------------------------------------------------------------------------
ln_alcbevpq |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
age_ref |
-.0135391
.0021931
-6.17
0.000
_cons |
5.07693
.1097273
46.27
0.000
4.861489
5.292371
------------------------------------------------------------------------------
(a) (5 points) What do your results say is the e
↵
ect of one year increase in age
on alcoholic beverage expenditures?
5
en
yer
dependent
Y
yo
I
149
age
is
associated
w
a
1
410
decrease
in
consumption
all
(b) (5 points) Compute the 75% confidence interval for the age coe
ffi
cient.
(c) (5 points) Predict the log expenditures on alcoholic beverages by a single
member household who is 30 years old. Assuming the average age in the
sample is 40 years old, build a 95% interval around your prediction that
accounts for both inherent noise in the process (i.e., the variance of the
error term of your regression model) and uncertainty in your coe
ffi
cient
estimates.
(d) (5 points) Why might your prediction interval be too narrow?
In other
words, what else might be inducing error in your prediction?
6
B
I
1.15
0021931
ESE
bl
537
35
3
0
0
Bo
B
lx
2
forecast
error
9510
Pred
int
4.672
I
predicted
Inexpediture
I
1.96
forecast
error
GE
uncertainty
in
coefficients
specification
error
assume
relationship
btwn
en
expenditure
age
is
linear
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Question 2. Grapefruits
(20 points)
The following two acceptance rules are being considered for determining whether
to take a delivery of a large shipment of grapefruits:
Rule 1: A random sample of ten grapefruits is checked, and the shipment is
accepted only if the average weight in the sample is between 5 and 7 ounces.
Rule 2: A random sample of 100 grapefruits is checked, and the shipment is
accepted only if the average weight in the sample is between 5.5 and 6.5 ounces.
Suppose the shipment contains grapefruits whose weight is distributed normally
with a mean of 6 ounces and a standard deviation of 2 ounces.
That is, the
weight of each grapefruit in the shipment can be considered a random variable
⇠
N
(6
,
2
2
). Weights of grapefruits in both the shipment and the samples are
independent of each other.
What is the probability of rejecting the shipment under each rule?
7
O
O
5 6
Vare
Z
Vardi
o4
INN
61.04
rejected
w
Pr
EL
5
Prix
n
2
1
Prix
27
L
I
Prez
LEE
211
Pr
Z
21058
2
1
1058
11
42
5
6
Var
I
Hot'YvavGi
von
N
61.04
rejects
Pr
Ics
5
Prix
6.5
2
1
Pv
26.5
2
l
Pr
Z
Larga
211
Pr
222.5
24
9938
0124
G
range
however
we
reject
less
bk
sample
size
higher
Question 3. Bad Chicken
(20 points)
Bob’s Grill buys its chicken exclusively from Sally’s Cheap Meat Company and
usually doesn’t have a problem. In the previous 5 years, they have only had
20 incidents of food poisoning due to bad chicken. Unfortunately, over the last
12 weeks, Bob’s had two di
↵
erent weeks where one customer got sick and one
week where two customers got sick.
Bob wants you to tell him if the weekly rate he’s observed over the last 12 weeks
is significantly di
↵
erent from the weekly rate he calculated from the previous 5
years.
(a) (4 points) What is the null hypothesis? What is the alternative hypothesis?
(b) (4 points) What is the sample standard deviation of the weekly rate during
the last 12 weeks?
8
historic
weekly
rate
575251
0
1
Ho
9
0078
Ha
Mto
07g
NYT
software
pure
chance
new
accidents
stat
sig
s
I
Z
xi
x
S
9
0
33372
2
1
11
13372
12
033312
I
999
to
89
2.774
54.424
5
06511
(c) (4 points) Using a one sample t-test and treating the historic rate as a
constant, what is the value of the test statistic?
You may assume the
number of incidents in a given week is approximately normally distributed.
(d) (4 points) Under the null hypothesis, what is the distribution of this test
statistic?
(e) (4 points) At a significance level of 5%, can you reject the null hypothesis?
9
3
1
1
1.36
the
Test
stat
should
be
t
statistic
w
11
d.fr
CV
w
G
G
2
tail
test
s
t
2.201
Maker
in
magnitude
cant
reject
to
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Question 4. Three Observations
(18 points)
Following are the year-end closing values for the Nasdaq Composite and S&P
500 stock market indices for the last three years, as well as average closing for
the three years:
Year
Nasdaq
S&P 500
2019
8973
3231
2020
12888
3756
2021
15645
4766
Avg
12502
3918
(a) (4 points) What is the sample variance of the S&P 500 closing values in
the sample above?
(b) (4 points) What is the sample covariance between the Nasdaq index and
S&P 500?
10
All
Plugging
into
formulas
Q
S
I
x
x
Sx
I
3231
3918
2
3756
391812
14766
39181
54
6081658
Say
Z
Xi
F
ly
5
3231
3918
8977
12502
3756
3918
12888
12502
4766
3918
15641
2513,57705
(c) (4 points) Suppose we regressed the Nasdaq index on the S&P 500 using
the data above. (i.e., Nasdaq is the dependent variable.) What would the
estimated slope coe
ffi
cient be?
(d) (3 points) What would the estimated intercept be?
(e) (3 points) What would the
R
2
be?
11
b
Sgt
4.13
bo
y
bit
12502
4413
3919
avg
NAS
b
estimates
avg
SEP
R
ra
Est
JE
RE
Question 5. Perceived Returns to Education
(20 points)
In 2010, Rob Jensen published a paper in the Quarterly Journal of Economics
titled “The (Perceived) Returns to Education and the Demand for Schooling.”
From the abstract:
Economists emphasize the link between market returns to education
and investments in schooling. Though many studies estimate these
returns with earnings data, it is the perceived returns that a
↵
ect
schooling decisions, and these perceptions may be inaccurate. Using
survey data for eighth-grade boys in the Dominican Republic, we find
that the perceived returns to secondary school are extremely low,
despite high measured returns.
Jensen goes on to conduct an experiment where he randomizes a sample of
schools in the Dominican Republic to a treatment group where he informs stu-
dents of the actual returns to schooling and a control group where he does not.
Four years later, he follows up with both groups of students and finds that the
1,033 control group students went on to complete an average of 9.75 years of
schooling.
The 1,041 treatment group students completed an average of 9.93
years of schooling. The standard deviation in the control group was 2.25 years
and in the treatment group it was 2.36.
(a) (4 points) What does the observed 0.18 year di
↵
erence in outcomes between
the two groups represent? Be specific about what the treatment is.
12
o
o
ATE
if
treatment
student
attending
school
when
stroente
i
informed
of
actual
return
to
schooling
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(b) (4 points) Assuming the variance in the two populations was equal, test
whether the observed di
↵
erence in the years completed is statistically sig-
nificant at the 5% and 10% levels.
(c) (4 points) What would it mean if I told you the Average Treatment Ef-
fect (ATE) was not the same as the Intent to Treat e
↵
ect (ITT) in this
experiment?
13
8
Stalinist
ha
psi
to
I
77
can't
reject
580
can
at
101
students
assigned
treatment
group
didnt
actually
get
treatment
(d) (4 points) What regression model would you estimate to get a
b
1
that was
exactly equal to the observed di
↵
erence in outcomes (i.e., 0.18)? Be specific
about what your observations are and how you define your variables.
(e) (4 points) Suppose instead of randomizing students to treatment and con-
trol, that you put all the male students in the treatment group and all the
female students in the control group. Give two reasons why the observed
di
↵
erence in average outcomes is not the Average Treatment E
↵
ect (ATE).
14
Obs
students
dependent
variable
ly
if
yrs
school
complied
explanatory
variable
di
I
in
treatment
group
o
in
control
group
Yi
Bot
B
dit
Ei
Selection
bias
Male
female
different
IT
bk
male
students
may
inherently
get
more
edu
than
females
bk
of
systemic
issues
NORMAL DISTRIBUTION TABLE z
0
±f
f
–
.00 .01
.02 .03
.04
.05
.06
.07
.08 .09
.0 .5000 .5040
.5080 .5120
.5160
.5199
.5239
.5279
.5319 .5359
.1 .5398 .5438
.5478 .5517
.5557
.5596
.5636
.5675
.5714 .5753
.2 .5793 .5832
.5871 .5910
.5948
.5987
.6026
.6064
.6103 .6141
.3 .6179 .6217
.6255 .6293
.6331
.6368
.6406
.6443
.6480 .6517
.4 .6554 .6591
.6628 .6664
.6700
.6736
.6772
.6808
.6844 .6879
.5 .6915 .6950
.6985 .7019
.7054
.7088
.7123
.7157
.7190 .7224
.6 .7257 .7291
.7324 .7357
.7389
.7422
.7454
.7486
.7517 .7549
.7 .7580 .7611
.7642 .7673
.7704
.7734
.7764
.7794
.7823 .7852
.8 .7881 .7910
.7939 .7967
.7995
.8023
.8051
.8078
.8106 .8133
.9 .8159 .8186
.8212 .8238
.8264
.8289
.8315
.8340
.8365 .8389
1.0 .8413 .8438
.8461 .8485
.8508
.8531
.8554
.8577
.8599 .8621
1.1 .8643 .8665
.8686 .8708
.8729
.8749
.8770
.8790
.8810 .8830
1.2 .8849 .8869
.8888 .8907
.8925
.8944
.8962
.8980
.8997 .9015
1.3 .9032 .9049
.9066 .9082
.9099
.9115
.9131
.9147
.9162 .9177
1.4 .9192 .9207
.9222 .9236
.9251
.9265
.9279
.9292
.9306 .9319
1.5 .9332 .9345
.9357 .9370
.9382
.9394
.9406
.9418
.9429 .9441
1.6 .9452 .9463
.9474 .9484
.9495
.9505
.9515
.9525
.9535 .9545
1.7 .9554 .9564
.9573 .9582
.9591
.9599
.9608
.9616
.9625 .9633
1.8 .9641 .9649
.9656 .9664
.9671
.9678
.9686
.9693
.9699 .9706
1.9 .9713 .9719
.9726 .9732
.9738
.9744
.9750
.9756
.9761 .9767
2.0 .9772 .9778
.9783 .9788
.9793
.9798
.9803
.9808
.9812 .9817
2.1 .9821 .9826
.9830 .9834
.9838
.9842
.9846
.9850
.9854 .9857
2.2 .9861 .9864
.9868 .9871
.9875
.9878
.9881
.9884
.9887 .9890
2.3 .9893 .9896
.9898 .9901
.9904
.9906
.9909
.9911
.9913 .9916
2.4 .9918 .9920
.9922 .9925
.9927
.9929
.9931
.9932
.9934 .9936
2.5 .9938 .9940
.9941 .9943
.9945
.9946
.9948
.9949
.9951 .9952
2.6 .9953 .9955
.9956 .9957
.9959
.9960
.9961
.9962
.9963 .9964
2.7 .9965 .9966
.9967 .9968
.9969
.9970
.9971
.9972
.9973 .9974
2.8 .9974 .9975
.9976 .9977
.9977
.9978
.9979
.9979
.9980 .9981
2.9 .9981 .9982
.9982 .9983
.9984
.9984
.9985
.9985
.9986 .9986
3.0 .9987 .9987
.9987 .9988
.9988
.9989
.9989
.9989
.9990 .9990
3.1 .9990 .9991
.9991 .9991
.9992
.9992
.9992
.9992
.9993 .9993
3.2 .9993 .9993
.9994 .9994
.9994
.9994
.9994
.9995
.9995 .9995
3.3 .9995 .9995
.9995 .9996
.9996
.9996
.9996
.9996
.9996 .9997
3.4 .9997 .9997
.9997 .9997
.9997
.9997
.9997
.9997
.9997 .9998
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t-Distribution Table
t
The shaded area is equal to
α
for
t
=
t
α
.
df
t
.
100
t
.
050
t
.
025
t
.
010
t
.
005
1
3.078
6.314
12.706
31.821
63.657
2
1.886
2.920
4.303
6.965
9.925
3
1.638
2.353
3.182
4.541
5.841
4
1.533
2.132
2.776
3.747
4.604
5
1.476
2.015
2.571
3.365
4.032
6
1.440
1.943
2.447
3.143
3.707
7
1.415
1.895
2.365
2.998
3.499
8
1.397
1.860
2.306
2.896
3.355
9
1.383
1.833
2.262
2.821
3.250
10
1.372
1.812
2.228
2.764
3.169
11
1.363
1.796
2.201
2.718
3.106
12
1.356
1.782
2.179
2.681
3.055
13
1.350
1.771
2.160
2.650
3.012
14
1.345
1.761
2.145
2.624
2.977
15
1.341
1.753
2.131
2.602
2.947
16
1.337
1.746
2.120
2.583
2.921
17
1.333
1.740
2.110
2.567
2.898
18
1.330
1.734
2.101
2.552
2.878
19
1.328
1.729
2.093
2.539
2.861
20
1.325
1.725
2.086
2.528
2.845
21
1.323
1.721
2.080
2.518
2.831
22
1.321
1.717
2.074
2.508
2.819
23
1.319
1.714
2.069
2.500
2.807
24
1.318
1.711
2.064
2.492
2.797
25
1.316
1.708
2.060
2.485
2.787
26
1.315
1.706
2.056
2.479
2.779
27
1.314
1.703
2.052
2.473
2.771
28
1.313
1.701
2.048
2.467
2.763
29
1.311
1.699
2.045
2.462
2.756
30
1.310
1.697
2.042
2.457
2.750
32
1.309
1.694
2.037
2.449
2.738
34
1.307
1.691
2.032
2.441
2.728
36
1.306
1.688
2.028
2.434
2.719
38
1.304
1.686
2.024
2.429
2.712
∞
1.282
1.645
1.960
2.326
2.576
Related Questions
Data is given to represent the number of each of the types of clubs three different schools in your area offer.
Academic Clubs Service Clubs Sporting Clubs
3
10
Eastern High School 6
Central High School 8
West-Side High School 4
19
19
12
Which of the following matrices can be used to accurately represent the data?
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ombine. Be sure to s
7 1 1
10 5
7
1 1
0 5 2 5 (Typ
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Compute the quantities in Exercises 1-8 using the vectors
6
2
·D·¤·B· A
V =
[3]₁
W = -1 X =
3
u=
2
3
-5
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2.
3.
y.
5n
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What is the five-number summary for this data set?
4, 6, 10, 13, 18, 28, 34, 46, 50, 58
Assume the numbers in each answer choice are listed in this order min, Q1,
median, Q3, max.
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please help me with the follow-up question d, e, f, and g
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I.
de
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QUESTION 3
A survey of "How long does it take you to eat breakfast?" has these results:
4
10
7
8.
7
7
1
7
8
6.
8
10
1
3
Which of the following charts represent the given data:
Chart A
Chart B
3.
5
5
5
LO
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Only need c
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