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Department of Economics
Econ 3120
Cornell University
Applied Econometrics
Spring 2020
Prelim 1 — Spring 2020
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. Gavin’s Diaper Company
(24 points)
Gavin runs a cloth diaper company. On any given day he will sell no diapers
with probability 0.25, 1000 diapers with probability 0.5, and 2000 diapers with
probability 0.25. Assume demand for diapers is independent across days.
(a) (4 points) How many diapers does Gavin expect to sell in a day?
(b) (4 points) What is the variance of the number of diapers Gavin will sell in
a day?
5
E
X
weighted
avg
of
diapers
sold
in
day
01.25
10001
5
20001.257
1000
expected
per
day
diapers
sold
Var
IX
v25
0
100072
05
1000
10
07202512000
1000
500,000
(c) (4 points) How many diapers do we expect Gavin will sell in 100 days?
(d) (4 points) What is the variance of the number of diapers Gavin will sell in
100 days?
6
100
E
Cx
i
COO
ooo
100
Var
Xi
50,0001000
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(e) (4 points) Using a normal approximation, what is the probability that
Gavin will sell more than 110,000 diapers in 100 days?
(f) (4 points) If it rains, the probability that Gavin will sell no diapers goes
up to 0.5. It rains 25% of the time. If Gavin sold no diapers, what is the
probability that it rained that day?
7
Y
diapers
he sells
iniou
days
YNN
100,000
50,000,000
Pr
47110000
Pr
4
1
1
2
o
Pr
271
41
L
Pr
74
41
1
9207
00793
F
sold
no
diapers
R
rained
Pr
NIR
S
Pr
R
025
Prints
Pr
RIN
Pr
NIR
PAR
Pron
9
5
Question 2. Life Insurance and Income
(24 points)
A life insurance company wishes to examine the relationship between the amount
of life insurance held by a family and that family’s income. From a random sam-
ple of 20 households, the company estimates a linear regression model where
the dependent variable is amount of life insurance held, and the independent
variable is income. Both are measured in thousands of dollars. The firm finds
the following results:
Source |
SS
df
MS
-------------+----------------------------------
Model |
246858.575
1
246858.575
Residual |
3710.37471
18
206.131929
-------------+----------------------------------
Total |
250568.95
19
13187.8395
-------------------------------------------------
ins |
Coef.
[95% Conf. Interval]
-------------+-----------------------------------
inc |
3.880186
3.644621
4.115751
_cons |
6.854991
-8.65711
22.36709
-------------------------------------------------
(a) (6 points) What is your estimate of the resulting change in the amount of
life insurance when income increases by $1,000?
(b) (6 points) Based on the confidence intervals given above, what is the stan-
dard error of this estimate?
8
SSR
Tss
An
income
increase
of
4000
983
880
in
insurance
held
small
sample
C
V
Must
be
the
tin
2,093
width
Lot
SE
SE
SE
1125
(c) (6 points) How much insurance do you predict a family that has $50,000
of income will hold?
(d) (6 points) What is the
R
2
of the regression?
9
bot
500
b
6085
3
88150
200
85
8
200
850
R2
L
Ets
1
33
368
985
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Question 3. Production
(20 points)
Consider a production function of the form log
Q
i
=
β
0
+
β
1
log
K
i
+
"
i
where
Q is quantity and K is the amount of capital used in production. You estimate
this model with 33 observations:
Source |
SS
df
MS
Number of obs
=
33
-------------+----------------------------------
F(1, 31)
=
66.93
Model |
3.09025184
1
3.09025184
Prob > F
=
0.0000
Residual |
1.43141164
31
.046174569
R-squared
=
0.6834
-------------+----------------------------------
Adj R-squared
=
0.6732
Total |
4.52166348
32
.141301984
Root MSE
=
.21488
------------------------------------------------------------------------------
logq |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+----------------------------------------------------------------
logk |
.9627495
.1176841
8.18
0.000
.7227312
1.202768
_cons |
.1569255
.3494736
0.45
0.657
-.5558306
.8696817
------------------------------------------------------------------------------
(a) (7 points) Interpret the coe
ffi
cient on log
K
.
10
A
1.1
9
of
Kapital
961
9
of
quantity
of
output
(b) (7 points) Test the hypothesis that you have constant returns to scale (i.e.,
doubling input yields double the expected output).
(c) (6 points) Explain why exponentiating the predicted log of quantity pro-
duced is a poor prediction of quantity produced.
11
Ho
coefficient
on
log
capital
I
N
3
3
small
j
E
test
with
N
2
af
Zz
2
sided
test
951
sig
level
C V
2.04
4477
51
3398
test
stat
lower
than
this
can't
reject
sample
size
hughenough
s
p
value
2
Pr
ZL
339
8
2
1
Pr
22.339
a
73338
a
lot
bigger
than
v05
can't
reject
Question 4. Workplace Knowledge Flows
(30 points)
Just last month (January, 2020), Sandvik and coauthors published the results of
an experiment designed to test di
↵
erent ways of improving the flow of knowledge
in a workplace (NBER Working Paper 26660).
Their experiment randomly
assigned salespeople in a firm to one of four groups: The first was a control
group where they did nothing special. In each of the three treatment groups,
they randomly organized salespeople into pairs. In the first treatment group,
pairs were encouraged to talk about sales techniques during short structured
meetings. In the second treatment group, pairs were given financial incentives
to increase their joint output during the experiment but not afterward. In the
third treatment group, pairs were given both treatments.
Output is measured as the log of sales revenue-per-call during the intervention
period, and it is summarized for each group here:
Sample mean
Sample std dev
N
Control
3.92
0.59
186
Treatment 1 (Structured-Meetings)
4.16
0.62
158
Treatment 2 (Pair-Incentives)
4.05
0.56
135
Treatment 3 (Combined)
4.18
0.64
174
Use a 5% significance level and two-sided tests for all tests below.
(a) (8 points) Compute the di
↵
erence in output between the control group and
treatment group 1. Is this an estimate of the average treatment e
↵
ect of
having a short meeting to talk about sales techniques? Why, and if not,
what is being estimated instead?
12
Difference
in
output
4.16
3.92
24
first
treatment
group
only
encouraged
to
do
the
treatment
Since
some
can
choose
to
opt
out
of
the
meetings
this
isnt
ATE
but
ITT
intent
to
treat
effect
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(b) (8 points) Compute the di
↵
erence in output between the control group and
treatment group 2. Is this an estimate of the average treatment e
↵
ect of
giving pairs a financial incentive to increase their joint output? Why, and
if not, what is being estimated instead?
(c) (7 points) Do you believe combining structured meetings with pair incen-
tives is more e
↵
ective than simply encouraging workers to hold structured
meetings? Use a hypothesis test to provide evidence for your answer.
13
diet
4005
3092
013
no
non
compliance
to
treatement
so
it
is
unbiased
estimator
of
ATE
One
sided
two independent
sample
test
of
equality
of
Mans
assume
variances
Hot
I
combined
output
to
structured
only
treatment
S
TEEsitcnz
itsft.es
2
289
Pr
22.289
1
Pr
747897
1
06141
385
7005
can't
reject
No
evidence
that
combined
treatment
better
than
just
structured
meetings
(d) (7 points) Suppose instead of running the experiment, the researchers had
surveyed workers and asked each if they had recently talked with any
coworkers about sales techniques.
Then they compared average sales of
workers who answered yes to average sales of workers that answered no.
Why would this be a poor estimate of the average treatment e
↵
ect of
talking with a coworker about sales techniques?
14
U
S
o
workers
who
have
convos
diff
from
solitary
workers
who
dont
which
might
effect
sales
selection
bias
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
951
O
so
so
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- 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?arrow_forwardombine. Be sure to s 7 1 1 10 5 7 1 1 0 5 2 5 (Typarrow_forwardCompute the quantities in Exercises 1-8 using the vectors 6 2 ·D·¤·B· A V = [3]₁ W = -1 X = 3 u= 2 3 -5arrow_forward
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