|
Practice for Exam 1 Econ
B2000, MA Econometrics Kevin R Foster, CCNY Fall
2011 |
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|
Not all of these questions are strictly relevant; some might require
a bit of knowledge that we haven't covered this year, but they're a generally
good guide.
1.
{this question was
given in advance for students to prepare with their group} Download (from
Blackboard) and prepare the dataset on the 2004 Survey of Consumer Finances
from the Federal Reserve. Estimate the
probability that each head of household (restrict to only heads of household!)
has at least one credit card. Write up a
report that explains your results (you might compare different specifications,
you might consider different sets of socioeconomic variables, different
interactions, different polynomials, different sets of fixed effects, etc.).
2.
Explain in greater
detail your topic for the final project.
Include details about the dataset which you will use and the regressions
that you will estimate. Cite at least
one previous study which has been done on that topic (published in a refereed
journal).
3.
This question
refers to your final project.
a.
What data set will
you use?
b.
What regression
(or regressions) will you run? Explain
carefully whether the dependent variable is continuous or a dummy, and what
this means for the regression specification.
What independent variables will you include?
c.
What other
variables are important, but are not measured and available in your data
set? How do these affect your analysis?
4.
You want to
examine the impact of higher crude oil prices on American driving habits during
the past oil price spike. A regression
of US gasoline purchases on the price of crude oil as well as oil futures gives
the coefficients below. Critique the
regression and explain whether the necessary basic assumptions hold. Interpret each coefficient; explain its
meaning and significance.
Coefficients(a)
|
Model |
|
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
|
| B |
Std. Error |
Beta |
||||
|
1 |
(Constant) |
.252 |
.167 |
|
1.507 |
.134 |
| return on
crude futures, 1 month ahead |
.961 |
.099 |
.961 |
9.706 |
.000 |
|
| return on
crude futures, 2 months ahead |
-.172 |
.369 |
-.159 |
-.466 |
.642 |
|
| return on
crude futures, 3 months ahead |
.578 |
.668 |
.509 |
.864 |
.389 |
|
| return on
crude futures, 4 months ahead |
-.397 |
.403 |
-.333 |
-.986 |
.326 |
|
| US gasoline
consumption |
-.178 |
.117 |
-.036 |
-1.515 |
.132 |
|
| Spot Price
Crude Oil Cushing, OK WTI FOB (Dollars per Barrel) |
4.23E-005 |
.000 |
.042 |
1.771 |
.079 |
|
a Dependent Variable:
return on crude spot price
5.
You are in charge
of polling for a political campaign. You
have commissioned a poll of 300 likely voters.
Since voters are divided into three distinct geographical groups, the
poll is subdivided into three groups with 100 people each. The poll results are as follows:
|
|
|
total |
|
A |
B |
C |
|
|
number in favor of candidate |
170 |
|
58 |
57 |
55 |
|
|
number total |
300 |
|
100 |
100 |
100 |
|
|
std. dev. of poll |
0.4956 |
|
0.4936 |
0.4951 |
0.4975 |
Note
that the standard deviation of the sample (not the standard error of the
average) is given.
a.
Calculate a
t-statistic, p-value, and a confidence interval for the main poll (with all of
the people) and for each of the sub-groups.
b.
In simple language
(less than 150 words), explain what the poll means and how much confidence the
campaign can put in the numbers.
c.
Again in simple
language (less than 150 words), answer the opposing candidate's complaint,
"The biased media confidently says that I'll lose even though they admit
that they can't be sure about any of the subgroups! That's neither fair nor accurate!"
6.
Fill in the blanks
in the following table showing SPSS regression output. The model has the dependent variable as time
spent working at main job.
Coefficients(a)
|
Model |
|
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
|
| B |
Std. Error |
Beta |
||||
|
1 |
(Constant) |
198.987 |
7.556 |
|
26.336 |
.000 |
| female |
-65.559 |
4.031 |
-.138 |
___?___ |
___?___ |
|
| African-American |
-9.190 |
6.190 |
-.013 |
___?___ |
___?___ |
|
| Hispanic |
17.283 |
6.387 |
.024 |
___?___ |
___?___ |
|
| Asian |
1.157 |
12.137 |
.001 |
___?___ |
___?___ |
|
| Native
American/Alaskan Native |
-28.354 |
14.018 |
-.017 |
-2.023 |
.043 |
|
| Education:
High School Diploma |
___?___ |
6.296 |
.140 |
11.706 |
.000 |
|
| Education:
Some College |
___?___ |
6.308 |
.174 |
14.651 |
.000 |
|
| Education:
4-year College Degree |
110.064 |
___?___ |
.183 |
16.015 |
.000 |
|
| Education:
Advanced degree |
126.543 |
___?___ |
.166 |
15.714 |
.000 |
|
| Age |
-1.907 |
___?___ |
-.142 |
-16.428 |
.000 |
|
a Dependent Variable: Time Working at main job
7.
Suppose I were to
start a hedge fund, called KevinNeedsMoney Limited
Ventures, and I want to present evidence about how my fund did in the
past. I have data on my fund's returns, Rett, at each time period t, and the returns on
the market, Mktt. The graph below shows the relationship of
these two variables:
a.
I run a univariate OLS regression, 
. Approximately what value would be estimated for the
intercept term, b0? For the slope term, b1?
b.
How would you
describe this fund's performance, in non-technical language – for instance if
you were advising a retail investor without much finance background?
8.
Using the American
Time Use Study (ATUS) we measure the amount of time that each person reported
that they slept. We run a regression to
attempt to determine the important factors, particularly to understand whether
richer people sleep more (is sleep a normal or inferior good) and how sleep is
affected by labor force participation.
The SPSS output is below.
|
Coefficients(a) |
|
|
|
|
|
||
|
Model |
Unstandardized Coefficients |
Standardized Coefficients |
|
|
|||
|
|
|
B |
Std. Error |
Beta |
t |
Sig. |
|
|
1 |
(Constant) |
-4.0717 |
4.6121 |
|
-0.883 |
0.377 |
|
|
|
female |
23.6886 |
1.1551 |
0.18233 |
20.508 |
0.000 |
|
|
|
African-American |
-8.5701 |
1.7136 |
-0.04369 |
-5.001 |
0.000 |
|
|
|
Hispanic |
10.1015 |
1.7763 |
0.05132 |
5.687 |
0.000 |
|
|
|
Asian |
-1.9768 |
3.3509 |
-0.00510 |
-0.590 |
0.555 |
|
|
|
Native
American/Alaskan Native |
-3.5777 |
3.8695 |
-0.00792 |
-0.925 |
0.355 |
|
|
|
Education:
High School Diploma |
2.5587 |
1.8529 |
0.01768 |
1.381 |
0.167 |
|
|
|
Education:
Some College |
-0.3234 |
1.8760 |
-0.00222 |
-0.172 |
0.863 |
|
|
|
Education:
4-year College Degree |
-1.3564 |
2.0997 |
-0.00821 |
-0.646 |
0.518 |
|
|
|
Education:
Advanced degree |
-3.3303 |
2.4595 |
-0.01590 |
-1.354 |
0.176 |
|
|
|
Weekly
Earnings |
0.000003 |
0.000012 |
-0.00277 |
-0.246 |
0.806 |
|
|
|
Number
of children under 18 |
2.0776 |
0.5317 |
0.03803 |
3.907 |
0.000 |
|
|
|
person
is in the labor force |
-11.6706 |
1.7120 |
-0.08401 |
-6.817 |
0.000 |
|
|
|
has
multiple jobs |
0.4750 |
2.2325 |
0.00185 |
0.213 |
0.832 |
|
|
|
works
part time |
4.2267 |
1.8135 |
0.02244 |
2.331 |
0.020 |
|
|
|
in
school |
-5.4641 |
2.2993 |
-0.02509 |
-2.376 |
0.017 |
|
|
|
Age |
1.1549 |
0.1974 |
0.31468 |
5.850 |
0.000 |
|
|
|
Age-squared |
-0.0123 |
0.0020 |
-0.33073 |
-6.181 |
0.000 |
|
a.
Which variables
are statistically significant at the 5% level?
At the 1% level?
b.
Are there other
variables that you think are important and should be included in the
regression? What are they, and why?
9.
Use the SPSS
dataset, atus_tv from Blackboard, which is a subset
of the American Time Use survey. This
time we want to find out which factors are important in explaining whether
people spend time watching TV. There are
a wide number of possible factors that influence this choice.
a.
What fraction of
the sample spend any time watching TV?
Can you find sub-groups that are significantly different?
b.
Estimate a
regression model that incorporates the important factors that influence TV
viewing. Incorporate at least one
non-linear or interaction term. Show the
SPSS output. Explain which variables are
significant (if any). Give a short
explanation of the important results.
10.
Estimate the
following regression:: S&P100 returns
= b0 + b1(lag S&P100 returns) + b2(lag interest rates) + ε
using
the dataset, financials.sav. Explain
which coefficients (if any) are significant and interpret them.
11.
A study by Mehran
and Tracy examined the relationship between stock option grants and measures of
the company's performance. They
estimated the following specification:
Options = b0+b1(Return on Assets)+b2(Employment)+b3(Assets)+b4(Loss)+u
where
the variable (Loss) is a dummy
variable for whether the firm had negative profits. They estimated the following coefficients:
|
|
Coefficient |
Standard
Error |
|
Return on
Assets |
-34.4 |
4.7 |
|
Employment |
3.3 |
15.5 |
|
Assets |
343.1 |
221.8 |
|
Loss Dummy |
24.2 |
5.0 |
Which
estimate has the highest t-statistic (in absolute value)? Which has the lowest p-value? Show your calculations. How would you explain the estimate on the
"Loss" dummy variable?
12.
Calculate the
probability in the following areas under the Normal pdf
with mean and standard deviation as given.
You might usefully draw pictures as well as making the
calculations. For the calculations you can
use either a computer or a table.
a.
What is the
probability, if the true distribution has mean -15 and standard deviation of
9.7, of seeing a deviation as large (in absolute value) as -1?
b.
What is the
probability, if the true distribution has mean 0.35 and standard deviation of
0.16, of seeing a deviation as large (in absolute value) as 0.51?
c.
What is the
probability, if the true distribution has mean -0.1 and standard deviation of
0.04, of seeing a deviation as large (in absolute value) as -0.16?
13.
Using data from
the NHIS, we find the fraction of children who are female, who are Hispanic,
and who are African-American, for two separate groups: those with and those
without health insurance. Compute tests
of whether the differences in the means are significant; explain what the tests
tell us. (Note that the numbers in
parentheses are the standard deviations.)
|
|
with health
insurance |
without
health insurance |
|
female |
0.4905 (0.49994)
N=7865 |
0.4811 (0.49990)
N=950 |
|
Hispanic |
0.2587 (0.43797)
N=7865 |
0.5411 (0.49857)
N=950 |
|
African
American |
0.1785 (0.38297)
N=7865 |
0.1516 (0.35880)
N=950 |
14.
A paper by Farber
examined the choices of how many hours a taxidriver
would work, depending on a number of variables.
His output is:
"Driver
Effects" are fixed effects for the 21 different drivers.
a.
What is the
estimated elasticity of hours with respect to the wage?
b.
Is there a
significant change in hours on rainy days?
On snowy days?
1.
For the ATUS dataset, use "Analyze \ Descriptive Statistics \
Crosstabs" to create a joint probability table showing the fractions of males/females
about the amount of time spent on the computer vs
watching TV (if either or both are above average). Find and interpret the joint probabilities
and marginal probabilities. Do this for
age groups as well.
2.
Calculate the probability in the following areas under the Standard
Normal pdf with mean of zero and standard deviation
of one. You might usefully draw pictures
as well as making the calculations. For
the calculations you can use either a computer or a table.
a.
What is the probability, if the true distribution is a Standard
Normal, of seeing a deviation from zero as large (in absolute value) as 1.9?
b.
What is the probability, if the true distribution is a Standard
Normal, of seeing a deviation from zero as large (in absolute value) as -1.5?
c.
What is the probability, if the true distribution is a Standard
Normal, of seeing a deviation as large (in abs0lute value) as 1.2?
3.
Calculate the probability in the following areas under the Normal pdf with mean and standard deviation as given. You might usefully draw pictures as well as
making the calculations. For the
calculations you can use either a computer or a table.
a.
What is the probability, if the true distribution has mean -1 and
standard deviation of 1.5, of seeing a deviation as large (in absolute value)
as 2?
b.
What is the probability, if the true distribution has mean 50 and
standard deviation of 30, of seeing a deviation as large (in absolute value) as
95?
c.
What is the probability, if the true distribution has mean 0.5 and
standard deviation of 0.3, of seeing a deviation as large (in absolute value)
as zero?
4.
A paper by Chiappori, Levitt, and Groseclose (2002) looked at the strategies of penalty
kickers and goalies in soccer. Because
of the speed of the play, the kicker and goalie must make their decisions
simultaneously (a Nash equilibrium in mixed strategies). For example, if the goalie moves to the left
when the kick also goes to the left, the kick scores 63.2% of the time; if the
goalie goes left while the kick goes right, then the kick scores 89.5% of the
time. In the sample there were 117
occurrences when both players went to the left and 95 when the goalie went left
while the kick went right. What is the
p-value for a test that the probability of scoring is different? What advice, if any, would you give to
kickers, based on these results? Why or
why not?
5.
A paper by Claudia Goldin and Cecelia Rouse (1997) discusses the fraction of
men and women who are hired by major orchestras after auditions. Some orchestras had applicants perform from
behind a screen (so that the gender of the applicant was unknown) while other
orchestras did not use a screen and so were able to see the gender of the
applicant. Their data show that, of 445
women who auditioned from behind a screen, a fraction 0.027 were
"hired". Of the 599 women who
auditioned without a screen, 0.017 were hired.
Assume that these are Bernoulli random variables. Is there a statistically significant
difference between the two samples? What
is the p-value? Explain the possible
significance of this study.
6.
Another paper, by Kristin Butcher and Anne Piehl
(1998), compared the rates of institutionalization (in jail, prison, or mental
hospitals) among immigrants and natives.
In 1990, 7.54% of the institutionalized population (or 20,933 in the
sample) were immigrants. The standard
error of the fraction of institutionalized immigrants is 0.18. What is a 95% confidence interval for the
fraction of the entire population who are immigrants? If you know that 10.63% of the general
population at the time are immigrants, what conclusions can be made? Explain.
7.
Calculate the
probability in the following areas under the Standard Normal pdf with mean of zero and standard deviation of one. You might usefully draw pictures as well as
making the calculations. For the
calculations you can use either a computer or a table.
a.
What is the
probability, if the true distribution is a Standard Normal, if seeing a value
as large as 1.75?
b.
What is the
probability, if the true distribution is a Standard Normal, if seeing a value
as large as 2?
c.
If you observe a
value of 1.3, what is the probability of observing such an extreme value, if
the true distribution were Standard Normal ?
d.
If you observe a
value of 2.1, what is the probability of observing such an extreme value, if
the true distribution were Standard Normal ?
e.
What are the
bounds within which 80% of the probability mass of the Standard Normal lies?
f.
What are the
bounds within which 90% of the probability mass of the Standard Normal lies?
g.
What are the
bounds within which 95% of the probability mass of the Standard Normal lies?
8.
Consider a
standard normal pdf with mean of zero and standard
deviation of one.
a.
Find the area
under the standard normal pdf between -1.75 and 0.
b.
Find the area
under the standard normal pdf between 0 and 1.75.
c.
What is the
probability of finding a value as large (in absolute value) as 1.75 or larger,
if it truly has a standard normal distribution?
d.
What values form a
symmetric 90% confidence interval for the standard normal (where symmetric
means that the two tails have equal probability)? A 95% confidence interval?
9.
Now consider a
normal pdf with mean of 3 and standard deviation of
4.
a.
Find the area
under the normal pdf between 3 and 7.
b.
Find the area under
the normal pdf between 7 and 11.
c.
What is the
probability of finding a value as far away from the mean as 7 if it truly has a
normal distribution?
10.
If a random
variable is distributed normally with mean 2 and standard deviation of 3, what
is the probability of finding a value as far from the mean as 6.5?
11.
If a random
variable is distributed normally with mean -2 and standard deviation of 4, what
is the probability of finding a value as far from the mean as 0?
12.
If a random
variable is distributed normally with mean 2 and standard deviation of 3, what
values form a symmetric 90% confidence interval?
13.
If a random
variable is distributed normally with mean 2 and standard deviation of 2, what
is a symmetric 95% confidence interval?
What is a symmetric 99% confidence interval?
14.
A random variable is
distributed as a standard normal. (You
are encouraged to sketch the PDF in each case.)
a.
What is the probability that we
could observe a value as far or farther than 1.7?
b.
What is the probability that we
could observe a value nearer than 0.7?
c.
What is the probability that we
could observe a value as far or farther than 1.6?
d.
What is the probability that we
could observe a value nearer than 1.2?
e.
What value would leave 15% of
the probability in the left tail?
f.
What value would leave 10% of
the probability in the left tail?
15.
A random variable is
distributed with mean of 8 and standard deviation of 4. (You are encouraged to sketch the PDF in each
case.)
a.
What is the probability that we
could observe a value lower than 6?
b.
What is the probability that we
could observe a value higher than 12?
c.
What is the probability that
we'd observe a value between 6.5 and 7.5?
d.
What is the probability that
we'd observe a value between 5.5 and 6.5?
e.
What is the probability that
the standardized value lies between 0.5 and -0.5?
16.
You know that a random variable
has a normal distribution with standard deviation of 16. After 10 draws, the average is -12.
a.
What is the standard error of
the average estimate?
b.
If the true mean were -11, what
is the probability that we could observe a value between -10.5 and -11.5?
17.
You know that a random variable
has a normal distribution with standard deviation of 25. After 10 draws, the average is -10.
a.
What is the standard error of
the average estimate?
b.
If the true mean were -10, what
is the probability that we could observe a value between -10.5 and -9.5?
18.
You are consulting for a
polling organization. They want to know
how many people they need to sample, when predicting the results of the
gubernatorial election.
a.
If there were 100 people
polled, and the candidates each had 50% of the vote, what is the standard error
of the poll?
b.
If there were 200 people
polled?
c.
If there were 400 people
polled?
d.
If one candidate were ahead
with 60% of the vote, what is the standard error of the poll?
e.
They want the poll to be 95%
accurate within plus or minus 3 percentage points. How many people do they need to sample?
19.
Using the ATUS dataset that
we've been using in class, form a comparison of the mean amount of TV time
watched by two groups of people (you can define your own groups, based on any
of race, ethnicity, gender, age, education, income, or other of your
choice).
a.
What are the means for each
group? What is the average
difference?
b.
What is the standard deviation
of each mean? What is the standard error
of each mean?
c.
What is a 95% confidence
interval for each mean?
d.
Is the difference statistically
significant?
Exam 1
20.
(15 points) Calculate
the probability in the following areas under the Standard Normal pdf with mean of zero and standard deviation of one. You might usefully draw pictures as well as
making the calculations. For the
calculations you can use either a computer or a table.
d.
What is the
probability, if the true distribution is a Standard Normal, of seeing a
deviation from zero as large (in absolute value) as 1.9?
e.
What is the
probability, if the true distribution is a Standard Normal, of seeing a
deviation from zero as large (in absolute value) as -1.5?
f.
What is the
probability, if the true distribution is a Standard Normal, of seeing a
deviation as large (in abs0lute value) as 1.2?
21.
(15 points)
Calculate the probability in the following areas under the Normal pdf with mean and standard deviation as given. You might usefully draw pictures as well as
making the calculations. For the
calculations you can use either a computer or a table.
d.
What is the
probability, if the true distribution has mean -1 and standard deviation of
1.5, of seeing a deviation as large (in absolute value) as 2?
e.
What is the
probability, if the true distribution has mean 50 and standard deviation of 30,
of seeing a deviation as large (in absolute value) as 95?
f.
What is the
probability, if the true distribution has mean 0.5 and standard deviation of
0.3, of seeing a deviation as large (in absolute value) as zero?
22.
(20 points) Below
is some SPSS output from a regression from the ATUS. The data encompass only the group of people
who report that they spent non-zero time in education-related activities such
as going to class or doing homework for class.
The regression examines the degree to which education-time crowds out
TV-watching time. The dependent is time
spent watching TV. The independents are
time spent on all Education-related activities as well as the usual demographic
variables. Fill in the blanks.
Coefficients(a)
|
Model |
|
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
|
| B |
Std. Error |
Beta |
||||
|
1 |
(Constant) |
160.531 |
14.658 |
|
10.952 |
.000 |
| time spent on
Education-related activities |
-.137 |
.023 |
-.224 |
__?__ |
__?__ |
|
| female |
-26.604 |
7.852 |
-.112 |
__?__ |
__?__ |
|
| African-American |
-4.498 |
__?__ |
-.014 |
-.417 |
.677 |
|
| Hispanic |
__?__ |
12.181 |
-.023 |
-.681 |
.496 |
|
| Asian |
-7.881 |
19.291 |
-.013 |
__?__ |
__?__ |
|
| Native
American/Alaskan Native |
-4.335 |
28.633 |
-.005 |
-.151 |
__?__ |
|
| Education:
High School Diploma |
1.461 |
13.415 |
.004 |
.109 |
__?__ |
|
| Education:
Some College |
3.186 |
__?__ |
.012 |
.311 |
.756 |
|
| Education:
4-year College Degree |
-47.769 |
13.471 |
-.144 |
-3.546 |
__?__ |
|
| Education:
Advanced degree |
__?__ |
18.212 |
-.131 |
-3.379 |
.001 |
|
| Age |
__?__ |
.276 |
.121 |
2.839 |
.005 |
|
| Weekly
earnings [2 implied decimals] |
.000 |
.000 |
-.041 |
-.990 |
.322 |
|
| In the Labor
Force |
-25.210 |
10.794 |
-.107 |
__?__ |
.020 |
|
| Has multiple
jobs |
.918 |
15.299 |
.002 |
__?__ |
.952 |
|
| Works part
time |
3.816 |
10.427 |
.015 |
.366 |
.714 |
|
a Dependent Variable: watching TV (not
religious)
23.
Using the same
SPSS output from the regression above, explain clearly which variables are
statistically significant. Provide an
interpretation for each of the observed signs.
What about the magnitude of the coefficients? What additional variables (that are in the
dataset) should be included? What
results are surprising to you? (Note your answer should be a well-written few
paragraphs, not just terse answers to the above questions.)
24.
Use the CPS
dataset (available from Blackboard) to do a regression. Explain why your dependent variable might be
caused by your independent variable(s).
What additional variables (that are in the dataset) might be included? Why did you exclude those? Next examine the regression
coefficients. Which ones are
significant? Do the signs match what
would be predicted by theory? Are the
magnitudes reasonable? (Note your answer
should be a well-written few paragraphs, not just terse answers to the above
questions. No SPSS output dumps either!)
25.
A colleague
proposes the following fitted line.
Explain how or if his model could be an OLS regression. There are 100 observations of pairs of 
and for simplicity
assume 
for all 
. For the first 99
observations, the fitted value, 
, is equal to the actual value, so 
. But for the 100th
observation the fitted value misses the true value by 2, so 
. If the fitted values
do not come from an OLS regression, how should the fitted model be changed?