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econometrics_assignment_4.docx
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Problem Set 4
Submission: please submit one file with your responses and one log file from EViews showing your
work, In addition copy your EViews table on your responses document when using to answer the
questions.
Book link:
http://economics.ut.ac.ir/documents/3030266/14100645/Jeffrey_M._Wooldridge_Introductory_Econ
ometrics_A_Modern_Approach__2012.pdf
Data: The first problem uses a data set from the Wooldridge textbook: crime2.
Question 1: Crimes and Police Officers
1. Open the data set and look closely at the variable names and descriptions. What is the level of
observation of this data set? How many observations are in this data set? How many cities are
represented in this data set?
2. Create a subset of these data for the year 1987 only. How many observations are in this
subsample? Use the 1987 subsample only for the remainder of this assignment. Report the
mean and standard deviation for the following variables: crimes officers pop. Your responses
should include the measurement units for each variable.
3. Regress the number of crimes in a city on the number of police officers. Interpret the coefficient
on the number of police officers. Do you think this is a causal relationship? Explain.
Question 2: Partialling Out and OVB
1. One potential source for omitted variable bias (OVB) is population size. Are population size and
number of police officers correlated? Describe the relationship between population and crime.
Given this information, do you think the regression coefficient on officers that you estimated in
question 1 is positively biased or negatively biased?
2. Partial out the effect of population on officers. Create a new variable that represents the
number of police officers in each city, after removing the effect of population. Name this new
variable officers_resid. Report the mean and standard deviation of this new variable.
3. Run a regression of crime on your new variable, officers_resid. Interpret the coefficient estimate
for officers_resid.
4. Compare the coefficient estimate on officers from the first question with the current coefficient
estimate. Describe the omitted variable bias that resulted from the exclusion of population from
the regression in question 1.
5. Consider the partial regression coefficient estimated for the variable officers_resid. Do you
believe that this coefficient represents the true, causal relationship between police officers and
crime? Explain your answer.
6. What source(s) of OVB still remain in this regression? Propose one omitted variable that you
would like to include in this regression. You can choose any variable, regardless of whether it is
in this data set or not. What do you believe about the relationship between your proposed
variable and officers? What do you believe about the relationship between your proposed
variable and crimes? Given these beliefs, describe the OVB that results from not including this
variable in the regression of crime on police officers.
For more context on Question 2, part 6, see the following news article:
https://www.washingtonpost.com/national/chicago-to-hire-hundreds-more-officers-to-combatviolence/2016/09/21/8c4fc926-8071-11e6-9578-558cc125c7ba_story.html
Question 3: Joint Hypothesis Tests
1. Estimate the following unrestricted model:
= 0 + 1 + 2 + 3 + 4 + 5 +
2. Report and interpret the coefficients on the variables pop and area.
3. For each of the two coefficients on the variables pop and area, can you reject the null
hypothesis that the coefficient is equal to zero at the 10% level? What about the 5% and 1%
levels? Fill out the table below with reject or do not reject.
Variable
Null Hypothesis
pop
0 : 2 = 0
area
0 : 3 = 0
= 0.10
= 0.05
= 0.01
4. Consider the null hypothesis that both coefficients are jointly equal to zero. What type of
hypothesis test would you use to test this hypothesis? What are the null and alternative
hypotheses?
5. What restricted model would you estimate in order to perform your hypothesis test? Give the
equation that you would estimate, following the format in part one of this question.
6. Calculate and report the test statistic to test this hypothesis. Give the numerator and
denominator degrees of freedom.
7. Look-up and report the appropriate critical values for the 10%, 5%, and 1% levels of
significance? The tables can be found in table G.3a-G.3c in your textbook (pages 834-836). Can
you reject the null hypothesis at each significance level?
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