Assignment #10
- PPol 603
- Due: Thursday, 15 November 2012
Type up your answers. Give proper credit to those you work with and/or the text(s).
Solve the following problems. Show all of your work, but keep your answers concise.
Highlight your (final) answer
to distinguish it from your other numbers and text. Include a copy of your input
(e.g. do file) or output (e.g. log file),
when it is an appropriate way to show your work.
However, do not include unnecessary output (i.e. no data dumps), and format any output
so that it is easily readable.
An appropriate time to include output is when you put your results
in a table--if your results are wrong, then graders have no idea how you came to your
conclusions (i.e. give partial credit) unless you provide some output. Explanation
includes statistical and substantive explanation (explain so that a statistical
layperson can understand it, and so that a
statistical analyst will see your erudition).
- {10 points}
a. Do Exercise 10.1 in Stock and Watson.
b. Do Exercise 10.7 in Stock and Watson.
- {40} In this problem we will use Stata to demonstrate the equivalence of different
approaches to panel data. Get the Stata data set (Guns) you will use for the next problem (E10.1).
Keep the observations for the years 1989 and 1999 only.
Use a non-robust (non-clustered) regression throughout, until directed otherwise. Present your
results in a table. Use the table provided in the next problem as a guide: You
do not need to report fixed effects, just whether you included them or not. Label
the columns to show what part of the problem you are reporting.
a. Run a simple regression of ln(vio) on shall for the year 1989
only; then for the year 1999 only (analogous to Stock and Watson Equations 10.2 and 10.3).
Remember to take the natural logarithm of vio.
b. Take the first differences of ln(vio) and shall, and run the first
differences regression with a constant (analogous to Equation 10.8). Compare the
coefficient on shall to part a.
c. Now run the first differences regression of part b. without a constant
(analogous to Equation 10.7). Compare the coefficient on shall to parts
a. and b.
d. Run a regression (using the regress command) including state dummy
variables to get the empirical results
of Equation 10.10 for this application. (Note that there is no constant in 10.10.)
What is the interpretation of a coefficient for a state? Test whether the state
dummy variables are (jointly) significant.
Compare the results to part c. What is the same, and what is
different, and why?
e. Run a regression (using the regress command) including state dummy
variables to get the empirical
results of Equation 10.11. (Note that there is a constant in 10.11.)
What is the interpretation of a coefficient for a state?
Test whether the state dummy variables are (jointly) significant.
Compare the results to parts c. and d. What is the same, and what is
different, and why?
f. Demean ln(vio) and shall to get the empirical results of
Equation 10.14. (Note that there is no constant.) Compare the results
to parts c., d., and e. What is the same, and what is different, and why?
Run the same regression including a constant, and compare to the demeaned regression
without a constant.
g. Run an absorbing regression (using the areg command). What is
the interpretation of the constant? Which of
the previous approaches is it equivalent to?
h. Run a "within" regression (using the xtreg command). What is the
interpretation of rho? What is
the interpretation of the constant? Which of
the previous approaches is it equivalent to? (Note that the appropriate R2
for a fixed effects regression is the within R2.)
i. Now add year fixed effects to the state fixed effects to see if your results
change. Run this three ways, using the regress command with
the dummy variables you generated; using the areg commmand; and using
the xtreg command. Compare the results of these three ways. What
happens to the coefficient of shall when you add year fixed effects?
j. Including both state and year fixed effects, use clustered (heteroskedasticity
and autocorrelation consistent) standard errors. Try to run this the three ways again,
comparing the results. What happens to the coefficient of shall? What
happens to the standard error?
- {25} Do Empirical Exercise E10.1 in Stock and Watson. Do not do part d.
Use all of the observations. Remember
to take the natural logarithm of the dependent variable. Use clustered
(heteroskedasticity- and autocorrelation-robust) standard
errors. You may use the following table
here
to report your results. Note that it does not require you to report all of the
coefficients (but it usually requires that you include them in the regressions).
Add the following parts:
- In all parts, calculate the adjusted R2.
- In parts b. and c., test whether the fixed effects are jointly
significant.
- In part c., remember to keep the fixed state effects when you add the fixed time
effects.
Remember to skip part d.
- {25} Case study: Do concealed weapons laws reduce crime?
Your boss, the Governor, is considering proposing a concealed weapons law to the
legislature.
There is a normative (constitutional) debate on such laws. However, as a policy
analyst, you have been asked to set aside that debate to consider the
empirical question: Do concealed weapons laws reduce crime? You may use any part of the analysis
you wish from the previous problem. In the context of a professional report,
you should answer several questions for the governor:
- Do concealed weapons laws reduce crime?
- Why do different analysts come to different conclusions about this question?
- Why are you using the approach you do (variables included, etc.)?
- Why is your conclusion the right one?
- Suppose one did pass a concealed weapon law in the state, what is your best guess
(and a reasonable range) as to what the effect would be?
- If you could be given more time and money, what other variables would you
include in your analysis?
- What are the limitations and weaknesses of your analysis?
Remember to include a statistical appendix (and a grader's appendix).
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