1. Guns and Crime Some U.S. states have enacted laws that allow citizens to carry concealed
weapons. These laws are known as “shall-issue” laws because they instruct local authorities to
issue a concealed weapons permit to all applicants who are citizens, mentally competent, and have
not been convicted of a felony (some states have some additional restrictions). In “may issue”
states, such as New York, applicants must demonstrate a reason for carrying a concealed weapon
(dangerous line of work, history of threats, etc.).
Proponents argue that, if more people carry concealed weapons, crime will decline because criminals
are deterred. Opponents argue that crime will increase because of accidental or spontaneous use
of the weapon. In this exercise, you will analyze the effect of concealed weapons laws on three
different categories of crimes: violent crimes; robberies (such as the robbery of a convenience store);
and murder (many of which are spontaneous acts of passion).
In order to access the data we will use the AER package. In order to access the data we will need to
install the package first (this only needs to be done once). Once installed the data() and ? commands
can access and describe the dataset. The commands below summarize how to do this:
1 # Installs the package ( run once )
2 install . packages (" AER ")
4 # Loads the dataset from the package
5 data (" Guns ",package =" AER ")
7 # Provides a detailed description of the data
8 ? Guns
Before continuing as a reminder of how to run a panel regression, we use the plm command
with the appropriately defined index variables and model. The generic command will be:
9 # Running a panel regression in R
10 plm ( y ~ x1 + x2 + ... , index =c(" entityVariable "," timeVariable ") , method =
" method ", effect =" individual ")
The “...”, entity and time variables, method and effect are left to you to fill in correctly. As
a series of hints: within is the method that does fixed effects while fd takes first differences;
individual does just individual effects, time does just time fixed effects, and twoway does both.
(a) Please run the series of regressions below. In each, report the coefficient on law, the standard
error on law, the t statistic, and the F test of all variables except the fixed effects. It may be
helpful to construct the table below:
(1) (2) (3) (4) (5)
Coefficient on law
SE on law
t stat on law
Regression F
Controls No Yes Yes Yes Yes
State FE No No Yes Yes Yes
Year FE No No No Yes Yes
Clustered SEs No No No No Yes
In order to get the robust standard errors and the F-test on all the coefficients we will use the
summary command, but informing it that we wish to use correct standard errors. Here is some
sample code (as usual, fill in the dots):
11 # Recovering HETEROSCEDASTIC - ROBUST standard errors
12 m1 = plm ( y~x ,...)
13 summary ( m1 , vcov = vcovHC ( m1 , type = "HC1 ", method =" white1 ") )
15 # Recovering CLUSTER - ROBUST standard errors
16 m2 = plm ( y~x ,...)
17 summary ( m2 , vcov = vcovHC ( m2 , type = "HC1 ", cluster =" group ") )
1. A linear regression of log murder rate on whether a state has a shall-issue law. Notice that
the crime rates are reported in levels, not in logs. You will need to apply the appropriate
transformation. Hint: You can apply the logarithm directly in a regression. E.g.,
18 # Logs directly in R
19 lm( log( y ) ~ x1 ,...)
2. Now include the following variables as controls: the percent of the state that is male male,
the percent of the state that is African-American afam, the percent of the state that is
Caucasian cauc, the log of income income, the log of density density, and the log of
the prison population prisoners. Notice that once again, you will need to transform the
variables that are not in logarithms.
3. Now run the same regression as in (ii) but adding state fixed effects. This requires using the
individual method.
4. Now run the same regression as in (iii) but adding time fixed effects. This requires using
the twoways method.
5. Finally, run the same regression as in (iv), but report the cluster robust standard errors.
(b) For all of the regressions above:
i. Write out the underlying statistical model being estimated.
ii. Interpret the coefficient on law and comment on its economic significance (i.e., it is a “big”
number, regardless of statistical significance).
iii. Perform a 5% significance test of the variable law
(c) Think of at least one omitted variable that is solved by the inclusion of state fixed effects.
For your answer to be valid three conditions will have to be met: (1) the variable must be
correlated with the probability of passing “shall-carry laws”; (2) the variable must be correlated
with the murder rate; (3) the variable must be state-specific, but time-invariant. In addition to
explaining why it meets conditions (1)-(3), describe the direction of the bias that results from
ignoring it.
(d) Think of at least one omitted variable that is solved by the inclusion of time fixed effects. A
similar set of three conditions to above will have to be met, properly modified for time fixed
effects. Also, describe the direction of the bias that results from ignoring your variable.
(e) Think of a variable that is not included in this regression and is also not solved by including
state level or time fixed effects. In what direction will this variable bias the regression?
(f) Think of a variable inside of U that is autocorrelated (but not constant), important for determining
crime rates, and is plausibly uncorrelated with X. The presence of such variables
are why we cluster standard errors. Comparing specifications (iv) and (v), how much does
controlling for autocorrelation in U matter for standard errors?
(g) ?? How would you include state-specific trends in these regressions? Two hints: (1) Adding a
common trend line is easy—it means including time as a regressor; (2) To add state-specific
trends, you will need some interaction terms.