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2022年12月27日
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# 这是一篇来自美国的关于计量经济学Problem Set 6的经济代写

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 effffect of concealed weapons laws on three difffferent 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 fifirst (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 “)

3

4 # Loads the dataset from the package

5 data (” Guns “,package =”AER “)

6

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 defifined 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 effffect are left to you to fifill in correctly. As a series of hints: within is the method that does fifixed effffects while fd takes fifirst difffferences;

individual does just individual effffects, time does just time fifixed effffects, and twoway does both.

(a) Please run the series of regressions below. In each, report the coeffiffifficient on law, the standard error on law, the t statistic, and the F test of all variables except the fifixed effffects. It may be helpful to construct the table below:

(1) (2) (3) (4) (5)

Coeffiffifficient 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 coeffiffifficients we will use the summary command, but informing it that we wish to use correct standard errors. Here is some sample code (as usual, fifill in the dots):

11 # Recovering HETEROSCEDASTIC – ROBUST standard errors

12 m1 = plm ( y~x ,…)

13 summary ( m1 , vcov = vcovHC ( m1 , type = “HC1 “, method =” white1 “) )

14

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 ,…)

1. 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.
1. Now run the same regression as in (ii) but adding state fifixed effffects. This requires using the individual method.
1. Now run the same regression as in (iii) but adding time fifixed effffects. This requires using the twoways method.
1. 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 coeffiffifficient on law and comment on its economic signifificance (i.e., it is a “big” number, regardless of statistical signifificance).

iii. Perform a 5% signifificance test of the variable law

(c) Think of at least one omitted variable that is solved by the inclusion of state fifixed effffects.

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-specifific, 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 fifixed effffects. A similar set of three conditions to above will have to be met, properly modifified for time fifixed effffects. 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 fifixed effffects. 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 specififications (iv) and (v), how much does controlling for autocorrelation in U matter for standard errors?

(g)  How would you include state-specifific 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-specifific  trends, you will need some interaction terms.

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