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Use the data in COUNTYMURDERS to answer this question. The data set covers murders and execu-tions (capital punishment) for $2,197$ counties in the United States. See also Computer Exercise $C 16$ in Chapter $13 .$(i) Consider the modelmurdrate $_{i t}=\theta_{t}+\delta_{0} \operatorname{execs}_{i t}+\delta_{1} \operatorname{execs}_{i, t-1}+\delta_{2} \operatorname{execs}_{i, t-2}+\delta_{3} e x e c s_{i, t-3}+$ $\beta_{5}$percblack$_{i t}+$ $+\beta_{77} \operatorname{perclo} 19_{i t}$ $+\beta_{8} p e r c 2029_{i t}$ $+a_{i}+u_{i t}$where $\theta_{t}$ represents a different intercept for each time period, $a_{i}$ is the county fixed effect, and $u_{i t}$ is the idiosyncratic error. Why does it make sense to include lags of the key variable, execs, in the equation?(ii) Apply OLS to the equation from part (i) and report the estimates of $\delta_{0}, \delta_{1}, \delta_{2},$ and $\delta_{3},$ along with the usual pooled OLS standard errors. Do you estimate that executions have a deterrent effect on murders? Provide an explanation that involves $a_{i} .$(iii) Now estimate the equation in part (i) using fixed effects to remove $a_{i} .$ What are the newestimates of the $\delta_{j} ?$ Are they very different from the estimates from part (ii)?(iv) Obtain the long-run propensity from estimates in part (ii). Using the usual FE standard errors,is the LRP statistically different from zero?(v) If possible, obtain the standard errors for the FE estimates that are robust to arbitraryheteroskedasticity and serial correlation in the $\left\{u_{i t}\right\} .$ What happens to the statistical significance of the $\hat{\delta}_{j} ?$ What about the estimated LRP?

(i) need to control for influence of past values (ii) no deterrent effect (iii) deterrent effect exists but not significant (iv) LR propensity is significant (v) see video

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Chapter 14

Advanced Panel Data Methods

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William J.

March 28, 2022

Could you provide the R codes for this exercise?

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part one mhm. It makes sense to include lacks of executions because it is possible that these leg values influence contemporary values of executions as well as the values of the dependent variable murder rate. In other words, murder rate can be affected by the number of executions up to three years ago. Part two, we apply l s to the equation from part one and looking at the values of the estimates on execution and its legs, Yeah, I do not find a deterrent effect because the estimates on these variables are positive. We expect a negative one. And this happened because it is possible that there are observed effects that correlate with both executions and moderating. Such observed effects can be county specific, which is captured in the A sub. I term we will control for a supply by estimating the equation in part one using fixed effects. And you may find that the estimates on the executions mhm variables are now having expected sign. They are negative, but all of them are insignificant. In Part four, we will calculate the long run propensity by using the tricks, Um, you an estimate. Instead, executions and lax You win regress the murder rate on executions, the difference between executions and its first leg, the difference between executions and its second lads, and the difference between executions and is third that yeah, the long run propensity wind B the coefficient of execution. I find the long run propensity to B minus 0.1476 with a standard era of point Oh seven 42 The long run capacity is the statistically different from zero. It is significant at the 5% level. For Part five, I will calculate the standard era robust to heterocyclic elasticity. And here are the results, so the beta doesn't change. The Betas are the same to what we get in part two, and I haven't report them in Part two, so you can refer to these results. The only thing you hear is the value of the standard errors. So using robust standard Iran's the significance level of these variables somehow improved. The first lack of executions is significant at the 5% level. The third lack of executions is significant at the 10% level executions itself, and it's thicker. Leg is are not significant, However, compared to part two, we find that these variables are estimated more precisely standard. A rounds are smaller and the values are greater for all executions. Variables for the long run propensity. Its value is still the same minus point on 476 And the standard Errol Clustered is point oh four five. So similar to the executions estimates, the centered error of long run capacity become smaller. Long run propensity is now significant at the 1% level.

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