Use the data in COUNTYMURDERS to answer this question. The data set covers murders and executions (capital punishment) for 2,197 counties in the United States. See also Computer Exercise C16 in Chapter 13. (i) Consider the model
murdrateit 5 ut 1 d0execsit 1 d1execsi, t21 1 d2execsi, t22 1 d3execsi, t23 1
b5 percblackit 1 b6 percmaleit 1 b7 perc1019it 1 b8 perc2029it 1 ai 1 uit, where ut represents a different intercept for each time period, ai is the county fixed effect, and uit 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 d0, d1, d2, and d3, along with the usual pooled OLS standard errors. Do you estimate that executions have a deterrent effect on murders? Provide an explanation that involves ai. (iii) Now estimate the equation in part (i) using fixed effects to remove ai. What are the new estimates of the dj? Are they very different from the estimates from part (ii)? (iv) Obtain the long-run propensity from estimates in part (iii). 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 arbitrary heteroskedasticity and serial correlation in the 5uit6. What happens to the statistical significance of the d ^j? What about the estimated LRP?