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

where θ_t represents a different intercept for each time period, α_i is the county fixed effect, and u_it 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 δ₀, δ₁, δ₂, and δ₃, along with the usual pooled OLS standard errors. Do you estimate that executions have a deterrent effect on murders? Provide an explanation that involves αi.

(iii) Now estimate the equation in part (i) using fixed effects to remove α_i. What are the new estimates of the δ_j? 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 δ̂_j? What about the estimated LRP?

murdrate, = 0; + dpexecs, + djexecs;1-1 + dzexecs;,-2 + 8zexecs;-3 + %3D Bspercblack, + B6percmale; + Biperc 1019; + Bsperc2029 + a; + uj.