Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 22

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 ?_t represents a different intercept for each time period, a_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 ?₀, ?₁, ?₂, and ?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 new estimates of the ?_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 {u_it}. What happens to the statistical significance of the ? What about the estimated LRP?