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

Exercise 23

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.

(i) Find the average value of murdrate across all counties and years. What is the standard deviation? For what percentage of the sample is murdrate equal to zero?

(ii) How many observations have execs equal to zero? What is the maximum value of execs? Why is the average of execs so small?

(iii) 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. What do we need to assume about a_i and the execution variables in order for pooled OLS to consistently estimate the parameters, in particular, ?₁ and ?₂?

(iv) Apply OLS to the equation from part (ii) and report the estimates of ?₁ and ?₂, along with the usual pooled OLS standard errors. Do you estimate that executions have a deterrent effect on murders? What do you think is happening?

(v) Even if the pooled OLS estimators are consistent, do you trust the standard errors obtained from part (iv)? Explain.

(vi) Now estimate the equation in part (iii) using first differencing to remove a_i. What are the new estimates of ?₁ and ?2? Are they very different from the estimates from part (iv)?

(vii) Using the estimates from part (vi), can you say there is evidence of a statistically significant deterrent effect of capital punishment on the murder rate? If possible, in addition to the usual OLS standard errors, use those that are robust to any kind of serial correlation or heteroskedasticity in the FD errors.