Use the data in COUNTYMURDERS for this exercise. 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 θ_t represents a different intercept for each time period, α_i is the county fixed effect, and u_it is the idiosyncratic error. What do we need to assume about α_i and the execution variables in order for pooled OLS to consistently estimate the parameters, in particular, β₁ and β₂?

(iv) Apply OLS to the equation from part (ii) and report the estimates of β₁ and β₂, 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 α_i. What are the new estimates of β₁ and β₂? 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.

Transcribed Image Text:

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