Use the state-level data on murder rates and executions in MURDER.RAW for the following exercise.
(i) Consider the unobserved effects model

where 6, simply denotes different year intercepts and a is the unobserved state effect. If past executions of convicted murderers have a deterrent effect, what should be the sign of β1? What sign do you think β2 should have? Explain.
(ii) Using just the years 1990 and 1993, estimate the equation from part (i) by pooled OLS. Ignore the serial correlation problem in the composite errors. Do you find any evidence for a deterrent effect?
(iii) Now, using 1990 and 1993, estimate the equation by fixed effects. You may use first differencing since you are only using two years of data. Now, is there evidence of a deterrent effect? How strong?
(iv) Compute the heteroskedasticity-robust standard error for the estimation in part (iii). It will be easiest to use first differencing.
(v) Find the state that has the largest number for the execution variable in 1993. (The variable exec is total executions in 1991, 1992, and 1993.) How much bigger is this value than the next highest value?
(vi) Estimate the equation using first differencing, dropping Texas from the analysis. Compute the usual and heteroskedasticity-robust standard errors. Now, what do you find? What is going on?
(vii) Use all three years of data and estimate the model by fixed effects. Include Texas in the analysis. Discuss the size and statistical significance of the deterrent effect compared with only using 1990 and 1993.

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