Estimating the Impact of the Death Penalty on Murder

This paper reviews the econometric issues in efforts to estimate the impact of the death penalty on murder, focusing on six recent studies published since 2003. We highlight the large number of choices that must be made when specifying the various panel data models that have been used to address this question. There is little clarity about the knowledge potential murderers have concerning the risk of execution: are they influenced by the passage of a death penalty statute, the number of executions in a state, the proportion of murders in a state that leads to an execution, and details about the limited types of murders that are potentially susceptible to a sentence of death? If an execution rate is a viable proxy, should it be calculated using the ratio of last year's executions to last year's murders, last year's executions to the murders a number of years earlier, or some other values? We illustrate how sensitive various estimates are to these choices. Importantly, the most up-to-date OLS panel data studies generate no evidence of a deterrent effect, while three 2SLS studies purport to find such evidence. The 2SLS studies, none of which shows results that are robust to clustering their standard errors, are unconvincing because they all use a problematic structure based on poorly measured and theoretically inappropriate pseudo-probabilities that are designed to capture the key deterrence elements of a state's death penalty regime, and because their instruments are of dubious validity. We also discuss the appropriateness of the implicit assumption of the 2SLS studies that OLS estimates of the impact of the death penalty would be biased against a finding of deterrence.