For potential murderers to possibly be responsive to deviations from the execution trend line, they have to be attentive to it. The studies are silent on two key questions: (1) Why are potential murderers attentive to the trend line in the number of executions? (2) Why do they respond to deviations from the trend line?
If time-series analyses find that homicide rates are not responsive to such deviations, it may be that potential murderers are responding to the trend line in executions but not to deviations from it. For example, a rising trend in the number of executions might be perceived as signaling a toughening of the sanction regime, which might deter potential murderers. Alternatively, if a time-series analysis finds that homicide rates are responsive to such deviations, the question is why? One possibility is that potential murderers interpret the deviations as new information about the intensity of the application of capital punishment—that is, they perceive a change in the part of the sanction regime relating to application of capital punishment. If so, a deviation from the execution trend line may cause potential murderers to alter their perceptions of the future course of the trend line, which in turn may change their behavior.
Yet, even accepting this idea, a basic question persists. Why should the trend lines fit by researchers coincide with the perceptions of potential murderers about trends in executions? Because there are no studies that include empirical analyses on the question of how potential murderers perceive the risk of sanctions, there is no basis for assuming that the trend line specified by researchers corresponds to the trend line (if any) that is perceived by potential murderers. If researchers and potential murderers do not perceive trends the same way, then time-series analyses do not correctly identify what potential murderers perceive as deviations. Because of this basic flaw in the research, the committee has no basis for assessing whether the findings of time-series studies reflect a real effect of executions on homicides or are artifacts of models that incorrectly specify how deviations from a trend line cause potential murderers to update their forecasts of the future course of executions.
To obtain a single estimate that specifies the effect of capital punishment on homicide, researchers invariably rely on a range of strong and unverified assumptions. In part (as discussed above), this reflects the lack of basic information on the relevant sanction regimes for homicide and the associated perceptions of risk. None of the studies accounts for the noncapital component of the sanction regime, and potential murderers’ risk perceptions are assumed to depend on observable frequencies of arrest, conviction, and execution. The ad hoc choices of alternative models of risk perceptions