across and in some cases within studies, a central task for this committee is to assess the validity of the models used in the studies.
We begin the chapter by describing the key features of the studies we reviewed and giving a brief overview of their data and methods. We then discuss the primary challenges to researchers using panel data and methods to inform the question of whether the death penalty affects the homicide rate: the difficulty in measuring changes over time in the relevant sanction policies for homicide and the difficulties in establishing that any changes in homicides that are concurrent with changes in the death penalty are caused by those changes in the death penalty and not vice versa or by other factors that affect both—such as other sanctions for murder. We conclude with our assessment of the informativeness of the panel research.
We begin our review of the panel research by briefly describing the regression models used in the studies. Our intention with this description is to establish the extent to which the methods are largely consistent across studies, as context for understanding the particular dimensions on which the studies differ.
The panel research makes use of multiple regression models involving “fixed effects” that take the following form:
where yit is the number of homicides per 100,000 residents in state i in year t, f(Zit) is an expected cost function of committing a capital homicide that depends on the vector of death penalty or other sanction variables Zit with corresponding parameter γ measuring the effect of the death penalty on the homicide rate. Importantly, this effect is assumed to be homogeneous across states i and years t.
A primary benefit of panel data is that one observes homicide and execution rates in the 50 states over many years. This allows researchers to effectively account for unobserved features of the state or of the time period that might be associated with both the application of the death penalty and the homicide rate. Some states, for example, might have unobserved social norms that lead to higher (or lower) execution rates and lower (or higher) rates or homicide: Texas is arguably different than Massachusetts in this regard. The panel data model in Equation (4-1) accounts for some of these differences with a state-specific intercept parameter, αi, referred to as a state fixed effect, that allows the mean homicide rate to vary additively