by state, and a time-specific intercept, βit, referred to as a time fixed effect, that allows the mean homicide rate to vary additively over time. These fixed effects account for unobserved factors that are state specific but fixed across time, such as the social norms that make Texas different than Massachusetts, and factors that are year specific but apply to all states, such as macroeconomic events that may affect homicide rates across the country. In addition to these fixed effects, some of the researchers also include state-specific linear time trends that allow each state’s homicide rate trend to vary (linearly) from the year-to-year national fluctuations.
The literature also includes a set of covariates, Xit, that are intended to control for additional factors that may vary with both state and year. These sets of covariates are largely similar across studies and include economic indicators, such as the unemployment rate and real per capita income; demographic variables, such as the proportion of the state’s population in each of several age groups; the proportion of the state’s population that is black; and the proportion of the state’s population that reside in urban areas. The covariates also include health and policy variables, such as the infant mortality rate, the legal drinking age, and the governor’s party affiliation; and crime, policing, or sanctioning variables, such as the number of prisoners per violent crime.
Finally, εit is a random variable that accounts for the unobserved factors determining the homicide rate.1 Researchers make two general assumptions about the relationship between the death penalty variables, Zit, and εit. The most common assumption is that the death penalty, as measured by the variable Zit, is statistically independent of the unobserved factors that determine homicide, as it would be in an ideal randomized experiment. An alternative route is to assume that there is some covariate, termed an instrumental variable, that is independent of εit but not of the death penalty.
Table 4-1 lists the studies reviewed in this chapter and a few of their key characteristics, and briefly notes each one’s results.2 This list does not
1In estimating these models, the data are typically weighted by state population.
2One characteristic that is not highlighted in Table 4-1 is the choice of outcome variable, yit. All of the studies listed in the table and reviewed in this chapter focused on the overall homicide rate (or the log-rate). However, there are a few studies in the panel data literature that examined different outcome measures. Most notably, Fagan, Zimring, and Geller (2006) focused on all capital murders, and Frakes and Harding (2009) examined child murders which, depending on the state and year, may or may not be death penalty eligible. Otherwise, the key characteristics of these two studies are similar to the ones reviewed in this chapter. Interestingly, although both studies focused on the impact of the death penalty on capital eligible murders, Fagan, Zimring, and Geller found no evidence that the death penalty deters murder,