US MUDER RATES & CAPITAL PUNISHMENT
This project investigates the relationship between murder and capital punishment (the death penalty) in the United States. We investigate the main dataset and test the following hypotheses:
Null Hypothesis: State murder rates increase and decrease over two-year periods as if “increase” or “decrease” were sampled random from a uniform distribution (like a coin flip).
Alternative Hypothesis: State murder rates are either more likely or less likely to increase than decrease over two-year periods.
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using the Test Statistic: absolute value of (number of increases in murder rates - number of decreases in murder rates).
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Then we apply a similar test to see whether U.S. states that suddenly ended or reinstituted the death penalty were more likely to see murder rates increase than decrease. In order to attempt to investigate the causal relationship between the death penalty and murder rates, we took advantage of a natural experiment where we defined the test as follows:
Population: All the states that had the death penalty before the 1972 abolition. (There is no control group for the states that already lacked the death penalty in 1972, so we omitted them.) This includes all US states except Alaska, Hawaii, Maine, Michigan, Wisconsin, and Minnesota.
Treatment group: The states in that population, in the year after 1972.
Control group: The states in that population, in the year before 1972.
Null hypothesis: Each state’s murder rate was equally likely to be higher or lower in the treatment period than in the control period. (Whether the murder rate increased or decreased in each state was like the flip of a fair coin.)
Alternative hypothesis: The murder rate was more likely to increase or more likely to decrease.
We concluded that, if p-value cutoff = 0.05, we reject the null hypothesis. We don’t have enough reason to believe that each state’s murder rate was equally likely to be higher or lower in the treatment period than in the control period.
Note about the data used in this project:
The main data source for this project comes from a paper by three researchers, Dezhbakhsh, Rubin, and Shepherd. The dataset contains rates of various violent crimes for every year 1960-2003 (44 years) in every US state. The researchers compiled their data from the FBI’s Uniform Crime Reports. Since crimes are committed by people, not states, this project accounts for the number of people in each state when we’re looking at state-level data. Murder rates are calculated as follows:
(Murder is rare, so we multiply by 100,000 just to avoid dealing with tiny numbers.)
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For the states that never had the death penalty, the test statistic 1971-1973 had an insignificant p-value which implied that over the years, the changes from increases to decreases, were coincidental. In the states that reinstated death penalty, the significant p-value implied that the death penalty deterred murder rates. While our analysis appeared to support the conclusion that the death penalty deters murder, a 2006 Stanford Law Review paper argues the opposite: that historical murder rates do not provide evidence that the death penalty deters murderers. To understand their argument we use plots to compare murder rates of states with and without the death penalty with a focus on the period around the two natural experiments of 1972 and 1976, to understand the evolution of murder rates over time for those groups of states. The line plot we generated above is similar to a figure from the paper. Canada has not executed a criminal since 1962. Since 1967, the only crime that can be punished by execution in Canada is the murder of on-duty law enforcement personnel. The paper states, “The most striking finding is that the homicide rate in Canada has moved in virtual lockstep with the rate in the United States.” Hence we focused on the assumptions we made in this project that led us to believe that the death penalty deterred murder, when in fact the line plots tell a different story. The underlying assumption while analyzing the data in this project was that capital punishment was the only factor affecting murder rates, since the murder rates increased when the death penalty was abolished or decreased when death penalty was reinstituted. The experiment did not take into account confounding factors that could’ve affected our murder rates.
