Nick Zanko
12/1/2013
Hypothesis
I will test to see if the level violent crime is deterred by the presence of capital
punishment.
Motivation
This is an interesting question to study because many people are on the fence between
the death penalty and the alternative of life without parole for three distinct reasons. First,
there is an ethical issue surrounding death as a punishment for crime. Second, the costs
associated with capital punishment are much higher than the costs associated with keeping a
prisoner incarcerated on a life sentence without parole. Lastly, not all states with capital
punishment have the same qualifications that necessitate capital punishment, - which might
explain why people are so conflicted about it - but all qualifications do require the act of
murder. For example, in New Hampshire a capital offense would be murder committed in the
course of rape, kidnapping, or drug crimes; killing of a police officer, judge or prosecutor;
murder for hire; murder by an inmate while serving a sentence of life without parole (Snell,
2011). It would be interesting to find out if citizens are safer if it can be determined that the
presence of the death penalty acts as a deterrent to violent crimes.
Literary Review
In the article entitled, “Understanding Why Crime Fell in the 1990s: Four Factors that
Explain the Decline and Six that Do Not” by Steven D. Levitt, the author analyzes three pieces of
data. First, there is an analysis of the percent changes in multiple categories of criminal activity
from 1973-2001. Then the paper presents the percent changes in crime rates for different
population groups from 1991-2001. Finally, Leavitt shows the homicide trends for major U.S.
cities while looking at what possible determinants that changed in some substantial way during
the 1990s. In Leavitt’s analysis, he concludes that crime fell in the 1990s due to four factors:
increased incarceration, more police, the decline of crack, and legalized abortion. His research
also showed that six factors commonly thought to impact crime rates did not significantly
contribute to the decline, namely the strong economy, changing demographics, innovative
policing strategies, gun laws and increased use of capital punishment. He also postulates that
the rising number of “crack babies” and children growing up in single-parent, unstable
households is likely to impact crime rates in the coming future (Levitt, 2004).
In another article entitled, “To execute or not: A question of cost?” by Deborah Hastings
of the Associated Press, Hastings discusses the costs and benefits between life in prison versus
capital punishments and the additional costs of imprisonment when someone is on death row –
as in the case of California, which has the largest death row population costing $90,000 per
inmate. She links the increasing number of convictions to the increased prevalence of DNA
evidence to support why death penalty trails are more expensive. To conclude, Hastings
finishes with some anecdotal evidence which postulates why the number of death sentences
given have been decreasing over time: “Reasons differ significantly, depending on who's
providing them: Pro-death penalty activists say it's because crime rates have declined and
execution is a strong deterrent; abolitionists say it's because jurors and judges are reluctant to
risk taking a life when future scientific tests could prove the accused not guilty.” While this
conclusion is not exactly scientific, it does point to the deep-seated human component
surrounding the controversial use of capital punishment (Hastings, 2009).
In the article entitled, “Does Capital Punishment Deter Murder,” author John Lamperti
uses regression analysis to substantiate statistical evidence that supports the claim that the
presence of the death penalty does increases murders. However, he also states that, as
evidenced by surveys, there is a body of anecdotal evidence which suggest that there are
murders which have in fact been averted because of the presence of the death penalty
(Lamperti, 1996).
The Death Penalty Information Center’s website provides a discussion of recent
deterrence studies relating to capital punishment. Here, a recent (April 2012) report by the
National Research Council of the National Academies is summarized. While the report does
concede that there has been much research done showing that violent crimes are not deterred
by the presence of capital punishment, it provides three distinct reasons why these studies are
inherently flawed. First, the studies ignore the effects of noncapital punishments that might
also be used. Second, the report has found that many studies have used incomplete or
implausible models of potential murderers’ perceptions of and response to the use of capital
punishment.
Lastly, the report finds flaw in the discovery that much recent research’s
estimates of the effect of capital punishment are based on statistical models that make noncredible assumptions (Fagan, 2009).
When all of this information is considered collectively, two distinct observations
emerge. First, there are studies that have been performed which show that capital punishment
is both deterred and encouraged by capital punishment. This suggests that current research
has not yet pointed to a definite conclusion. Second, as the last piece of literature suggests, an
investigation into the validity of research done concerning the hypothesis reveals that studies
which show a positive correlation between capital punishment and an increase in violent crimes
are inherently flawed. Because of this, I intend to develop my own model which might more
accurately demonstrate a definitive answer by removing these inherent flaws.
Model
The model I have developed is displayed below:
Violent crimes = B1 +B2(single parent household rate) +B3(unemployment rate)+ B4(percentage
of high school graduates) +B5(median income)
Where B2 > 0 (effect of economic condition on rational choice theory)
B3 > 0 (environmental effect on behavior)
B4 > 0 (education effect on opportunity cost)
B5 > 0 (demographic effect on opportunity cost)
When unemployment rates are high (and power shifts back into the hands of the
employer, creating lower wages), people may find criminal activity more enticing, suggests
Holly Trogdon in “The Unemployment-Crime Relationship.” Being unemployed gives rise to two
contributing factors. One, people have a great deal of time on their hands that would have
otherwise been occupied with employment. Two, those who are unemployed are often forced
to live on far less of an income than when they were employed. Given this, engaging in crime –
especially profitable crime – might seem more attractive as the opportunity cost associated
with engaging in criminal activities is lowered (Trogdon, 2006).
Heather Antecol and Kelly Bedard’s paper called, “Does Single Parenthood Increase the
Probability of Teenage Promiscuity, Substance Use and Crime?” cites several bodies of work
which show a strong positive correlation between single-parents households and crime rates.
Much of work done suggests that there are several highly-correlated reasons behind this
assumption (related poverty, absence of role-models, disruption of stability brought on by
divorce, age of mother at birth and number of subsequent births), but the implication still pans
out (Antecol & Bedard, 2006).
As evidenced by Allison Oliver’s work entitled, “The Economics of Crime: An Analysis of
Crime Rates in America,” literary review suggests that the higher a person’s educational
attainment is, the better able a potential criminal is able to analyze the costs and benefits
associated with crime. This can lead to deterrence because of a more accurate assessment of
the opportunity cost of committing crime. In regards to income level, Oliver finds that as a
person’s income level rises, his opportunity cost of committing crime also rises, which may act
as a deterrent. She also notes that crime is more prevalent among young adult minority males,
who have far less of an earnings potential than their better-educated, more established
counterparts (Oliver, 2006).
Data Sources and Descriptions
Preliminary Evaluation of Data
I will use the data given by the U.S Census Bureau to find the violent crime rates of states with
and without death penalty, which can be accessed via US Census publications (“Crime Rates by
State,” 2013). I will also find out how many criminals in these states with the death penalty are
given the death penalty, along with how many are executed each year; the Bureau of Justice
Statistics provides several reports by state which can be compiled to obtain this information
(Bureau of Justice Statistics, 2013). I will compare states with similar populations and control
for other factors that contribute to homicide rates: demographic information (“Crime Rates by
Type,” 2013), rate of single parent households (“Single-Parent Households,” 2013),
unemployment rates (Bureau of Labor Statistics, 2011), and high school dropout rates (Stillwell
& Sable, 2013). As you may know, capital punishment is only used against cases of homicide,
but the involvement of violent crimes does create circumstances for murder (“Murder Victims –
Circumstances,” 2013).
Note: I will be making my own data tables from the census resources for states that have
had capital punishment for an extended amount of years; the provided links are examples that
the data does indeed exist.
Finalized Data Set (with Descriptions)
Attached below is a table which summarizes what kinds of data were used in the
regression and how to interpret the data. It should be noted that not all of these data sources
appear in the final model, as part of the modeling process includes determining which variables
significantly contribute to regression analysis and which do not. For a detailed explanation
regarding the process used to conclude variables which were actually found to be significant in
the formulation of this project’s regression model, please find the section entitled “Model
Estimation and Hypothesis Testing.”
Empirical Project: Data Legend
Variable
DP
VC
VCR
URS
Definition
A dummy variable for states with
the Death Penalty in 2010
Gross of violent crimes in a state
for the year of 2010
The Violent Crime Rate in a state
for the year of 2010 (%)
Source
Bureau of Justice Statistics
Federal Bureau of Investigation
Federal Bureau of Investigation
Unemployment Rate in a state for
the year of 2010 (%)
Bureau of Labor Statistics
Minc
Median Income in a state for the
year 2010
http://www.census.gov/hhes/www/i
ncome/data/statemedian/
AFGRi
Average Freshmen Graduation
Rate in a state for a 2009-2010
period (%)
National Center for Education
Statistics
Pop2010
Cp
Exec
sphr
Total Population in a state in the
year 2010
http://www.census.gov/2010census/
data/apportionment-dens-text.php
Total of criminals sentenced to
Capital Punishment in a state in
the year 2010
Bureau of Justice Statistics
Total of criminal of prisoners
Executed in a state for the year
2010
Bureau of Justice Statistics
Percentage of Single Parent
Households in a state of the year
2010
http://datacenter.kidscount.org/data/
acrossstates/Rankings.aspx?ind=106
Before any analysis could be performed in SAS, it was necessary to “clean” the data – ie,
transforming the data into a useable format. For example, median income was given as per the
original data set in whole dollar amounts. I found it more useful to use the median income data
in $1000’s instead. I also converted the given percentage from whole numbers to decimal
values. Additionally, the development of this project necessitated the formation of additional
variables that could not be found explicitly through the use of the data sources. For example, in
order to find the violent crime rate I created a variable which took the number of violent crimes
divided by the population (which was given in 1000s). Unlike the raw data of violent crimes,
this violent crime rate controls for population statistics; without this control, it is impossible to
tell whether a larger state like California has a higher violent crime rate because its citizens are
in fact more violent or because it has a much higher population that other states.
Model Estimation and Hypothesis Testing
Model Creation and Assumptions
Once all of the variables were in a format that I found to be usable, I introduced the final
data set into SAS and began using regression techniques to determine which of the variables I
had included were actually statistically significant to the number of violent crimes committed.
To accomplish this, I ran a stepwise multiple regression in SAS, which adds in variables one at a
time in “steps” and shows the regression output in residuals, parameter estimates, and ANOVA.
I then omitted the non-significant variables until only significant predictive variables in the
number of violent crimes remained. This part of the process was by far the most time
consuming, because it required analyzing a large number of models to figure out which among
them not only did not violate any of the five assumptions for regression, but which resulted in
the highest adjusted R^2 value. It also required me to strategically select which combination of
variables to look at so that any multicollinearity could be reduced; for instance, I could not run
UR and URS variables together because they contain the same data, but I could run them
separately to see which had a better effect in the resulting regression model.
Hypothesis Testing
The final model which I selected shows that only three of the variables – the
unemployment rate as a percentage, the percentage of single parent households, and the
existing rate of violent crimes per 1000s state citizens were significant predictors in the number
of violent crimes. The final regression model as found by SAS output is shown below.
Adjusted R^2 – Model Accuracy
Here, we look at the adjusted R^2 value to determine whether or not the variables used
in the model can act as accurate predictors for the model. As R^2 approaches 1, this indicates
that the included variables account for much of the variability in the dependent variable – here,
violent crimes. Because adjusted R^2 here is above 0.3, which is a typical minimum cutoff used
for real-world data, we can conclude that the variables in the model account for a significant
amount of the variability in violent crimes, making this model sufficient for accurate prediction
of violent crimes.
ANOVA – Model Fit
After looking at the accuracy of the model, the next thing we should analyze is whether
or not the model is a good fit for the data. This can be accomplished by looking at the ANOVA
output. In ANOVA testing, the null hypothesis states that the model is that all of the beta
values associated with the variables are zero, and therefore have no effect in the final model.
The alternative hypothesis, then, is that at least one of the betas is nonzero. Because the Pr>F
value is less than 0.0001, we reject can conclude with 99.99% confidence that at least one of
the betas for one of the variables is not zero and has an effect on the model. This shows that
the model has good overall fit for the data. Later, we can look at the parameter estimates to
determine which of the betas are nonzero and what their values are for the final regression
model.
Assumptions of Regression
After we are able to determine whether the model is accurate and is a good fit for the
data, we need to determine whether or not the five assumptions for regression have been
violated. Using the residuals, we can figure out the first four. Here, the residual plot for
quantiles (under the Fit Diagnostics) shows that the data approximately follows the heavy black
line. This indicates that the assumption of normality is supported. We can also see by the
residual plots (see Residuals by Regressors) of each of the variables that the assumptions of a
linear relationship, homoskedacity, and independence are supported because there is no
pattern to the residuals in any of the plots (ie, the plots are random). Lastly, to determine if any
multicollinearity exists between any of the variables, we can look at the VIF scores as presented
in the Parameter Estimates output. A VIF score above 10 indicates that there is significant
multicollinearity which should be amended. Here, we see that all of the VIF scores for all of the
variables are well below 10, which proves that the assumption of no multicollinearity is
supported.
Parameter Estimates and the Formation of the Model
Now that we know that 1) the model is accurate, 2) the model is a good fit, and 3) none
of the assumptions of regression are violated, we can move forward to find the final prediction
expression of the model. Here, we look at the p-values for each of the variables, as given by
Pr>F in the first table and Pr>|t| in the second. The null hypothesis for analyzing the variables
states that all betas associated with all of the variables are zeo, and the alternative hypothesis
is that they are not zero. When this hypothesis test is applied to each of the resulting variables
of the stepwise regression, we see that all of the p-values are less than 0.05. From this, we
reject the null hypothesis for each variable and conclude with 95% confidence that none of the
betas are 0.
Interpretation of the Results
To formulate the final prediction expression for the final model, we return to the table
with the parameter estimates. Because we rejected the null hypothesis for each variable, we
include each of the variables in the prediction expression. Using the associated beta values
found by SAS, we find that the final model is this:
vc = -271.157 + 1301.278*sphr + 1744.261*urs + 396.008*vcr
As evidenced by the final model, each of the included variables – percentage of single-parent
households, unemployment rate as expressed as a percentage, and the violent crime rate per
1000 state citizens – all have a positive effect on the number of violent crimes. In other words,
the higher the percentage of single-parent households within the state, the higher the
unemployment rate within the state, and the higher the rate of violent crimes per capita, the
higher the number of violent crimes committed within the state. Here, it is evident that violent
crimes occur due to a combination of economic, socioeconomic, and environmental factors.
The previously cited studies are supported by these findings, which stated that there is a strong
positive correlation between single-parent households and level of unemployment in criminal
activity. Additionally, this research here finds that another influencing factor in the prevalence
of violent crimes committed is whether or not the area is already rife with violent crimes. This
suggests that cascade theory (based on Bayesian mathematics) – the propensity to do
something because other people are doing it – is also at play.
Conclusions and Limitations of the Study
In conclusion, my research shows, coincident with previous related studies, that
committing violent crimes which could lead to capital punishment are related to single-parent
household rates, unemployment rates, and present rates of violent crime per capita. However,
my initial hypothesis that the presence of the death penalty as a form of punishment acts as a
deterrent to violent crimes was not supported. By running the data in SAS, I found that neither
the presence of the death penalty, the number of criminals sentenced to capital punishment,
nor the number of criminals executed by the death penalty have a statistically significant
influence over the number of violent crimes committed.
Without more readily available data about the types of people who commit violent
crimes which are punishable by the death penalty, I cannot find a way to analyze precisely what
factors either deter or encourage this kind of criminal behavior. As an extension to this study, I
would like to pick one representative state – one that matches overall US demographics, so that
its findings could be extrapolated to the US population as a whole – and further investigate
legal statistics regarding crimes which are punishable by death. Through this, I might be able to
come up with a sort of “criminal profile,” or a list of demographic and environmental criteria
which dictates what kind of people are most likely to commit violent crimes that can be
punished by the death penalty. These findings would be useful to the Justice Department
because it would allow judicial and criminal authorities to put into place public programs aimed
directly at these people to preventing violent crimes, thereby reducing the overall violent crime
rate and potentially the need for the death penalty.
References
Antecol, H., & Bedard, K. (2006). The unemployment-crime relationship. (Master's thesis, University of
California). Retrieved from http://econ.ucsb.edu/~kelly/youth_nov04.pdf
Bureau of Justice Statistics, US Department of Justice. (2013, April 11). News releases. Retrieved from
http://www.bjs.gov/
Bureau of Labor Statistics, U.S. Department of Labor. (2011). State unemployment rates in
2010. The Editor's Desk. Retrieved from http://www.bls.gov/opub/ted/2011/ted_20110301.htm
Hastings, D. (2009, March 09). To execute or not: a question of cost?. NBCnews.com. Retrieved from
http://www.nbcnews.com/id/29552692/ns/us_news-crime_and_courts/t/execute-or-notquestion-cost/
Fagan, J. (2009). Discussion of recent deterrence studies. Retrieved from
http://www.deathpenaltyinfo.org/discussion-recent-deterrence-studies
Lamperti, J. (1996). Does capital punishment deter murder?. (Master's thesis, Dartmouth
College). Retrieved from
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/JLpaper.pdf
Levitt, S. D. (2004). Understanding why crime fell in the 1990s: four factors that explain the decline and
six that do not. Journal of Economic Perspectives,18(1), 163-190. Retrieved from
http://pricetheory.uchicago.edu/levitt/Papers/LevittUnderstandingWhyCrime2004.pdf
Oliver, A. (2002). The economics of crime: an analysis of crime rates in america. The Park Place
Economist,X, 30-35. Retrieved from http://www.iwu.edu/economics/PPE10/alison.pdf
Snell, T. L. US Department of Justice, Bureau of Justice Statistics. (2011). Capital punishment, 2010 –
statistical tables (NCJ 236510). Retrieved from website:
http://bjs.gov/content/pub/pdf/cp10st.pdf
Stillwell, R., & Sable, J. US Department of Education, Institute of Education Sciences. (2013). Public
school graduates and dropouts from the common core of data: school year 2009–10(NCES
2013309REV). Retrieved from website: http://nces.ed.gov/pubs2013/2013309rev.pdf
Trogdon, H. (2006). The unemployment-crime relationship. Informally published manuscript,
Department of Economics, University of Central Florida, Orlando, FL, Retrieved from
http://www.bus.ucf.edu/faculty/rhofler/file.axd?file=2011/2/Trogdon - Unemployment &
Crime.pdf
US Department of Commerce, United States Census Bureau. (2013). Crime rates by state, 2008 and
2009, and by type, 2009. Retrieved from website:
http://www.census.gov/compendia/statab/2012/tables/12s0308.pdf
US Department of Commerce, United States Census Bureau. (2013). Crime rates by type of offense: 1980
to 2009. Retrieved from website:
http://www.census.gov/compendia/statab/2012/tables/12s0307.pdf
US Department of Commerce, United States Census Bureau. (2013). Murder victims – circumstances and
weapons used or cause of death. Retrieved from website:
http://www.census.gov/compendia/statab/2012/tables/12s0310.pdf
US Department of Commerce, United States Census Bureau. (2013). Single-parent households: 1980 to
2009. Retrieved from website:
http://www.census.gov/compendia/statab/2012/tables/12s1337.pdf