The Rise and Fall of the U.S. Homicide Rate towards the End of the
20" Century
- A System Dynamics A pproach -
Kaveh Dianati and Roland Maximilian Happach
European Master in System Dynamics Programme
kaveh.dianati@gmail.com, max.happach@googlemail.com
Abstract
The goal of this paper is to investigate the underlying structure of the socio-economic
system leading to the developments of Homicide Rate in the United States during the last two
decades of the twentieth century. Specifically, we focus on the effect of the crack cocaine
epidemic, and the arms race among street gangs associated with it, on the mentioned
developments. We build a System Dynamic model to study the interconnected fabric of important
factors. The analysis shows that the arms race triggered by the growth in crack cocaine market,
and the reactive policies directed towards having a more effective police force and a higher
number of police can explain the overall pattern of the studied behaviour.
Key Words
U.S. Homicide Rate, System Dynamics, Arms Race
Introduction
The plotted graph of the homicide rate, as well as the overall crime rate, in the U.S. between
1960 and 1990 resembles a long uphill hike and a short walk on a plateau. Whereas experts
predicted stabilization or even worsening of this situation for the upcoming years (Fox, 1996;
Levitt, 2004) the US surprisingly experienced a sharp drop in both crime and homicide rates
within the 1990s decade. This development led to a heated discussion about possible reasons
among experts, researchers and professionals who claimed to know what happened and why.
However, the more contradicting arguments delivered by debaters, the less it can be believed that
an ultimate explanation has been found.
Many of the debaters have linked the decline to the improved economic situation (Blumstein
& Rosenfeld, 1998; Neumayer, 2003; Freeman, 1996; Donohue J. J., 1998). Levitt (2004), in
contrast, believes that economic welfare is important for property crimes but not so much for
violent crimes. Ruhm (2000) shows some contradicting results, making it difficult to daim
definitive negative correlation between economic welfare and homicide rate. Others correlated
the decreasing rates to the availability of weapons especially guns and the laws conceming
carrying them (Farley 1980). In particular, Blumstein & Rosenfeld (1998) hold an arms race as a
reinforcing cycle responsible for the sharp rise in homicide rates, also arguing that the
effectiveness of police confiscating guns contributed to a downtum in violent crimes. On the
1
other hand, Marvell (2001) argues that a ban of weapons leads to more violence, especially
against juveniles. He links the absence of guns to more offenses against younger criminals.
Furthermore, changing demographics was mentioned as an explanation for the decline of
homicides in 1990s (Levitt, 2004; Blumstein & Rosenfeld, 1998). Moreover, Levitt & Donohue
(2001) maintained the legalization of abortion in the 1970s to make a significant contribution to
the fall in crime. However, Foote & Goetz (2005) claim that this finding is based on calculation
mistakes. Furthermore, the number of policemen, neglected by Donohue in 1998 (J. J. Donohue
1998), is a major explanatory reason in his paper together with Levitt (Donohue und Levitt
2001).
As can be seen, the joke about economists that goes "if you ask 10 economists a question,
you get 10 different answers" apparently also holds true for criminologists. Certainly, there are
factors on which the majority of researchers agree. This includes the idea that developments in
the drug-market significantly influenced homicide rates during the late 20” century (Levitt,
2004; Blumstein & Rosenfeld, 1998; Maxfield, 1989).
In previous studies related to this subject, authors rarely looked at these developments from
a holistic and dynamic standpoint. Most of these researches are based on time-series and cross-
sectional, mostly linear, regressions analysis. The dominant way of thinking here is what Barry
Richmond calls “laundry list thinking”. Only a few researchers concluded closed-loop causal and.
possible non-linear relationships from crude data analysis. We believe that a System Dynamics
approach is a suitable approach here because we see the developments in the homicide rate not as
caused by several straightforward linear 'cause-leads-to-effect' relationships, but as the result of a
complex chain of closed-loop feedbacks of several cause-effect relationships each within the
socio-economic system. In this paper, we build a System Dynamics model that incorporates
feedback loops that we consider as important in reinforcing homicide rates and eventually
balancing it out
But first, we are going to define precisely the Dynamic Problem that we intend to model.
Secondly, we present our hypothesis of how this problem developed. In the third section, we
analyze our model by comparing its result with historical behaviour and running tests for
validating the model. Next, we present a discussion of relevant policies and policy
implementation issues. Lastly, we conclude by providing a summary of our research and a
discussion of its strengths and limitations.
Dynamic Problem
In this study, we focus on homicide rate which is considered to be the most reliable and
accurately measured type of crime (Levitt, 2004; Donohue J. J., 1998). Further, the correlation of
homicide to overall crime rate is 0,833 and it can therefore be seen as representative of the
overall crime rate. The data is taken from the FBI Unified Crime Report (UCR) and
Supplementary Homicide Report (SHR) reports.
The homicide rate in the U.S. increased by more than 30 percent during the second half of
the 1980s decade, but then showed an unexpected decline of about 40 percent during the 1990s.
Eventually, it stabilized in the last years on a level of 4.8 homicides per 100,000 inhabitants.
2
Not all homicides are of the same nature. For the purpose of our study, we disaggregate
homicides into two categories: family-related and non-family related. Family-related homicides
show a slow almost linear decline during the period of our concem (J. J. Donohue 1998). The
scale of its change during this period is so small that it does not play an important role in the
pattem of rise and fall that is our interest. Therefore, we decided to define our problem as
explaining the rise and fall pattem of non-family related homicides during the last 15 years of the
twentieth century.
The corresponding development of the homicide rate in the period can be seen in
Figure 1. Our aim is to provide an explanation of the rise within the 1980s and the following
decline in the 1990s. We aim to identify the elements of the system and the dynamic
relationships between them that led to the tumaround.
ico)
iS
Q
@ Historical Data
@ General Pate
NNN
UR
Homicides per 100,000 residents in persons/year
Sun aArANA Dw ow
iS) g
N
at
ie
ZESRSSSRSSSESESSSRIFRRRRSRSRE
Figure 1. Homicide rate without family related murder per 100,000 residents (Source: FBI SHR Data)
The blue line shown in Figure 1 presents the historical data. Saeed (1998) points out that a
reference mode is not just historical data; rather, historical data is only a starting point for
building it. A reference mode is a qualitative and abstract concept that represents pattems rather
than precise historical data (Saeed 1998). The red line in Figure 1 shows the general pattem of
tise and fall in which we are interested. This excludes the minor breaking points and short-term
trends in historical data.
Dynamic Hypothesis
For the rise and fall pattem in homicide rates during the late 1980s and 1990s, different
explanations have been offered in the criminology literature. One explanation that has been
supported extensively by acclaimed authors of the field is the one that relates the behaviour of
homicide rates to the developments in the crack market (Donohue, 1998; Blumstein &
Rosenfeld, 1998). Quoting from Blumstein & Rosenfeld (1998), "Rates of serious violence,
3
including homicide, went up during the rise phase of the crack epidemic and have been dropping
during the decline phase. Ass the crack epidemic spread in the mid to late 1980s so did the danger
around inner city drug markets, driving up the incentive for more kids to arm themselves in an
increasingly threatening environment. That environment also became a prime recruiting ground
for urban street gangs. Once kids acquired guns to protect themselves from other kids, a classic
amms race began, and firearm violence diffused away from the drug markets."
There are at least three important reasons supporting the plausibility of this explanation:
1. The drug-market hypothesis directs attention to the population groups in which the
changes in homicide were concentrated: youth, and on African-American youth in
particular, who disproportionately participated as sellers in inner-city crack markets.
2. This hypothesis is causally symmetric, meaning that it accounts for both the increase and
the decline in violence & homicide rates.
3. The focus on changes in drug markets also helps to account for the variable timing of the
peaks and declines in homicide across cities. A large coastal city such as New Y ork, for
example, where crack took hold earlier and where it peaked sooner than in other cities,
should have experienced a drop in its rate of homicide sooner than in other cities - and it
did. Trends in homicide rates in smaller cities are generally lagging behind larger cities.
Also, some of the decline in homicide rates is almost certainly related to the economic
expansion during the 1990s. Unemployment rates dropped significantly, and consumer
confidence was higher than in nearly three decades. Importantly, economic gains were been
shared by racial minorities, teenagers, and high school dropouts, groups at disproportionate risk
for serious criminal violence.
Moreover, a number of reactive efforts to fight the drastic rise in violence during the late
1980s certainly contributed to the subsequent improvement during the 1990s. Notable among the
reactive forces are police efforts to remove guns from kids. To the extent that the carrying is
reduced thereby, it in tum reduces the concem over self- protection, and thereby diminishes the
incentive for others to carry their own guns. Thus, the contagious escalation characteristic of the
tise period can display a similar contagion process of disarmament during the decline period.
Thus, our hypothesis for the studied problem is the following: The rise of the crack cocaine
market in the mid 1980s immediately led to an increase in violent incidents in susceptible
communities. This triggered an increased rate of acquisition of guns by criminals, involved in
any kind of crime, to protect themselves in the increasingly dangerous environment. More and
more immature street kids armed with firearms meant dangerous toys landing in the hands of the
wrong people. This can also be thought of as an example of a classic arms race. This assumption
is also consistent with other sources in the literature. Decker (1996) argues that gang members
perceive a threat from rival gangs and get armed in order to protect their comers. Strodtbeck and
Short Jr. (1964) state that camying a gun is a method to gain respect in the gang especially
among newcomers. We combine both theories arguing that the boom in the drug market led to
more guns and more criminals. This resulted in an escalation of armament which led to the peak
in homicides, not only because of drug-related homicides, but because with more guns carried by
criminals the violence diffused away from the drug market and caused more homicides in any
kind of potentially violent situation. Eventually, reactive efforts such as raising investment in
4
hiring new police force and adopting new strategies against possessing and carrying illegal guns,
and also the independent effect of a thriving economy, drove down the homicide rate.
Causal Loop Diagram
Based on all the
insights obtained through a
review of the subject
literature, we built a causal
feed-back loop model,
following the System
Dynamics approach. First,
let us have a look at the
basic feedback structure
that generated. the
developments in homicide
rate that we intend to
explain.
Our variable of interest
is ‘Homicides’, located at
the right hand side of
Figure 2.
The number of
homicides committed is
affected by the number of
‘Criminals’, and the
amount of ‘Guns per Figure 2. Causal Loop Diagram
Criminal’. Criminals commit homicides in different kinds of violent situations, such as robbery,
street fights, or gang disputes. Whether these situations lead to homicide or not depends on the
average number of guns carried by criminals, which is shown in the variable ‘Guns’. Therefore,
the variable ‘Guns per Criminal’ represents a measure of threat. The bigger this number, the
more criminals possess a gun leading to more threat for others not carrying a gun.
In our model, the decision of susceptible persons on whether or not to lead a life of crime
depends on an evaluation of the ‘Perceived Risk’ against the relative rewards included. The
relative reward perceived is increased by new profit opportunities from the drug market and
decreased by legitimate income eaming opportunities provided, which is affected by
‘Unemployment within Susceptible Commumities’. Both perceptions - reward and risk - are
changing slowly, indicated by a delay.
The major reinforcing feedback loop that is driving up homicides during the second half of
the 1980s decade is loop R1: As more ‘Criminals’ acquire guns through illegal gun distribution
channels that are aggressively profiting from the demand generated by the expanding crack
market, more peers are going to feel threatened and buy guns for themselves. The larger base of
gun possession is going to stimulate more gun acquisition the next time round. This loop refers
to the arms race. Moreover, there are two reinforcing effects R2&R3 resulting from risk
5
perception. Firstly, as the number of criminals increases, ceteris paribus, it will lower the ‘Gun
per Criminal’ ratio and, consequently, reduce homicides. Further, less police will be hired which,
in tum, leads to lower ‘Perceived Risk’ and more ‘Criminals’. Secondly, more ‘Criminals’ in the
neighbourhood leads to lower perception of risk in becoming a criminal. This effect is shown in
R3. Both latter reinforcing loops are delayed because of the time needed to change perceptions
and hiring additional police and play a minor role.
There are several major balancing feedback loops that have counteracted violence and
contributed to the downtum of homicide rates are. All of these loops operate with delay. Higher
“Homicides per Year’ lead to higher investment in police force effectiveness, called ‘Police
Productivity’ and a larger number of ‘Police’. ‘Police Productivity’ refers on the one hand to
confiscation, i.e. finding illegal guns, which is not necessarily linked to arrests. On the other
hand, the productivity in arresting people can be increased by more aggressiveness and new
strategies. Thus, the more numerous and more effective cops are going to drive violence down
through confiscating illegal guns (B5&B6), and through more Arrests (B3&B4). More effective
Police Force drives up the perceived risk in becoming a criminal and thus negatively affects the
number of criminals (B1&B2). We distinguish between the number of police and their
productivity because they represent different but important leverage points for policy.
There are two major exogenous effects that are significant in this system. ‘Unemployment
within Susceptible Communities’ which directly affects criminalization with a certain delay, and.
developments in the Drug Market that is related with high potential profit which leads to an
increase in the number of criminals and guns carried by those. This shock is immediate because
of the high potential profit related to crack cocaine.
Model Analysis
Comparison with the Reference Mode
Assuming that the drug market went through a period of boom & bust and using a pulse
function starting at 1984 and ending in 1991 to model it, the following figure shows the
comparison of the behaviour of our model versus historical data Clearly, the underlying
structure replicates quite well the real world pattem.
As can be seen in
Figure 3, the rise and fall
pattem of the reference
mode is evident in both
graphs. However, the two
graphs are not exactly
similar in regad to
differences in rising points,
peaks and slopes. The
simulation shows a rise a
litle eadier in timg a
Homicides per 100.000 Residents
Year
Figure 3. Simulated Behaviour vs. Reference Mode
slightly lower peak and a slower rising slope in comparison with the reference mode. The
simulated behaviour has some damped oscillations in the end, which has not been exactly the
case in the real world. Thus, our model seems to show a rise in the homicide rate in the future,
over which some experts have expressed concem (J.J. Donohue 1998).
Policy Design and Implementation
This paper studies a historical problem rather than a currently existing one. Some policies
regarding the problem of extremely high homicide rate in the beginning of the 20” century have
already been implemented and some favourable results have already resulted. Thus, the most
important policy levers are already built-in parts of our model, and constitute our major
balancing feedback loops which are already discussed. Therefore, in this part we intend to
summarize which policies have been used in order to achieve the decline. We then set off on
evaluating them. In the coming discussion, we also want to point out what could have been done
in a better way in order to have a sustainable stabilization, and also, where we see risks for the
future.
There were many policies involving the police force, regarding both the number of police
hired and also policing strategies. In the historical data, we observe a rise in the number of police
beginning in 1984 and peaking in 2000 at 25% higher. Since then, the number of police per
capita has been falling slowly and steadily, along with the falling crime rate but with a delay of
around 7 years. This policy helps reduce crime both directly through arresting more of the
criminals, and indirectly, and perhaps more importantly, through increasing the perceived risk in
becoming a criminal, and thus, limiting the inflow to the stock of criminals. The policy of
increased hiring is embedded in our model and therefore, the model successfully reproduces the
pattem of rapid rise and slow decline in the number of police.
Another major police-related policy is adjustments in police strategies (Levitt,
Understanding Why Crime Fell in the 1990s: Four Factors that Explain the Decline and Six that
Do Not 2004). One important strategy conducted was increased attempts at confiscation of
illegal firearms, such as stop-and-frisk initiatives (Montgomery, 1996; Dilulio, 1996),
“voluntary” searches of homes suspected of containing weapons or promised bounties for reports
leading to confiscation of illegal guns (Blumstein & Cork, 1996). Further examples of gun
related policies are the Violent Crime Control and Law Enforcement Act 1994, which among
others regulates the sale of handguns to juveniles (Violent Crime Control & Law Enforcement
Act 1994 1994). Blumstein & Rosenfeld explain the dynamic effect of this policy most
eloquently: "The theory behind the confiscation strategies lies not only in the benefits of the
confiscation itself, but in the broader deterrent threat that the risk of confiscation has on the
carrying of the weapons or on the brandishing of a gun. To the extent that the carrying is reduced.
thereby, it in tum reduces the concem over self: protection, and thereby diminishes the incentive
for others to camy their own guns. Thus, the contagious escalation characteristic of the rise
period can display a similar contagion process of disarmament during the decline period."
Further proof of changes in the confiscation strategies is the 1990 launched legal ban of weapons
from schools in the Gun-Free Schools Zone Act (The Crime Control Act of 1990 1990) and the
appearance of weapon tracing statistics in the intemet since early 2000s. We conclude that a
a
special gun tracing department or task force was put into place. Confiscation is built in as an
important variable in our model, which contributed a lot to the regeneration of the decline period
of homicides. Without this policy structure the model was not at all able to reproduce the rapid
decline in homicides.
Furthemore, a policy implementation issue that must be taken into account is the delay
involved between investing in police force and observing results. These delays were included in
our model to correctly reproduce the reference mode of behaviour. At the moment, since
homicide rate is relatively low, police force is well likely to become the victim of budget
shortages. Decision-makers must not reason that since budget cuts did not show an immediate
effect on crime, it is a wise decision to cut police budgets. Important delays inherent in the effect
of the strength of police force and homicide rate, or crime rate in general, must be
acknowledged. In fact, our model shows an eventual rising of homicides up again after 2000,
which is to some extent in harmony with actual historical data. This is because of the fact that in
our model we presumed a ‘Normal Homicides’ as a constant parameter, based on which
investment decisions on police is made. Since this perception of what is ‘normal’ does not change
during our simulation period, homicide rate tends to be pulled slightly towards it. Therefore, in
the real world, if the goal is to bring homicide rate as low as possible, the 'normal' value for this,
and along with that the ‘normal level of investment, should be constantly adjusted.
In conclusion, according to our modelling and analysis, two major rates were the vicious
drivers that made homicide go up in the late 1980s: 'Criminalization' & ‘Acquisition’ (of guns).
Whatever policy that could pull down these rates would have helped reduce the peak in
homicides. Regarding Criminalization, an important long-term policy lever is education.
Educating members of crime-susceptible neighbourhoods expands their legitimate money-
eaming opportunities and reduces their perceived reward in becoming a criminal, while of course
educating them about the high risks. Along with efforts pointed towards education that give
delayed results, short-term policies of increasing legitimate income available for low-skill jobs
can also be used. This policy should be used with care, not so that the system becomes too much
reliant on a tranquilizer that kills the pain but does not cure the disease. Blumstein & Rosenfeld
(1998) provide a useful discussion on this. As for gun Acquisition, the police should be wary of
the likely arms race that comes along with booms in the drug-market. This means that initiatives
should be specifically directed towards stopping gun dealers that see drug booms as perfect
opportunities, from distributing guns in the society. Also, a more preventive strategy is to launch
campaigns against drug use. These campaigns should be launched nationwide, not only focussing
on certain age groups or social classes. Such a preventive campaign is right now ongoing against
Methamphetamine. Posters, discussions with school kids, and TV shows are examples of the
media that is being effectively used to treat the topic. That is a first step into the right direction,
even though we cannot be certain about whether or not the message reaches all social groups.
Conclusion
In this paper we studied the underlying structure of the socio-economic system leading to the
developments of Homicide Rate in the United States during the last two decades of the twentieth
century. Homicide Rate started to rise rapidly around 1984 from an initial level of around 6.6
8
homicides per 100,000 residents per year, peaked in the early 1990s at about 8.6 homicides per
100,000 residents per year, and then declined by more than 40 percent to reach a new, somewhat
stable, level of around 4.8 homicides per 100,000 thousand residents per year.
There is no shortage of explanations for this pattem of behaviour in homicide rate. Having
studied some of the most influential articles in the subject literature, we came up with a
dynamics story that, in our opinion, explains well the structure and dynamics leading to this rise
and fall.
The rise of the crack cocaine market in the mid 1980s immediately led to an increase in of
criminals and guns leading to more violent incidents in susceptible communities. However, this
effect of increased level of violence due to the drug business alone is far from enough to explain
the drastic rise in homicides. Nonetheless, this effect was strong enough to stimulate an increased
rate of acquisition of guns by criminals, involved in any kind of crime, to protect themselves in
the increasingly dangerous environment. This can be thought of as an example of a classic arms
race. An increased level of guns camied by street criminals with an immaturely low threshold of
readiness to use them, in any kind of potentially violent situation and not just drug-related fights,
led to the peak in homicides. Eventually, reactive efforts such as raising investment in hiring new
police force and adopting new strategies against possessing and carrying illegal guns drove down
the homicide rate. Furthermore, the growing economy of the 1990s contributed to this trend by
providing more legal money eaming opportunities for ghetto kids and decreasing the rate at
which they enter a life of crime. The System Dynamics model that was created in this research
validates this hypothesis and makes it easy to visualize and to communicate to policymakers as a
guideline for future decisions. The model, or an improved version of it with a specific purpose,
can also be used to test different potential policies.
In previous studies related to this subject, authors rarely looked at these developments from
a holistic and dynamic standpoint. In his review paper, Levitt (2004) collects 10 of the most cited
reasons regarding the rapid decline in the 1990s, ranging from legalization of abortion to laws
against carrying concealed weapons, and to increased number of police. The reviewed
hypotheses have appeared either in scientific joumals, mostly applying econometric and
regression methods to test their theories, or in the media, which apply common sense as their
primary source of evaluation. These hypotheses predominantly involve reasoning based on
correlation, coincidence, simultaneity, and spatial or temporal proximity. The predominant line
of reasoning in the articles that Levitt reviewed has been an open-loop way of thinking, assuming
a single cause with a straightforward ‘cause-leads-to-effect' way of thinking for the studied
developments. The System Dynamicist's point of view, on the hand, is that "the word
is dynamic, evolving, and interconnected" and "Effect is rarely proportional to cause" (Sterman,
2000: 22).
Indeed, some of the articles in the subject literature, the ones that helped us come up with
our dynamic hypothesis, did look at the problem in a complex and dynamic manner. The paper
that was most influential for us was Blumstein & Rosenfeld's "Explaining Recent Trends in U.S.
Homicide Rates" (1998). In their paper, Blumstein & Rosenfeld supported their story by
providing several time-series data of the major variables and reasoning based on them. As such,
their explanations were very well-founded if evaluated by common sense, but still lacked
9
scientific rigour. Translating the hypothesis inspired by this article into an system dynamics
model, we believe, provided the missing rigour.
Nevertheless, our study is prone to be criticized for many different reasons. Some of the major
limitations of our research are:
Occasional arbitrary choice of values for model parameters. Of course we ran several
sensitivity tests to test the sensitivity of the ability of the model to regenerate the reference
mode to different parameters. The model showed quite sensitive to some parameters. A few
of our assumptions for these sensitive parameters lack the necessary support in real-world
data. These include 'Arms Race Constant’, initial number of ‘Criminals' in a society of
100,000 residents, and the initial number of ‘Guns' camied by those.
Also, a decisive element of our model is the ‘Drug Market’ variable which currently is a
pulse with a constant value of one, starting in 1984 and ending in 1991, representing an
assumption that the volume crack market suddenly grew to a certain level, stayed constant
for 7 years, and then suddenly dropped. This is a questionable assumption. We can reason
that changing this behaviour within reasonable ranges does not change the overall pattem of
behaviour, but still we need to collect more data about the emerging and fading of the crack
market. However, the research shows the linkage between the sudden appearance and
unfavourable social outcomes. Crack cocaine quickly eclipsed other drug profits. That came
along with violence, which later declined in the mid-90s as the market matured, prices fell
sharply and property rights were established (Fryer Jr. et al, 2005).
The way that we modelled the reward side of becoming a criminal, which is changed,
directly and with a simple formulation, through the payoff of the drug market against the
payoff of legitimate available job is simplistic. Moreover, Levitt and Venkatesh (2000) find
that economic factors are unlikely to sufficiently describe involvement in criminal activity.
There is considerable room for improvement in the part of the model that captures people's
decision on whether to become a criminal or not.
An important assumption of our model is the aggregation of all criminals in one stock. This
presumption can easily be the target of criticism since demographic groups of criminals or
potential criminals behave in different ways. For a more detailed explanation of the issue at
hand, we recommend future researchers to divide this single population stock into multiple
age & demographic groups. Blumstein & Rosenfeld (1998) provide a very useful
comparison of the behaviour of these different demographic groups regarding our subject.
One important variable in our model is Normal Homicides, which is constant at 6.61
homicides per year, the starting point of historical data. We then adjust this 'Normal' value to
changes in the endogenous variables than determine Homicides. This ‘Normal’ value is also
the reference value for adjusting investments in the Police force. The assumption that the
value considered as 'Normal' by policymakers is constant is very simplistic. An important
improvement to make our model more realistic is to adjust this perception over time,
possibly using a TREND function.
In formulating Perceived Risk, we assume that potential criminals have a rough idea of the
ratio of Arrests/Criminals, meaning that they adjust their perception based on an estimation
of what percentage of criminals are eventually arrested. This assumption may or may not be
true and needs validation/improvement since some neighbourhoods tend to have a higher
percentage of criminal residents than other.
10
References
Blumstein, Alfred, and Daniel Cork. “Linking Gun Availability to Y outh Gun Violence".” Law
& Contenporary Problems Vol. 59 No.1 Kids, Guns, and Public policy, 1996: 5-24.
Blumstein, Alfred, and Richard Rosenfeld. “Explaining Recent Trends in U.S. Homicide Rates.”
The J ournal of Criminal Law and Criminology Vol. 88 No. 4 Symposium: Why Is Crime
Decreasing?, 1998: 1175-1216.
Decker, Scott H. “Collective and Normative Features on Gang Violence.” Justice Quarterly
Vol.13 No. 2, 1996: 243-264.
Donohue, JohnJ. “Understanding the Time Path of Crime.” The J ournal of Criminal Law and
Criminology Vol. 88 No. 4 Symposiun: Why Is Crime Decreasing?, 1998: 1423-1452.
Donohue, John, and Steven Levitt. “The Impact of Legalized Abortion on Crime.” The Quarterly
Journal of Economics Vol. 116 No. 2, 2001: 379-420.
Farley, Reynolds. “Homicide Trends in the United States.” Demography Vol. 17 No. 2, May
1980: 177-188.
Foote, Christopher, and Christopher Goetz. “Testing Economic Hypotheses with State-Level
Data: A comment on Donohue and Levitt (2001).” Federal Reserve Bank of Boston working
paper 05-15, 2005.
Fox, James. “Trends in Juvenile Violence: A Report to the United States Attomey General on
Current and Future Rates of Juvenile Offending.".” 1996.
Freeman, Richard. “Why Do So Many Young American Men Commit Crimes and What Might
We Do About It?” The Journal of Economic Perspectives Vol. 10 No. 1, 1996: 25-42.
FryerJr.,, Roland G., Paul S. Heaton, Steven D. Levitt, and Kevin M. Murphy. “Measuring the
Impact of Crack Cocaine.” National Bureau of Economic Research Paper Series No. 11318,
2005.
Jr, JohnJ. Dilulio. “How to Deal with the Y outh Crime Wave.” The Weekly Standard,
September 1996: 30.
Levitt, Steven D. “Understanding Why Crime Fell in the 1990s: Four Factors that Explain the
Decline and Six that Do Not.” The Journal of Economic Perspectives Vol. 18 No.1, 2004: 163-
190.
Levitt, Steven D., and Sudhir Alladi Venkatesh. “An Economic Analysis of a Drug-Selling
Gang's Finances.” The Quarterly J ournal of Economics Vol. 115 No. 3, 2000: 755-789.
Marvell, Thomas. “The Impact of Banning Juvenile Gun Possession.” J ournal of Law and.
Economics Vol. 44 No. 2 Part 2 Guns, Crime, and Safety: A Conference Sponsored by the
American Enterprise Institute and the Center for Law,Economics, and Public Policy at Yale Law
School, 2001: 691-713.
Maxfield, Micheal. “Circumstances in Supplementary Homicide Reports: Variety and Validity.”
Criminology Vol. 27 No. 4, 1989: 671-695.
Montgomery, Lori. “Crime Falls in Big Cities as Murders Drop by 8%.” Pittsburgh Post-
Gazette, May 1996.
Neumayer, Eric. “Good Policy Can lower Violent Crime: Evidence from a Cross-National Panel
of Homicide Rates, 1980-1997.” Journal of Peace Research Vol. 40 No. 6, 2003: 619-640.
Ruhm, Christopher. “Are Recessions Good For Y our Health?” Quarterly Journal of Economics
Vol. 115, 2000: 617-650.
11
Saeed, Khalid. “Defining a problem or constructing a reference mode.” Worcester: Worcester
Polytechnic Institute, 1998.
Sterman, John D. Business Dynamics. Systems Thinking and Modeling for a Complex World.
United States: McGraw-Hill, 2000.
Strodtbeck, Fred L., and James F. Short Jr. “An Explanation of Gang Action.” Social Problems
Vol. 12, 1964: 127-140.
The Crime Control Act of 1990. Pub.L. 101-647, 104 Stat. 4789 (1990).
Violent Crime Control & Law Enforcement Act 1994. Pub. L. No. 103-322 108 Stat. 1796
(1994).
12
Appendix A: Stock and Flow Diagram
The structure of our model includes some essential building blocks which are of
Paramount importance to its dynamic behaviour. These blocks are what we are going to
elaborate on in this section.
‘Criminals’ and 'Guns' carried by those criminals are the two decisive stocks in the
model, shown in Figure 4. These stocks bring about inertia and potential policy resistance
to the real-world system. Also, the major loop, R, shown in the causal loop diagram in
Figure 2 including the stock of ‘Guns’ and the ‘Gun per Criminal’ ratio, ,is a sef-
reinforcing vicious entity.
o
)
O
Arrests
om
Confiscation
Criminals
riminalization
Guns per C
O
-
[Arms Race Constant
Figure 4. The two stocks of 'Criminals' and 'G uns' and their
interaction
Guns
Another structural
characteristic of the system is the
delay involved in the effect of
“Homicide per Year’ on ‘Police’
over ‘Hiring’ seen in Figure 5
which represents the time it takes
for decision-makers to perceive
the criticality of the situation, to
invest more in the recruiting and
training of more police to counter
the growing violence in the
streets. Further the effect of
“Homicides per Year on the
productivity of police force is shown. Again, the time perceiving criticality is shown. These
delays pemmits violence to go unchecked for quite some time.
A last important characteristic in the model is the
nature of becoming criminal, called ‘Criminalization’.
This inflow is influenced by the risk perception, which
is the ratio of ‘Arrests’ to ‘Criminals’ and the reward
perception, which is influenced by the exogenous
variable ‘Legal Income Opportunities’. As already
mentioned in the description of the causal loop diagram,
both - risk and reward - is perceived with a delay. The
basic structure can be seen in Figure 6. Fora full list of
equations refer to Appendix B.
Perceived Risk
Effect of Reward
Side on
Criminalization
Figure 6. The Inflow of Criminals is Influenced by Delayed
Perceptions I
Criminalization
Arrests
Homicides per Year
@-
‘olice Productivity in
Confiscation
Police Productivity in
Arrests
Police
Hiring
Retirement
Figure 5. Delayed Reactive Forces
Against Homicides
Appendix B: list of Equations and Documentation
**All Graph functions are shown in the separate section at the end of this Appendix.
* Our model assumes a total population of 100,000 residents. All variable values
should be regarded with this in mind.
Constants
Name Unit Initial
Value
Anms Race Constant gun/year 5.5
Effect of Drug Market on Criminalization criminal/year 10
Minimum Wage dollar/year 15,000
Nonmal Acquisition gun/year 30
Nonmal Criminalization criminal/year 100
Nonmal Guns per Criminal gun/criminal 03
Nonmal Hiring cop/year 10
Normal Homicides person/year 6.61
Normal Legal Income Opportunities dollar/year 7,900
Nonmal Police Productivity in Arrests criminal/(year*cop) 1/3
Nonmal Police Productivity in Confiscation gun/(year* cop) 0.1
Nonmal Violent Criminal Incidents incident/year 1,000
TimeToRetire year 30
Stocks
Name Equation Unit Initial
Value
Criminals | Criminals(t) =Criminals(t — 1) | criminal = criminal + years 1,000
+At * (Criminalization - * (criminals/year -
Arrests) criminals/ year)
Guns Guns (t) =Guns (t — 1) +At * | gun = gun + years * 300
(Acquisition - Confiscation) (guns/year - guns/year)
Police Police (t) =Police(t — 1) +At | cop=cop + years * 300
* (Hiring Retirement) (cops/year - cops/year)
Flows
Name Equation Unit Initial
Value
Acquisition ‘Normal Acquisition’ +'Drug =gun/year + 60
Market’ * (1+4Guns per “unitless’ * (1 +
criminal'/'Nonmal Guns per gun/criminal /
Criminal’) * ‘Arms Race Constant’ | gun/criminal) * gun/year
I
+Criminalziation * ‘Guns per + criminal/year *
criminal! gur/criminal
Arrests Police*'Police Productivity in Criminal/year = cop * 100
Arrests*GRA PH(Criminals,0<<c _| criminal/(year*cop) *
timinals>>,100<<criminals>>) “unitless’
Confiscation GRAPH(Guns,0<<guns>>,20<<y | gun/year = ‘unitless’ * 60
uns>>) * Police* ‘Police cop * guns/(year*cop) +
Productivity in Confiscation’ + criminal/year *
Arrests * 'Guns per criminal’ gun/criminal
Criminalziation | (‘Normal Criminalization' + ‘Drug imi = 100
Market’ * 'Effect of Drug Market | (criminal/year +
on Criminalization') *GRAPH “unitless’ *
(‘Perceived criminal/year) *
Risk’,0<<1/year>>0.02<<l/year> | ‘unitless’ * ‘unitless’
>) * DELAYINF( Effect of
Reward Side on
Criminalization', 10<<years>>,3,1
)
Hiring ‘Normal Hiring’ * DELAY INF( cop/year = cop/year * 10
‘Effect of Homicides on “unitless’
Hiring’, 1<<years>>3,1)
Retirement Police/TimeToRetire cop/year = cop / year 10
Auxiliaries
Name Equation Unit Initial
Value
Drug Market STEP(1,1984.5<<@year>>) - “unitless’ (0)
STEP(1,1991<<@year>>)
Effect of GRAPH(Homicides / ‘Normal “unitless’ = GRAPH( 1
Homicides on Homicides',0,0.1) person/year /
Hiring person/year)
Effect of GRAPH(Homicides / ‘Normal criminal/(year*cop) = 0
Homicides on Homicides',0,0.1, GRAPH(person/year /
Police <<criminals/(year*cop)>>) person/year)
Productivity in
Arrests
Effect of GRAPH(Homicides / ‘Normal cop) = 0
Homicides on Homicides' GRAPH (person/year /
Police ,0,0.1,<<guns/(year*cop) >>) person/year)
Productivity in
Confiscation
Effect of Reward | GRAPH(‘Legal Income ‘unitless’ = 1
Tl
Side on Opportunity’ / ‘Normal Legal GRAPH(dollar/year /
Criminalization | Income Opportumities',0,0.1) dollar/year)
Guns per Guns/Criminals gun/criminal = gun/ 0.3
Criminal criminal
historical GRAPH(TIME, 1984<<@year>>,1 | person/year =GRAPH 6.61
Homicide Rate | <<year>>,<<persons/year>>)
without family
homicides
historical Police | GRAPHCURVE(TIME, cop =GRAPHCURVE 207.9
Force STARITIME, 1<<years>>,
Development <<tops>>)
Homicides ‘Normal Homicides' * (‘Guns per = 6.61
criminal / ‘Normal Guns per person/year *
Criminal’) * (‘Violent Criminal (gun/criminal /
Incidents’ / ‘Normal Violent gun/criminal) *
Criminal Incidents’) (incident/year /
incident/year)
Legal Income 1-'Unemployment within dollar/year = (1 - 7,500
Opportunity Susceptible Communities’) “unitless’) * dollar/year
*'Minimum Wage’
Perceived Risk | DELAYINF(Anests/Criminals, /year = criminal/year / 0.1
0.5<<years>>,6,0.1<<I/year>>) criminal
Police ‘Nommal Police Productivity in criminal/(year*cop) = 13
Productivityin | Anests' +DELAYINF(‘Effect of criminal/(year*cop) +
Arrests Homicides on Police Productivity | criminal/(year*cop)
in Anrests', 1<<years>>,10,0
<<criminals/(year*cop)>>)
Police ‘Normal Police Productivity in gun/(year*cop) = 0.1
Productivityin | Confiscation'+ DELAY INF (‘Effect | gun/(year*cop) +
Confiscation of Homicides on Police gun/(year*cop)
Productivity in Confiscation!,
1<<years>>, 10,0
<<yuns/(year"*cop) >>)
Unemployment | GRAPH(TIME,1995 ‘unitless'=0.5- GRAPH | 0.5
within <<@year>>, 1<<year>>)
Susceptible
Communities
Violent Criminal | ‘Nomal Violent Criminal incident/year = 1,000
Incidents Incidents* GRAPH(Criminals, incident/year *
O<<criminals>>, GRAPH(criminals) *
100<<criminals>>)*GRAPH GRAPH(cop)
(Police,200<<cops>>,25<<cops>>)
Graph Functions
Variable Name Graph
Effect of Homicides on
Hiring Zoom
2
15:
1
Os:
0
i) 1 2 3
X axis Y axis:
Min: Step: Min: Max
QO Oo 05 25.
Effect of Homicides on x oY Input: Homicides/Normal Homicides’ [Zoom
Police Productivity in Arrests R
o1 0 GW
02 0
03 0
04 0 E
o5 0 r 05:
o6 0
a7 0
o8 0 Fy
03 0
1 Q
1005
Unit ¥:— criminals/(y 0 O5 1 15
Points X avis Y axis
Count Gs Min Step: Min: Max:
16 @o 0 01 a1 1
Effect of Homicides on xX oY Input: Homicides/Normal Homicides’ []Zoom
Police Productivity in [Oo |
* o1 0 7
Confiscation 02 0 ame
03 0 “
o4 0
o5 0
o6 0
o7 oO
os 0 r
aa 0.0
1 it)
11000 + 01
Unit'Y: guns/(year 0 05 1 15
Points X axis Y axis
Count Min: Step: Min Max
16 (a) 0 On 01 01
Effect of Reward Side on
Criminalization
historical Homicide Rate
without family homicides
Unemployment within
Susceptible Communities
1
1.986
1/98?
1/988
1,983
1/390
1381
1/992
1,993
1,994
1
Unit'Y;petsons/ye
Points
Count = (ins)
2
x ¥
1 Coa)
VI
Input: ‘Legal Income Opportunity’/Normal [Zoom
2
1
4
a 05 1 15
X avis Y avis
Min: Step Min Max.
0 a4 4 3
Input: TIME Zoom
1.984 1.989 1.994 1.999
X axis Y axis
Min Step: Min Max.
19BAC<@y T<<yean> 3 1
Input: TIME fi
02
1
a
1.995 2.000 2.005
% axis Y axis
Min Step: Min Max.
1995<@y Ix<yeap> 0.1 03
2.004
2.010
Violent Criminal Incidents
GRAPH(Criminals)
Input: Criminals
05.
0 500
X avis
Min: Step:
O<<eriminal 100<<erimit
Input: Police
X avis
Min: Sten
200<<cops 25«<cops>
VII
1.000 1.500
Y axis:
Min: Max:
01 15
Zoom
Appendix C: Detailed Model Analysis
Structure Behaviour Tests
Going back to the Dynamic Hypothesis section, we remember that we hypothesized
that the major dynamics in our model comes from an ‘arms race’ in criminals. To test this
hypothesis, we eliminate this dynamic by setting ‘Arms Race Constant’ to zero and we
simulate the model. Without an arms race there would still be a slight increase in homicides
along with the outbreak of the crack cocaine market. However, the peak would be much
lower if it was not for the climate of increasing threat of violence in the streets. Of course,
in that case homicide rate would not go as low as they actually did because there would not
be an equally high feeling of urgency to invest in having more cops. That is why we would
also have a higher trough in homicide rate at the end of the decade if it was not for the arms
race. With this test, we can be confident that the main pattem of behaviour in the model is
being produced due to endogenous dynamic, and not because of the exogenous inputs fed
into it.
Cutting the feedback from “Homicides per Year’ to all reactive policies (Police and
Productivity, B3-B6), the homicide rate would stay high. Adding the effect of ‘Homicides
per Year’, i.e. cutting loops B4 & B6, shows that ‘Hiring’ has a big impact on the overall
pattem. The other loops show less important influence on the simulated pattem. For further
details and proof, please see the end of this Appendix.
Extreme condition tests
a) Playing with Cops
One of our assumptions in the model is an initial number police. To test the plausibility
of our model structure, we conducted an extreme condition test on this particular value.
Firstly, we wanted to see what behaviour the model would generate in an initial absence.
Secondly, we run the model with an initial excessively high police force.
As can be expected a
fast increasing homicide
rate results from the
absence of cops.
However, eventually the
homicide rate should be
heading down because the
as homicides rise more
policeman will be
Figure 7. Playing with Cops: Left Side: Homicide Rate | Right Side: Police recruited, which leads to
ae a ora et ilabemct ae © ne aes. Also, if there
are too many policemen,
VIII
the homicide rate has to decline. Towards the end of the time horizon the homicide rate
starts to rise again. This can be due to the fact that the presence of too many policemen
leads to alow homicide rate which negatively affects the hiring of police force. That in tum
pushes the homicides to a higher level. The simulation generates behaviour according to
our expectations, shown in Figure 7.
b) Playing with Guns
Another assumption in the model is an initial number of ‘Guns’ by ‘Criminals’, equal to
300 guns, implying that to begin with, thirty percent of the ‘Criminals’ possesses guns. Our
Firstly, doubling this
number, meaning — that
initially more than the
half of the criminals is in
possession of a gun, leads
to a very high initial
homicide rate.
Nevertheless, this high
level of homicide leads to
hiring more and more Figure 8. Playing with Outlaws with 'Gun' adjustment: Left Side: Homicides
cops, which results in an Per Year | Right Side: Police Stock - Legend: green - base run (1000
PS; l criminals), red - absence of criminals (1 criminal), blue - a lot of criminals
eventual OWEr (2000 criminals)
equilibrium for homicide
rate. Secondly, with no initial guns there would be no homicides. As more people become
criminals they also carry guns with themselves, and therefore, the homicide rate will not
remain zero. The simulated pattem of these extreme conditions reflects our expectations.
c) Playing with outlaws
A further presumption is the initial value of 1000 for presence of criminals, who are
carrying guns and provoking violent incidents. In the following, we will challenge the
model into both extreme conditions, firstly the initial near-absence of criminals! and then
their excessive initial presence.
Figure shows the simulated pattem of the two extreme conditions as well as the base
run. The results are counterintuitive and caused by model specifics. For the first case, the
near-absence of criminals, we expected an absence of violent incidents leading to almost no
homicides. However, the behaviour shows an excessive increase in homicides. Moreover
the latter case does not meet our expectations. The excessive presence of criminals should
lead to a high initial value in homicides which decreases as the number of policemen is
increasing. These anomalies are in fact logical, since we need to manipulate the initial
number of guns along with the initial number of criminals. These results from an
1 The total absence of criminals is not possible because of the ratio ‘Guns per Criminals’ which would lead to
adivision by zero which is mathematically not defined.
Ix
assumption that few armed criminals are more dangerous than many unarmed criminals. An
adaptation of the ratio of ‘Gun per Criminal’ is going to result in more realistic behaviour.
Therefore, in our next experiment we change also the initial number of guns so that every
other criminal possesses a gun in both cases at the starting point of the simulation. The
results of this simulation are shown in Figure 9. Indeed, the behaviour meets our
expectation. A higher
initial mumber of
ciminals with a same
vaio of ‘Guns per
Criminal’ implies a
higher homicide rate.
This leads to a higher
police force amesting
criminals. The effect of
the guns rece is still
taking place but is
therefore lower than in Figure 9. Playing with Outlaws: Left Side: Homicides per Y ear | Right Side:
Police Stock - Legend: green - base run (1000 criminals), red - absence of
the base run because of criminals (1 criminal), blue - hords of criminals (2000 criminals)
the already strong police.
The higher than normal homicide rate leads to an accelerated hiring rate which - with a
delay - eventually pulls down the homicide rate. In the case of the absence of criminals, the
homicide rate is down, but as the drug market shock appears, the stock of criminals start to
grow, the arms race takes place and the homicide rate starts to grow. The homicide rate
stabilizes eventually because of the presence of police force.
Sensitivity tests
In this section, we are going to study the sensitivity of the behaviour of the model
towards changes in three parameters: ‘Normal Police Productivity in Confiscation’, ‘Arms
Race Constant’ and ‘Unemployment within Susceptible Commumities’. The first two were
identified as important variables in the Structure-Behaviour-Test.
a) Normal Police Productivity in Confiscation.
For this experiment, we tested the behaviour of the model against 10% changes in the
value of ‘Normal Police Productivity in Confiscation’ in both directions. We expect
homicides to rise with less productivity and to go down with more productive police
officers. The model behaves logically and according to expectations. It should be noted that
the model is quite sensitive to changes in this parameter.
b) Ans Race Constant
The ‘Arms Race Constant’ is a parameter that we use to switch the ams race within
criminal communities on and off and to set the strength of this vicious cycle. We observe
the model’s behaviour with 50% strengthening and 50% weakening of this effect.
Naturally, we should have more
homicides with a stronger arms race and vice
versa. The following figure shows that the
model stands this test well. Figure shows
that our expectations are right A high
sensitivity can be inferred.
c) Unenployment within Susceptible
Communities
We assumed an initial unemployment of
50% among the major players in the system.
that we are studying, who are youth living in
poor neighbourhoods. In this section, we are
going to mm simulations to examine the
reaction of our structure to improvement and
worsening in legal employment opportunities
available to these people.
Homicides per 100.000 Resients
Figure 10. Sensitivity of Arms Race Constant: green -
base run, red - 50% (2.75 guns/year), blue - 150% (7.75
guns/year)
The behaviour is quite sensitive to change in the unemployment. Less unemployment
leads to fewer homicides. It is in fact logical.
Kirst, the motivation is lower to become a
criminal since the probability of eaming legal money is higher, and, secondly, people have
less time to do no good. An increase in unemployment consequently increases homicides.
Tn conclusion, the model reproduces our expectations.
Details of Structure-behaviour Tests
i,
As already stated in the Model Analysis
Cutting out the arms race loop R1
section, cutting out the major reinforcing
feedback loop R1, representing the ‘arms race’, removes the capability of the model to
reproduce the reference mode, shown in Figure 11.
XI
@ BaeRn
a " @ Without Ans Race
Homicides per 100.000 Residents
Year
Figure 11. Structure Behaviour Test: Cutting Arms Race
ii. Cutting out All Reactive Adjustments of Police B3, B4, BS, B6
If we cut the feedbacks from Homicides to Hiring, to Police Productivity in Arrests,
and Police Productivity in Confiscation, the following is the behavior that we will get.
H
3
2
3 , @ BaseRun
g @ Without Reactive
7 Policies
3 @ Historical Data
=
2
1.980 7985 7,990 185 2,00 2,008 210
Year
Figure 12. Structure-Behaviour Test: Cutting Reactive Policies
As can be seen in Figure 12, Homicides would start to fall naturally around 1991 when.
the crack market matures, but it falls at a very slow rate.
iii. | Adding the effect of Homicides on Hiring, B3& BS
XII
If we only add the feedback from Homicides to Hiring, we get the following behavior.
persons/year
@ BaseRun
@ Without Effect on
Productivity
@ Historical Data
Homicides per 100,000 Residents
5
1,980 1.085, 1,990 1,995 2,000 2,005, 2.010
Year
Figure 13. Structure-Behaviour Test: Cutting Effect of Homicide on Productivity B4 and B6
This means that hiring more and more police, without improved productivity, makes a
big difference, as can be seen in Figure 13. Still, we have a quite large discrepancy with the
historical behavior.
iv. Adding the Effect of Homicides on Police Productivity in Arrests B4
If investment is made to improve Police Productivity Arrests, along with the previous
policy of increased Hiring the behavior that we get is quite close to the base run.
@ BaseRun
Without Effect on.
© productivity in
Confiscation
@ Historical Data
Homicides per 100.000 Residents
Year
Figure 14. Structure-Behaviour Test: Without Effect of Homicides on Productivity in Confiscation B6
XIII
By adding this effect, we get closer to the reference mode. This can be inferred from
Figure 14. Right now we only need to add the final Effect of Homicides on Police
Productivity in Confiscation to have all feedback loops running and obtain the green line.
v. Cutting out the feedback involving Perceived Risk, B1 & B2
a
@ Base Run
e Without the loops
involving Perceived
Risk
s.
Homicides peryear per 100.000 residents in’
pessons/year
1,980 1.985 1,990 1,995 2,000 2,005
Figure 15. Structure Behaviour Test: Cutting the loops involving Perceived Risk
Figure 15 shows the simulated pattem without perceiving risk as a balancing loop for
the ‘Criminal’ stock. The important change can be seen at the end of the simulation. More
homicides will indicate more policemen to be hired, this leads in tum to more arrests. Since
there is no perceived risk resulting from these arrests, more criminalization takes place as
otherwise would have been. Consequently, homicide rate does not drop as low as
otherwise.
XIV
Appendix D: Model Boundaries
* Our model assumes a total population of 100,000 residents. All variable values should be regarded with this in mind.
Endogenous Exogenous Exduded
Variable Name Description Variable Name Description
Homicides Number of Homicides per Nomml Homicides Starting & Reference Value for ‘Abortion’ Hypothesis
Year Homicides in the model
Criminals Severity of Punishment for
Violent Crimes
Criminalization Rate at which new people Nonmal Criminalization | Equilibrium Value for Effect of Education
become Criminals Criminalization.
Anrests Effect of Culture & Social
Upbingi
Perceived Risk ~in becoming a criminal Family-Related Homicides
Guns Illegal guns carried by Effect of Demographics
Criminals and different age cohorts
Acquisition ~of illegal guns by Criminals Nonmal Acquisition Equilibrium Value for Acquisition | Effect of Criminals’
Experience
Confiscation
Guns per Criminal | Percentage of Criminals that Anns Race Constant | A ‘Switch! to tum on/off the effect
carry Guns of R1 loop
Violent Criminal __ All violent criminal situations
Incidents likely to lead to murder (Drug
fights, robberies, etc.)
Police Number of Police
VII
Hiring Nonmal Hiring Equilibrium Value for Hiring
Retirement Time to Retire
Police Productivity in | Number of Arrests per Police Nomnal Police Equilibrium Value for ~
Arrests perYear Productivity in Arrests
Police Productivity in | Number of Confiscations per Nomnl Police Equilibrium Value for ~
Confiscation Police per Y ear Productivity in
Confiscation.
Effect of Homicides | (further Investment is implicit)
on Police
Productivity in
Arrests
Effect of Homicides | (further Investment is implicit)
on Police
Productivity in
Confiscation.
Legal Income Yearly legal income Unemployment within.
Opportunity potentially available to people — Susceptible Comnumities
susceptible to criminalization
Minimum Wage Anestimate of income available
to generally low-skill street kids
once they get ajob
Effect of Reward | Effect of Legal Income Drug Market A ‘Shock’ (modeled as a pulse),
Side on Opportunity vs. Potential representing the rise and eventual
Criminalization Profits from Drug Market on maturation of the market for crack
Gairelcation
