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Unformatted text preview: LAW ENFORCEMENT ECONOMICS Christian R. Reinarz Brigham Young University
Provo UT, 84604
April 2009 Law Enforcement Economics
Christian R. Reinarz BYU Econometrics 388
April 2009 ABSTRACT This paper explores the inner workings of violent crime and what variables play the most 9 \[
inﬂuential role in determining its outcome. This is done by extracting data from both the Bureau
of Labor and Statistics and the Bureau of Justice Statistics as it relates to unmlgynent, annual,
polici wage, number of police ofﬁcers employed, population size and nonviolent crime rate. " Q
There have been similar studies such as this; perhaps most notably is Steven D. Levitt ﬁom the University of Chicago. Levitt performed a study entitled, “Understanding Why Crime Fell in the
I 990s: Four Factors that Explain the Decline and Six that Do Not. ” The ﬁndings included in
Levitt’s research offer additional credence to the ﬁndings included in this paper. A dissimilar
ﬁnding however, and most controversial, was that the legalization of abortion had overall the
most signiﬁcant effect in reducing crime. Instead of entering the scorching debate of abortion,
this paper focuses on the before mentioned variables. Our results from running a regression
using OLS show the most signiﬁcant of these variables appear to be population size (a positive
effect) and annual police wage (a negative effect). The lesser signiﬁcant results show
unemployment having a positive effect on violent crime while size of the police force has a
negative effect. Although these results are not ground breaking, they do provide further insight
into what policies might be implemented toward the reduction of violent crime. F,H,‘_.w___._7nu n . INTRODUCTION Whether planning a future vacation or making a quick trip to the grocery store in the
middle of the night, the thought lurks in the back of nearly everyone’s mind whether a Violent
crime will happen to them. This fear of falling prey to a criminal inﬂuences daily decisions and
thus dictates one’s actions. Because violent crime determines so many subconscious decisions,
this paper explores important factors inﬂuencing the amount of Violent crime in a particular area.
This is done by evaluating how population, unemployment, number of police ofﬁcers, annual
police wages, and nonviolent crime rates inﬂuence the overall total Violent crime. Although
these do not encompass all factors playing into total violent crime, it does provide a simpliﬁed ﬁrst step in understanding the most basic inﬂuences. The importance of understanding the basic inﬂuences stems from the fact it was not long
ago when the subject of increasing crime rates was the subject of every politician’s conversation.
This heated topic resulted from the inability to curtail the rate of crime while few solutions were
being conjured. Due to the almost crisis like rate in crime prior to the 1990’s, experts forecasted
an exponential growth in crime by the mid—1990’s. These forecasts were the cause of intense
anxiety levels while policymakers worked vigorously to ﬁnd solutions. It was later learned that
any solutions they found would be unnecessary as an unexpected change occurred. Without
warning, crime rates suddenly plunged. This declining trend continued for several years While
lawmakers mistakenly attributed the decline to better policing strategies, stricter gun control
laws, growmg capital punishment and so forth. It was not until Steven D. Levitt, an economist
ﬁom the University of Chicago, came along. Levitt performed a study titled, “Understanding Why Crime Fell in the 1990s: Four Factors that Explain the Decline and Six that Do Not. ” In that studyﬂt’tgoncluded the four real reasons for the sudden drop in crime rates which were
included; increases in the number of police ofﬁcers, rising prison population, receding crack
epidemic, and the legalization of abortion (Levitt, 2004). Legalization of abortion had the most
signiﬁcant effect over the four mentioned simply for the fact that the number of unwanted
babies, or babies born into poverty were severely reduced. Despite Levitt’s ﬁndings igniting an
explosion of controversy, the subject of crime remains interesting when attempting to explain its
variables. The reader should consider the opinions and Views of this paper somewhat partial to the
fact the author has several years of law enforcement experience having served on the Phoenix
SWAT team for ﬁve years. This allowed a ﬁrsthand experience and observation of the data presented. While there is various research noted in the reading, the author will also include information gathered through personal experience adding ﬂavor to the already spicy subject. This paper ﬁrst offers a description of the data provided while discussing theoretical
foundations and variables, including both exogenous and endogenous, as well as a description of
the model. Following the model , the test assumptions and estimations will be provided. There,
information is presented as to the type of distribution assumed, along with issues of
heterorskedasticity and endogeneity being addressed. The next section will interpret and analyze the results, while the final section will provide a summary and conclusion of the results. Description of the Data When considering violent crime in a particular region one must consider what factors inﬂuence such a statistic. Some of these factors could include education, unemﬂgyment, family
k.“ background, presence and size of drug trafﬁcking, population size, size oithgpolice—force, and so on. Undoubtedly the variables just listed play some role in the amount of violent criine. What
we want to know is how much of an inﬂuence do these play. In order to answer this question
one must retrieve adequate data to be analyzed. Herein lays the dilemma; how to obtain
education and family background information on every person, or how to measure the size and
presence of drug trafﬁcking? Instead the variables chosen and most easily measured were total
violent crime, population size, size of the police force, police wages, and nonviolent crime
rate. This information was obtained by using data published through the Bureau of Justice
Statistics (BJS) and the Bureau of Labor Statistics (BLS). From the BJ S, data was collected on
the total violent crime, population size, violent crime rate, and nonviolent crime rate. In this
case, the term rate is deﬁned as per 1000 people. At the BLS website data was obtained on the
unemployment rate, size of the police force, and police wages. Data on these areas were
collected on all 51 states of the United States and put into a table. This table was then input into
STATA resulting in the calculations presented in the DESCRIPTION OF THE MODEL section. These tables are made available in the appendix to this paper (Table l). Description of the Model The model used for this research is the Basic Multiple Linear Regression Model which
takes on the form y: = [99 —1— Six, + 3236‘ —§— —‘:— ,8ka :— at. In this model the X’s represent
exogenous variables, or explanatory variables, while Y represents the endogenous variable. The
difference between endogenous and exogenous variables is that endogenous variables are those a
model attempts to explain and is determined by the model’s solution. The exogenous variables are those the model takes as given and are independent of the model’s solution. The term Bu represents the intercept while E1 measures the slope, or rather, the change in y with respect to 3:1,
holding any other factors constant. This process would repeat itself for as many E’s you have in
the equation. The term labeled a, is called the error term. This term contains all the other factors that affect y with exception to the ones listed in the equation. A key assumption for this model is the conditional expectation that E£ulx1,.x3, ..., sagC} = G. This requires that all factors in the error term be uncorrelated with the explanatory variables. With our model we will run an OLS regression of y on all the fa. OLS is the abbreviation for Ordinary Least Squares. The purpose of the OLS is to choose estimates to minimize the sum of the squared residuals. Now that the basics have been laid, it is time to present the model. Because the objective
is an attempt to explain violent crime that will be the endogenous variable, while the factors that
explain and are exogenous to the model are population, unemployment, number of police
ofﬁcers, annual wage of police ofﬁcers, and nonviolent crime rate. Putting these together the equation becomes: violentcritot = Bo —:— 511002;) + Ezunemgo :— ngF'af'pal —%— ﬁépwage ‘:— Bsnonv + 5:. Once the equation is determined, the data collected is entered into STATA Where an OLS regression is performed yielding the following results: df Number of obs F( 5, 45)
Model 5.2822e+10 5 1.0564e+10 Prob > F
Residual 2.2859e+09 45 50796848.3 R—squared '
Adj R—squared = 0.9539
5.5108e+10 50 1.1022e+09 Root MSE = 7127.2 violentcri~l Coef. Std. Err. t P>ltl [95% Conf. Interval] population .0056147 .0004055 13.85 (9.0003 .0047979 .0064315 unemplymen~e '676.2869 586.2142 1.15 0.255 —504.4091 1856.983 ofpolice —.2572499 .1841386 —1.40 0.169 —.6281241 .1136243
annualmean~e —.2219156 .119876 —1.85 (%¥JEZ::> .4633582 .019527
nonviolen~te —.7324133 1.420238 —0.52 .609 —3.59292 2.128094 _cons 4267.278 6225.565 0.69 0.497 —8271.653 16806.21 The number of observations in this data set is n = 51, R2 = .9585, and the adjusted sz= .9539. Variable population 5743425 6458932 522830 3.66e+07
crimerate 51 3624.908 946.1304 1821.5 6328.2
laborforce 51 3008733 3351411 290126 1.85e+07
unemplymen~e 51 7.843137 1.909686 4.8 12.5
ofpolice 51 12269.61 13899.95 990 60920 46724.9 9824.605 72510
51 25951.61 33198.68 772 191025
51 1695.176 1795.003 123 9013
51 322.4706 400.682 12 2260
185676 210766.4 1108660 annualmean~e
violentcri~l
rape murders
nonviolen~me violentcri~e 427.202 230.013 118 1414.3
nonviolen~te 51 3197.706 773.2563 1652.3 4913.9
totalcrime~e 51 3624.908 946.1304 1821.5 6328.2 To begin with, observe the slope intercept is 4267.28. This means if the explanatory
variables of pop, unemp, #oﬁrol, pwage, and nonv are set to = zero, then the predicted number of
violent crimes would be approximately 4267. It is ok to disregard this number due to the
unlikely nature that there is zero of any of the explanatory variables all at once. Rather it is
important to observe the numerical values next to the explanatory variables. First, .006p0p. Because this is a positive value, it is then inferred there is a positive relation between population size and violent crime. Holding all else constant, for every one thousand unit increase in
population results in 6 additional violent crimes. This tells us that as population increases so
does Violent crime but in very small increments. However this may be alerting to cities such as
Gilbert Arizona who experienced a population growth of 100,000 in just 3 years. This means
their violent crimes increased by 600! It is also important to note the pValue which determines
whether this statistic is signiﬁcant or not. Because the pvalue in this case is less than .05, it is
therefore signiﬁcant. Using this same logic as we evaluate the pValue column, the only other
possibly signiﬁcant statistic is annual police wage at .071. Though it is barely above .05, it is
still very close and to keep this paper interesting we will go ahead and say it is signiﬁcant. Next is 676.3unemp and just as population had a positive relationship, so does unemployment, though on a much larger scale. For every one unit increase in the unemployment
rate there is an additional 676 violent crimes being committed. Attention employers, beware C)
before you decide to hand out pink slips! This means the local unemployment rate plays a serious role in the amount of local violent crime, but since the pvalue is far above the .05 level it is not therefore statistically signiﬁcant and can be disregarded. Next is .257#0]pol. Here we have a negative relationship between the number of police employed and violent crime. This is
pretty intuitive already, but just for clarity we will say it anyway. The more police ofﬁcers there
are, the less violent crime there will be. For every one thousand unit increase in the number of
police, there will be a decrease in Violent crime by 257. Again though, because of the pvalue it is not signiﬁcant. Our next variable .221pwage also has a negative relationship with violent crime, and as discussed before its pvalue lies just outside .05, but still we will say it is
signiﬁcant. This would be useful for city mayors when contemplating pay increases in law enforcement ofﬁcers. For every $1000 increase in annual wage, there will be 221 fewer Violent crimes. Our last variable, .732n0nv shoes a negative relationship between nonviolent crime and violent crime. This would be difﬁcult to explain in terms of why violent crime goes down as
nonviolent crime goes up, but we could assume Violent crime and nonviolent crime are related.
Under this assumption, it might be explained that nonviolent crime may be getting easier to
commit and therefore the use of violence is unnecessary. Since the pvalue in this case is also
above the .05 level, it is insigniﬁcant and no ﬁarther explanation is needed. The most exciting news about our results is the fact that the R3 value is so high. This term allows us to test a group of variables to see it if is important for explaining the amount of
Violent crime. If this ﬁgure was small (closer to zero), this would tell us our explanatory variables need to be han ' slips because they are doing a very poor job in explaining Violent crime. However our results show fi‘2 = .9539, extremely close to 1. This either means l’
the researcher was achh and should get an A on this paper, or 9‘3
that the randomly selected explanatory variables are doing an amazing job in explaining violent
crime and should get a raise. Though the results are pretty convincing we must consider some effects that might distort
this information. One is autocorrelation. Autocorrelation can affect the results of the data if it is _ m time series or panel data. It can affect the results when there is correlation between the errors
from different time periods. Because we did not use time series or panel data, this affﬂoes
W. Another consideration is homoskedasticity (constant variance) vs. heteroskedasticity
(not constant variance). An example of this may be comparing uneducated individuals wages
verstﬁeducated individuals wages. Typically those with lesser education will experience smaller variances in wages while those who are educated will have larger variances. To test for this in our model, we used both the hettest and the estat hettest while using an Fstatistic (Breusch
W \‘w a" WV 3"
WV
L
fl 1 Pagan). In both tests our hypothesis was that our model was homoskedastic with a signiﬁcance level of .05. In the hettest our results returned Breusch—Pagan / CookWeisberg test for heteroskedasticity
Ho: Constant variance _
Variables: fitted values of violentcrimetotal chi2(1)
Prob > chi2 2.40
0.1213 Essentially, this means we do not reject the hypothesis at the .05 level. To conﬁrm these ﬁndings we conducted the second test listed and > imerate, fstat Breusch—Pagan / Cook—Weisberg test for heteroskedasticity
H0: Constant variance
variables: population unemplymentrate ofpolice annualmeanwage nonviolentcrimerate
F(5 , 45) = 0.85
Prob > F = 0.5189 There Just as suspected this conﬁrms the ﬁndings in the ﬁrst test that our sample estimate is homoskedastic or has constant variance. Another'important feature we must determine is the distributional form. By doing this
we are able to determine the skewness and kurtosis. The difference between the two is that
skewness is a measure of how far a distribution is from being symmetric, while kurtosis is a measure of the thickness of the tails. Our hypothesis then would be that this is a normal distribution with an a = 0.05. Our ﬁndings show: (9
Skewness/Kurtosis tests for Normality
—— joi nt
Variable Obs Pr(skewness) PrCKurtosis) adj chi2(2) Prob>chi2
e 51 0.820 0.562 0.39 0.8210 ————' “d 7 —— One last important consideration is endogeneity. This occurs when an endogenous explanatory variable exists. Essentially what this is saying is that we chose our exogenous variables that we think explain the endogenous variable, but does our endogenous variable explain any of the exogenous ones. The answer to this question in regards to our model is yes,
endogeneity does exist. One way to know for sure is by performing the hausman test. Without
performing this test we don’t know the full extent of endogeneity. In our case the number of
police ofﬁcers explains violent crime and vice versa. Once we identiﬁed this disruption, we
need to create an instrumental variable that explains violent crime only through the number of
police ofﬁcers. One idea for an instrumental variable is municipal budgets. The numberof
police ofﬁcers employed in a city is in large part determined by the city’s budget. Once this
instrumental variable is created and the proper data obtained, we then perform the hausman test
to determine the affects of endogeneity. However, due to the limited data provided and the time
constraints given this test could not be performed. It is important to note then that these considerations are taken into account when interpreting the model. 10 Summary and Conclusions It can be concluded ﬁom the model that while population, police wages, number of police
employed, and the number of nonviolent crimes play a role in the total number of Violent crime,
population and police wages play probably the most signiﬁcant considered role in the number of
violent crimes that occur within in a particular area. So how applicable is this model to the real
world? The more ofﬁcers on the street, the more arrests were made, which results in less violent
crime committed. To provide an incentive that would attract more ofﬁcers, a department would
to offer higher salaries and/or more beneﬁts. In the Phoenix Metropolitan Area, there were
numerous suburban police agencies competing one with another for ofﬁcers as population
growth soared. One‘way to attract these ofﬁcers was to offer higher wages. In the suburban
areas with the highest wages, based on these results, would have experienced some decrease in
their violent crime. Today, greater challenges exist as ﬁnancial crisis plagues this country. Consequently we
can see from the news media an increase in Violent stories matriculating through the nation. If
one were a policy maker within a particular state considering ways to reduce the Violent crime
rate, the information provided in this paper would be useful. Our most signiﬁcant option would be to try to increase police wages and control population growth. 11 BIBLIOGRAPHY “Macroeconomics” 2007 Sixth Edition by Gregory Mankiw “Introducton Econometrics, A Modern Approach ” 2006 Fourth Edition, Jeffrey M.
Wooldridge Bureau Of Justice Statisitics http://wwwojpnsdoj.gov/bjs/welcome.html
Bureau Of Labor Statistics ht_tp://WWW.bls.gov/ Journal of Economic Perspectives, “Understanding Why Crime Fell in the
19905: Four Factors that Explain the Decline and Six that Do Not”, Steven D. Levitt Crime—Volume 18, Number 1——Winter 2004 12 Christian Reinarz Friday April 10 14:53:11 2009 Page 1 ___/ / /___/ / /___
Statistics/Data Analysis / User: Law Enforcement Economics£space —4)
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