Regression analysis. (economic)
APPLIED ECONOMETRICS I – ECONOMICS 1150
From Poorhouse to Jailhouse: A Study of Violence in Society
Anne Davis, Andrea Kostura
5/10/2010
This paper analyzes the effect of different socioeconomic variables on violent crime. Using data on 2,106 cities in the United States, we regress violent crime rates per 100,000 people on different measures of poverty, education, and diversity. The results indicate that an increase in poverty and diversity is positively correlated with rising violent crime rates. Education is also significant in explaining the level of violent crime; we find that as the number of people with a high school degree or less increases, violent crime is expected to increase. Therefore, we believe that policy that encourages further education should be effective in reducing violent crime. In this paper, we state that something is in the public interest if the benefits of an activity are greater than the cost. Since there are considerable costs associated with violent crime, we believe it would be in the public interest to support education because it would benefit society as a whole.
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Introduction
The United States of America has one of the highest violent crime rates of the
industrialized world; according to the 2008 Crime Clock of the Federal Bureau of
Investigation one violent crime is committed every 22.8 seconds. The murder rate in
America is more than three times higher than in most of Europe. Not all of this can be
explained by guns, as the murder rate in New York City has consistently been at least 10
times higher than that of London for the past 200 years and private handgun ownership
was not fully prohibited in the United Kingdom until the passage of the Firearms Act of
1997 (Wilson and Petersilia 200?, 540-541). Crime is clearly a significant problem in the
United States that drains the resources of the government at all levels and plagues many
Americans. As such, it is an issue that demands national attention on a variety of levels.
However, in order to present solutions to this pressing problem, a more thorough
understanding of the causes and impacts of crime is needed. By researching the effects
that different variables have on violent crime rates, policy makers will be better equipped to
formulate effective programs to deal with and prevent violent crime. Previous studies,
which will be discussed in the literature review, have shown that there is a significant
relationship between violent crime and socioeconomic factors such as education level,
poverty, and diversity. Although we include other variables, in this study we are primarily
interested in the effect of poverty and education on violent crime. Messner and Tardiff find
that the percentage of poor people in a city is highly positively correlated with crime rates
(1986, 297; 306-308). Lochner finds that more educated males commit fewer crimes, on
average (2004, 1-2). These, like other previous studies, look at the issues of education
and poverty separately. We believe that education and poverty are jointly significant in
explaining violent crime, and therefore, include both in our model. Our study seeks to
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address a gap in the literature that treats education and poverty as two separate issues
when explaining crime. The impact of education and increased opportunities are of
fundamental importance in order to break the cycle of poverty, and help reduce crime.
Encarta broadly defines public interest as something that is to “the general benefit
of the public.” Of course there will be monetary costs associated with any policy, but
following traditional economic theory, if the benefits are greater than the costs, then we
believe the policy would be in the public interest. The costs of violent crime are
substantial. Miller, Cohen, and Rossman estimate the costs of violent crime in 1987 as
follows: $10 billion in potential health-related costs, $23 billion in lost productivity, and
almost $145 billion in reduced quality of life. These are monumental costs so it should be
in the public’s interest to decrease violent crime (1996, 186). Other costs that cannot be
quantified such as feelings of security, and a sense of community are of utmost importance
as well.
Review of Literature and Economic Theory
Most economic theory looks at crime through a lens of rational cost-benefit
decision-making. This idea posits that the propensity to commit crime is a matter of utility,
how much satisfaction an individual derives from criminal activity as compared with other
things, like leisure time, and time spent in productive activities (Witte and Witt 2000, 4).
This has spurred a large body of literature related to the interaction between incentives
and crime. The goal of policy should be to increase incentives, or following economic
theory, increase the costs of crime and increase the benefits of work and leisure activities.
The socioeconomics theory of crime plays a critical role in estimating the likelihood of
committing crime by studying what factors contribute to a susceptibility to commit crime.
Many theorists, such as Lochner, Short, Wilson, and Witt and Witte, agree that levels of
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education and economic status are two of the most important determinants of crime.
When the economy is doing poorly, crime rates increase. There is a large body of
literature that studies the relationship between criminal behavior and poverty. It has been
shown that crime rates are higher for those in the lowest socioeconomic groups of society;
this is known as a sub-culture of poverty (Forst 1993, 90; 103). A study by Messner and
Tardiff found that the percent of poor people in a given society is highly correlated with
crime rates (1986, 297; 306-308). Likewise, many other studies attest to the significance
of poverty in determining crime rates (Williams, 1984; Wilson, 1987; Kirk, 2008). At the
same time, poverty is correlated with other socioeconomic variables, such as race and
family structure (Short 1997, 51). Poverty can be measured in many ways; our study
includes several different measures of poverty including median home value, percentage
of households on public assistance, and percentage of families living below the poverty
line. This leads to hypothesis one: as median home value increases, violent crime is
predicted to decrease. Hypothesis two: as the percentage of households on public
assistance and the percentage of the population living below the poverty line increase,
violent crime is expected to increase. A related measure of the performance of the
economy would be the number of homes that are vacant. In a study done by the Federal
Reserve Bank of Cleveland, it is shown that home abandonment and foreclosure
contribute to a rise in crime rates (The Federal Reserve Bank of Cleveland 2008, 2-4).
Vacant properties contribute a potential location for crime, in addition to being linked to
poverty or job loss. Hypothesis three: as the ratio of vacant housing units to occupied
housing units increases, it is expected that violent crime will increase. This variable was
used to assess the potential impact that vacant houses have in a community by looking at
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the density of vacancy as compared with owner occupied homes. The ratio was converted
to a percent for easier measurement and interpretation.
The final area of importance for this study that theorists link with crime is both social
and economic: education. More poorly educated people are often lower skilled workers,
and tend to be poorer; in data from 1993, it can be seen that more than 67 percent of men
serving time in jail or prison did not have a high school education (Lochner 2004, 2). This
relates back to economic cost-benefit theory, where time spent in other activities yields
lower utility for a less educated person than for a more educated person. Education
increases human capital, which increases the opportunity cost of crime and the potential
market wages (Lochner and Moretti 2004, 155-189; Witte and Witt 2001, 4). Lochner finds
that older, more educated males commit fewer crimes, on average (2004, 1-2). So,
hypothesis four: an increase in people with a high school degree or less, results in an
increase in violent crime rates.
In an effort to avoid omitted variable bias, several other variables were included that
were not of primary interest. The following variables, such as population size, and ethnic
diversity have been shown to be important in many studies, but are hard to change
effectively with policy. People in rural areas and small towns are, on average, poorer than
those residing in the cities (Forst 1993, 32; Short 1997, 104-105). However, as population
increases, it is expected that violent crime will increase also even though poverty is
positively correlated with crime. In addition, stability of society is another common variable
included in crime research. Shihadeh and Steffensmeier find that the percentage of
families headed by single mothers is positively correlated with an increase in violent crime
(1994, 732-734; 737-740). This same result is found by Land, McCall, and Cohen (1990).
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Undoubtedly, this variable is tied to poverty, which explains some of its significance within
the model.
Another subgroup that has been identified in work by Forst, and Short, is racial
groups, specifically blacks. Part of this is most certainly related to the reality that minority
groups tend to be economically marginalized and members of the poorest strata of society
(Short 1997, 51; Land, McCall and Cohen 1990, 922-963). However, it can be seen that
other minority groups, such as Native Americans, Mexicans, Vietnamese and Puerto
Ricans are all, on average, poorer than blacks, but have substantially lower violent crime
rates (Forst 1993, 99; 105-110). Many theorize that this is related to a “subculture of
violence,” that is seen more in black culture and is translated into racial patterns of violent
crime (Forst 1993, 104-110). As the percentage of blacks in a society increases, it is
predicted that violent crime will also increase. Studies show that ethnic diversity within
society is also predicted to increase crime rates because of the different ethnic
subcultures, lack of assimilation, and ethnic friction (Short 1997, 50). So, as the level of
diversity in a society increases, violent crime is expected to increase.
Description of Econometric Model
This study uses data on socioeconomic indicators from 2,106 cities to estimate their
effect on violent crime rates in 2000. Violent crime is defined as murder, rape, assault and
robbery. The data came from the Offenses Known to the Police Dataset from the Uniform
Crime Reporting Database of the Federal Bureau of Investigation and the 2000 Decennial
United States Census. It is from the year 2000, and includes 2,106 cities and towns with
populations over 10,000 in the United States. We chose the year 2000 due to the
availability of data and the fact that it is a relatively recent year. All 50 states and the
District of Columbia are represented. However, there was only one city included from
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Hawaii whereas, there were many cities included from some states, such as California and
Texas, meaning that some states are overrepresented in comparison with others.
We also created a diversity index of ethnicity. The Dindex is measure of the
heterogeneity of a population. The value lies between 0 and 1; a value close to 0 indicates
a highly homogenous population and a value close to 1 indicates a highly heterogeneous
population. It is based on the proportion of people who are white, black, native, Asian,
Pacific Islander, other, and multi-ethnic. The index used was the index of diversity as
created by Gibbs and Martin (1962, 670-672) and specifically used for ethnic diversity of a
population by Blau (2000, 401).1
Our model is:
ViolentCrime = β0 + β1lCensus + β2%HS + β 3%Black + β4DIndex + β5%SingleMom +
β6lMHV + β7%HHPubAssist + β8%Poor + β9%Vacant + u, where:
1(1−�=1���2) = The Index of Diversity, where p is the proportion of individuals or objects in a category, and n is the number of categories. Latinos are not identified as a separate category because the census does not classify them separately.
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Table 1: Variable Definitions and Descriptive Statistics Symbol Variable Definition Expecte
d Sign Mean Std Dev. Min Max
ViolentCrime The proportion of violent crimes per 100,000 people
------ 443.7093 419.8388 0 2883.842
lCensus The log of the population of all 2106 cities in 2000
Positive 60798.01 229008.7 709 8008278
%HS Percent of the population with a high school degree or less
Positive .4574802 .1529567 .058005 .9073921
%Black Percent of the population that is black
Positive .1022931 .1530621 0 .9585475
Dindex Measure of ethnic diversity within a society
Positive .3152891 .1873605 .0172984 .7830377
%SingleMom Percent of families with children that are headed by single mothers
Positive .1143783 .050946 0 .4272276
lMHV The log of the median home value, where home value is the amount for which the owner believes the house would sell on the open market.
Negative 11.66655 .5463506 10.1105 13.81551
%HHPubAssist Percent of all households on public assistance
Positive .034875 .0258552 0 .1804097
%Poor Percent of the population living below the poverty line
Positive .124542 .0803762 .0037031 .5428688
Vacant Ratio of vacant housing units to occupied housing units
Positive .0762289 .0804158 0 1.719453
Sources: Data adapted from the 2000 Uniform Crime Report, the Federal Bureau of Investigation; the 2000 Census, the United States Census Bureau.
There are a few problems to be aware of when considering this model. First, testing
in Stata provides evidence for multicollinearity between most of the variables, such as
poor, public assistance, single mother, black, and high school. There is nothing to be
done about multicollinearity, but it is important for the reader to be aware that it is present.
It also means that the p-values are higher than they probably should be. This correlation
among variables is to be expected since many of most of these variables are part of the
cycle of poverty. This makes it hard to control for things such as poverty across race, or
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education level, because poorer people tend to be more poorly educated and of a minority
ethnic group. Omitted variable bias presents another problem. Undoubtedly, there are
other variables that affect the level of violent crime in society that were not included in this
model. Some of these, such as psychological states, personality, or crimes of passion are
difficult to quantify and thus are part of the error term.
A final, important problem is one of heteroskedasticity. We tested for
heteroskedasticity using the Breush-Pagan test and the White test and found evidence to
reject the null hypothesis of homoskedasticity. For the Breush-Pagan test, the LM statistic
is 3276.208 with a p-value of 0. Using the White test, the general test statistic is 111.1506
and the p-value is 7.7e-06. Both of these results provide evidence of heteroskedasticity.
This was corrected for by running a regression to calculate the robust standard errors; this
regression will be referred to as the robust regression. This regression has the accurate
standard errors and t statistics.
Results
Our model contains only nine explanatory variables. This is because in previous
regressions several of the variables considered were very statistically insignificant, such as
median household income, percent foreign born, and homes rented. Thus, these variables
were dropped from the regression. We have also experimented with different functional
forms and finally settled on using the log of population and the log of median home value.
Using different specifications in the model increased the R-squared and the significance of
the variables. The R-squared is 0.5663 and the adjusted R-squared is 0.5644. This
means that this model explains about 56 percent of the variance in violent crimes.
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Table 2: Regression Results of Violent Crime on Education and Poverty Dependent Variable: Proportion of Violent Crimes Model ________________________________________ Intercept lPopulation High School Black Diversity Index Single Moms lMedian Home Value Public Assistance Poor Vacancy R-squared Number of Observations ________________________________________
OLS ________________________________________ -1650.811*** (243.5532) [247.8654] 70.26156*** (6.988612) [7.739343] 417.8408*** (66.01002) [60.10737] 964.5477*** (63.93466) [105.7798] 237.9881*** (47.35428) [59.12994] 1180.249*** (241.7778) [291.8789] 62.92453*** (17.9631) [17.64425] 1424.586 *** (416.1382) [503.4474] 422.0795*** (132.4789) [156.4959] 471.6322*** (79.42515) [134.3619] 0.5663 2106 ________________________________________
Notes: Sources: the 2000 Uniform Crime Report, the Federal Bureau of Investigation; the 2000 Census, the United States Census Bureau Standard error in parentheses. Robust standard error in square brackets. Statistical Significance: *** = 0.01 level based on the robust regression.
The results proved to be very interesting. This analysis will focus on the variables
high school, public assistance, poor, vacancy and log of median home value. The
coefficient on high school indicates that on average, a one percentage point increase in
the number of people that have a high school degree or less is expected to increase the
number of violent crimes by 417.84 per 100,000 people. This is very significant in the
robust model with a p-value of 0. This is expected because other studies, mentioned in
the literature review, have found that increases in years of education are expected to lead
to decreases in violent crime. This means that policymakers should focus on programs to
keep students in high school and encourage opportunities to seek further education, such
as college, or vocational training. This will increase the income generating ability of
individuals and help break the cycle of poverty. Education is a means to move beyond
poverty, but unfortunately, poorer people often receive an inferior education. Because
poverty and education are self-reinforcing, it is important to improve the quality of
education as well.
The coefficient on public assistance indicates that, on average, a one percentage
point increase in the number of households on public assistance is expected to increase
the number of violent crimes by 1424.59 per 100,000 people. This variable is very
significant in the robust regression with a p-value of 0.005. Similarly, the coefficient on
poor indicates that, on average, a one percentage point increase in the percent of people
living below the poverty line is expected to increase the number of violent crimes by
422.08 per 100,000 people. This variable is significant in the robust model with a p-value
of 0.007. Due to multicollinearity, this p-value may be misleadingly high. Also, the
coefficient on vacancy indicates that, on average, a one percentage point increase in the
ratio of vacant houses to occupied houses is expected to increase the number of violent
crimes by 471.63. This result is very significant in the robust model with a p-value of 0.
The maximum ratio observed was 1.71, which means that almost twice as many houses
were vacant as were occupied. This without doubt has serious repercussions for the
community at large, decreasing home values, and contributing many potential locations for
crime among others effects. These results for these variables are expected because the
positive correlation between poverty and violent crime has been found in other studies, as
mentioned in the literature review. These three variables are indicators of the overall
performance of the greater macro-level economy. Thus, it is important for policy to focus
on increased jobs and community programs, such as computer instructional sessions, in
order to reduce the number of poor people and the number of people who need
government assistance. It cannot be forgotten that education is still critical in order to help
raise people out of poverty and create long-term effects.
Surprisingly, the coefficient on log of median home value means that on average, a
one percent increase in the median value of a home is predicted to increase the number of
violent crimes by .6292 per 100,000 people. This result is very statistically significant with
a p-value of 0, but since the number is so small it is not very economically significant. In
addition, it is not the sign that was expected. The hypothesis was that as median home
value increased, violent crime should decrease, but this is not what is observed. This
could be because homes in cities are typically more expensive and thus, have a higher
value than in smaller towns and rural areas and violent crime is higher in cities. The
maximum median home value observed was $1,000,001 which is in Hillsborough,
California in the San Francisco Bay area. The minimum median home value is $24,600
which is in Pecos City, Texas, a town with a population of around 10,000, one of the
smallest populations in our sample and Pecos City is the largest city in its county. So, it
would appear that areas with higher home values, such as larger cities, would be
correlated with a rise in crime because of other factors that are more prevalent in cities,
such as ethnic diversity, and population density, not necessarily because wealthier people
commit more crime. A way to correct for this in the future would be to break down the
cities by neighborhoods.
Conclusion
Numerous previous researchers, such as Messner and Tardiff, Forst, Short,
Lochner, and Wilson, have examined the impact of an assortment of socioeconomic
variables on violent crime. We chose to focus on poverty and education because we
believe those are the variables most likely to be manipulated by policy. Other variables,
such as population size and diversity level are generally beyond the reach of policy
makers. In our model, poverty was measured by poor, public assistance, log of median
home value, and vacancy, and education was measured by high school. We hypothesized
that median home value would be negatively correlated with violent crime, while the
percentage of households on public assistance, the percentage of the population living
below the poverty line, and the number of homes vacant would be positively correlated.
As anticipated, these variables were all positively correlated with violent crime as indicated
by the positive values of the coefficients in the basic model. They were all statistically and
economically significant. Unexpectedly, the coefficient for log of median home value was
also positively correlated with violent crime. As discussed previously, we believe that this
may be because home values are higher in large cities, where violent crime is more
prevalent. It is also important to note that although this coefficient was statistically
significant, it was not economically significant.
Since education and poverty are both statistically and economically significant in
explaining violent crime, policy that favorably influences these variables ought to decrease
violent crime. Thus, in order to properly address violent crime, education and poverty must
be understood in terms of one another. Ideally, policy should encourage people to finish
high school and then continue on to further education. Logically, the focus should be on
people living in poverty because they are the ones who would benefit the most from
additional education. Higher education yields a greater income generating ability and
more employment opportunities which in turn decreases the incentives to commit a violent
crime. This would reduce the number of violent crimes and the costs connected to them.
Therefore, this solution would be in the public’s interest because society as a whole would
benefit from the increased productivity of the workforce and from the decrease in costs
directly associated with violent crime.
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