qmss 5999 - thesis - avaughn
TRANSCRIPT
RUNNING HEAD: CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
A Time Series Analysis of Crime Rates and Concern for Crime in the United States: 1973-‐2010
ABSTRACT: Real crime rates may not be the only source of information people use to assess their fear of crime. The present study conducts time series analysis to explore if society does or does not incorporate other information factors into their concern for crime. Using data from the FBI’s Uniform Crime Reports and the General Social Survey, I explore the relationship of concern for crime and real crime rates across domains that include covariates of demographic information, national priorities and opinions, and societal values for the years 1973-‐2010. The study finds support for the argument that people use violent crime rates to logically determine their concern for crime as opposed to using competing sources of information.
Alexandra Vaughn Columbia University QMSS 5999 Thesis
Spring 2012
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
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Table of Contents
1. Introduction 1
1.2. Hypothesis 2 2. Literature Review 4
2.1. Crime and Public Perception 4 2.2. Crime and Demographics 8 2.3. Crime, National Priorities, and Political Opinion 10 2.4. Crime and Social Values 11
3. Data & Methodology 12 3.1. Data 12 3.2. Variables 17 3.3. Tests 21
4. Results 27
4.1. Descriptive Statistics 27 4.2. Crime and Demographics 38 4.3. Crime, National Priorities, and Political Opinion 42 4.4. Crime and Social Values 45
5. Discussion 48
Appendix 53
References 58
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1. Introduction
After peaking in the 1990s, crime rates have steadily declined for two decades. Public
concern for crime has also decreased in recent years, although people continue to believe
crime is out of control. The symmetry of trends in crime rates and concern for crime over time
and the paradox of people’s belief about the state of crime raise the question: do people
logically use true crime rates to derive their concern for crime or do they use competing
sources of less relevant information. Understanding how crime rates may or may not influence
people’s beliefs about their relative safety and the state of crime has implications for decision-‐
makers and policy advocates. Better knowledge of the relationship can focus alignment of
crime prevention more closely with public opinion so that the public accurately perceives crime
prevention as having a positive effect. This paper aims to address the question: if the public’s
concern for crime and actual crime rates trend together over time, do people appear to
logically refer to the crime rate, and what societal characteristics and concerns may help
explain this relationship.
I use a collection of variables from the General Social Survey (GSS) and FBI Uniform
Crime Reports (FBI UCR) to investigate the relationship between public concern for crime and
crime rates. Additionally, I include the several demographic, policy, and societal concerns that
may influence the relationship between concern for crime and crime rates. By including
demographic information and public opinion questions, I will also be able to examine if these
variables may account for people’s concern for crime although they may be irrelevant sources
of information compared to true crime rates. Criminal and forensics research has established
that crime rates may not the only source of information people use when determining their
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fear of crime (Bakhan & Cohn, 2005). However, contrary research shows that crime rates have
been falling for the last two decades after years of steep increases and fear of crime appears to
be following similar trends across time (McDowall & Loftin, 2009). Since I am concerned with
the relationship between concern for crime and crime rates over time, I progress through a
series of regression and time series analysis that allow me to understand what occurs over
several years rather than from a cross-‐sectional analysis at a single point in time. I conduct
traditional Ordinary Least Squares (OLS) regression, First Differences, and Prais-‐Winston
Feasible Least Squares (FLS) regressions for time series to explore the relationship between
concern for crime and actual crime rates and expand upon previous literature that has explored
these trends over time, nationally, and with the addition of control variables.
1.2. Hypothesis
I explore the question do people logically use the true rate of violent crime in the United
States to determine their concern for crime for the years 1973-‐2010 and what does the
relationship look like over time?
Within the context of this larger objective, I seek to explore the following: if people do
not logically use real crime rates, what other sources of information do people use to form their
opinions of and concern for crime:
- Specifically, do demographic trends correlate with concern for crime along with real
crime rates across time?
- Do preferences for other national priorities and political opinions correlate with people’s
concern for crime across time?
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- And, do measures of social values correlate with concern for crime and crime rates
across time?
I will answer these questions by first looking at the summary characteristics of the GSS
respondents who answered a question about national crime. The initial, summary analysis will
be done at the individual level and will allow me to examine if there are any underlying
characteristics and demographic trends that distinguish those who have “high concern” for
crime versus those who are “neutral” or have “low concern” for crime across demographics and
opinions.
Additional analysis will take place at the aggregate level after the data have been
collapsed by year to examine trends of concern for crime across time rather than just across
individuals. I will consider people’s concern for crime across three domains: concern for crime
as it relates to demographics, concern for crime within the space of national priorities and
politics, and concern for crime as it relates to people’s social values. Within the three domains
under consideration I will conduct initial, simple Ordinary Least Squares (OLS) regressions,
include a year trend in OLS, run First Differences, and finally, explore time series analysis using a
Prais-‐Winston Feasible Lease Squares (FLS) regression. Time series analysis will be
complimented by heteroscedasticity and serial correlation tests to check the integrity of the
data. Durbin’s alternative h-‐statistic test will check for serial correlation in the errors of the time
series regression model. The h-‐statistic statistic is a useful tool to check for autocorrelation
because it also works with models whose explanatory variable are not strictly exogenous
(Wooldridge, 2009). A heteroscedasticity check will confirm whether or not the models have
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any left out variables that are creating bias because they have an effect on the dependent
variable.
2. Literature Review
2.1. Crime and Public Perception
The changing picture of crime rates and public attitudes towards crime over time is a
complex relationship that may not be fully explained by univariate analysis of crime rates on
people’s concern for crime. Criminologists, law enforcement agencies, and researchers from
many academic disciplines have noticed that the public has maintained the belief that violent
crime is out of control despite the fact that crime rates have been steadily declining for years. A
2008 study confirms that despite dramatically decreased crime rates in recent years, the public
continues to believe that violent crime rates are out of control (Duffy, Wake, Burrows, &
Bremner, 2008). As long as this belief persists, the public tends to blame the government for
failing to properly address their beliefs about crime rates and for neglecting to meet their
personal safety needs (Duffy, et al. 2008). Researchers, policy makers, and law enforcement
officials in the U.S. benefit from awareness of the public’s varying relationship with true crime
rates. If we can better understand if and when people are making logical decisions about their
concern for crime relative to crime rates, we can address how to improve instances of
irrationality when people use competing sources of information to learn about crime.
Public perceptions of crime may be swayed by several contributing factors. Felson
(2002) contributes a theory for predicting people’s concern for crime and attempts to explain
why concern for crime and falling crime rates do not always align. Felson’s random crime fallacy
argues that people believe crime is random and unpredictable, while the opposite is more likely
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true – that crime events are actually predictable. The random crime fallacy is helpful to begin a
conversation about crime rates and fear of crime. However, I am interested in explaining what,
if any, other variables and opinions are used as competing sources when people form their
concern for crime.
One source of information that people may use to is the media. According to Duffy et al.
(2008), the public’s exposure to television may significantly influence the publics’ perception of
the state of crime. Several studies have looked at time spent watching TV crime shows and the
news as predictors of attitudes towards crime (Buijzen, Walma van der Molen, & Sondji, 2007;
Gerbner, & Gross, 1976; Gilliam, & Iyengar, 2000; Gilliam, Iyengar, Simon, & Wright, 1996).
Heath and Gilbert (1996) review the literature on media and fear of crime in order to
understand what is the prevailing opinion. They find many contradictions in researchers’
conclusions, especially given the disparate survey methods, data collection, variable sources,
and populations used. For instance, they find that television portrays society as suffering from
much more crime than is true in reality, but when Heath and Gilbert (1996) examine studies
that measure if TV with intensified and extremely violent crime influences viewers to develop
an unrealistic opinion of crime the link between media and fear of crime fails to be significant.
The weak relationship is maintained when they review studies that look at TV viewing with
other independent and control variables included. From their review, they conclude that when
TV viewing and crime content on TV are examined independently, TV and media influence fear
of crime. Essentially, they infer that some television seems correlated with crime for some
viewers. However, when control and demographic variables are included the relationship
deteriorates (Heath & Gilbert, 1996). Despite contradictions, crime perception and media have
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done much for the literature and our understanding of how people may obtain crime
information from this source of communication. I choose to include it as a control variable, but
focus on studying people’s concern for crime outside of this relationship. I include many other
control variables, as well, in order to get a better understanding if any additional factors shape
Americans’ attitude toward crime rather than actual crime rates.
Across a variety of fields, including criminology, anthropology, sociology, and other
disciplines, crime research uses different sources to measure crime rates and of fear of crime.
One widely used source of data is the GSS. It includes a variable, natcrime, that asks about
people’s opinion on the government’s efforts and spending to halt crime; it is often used in
crime studies as a measure of public sentiment about crime. Using the GSS, Frost and Clear
(2009) argue that decreases in fear of crime are not due to better punitive measures, but rather
decreasing crime rates. They demonstrate that as of 2010, fear of crime does not even rank on
citizens’ list as one of America’s most pressing issues, whereas in the 1980s and early 1990s
when crime rates were at their peak, it consistently ranked in the top five on Gallup poll surveys
(Frost & Clear, 2009). As recently as early the 2000s, Smith (2011) also takes note of Americans’
decreasing opinion that crime should be addressed as a top national priority, while it ranked for
many years as a top concern. Despite people’s decrease in fear of crime, 60% of Americans in
2010 say that the government is not spending enough to combat crime (National Opinion
Research Center, 2011).
The literature suggests that U.S crime rates, American’s concern for crime, and their
calls for more measures to fight crime do not align. As a result, research tries to explain the
disconnect between them. Attempts to do so have begun to question if competing source of
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information and other control variables may uncover more information about the relationship.
Yet, the gap between actual fear of crime and concern for crime leaves room for further
research and exploration into the dynamics that make up people’s concern for crime.
Furthermore, the majority of this research has been done with cross-‐sectional analysis of
society. It is not to be unexpected that an aggregate study that looks at yearly trends might
point to the fact that media’s role is diminished across time.
Research on crime rates is conducted at various geographical levels of analysis. In
particular researchers and criminologists have been interested in whether the decline in crime
rates seen since the 1990s persists at the national-‐level, as well as at the city-‐level. A significant
body of research that looks at crime trends examines the trend at the national level rather than
locally (Blumstein, 2006; Rennison & Planty, 2006; Rosenfeld, 2002). Many studies that use
national level crime rates and fear of crime find that national annualized data for many years
rather than cross-‐sectional data is easier to procure than city-‐level crime across the U.S. While
there are studies that examine crime rates in cities, states, and smaller regions of analysis their
methods, variables, and surveys are not always consistent enough to compare across different
locations. Using national data enables consistent variables, McDowall & Loftin (2009) conduct
one of few studies that has explicitly examined national versus city crime rates for patterns.
They use annualized panel data of the Uniform Crime Rates from 130 U.S cities for the years
1960 to 2004 to compare crime rates of the nation’s major urban areas against national crime
rates to measure the degree to which U.S crime rates follow a national trend. They determine
that a consistent pattern exists at both levels by demonstrating that increases in the crime rate
in one city occur during crime increases across other U.S cities. Their work supports the claim
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that crime follows a national trend; the city-‐level data they use represents a similar trend in
crime rates. There is support for looking at national-‐level crime trends. This study is consistent
with previous studies that look at annual and time series crime trends that look the trend at the
national level.
2.2. Crime and Demographics
Individual demographics and personal characteristics may play a role in people’s
interpretation of information about crime. For example, beliefs about demographic factors and
racial composition of criminal offenders influence attitudes towards criminal punishment and
fear of crime (Chiricos, Welch, Gertz, 2004). People may approach information about criminal
events not only from the context of their own race, but also from pre-‐conceived beliefs about
the nature of criminal actors (Barkan & Cohn, 2005). Barkan and Cohn (2005) find a positive link
between racial prejudice and increased concern for crime using the GSS natcrime variable to
investigate race and opinions on crime. They find that whites, especially those with more racial
prejudice, are more likely want more money spent on fighting crime. Conversely, Baulmer
(1979) does not find any patterns, although he suggests that racial concentrations in
neighborhoods and familiarity with surroundings mitigate fear of crime. There does not appear
to be a consensus in the literature on the role of race in people’s concern for crime, which
highlights the need for exploration into the role it may.
In addition to race, other demographic factors contribute to the public’s and concern for
crime. Fear of crime displays consistent gender divergence (Baulmer, 1979); women tend to be
more afraid than men (LaGrange & Ferraro, 1989). Older respondents, as an age group, tend to
be more afraid of crime than other age groups (Baulmer, 1979). Franklin and Franklin (2008)
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confirm previous research that, in general, women and elderly citizens are more fearful of
crime. Interestingly, they also find that as women age their fear of crime reduces, however this
is not the case for men. Gender and age appear to play a role in predisposing people towards
fear for crime, but there may be interactions or mitigating factors that can reduce the risk of
fear of crime in these subpopulations. Marvell and Moody (1991) demonstrate that variations
over time in the age structure of the population do not mirror crime trends as expected. They
reviewed a large number of studies in the late 1980s and early 1990s and find that a decrease in
the proportion of teenagers and young adults in the population did not, in fact, precede a dip in
crime levels as they expected. This finding minimized the role that the number of younger
members in society previously played in crime trend theorizations. For age, race, and gender it
appears that researchers do not agree on these demographics’ relationship with concern for
crime.
Marriage status appears to play a role in people’s fear of crime (Toseland, 1982). Those
who are married have been found to display more fear of crime than unmarried people.
Although Toseland (1982) uses GSS data for his analysis he limits his study to one survey year,
so it is unknown if these trends persist with time. Studies have not specifically looked at
whether presence of kids under 18 in the household appears to play a role in people’s concern
for crime, but the more persons in the household under respondents care has been shown to
increase concern for crime (Toseland, 1982). I include number of kids in the household because
it may show an additional contingency towards concern for crime. It does appear that both
marriage and number of household members increase people’s fear of crime, which makes
them interesting variables to include in multivariate analysis with violent crime rates.
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Although demographic factors have received much attention in fear of crime research,
they have not been consistently compared with actual crime rates’ relationship on concern for
crime, nor has a consensus been reached on what direction their relationship is with concern
for crime and violent crime rates.
2.3. Crime, National Priorities, law, and Political Opinion
Literature has explored the public’s concern for crime and its link to societal attitudes
towards national priorities and the law, such as the death penalty (Johnson, 2009) and handgun
ownership (Holbert, Shah, & Kwak, 2004; Ludwig, Cook, & Smith, 1998; Moody & Marvell,
2005), and political opinion (LaFree, 1999). There is scare literature on the relationship between
fear of crime and people’s opinions on other national issues. Smith (2011) shows through
analysis of GSS surveys from 1974-‐2010 that crime was consistently ranked as a top national
priority through the 1990s. This increasing trend also coincided with peaks in crime rates. When
crime began to fall in the 1990s, Smith (2011) identifies the point in time when fighting crime as
a national priority begins to loose favor. Despite our understanding of the synchronicity of
crime rates and fighting crime as a top priority, I do not find any research that has measured if
changes in top national priorities influence people’s attention to concern for crime.
Changes in policy, politics, and policing strategies may drive relationships between
concern for crime and what the public believes to be the state of crime. In this domain I include
a measure of hours spent watching TV per week. It fits with this domain as an opinion variable,
because it research suggests that people who watch TV may be influenced by crime reports and
fictional crime on TV (Buijzen, Walma van der Molen, & Sondji, 2007; Gerbner, & Gross, 1976;
Gilliam, & Iyengar, 2000; Gilliam, Iyengar, Simon, & Wright, 1996). Since media and crime
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research is inconsistent in its conclusion of how strong the influence of media is on people’s
concern for crime (Heath & Gilbert, 1996), its inclusion here will add to this discussion. Thus,
the second domain examines what other sources of opinion and beliefs may explain the
relationship between crime rates and concern for crime it is appropriate to include.
2.4. Crime and Social Values
Evidence suggests that values, personality characteristics, and emotional states may
contribute to people’s fear of crime and victimization risk. LaFree (1999) found social
institutions and values to be instrumental in explaining his theory of crime rate explosions in
the 1960s and 1970s. For those decades, American society was filled with growing political
distrust and social disintegration, whereas a process of stabilization of traditional social values
and institutions in the 1990s may account for the decrease of crime (LaFree, 1999). Using a
measure of people’s trust for society may tap into a boarder measurement of trust than
political distrust. It can shed light on how overall levels of trust inform people’s concern for
crime. Trust as a social value may be useful in representing some portion of the morals and
values that people use when they approach issues of crime. It has been found to be a more
significant in predicting fear of crime than age, isolation from society, and income (Mullen &
Donnermeyer, 1989; Toseland, 1982). However, Mullen & Donnermeyer’s (1985) sample is
located in a rural proportion of the country and does not represent a national sample, so
extending their conclusion outside a rural population is tenuous. However, a measure of trust in
society may yield insight into whether high or low trust plays a role in concern for crime given
crime rates. Johnson (2009) suggests that anger about crime is a positive predictor of attitudes
about criminal punishment, when racial prejudice, fear of crime, attributions for criminal
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behavior, and political ideology are controlled for. The GSS does not have an emotional
question that measures anger. Instead I propose using a happiness measure from the GSS as an
emotional variable in analysis. Overall, studies that explore the role of values and emotional
content in fear of crime research are few (Toseland, 1982), but there is preliminary evidence
that in cross-‐sectional studies these values and emotions may influence fear of crime.
3. Data & Methodology
3.1. Data
I hypothesize that people logically use real crime rates to determine their concern for
crime. If logic appears to fail, I am interested in seeing it they incorporate competing social,
demographic, and other informational cues to derive a sense of what they believe are
reasonable expectations for their concern of crime.
I analyze the relationship between the U.S. public’s concern for crime and real crime
rates across the years 1973-‐2010. I incorporate two sources of data into my analysis. In order to
get a measure of the rate of crime, I use violent crime rates from the FBI UCR (Federal Bureau
of Investigation). As a measure of the public’s concern for crime, I choose a question from the
GSS (National Opinion Research Center) as my source. The GSS is particularly useful because it
has asked a set of time-‐invariant questions to a representative sample of the United States
population since 1972. It asks opinions about demographic characteristics, socio-‐economic
factors, social values traits, and opinions of national priorities that have been asked every
survey year. In addition to using the GSS for the concern for crime variable, it is also the source
of the additional independent variables I use to examine the relationship between crime rates
and concern for crime change across time.
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For the purposes of this study, I focus on crime rates that come from institutional
records, namely from crime reports. Thus, the source of crime data in this project will be the
FBI’s UCR. A benefit of this dataset is the collection institution – the FBI – is a national law
enforcement agency, collection procedures have been standardized since 1930, and it is
nationally representative (FBI, 2011).
3.1.1. The FBI Uniform Crime Reports
I choose to operationalize the measurement of crime rates in the U.S. using the FBI’s
UCR. Collection of the UCR been standardized since 1930 when the UCR was first established as
a source of reliable, uniform crime statistics for the country. Individual, independent law
enforcement boroughs, offices, and states report police-‐collected measures of crime to the FBI
on a monthly basis. Nearly 17,000 law enforcement agencies across the United States report
crimes to be collected, analyzed, and published in the UCR and FBI’s annual Crime in the Unites
States (FBI, 2011). An estimated that 97% of the U.S. population is represented in the FBI UCR,
and the highest participation rates are within metropolitan cities (Mosher, et al. 2002).
Accordingly, coverage of reported crimes can be assumed relatively complete across the
country.
I source the crime rate data from the FBI’s UCR online data section. I use 1973 as the
first year of analysis because it is when the GSS started to include a measure for concern for
crime – the dependent variable in my analyses. Crime in the UCR are recorded in two parts:
Part I violent crimes, which includes murder, robbery, rape, and assault, and Part II – lesser
degree crimes such like drug offenses, fraud, public order offenses, and weapons violations.
Part II crimes are only recorded if someone is arrested and often not reported to the police,
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which makes these crimes difficult to estimate and measure (Block & Maxfield, 2011). Even
with the two categories, the Uniform Crime Reports do not include an exhaustive list of all
types of crime. The largest source of under reported crimes are personal crimes that do not
involve injury and property crime such small monetary losses because they are least likely to be
reported to the police (Block & Maxfield, 2011). Because Part I is considered the more reliable
collection of crime incidents based on the fact that crimes of this nature are reported to the
police and their collection is more consistent, I use total violent crime. Including crime rates
across many years will enable a comparison of crime rates as they change in time.
3.1.2. Limitations of the FBI UCR
A major consideration in criminal research is the issue of measuring crime and
understanding the characteristics of the data and measurement methodologies. Crime is
measured from a variety of perspectives; many sources, surveys, and institutes collect counts of
crime events for a variety of reasons with a range of tools, goals, and measures. Crime can be
examined from the perspective of institutional records, victimization studies, first-‐person self-‐
reports and accounts of crimes committed, and recollections of crimes witnessed or
experienced via victims have all been used as sources of crime research (Mosher, Miethe, &
Phillips, 2002).
Inaccuracies in reporting lead to potential confounding in police reports. Outside
influences can exert pressure on crime record keepers so that records reflect numbers that
politicians, chiefs of police, and other decision-‐makers would like to see because the doctored
reports are professionally flattering rather than accurate accounts of the crime taking place
under their watch. External pressure may influence crime record keepers to inflate or deflate
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actual numbers. In instances when numbers are inflated, competition for monetary support
and funding for departments are the incentives (Mosher, et al. 2002). Conversely, reports may
undercount instances of offenses in order not to receive more negative attention than wanted
for high levels of offenses. From year-‐to-‐year or city-‐to-‐city if there are significant changes in
the numbers, investigators cannot exclude the influence that altering the number of offenses,
unintentionally or intentionally, may have on data accuracy. The UCR, however, does test if
annually reported rates are inconsistent year-‐to-‐year and corrects for inaccuracies (See
Appendix, pg. 48 for more).
3.1.3. The General Social Survey
The literature reviewed above includes studies that use a variety of sources and surveys
to measure public biases towards crime as opposed to a nationally consistent source across all
studies and years. Most of the studies also use cross-‐sectional analysis rather than time series,
which is easier to implement, but does not provide information about variables over time.
Cross-‐sectional analysis enables researchers to look at society at one point in time only and
limits their ability to extrapolate beyond the population sample used or beyond the time used.
Time series analysis overcomes the inability to extend analysis beyond the timeframe of cross-‐
sectional analysis because it uses multiple years. The results inform researchers about trends in
the data that occur over time.
The GSS is a useful source of data in comparison to what has previously been used in
some studies because it includes many valuable covariates, is time-‐invariant in structure, and is
nationally representative. It is particularly useful because of its time consistent format. The
flexibility in data it provides allows me test alternative explanations for the connection between
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concern for crime and crime rates. Furthermore, the GSS asks a set of questions that are
deliberately constant across time, which allows for time series analysis of a large range of
issues. Given the advantages of the GSS, I use it as the source of my dependent variable and
covariates.
Rasinski (1989) has completed work on the flexibility of the wording on the GSS
“government spending” questions. He shows that multiple versions of the same question give
people the opportunity to flexibly interpret the question. In his study, using GSS data to
measure fear of crime, Toseland (1982) argues that measures of concern for crime and fear of
crime can be inferred from survey questions and applies these definitions to his work.
Furthermore, Warr (1995) notes that public opinion studies on concern for crime are few, and
that researchers are often forced to compromises on the available items to include in their
work. These studies conclude that fear of crime and the GSS variable natcrime are both
decreasing over time, which indicates the two measures might be accessing some amount of
“concern for crime.” In light of these studies, I argue that it is reasonable to consider natcrime
as one permutation of people’s concern for crime and use it as such in this paper.
The GSS is nationally representative survey that has sampled members of the U.S.
population since 1972. Most of the data is collected via face-‐to-‐face interviews; a minority
interviews are conducted over the phone or with the aid of computer assisted personal
interviews (National Opinion Research Center, 2011). Covariates on the GSS include a core set
of demographics, attitudinal questions, life topics, opinions, and several sets of special interest
topics that appear in rotation. I use survey years from 1973-‐2010. Missing survey years are
1979, 1981, 1992, 1995, 1997, 1999, 2001, 2003, 2005, 2007, and 2009; the majority of missing
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years can be explained from the introduction of biennial surveying in 1995. I take these gaps
into account and perform transformations and imputation on the data to overcome missing
years; I explain this process below. I source the cumulative GSS dataset from the NORC online
distribution page (NORC, 2011).
3.2. Variables
3.2.1. Dependent Variable
The dependent variable is concern for crime. It comes from a question from the GSS –
natcrime1 – that asks individuals how they rate the government on spending enough to halt
rising crime rates. The GSS does not include a variable that directly asks participants their
opinion of the level of crime or how safe they feel, nor is there a national-‐level study or survey
that uses a similar dependent variable and includes as many useful control variables. However,
previous research has established that natcrime follows the same trends across time as actual
crime rates and may be tapping into some measure of “concern for crime” (Frost & Clear,
2009). As a result I am confident that this study follows the arguments previous research has
established. For ease of interpretation, I recode natcrime scale to read from low to high
concern for crime, instead of in its original form from high to low concern for crime. Responses
are valued at 1 = little concern for crime, 2 = neutral concern for crime, and 3 = a lot of concern
for crime. I interpret natcrime to indicate that people are likely to report the need for more
national spending on crime when they believe not enough is being done to combat the crime.
This side of the scale represents “much” or high concern for crime. The other side of the
1 The GSS prompt for national crime states. “68. We are faced with many problems in this country, none of which can be solved easily or inexpensively. I'm going to name some of these problems, and for each one I'd like you to tell me whether you think we're spending too much money on it, too little money, or about the right amount. e. Halting the rising crime rate.”
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natcrime scale to signifies that people are more likely to report that too much is being spent on
battling crime, when they have “a little” or low concern for crime. For ease, for the remainder
of the study I refer to natcrime as concern for crime.
3.2.2. Independent Variables
The FBI UCR measures the violent crime rate by aggregating murder, robbery,
aggravated assault, and forcible rape counts per 100,000 in habitants. The UCR counts these
crimes as Part I offenses. Although, these four types of crime also exist as a unique count on
the UCR, I choose to use the rate of total violent crimes, which is the aggregate of the four
unique types of crime. Warr (2005) finds that people use an overall count of crime rather than
specific types of crime to assess the state of crime in society and to determine how safe they
feel. MacDonald (2002) & Sampson (1987) suggest that violent crime is the most reliable
measure of crime. I choose crimes that rank higher in seriousness under the logic that public
perception of crime trends will be similar for crimes of similar seriousness. Furthermore using
the crime rate per 100,000 inhabitants instead of the pure count of incidents takes into account
the fact that the number of crimes committed tends to increase with time and that states,
cities, and precincts vary in population size. As a result of this standardization comparison of
crime rates nationally and across years is possible.
Of the types of violent crime recorded by the FBI, aggravated assault is consistently the
most prevalent crime and accounts for the majority of that make up the total violent crime rate
across all years (Table 1A in Appendix). All types of crime reach their peak in the early 1990s.
Recent years have shown a return to total violent crime levels not seen since the early 1970s, as
evidenced by minimum rates crime in 1972 and 2010 (Figure 1).
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
19
Figure 1.
I tested if violent crime is the appropriate crime rate to use rather than the individual
types of crime. Separately, I regressed the four individual types of crime rates on people’s
concern for crime in OLS. I also regressed the total violent crime rate on people’s concern for
crime in its own regression. The specific types of crime are not statistically significantly related
to how people rate their concern for crime. A more detailed discussion is contained below in
the results (Table 3, below).
In addition to the FBI UCR violent crime rate, I use attitudinal questions and
demographic variables from the GSS as independent variables. The GSS attitudinal and opinion
variables are used to test if their addition to the models helps predict changes in concern for
crime in accordance or divergence from crime rates. All GSS variables included in the study are
asked for the survey years 1973-‐2010.
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
20
I group the GSS variables into three domains for analysis. The first domain is
demographics. This includes the variables gender, age, race, married, kids, and income. Gender
is a binary variable with the values 1 = male or 0= female. Age is a continuous variable of
respondents’ aged 18 years and above. Race is also coded as binary with 1 = white and 0 =
other. Although the United States is a deeply multicultural country, in the GSS race question
continues to be asked in the same manner as it has been since it was first asked in 1972.
Otherwise, had changes been made to the structure of the question, researchers would not be
able to compare responses and societal changes over time. We are constrained by the original
question design, even though more diverse racial data would lead to richer analysis. Married
has been created from the original GSS marital. It is valued 1 = married and 0 = other. Marital
includes several categorical responses on the GSS but recoding married to be a binary variable
simplifies interpretation. Kids is a measure of whether there are children under 18 in the
household, 1 = yes, 2 = 0. Income is a self-‐reported, continuous variable measured in real
dollars.
The second domain is includes measures that capture opinions of national priorities and
politics. Political views have been rescaled to create a binary variable that values liberal = 1 and
not liberal (i.e. conservative) = 0. National Priorities is a measure that captures people’s
attention to other national priorities and government spending issues. It represents a scale of
concern for government spending on other national issues that were: national defense, the
drug problem in the U.S., national welfare programs, national healthcare, and the education
system. Chronbach’s alpha is 0.45. During interpretation, I am interested to see how its changes
on a yearly basis predict concern for crime. It serves as a measure of how concerned society is
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
21
as a whole with a variety of other government concern. TV hours is a continuous, self-‐report
variable of respondents’ reported hours of TV viewing per week.
The third domain consists of measures attitudinal and trust with the U.S. population
that I refer to as social values. Trust asks can people be trusted; fair asks if people are
inherently fair or try to take advantage of others. Both are binary such that 1 = yes, 0 = no.
Happy is a measure of general, individual happiness of GSS respondents. It is valued on a three
point scale: 1 = “not too happy”, 2 = “pretty happy”, and 3 = “very happy”.
3.3. Tests
In order to evaluate the relationship between concern for crime and crime rates across
time I conduct a series of analytical tests. I begin by examining if there are demographic and
other differences in opinion differences for those who rate their concern for crime as high
versus low concern for crime. After establishing if any trends exist among the people who have
“a lot” of versus “a little” or neutral concern for crime, I test basic regression assumptions of
concern for crime and crime rates across three domains using multivariate OLS. The OLS model
across all three domains will take the same format:
𝑌! = 𝛼 + 𝑏!𝑋!! + 𝑏!𝑋!! +⋯+ 𝑏!𝑋!" + 𝜀!
Where, 𝑏! represents the expected change in value of 𝑌! given 𝑋!", and 𝜀! is the value of the
deviation by 𝑌! from the mean distribution value. It represents the effects on 𝑌 not accounted
for in the model (Berry & Feldman, 1985).
Due to variations in each variable and possible non-‐stationary across time, general OLS
assumptions may signify that OLS may not be the appropriate test for this study. Spurious
relationships may result, and the interpretation gleaned from OLS analysis does not accurately
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
22
describe the relationships that exist with the type of data I use. OLS assumes six basic
assumptions: that the mean of the error terms is zero, the variance of the error term is
constant, the error terms are uncorrelated, the independent variables are uncorrelated with
the error term, 𝜖, there is no perfect collinearity between independent variables, and 𝜀! is
normally distributed for each set of k independent variables (Berry, 1993).
Additionally, since values in time may be more closely related to values from other years
or close time periods, I am not only interested in the random distribution of the values of
concern for crime and crime rates, but also the order in which values occur across all years
(Ostrom, Jr., 1990). As a result, I also take advantage of First Differences analysis and traditional
time series studies applying Prais-‐Winsten regressions on the variables for all domains. The First
Differences model will take the form:
∆𝑦! = 𝑎∗ + 𝑏!∆𝑋! + 𝑏!∆𝑋! +⋯+ 𝑏!∆𝑋! + ∆𝑒!
Where, ∆ denotes the change from t =1 to t = 2. The unobserved effect will “differenced away”,
such that 𝑎∗ = 0 (Ostrom, 1990). The idiosyncratic error term ∆𝑒! at each time 𝑡 is assumed
uncorrelated with the independent variables, 𝑏!𝑋! in all time periods (Wooldridge, 2009). First
Differences measures variations of ∆𝑥! across 𝑖 in order to predict changes in ∆𝑦! over time. It is
often employed to deal with autocorrelation (Ostrom, 1990). The alternative Durbin statistic,
Durbin’s h-‐statistic, is an appropriate test to check for AR(1) serial correlation time series
analysis (Wooldridge, 2009). It works by running an OLS regression to obtain the residuals, 𝑢!
and then runs a regression on the residual of:
𝑢!𝑜𝑛 𝑥!!, 𝑥!!,… , 𝑥!" ,𝑢!!! for all 𝑡 = 2,… ,𝑛
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
23
which produces the coefficient 𝜌 and the t-‐statistic, 𝑡𝜌. 𝑡𝜌 tests H0 = 0 against H1 ≠ 0, which
allow for usual tests of the hypothesis that there is no autocorrelation against the alternative
hypothesis of positive, first-‐order autocorrelation (Ostrom, 1990).
Prais-‐Winsten estimation is a time series regression used to overcome AR(1) serial
correlation of one lag in linear models (Ostrom, 1990). Prais-‐Winsten takes the form:
𝑌! − 𝑝!"𝑌!!! = 𝑎 1− 𝑝!" + 𝑏 𝑋! − 𝑝!"𝑋!!! + 𝑣!
Prais-‐Winsten regression obtains initial OLS estimates and calculates residuals, minimizes 𝑝 and
replaces it with 𝑝!", and applied OLS to the equation above. The iterations are repeated until
convergence (Ostrom, 1990).
It is important to note that I compute summary statistics and initial analysis at the level
of individuals. In order to assess people’s variation in concern for crime across these domains
comparison must be person-‐to-‐person. However, the order of analysis across time must be
done at the level of year. Each variable is collapsed by mean so mean values per year are
compared across time. This is necessary since individuals and incidents of crime are not the
same every year and because FBI UCR crime rates are not individual-‐level measures, but rather
annual, national counts. Mean values of the variables can be examined for trends that appear
over time. Completing analysis at two levels will enable exploration into whether the data used
supports previous research that people do not derive their concern for crime directly from
falling crime levels over time (Duffy, et al. 2008; Warr, 2005). However, the most important
level of analysis for this project is by year, because I examine trends over time rather than using
a cross-‐sectional analysis, which has been the method of most previous research into crime and
fear of crime.
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
24
In order to compare trends in concern for crime and total violent crime rates over time
the data must be quantified within the same unit of time (Cromwell, Hannan, Labys, & Terraza,
1994). I explore summary statistics while the GSS data are at the individual level. I must position
the GSS variables on the same collection-‐level as the FBI UCR crime rates so that they are at the
year unit of time and nationally representative, I condense the GSS variables into their means
values by year because analysis will compare their mean values over time. Thus, I can explore
the nature of linear or non-‐linearity of the trend of crime rates and concern for crime using OLS
with the year trend included, First Differences, Durbin’s alternative statistic, and Prais-‐Winsten
Feasible Least Squares.
For the OLS models I perform imputation and compute two year averages of variables as
two methods of dealing with missing time data. In effect, for every year of comparison – 1973-‐
2010, each variable is condensed around its mean values that are compared against other
years. Averages by two-‐year increments for the years 1973 through 2010 are computed to
create 19 observations. Creating two-‐year averages ensures that year gaps when the GSS was
not asked are taken into account.
For analysis using First Differences, the Durbin’s alternative statistic test, and Prais-‐
Winsten I use imputation to estimate missing year values. Transformations may be necessary
with time series data when there are missing values in order to properly incorporate
stationarity into time series analysis (Cromwell, et al. 1994). Multiple interpolation works by
substituting or estimating multiple missing data points within the range of known values. It
produces consistent estimates, can be used with the data and models of this study (Allison,
2002). However, if too many missing values need to be interpolated its usefulness is at risk
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
25
because the transformed can start driving that data. Creating two-‐year averages across the
survey years the effect of the two methods is very similar, although performed via a slightly
different method and results in a smaller number of observations. Figure 2 and Figure 3 display
the mean trends of concern for crime over time for comparison. Figure 2 is the two year
averaged method with 19 observations. Figure 3 is the interpolated version with 38
observations. They follow similar trends; the trend line in Figure 3 is a bit more smoothed
because there are more data points from the estimated missing values.
Tables 1-‐2 compare OLS regressions with the year trend included using the two methods
to account for missing year values. In both regressions, violent crime is a statistically significant,
positive predictor of people’s attitude of concern for crime. Additionally, inclusion of the year
trend reveals a decreasing trend in people’s concern for crime outside of any other factors’
influence (β = -‐0.007 in Table 1; β = -‐0.003 in Table 2) The results support my use of the two-‐
year averages of time for all analysis and results, because imputation and interpolation of
variables run the risk of interpolating too much information, which can start driving the data in
a spurious manner. Since almost a third of survey years are missing, I consider estimating that
many years too great a risk to the data. I have demonstrated that using the two year averages
produces similar results to when the data is imputed in order to justify using the two-‐year
averages method to account for missing years. Tables 2A-‐4A(Appendix) provide further
evidence that two-‐year averages and imputated years produce similar output for these data;
the tables are OLS regressions with the year trend across all three domains.
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
26
Table 1. OLS Regression – Time in Two Year Averages Coefficient t p Violent Crime 0.0003 4.14 0.001 Year -‐0.007 -‐5.12 0.000 N = 19 Adj. R2 = 0.738
Table 2. OLS regression – Missing Years Imputed
Coefficient t p Violent Crime 0.0003 7.15 0.000 Year -‐0.003 -‐7.71 0.000 N = 38 Adj. R2 = 0.773
The preceding outline introduces how I intend to test the hypothesis if people use real
crime rates to rationally decide their concern for crime rather than competing sources of
information. Instead, if people are not rational they may incorporate relevant social,
demographic, and other informational cues to derive a sense of what they think are reasonable
expectations for concern for crime.
Figure 2. Figure 3.
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
27
4. Results
4.1 Descriptive Statistics
The total number of people who respond to concern for crime on the GSS is 30,821 for
all years. For the years 1973-‐2010, people’s concern for crime has a mean of 2.62 and a
standard deviation of 0.60 (Appendix Table 5A). The sample skews negatively towards little
concern for crime. The mean for the violent crime rate is 549.97 (per 100,000 people) with a
standard deviation of 99.73 and a range (401, 758.2). The year with the highest rate of reported
violent crime was 1991; the lowest rate was in 2010 (401 versus 417.4 in 1972). For summary
statistics on the individual types of violent crime refer to the appendix (Appendix Table 1A).
The majority of violent crimes are incidences of assault and robbery. The individual
types of crime do not strongly predict a relationship with concern for crime compared to the
total rate of violent crime. I establish this through a comparison of simple OLS regressions for
the unique crime types’ rates and the total violent crime rate. As a result, I use total violent
crime rate as the variable of investigation with concern for crime going forward, as opposed to
the individual crimes, which I explain in more detail above.
An OL S regression on concern for crime using the four unique types of crime on concern
for crime does not show significant trends across the crimes (Table 3, Model 1). When I do the
same for violent crime, the results do reach significance, suggesting that the total violent crime
rate rather than individual rates is the source of information that people use for crime rates, as
previous research has suggested (Table 4). I also include a regression of the individual crime
rates with year trend included (Table 3, Model 2). None of the crime variables’ coefficients
succeeding in reaching statistical significance. Adding the year trend does not improve the
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
28
value of adjusted R2, or it seems the model with individual crimes. However with the year trend
included the direction of the coefficients changes, which suggests the year trend is accounting
for some degree of spurious or omitted variables in Model 1 (Table 3).
In the OLS model 1 (Table 4) using total violent crime as the independent variable, an
increase in one incident of violent crime (per 100,000 population) predicts a less than one
percent increase in people’s concern about crime, at significance p = 0.004 (F[1,17] = 10.84, R2 =
0.38, Adjusted R2 = 0.35). The value of adjusted R2 suggests that 38% of the variance in the
model is explained by the effect of violent crime on concern for crime. Given the low value of
adjusted-‐R2, other sources of information may help people make the decision of how
concerned they are about crime. When a year trend is included in the OLS model with violent
crime, every 1 increase in the violent crime rate (per 100,000 inhabitants) predicts a less than
1% increase in people’s concern for crime (Table 4, Model 2). There is also a statistically
significant year trend that signifies, net of all, other factors, concern for crime seems to be
decreasing in the population each year as some sort of artifact or time (p < 0.001) (Table 4,
Model 2). Model 2 has a higher adjusted-‐R2 value which indicated including the year trend may
account for some spuriousness that was present in Model 1 (Table 4). Thus if I were to stop
analysis at a univariate OLS regression, I could miss important and real trends. Indeed, I remedy
this risk by incorporating the variables of the three domains into analysis for multivariate
analysis of concern for crime.
Accordingly, the results compared in Tables 3 and 4 support using the total violent crime
rate for analysis and are consistent with previous literature. The individual crime rates’
coefficients show non-‐significance in predicting people’s concern for crime whereas, the total
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
29
violent crime rate may influence how much concern for crime people have. People may look at
the overall number of events rather than rates for specific types of crime to determine how
much crime is happening and how safe they deem society to be, which is supported by previous
research (Warr, 2005). Since I establish here that the total violent crime rate is the valid
measure of crime to use in this analysis, it will be the only variable of crime in further analysis.
Table 3. OLS Regression with Individual Crime Rates Averaged
OLS no year trenda (1)
OLS with year trendb (2)
Murder 0.006 -‐0.008 Rape -‐0.004 -‐0.004 Robbery 0.001 0.001 Assault 0.0001 0.0002 Year -‐ -‐ -‐0.003 aAdj. R2 = 0.737
bAdj. R2 = 0.728 -‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01
Table 4. OLS Regression with Violent Crime Rates
Averaged
OLS no year trenda (1)
OLS with year trendb (2)
Violent Crime 0.0004*** 0.0003* Year -‐ -‐ -‐0.007* aAdj. R2 = 0.353
bAdj. R2 = 739 -‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01
Summary statistics reveal insightful patterns for people’s concern for crime, when
examined across gender, age, race, marriage, and kids in household (Table 5). In all three of the
domain’s summary statistic tables, the rows reveal respondents’ concern for crime as a
percentage of the total for each variable. The total across rows will be 100% for the variable
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
30
listed at left. For example, less than 5% of females responded with low concern for crime,
whereas almost 7.5% of males have low concern for crime. Both males and females tended to
rate their concern for high rather than low or neutral (64% of males and 71% of females have
high concern for crime), but more females than males to have “much concern for crime.” Age is
relatively equally distributed across the scale of concern for crime with almost equal standard
deviations. By race, white respondents and respondents of other races are more likely to have
concern for crime, but non-‐white respondents’ rate high concern for crime with a greater
percentage, 73% versus 67%, respectively. There is little to no difference in the percentage
distribution of concern for crime for respondents who are married versus not married. Using
just summary statistics for marriage and concern for crime it does not look like the state of
marriage mediates people’s concern for crime. Likewise there is little difference across the scale
of concern for crime by those who have kids under 18 years in the household versus those who
do not. Having kids in the house does not seem to mediate concern for crime. Those with a lot
concern for crime is made of females in the middle of years age (i.e. mid-‐life) who are not
white, and are married with kids in the house. Non-‐white respondents show they are more
likely to have a lot of concern for crime rather than little for crime compared to white
respondents’ distribution across concern for crime. Across all of the demographic variables the
majority of individuals have much concern for crime; consistently, we above 60% of
respondents for all control variables with much concern for crime. Knowing that crime rates
have steadily declined since the early 1990s, these results lend themselves to previous claims
that people may not be rationally assessing their concern for crime given true crime rates.
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
31
In the national priorities and political opinions domain, there are similarly few patterns
to discern, but again across all control variables a majority of people respond that they have
high concern for crime (Table 6). More people who have high concern for other national
priorities also have high concern for crime than low concern for crime. People who consider
Table 5. Descriptive Statistics of Domain Two Variables and Concern for Crime Concern for Crime Much Neutral Low Sex (%) Female Male Age (years) *** Age 18-‐25 (%) Age 26-‐35 (%) Age 36-‐45 (%) Age 46-‐55 (%) Age 56-‐65 (%) Age 66-‐75 (%) Age 76-‐85 (%) Race (%) White Other Married (%) Yes No Kids (%) Yes No
71.02 64.11 48.02a
(17.87)a
66.77 68.12 66.90 67.83 70.12 68.07 67.33 66.74 73.41 68.44 67.20 68.97 67.18
24.24 28.43 44.26a
(17.21)a
28.50 26.56 27.48 26.08 23.24 24.69 24.37 27.32 20.49 25.73 26.65 26.11 26.35
4.74 7.46 45.30a
(17.36)a
4.72 5.31 5.61 6.09 6.63 7.25 8.30 5.94 6.10 5.83 6.15 4.93 6.47
-‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01 -‐ ***a Values represent means and standard deviations
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
32
themselves liberal are concentrated in slightly lower percentages towards high concern for
crime. 71% of conservative respondents have high concern for crime, whereas 65% of liberal
respondents have high concern for crime. However, liberal respondents are concentrated in
greater percentages around neutral concern for crime (29% versus 22%).
In the third domain, the percentage of respondents who have much concern for crime is
higher across all variables (Table 7). Almost 70% of those who rate themselves are pretty happy
have much concern for crime, whereas only 8% of very happy people have little concern for
crime. For those who are pretty happy and not too happy, the pattern is similarly clustered
around people responding that they have high concern for crime. People who are trusting and
rate society as fair respond that they have much concern for crime with a slightly lower
percentage than those who are not trusting and do not believe society will treat them fairly
(trusting and high concern for crime = 63.95%, fair and high concern for crime = 65.49% versus
not trusting and high concern = 70.20% and society is not fair and high concern for crime =
Table 6. Descriptive Statistics of Domain Two Variables and Concern for Crime Concern for Crime Much Neutral Low National Priorities (%) Health Welfare Drugs Education
72.97 74.50 81.40 78.86
22.72 20.71 15.82 23.43
4.31 4.79 2.78 4.70
Political Views (%) Liberal Conservative
65.38 66.53
28.86 26.58
5.94 6.90
-‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01 -‐ b Values represent means and standard deviations
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
33
71.41%). The summary information of these variables suggests further investigation is
warranted to understand their possible relationship with people’s concern for crime.
Across all domains, covariates, and demographic characteristics summary statistics point
towards skewness in the data towards low concern for crime, such that people are
concentrated around high concern for crime. Thus, it is worth investigating if these variables
inform people of or help to explain the relationship between concern for crime and true crime
rates, especially since crime rates have been falling since the early 1990s and people’s
persistent high concern for crime does not seem to rationally align with crime rates given this
information (Table 7).
Table 7. Descriptive Statistics of Domain Three Variables and Concern for Crime Concern for Crime Much Neutral Low Happy (%) Very happy Pretty happy Not too happy Trust (%) Yes No Fair (%) Yes No
68.36 68.14 69.75 63.93 70.20 65.49 71.41
26.05 26.18 22.07 30.19 23.52 28.88 21.57
5.60 5.68 8.18 5.88 6.28 5.62 7.02
-‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01 -‐ b Values represent means and standard deviations
The final descriptive transformation I perform on the data is to explore the nature of
possible splines. Splines are a useful tool for modeling simple non-‐linear time trends (Marsh &
Cormier, 2002). Splines can often model non-‐linear trajectories that appear to change direction
after a particular period in time (Marsh & Cormier, 2002). For example, in the 1990s concern for
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
34
crime appears to begin dropping (Figure 4), and splines are able to capture this abrupt drop and
model multiple linear trends within the data. In essence splines work to join two or more
regression lines that may exist in the data across time by fitting and smoothing turns and kinks
in time (Marsh & Cormier, 2002). An alternative to using splines is polynomial regression, which
I tested by including the multinomial version of time. This did not reveal any significant trends
and suggests that splines’ success in modeling multiple linear trends in the data is a better fit. It
also runs the risk of creating mulitcollinearity with each additional term and fails to capture
sudden changes in slope (Marsh & Cormier, 2002). Given Figure 4, I argue a sudden change in
slope does occur in the 1990s in the concern for crime variable.
Figure 4.
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
35
Figure 5.
I determine that there should be a knot at year 1991 in the data based on the possible
trends depicted in Figure 5 (Marsh & Cormier, 2002). The first spline is 1973-‐1991 and the
second spline is 1991-‐2010. The regression output for this regression models new linear trends
taking 1991 as the knot-‐year as the place where the linear trend changes. The regression
output can be seen in Table 6A in the appendix. The first spline indicates that there is a positive
trend for people’s concern for crime for each increasing year until 1991. A 0.002 point increase
in people’s concern for crime is predicted for each additional year until 1991 (N = 30, 821, β =
0.002 p = 0.001, adjusted-‐R2 = 0.0062). After 1991, there is a statistically significant decrease in
concern for crime predicted. Each additional year predicts a 1% decrease in concern for crime
(β = 0.01 p < 0.001). The low adjusted-‐R2 value suggests the spline regression model is not
modeling all the effects that determine people’s concern for crime. A test for heteroscedasticity
(p = 0.944) and a Durbin alternative statistic (p = 0.0246) confirm that neither are present in the
linear spline model. Thus, splines are useful to understand the basic changes in the linearity of
concern for crime over time, but there is a lot of variation unexplained, which is why I continue
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
36
to higher-‐leveling modeling and attempt to capture more of what determines the relationship
between people’s concern for crime and violent crime rates. I explore this relationship father by
analyzing the relationship across the three domains of variables using different time series
modeling techniques.
As a final check on the variables before heading into analysis of concern for crime and
crime rates across the three domains, I explore the stationarity of the two variables: concern
for crime and the violent crime rate (per 100,000 inhabitants). Time series analysis assumes a
constant error values, means, and standard deviations across time. By checking these
characteristics I can confirm whether I should include analysis that checks for heteroscedasticity
and serial correlation in my analysis. Figure 4 and Figure 6 show the trend of the mean of
concern for crime over time. They show that the values are non-‐stationary across time. The
mean of concern for crime appears to increase without a clear trend until the 1990s and then
continuously decreases (Figure 6). Figure 5 and Figure 7 show the trend of the mean and
standard deviation of the violent crime rate for all years. The violent crime rate, like concern for
crime, increases until the 1990s (Figure 7). After 1991 the rate of violent crime appears to
decrease over time, while concern for crime appears much more variable until the early 1990s
when the trend decreases.
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
37
In light of these non-‐stationary trends, standard OLS could produce spuriousness in the
results. The present study collapses variables around mean values to compare by year and
includes tests that check for risk factors in the data. I perform basic checks on the data from the
OLS regression in Table 4 (above) to confirm whether the results are being spuriously driven by
other factors and require more analysis. I check normality and fail to reject the null hypothesis
that the sample comes from a normally distributed population, and conclude the data when
Figure 4. Figure 5.
Figure 6. Figure 7.
2.5
2.55
2.6
2.65
2.7
Mea
n
1970 1980 1990 2000 2010Year
Mean of Concern for Crime by Year40
050
060
070
080
0M
ean
1970 1980 1990 2000 2010Year
Mean of the Violent Crime Rate, by Year
0.0
2.0
4.0
6St
anda
rd D
evia
tion
0 5 10 15 20Year (in Two Year Averages)
Standard Deviation of Concern for Crime
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
38
collapsed by two year averages come from a normally distributed population (p = 0.211). I
check for heteroscedasticity and fail to reject the null hypothesis that there is no
heteroscedasticity (p = 0.445). I check up to three lags for autocorrelation using Durbin’s
alternative h-‐statistic and fail to reject the null hypothesis that no autocorrelation is present
(one lag: p = 0.742; two lags: p = 0.568; three lags: p = 0.687). These tests suggest the data are
free from these risks, however there is a low number of observations and I choose to include a
year trend in further analysis to ensure that analysis is picking up any omitted variables that
relate to both crime rates and concern for crime. Thus my analysis across the three domains
includes checks of heteroscedasticity and autocorrelation. Including First Differences and Prais-‐
Winsten feasible least squares regressions will correct for these risks if they arise in my analysis
and will enable me to investigate the relationship of concern for crime and violent crime rates
over time with properly controlled data.
4.2 Crime and Demographics
A standard OLS regression on concern for crime using the rate of violent crime and
demographic variables does not reveal many statically significant patterns (Table 8). When the
violent crime rate increases, so too is concern for crime predicted to increase (N = 19, β =
0.0004, p < 0.01, R2 = 0.74), holding all other factors constant. Although the other variables in
the OLS model do not show significance, they do operate in the expected direction for reach
relationship. Males are predicted to have a lower concern for crime than females; each
additional year of age predicts an increase in concern for crime; those who are married are
expected to have higher concern for crime, as are those who have children under 18 in the
household. Inclusion of the year trend picks up on potential omitted variables that may drive
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
39
part of the relationship between concern for crime and crime rates. Although the adjusted-‐R2
value is high for this model, I chose to interpret it with caution because in OLS it may be a result
over over-‐fitting with so many variables included in the model. I fail to reject the null
hypothesis of no autocorrelation with one lag and conclude there is no autocorrelation in the
model (1) (Chi2 = 1.361, p = 0.243). Furthermore there is no serial correlation in the model (p =
0.195).
Table 8. Regression Models for Demographics Domain OLS (1) OLS with year (2) Prais-‐Winston (3) Violent Crime 0.0004***
(0.0001) 0.0004*** (0.0001)
0.0004* (0.0001)
Male -‐0.845 (0.799)
-‐0.347 (0.991)
-‐0.578 (0.898)
Age 0.0001 (0.012)
0.007 (0.015)
0.012 (0.013)
Race -‐0.425 (0.214)
-‐0.412 (0.217)
-‐0.561** (0.194)
Married 0.462 (0.330)
0.277 (0.397)
0.303 (0.3)
Kids 0.135 (0.133)
0.064 (0.157)
0.07 (0.127)
Year -‐-‐ -‐0.006 (0.007)
-‐0.007 (0.006)
Adj. Durbin-‐Watson 1.361 2.24 2.36 Rho Adj. R2
-‐-‐ 0.746
-‐-‐ 0.740
-‐0.52 0.995
-‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01 -‐ Standard errors in parenthesis
Including a time year with the year variable does not change the significance of the
independent variable’s coefficients in OLS by much, the relationships between the variables and
concern for crime can be interpreted net of time (Table 8, Model 2). For each subsequent year
of the survey, concern for crime is predicted to decrease. This trend is seen in Figure 2, which
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
40
depicts the average rating of concern for crime across time. However, the OLS model with a
time trend does not take into account that each year is important in its specific place in time. I
fail to reject the null hypothesis of no autocorrelation with one lag and conclude there is no
autocorrelation in the model (2) (Chi2 = 2.24, p = 0.135). Furthermore there is no serial
correlation in the model (p = 0.195).
Following the OLS model with a year trend included I ran First Differences on the
demographics domain variables with the year variable included to capture the year trend (Table
9). I interpret the coefficient on the rate of violent crime to show that a 1% increase, a 0.03%
increase is expected in people’s average concern for crime given a three point concern for
crime rating scale, net of all other differences at any point in time. However, this result is not
statistically significant, nor do any other coefficients in the model reach statistical significance.
The overall adjusted-‐R2 = 0.2 value for the model is quiet low, although not unexpected for
aggregate level data, and suggests that only about 20% of the variation of the relationship
between the variables is explained by the model. First differences takes care of
heteroscedasticity (p = 0.313). There is marginal serial correlation of the first-‐order in the model
as evidenced by a Durbin alternative test (Chi2 = 4.094, p = 0.043).
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
41
Table 9. First Differences Model for Demographics Domain First
Differences d.Violent Crime 0.0003
(0.0003) D.Male 0.476
(1.147) D.Age 0.003
(0.-‐23) D.Race -‐0.340
(0.259) D.Married 0.243
(0.578) D.Kids 0.138
(0.224) D.Year -‐0.0008
(0.003) Adj. Durbin-‐Watson 0.043 Adj. R2 0.2 -‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01 -‐ Standard errors in parenthesis
The final model I ran on the first domain is Prais-‐Winsten estimation (Table 8, Model 3).
The rate of violent crime and race are the only statistically significant coefficients on concern
for crime. For each percent increase in the rate of violent crime, people’s average concern for
crime is expected to increase by 0.04% (N = 19, β = 0.0004, α < 0.001). A 1% increase in the
proportion of white respondents predicts a -‐0.561 decrease in concern for crime, net of all
other factors and at any point in time (β = -‐0.561, α < 0.05). Across the four tests, violent crime
is a statistically significant predictor of crime in the demographics domain. In the Prais-‐Winsten
model the proportion of white versus non-‐white respondents seems to play a role in
determining concern for crime at a marginally statistically significant level. Although the
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
42
demographic variables fail to reach statistical significance, analysis suggests the variable do
trend in the expected direction for these variables.
4.3 Crime, National Priorities, and Political Opinion
The second domain of exploration is national priorities, political views, and media. To
begin I ran a basic OLS regression on concern for crime with the independent variables of the
rate of violent crime and the national priorities variables (Table 10, Model 1). This test was to
determine if as people increase their focus on other national priorities their attention to
concern for crime changes in a significant way. The results of the simple OLS indicated that an
increase in concern for other national priorities predicts a decrease in concern for crime at a
non-‐significant level . Political views and hours spent watching TV create positive change in the
level of people’s concern for crime, but neither were significant. Violent crime does predict a
statistically significant increase in people’s concern for crime – across Models 1, 2, and 3.
Table 10. Regression Models for National Priorities and Politics Domain OLS (1) OLS with year (2) Prais-‐Winsten (3) Violent Crime 0.0004*
(0.0001) 0.0003*** (0.0001)
0.0003*** (0.0001)
Political Views 0.184 (0.475)
0.137 (0.387)
0.072 (0.370)
National Priorities -‐0.213 (0.118)
0.048 (0.135)
-‐0.008 (0.126)
TV Hours 0.118 0.135
0.008** (0.117)
0.082 (0.119)
Year -‐ -‐ -‐0.007** (0.002)
-‐0.006** (0.002)
Adj. Durbin-‐Watson 0.066 0.111 2.05 Rho -‐ -‐ -‐ -‐ -‐0.243 Adj. R2 0.517 0.68 0.962
-‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01 -‐ Standard errors in parenthesis
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
43
Contrary to expectations in Model 1, when people’s concern for other national issues
increased, it predicted a decrease in people’s concern for concern for crime, although the result
is not statistically significant. Also, for each 1% increase of the population responding as having
liberal political views, there is a predicted 18% increase in people’s concern for crime; however
this results fails to reach significance. It should be noted the low number of observation may
contribute to the amount of non-‐significance seen in my analysis. In Model results may also be
driven by spurious factors, which is why a year trend is included in Models 2, 3, and 4 to try to
account for variables that may be driving the relationship but are not included. For the OLS
model without year trend (Table 10, Model 2), a heteroscedasticity test fails to reject the null
hypothesis that there is homoscedasticity in the data (Chi2 = 2.40, p = 0.122). A Durbin
alternative test fails to reject the null hypothesis that there is no serial correlation in the
residuals in the OLS model with year trend (Chi2 = 0.066, p = 0.8). Including two and three lags
in the model also creates situations in which the adjusted DW test fails to reject the null
hypothesis. In the OLS Model (2) with a year trend included, violent crime and the year trend
significantly predict changes in people’s concern for crime in the expected directions – positive
for the crime rate and negative for the year trend. A heteroscedasticity test for Model 2 fails to
reject the null hypothesis that there is no heteroscedasticity (Chi2 = 1.01, p = 0.315). A Durbin
alternative test fails to reject the null hypothesis that there is no serial correlation in the
residuals in the OLS model with year trend (Chi2 = 0.111, p = 0.739). Including two and three
lags in the model also fails to reject the null hypothesis that there is serial correlation (two lags:
p = 0.751; three lags: p = 0.893).
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
44
After running the OLS models, I ran First Differences on the second domain of variables
with the year variable included (Table 11). I interpret the coefficient on the rate of violent crime
to show that a 1% increase, a 0.03% increase is expected in people’s average concern for crime,
net of all other differences and at any point in time. However, none of the coefficients in the
model reach statistical significance. The direction of the relationship for political views is the
same direction as predicted by the OLS Model (1) and by Model (3) such that someone who is
liberal is predicted to have a decreased level of concern for crime (Table 10). In OLS model (2)
the relationship is positive. This may indicate some sort of deficiency in the variable to measure
a relationship with concern for crime, since Chronbach’s alpha was moderately low (α = 0.45).
In the First Differences Model (Table 11), the adjusted-‐R2 = 0.085 value for the model is low and
suggests that the model might not be fitting the correct trend to the data. The model does not
have any first-‐order autocorrelation (Chi2 = 0.633, p = 0.426) nor does it have any
heteroscedasticity (Chi2 = 0.06, p = 0.808).
Table 11. First Differences Model for National Priorities and Politics Domain First Differences Violent Crime 0.0003
(0.0003) Political Views 0.222
(0.44) National Priorities 0.244
(0.196) TV Hours -‐0.122
(0.109) Year 0.0007
(0.003) Adj. Durbin-‐Watson 0.663 Adj. R2 -‐0.088 -‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01 -‐ Standard errors in parenthesis
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
45
The final model I ran on the national priorities domain is a Prais-‐Winsten test. The rate
of violent crime is the only statistically significant coefficient on concern for crime. For each
percent increase in the rate of violent crime, people’s average concern for crime is expected to
increase by 0.03% (N = 18, β = 0.0003, α < 0.01). Also, the test is successful because the Durbin-‐
Watson statistic approaches 2, which suggests no autocorrelation in the model (Durbin-‐Watson
= 2.05).
4.4. Crime and Social Values
The third domain of independent variables is social values measures. An OLS regression
on concern for crime using social values and emotions variables highlighted the ways in which
people’s judgments about society’s “goodness” or their emotional state predict changes in
concern for crime (Table 12, Model 1). When people believe that society is trustworthy, there is
an increase in people’s concern for crime. Likewise, when people judge society inherently fair
versus not fair, it is predicted that there is a positive change in people’s concern for crime.
Oddly, when people increased their happiness by a unit on the three point GSS scale, they are
predicted to have stronger feelings of concern for crime. Intuitively one might expect that
positive rating on social values would predict decreases in concern for crime. However, it may
be that getting people to make value statements about society’s positive qualities might draw
their attention to its failures – in this case the state of crime. Also, it is important to note that
none of these variables is significant. Violent crime does statistically significantly continue to
positively predict people’s concern for crime (N = 18, β = 0.0003, p < 0.01, R2 = 0.62).
Model 2 (Table 12) is an OLS regression on concern for crime with the year trend
included. The direction of the variables’ relationship with concern for crime for all three of the
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
46
domain variables flips when the year trend is included. Although, none are significant the
relationship interpretation is what is expected compared to Model 1. Here the trend points to
people being trusting have less concern for crime, which is supported by the literature (Mullen
& Donnermeyer, 1989). The trend for those who rate society as inherently fair and not trying to
take advantage of people suggests that they will have decreased concern for crime. Finally, for
those who respond that they are happiest (on the three point scale) the trend suggests they will
also have decreased concern for crime. There is not any heteroscedasticity (p = 0.424), not does
Durbin’s h-‐statistic show that there is no first-‐order autocorrelation in the model (Chi2 = 0.843,
p = 0.359). The addition of two and three lags to the test does not change the state of no
autocorrelation in the model. All three variables’ relationships with concern for crime are
logical and expected, and perhaps if there were more observations to add robustness to the
models statistically significant results would emerge.
Table 12. Regression Models for Social Values Domain OLS (1) OLS with year (2) Prais-‐Winsten (3) Violent Crime 0.0003**
(0.0001) 0.0003** (0.0001)
0.0003* (0.0001)
Trust 0.439 (0.349)
-‐0.122 (0.400)
-‐0.152 (0.411)
Fair 0.316 (0.303)
-‐0.190 (0.354)
-‐0.146 (0.314)
Happy 0.198 (0.412)
-‐0.222 (0.411)
0.496 (0.377)
Year -‐ -‐ -‐0.009** (0.004)
-‐0.010** (0.004)
Adj. Durbin-‐Watson 0.891 0.843 2.107 Rho -‐ -‐ -‐ -‐ -‐0.384 Adj. R2 0.616 0.702 0.994
-‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01 -‐ Standard errors in parenthesis
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
47
Following the OLS analysis, I ran First Differences on the societal values and emotion
domain of the variables with the year variable included (Table 13). I interpret the coefficient on
the rate of violent crime to show that a 1% increase in the crime rate predicts a less than 1%
increase in people’s average concern for crime, net of all other differences at any point in time.
However, none of the coefficients in the model reach statistical significance. The value of the
coefficients on trust, fairness, and happiness continue to change model to model. The
extremely low adjusted-‐R2 = -‐0.0798 value for the model is low and negative and suggests that
the first difference model is having trouble using differences to determine the true state of the
relationship between the variables. Perhaps, people’s trust in society, rating of society’s
fairness, and people’s personal level of happiness may not have strong bearing on their
determination of concern for crime. Durbin’s alternative h-‐statistic fails to reject the null
hypothesis that there is first-‐order serial correlation (Chi2 = 2.659, p = 0103).
Table 13. First Differences Model for Social Values and Emotions Domain First Differences Violent Crime 0.0003
(0.0003) Trust -‐0.116
(0.413) Fair -‐0.541
(0.446) Happy 0.663
(0.545) Year 0.0016
(0.003) Adj. Durbin-‐Watson 0.103 Adj. R2 -‐0.08
-‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01 -‐ Standard errors in parenthesis
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
48
The last test is a Prais-‐Winsten estimation (Table 12, Model 3). The rate of violent crime
is the only statistically significant coefficient on concern for crime. A 1% increase in the rate of
violent crime leads to a 0.03% increase in people’s average concern for crime (N = 18, β =
0.0003, α < 0.000). Also, the model is free of autocorrelation because the Durbin-‐Watson
statistic approaches 2 (Durbin-‐Watson = 2.107).
5. Discussion
In this study, I examined if people’s concern for crime and true violent crime rates trend
together over time. I was interested in studying if people logically use crime rates rather than
other sources of information to assess their concern for crime. Previous literature has tried to
explain the dynamics that contribute to people’s concern for crime. Warr (2005) argues that the
way in which people derive their concern for crime is a complex process that is not only related
to their knowledge of crime rates. I find that crime rates appear to be the main source of
information people use to establish their concern for crime across time.
In order to test this relationship and explore other contributing factors, I included
several independent covariates from the GSS to examine if additional variables across three
domains predicted p concern for crime when information about true crime rates was included
in analysis. I included demographic variables to understand which sub-‐groups and portions of
U.S. society are likely to be more or less concerned with the state of crime. National priorities,
political opinions, and media habits were included to see how concern for crime will change as
people focus on other national priorities and public opinion sources over time. I also included
social values and emotions variables from the GSS to assess if changes people’s responses to
these questions moved in conjunction with or opposition to concern for crime across the years
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
49
1973-‐2010. None of these variables appeared to be significant factors in determining people’s
concern for crime across all years. Given analysis of several control variables, it appears that
people respond rationally to information about crime rates and use them to develop their
levels of concern for crime.
I ran initial analysis using ordinary least squares regressions across three domains of
investigation. I followed with First Differences and Prais-‐Winsten feasible least squares
regression. The latter two tests are designed to control for possible risks in the data in the form
of heteroscedasticity and serial correlation. OLS regression, even with time trends included,
may have spurious results because it assumes certain patterns in the data that may not hold
with time series analysis. In the present study, consistent checks for heteroscedasticity and
serial correlation show that there is none present when I use two year averages to collapse the
data by year for analysis. Conversely, First Differences is recognized as being capable of
correcting time series autocorrelation – a common analytical complication of time series
(Ostrom, Jr., 1990), and it is easy to run and interpret. Finally, because First Differences deals
with serial correlation further time series tests are unnecessary for the purposes of the study
beyond the tests I have included. However, First Differences is a very parsimonious test. Across
all three domains, the variables fail to produce any significant results.
A large body of previous research has explored the influence that media exposure has
on people’s fear of crime. I find that at the aggregate level of analysis rather than using a cross-‐
sectional design, TV hours was only a marginally significant predictor of people’s concern for
crime in one model – OLS with a year trend included. It also did not to alter the relationship
between actual crime rates and concern for crime. That TV hours had a slight relationship with
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
50
concern for crime is not surprising given the extensive literature about media sensationalization
about crime, nor is it a surprise that it does not drive the overall concern for crime relationship.
The study intended to analyze if people use crime rates to get information about their concern
for crime, and even with the inclusion of the media variable the relationship holds.
Readers should not overlook potential limitations in the data. In all models observations
are low – to the point that all models have less than 30 observations. The small number of
observations creates possible bias because we cannot assume the observations are
independent and individually distributed under the assumptions of the central limit theorem
(Berry & Feldman, 1985). I confirm that the concern for crime variable is normally distributed
after the data transformation. Yet, in all models there are a maximum of 19 observations.
Although many of the models do not show statistical significance, given the constraint of
observation numbers, interpretation of the results does show that the variables tend to predict
the expected relationship with concern for crime. Thus, I am reassured that the relationship
between concern for crime and total crime rates does exist. In all models expect for First
Differences violent crime rates predict increases in concern for crime, indicating that people
logically use crime rates to determine their concern. Future studies will benefit from more
years of observations to take into account, and their examination will hopefully show statistical
significance where we expect relationships to exist between violent crime and concern for
crime.
Other limitations include the datasets used. Given prior knowledge that the FBI UCR
report are known to have inaccuracies or be lacking full participation of law enforcement
agencies around the country, it is possible that missing data have taken a toll on accurate
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
51
exploration into the possible relationship between concern for crime and actual crime rates
over time. In order to understand if this is a major concern for researchers, further studies
could explore the reliability uncertainty concerns that have been raised about the FBI UCR.
Although the models contain variables of non-‐significance, these results are not
necessarily a disappointment nor should it be a deterrent from interpretation. The rate of
violent crime is a consistently positive predictor of people’s concern for crime with statistical
significance. When the rate of violent crime rises or falls, people’s concern for crime is expected
to move in the same direction. The results suggest that people do, in fact, use information
about crime rates to accurately perceive their concern for crime. Previous literature has studied
a wealth of covariates to better understand if anything mediates the relationship between
concern for crime and violent crime rates. I find here that none of the covariates from three
domains are useful predictors of concern for crime when violent crime rates are also
considered. The trends still exist, and I expect that with the availability of more years of data
the full nature of these relationships will be revealed.
In the present study I explore the relationship of people’s concern for crime and crime
rates for the years 1973-‐2010. I conclude from this information that people appear to logically
refer to crime rates when determining their concern for crime across time rather than using
other competing sources of information. Demographic, national priorities, opinions, and values
and emotions may play a role by informing some people some of the time about the state of
crime. However, across time and at the aggregate level these variables do not drive the
relationship of concern for crime and crime rates. Recognizing how crime rates influences
people’s beliefs about their safety and crime has implications for decision-‐makers and policy
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
52
advocates. Increased knowledge of the relationship can focus alignment of crime prevention
more closely with public opinion so that the public accurately perceives crime prevention as
having a positive effect. In conclusion, it does appear that for the years studied, across a
national sample, people’s concern for crime has been decreasing over the years and that the
main source of information that people use to determine their concern for crime is crime rates.
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
53
APPENDIX
FBI UCR Data Limitations
However, the UCR is not without its constraints, controversies and inadequacies. Thus,
readers should be aware of the weaknesses of UCR crime data collection. The unique system
that goes into keeping police records and further compilation and storage by the FBI creates
opportunities for error and manipulation (Milkakovich & Weis, 1975). Effects that influence that
reported numbers of crime within the UCR include the crime coding process, adherence to the
UCR Reporting Handbook, and ambiguities in crime definitions (Mosher, et al. 2002). Although
the UCR is subject to inaccuracies and poor accounting each year, it is not the only measure of
crime to face these risks. Despite the recognized issues with the UCR, I use it as the source of
crime rates because of its long existence, attempts at standardization and record-‐checking,
several levels of analysis of crime and the fact that it is the most comprehensive, single
directory of crimes for the U.S. Additionally, as a whole the UCR data collection tries its best to
get accurate counts of crime and corrects for flaws when identified.
The FBI UCR records crimes using the Hierarchy Rule. Under this classification system
each event of crime can only be reported to the UCR based on its highest ranking offence,
regardless of whether more than one type of crime occur in each event2. Since only one type of
crime can be recorded per event, the rest are not captured in UCR reporting (Mosher, et al.
2002). This can lead to an undercount of levels of crime, in addition to other recording
malpractices that may occur. Two major compromises may result from using this method. The
2 Under the Hierarchy Rule, if a reporting law enforcement agency records a crime that includes an assault and robbery, the incident would only be captured once in the UCR as a robbery not as an assault. Although both crimes are types of violent crime, robbery ranks higher according to hierarchy rule standards.
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
54
first is that not all offenses are recorded when multiple offenses occur within the same
incident, as explained above. The second is the assumption that reporting agencies will
truthfully ignore multiple offenses rather than including them as separate offenses in effect
meaning they report these accounts as separate crime. The latter issue is an important
consideration since it means that agencies have to go through crime report to standardize their
crime counts for the UCR separately from their own accounting methods. While this is a risk,
the consistent methodology and standardization of reporting measures that has been in place
since 1930 is more important and ensures consistent methodology year to year.
FBI UCR Crimes
TABLE 1A. Crime Rates Summary Statistics, 1973-‐2010 Crime
Minimum (rate per 100,000)
Maximum (rate per 100,000)
Mean (Std. Deviation)
Murder Rape Assault Robbery Total Violent Crime
4.8 (2010) 24.5 (1973) 200.5 (1973) 119.1 (2010) 403.6 (2010)
10.2 (1980) 42.3 (1991) 440.5 (1993) 272.7 (1991) 758.2 (1991)
7.68 (1.67) 7.68 (1.67) 315.33 (67.66) 193.24 (41.32) 554.149 (99.73)
All crime rates given per 100,000 citizens Year in parentheses
There are four unique offenses measured as crime rates for murder, rape, robbery, and
assault. Table 1A displays their summary statistics. Crimes peak in the early 1990s except for murder, which spikes in 1980. Minimum rates are reached in 2010. Imputation I tested the two-‐year averages model with 19 time observations versus output from the imputed model with 27 time observations. (Table 2A-‐4A).
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
55
Table 2A. Demographics Domain – Comparison of Time Collapsing Methods Averaged
OLS with year trend
Time Series Fill
OLS with year trend
Violent Crime 0.004** Violent Crime 0.0004* Male -‐1.482 Male -‐0.723 Age 0.017 Age 0.009 Race -‐0.534** Race -‐0.359 Kids 0.171 Kids 0.099 Income 7.73e-‐06 Income 3.61e-‐06
Year -‐0.009 Year -‐0.003 N = 19 Adj. R2 0.75
N = 27 Adj. R2 0.72
-‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01
Table 3A. National Priorities & Politics Domain – Imputation Comparison Time as Two-‐Year Averages
OLS with year trend
Time as Imputed
OLS with year trend
Violent Crime 0.0003** Violent Crime 0.0003* Nat’l Priorities 0.053 Nat’l Priorities 0.192 Political Views 0.152 Political Views 0.055 Year -‐0.007** Year -‐0.003* N = 19 N = 26 Adj. R2 0.71 Adj. R2 0.71 -‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01
Table 4A. Social Values & Emotion Domain – Imputation Comparison Time as Two-‐Year Averages
OLS with year trend
Time as Imputed OLS with year trend
Violent Crime 0.0003** Violent Crime 0.0004* Trust -‐0.122 Trust 0.042 Fair -‐0.190 Fair -‐0.097 Happy -‐0.222 Happy -‐0.261 Year -‐0.009** Year -‐0.004*** N = 18 N = 23 Adj. R2 0.70 Adj. R2 0.72 -‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
56
Summary Statistics
Table 5A. Descriptive Table of Concern over Crime
A little Neutral
A lot
Total
N 20,927 8,055 1,839 30,821 Mean (St dev.)
-‐ -‐ -‐ -‐
-‐ -‐ -‐ -‐
-‐ -‐ -‐ -‐
2.62 (0.60)
Table 6A. Splines Regressions
Concern for Crime a Spline Regression Spline 1973-‐1991 0.002*
(0.001) Spline 1991-‐2010 -‐0.01*
(0.001) Durbin-‐Watson Statistic 1.344 F(2,24) 23.66 Adj. R2 0.0062 -‐ * Difference is significant at p < 0.001 -‐ **Difference is significant at p < 0.05 -‐ *** Difference is significant at p < 0.01 -‐ Standard Errors in parentheses
Significance Tests
Table 7A. Significance tests for Concern for Crime across National Priority Variables Concern for Crime A Little A lot
Drugs
1.84 (0.86)
2.70 (0.55)
Education
2.25 (0.84)
2.63 (0.58)
Arms
1.83 (0.80)
1.93 (0.58)
Child Care
2.56 (0.77)
2.56 (0.60)
CRIME RATES AND CONCERN FOR CRIME TIME SERIES ANALYSIS
57
Table 8A. Significance tests for Concern for Crime across Social Values Domain Concern for Crime A Little A Lot
Happy
2.14 (0.67)
2.20 (0.64)
Trust
0.39 (0.49)
0.39 (0.49)
Fair
0.56 (0.5)
(0.59) 0.49
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