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Spillover Crime and Jurisdictional Expenditure on Law Enforcement: a Municipal Level Analysis
Elizabeth Newlon Department of Economics
University of Kentucky enewlon@uky.edu
(April, 2001)
The author is deeply indebted to Dennis Epple for his comments and guidance. I also would like to express my gratitude to John Engberg, Richard Romano, Chris Bollinger and Daniel Nagin for their helpful comments. I am grateful to the MacArthur Foundation for their financial support of this research. All errors are my own.
Abstract: This paper finds evidence for the existence of significant effects of spillover crime on municipal expenditure by studying how enforcement expenditure varies with the spatial structure of metropolitan areas. There are limited data on the location of criminal activities and the corresponding residence of the perpetrators. I turn, instead, to the spatial structure of a metropolitan area to measure the amount of spillover because travel distance between municipalities affects the net benefit to criminals to relocating their activities. Two potential sources of endogeneity bias create another set of challenges to measuring the impact of spillover crime on enforcement. The first source of bias is the endogeneity between expenditure and municipal level demographic characteristics, due to Tiebout sorting. I address this issue with an empirical test that relies on metropolitan level variation to identify the key relationship between travel distance and enforcement expenditure. A second source of bias is the endogeneity between crime and enforcement. The model utilizes the innovation of temperature-based instruments to identify the relationship between enforcement and interjurisdictional movement of criminals, while controlling for the crime rate. For the analysis, a database was created for metropolitan areas in the U.S. from multiple sources. The empirical evidence shows that the spatial structure of metropolitan areas significantly affects the aggregate expenditure by municipal governments. This result is robust to variations in the specification of the model. The direction of the relationship between expenditure and travel distance supports the prediction that spillover crime affects enforcement expenditure.
2
The interaction between different communities’ enforcement activity through
spillover crime exists largely in the realm of examples. One such example comes from
Pittsburgh in early 1991: during a mayoral election, the Pittsburgh narcotics squad added
100 narcotics officers in a major crackdown on the narcotics trade in the eastern part of
the city. Within a month of the crackdown, Wilkinsburg, a municipality contiguous to
the targeted area, was experiencing a startling increase in drug-related crime, leaving the
police chief of Wilkinsburg wondering "if his town of 21,000 people might be the victim
of the success of drug strike forces in adjacent Pittsburgh, driving dealers into a town
with fewer police." (Pittsburgh Post-Gazette, 1992). Soon after, Wilkinsburg responded
by stepping up its own policing efforts.
The interaction between Pittsburgh and Wilkinsburg, and other such examples,
demonstrate that enforcement decisions in one community can affect crime in a
neighboring community. But they beg the question: how widespread and common is this
interaction? And, does the externality inherent in spillover crime influence the
equilibrium allocation of police across decentralized municipalities?
The effect of interjurisdictional crime on enforcement levels is not a given. It
depends on whether local police are more effective in relocating criminal activity to
another jurisdiction than in incapacitating the perpetrators within their jurisdiction. If
police predominately relocate criminal activities, policing generates a negative
externality for neighboring jurisdictions. When this is true, the safety of one community
is increased at the expense of its neighbors. Not wanting to be on the receiving end of
this interaction gives communities the incentive to compete for safety through their
relative expenditures on police.
Theoretical work on this topic by Marceau (1997) and Newlon (1999) predicted
over-expenditure on enforcement in the presence of decentralization when communities
benefit from the relocation of their indigenous criminals. Thus a measure of the volume
of spillover crime is important because it is tied to the efficiency of municipal
expenditures. The focus of this paper is to present evidence that spillover crime exists by
testing for its predicted impact on expenditures of municipalities in metropolitan areas.
3
Interjurisdictional Crime
Behavioral models of criminals in fixed residences, but with mobile activities,
depend on two major, relatively defendable assumptions. The first states that criminals
will travel to find opportunities, some far enough to enter other jurisdictions.1 Studies of
the spatial behavior of criminals provide one source of evidence for the existence of
cross-jurisdictional travel by opportunistic criminals. Direct interviews with criminals
have enabled researchers to estimate for several cities the spatial range of criminal
activity. The spatial range was measured around the residence of each participating
criminal. Reppetto (1976), Capone and Nichols (1976), and Pope (1980) demonstrated
that, in their sample, most burglaries and robberies are committed from 1.5 to 3 miles
from the perpetrator's home. In particular, Pope found that 48% of burglaries occur more
than 1 mile from the burglar’s residence. For criminals residing within a mile of the
municipal boundary, that radius will place some of their crimes in neighboring
communities.
A second line of research provides more detail on the spatial behavior of
criminals. Routine activity theory, proposed by Cohen and Felson (1979) and
empirically tested by Sherman, et al. (1989), as well as the "geometry of crime"
literature, spearheaded by Brantingham and Brantingham (1984, 1993, and 1995), model
criminals as searching for opportunities in "nodes" along "paths" of routine activity.
Nodes include where offenders work or go to school, shop or find entertainment (such as
bars), as well as where they live. Thus, the criminals who have paths that cross
municipal boundaries will search for criminal opportunities in nodes in other
jurisdictions.
The second major assumption behind spillover crime is that criminals respond to
differentials in enforcement. Differentials in enforcement theoretically create
differentials in the expected profit from crime if enforcement increases the probability of
arrest. I treat as a stylized fact that there is a positive marginal product of police with
1 It is logical to expect criminals, if afraid of being reported, will travel far enough from home that they will not be recognized. Yet in a dense urban area this might mean traveling only as far as the next street.
4
respect to arrests. What is not completely evident is that criminals change their activity
in response to arrest rates beyond forced cessation due to incarceration.
Levitt (1997) established that crime rates significantly decrease when the officer
rate increases. However, Levitt studied noncontiguous cities; hence, the scope of his
analysis does not permit any inference about the role of displaced criminal activity in the
decrease in crime. The story of Pittsburgh and Wilkinsburg suggests that an increase in
enforcement in one city can result in an increase in crime for a neighboring city.2
Statistical evidence for the relocation of criminal activity in response to increased police
protection can be found in the "hot spot" literature. Here criminals were found to move
among centers of activity, such as nuisance bars where fighting and drug activity are
present, in response to increased police attention.3 Olligschlaeger (1997) used data on
nuisance bars to predict the pattern of criminal responses to increased enforcement to
better optimize police strategy. Key to this response interaction is the repetitiveness of
criminal activity. If police respond post hoc to crimes that have little possibility of
prevention, relocation will be unlikely (Barr and Pease, 1990; Hesseling, 1993; and
Poyner, 1993). The hot spot and the geometry of crime literatures show that some types
of criminal activity are concentrated in a finite number of locations; thus, police have the
opportunity to be proactive and take preventative measures. One such preventative
measure is to drive criminals out of that area.
There is an existing literature in economics that has attempted to find evidence
that intercommunity differences in police levels affect spillover between communities
(Mehay, 1977; Fabricant, 1979; Hakim, et al., 1979; Buettner and Spengler, 2001). All
of the analyses are at the neighborhood or jurisdictional level. They provide support that
spillover crime exists, in particular for property crimes. However, they commonly do not
address two potential sources of endogeneity bias. The first source of bias comes from
Tiebout sorting of individuals across municipalities and enters the model through the use
of municipal level variation. The second source of bias arises from the endogenous
relationship between enforcement and crime. If the analysis attempted to control for
2 Pittsburgh hired additional officers right before a mayoral election, echoing the instrument used in Levitt’s analysis. 3 When police cracked down on a nuisance bar, they found that another bar that had been relatively peaceful would erupt in activity.
5
crime without instrumenting, the results for their spillover crime measure are potentially
biased.
The specification of my model endeavors to deal with both of these sources of
endogeneity. I explore the effect of spillover on municipal expenditure by studying how
enforcement varies with the spatial structure of metropolitan areas. The spatial structure
of a metropolitan area determines the travel distance between neighboring communities;
in turn, travel distance affects the net benefit to criminals of relocating their activities.
My analysis is at the metropolitan level, which allows me to attend to the endogeneity
issues associated with municipal-level variation present in previous empirical studies of
spillover crime.
In order to address the endogeneity between crime and enforcement, the empirical
model uses the innovation of temperature-based instruments to identify the relationship
between enforcement and interjurisdictional movement of criminals while controlling for
the crime rate. It has been argued by criminologists that opportunity makes an individual
a criminal and that anyone can be a criminal given the right opportunity. Temperature is
a correlate to the opportunities available across many categories of crime; for example, in
warmer weather there are more pockets available to pick. It is a good instrument because
it relates to the opportunities available to criminals yet not to the policing level in each
community.
Comparative-static predictions in Newlon (2000), addressing the relationship
between aggregate metropolitan expenditure and the average travel distance to a
municipal boundary, yield two tests for spillover crime as well as its impact on municipal
level enforcement expenditure. The empirical analysis reveals that the spatial structure
of metropolitan areas significantly affects aggregate metropolitan police expenditure by
municipal governments. The significant relationship between expenditure and travel
distance supports the prediction of Newlon (2000) that spillover crime affects
expenditure at the municipal level. This evidence indicates that distortions in municipal
expenditure are created by the negative externality of spillover crime and lends greater
importance to the theoretical result of over-expenditure on enforcement.
The structure of the paper is as follows: Section 1 outlines the theoretical basis for
the empirical test of over-expenditure. Section 2 presents the specification and
6
identification strategy. Section 3 describes the data. The results of the estimation are
discussed in Section 4.
Section 1: Decentralized Expenditure on Enforcement
Identification Issues
When investigating community decisions at the municipal level, the main
identification issue to address is the unwanted effect of Tiebout sorting on estimates. The
theory of Tiebout sorting implies that community amenities both are predicted by and
will predict demographic variables. Any characteristics of communities that change with
population flows should therefore be suspected of being endogenously determined. In
the case of this analysis, enforcement expenditure and characteristics of communities
such as income, race, and education can interact in this manner. Due to the potential
endogeneity of the independent variables with the dependent variable, the estimation
must be at the metropolitan level to avoid municipal-level variation. Aggregating
removes the endogeneity bias because information on the relative differences between
communities has been eliminated.
Another issue is the endogeneity between crime at the metropolitan level,
included as a control variable not as a measure of spillover crime, and metropolitan level
enforcement expenditure. Because this is not a Tiebout sorting issue, I cannot rely on
aggregation to eliminate the bias to the coefficient. For this problem, temperature based
instruments were used to eliminate enforcement’s effect on crime. The details of the
temperature instruments are presented below.
Measuring Spillover Crime
7
One impediment to the measurement of the level of spillover crime is the lack of
data on residences of apprehended criminals.4 A few cities such as Los Angeles provide
data for various crimes on the residence of the apprehended criminals along with the
location of their crime.5 But this kind of data is not consistently provided across cities,
making it difficult or impossible to do the cross-metropolitan area analysis necessary to
avoid Tiebout sorting bias. Data collected from these cities does not include surrounding
municipalities either. Even if data did exist, municipal level data on criminal behavior
introduces a new source of misspecification do to its endogeneity with enforcement
expenditure. Therefore, observations of spillovers between communities used without a
viable instrument for enforcement’s effect on crime will not be preferable to a measure of
spillover crime that is unrelated to enforcement. In order to empirically test for the effect
of spillover crime on enforcement, a method of measuring spillover crime is required.
The measure developed in this paper employs the travel distance to a neighboring
community as a proxy for the level of spillover crime.
Criminals must live somewhere and therefore every community has a set of
resident criminals, living at various distances from the boundary of the community.
Following Becker’s model of a rational criminal (Becker (1968)), I assume a criminal
searches for the highest expected pay off when committing a crime. Part of the
criminal’s maximization problem is to weigh the benefits against the costs of commuting
to another community to commit a crime. In other words, when criminals leave their
home community to commit a crime, it is because the net expected benefit from the crime
is larger than the cost to them of commuting.
Relocating activity can generate a range of costs for criminals. At a minimum, it
is more time consuming the farther a criminal travels. If they must transport goods back
to their residence as well as get to a safe spot quickly, the farther they are, the larger the
added costs. Another likelihood is that the familiarity of an area decreases with distance
from a home base, thus increasing the risk of apprehension.6 Travel distance within a
4 Even if residence data on apprehended criminals were available, data would still be missing on non-apprehended criminals as well as non-reported crimes. Also selection bias would be present in the data because apprehension rates by police differ across crimes as well as across types of criminals. 5 Fabrikant (1979) and Mehay (1977) use data from Los Angeles to test for spillover crime and its impact. 6 As noted by Deutsch, Hakim and Weinblatt (1984), familiarity with an area affords criminals more information on opportunities and police activity.
8
metropolitan area is correlated to many of these relocation costs to a criminal. The
analysis presented in this paper uses a measure based on the average travel distance
within a community. The measure only depends on information within the community
since only the boundary crossing is relevant; more detailed location information is not
necessary.
A measure based on the travel distance within a community has several benefits.
One important benefit is that the use of travel distance does not introduce endogeneity
bias. An area-based travel distance measure would avoid Tiebout bias because it is
uncorrelated with the demographic characteristics of municipalities. It is the endogeneity
of criminal behavior with demographic characteristics and enforcement expenditure that
creates specification problems in a model with an exactly measured spillover level.7
Travel distances on the other hand are determined by the placement of municipal
boundaries. Municipal boundaries in most metropolitan areas are historically drawn and
highly static (Epple and Romer, 1989). Viewed from the context of the present,
municipal boundaries are often rather arbitrary lines drawn on a map. Thus, it is of
considerable interest to assess whether such relatively arbitrary boundaries have
important real effects. The often-unique character of metropolitan areas results in
considerable variation in the relative sizes of municipalities across metropolitan areas.
Cross-metropolitan variation in the sizes of municipalities coupled with the relative
inflexibility of boundaries over time provides an attractive source of variation for testing
my key theoretical prediction
A Model of Metropolitan Municipalities
The foundation of the theoretical model is a linear-spatial representation of a
multi-jurisdictional metropolitan area.8 Figure 1 presents the benchmark spatial-
characterization of neighboring communities in a metropolitan area.
7 If spillover exists and the data for spillover levels were available, average travel distance would be a good instrument. 8 The model was developed in Newlon (2000).
9
The far left-hand boundary is the location of the central business district (CBD)
and the outer boundary of the metropolitan area is M. The theoretical model has 2-
contiguous municipalities, indexed by i=1,2. The boundary between the two
communities is labeled (b), and it partitions the metropolitan area into a central city on
the left-hand side, next to the CBD, and a suburban community, on the right-hand side.
Distributed across the metropolitan area is a continuum of residences
corresponding to the population distribution within the area. The population distribution,
f(x), is assumed to be either uniform or downward-sloping. This allows the population in
the suburban community to be at most as dense as that in the central city. The total
population (N) in the metropolitan area is assumed fixed.
Criminals inhabit a proportion of the residences available at each location
implying a distribution of criminal residences, g(x). The indigenous criminals per capita
are assumed to be constant or decreasing with distance from the CBD. The case in which
10
per capita indigenous criminals increases with distance from the CBD is not considered
because crime gradients in metropolitan areas have been observed as decreasing with
distance from the CBD (Shaw, 1929; Schmid, 1960; and Brantingham and Brantingham,
1984). Figure 1 presents a illustration of distributions of population and criminal
residences across the metropolitan area.
Within each community there is a positive, exogenously given number of local
criminals called indigenous criminals. The exogenous number of criminals residing in
each community is set by the location of b, which partitions the distribution of criminal
residences. Let the number of resident criminals be denoted by iR , where i = 1,2.9 The
number of criminals living in each community is exogenously set because this paper is
looking at the location of the criminal act and not the decisions of an individual about
whether to become a criminal.10 This assumption also indicates a fixed number of
criminals in the metropolitan area.
The number of criminals active in each community is an equilibrium concept that
determines the crime level in each community. There are different expected payoffs in
each community, reflecting the community’s gross benefits to crime11 and probability of
apprehension. Criminals maximize their utility by maximizing the expected net payoff
from their criminal acts. Each criminal’s net payoff is determined by the expected payoff
in the community where they commit crimes minus their private cost of travel. For
crimes committed within their own community, private costs to travel are normalized to
zero. Therefore, criminals will relocate on the condition that the difference in expected
profits, between their non-home and home community, is positive and will cover their
cost to relocating. An equilibrium in criminal activity is defined as an allocation of
criminals to communities such that no criminal can increase his/her utility by relocating
9 The number of criminals residing in Community 1 is ( )∫=b
dxxgRR0
1 , and in Community 2 is
( )R R g x db
M
2 = ∫ x , where R is the total number of criminals in the metropolitan area.
10 I am implicitly assuming that it will always be profitable for these individuals to commit crimes. The criminals are choosing to maximize this profit. 11 The benefits to crime represent resources in the community available to victimize, whether material or human.
11
his or her activities.12 The equilibrium condition, detailed in Appendix 1, gives the
number of criminals active in each community (Ri). A convenient normalization is to
assume that criminals who are not apprehended commit one crime, thus Ri is also the
number of crimes in a community.
In order to reduce crime, each community taxes the income of its residents to fund
a police force. Let police jurisdictions be one and the same with municipalities. The
jurisdictions thus have separate tax and spending authorities, making policing
decentralized in the metropolitan area.
When considering expenditure on policing, voters only consider the costs and
benefits to their community. In each community, expenditure on enforcement is
determined by majority rule. I assume that each non-criminal resident has an endowment
of income (yi). Income levels are characterized by a distribution such that the median
income is a function of the boundary, ( )byi~ . The distribution of incomes is restricted to
keep the median income in the suburb at least as large as that in the central city.
There are two goods in the economy: a "composite" private commodity (c), and
the public good, "safety" (S). Safety in a community is expressed as the probability that
an average citizen will not be a victim of crime. A citizen has utility, U c( Si i, ) 13, where
i=1,2. Utility is assumed to be state-dependent with two possible states: the victimization
state and the non-victimized state. Finally, ( )Si i,U c is assumed to satisfy the "single-
crossing" condition for all possible incomes, corresponding to a positive income
elasticity of demand for safety.
Safety is assumed to be a function of the number of criminals such that only the
criminals not arrested or relocated commit their one crime. Police affect the crime level
directly through arrests and indirectly through relocation of criminal activity. Because
prevention, incarceration and deterrence all result in a criminal being unable to commit
his/her intended crime, an arrest can be interpreted more broadly than just as an
incarceration. If the crime rate represents an individual’s probability of being victimized,
let safety be one minus the crime rate:
)12 For the proof that the crime location equilibrium is stable and unique, see Newlon (2000) 13 U c is continuous and quasi-concave, and Uc and US are both positive. ( Si i,
12
( )( )S
R P E RNi
i i i
i
= −−
1,
, for i = 1, 2,
where Ei = the expenditure level on enforcement, Ni = the population and P(Ei,Ri)
= the number of arrests produced by police. The decisions of the neighboring community
enter into the safety equation through Ri, because criminals respond to the difference in
apprehension rates between the communities. Therefore, the safety level in both
communities depends on the equilibrium expenditure on both police departments.
As in Newlon (2000), the equilibrium expenditure levels ( )E E1 2, meet the
following criteria: the expenditure pair is an intercommunity equilibrium in the presence
of mobile criminals if it results in an allocation of criminals and enforcement to
communities such that
(1) Criminal activity is in equilibrium.
(2) Each community is in internal equilibrium.
The internal equilibrium of a community is defined as an allocation that balances
the community's budget and maximizes the utility of the representative voter.14
The theoretical framework developed above encompasses two equilibrium
concepts, that for the criminals and that for the communities. The two theoretical
predictions used to test for the effect of spillover crime are derived from this framework.
Predictions from Theory
Two tests for the effect of spillover crime emerge from contrasting the effect of
travel distance at the municipal and metropolitan level on aggregate per capita
expenditure in the closed-community and open-community cases. The closed-
community case (CCC) defines the state where there is no relocation by criminals
between communities; therefore travel distance between communities has no direct effect
on per capita expenditure, either at the municipal or metropolitan level. In the open-
community case (OCC), a change in the travel distance to a neighboring community
affects the incentive of criminals to relocate, thus associating changes in average travel
14 Newlon (1999) demonstrated that the equilibrium as defined is unique.
13
distance with changes in per capita expenditure on police. The predictions presented in
this section are presented formally as propositions in Appendix 2.
There are two measures of travel distance used for the tests: municipal travel
distance and the metropolitan average travel distance. Returning to the spatial model
presented in Figure 1, the boundary (b) between the central city and the neighboring
suburban municipality defines the municipal level travel distance for each community.
For the central city, the maximum travel distance to the other community is b. In the
suburban community, the maximum travel distance is M-b, where M is the distance from
the CBD. The first test corresponds to the case where only one community’s travel
distance changes, when either b or M shifts out. The second test looks at the change in
the average travel distance for the metropolitan area. It assumes M to be held constant.
In this case as b shifts, the population-weighted average travel distance in each
municipality will change. In the case of the central city, the average travel distance will
increase, thereby increasing the average cost for criminals to relocate. The opposite
occurs in the suburban municipality. Assuming that the central city has the larger
population results in average travel distance increasing in b.
The association between a change in b, generally referred to as a boundary shift,
and the average travel distance is complicated by the boundary’s relationship with three
variables that also affect expenditure. For a fixed distribution of population, the
population’s associated incomes, and criminal residences across the metropolitan area, a
boundary shift results in a simultaneous perturbation of population (Ni), median
income ( )iy~ and indigenous criminals ( Ri ) in both municipalities. The population-
weighted metropolitan averages included in the estimation equation control for changes
in all of these variables, this will be established below.15
The predictions are derived from comparative statics done on municipal level
demand for enforcement. The key result used in both predictions is that municipal level
expenditure decreases as municipal level travel distance increases in the OCC but does
not change with travel distance in the CCC: 15 Ri cannot be measured at the municipal level but it due to the metropolitan area being a closed system of communities, it can be measured at the metropolitan level. The crime level in any municipality is
14
CCCin 0
OCCin 0
=
<
i
i
i
i
dTDdE
dTDdE
(1)
where i = 1,2. TDi enters the community’s problem through the price of safety,
the dollar cost of relocating a single criminal, generating the result in (1). The farther a
community has to move the average criminal to relocate their activities, the higher the
cost of safety.
From the above relationship I derive two test predictions.
Prediction 1: Holding all other travel distances fixed, expenditure per capita in
the metropolitan area increases with the travel distance in one community only in the
OCC:
0
0
=
<
i
i
dTDdeinresultsCCC
dTDde
inresultsOCC for i = 1,2.
Prediction 2: Expenditure per capita in the metropolitan area, holding the total
land area (M) fixed, will not change with average travel distance (ATD) in the CCC:
0
0
=
><
dATDdeinresultsCCC
dATDde
inresultsOCC
comprised of crimes by both resident and commuting criminals. When aggregating, the spill-ins and –outs cancel leaving the fixed number of resident criminals.
15
Prediction 1 follows almost directly from (1), which is the primary effect of the
change in travel distance on the home community’s expenditure. This coupled with a
secondary effect on aggregate expenditure created by the neighboring community’s
reaction to the dislocated criminals from the home community produces the result.
Prediction 2 requires a little more explanation because it is composed of
municipal level effects that work in opposing directions. When land area is fixed, and
one community’s travel distance changes, the other community’s travel distance must
change in the opposite direction. Returning to result (1), it is clear that in the OCC,
expenditure in each community will also be changing in opposite directions, and at
different rates. Therefore, when the municipal level effects are aggregated to the
metropolitan level, it is not possible to predict the net direction of the effect. To further
demonstrate Prediction 2, I turn to a computational model. The computational model
demonstrates the most counter intuitive claim in Prediction 2: that aggregate expenditure
per capita can increase as Community 1’s travel distance increase and Community 2’s
decreases.
Appendix 3 presents the specifications used and reports the data employed in the
calibration. The calibration of the model uses U.S. data from 1990 as well as reported
elasticities from relevant research. The median income in both communities uses the
national median in 1990 of $29,943 (Statistical Abstract of the United States, 1992). A
uniform distribution is assumed for the population and criminal residences.
16
Figure 2 presents the aggregate- and community-level equilibrium per capita
expenditure for a range of travel distances in both communities. On the x-axis is the
percent shift of b to the right, increasing the size of the central city and decreasing the
size of the suburban community. As predicted, the per capita expenditures in the two
communities change inversely. In the case of Community 1, expenditure is decreasing in
response to an increasing cost of safety. As the travel distance increases in Community
1, the proportion of crimes that can be relocated to the other community for a given
expenditure per person decreases. On the other hand, Community 2, whose travel
distance decreases, can export a greater proportion of its criminals at a given expenditure
per capita. Aggregate expenditure per person for the metropolitan area increases, or
decreases, depending on the absolute levels of expenditure and relative changes in both
expenditures. The computational results when the communities are closed are a constant
expenditure per capita of $61.44.
17
The predictions, though based on a linear-characterization of communities
presented in Figure 1, can also be thought of as coming from a standard concentric circle
model of urban areas. The linear-model is a one-dimensional slice out of the two-
dimensional model presented in Figure 3.
The three boundaries still maintain their original purpose, such that only b is
permeable to relocating criminals. In the 2-dimensional model, the radius changes rather
than b but they are equivalent changes with respect to the communities and criminal’s
problems. Thus, one can see that a change in TDi due to a boundary shift will not affect
expenditure in the CCC.
Section 2: The Empirical Model
The first-order condition for choice of enforcement level in a municipality
from the model in Newlon (2000) is the foundation for both the empirical models. The
first-order condition for municipality i in metropolitan area j is
( ) ( )dSde
U S e y U S e yij
ijS ij ij ij c ij ij ij⋅ −, , , , 0= . (2)
18
Spillover crime impacts the community’s expenditure choice through dSde
, the marginal
change in safety due to a change in expenditure on enforcement or one-over the price of
safety. As detailed in Newlon (2000), dSde
depends on the interplay between the
enforcement efforts of police via the production function for arrests, and the choices
faced by criminals, including the decision about where to commit crimes. It is the
determinants of dSde
that appear in the estimation equation.
The role of spillover crime can be clarified by turning back to the closed
communities case (CCC) in which spillover crime does not occur. In a closed
community, dSde
will depend on the level of e and on the number of indigenous criminals.
In addition, dSde
may depend on topographical features (Ω) that affect the ease with
which police move within the community. These topographical features, whether natural
(e.g., rivers) or man-made (e.g., bridges, detours), may impact police performance, for
instance by slowing response time. Of course, factors that affect the ability of police to
move within a municipality may affect the movement of criminals as well. Hence,
although it is important to control for the potential effects of variables such as natural
barriers, the net effect of such variables is not predictable. In addition, demographic
characteristics (X) such as population density may also influence the effectiveness of
police in apprehending criminals.
After accounting for the effect of demographic variables and topographical
features, within a closed community there should be no effect per se of average travel
distance to the boundary of the municipality. By contrast, in an open set of communities,
travel distance (TD) plays a central role. Thus, by testing whether variation in (TD) leads
to variation in enforcement, I test for the presence of spillover crime.16
16 TDij can also affect enforcement through the production of police. Travel distance increases the response time of police there by diminishing their productivity. Therefore TDij would have a positive predicted relationship to metropolitan expenditure if going through policing. I control for this relationship by using variables derived from TDij when possible. In the estimation of Proposition 2 I use population size and population density in a metropolitan area, both of which may give rise to economies or diseconomies in policing. TDij measures the average distance a person has to travel to leave the
19
Replacing dS
with its determinants in (2), and solving for ede
TD
ij gives me
ijijijijijijij XySfe ε+Ω= ),~,,,( (2)
Finally, I modify (2) by substituting Sij with the crime rate (rij).
The metropolitan level is the Metropolitan Statistical Area (MSA).17 I aggregate
the municipal level observations in from the municipal level equation (2) by using a
population-weighted average. The final equation is linear therefore, Nj, ∑i
ijijj
NyN
~1 and
other variables control for corresponding the municipal level variables. The MSA level
crime rate also has the added benefit of controlling for differences in municipal level
resident criminal rates because the aggregation procedure allows spill-ins and –outs to
cancel: ∑∑∑ ===i
ijji
ijji
ijijj
j RN
RN
NrN
111r .
I now turn to the measurement of other variables appearing in (2). The travel
distance to a neighboring community (TDij) is estimated using data on the area of the
municipalities in each MSA. The travel distance to a boundary for a given municipality
is approximated by assuming a circular boundary and a uniform population density for
that municipality. The travel distance measure for that municipality is calculated as a
radius from the center of the circle. The population-weighted average of the results for
all municipalities yields the average number of miles to a contiguous community across
all municipalities in the metropolitan area. A population-weighted measure for the
average travel distance (ATD) in the MSA is necessary because a measure based
exclusively on area tends to over-weight the suburban fringe at the expense of the central
city.
The variables in Ω are features that either inhibit or facilitate apprehension of
criminals within a municipality. My empirical analysis includes the number of rivers,
bridges and ravines. (I have included bridges since they ameliorate the negative effect of
community. After controlling for travel time or population density, this measure would seem to be, at best, tenuously linked to scale effects on the productivity of police. 17 The Census defines an MSA as a freestanding metropolitan area with a high population density in which multiple communities are economically and socially integrated.
20
rivers on travel.) In addition, I have included population density, which may also affect
the productivity of police.
Within a community, median income affects choice of enforcement, as shown in
equation (1). The median income of the MSA is not the only income variable included.
The theoretical framework for exploring community boundaries assumes a fixed income
distribution across the MSA. Thus, the income variance for the MSA is included to
control for the metropolitan income distribution varying with the spatial characteristics of
the MSA. However, controlling for metropolitan-level differences in income distribution
does not imply a control for the variance among municipal median incomes. The theory
analog can be seen in Figure 1. Assuming a distribution of incomes where income
increases with distance from the CBD, the median income in each community increases
with a boundary shift to the right. If median incomes vary with the boundary, the
predictions for the relationship between aggregate expenditure and average travel
distance for both open and closed communities will be different. Using the sum of
municipal median income weighted by the population, I measured the effect of cross-
community differences in relative municipal income.
For mechanically similar reasons to a boundary shift’s association with municipal
median income, two other variables change: indigenous criminal and the proportion of
population in each municipality. In order to use the test for spillover I must control for
cross-municipality differences for these community characteristics. The number of
indigenous or resident criminal is not directly measurable. On the other hand, income is
a correlate of many determinants of crime such as education, age, and opportunity costs
to incarceration. Therefore the sum of municipal median income weighted by population
doubles as a control for relative levels of indigenous criminals in the municipalities of
each MSA.
Finally, to control for variance in the cross-municipality proportion of population
in each MSA, I use the variance of population proportions. As the boundary shifts out,
variance of population proportion will increase and thus control for changes in the sizes
of the municipalities.
The demographic variables measure both the demand for enforcement and the
supply of crime. Previous research could not justify the exclusion of some variables from
21
either structural equation. Beyond the obvious psychic and pecuniary losses, there is
little micro-level research on individual characteristics that correlate with preferences for
enforcement. There is, on the other hand, substantial modeling and empirical research on
the correlates to criminal behavior (see Eide et al., 1994, for a review). Two general
categories of variables are (1) the benefits and (2) the costs of crime. Variables in the
first category are generally measures of the gross pecuniary gains to crime, such as the
upper tail of the income distribution. The second category measures the opportunity cost
to crime as well as the cost of punishment. Variables that measure the opportunity cost
to crime are proxies for foregone legal benefits such as wage income. Proxies include
measures of the lower tail of the income distribution, such as unemployment and
education.18 The cost of punishment is represented by the arrest-rate component of
safety. Another set of variables in this category measures the elusive effect of norms,
wants and beliefs on individual behavior. One source of measures is the social and
economic environment of the community. Examples of environmental factors that affect
criminal behavior are the number of female-headed households and the level of income
inequality. Finally, there is a set of variables that corresponds to individual
characteristics such as gender, age, and race that are correlated to crime. The relationship
between crime and these variables does not have any one explanation but, most notably
in the case of race, often reflects the group’s opportunity costs and benefits to crime
rather than norms, wants, and beliefs.
Identification Strategy
The estimation equation in (2) has two sources of endogeneity: the population-
based measure of the average travel distance and the crime rate. The set of structural
equations is presented in Appendix 3. In general, the use of MSA-level data avoids the
problems associated with the endogeneity of demographic variables created by Tiebout
sorting (Tiebout, 1953). At the municipal level, sorting by individuals into the multiple
communities of an MSA makes the demographic characteristics of municipalities 18 Interpretation of opportunity cost variables is confounded by their interaction with the benefits from crime. For example, an unemployment decrease predicts increases in the opportunity cost and in the
22
endogenous. Instruments are not available at the level of municipalities. Assuming no
sorting between MSAs, MSA-level data are not affected by the endogeneity that plagues
its component data because locational information is not used.
The use of municipal population in measuring average travel distance creates
potential endogeneity of the variable. At the metropolitan level, instruments are available
based on the areas of municipalities. I treat municipal areas as exogenous because their
boundaries are highly inflexible (Epple and Romer, 1989). One instrument is calculated
by removing population from the measure of travel distance and weighting the average of
municipal distances using their share of the total MSA area. A second instrument is a
Herfindahl Index of the concentration of municipal area. The Herfindahl Index increases
as the MSA is concentrated in fewer municipalities.
Finally, estimating the enforcement equation requires a set of instruments for the
crime level. The use of OLS in estimating a simultaneous structural model of crime and
enforcement has long been recognized as producing biased and inconsistent estimates of
parameters (Fisher and Nagin, 1978; see Cameron, 1988, for a review). Instruments for
crime must be used in order to get meaningful estimates for the structural parameters in
the enforcement equation.
The instruments I selected are derived from temperature data exploiting the
relationship between temperature and criminal opportunity. In previous research, crime
rates are observed to vary seasonally; moreover, depending on the type of crime, the rates
vary substantially with the monthly temperature within a city (Dodge, 1980 & 1988;
Corman and Mocan, 1996). In the time-series graphs for different type of crimes from
Corman and Mocan, one can find visual evidence of the seasonal variation of crimes in
New York City. As Dodge observes in his 1988 analysis19 of the seasonality of crime,
the most common pattern in crime rates is an increase in the summer months of June,
July and August with the antipode at the winter months of January, February and March.
benefits to crime because there are higher pecuniary gains to crime. 19 Dodge used two measures of seasonality: one measure is for the amount of seasonality and the other is for consistency.
23
This general pattern does not match all crimes but it provides strong evidence that crime
rates are correlated with temperature.20
The underlying behavioral reasons for this pattern relate to temperature’s effect
on human behavior. Daily routines change in response to changes in temperature,
providing criminals with different opportunities. For example, in warmer weather the
probability of victimization increases as people spend less time at home or leave their
property unguarded (Felson, 1998). Another by-product of warmer weather is increased
time spent outdoors, leading to an increased likelihood of robberies or stranger-to-
stranger assaults (Dodge, 1988; Felson, 1998). Likewise, people are also more likely to
leave their windows open on warm nights, providing easy entry for burglars and rapists.
The evidence for seasonal variation of crime rates suggests that temperature differences
across cities offer one explanation for cross-community variation in crime rates. Thus,
measures of temperature can be considered as a valid instrument for the crime rate.
Using temperature as an instrument raises the issue of the correlation of average
annual temperature with the cultural delineation between the north and the south.
Historically, the southern states have tended to have higher violent crime rates
(Sourcebook of Criminal Justice Statistics, 1990). Research by Cohen et al. (1996) and
Nisbett et al. (1996) shed light on the cultural underpinnings of the differences between
northern and southern violence. If cultural differences affect the demand for police,
temperature may be correlated with the error term of the enforcement equation. I
addressed this potential source of regional variation through the use of census defined
regional indicator variables.
I selected temperature-based instruments to represent the effects of cold and warm
temperatures. In order to measure the influence of warm to hot days, I used the number
of cooling degree days, which are defined as the sum of the positive differences between
daily average temperatures and 65 degrees. The "cooling year," during which pertinent
data are accumulated, runs from January 1st to December 31st. I used the 30-year
average for annual cooling degree days from 1961 to 1990. 20 Dodge found that the crimes with high to moderate seasonality are household larceny, unlawful entry, rape, assault, and personal larceny with contact. Crimes with low levels of seasonality are robbery, motor vehicle theft, forcible entry, and personal larceny without contact. “Household” crimes denote crimes that take place within or around the home. “Personal” crimes are away from the victim’s residence.
24
The second temperature instrument measures the variance in temperatures.
Cooling degree data alone do not differentiate between communities with large variation
in temperature and those with consistently moderate temperatures. For example, San
Francisco and New York City have similar cooling degree days. Cities with greater
seasonal variation have their accumulation of cooling days in a relatively narrow space of
time. This could potentially affect criminal opportunities differently than in a more
temperate city. I used the average monthly temperature for December, January, and
February, a measure the severity of winter.
Section 3: Data
The data were collected in 1990 from 284 MSAs in the continental United States.
MSAs in Alaska and Hawaii, as well as 12 other MSAs from across the US were
excluded due to missing data. The New England states created a potential source of error
for the remaining data. Unlike the rest of the United States, New England does not
define MSA at the county level, resulting in MSAs that contain portions of counties or
share counties. Aggregating from county level to MSA level therefore necessitates
splitting the counties in some way. Aggregating using weights, derived from the
proportion of each county's population that resides within the MSA, would introduce an
additional source of measurement error. Furthermore, some MSAs in New England
partition the same county, resulting in possible Tiebout sorting between the MSAs. In
light of these considerations, the 17 MSAs in the New England Division were removed,
leaving a final data set of 255 observations.
The data set was derived from a variety of sources, most notably the Census of
Population and Housing and the Uniform Crime Reports. Merging was difficult because
identification codes were not uniform. The basic data building method was to aggregate
to the county level, when necessary, and then to the MSA level. At the MSA level the
final data were merged. Details on the data are in Appendix 4.
25
The MSAs in the sample make up 71% of the population in the US. The rate of
index crimes for these MSAs is 6,565 per 100,000 persons as compared to 5,820 for the
entire US. Table 3 presents the summary statistics for the regression variables. Violent
crimes comprise murder, forcible rape, robbery, and aggravated assault. Nonviolent
crimes are burglary, larceny-theft, and motor vehicle theft. I will refer to the nonviolent
crimes as property crimes, although robbery entails the loss of property. The police
officers are both local and county.
Section 4: Results
In estimating the model I have included several municipal level variables to
increase the precision of my estimates.21 The coefficients on the municipal variables
themselves are biased, but Hoxby and Passerman (1998) show that the inclusion of
municipal level variables does not bias metropolitan level variable coefficients, so long
as several procedures are observed. In the specification of the model, municipal-level
observations are formulated as deviations from the metropolitan mean, while the means
of the municipal-level variables for each metropolitan area are also included. For the
estimation of the model, a special weighting matrix is used to address the existence of
grouped errors associated with the municipal level observations in each metropolitan
area. These specification and estimation techniques protect the metropolitan level
variables from bias but they do not allow interpretation of the coefficients on municipal
level variables. Thus, in presenting my results, I do not include the estimates from
municipal level variables.
Prediction 1
The empirical model used to test Proposition 1 has two endogenous variables:
crime rate and the average of municipal median incomes. The key variable for testing
21 Hence, the municipal variables are not controlling for cross-municipal differences within each metropolitan area. If they were I would have to use instruments.
26
Proposition 1 is municipal travel distance (TDij), which is area-based and therefore not
endogenous. There is a possibility that TDij affects the productivity of police in each
municipality. If so, this creates a confound to the negative relationship predicted by
Proposition 1 TDij has to expenditure on police, through spillover crime. I include two
variables based on the same information as TDij in order to explain part of travel
distance’s affect on police productivity. These variables are the Herfindahl index of
municipal concentration and the metropolitan level area-based average travel distance.22
The instrumental variables for this analysis are the two temperature-based
variables and the land area of the MSA. The temperature-based variables instrument for
crime rate. Land area instruments for the average of municipal median incomes. Since
the average of median incomes is suspected to be changing with the spatial partition of
the metropolitan area land area is a natural choice. I want to avoid using an instrument
based on travel distance since this may have a direct effect on enforcement through the
productivity of police. Land area does not have a statistically significant correlation to
TDij. There is a high correlation between land area and the average of median incomes,
orders of magnitude larger than the latter’s correlation to the travel distance-based
variables.
The first-stage results for the endogenous variable crime rate are presented in
Table 2. The temperature instruments are both significant predictors of the crime rate.
Since the results are very similar to the first-stage results for the model used to show
evidence for Proposition 2, I will defer my analysis of these results until Table 4 is
discussed. Suffice to say that the temperature variables demonstrate robust evidence of
being correct instruments for crime rate across both specifications.
The second-stage results as well as ordinary least squares (OLS) results are
presented in Table 3. Column 2 (IV1) contains the estimates from the benchmark model.
In the first row of IV1, municipal travel distance has statistically significant negative
relationship with enforcement in MSAs. This is in line with the prediction of Proposition
1. The relationship is insignificant in the OLS estimation. One explanation for the
change in significance comes from the average municipal median household income.
After instrumenting, its coefficient becomes negative, pointing to Tiebout bias. The 22 These variables are used in the test of Proposition 2 as instruments.
27
biased variable may not control for median incomes varying with municipal boundaries
as well as the fitted value of average median income. Thus the fitted value from the
reduced form is better able to explain variation previously explained by TDij.
Prediction 2
Tables 4 and 5 present the first-stage results for the benchmark model. I have
chosen not to present the first-stage results for the endogenous control variable average
municipal median income. Average municipal median income has a strong relationship
to the instruments; it is for the sake of brevity that it is not included. 23
The reduced-form results in Table 4 indicate that cooling degree days and winter
temperatures are significant predictors of crime rates, even after controlling for regional
and demographic differences. The number of cooling degrees is a small but strongly
significant positive predictor of crime rates, with a p-value of less than .0001. Referring
to Table 1, the average sum of positive deviations from 65° (cooling degree days) is
1,437.99. The model suggests that an increase of one half of a standard deviation from
the mean of cooling degree days (equivalent to approximately a 40% increase)
corresponds to an average increase of 115.8 crimes per 100,000 persons. This is about a
2% increase in crimes per 100,000.
The effect of overall warmth is small in magnitude, but coupled with the larger
significant effect of average winter temperature, there is strong evidence for the
relationship between warmer temperatures and crime. The positive effect of average
temperature during the winter months on crime rates is significant with a p-value < .0001.
The estimate predicts that, for an increase of one forth of a standard deviation in average
winter temperature (or 18.32°), there is a corresponding increase of 392.55 crimes per
100,000 persons.24 In percentage terms, a 25% increase in winter temperature is
associated with about a 7% increase in crimes per 100,000.
Controlling for cooling degrees, the effect of winter temperatures implies the
lower the variance in temperatures over the year, the higher the crime rate. The
23 Results for the non-included endogenous variables are available from the author. 24 Note that this result means the average MSA has an increase of about 2,689 crimes in total.
28
relationship between temperature variance and crime denotes a statistical difference
between cities such as San Francisco and New York that have about the same cooling
degree days. One explanation is that during the summer, criminals in New York do not
play “catch up” with the criminals in San Francisco. Cities, such as San Francisco, with
mild winters give their criminals more time per year to be active; therefore they are
associated, on average, with higher crime rates. Another explanation is that criminals,
like most people, prefer not to go through cold winters, hence cities with warmer winters
have more criminals. Either answer is a fine motivation for winter temperature as an
instrument for crime.
A Wald test reveals that the cooling degrees and winter temperatures are jointly
significant, with a p-value < .0001. The combined results for cooling degrees and winter
temperatures, even after controlling for demographic and regional differences, suggests
that communities that are warmer on average provide greater opportunities for
criminals.25 The results also imply the southern states, from east to west coast, will be
impacted the most by temperature effects. This indicates that criminal opportunity, and
not just cultural reasons, can explain the observed higher crime rates, on average, in
southern states.
Table 5 displays the results from regressing the population-based travel distance
measure onto the exogenous variables. As expected, the travel distance measure using
only area is highly significant and positively related to the population-based measure.
Likewise, the Herfindahl index's estimate shows that as the number of municipal
governments within an area decreases, the average travel distance to a border increases.
Table 6 displays the second stage results as well as OLS estimates. The first
column presents the OLS estimates and the second column, the benchmark instrumental
variables model. The Ramsey Test for functional form suggests that a linear model is an
acceptable specification. Heteroskedasticity is present, and the standard errors given for
the OLS estimates are White heteroskedasticity consistent. Using the Wu-Hausman test
for exogeneity, I could not reject the hypothesis that crime rates and ATD must be treated
25 Since I cannot control for the number of criminals, it is not possible to say if the productivity of criminals is higher in warmer communities or if there is a higher numbers of criminals per capita. Evidence from Dodge (1980, 1988) indicates that the productivity argument cannot be disregarded.
29
as endogenous, evidence that OLS is not the correct estimation method. Hereafter I refer
to the IV estimates in column 2 of Table 6 as the benchmark model.
The first row demonstrates that the sign and the significance of average travel
distance (ATD) is robust to either estimation method. The magnitude of the relationship
between ATD and officers per capita increases when instruments are used. Largely, OLS
and IV have similar estimates although one exception is the change in the sign of crime
rate from OLS to IV estimation. Influential research by Fisher and Nagin (1978) has
shown that endogeneity exists between the criminals and enforcement per capita; the
results from my model do not contradict that finding. One explanation for the negative
relationship is that the TDij based instruments are affecting the fitted value of crime rates.
Thus the fitted value of crime rate has an additional relationship to the officer rate due to
the instruments potential relationship to the productivity of police.26
The benchmark model shows that expenditure per capita has a significant positive
relationship with ATD. For an illustration of the magnitude of the enforcement elasticity,
let the average travel distance increase by a quarter of a mile, which is equivalent to a
14% increase from the metropolitan average in Table 1. For this change, the model
predicts an increase of 20 officers per 100,000 persons. This is an 11.5% increase
relative to the mean. The additional expenditure is clearly not the level of over-
expenditure, since the change in aggregate expenditure does not measure the difference
in total expenditure from the optimal level. But, it reveals the magnitude of the result’s
relationship to the test prediction. This strong positive relationship suggests that
competition to expel criminals exists at such a level that there is a significant deviation
from the closed-community predictions.
The other determinants of the model are grouped into categories. The first is
Income Measures. The positive coefficients on income level measures, median
household income and percent of the population with income over $100,000, provides
evidence in support of the single-crossing in income assumption for safety, which
requires there to be a positive income elasticity of demand for enforcement. Also,
income variance at the MSA level is associated with higher enforcement per capita.
26 These variables were in the previous estimation used as control variables for this relationship.
30
Another category that plays a large role in the analysis is Spatial Characteristics.
Land area enters as a control on the total land area. In terms of the model in Figure 1, it
holds M fixed as b varies. Combined with population, it also controls for population
density, which affects policing efficacy. The significant positive effect of population
density on the officer rate suggests decreasing returns to scale in enforcement production.
Another important spatial variable is the CMSA indicator. A CMSA is an MSA with two
or more consolidated metropolitan areas. The positive intercept for CMSAs indicates
that the larger MSAs, on average, have higher enforcement rates. This result is
consistent with decreasing returns to scale.
The last column in Table 6 addresses the robustness of the relationship between
enforcement and ATD with respect to the extra control variable the average of municipal
median income and municipal variance of population. What the variation shows is how
little the key empirical result depends on this control variable.
Results for the Hausman Omnibus test are reported at the bottom of Table 6 for
the two variations. The results are mixed: only after removing the variable variation of
municipal population does the Omnibus test reject the exclusion restrictions above the
just-identified model.
Section 5: Conclusions
The elusive nature of spillover crime has made its existence and impact difficult
to prove. In this paper, I turn to the costs that criminals consider when choosing a
location in which to commit crime. The most easily measurable cost is the cost of
moving between locations; in particular, the cost to relocating activity, rather than
residence, to another community. By linking the cost of traveling to enforcement
expenditure in communities, I have been able to test for the predicted affect of spillover
crime on decentralized municipal jurisdictions.
Strength of the test rests, in part, in its use of exogenously set municipal
boundaries. The exogeneity of the boundaries avoids endogeneity issues raised by
31
Tiebout sorting that have plagued previous empirical work. Unless they create cross-
community differences for criminals relocating their activities, the boundaries clearly do
not relate to expenditure on policing (after using controls for regional and demographic
differences). When exporting criminals is possible, these marginal differences in
criminal relocation affect community enforcement decisions by communities because
they have different marginal benefits to enforcement.
The results show a robust significant relationship between average travel distance
and aggregate expenditure per capita in metropolitan areas. Removal of potentially
sensitive variables does not affect the sign or the significance of the result. Due to
aggregation to the metropolitan level, theory does not require a specific qualitative
relationship between travel distance and enforcement expenditure. It is sufficient to
show a relationship between the two to prove the open-community case to be the relevant
characterization of communities. However, further tests show evidence in favor of the
predicted negative relationship between municipal travel distance to a neighboring
community and aggregate expenditure on enforcement.
The relationship between average travel distance and expenditure on enforcement
provides validation of the open-community characterization of metropolitan areas. One
result of the significance of the open-community characterization is the doubt it casts on
the Pareto optimality of decentralized municipal enforcement. Results from normative
analyses of decentralized municipal expenditure on enforcement predict over-expenditure
on enforcement when crime can be exported to other jurisdictions. (Marceau, 1997, and
Newlon, 1999). When criminals respond to differentials in community enforcement by
relocating activities, an externality exists because communities can increase their public
provision of safety at their neighbor’s expense. Over-expenditure on enforcement results
because the full cost of enforcement is not internalized by communities; thus, the
Samuelson condition does not hold, and the allocation of expenditure to communities is
not Pareto optimal. Future empirical work in this area must address the degree of
expenditure distortion due to spillover crime.
32
APPENDIX 1
Let Ri = the number of criminals that attempt crimes in Community i , R = the
number of criminals in the metropolitan area, and Ei = expenditure on enforcement in
Community i. My focus is on cross-border crime hence, I simplify by assuming that
there are no “dropouts” of criminals from the system, R R R1 2≡ − .
Criminals have a probability of arrest in each community of
( ) ( )p E RP E R
Ri ii i
i
,,
= , i = 1,2.
where P(Ei, Ri) is the production function of arrests. For the probability of arrest and the
arrest function, I assume:
1. pE>0, pR<0, pEE<0, pRR>0, and pER<0.
2. PER>0.
The probability of arrest displays the positive externality in crowding of criminals used in
Freeman et al. (1996) and Schrag and Scotchmer (1997). Intuitively, for any police
expenditure level, the larger the number of criminals in the community, the less likely
any one will be apprehended. I place two more assumptions on the probability of arrest
to insure p∈[0,1]:
1. ( ) limp p YMAX R= R ≤→0 1,
2. ( )lim R R p E R E→ ≥ ∀, 0
where Y is aggregate endowed income in the community and pMAX is the maximum
affordable probability of arrest.
The following uses the spatial characterization from Figure 1. Treating
parametrically, the equilibrium allocation (E E1 2, ) ( )R R1 2, sets the difference between the
two communities in net expected benefits to criminals as equal to the travel distance of
the last criminal to relocate:
( )[ ] ( )[B z p E R B z p E R x1 1 1 1 2 2 2 2− ⋅ − − ⋅ = −, , ~] b (1_1)
where Bi is the gross benefits to crime, zi is the punishment cost, and ~x is the distance
from the CBD of the residence of the last criminal to relocate. The normalization to cost
to travel is assumed to be equal to one.
33
Newlon (1999) demonstrated that (1_1) is stable. The equilibrium is also unique
when and b K p MAX< ⋅2 2 M b K p MAX− < ⋅1 1 .
Let the distribution of criminal residences be g(x) where x is the distance from
the CBD. Figure 1 presents an example of g(x). The distribution is assumed to be
uniform or decreasing in distance from the CBD. To simplify the exposition, let B1=B2
and z1=z2=z. Using (1_1) and the cumulative distribution function of criminal
residences, G(x), crime in Community 1 is
( ) ( )[[R R G z p E R p E R b1 2 2 1= ⋅ ⋅ − +, , ] ]1 (1_2)
and in Community 2 is
( ) ( )[[R R R G z p E R p E R b2 2 2 1= − ⋅ ⋅ − +, , ] ]1 . (1_3)
34
APPENDIX 2: Derivation of Predictions for Aggregate Expenditure.
This section characterizes the relationship between the travel distance in the
municipalities and the aggregate per capita expenditure (ej) on policing for a metropolitan
area. The results are presented in two propositions. The first proposition looks at how a
change in only one municipality’s travel distance affects expenditure at the metropolitan
level, ej. In deriving this result I assume the other municipalities’ travel distances are
held fixed. This allows me to focus in on the size of the effect of spillover at the
municipal level.
In the second proposition, municipal travel distances are a function of a fixed land
area for the metropolitan area. Therefore if one municipality’s travel distance changes, it
affects the TDij of all the other municipalities. Here I am testing for an average travel
distance effect on ej.
Both predictions used to test for the effect of spillover crime on police
expenditure are derived from the same key municipal result. In Newlon (2000), it was
shown for the Open Community Case (OCC), that if municipal travel distance to another
community (TDij) increases then municipal expenditure on enforcement (Eij) will
decrease,
0<ij
ij
dTDdE
for i = 1,2. (A2_1)
The negative relationship between expenditure and travel distance is a result of travel
distance’s effect on the price of safety in the community. As the travel distance in the
community increases, there is an increase in the price of safety. Intuitively, the price of
safety increases because the number of criminals exported per dollar has decreased with
the increase in the travel distance.
On the other hand, in the Closed Community Case (CCC), because criminal
activities are not cross jurisdictional, travel distance does not affect the safety of voters
and there is no relationship between Eij and TDij :
35
0=ij
ij
dTDdE
for i = 1,2. (A2_2)
Throughout the analysis presented in this appendix I treat communities as
“islands” such that no one lives near the boundaries, but criminals still differ in their
inclination to commute to commit crimes. This treatment allows the empirical model to
correspond to the theoretical model. A complete theoretical modeling of the effect of a
change in TDij includes all variables that depend on the placement of municipal
boundaries (b). But the estimation equation controls for municipal population (Nij) ,
resident criminals ( )ijR , median income ( )ijy~ and other variables that change with TDij.
Therefore to be consistent, the theoretical predictions assume these variables are fixed.
PART 1: Municipal Travel Distance and Metropolitan Expenditure per capita.
In Proposition 1, presented below, I assume that the travel distance in
municipalities is independent:
0 1
2 =j
j
dTDdTD
. (A2_3)
This assumption requires land area not fixed be fixed. One can imagine the change in the
travel distance occurs in the boundary municipalities.
Proposition 1: If travel distance in municipalities vary independently,
Then only in OCC does 0<ij
j
dTDde
for any i = 1,2.
The basis of this result is that expenditure per capita at the metropolitan level decreases
with an increase in the travel distance of one municipality only in the OCC because in the
CCC, (A2_2) holds.
36
Proof:
Aggregating municipal expenditure up to per capita expenditure in metropolitan
area j gives me
j
jjj N
EEe 21 +
= (A2_4)
where Nj is the total population in the metropolitan area.
Next I differentiate equation (A2_4) with respect to TDij. For expositional
purposes I use TD1j. The use of community 1’s travel distance is arbitrary; the result is
the same for either community’s travel distance.
+++=
j
j
j
j
j
j
j
j
j
j
j
j
jj
j
dTDdTD
dTDdE
dTDdTD
dTDdE
dTDdE
dTDdE
NdTDde
1
2
2
2
1
2
2
1
1
2
1
1
1
1 .
Using the result in (A2_3), the above derivative simplifies to
+=
j
j
j
j
jj
j
dTDdE
dTDdE
NdTDde
1
2
1
1
1
1 (A2_5)
A change in TD1j does not directly affect E2j, it changes only in reaction to a change in
R1j. To demonstrate this, I start by expanding j
j
TDE
1
2∂ and rewriting (A2_5) to get
⋅⋅+=
j
j
j
j
j
j
j
j
jj
j
dTDdR
dRdR
dRdE
dTDdE
NdTDde
1
1
1
2
2
2
1
1
1
1 (A2_6)
37
i. In the CCC, clear 01
=j
j
dTDde
because from (A2_2) 01
1 =j
j
dTDdE
and
01
2 =j
j
dRdR 27.
ii. In the OCC, because jj RRR 21 += , spill-ins are one-to-one with spill-outs
and 11
2 −=j
j
dRdR
. Using this information, (A2_6) can be rewritten as
01
1
1
2
2
1
1
1
<
⋅−=
j
j
j
j
j
j
jj
j
dTDdR
dRdE
dTDdE
NdTDde
(A2_7)
From (A2_1) 01
1 <j
j
dTDdE
and from Newlon (2000), I have 02
2 >j
j
dRdE
. The sign of
j
j
dTDdR
1
1 is best demonstrated in two parts.
i. Assume at a given equilibrium ( )*2
*1 , jj EE , that 21 pp ≤ .
In this case, community 2 is exporting criminal activity into community 1, therefore the crime equation for community 1 is
( 122
211 pp
TDR
CRRj
jjj −⋅+= ) . (A2_8)
Differentiating (A2_8) gives 01
1 =j
j
dTDdR
.
ii. Assume at a given equilibrium ( )*2
*1 , jj EE , that . 21 pp >
27 Although jj RRR 21 += , in the CCC jj RR 11 ≡ and jj RR 22 ≡ . Because both jR1 and jR 2
are fixed, it follows that 01
2 =j
j
dRdR
.
38
In this case the exporter is community 1 and thus their crime equation is
( 121
111 pp
TDR
CRRj
jjj −⋅+= ) . (A2_9)
Differentiating (A2_9) results in
( )
0
12
2
1
1
1
1
1221
1
1
1 >
∂∂
+∂∂
+
−⋅−
=
jjj
j
j
j
j
j
Rp
Rp
TDR
ppTDR
C
dTDdR
,
because the denominator is positive, see Newlon(2000).
#
PART 2: Average Municipal Travel Distance and Metropolitan Expenditure per capita.
For Proposition 2, I assume that land area (M) is fixed. This implies that municipal travel
distance is not independent and can be characterized as functions of each other,
TDij(TDkj) where i ? k. In the 2-community model, travel distances combine to equal the
total land area,
MTDTD jj =+ 21 . (A2_10)
Differentiating (A2_10) results in the following relationship between travel distances,
12
1 −=j
j
dTDdTD
. (A2_11)
I define the average travel distance (ATDj) in the metropolitan area as a population-
weighted average
39
j
jj
j
jjj N
NTD
NN
TDATD 22
11 += . (A2_12)
Proposition 2: If municipal travel distances vary inversely,
Then only in the OCC does 0≠ij
j
dATDde
for any i = 1,2.
Proof:
The derivative of ej with respect to ATDj is composed of two parts28
j
j
j
j
j
j
j
j
j
j
dATDdTD
dTDdTD
dTDde
dTDde
dATDde 1
1
2
21
⋅
⋅+=
Simplifying using (A2_11), I get
j
j
j
j
j
j
j
j
dATDdTD
dTDde
dTDde
dATDde 1
21
⋅
−= . (A2_13)
Expanding results in (A2_13) gives
j
j
j
j
j
j
j
j
j
j
jj
j
dATDdTD
dTDdE
dTDdE
dTDdE
dTDdE
NdATDde 1
2
1
1
2
2
2
1
11⋅
−+
−= , (A2_14)
where 021
1
>−=j
j
j
j
j
j
NN
NN
dTDdATD
jj NN 21 >
due to the assumption that the central city has the larger
population, .
40
In equation (A2_14), the sign of the derivatives ij
ij
dTD
dE in
−
j
j
j
j
dTDdE
dTDdE
2
2
1
1 are
the same. The same holds for the sign of the derivatives kj
ij
dTDdE
, where i ? k, in
−
j
j
j
j
dTDdE
dTDdE
2
1
1
2 . These two results imply for the OCC that the direction of the
relationship between ej and ATDj is ambiguous. Both parts of the derivative can be
either negative or positive, depending on the relative size of the expenditure response in
the communities. The results in the computational analysis presented Figure2 show that
expenditure is increasing in average travel distance for a range of boundary
specifications. There is no ambiguity in the CCC because ij
ij
dTD
dE=
kj
ij
dTDdE
=0 for i = 1, 2
and where i ? k.
#
28 I chose to differentiate with respect to TD1j because it has a positive relationship to ATDj. To use TD2j would not change the conclusion of the proof.
41
APPENDIX 3
A computational model allows the development of a more complete picture of the
relationship between relative community characteristics and expenditure levels, and in
turn, relative safety and crime rates. I have strived, whenever possible, to calibrate the
computational model to existing empirical evidence. This appendix discusses the
calibration of the utility and production of arrests functions.
The calibration strategy is based on a symmetric equilibrium. The symmetry of
communities required for such an equilibrium reduces the calibration to only one of the 2
communities. An added benefit of the symmetric equilibrium is that it results in no
spillover between the communities, thus allowing for the calibration of the number of
resident criminals, a variable impossible to get accurate data for. The calibration
strategy dictates the choice of the data source. Municipal level data are likely to reflect
spillover if the municipality is not surrounded by perfectly symmetric communities.
Therefore, national-level data and scale-free empirical results offer the best
approximation to a symmetric equilibrium because they best approximate a zero-
spillover situation without eliminating expenditure distortions. Where necessary, scale-
free specifications are utilized to ameliorate the size of national data. Finally, it can be
shown that the parameters that cannot be set with data are not pivotal since the result of
increasing per capita expenditure in Figure 2 exists for a wide range of values for these
parameters.
Specification, Data and Results:
Most of the calibration data used are from 1990. The exceptions are published
results, often involving data spanning many years. A community has a population of
248,728,000 persons and a median income of $29,243 (Statistical Abstract, 1992). The
expenditure per person on local, state, and federal police is $127.87 (Statistical Abstract,
1993).29 The form of the state-dependent utility function is
( ) ( ) ( ) ( )U y e S S y e S y e BA A− = ⋅ − + − ⋅ − − −, ( )1 1 .
29 The lion's share of that expenditure came in at the local level at $92.80 per person (Statistical Abstract, 1993).
42
In addition to the expenditure per capita, I also use the estimate of .71 for the income
elasticity of demand for enforcement from Bergstrom and Goodman (1973) to calibrate
the utility function. The resulting calibration of the utility function is: A = 0.5019 and B
= 1720.70.
In the computational program, I allow for the justice system’s effect on the
probability of criminal punishment. In 1990, the total number of crimes cleared by arrest
is 2,909,137 (Sourcebook of Criminal Justice Statistics, 1998). Data on the percent of
arrests leading to conviction or guilty pleas is imperfect but upper estimates from Mulkey
(1975) place it at 45.7%. I set the probability of punishment given arrest (f) at 45%. The
arrests function is Cobb-Douglas with constant returns to scale. For per capita
punishment or apprehension, the functional form is
( )ρβ
αα= ⋅
−f e r 1 .
The calibration of the punishment equation results in a low enforcement elasticity
of α = 0.1944, making the production of arrests highly dependent on the number of
criminals in the community. The parameter (β) adjusts the expenditure level to reflect
the officers and equipment purchased, and put the expenditure variable in units close to
those of the resident criminal per capita. The calibrate value is β = 19,736.51.
The actual number, rather than the reported number, of crimes, sets the safety
level. I use the percent of crimes reported to police, approximately 40% (Bureau of
Justice Statistics, 1994), to adjust the reported crime rate, .054, for index crimes (murder,
rape, assault, robbery, burglary, larceny, and motor vehicle theft) to the actual crime rate,
(ac) of .135 (Sourcebook of Criminal Justice Statistics, 1998). In addition I remove the
restriction that criminals commit only one crime. In the computational model, I assume
criminals commit K crimes if they are not arrested, and otherwise commit ~K crimes
before arrest. The safety equation is
( )( )S ac K r K= − = − ⋅ − + ⋅1 1 ρ ρ~ .
I use empirical results from Levitt (1996) to calibrate the actual crime rate. Levitt
estimated that an average criminal released from prison commits 15 crimes. I interpret
this result to be the average of two types of criminals: 1) those that remain free during the
43
following year, and 2) those that are re-arrested. I am thus able to calibrate the criminal's
effort level (K) and the number of criminals residing in the community, r . Because I do
not have data on the average number of crimes that criminals commit before arrest, I set
the average as at the value of zero used in the theoretical analysis. Thus criminals are
apprehended attempting their first crime. The results in Figure 2 are robust to a full
range of pre-arrest crimes from almost all K to no crimes actually accomplished. The
calibrated number of crimes committed on average by an unarrested criminal is 22.33.
The per capita number of criminals residing in the community is 0.0102.
Finally, I have chosen not to use the elasticity of crime rate with respect to the
officer rate reported in Levitt (1997). Having found that Levitt's estimate implies a large
difference between the open- and closed-community expenditure levels, I use instead a
lower elasticity of –0.2418 in order to dampen the spillover effect. As such, communities
in the CCC spend $61.44 per person; starting from the symmetric equilibrium, this is a
little less than half of the OCC expenditures.
The choice of the length of the symmetric communities, or M in Figure 1, is not
as important as its relation to the gross cost of punishment, z (see Appendix 1). The
resulting calibration is the same for any fixed ratio of punishment to travel cost (z/b)
where b is the length of one community. I use a ratio of 1 so that the cost to punishment
is larger than the relocation distance for all but those with the farthest distance to travel.
44
APPENDIX 4
The system of structural equations is
e f r y Xj j j j j j= ( , , , , )∆ Ω j+ ε (A_4.1)
and
(r g e X Wj j j j j j= , , , ,∆ Ω η) j+
j+
(A_4.2)
( )PD h AD Xj j j= , ν (A_4.3)
where j indexes the metropolitan area, e is the officers rate, r is the crime rate, X is a
vector of demographic characteristics, PD is the population-based average distance
measure, AD is the area-based average distance measure, W is a vector of temperature
measures, ∆ is a measure of costs to criminals of relocation of activity, and Ω is the
spatial costs of policing.
45
APPENDIX 4
The two main types of numerical identification codes were created separately by the
Census Bureau and the Federal Bureau of Investigation. The demographic and municipal
structure data comes from the 1990 Census STF3A files. Impediments data also use
census codes, despite having been collected by the National Geographic Survey for their
Geographic Names Information System. Crime and enforcement data were collected by
the FBI in cooperation with local and state law enforcement at the jurisdictional level.
The Inter-university Consortium on Political and Social Research (ICPSR) provided a
translation algorithm between the two types of code at the county level. They are
currently working on a municipal-to-jurisdictional bridge.
Impediments: The structure of the data makes it nearly impossible to get a count of
linear features for each county from the raw data publicly available to researchers. The
Geographic Names Information System proved invaluable by transforming the county
level data for streams, ridges, and bridges.
Temperature: The variables collected for temperature are the normals for monthly and
annual temperature, heating degree days and cooling degree days. Normals are 30-year
average values from the years 1961-1990. Cooling degree days is the sum of the positive
difference, respectively, between daily average temperature and 65 degrees. They are
accumulated from January 1 to December 31. All of the data comes from the National
Oceanic and Atmospheric Administrations (NOAA) national climactic data center. Some
of the data are extracted from the Comparative Climatic Data File. The rest of the data
are collected by hand from the normals files for all stations across the United States.
Unfortunately, these files do not identify stations by name. I use the NCDC station
locator web site to match the cooperative station number with the location of the station.
46
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50
Table 1: Summary Statistics
Variable Mean Median Std. Dev. Maximum Minimum Population 685,125.30 240,282.00 1,663,775.00 18,087,251.00 56,735.00 Officer Rate 208.00 177.50 256.98 4,127.55 70.76 Crime Rate 5,632.43 5,462.05 1,998.09 11,974.71 351.15 Violent Crime Rate 576.21 535.02 342.45 1,793.72 46.14 Property Crime Rate 5,056.19 4,967.01 1,756.81 11,375.22 303.31 Average Distance to a Border (in miles) 1.80 1.51 1.02 8.15 0.62 Number of Streams 188.23 106.50 221.98 1,411.95 0.00 Number of Ridges 11.41 2.00 30.54 303.00 0.00 Number of Bridges 7.71 3.00 14.31 102.00 0.00 Number of Annual Cooling Days 1,437.99 971.03 1,141.00 4,305.00 51.00 Average Temperature in Winter Months 37.29 12.55 36.63 68.27 8.33 Median Income 28,146.63 27,517.00 4,416.45 42,250.00 16,703.00 Within-City Variance in Income 0.44 0.43 0.11 1.25 0.24 Percent Black 0.10 0.07 0.10 0.46 0.00 Percent Hispanic 0.07 0.02 0.13 0.94 0.00 Percent Female-Headed Households 0.14 0.12 0.05 0.35 0.06 Percent Older Than 24 Years 0.63 0.63 0.04 0.78 0.43 Percent With a College Degree 0.24 0.23 0.06 0.42 0.11 Mean Public Assistance Per Household 3,784.51 3,678.44 764.52 7,300.10 2,592.55 Percent of Population With Income Above $100,000 0.03 0.03 0.01 0.10 0.01 Percent of Population in the Labor Force 0.65 0.65 0.05 0.79 0.50
All rates are per 100,000 residents. The sample used is a set of 255 MSAs . The mean public assistance per household is in 1983 dollars.
51
Table 2: First-Stage Results for Crime Rate
Dependent Variable: Log of the Crime Rate
White Heteroskedasticity-Consistent Standard Errors & Covariance All rates are per capita
OLS Std. Error Weather Instruments:
Log of the Number of Cooling Days 0.060 0.012 Log of the Average Temperature in Winter 0.276 0.022
Income Measures:
Log of the Median Household Income -0.122∆ 0.078 Within-City Variance in Income -0.002∆ 0.051 Percent of Population with Income Over 100,000 3.333 0.859
Spatial Characteristics:
Log of Land Area -0.079 0.013 Herfindahl Index -0.933 0.154 Log of Area-Based Average Travel Distance 0.325 0.029 Log of Municipal Travel Distance 0.024 0.003 Log of Population 0.007∆ 0.012 Log of the Number of Streams -0.041 0.011 Log of the Number of Ridges -0.022 0.003 Log of the Number of Bridges 0.013 0.003 CMSA Indicator 0.029 0.008
Demographic Variables:
Percent Black 0.321 0.093 Percent Hispanic -0.100∆ 0.138 Percent Female Headed Households 5.470 0.346 Percent of Population over 24 0.958 0.202 Percent with a College Degree 1.265 0.127 Log of the Mean Public Assistance Per Household -1.658 0.348 Percent of Labor Force Employed -4.348 0.506 Percent of Population in the Labor Force 2.464 0.174
Division Indicators:
East North Central Division 0.251 0.013 West North Central Division 0.239 0.016 South Atlantic Division 0.001∆ 0.013 East South Central Division -0.017∆ 0.018 West South Central Division 0.083 0.023 Mountain Division 0.045∆ 0.050 Pacific Division 0.021∆ 0.025 Constant (Middle Atlantic Division) -1.616∆ 1.006
F-statistic 682.322 R-squared 0.727 Adjusted R-squared 0.726 S.E. of regression 0.198 All coefficients are significant at a p-value <.001 unless market with a ∆. Average distance is measured in miles. The mean public assistance per household is from 1983.
52
Table 3: Estimates for Municipal Travel Distance
Dependent Variable: Log of Local and County Officer Rate
Observations: 9272 All rates are per capita Instrumental Variables OLS 1 2
Log of Municipal Travel Distance (TDij) -0.001∆ -0.025 0.011
Endogenous Variables:
Crime Rate 0.286 0.152 0.156 Log of the Average Median Household Income 2.317 -5.020 -
Income Measures:
Log of the Median Household Income -2.134 4.919 0.091 Income Variance -0.060∆ 0.005 0.026 Percent of Population with Income Over 100,000 7.044 0.193 0.316
Spatial Characteristics:
Herfindahl Index 0.181 0.113 0.042 Log of Area-Based Average Travel Distance 0.186 0.183 0.256 Log of Population -0.064 -0.018 -0.161 Log of the Number of Streams 0.015 0.046 0.001 Log of the Number of Ridges -0.008 -0.105 -0.025 Log of the Number of Bridges 0.026 0.340 0.151 CMSA Indicator 0.096 0.310 0.149
Demographic Variables:
Percent Black 0.317 0.000 0.110 Percent Hispanic -0.234 -0.063 -0.073 Percent Female-Headed Households 2.708 0.298 0.226 Percent of Population Over 24 Years 0.092∆ 0.075 0.017 Percent with a College Degree 0.641 0.194 0.144 Log of Mean Public Assistance Per Household 2.323 0.211 0.164 Percent of Labor Force Employed 2.650 0.212 0.135 Percent of Population in the Labor Force -0.604 -0.057 -0.055
Division Indicators:
East North Central Division 0.118 0.171 0.194 West North Central Division 0.092 0.131 0.137 South Atlantic Division 0.041 -0.045 0.071 East South Central Division 0.017∆ -0.008 0.019 West South Central Division 0.058 0.052 0.086 Mountain Division -0.064 -0.024 -0.011 Pacific Division -0.451 -0.321 -0.272 Constant (Middle Atlantic Division) -9.841 -0.001 -0.003
R squared 0.788 0.827 0.748 Omnibus Test - 176.335 136.280 All coefficients are significant at a p-value <.001 unless market with a ∆. Average distance is measured in miles. The mean public assistance per household is from 1983.
53
Table 4: First-Stage Results for Crime Rates
Dependent Variable: Log of the Crime Rate
White Heteroskedasticity-Consistent Standard Errors & Covariance All rates are per capita
OLS Std. ErrorWeather Instruments:
Log of the Number of Cooling Days 0.059 0.012 Log of the Average Temperature in Winter 0.284 0.022
Income Measures:
Log of the Median Household Income -0.131∆ 0.078 Within-City Variance in Income -0.017∆ 0.052 Percent of Population with Income Over 100,000 3.412 0.865
Spatial Characteristics:
Herfindahl Index -0.969 0.156 Log of Area-Based Average Travel Distance 0.347 0.030 Log of Population 0.006∆ 0.012 Log of the Land Area -0.081 0.013 Log of the Number of Streams 0.012 0.003 Log of the Number of Ridges -0.023 0.003 Log of the Number of Bridges -0.040 0.011 CMSA Indicator 0.022 0.008
Demographic Variables:
Percent Black 0.331 0.093 Percent Hispanic -0.075∆ 0.138 Percent Female Headed Households 5.542 0.344 Percent of Population over 24 0.963 0.202 Percent with a College Degree 1.302 0.126 Log of the Mean Public Assistance Per Household -1.752 0.347 Percent of Labor Force Employed 2.464 0.174 Percent of Population in the Labor Force -4.394 0.509
Division Indicators:
East North Central Division 0.260 0.013 West North Central Division 0.245 0.016 South Atlantic Division 0.004 0.013 East South Central Division -0.008 0.018 West South Central Division 0.084 0.023 Mountain Division 0.056 0.050 Pacific Division 0.026 0.025 Constant (Middle Atlantic Division) -1.498 1.014
F-statistic 695.498 0.000 R-squared 0.725 Adjusted R-squared 0.724 S.E. of regression 0.198
All coefficients are significant at a p-value <.001 unless market with a ∆. Average distance is measured in miles. The mean public assistance per household is from 1983.
54
Table 5: First-Stage Results for Average Travel Distance
Dependent Variable: Log of the Distance Measure
White Heteroskedasticity-Consistent Standard Errors & Covariance All rates are per capita
OLS Std. Error Travel Distance Instruments:
Herfindahl Index -0.985 0.082 Log of Area-Based Average Travel Distance 0.785 0.020
Weather Instruments:
Log of the Number of Cooling Days 0.054 0.009 Log of the Average Temperature in Winter 0.002∆ 0.019
Income Measures:
Log of the Median Household Income -1.196 0.071 Within-City Variance in Income -0.663 0.051 Percent of Population with Income Over 100,000 8.456 0.746
Spatial Characteristics:
Log of Population 0.098 0.007 Log of the Land Area -0.178 0.011 Log of the Number of Streams 0.000∆ 0.003 Log of the Number of Ridges -0.019 0.003 Log of the Number of Bridges 0.071 0.008 CMSA Indicator -0.115 0.009
Demographic Variables:
Percent Black 0.495 0.074 Percent Hispanic 0.636 0.085 Percent Female Headed Households 1.371 0.358 Percent of Population over 24 1.112 0.109 Percent with a College Degree 0.616 0.069 Log of the Mean Public Assistance Per Household -0.869∆ 0.319 Percent of Labor Force Employed 0.881∆ 0.126 Percent of Population in the Labor Force 2.238 0.476
Division Indicators:
East North Central Division 0.273 0.008 West North Central Division 0.180 0.012 South Atlantic Division 0.075 0.009 East South Central Division 0.370 0.014 West South Central Division 0.271 0.020 Mountain Division 0.354 0.034 Pacific Division 0.266 0.027 Constant (Middle Atlantic Division) 7.755 0.794
F-statistic 1236.517 0.000 R-squared 0.824 Adjusted R-squared 0.823 S.E. of regression 0.182 All coefficients are significant at a p-value <.001 unless market with a ∆. Average distance is measured in miles. The mean public assistance per household is from 1983.
55
Table 6: Estimates from Average Travel Distance Dependent Variable: Log of Local and County Officer Rate
Observations: 9272 All rates are per capita Instrumental
Variables OLS 1 2
Endogenous Variables:
Log of the Distance Measure 0.061 0.824 0.820 Crime Rate 0.295 -0.340 -0.370 Log of the Average Median Household Income 2.587 2.883 -
Income Measures:
Log of the Median Household Income -2.222 -2.423 0.313 Income Variance 0.127 0.165 0.138 Percent of Population with Income Over 100,000 5.034 0.268 0.256
Spatial Characteristics:
Log of Population -0.099 -0.427 -0.342 Log of Land Area 0.044 -0.039 -0.071 Log of the Number of Streams 0.005 -0.124 -0.102 Log of the Number of Ridges -0.008 -0.029 -0.092 Log of the Number of Bridges 0.019 0.105 0.210 CMSA Indicator 0.092 0.153 0.252
Demographic Variables:
Percent Black 0.473 0.176 0.110 Percent Hispanic -0.092∆ -0.127 -0.125 Percent Female-Headed Households 2.707 0.295 0.366 Percent of Population Over 24 Years 0.374 -0.009 0.034 Percent with a College Degree 0.812 0.112 0.128 Log of the Mean Public Assistance Per Household 1.292 0.065 0.071 Percent of Labor Force Employed 1.288 -0.054 -0.013 Percent of Population in the Labor Force -0.837 0.009 0.017
Division Indicators:
East North Central Division 0.107 0.136 0.120 West North Central Division 0.089 0.137 0.123 South Atlantic Division 0.093 0.042 -0.039 East South Central Division 0.067 -0.143 -0.166 West South Central Division 0.113 -0.017 -0.039 Mountain Division 0.099 -0.084 -0.091 Pacific Division -0.294 -0.329 -0.354 Constant (Middle Atlantic Division) -10.214 0.000 0.009
R squared 0.775 0.871 0.872 Omnibus Test - 13.477 44.454 All coefficients are significant at a p-value <.001 unless market with a ∆. Average distance is measured in miles. The mean public assistance per household is from 1983.
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