POLICE PRESENCE, RAPID RESPONSE RATES, AND CRIME PREVENTION Sarit Weisburd*

Abstract—This paper estimates the impact of police presence on crime using preventative patrol philosophy came under significant criti- a unique database that tracks the exact location of Dallas Police Department cism after an experiment conducted over four decades ago, patrol cars throughout 2009. To address the concern that officer location is often driven by crime, my instrument exploits police responses to calls the Kansas City Policing Experiment, failed to find any im- outside their allocated coverage beat. This variable provides a plausible shift pact of increased preventative patrol on crime.2 While some in police presence within the abandoned beat that is driven by the police goal argue that this could be a result of implementation as there is of minimizing response times. I find that a 10% decrease in police presence at that location results in a 7% increase in crime. This result sheds light on no evidence regarding the actual dosage of police presence the black box of policing and crime and suggests that routine changes in received by treatment and control areas, there is no denying police patrol can have a significant impact on criminal behavior. that this study left its mark on the literature.3 Today, innovative crime prevention programs tend to fo- cus on high dosages of deterrence in small areas or over short I. Introduction time periods (e.g., hot-spot policing, pulling-levers policing, police crackdowns), as well as community interventions via OES police presence deter crime? While it was once 4 Dgenerally accepted that the role of police officers was neighborhood policing or broken-windows policing. These apprehending criminals after they committed a crime, to- crime prevention techniques are often difficult to practice day a growing body of research shows that increased in- alongside a rapid-response philosophy. Rapid response dic- vestment in policing results in lower crime rates.1 Specifi- tates a low dosage of police officers across the city, which cally, previous papers have found that larger police forces makes officers unavailable for more concentrated crime pre- and high doses of police presence in small areas result in vention programs. My analysis, which uses a precise measure lower crime rates (see Levitt, 1997; Evans & Owens, 2007; Di of the dosage of police presence throughout Dallas, Texas, Tella & Schargrodsky, 2004; Draca, Machin, & Witt, 2011). suggests that we may have been too quick to embrace the con- However, the literature has largely ignored the fact that the clusion that general shifts in patrol across a large city cannot rapid response philosophy where police officers are spread have a significant impact on crime. Indeed, my analysis shows thinly throughout the city and much of an officer’s time is that preventative patrol in the context of a rapid-response phi- dedicated to responding to emergency calls remains the dom- losophy can provide significant deterrence of crime. inant patrol strategy applied by police departments world- Analyzing the immediate impact of police presence on wide. This paper examines the impact of this rapid response crime requires access to information on the location of police strategy on deterrence. More specifically, will adding addi- officers and crime over time. Such information has begun to tional officers to the current patrol system have any impact on be available because of the use of management information crime? systems in policing that detail the exact locations (x, y coordi- Since the 1930s, police patrol in U.S. cities has been dom- nates) of crime events, as well as automobile locator systems inated by the rapid response system: police agencies have pa- (the automated vehicle locator, AVL) that track where po- trol cars drive around in police beats ready to respond rapidly lice vehicles are when they patrol the city. While most police to an emergency call. When they are not responding to such agencies now analyze data on crime events, the use of AVL calls, they spend their time in what has been termed random systems to analyze where police patrol is rare and seldom in- preventative patrol, showing their presence in the beats to tegrated with crime data. In Dallas, over the course of twelve deter offending (see Kelling & Moore, 1988). The random months throughout 2009, AVL systems were active in all 873 police patrol vehicles, and data on their location were saved

Received for publication October 9, 2018. Revision accepted for publica- tion October 21, 2019. Editor: Shachar Kariv. ∗Weisburd: Tel Aviv University. 2This experiment took place between October 1972 and September 1973 I thank the Police Foundation for providing me with the data for this study. in the South District of Kansas, Missouri. The experiment divided the fifteen This work would not have been possible without the help of Elizabeth Groff beats of this district into three areas: reactive, where police entered the area and Greg Jones. I also thank Lieutenant Rupert Emison and Lieutenant Scott only to respond to calls; proactive, where police visibility was increased to Bratcher for providing insight and information on the Dallas Police Depart- two to three times its baseline level of patrol; and control areas, where the ment. I am very grateful for the GIS assistance provided by Adi Ben-Nun, baseline level of patrol from before the experiment was maintained. Nir Horvitz, Elka Gotfyrd, and Ruthie Harari-Kremer at the Hebrew Uni- 3See Larson (1975) for a review of concerns regarding the implementation versity Center for Computational Geography. This research was supported of the Kansas City Experiment. by the Israel Science Foundation (grant 0610114502). 4See Braga (2012) and Telep and Weisburd (2012) for a review of cur- A supplemental appendix is available online at https://doi.org/10.1162/ rent deterrence strategies. Pulling-levers policing targets a small number rest_a_00889. of chronic offenders, while hot spots policing focuses on a small number 1See surveys of the literature conducted by Cameron (1988), Marvell and of chronically crime-ridden geographic locations. Police crackdowns take Moody (1996), Eck and Maguire (2000), and Chalfin and McCrary (2017) place by shifting large groups of police to focused areas. Broken windows and microgeographic interventions by Sherman and Weisburd (1995), Braga policing aims to reduce public disorders before actual crime occurs. Neigh- et al. (1999), Di Tella and Schargrodsky (2004), Gould and Stecklov (2009), borhood policing is a strategy where specific officers conduct activities in Nagin (2013), Weisburd et al. (2015), and MacDonald, Fagan, and Geller designated neighborhoods in order to create a consistent relationship be- (2016). tween these officers and residents of that area.

The Review of Economics and Statistics, May 2021, 103(2): 280–293 © 2019 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology https://doi.org/10.1162/rest_a_00889

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FIGURE 1.—THE DATA WERE COLLAPSED AT EACH VEHICLE ALLOCATION POINT.GENERALLY EITHER ZERO, ONE, OR TWO CARS ARE ALLOCATED TO PATROL A GIVEN BEAT AT A GIVEN HOUR.HOWEVER, IF A CAR DID NOT BEGIN OR END PATROL ON THE HOUR, THIS RESULTS IN A FRACTION OF CAR ALLOCATION. THE SIZE OF THE CIRCLE RELATES TO THE DENSITY OF OBSERVATIONS AT THAT CAR ALLOCATION POINT.

and stored.5 I focus on the beat (a geographic patrol area av- riskier periods and the fact that the occurrence of a crime is eraging 1.7 square miles in size) each car was allocated to likely to increase police presence as officers are called to patrol, as well as where these officers were actually present respond to the incident. Indeed, each year, beat-level police throughout the day. Information on incidents of crime was ac- allocation in Dallas is based on calls for service and crime quired from a separate database that tracks calls for service from previous years (using Staff Wizard software). Division (911 calls) placed by local citizens to the police department.6 commanders then adjust these allocation decisions based on Thus, the current project is not motivated by a specific polic- weekly Compstat meetings where current crime concerns are ing experiment; or large change in routine police activity; discussed and areas in need of additional police attention are rather, it takes advantage of a large amount of data (roughly identified. This type of well-managed police allocation would 100 million pings of information) to provide an estimate of result in a positive correlation between policing and crime, the social returns of an additional hour of police patrol in the which is illustrated in figure 1. Generally, areas and times with current policing system. higher levels of allocated patrol tend to have higher levels of A deterrence mechanism that is based on police interac- both police presence and crime.7 Thus, while this data set tions would imply that areas or times of day with higher levels provides a unique picture of police presence across a city, the of police presence will report less crime. However, this ig- location of officers may be determined by factors unobserved nores both the allocation of officers to riskier locations during by the econometrician and correlated with crime.

5The AVL data do not include the location of officers on motorcycle and 7While there are 873 Dallas patrol vehicles tracked in this study, on aver- horseback (mounted division). The motorcycle patrol unit consists of 42 age 132 cars are on active patrol per hour. These cars are allocated among officers, and the mounted division consists of 17 police officers. 232 beats at the beginning of their shift. Thus, the most common allocation 6I separate calls that relate to crime into the following categories: violent points are either 0 or 1 car allocated per hour. The reason that police pres- crimes, burglaries, thefts, and public disturbances. I focus on 911 calls as ence (defined by the location of police vehicle throughout the shift) does not they are less likely to suffer from reporting bias than reported crimes and have a one-to-one relationship with police allocation is that officers often are more likely to provide the exact time at which the incident occurred. spend time outside their allocated coverage beat.

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My identification strategy stems from the two distinct re- side the beat being currently patrolled. While this instrument sponsibilities facing police patrol cars: proactive and reac- has a weaker first stage in terms of predicting police presence tive policing. While police may be allocated to a certain area in the beat, the exclusion restriction is more compelling.10 (beat) in order to create a deterrence effect and lower the My results suggest that the number of officers patrolling expected benefit of committing a crime, they are also re- a beat has a significant impact on the probability of crime. sponsible for answering emergency calls within their larger I first demonstrate that as reported in previous studies, there division quickly—generally, in under 8 minutes.8 I use inci- is a positive correlation in the data between police presence dents that can result in patrol officers being assigned to calls and crime. This positive correlation remains significant even outside their area of patrol to capture an element of random- when controlling for beat and time fixed effects. This suggests ness regarding whether police are present at a given location that police departments may be able to quickly adjust police and time. Thus, I introduce the outside calls ratio (OCR) in- presence to changing crime risks within locations over time. strument, which is equal to the number of calls an officer It is only when instrumenting for actual police presence with patrolling this beat is likely to address outside the beat. It is either the OCR or OC that I can identify a deterrence effect. I calculated as the ratio of outside calls to allocated outside pa- estimate that a 10% decrease in police presence results in a 7% trol. The instrument is motivated by the idea that assignment increase in crime. I provide evidence that this result cannot to an outside beat is a function of both the density of outside be explained by displacement of crime to neighboring beats. calls and outside police presence. This measure is different While police departments often consider rapid-response from realized outside assignment, which could be driven by times (minimizing the elapsed time between receiving an crime risks at the beat level. emergency call and responding to that call) to be one of the In order to ensure that the OCR is not correlated with most important tools for solving crimes, criminologists ar- crime at the beat, I focus on outside 911 calls reporting in- gue that no evidence exists to support that claim (Sherman, cidents related to mental health, child abandonment, fire, 2013).11 Not only have few studies examined the impact of animal attacks, dead people, suicides, abandoned property, rapid-response times on solving crimes, but also no attempt fireworks, and drug houses. Reports of crime are not in- has been made to measure the impact of rapid response tools cluded in these outside calls in order to avoid the concern on the deterrence capacity of the police. My results provides that crimes occurring across beats may be correlated. I also an estimate of both the deterrence created by routine police focus on out-of-beat patrol allocation as opposed to out-of- activities and the possible community safety costs of police beat police presence. Out-of-beat police allocation is de- officers dividing their time between preventing future crimes termined at the start of the shift as opposed to out-of-beat and responding to past crimes. presence that is immediately affected by the distribution of These results join an empirical literature on measuring de- calls and crime. My results are robust to controlling for beat, terrence that focuses on applying techniques to mitigate si- month, day of week, and weekend×hour of day fixed effects. multaneity bias. My estimated elasticities of −0.9 regarding The main threat to the exclusion restriction for this pro- the impact of a change in police presence on violent crime and posed instrument is that even keeping outside calls constant, −0.6 on property crime fall at the higher end of the range of a decrease in out-of-beat patrol allocation will increase the elasticities of between −0.4 and −1 (violent) −0.3 and −0.5 OCR. While this is likely to increase the probability that a (property) reported in previous work (see Levitt, 1997, 2002, local patrol officer will abandon his or her beat, one could and Evans & Owens, 2007).12 be concerned that the decrease in out-of-beat patrol alloca- Both Levitt (1997, 2002) and Evans and Owens (2007) ap- tion was a result of a general decrease in crime concerns at plied instrumental variable strategies to estimate the elastic- the division level (both inside and outside the beat).9 In this ity of crime to police force size. Chalfin and McCrary (2017) case, applying the OCR could bias the estimated deterrence raise concerns regarding weak instruments in these papers effect toward zero. To address this concern, I introduce an and point out that these studies show a wide range of estimates additional instrument of outside calls (OC). This instrument that are often not statistically significant at conventional is equal to the numerator of the OCR and is a weighted sum of calls, unrelated to crimes, occurring within the division out- 10In the analysis. I interact the instrument with an indicator for division. This strengthens the first stage of the instrument so that it does not fall under the weak instruments category. 8A complete summary of the Dallas Police Department goals as well as 11The general embracement of rapid-response policing is evident in the performance can be found in the “Dallas Police Department Management summary of “best practices in police performance measurement” provided and Efficiency Study” conducted by Berkshire Advisors (2004). by the Rand Corporation (Davis, 2012). Using data from the Kansas City 9Alternatively, one could be concerned that a decrease in out-of-beat patrol Preventative Patrol Experiment, Kelling et al. (1974) found no impact of allocation may be driven by an increase in police patrol within the beat as the response times on solving crimes. However, Blanes i Vidal and Kirchmaier division has a set number of officers to allocate. This would imply that the (2018) find that faster response times increase the likelihood of detecting OCR would be positively correlated with police presence. I therefore focus crimes when using an instrumenting strategy based on the distance of the only on outside officers assigned to patrol in the sector where the outside call incident from police headquarters. Mastrobuoni (2019) reaches a similar took place. Since there are roughly five sectors in each division, the count conclusion when analyzing the outcomes of quasi-experimental variations of officers assigned to one sector should not define officer allocation in any in police presence in the city of Milan. given beat. Indeed, the data show the opposite trend where an increase in 12See McCrary (2002) for some concerns regarding estimates produced the OCR results in a decrease in police presence. in the Levitt (1997) paper.

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confidence intervals. The instruments used in this research tion on the precise location of both crime and police in 2009. avoid this critique with first-stage F-statistics of above 40 The DPD call database records the time and location of each for both the OCR and OC instruments. The deterrence es- report of crime to the department. The AVL database tracks timates reported in this paper also fall within much smaller the location of police cars throughout the day. Together they confidence intervals. provide an opportunity to understand how police presence An additional branch of the literature focuses on exogenous has an impact on crime.13 changes in police presence that are driven by threats or ac- Dallas is an ideal location for research using AVL data tual acts of terrorism (Di Tella & Schargrodsky, 2004; Klick since it is mostly flat and thus is able to provide fairly pre- & Tabarrok, 2005; Draca et al., 2011; Gould & Stecklov, cise latitude and longitude points with minimal missing data. 2009). Di Tella and Schargrodsky (2004) and Draca et al. Dallas police patrol is divided into seven patrol divisions (2011) report smaller elasticities of crime with respect to (Central, North Central, Northeast, Northwest, South Central, police presence of between −0.3 and −0.4. Similarly, Mac- Southeast, Southwest), each commanded by a deputy chief of Donald, Fagan, and Geller (2015) report an elasticity of crime police. Figure 2 provides a map of the city divided into divi- with respect to police presence of −0.33 when examining an sions and beats. There is some variation in the characteristics increase of 200% in police presence in the area surrounding of beats across different divisions in the city, as illustrated by the University of Pennsylvania campus. This estimate shrinks table 1. Beats in the Central division are smaller, averaging further when focusing on randomized experiments. Sherman 0.6 square miles, while beats in other divisions average 1.8 and Weisburd (1995) found that doubling police patrol at square miles. Beats in the South Central division have a higher hot-spot locations in Minneapolis resulted in a 6% to 13% percentage of black residents, while beats in the Southwest decrease in crime. Blattman et al. (2018) report that an inter- have the highest percentage of Hispanic residents. Residents vention that included doubling police presence at high street of the North Central division report higher incomes. These segments in Bogota led to a decrease in city-wide crime of characteristics highlight the importance of focusing on crime below 2% when accounting for spatial spillovers. outcomes at the beat level as different parts of the city may This paper offers a bridge between the detailed location- require different levels of police presence and face different specific data that are analyzed in randomized experiments and crime risks. the aggregate data that are usually available at the city level. The analysis is conducted on geographic beats at hour-long To the best of my knowledge, Blanes i Vidal and Mastrobuoni time intervals. I use the call database to count the number of (2018) is the only other paper that has attempted to look at crimes called into 911 for each beat b and hour h. Focusing the geographic distribution of police officers throughout an on 911 calls as opposed to crime reports is expected to lower entire city using precise GPS-level data on police location. concerns regarding selective reporting of incidents. While I They take advantage of a natural experiment where police cannot rule out the possibility that in certain beats, crimes may spent an extra 10 minutes per week in a 200 meter radius not be called in to the police, this should not affect my results of an area where a burglary was reported for the week fol- when controlling for beat fixed effects. A larger concern is lowing a burglary. Interestingly, they find no effect of this whether the presence of a police car in an area may reduce change in weekly level police patrol on crime. I focus on calls to 911 as people can speak directly with the patrolling police presence at the hourly level within Dallas beats (av- officer. Importantly, 911 is the generally accepted protocol for eraging 2.7 km2) and examine whether routine changes in reporting crime. Beats average 1.7 square miles and roughly police behavior can have significant impacts on crime. One 40 minutes of patrol per hour, thus reporting via 911 will important difference between these two studies is that this usually be significantly faster.14 project focuses on moving police away from an area they The original database included 684,584 calls recorded have chosen to patrol, while Blanes i Vidal and Mastrobuoni throughout 2009 in Dallas. My final call database consists (2018) focus on sending officers to patrol a specific location. of 556,978 calls after removing duplicate calls and excluding This paper proceeds as follows. In the next section, I intro- calls that were classified as hang-ups.15 The main analysis duce the data used for this project, as well as my technique focuses on 289,030 calls reporting incidents of crime. These for measuring police presence. Section III discusses the em- crimes are classified into the following categories: public pirical strategy and presents estimates of the impact of police presence on different types of crimes. Section IV explores the mechanisms of deterrence that are driving my results. Section 13Using geographic mapping software, I collect additional information on population size as well as miles of roads across different areas in Dallas. V concludes. These data are combined with information on daily temperature, visibility, precipitation, sunrise, and sunset times in order to control for variability in the probability of crime over time. II. The Data 14Using internal DPD data, a source from the Dallas Police Department estimated that roughly 90% of reported crimes are initiated using 911 calls. Dallas, Texas, is the ninth largest city in the United States, The remaining 10% are likely to be a combination of officer-initiated calls with roughly 1.2 million residents and 3,266 sworn police of- (often related to traffic stops), sex assault victims (reporting from trauma centers, hospitals, colleges, and victims’ advocates), as well as residents ficers spread over 385 square miles. I use two separate Dallas reporting both to patrol officers and arriving directly at the police station. Police Department (DPD) databases that provide informa- 15Details of the data cleaning process are in online appendix A.

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FIGURE 2.—DALLAS BEATS

disturbances, burglaries, violent crimes, and theft.16 Gener- Beginning in the year 2000, Dallas police cars were ally, crime in Dallas tends to peak in May and plummet in equipped with AVL (873 tracked vehicles), which create December, but there are significant fluctuations in the crime pings roughly every 30 seconds with the latitudinal and lon- rate throughout the year.17 gitudinal coordinates of these vehicles. Each ping includes the radio name of the vehicle, which provides information on the allocation of the police vehicle. Thus, a ping with radio 16A crime is classified as a burglary if it involves entering a structure with the intent to commit a crime inside. Stabbings, shootings, robberies, name A142 refers to a car that was allocated to patrol beat assaults, kidnappings, and armed encounters are classified as violent crimes. 142 during patrol A (during the first watch that takes place Public intoxication, illegal parking, suspicious behavior, prostitution, loud between 12 a.m. and 8 a.m.).18 music, gunfire, speeding, road rage, and panhandlers are classified as public disturbances. 17Figure 1 of online appendix C graphs crime rates in Dallas over the 18Cars are often allocated to more than one beat; therefore, the radio name twelve months of 2009. serves as a proxy for allocation to a given beat. While it would be preferable

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TABLE 1.—BEAT CHARACTERISTICS SUMMARIZED BY DIVISION Average Time Constant Beat Characteristics Average Hourly Beat Characteristics Road Size HH Percent Percent Allocated Police Outside Outside Population Miles (Miles2) Income Black Hispanic Total Crimes Police Presence Calls Calls Ratio (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Division = Central (29 Beats) Division = Central (N = 252,387) 3,258.00 6.22 0.61 38,409.59 0.15 0.29 0.132 0.754 0.932 0.013 0.104 (2,695.87) (3.77) (0.32) (13,329.34) (0.12) (0.2) (0.375) (0.714) (1.733) (0.023) (0.259) Division = North Central (22 Beats) Division = North Central (N = 191,532) 8,613.86 9.53 1.68 75,819.55 0.12 0.25 0.148 0.815 0.821 0.014 0.085 (4,148.73) (6.3) (1.18) (18,981.49) (0.08) (0.21) (0.4) (0.607) (1.055) (0.027) (0.198) Division = Northeast (41 Beats) Division = Northeast (N = 356,249) 6,252.76 5.97 2.25 44,423.30 0.23 0.33 0.156 0.654 0.460 0.014 0.092 (2,986.75) (3.88) (7.22) (14,233.6) (0.15) (0.16) (0.411) (0.664) (0.761) (0.021) (0.156) Division = Northwest (31 Beats) Division = Northwest (N = 269,700) 4,913.36 8.97 1.52 38,770.48 0.15 0.45 0.139 0.595 0.745 0.017 0.139 (3,381.12) (5.45) (1.09) (21,082.2) (0.16) (0.26) (0.385) (0.582) (1.229) (0.025) (0.263) Division = South Central (37 Beats) Division = South Central (N = 321,567) 3,081.38 6.37 1.49 28,069.28 0.72 0.25 0.144 0.636 0.440 0.017 0.113 (1,445.97) (5.37) (1.6) (8,138.18) (0.17) (0.16) (0.39) (0.621) (0.79) (0.024) (0.185) Division = Southeast (39 Beats) Division = Southeast (N = 339,378)) 3,997.67 6.32 1.63 27,410.70 0.44 0.47 0.166 0.770 0.430 0.018 0.100 (1,832.93) (3.63) (1.79) (8,372.98) (0.27) (0.24) (0.423) (0.741) (0.782) (0.025) (0.196) Division = Southwest (33 Beats) Division = Southwest (N = 287,166) 5,842.94 8.97 2.27 34,301.05 0.26 0.62 0.194 0.702 0.615 0.021 0.129 (3,087.18) (7.3) (3.32) (8,708.15) (0.23) (0.24) (0.459) (0.658) (0.997) (0.028) (0.24) Standard deviations are presented in parentheses. Allocated Presence is the number of police vehicles allocated to beat per hour (60 minutes = 1 vehicle). Police presence is the number of vehicles present in beat per hour (60 minutes = 1 vehicle).

The AVL data also include a report indicator for vehicles ping from the AVL into a beat.20 The vehicle pings are then that are responding to a call for service. This indicator pro- used to count the minutes of police presence over each hour- vides information on whether the vehicle is on general patrol long interval of 2009. I define minutes of presence for each or responding to a call. In contrast to an aggregate count of car as the elapsed time between first entrance and first exit police officers per city, these data present an opportunity to from the beat. If the car exited the beat and later returned, it is map the activity of each individual squad car throughout the categorized as a new first entry and first exit. Thus, a car that day. is present in beat 142 between 6:50 and 7:20 will contribute The call database and AVL data set are the actual data 10 minutes of presence in hour 6 and 20 minutes of presence that the Dallas Police Department uses to assign officers to in hour 7. If that same car returns to the beat at 7:30 and exits 911 incidents. Thus, when a 911 call is placed in Dallas, the at 7:50, it will contribute 40 minutes of presence in hour 7. call taker records basic information on the incident (location, Only cars that were in a beat for at least 5 minutes of that caller name, classification of incident, and time) and defines hour can contribute to minutes of presence.21 Importantly, the severity of the incident. This information is loaded into the this measure of actual presence can be very different from computer-aided dispatch (CAD) system, which is the source patrol assignment. While beats in the Southern divisions of for the call data. This incident then appears on the computer Dallas generally receive a higher allocation of officers than of the police dispatcher for the relevant division where the beats in the Northern divisions, actual police presence is gen- incident was reported.19 The police dispatcher assigns the in- erally higher in the North.22 My identification strategy builds cident to a patrol car based on priority (as recorded in call around the idea that actual police presence over time is not data) and distance of car (as tracked in AVL data). When fully determined by the allocation of officers. possible, the incident is assigned to the police officer allo- Table 1 summarizes the mean hourly values for crime, po- cated to the beat of the incident, but since this officer can lice allocation, and police presence by beat at the division be otherwise occupied and most calls require two officers, level. The majority of crimes occur in beats that are located officers are often assigned to out-of-beat calls. While it is on the Southwest side of the city (with an average crime rate possible during severe emergencies for police dispatchers to of 0.194). On average police officers are allocated to cover coordinate and allocate officers across divisions, police are generally dispatched to calls within their division. To create a database of police location, I divide the city of 20The study focuses on 232 out of 234 beats in Dallas. Two beats were Dallas into 232 geographic beats of analysis and map each excluded from the analysis because they are composed primarily of water. 21I set a lower bound of presence at 5 minutes in order to focus the analysis on cars that were likely to be patrolling the given beat and not simply driving to have data on the exact allocation, this can still provide insight into the through the area. general area of allocation. 22See figures 2 and 3 of online appendix C, which separately graph police 19Each of the seven divisions has its own set of dispatchers. allocation and actual presence in Dallas over 2009.

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beats for 60% to 80% of each hour. The highest level of police allocated to patrol, even when actual police presence (Pbh ) allocation is in the North Central division where, on average, was only 0.5 as the car was only physically patrolling the beat each beat has an allocated officer for over 80% of each hour, for 30 minutes of that hour. Sector_PA = PA is kh j∈Sk ,h jh while in the Northwest division, a patrol officer is allocated the amount of time (in hours) patrol cars were allocated to to a beat for only about 60% of every hour. However, police spend in the sector (Sk ) surrounding beat k during hour h. allocation only refers to whether there was an active patrol OPatrolbh is calculated for each beat (b) and hour (h) as a officer at this hour of the day whose radio name referred to weighted average of allocated patrol cars in the sectors within the given beat. Actual police coverage varies significantly division Db where calls took place: from allocated coverage, with the largest average difference  observed in the Southeast division. While allocated coverage OPatrolbh = Sector_PAkh × nkh × wbk . (2)

is determined at the start of an officer’s shift, police presence k=b∈Db,h is a function of the events and crime concerns that develop throughout the day. It is important to note that Sector_PAkh in equation (2) is The simultaneous relationship between police presence a count of police allocation outside the given beat b. Thus, and crime is already made apparent in table 1. Beats in the when the sector of the outside call (k) is the same as that of the given beat b, Sector_PA = PA − PA . The vari- Northeast division average 30% less police presence than kh j∈Sk ,h kh bh beats in the Southwest division, yet beats in the Southwest able OPatrolbh provides a weighted measure of the number of division report a higher crime rate. In order to identify a causal officers who are in the area surrounding beats where relevant effect of policing on crime, I focus on an instrument that af- outside calls occurred. This may affect the likelihood that an fects the level of police presence in a given beat but should officer from beat b will abandon his beat. not have a direct impact on crime. I define the OCRbh as Outside Calls (OCbh ) are calculated for each beat (b) and OCbh hour (h) as a weighted average of the number of calls oc- OCRbh = . (3) OPatrolbh curring in division Db outside of beat b. Hour h is a time variable beginning at 0 at 12:00 a.m. on January 1, 2009, In the next section, I lay out my empirical strategy for es- = , and culminating at h 8 736 at 11:00 p.m. on December timating the deterrence effect of police presence on crime. I 30, 2009. Thus, I sum the number of 911 calls received in di- discuss unobserved factors that can create bias in estimating vision Db outside of beat b during hour h reporting incidents this effect and explain how the instruments address these con- related to mental health, child abandonment, fire, animal at- cerns. My results illustrate that even with very detailed micro- tacks, dead people, suicides, abandoned property, fireworks, data, absent an exogenous shift in police presence, policing and drug houses. Importantly, instead of calls occurring in and crime remain positively correlated. all k beats of the division being counted equally, OCbh is a weighted sum,  III. Empirical Strategy and Results OCbh = nkhwbk , (1) In equation (4), I model the occurrence of a crime (Cbh ) as k=b∈D ,h b a function of police presence (Pbh ):

where nkh is the number of calls that occurred in beat k during Cbh = xbhβ0 + β1Pbh + γt + ηb + εbh. (4) hour h and wbk is the estimated probability that an officer in b k beat will be assigned to a call in beat (See online appendix Cbh is a count of the number of 911 calls reporting inci- B for a description of this process). dents of crime (violent crimes, burglaries, thefts, and public The Outside Calls Ratio OCRbh divides the OC instrument disturbances) at beat b during hour h. The variables included from equation (1) by the number of officers allocated to patrol in xbh capture time-varying environment characteristics that 23 in the sectors surrounding the outside call beats. In order could have an impact on the costs and benefits of crime (e.g., to create this instrument, I calculate aggregate measures of weather, visibility). The focus of my analysis is Pbh, a count police presence at the beat and sector levels. of the amount of time police officers spent patrolling inside I define PA bh as the amount of time (in hours) patrol cars beat b at hour h. If one police vehicle was present for a full b h. were allocated to spend in beat during hour The allocation hour (h) at beat (b), then Pbh = 1. A single patrol car in the PA of police vehicles ( bh ) is determined by assignment at the beat that was present for only 30 minutes will result in a Pbh start of their shift and is different from police presence (Pbh ), value of 0.5; alternatively, and two cars that were present PA a measure of where they actually patrol. For example, bh over the entire hour will result in Pbh = 2. The time and beat would be equal to 1 at a beat and hour where one car was fixed effects γt and ηb account for the differential probabili- ties in crime across different times and beats. If policing is

23 uncorrelated with the remaining unobserved factors affect- The Dallas police department divides the city of Dallas into seven divi- ε , β sions, and each division is split into sectors. Each sector consists of roughly ing crime ( bh ) then 1 estimates the amount of deterrence seven beats. created when police coverage is increased by one car.

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FIGURE 3.—RESIDUALS WERE CALCULATED FOR POLICE PRESENCE, CRIME, AND OUTSIDE CALLS BY REGRESSING EACH VARIABLE ON WEATHER, TIME OF DAY, AND DATE CHARACTERISTICS.IDROP RESIDUALS THAT ARE NOT FOUND ACROSS ALL BEATS OR APPEAR IN LESS THAN 10% OF THE SAMPLE.THE DATA WERE COLLAPSED AT EACH CALCULATED OC RESIDUAL POINT, AND THE LOWEST RESIDUAL OF −0.025 WAS INDEXED TO 0. OUTSIDE CALLS ARE DEFINED AS THOSE REPORTING INCIDENTS RELATED TO MENTAL HEALTH, CHILD ABANDONMENT, FIRE, ANIMAL ATTACKS, DEAD PEOPLE, SUICIDES, ABANDONED PROPERTY, FIREWORKS AND DRUG HOUSES.THE SIZE OF THE CIRCLE RELATES TO THE DENSITY OF OBSERVATIONS AT THAT RESIDUAL OC POINT.

My main concern is the endogeneity of policing Pbh. It in surrounding areas that provide a first stage for police pres- has been well documented that police allocation is far from ence Pbh, exogenous. In a well-functioning police department, officer = α + α + θ + ρ + δ . allocation will be highly correlated with crime. Using detailed Pbh xbh 0 1OCbh t b bh (5) geographic data can complicate the relationship, as one would expect that when a crime occurs in a given hour, more police While the allocated level of presence can be determined δ will immediately enter the beat in response to that crime. Even by the perceived crime risk in that area ( bh), actual presence after removing cars that are specifically assigned to respond to is affected by an exogenous factor, OC one as defined in α the call, I cannot rule out a situation where additional officers equation (1). The estimated coefficient on the instrument ( 1) may be drawn to the location of the crime incident for backup is expected to be negative, since an increase in outside calls purposes. An additional concern is that there may be seasonal should decrease police presence in the beat (Pbh ). Figure 3 differences in crime risks that are addressed by the police shows that beats and intervals of time with a higher measure of OC have lower levels of police presence and higher levels force by means of changing police allocation across beats 24 and time. of crime. The Dallas Police Department has a stated goal of answer- Table2 presents regression estimates for the general impact ing all serious 911 calls (priority 1) within 8 minutes and of the OCR and OC on police presence as defined in equation priority 2 calls (e.g., potential for violence or past robbery) (5). I find that increasing the OCR by 1 decreases police within 12 minutes (Eiserer, 2013). Thus, the preplanned allo- coverage by 0.055 (SE 0.003), which is significant at the 1% cation of an officer to a beat can be disrupted by an influx of level. Not surprisingly, without information on outside patrol, emergency calls. It is exactly this differentiation between the 24Outside calls is a weighted sum of outside incidents related to men- endogenous choice of sending officers to higher-risk crime tal health, child abandonment, fire, animal attacks, dead people, suicides, locations and the plausibly random timing of emergency calls abandoned property, fireworks, and drug houses.

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TABLE 2.—OUTSIDE CALLS AS PREDICTORS OF POLICE PRESENCE TABLE 3.—THE EFFECT OF POLICE PRESENCE ON CRIME Instrument = Outside Instrument = Outside IV = Outside IV = Outside Calls Ratioa Callsb OLS Calls Ratiob Callsc (1) (2) (3) OCR Interactions OC Interactions Police Vehiclesa 0.012*** −0.185*** −0.181*** − *** − *** Instrument 0.055 0.078 (0.0004) (0.032) (0.054) (0.003) (0.026) Temperature 0.002*** 0.002*** 0.002*** × − *** − *** Instrument South 0.080 0.687 (0.0001) (0.0001) (0.0001) Central (0.008) (0.051) Precipitation −0.001*** −0.001*** −0.001*** × − *** − *** Instrument Southeast 0.044 0.224 (0.0003) (0.0004) (0.0004) (0.009) (0.050) Twilight 0.007*** 0.006*** 0.006*** × − *** Instrument Southwest 0.044 0.016 (0.002) (0.002) (0.002) (0.006) (0.065) Holiday 0.013*** −0.006 −0.006 × − *** Instrument North 0.070 0.107 (0.004) (0.006) (0.007) Central (0.008) (0.071) Dark −0.00002 0.0004 0.0004 × − *** − *** Instrument Northeast 0.052 0.273 (0.002) (0.003) (0.003) (0.006) (0.053) Beat FE Yes Yes Yes × − *** − Instrument Northwest 0.055 0.032 Month FE Yes Yes Yes (0.006) (0.069) Day of Week FE Yes Yes Yes *** *** Instrument × Central −0.052 0.834 Weekend × Hour FE Yes Yes Yes (0.009) (0.110) First-Stage 321.73 40.81 Beat FE Yes Yes Yes Yes F-Statistic Month FE Yes Yes Yes Yes Observations 2,017,676 2,017,676 2,017,676 Day of Week FE Yes Yes Yes Yes × Each observation is a beat and hour in 2009. The average crime rate is 0.15 (SD 0.4), average police Weekend Hour FE Yes Yes Yes Yes presence is 0.605 (SD 1.078). Standard errors in parentheses account for geographic clustering within a Observations 2,017,676 2,017,676 2,017,676 2,017,676 10 km radius and serial correlation of 5 hours. aThe number of police vehicles patrolling the beat at given hour (60 minutes of presence = 1 vehicle). Each observation is a beat and hour in 2009. Standard errors in parentheses account for geographic bThe OCR is a proxy for police activity outside the beat. It is calculated by dividing the weighted sum clustering within a 10 km radius and serial correlation of 5 hours. Standard deviations are presented in of outside unrelated calls by the weighted sum of officers assigned to patrol the sector where the call brackets. All specifications control for temperature, precipitation, twilight, darkness, and whether it is a took place. Outside unrelated calls are defined as those reporting incidents related to mental health, child holiday. a abandonment, fire, animal attacks, dead people, suicides, abandoned property, fireworks, and drug houses. The OCR is a proxy for police activity outside the beat. It is calculated by dividing the weighted sum cOC is a weighted sum of 911 calls that are unrelated to crime occurring within the division outside the of outside unrelated calls by the weighted sum of officers assigned to patrol the sector where the call beat. This instrument is interacted with division in order to allow out of beat calls to have different effects took place. Outside unrelated calls are defined as those reporting incidents related to mental health, child in different divisions. abandonment, fire, animal attacks, dead people, suicides, abandoned property, fireworks, and drug houses. Significant at ∗10%; **5%; and ***1%. bOutside calls is a weighted sum of 911 calls that are unrelated to crime occurring within the division outside the beat. Significant at ∗10%; **5%; and ***1%. strumental variable analysis conducted in this paper always the precision of the instrument in predicting police presence includes this interaction for the OC instrument. in the beat decreases. Specifically, I find that an additional I estimate the impact of police presence on all crimes us- OC decreases police presence by 0.078 (SE 0.026)). One ing equation (4) for fixed effects and 2SLS specifications. explanation for this noisier estimate is heterogeneity across I compute heteroskedasticity and autocorrelation-consistent locations in their response to outside calls. While the OCR standard errors for all specifications (see Conley, 1999). The takes into account that an officer is more likely to be assigned focus of this paper is estimating β1, the impact of an addi- to an out-of-beat call when that call takes place in an area tional police vehicle in a given beat (b) and hour (h) on crime where police are spread thinly, this does not hold for the outcomes (Cbh ). In the fixed-effect model (column 1 of table OC instrument. A source of heterogeneity could be that in 3) I find that an increase in police presence seems to imply an areas and hours when police presence is more saturated, an increase in crime even when controlling for weather as well as increase in calls in a neighboring beat could actually bring time fixed effects (month, day of week, and weekend×hour) more officers to the area as officers drive through on their and beat fixed effects.26 These results suggest that the pres- way to respond to the call. ence of an additional police car at a given beat results in a To maximize the flexibility of the OC instrument, I interact significant 0.012 increase in crime (at an average crime rate it with an indicator for police division. This allows different of 0.15). divisions to follow different protocols or face different con- Two-stage, least-squares estimates appear in columns 2 straints regarding between beat allocation. After including and 3 of table 3. The estimate in column 2 measures the these interactions, the first-stage F-statistic on the OC in- deterrence effect when actual police presence (Pbh ) is instru- strument is 40.81. While an increase in the OCR results in a mented with the OCR; column 3 provides an estimate of the significant decrease in police presence across all seven divi- effect when applying the alternative OC instrument. These sions, the effect of OC is more varied and exhibits a positive two-stage, least-squares estimates provide an opportunity to effect on police presence in beats in the Central division that 25 are typically small in size and very close together. The in- average causal effect of police presence on crime is the same for the compli- ers (those for whom outside calls decrease police presence) and the defiers (those for whom outside calls increase police presence) (following Angrist, 25While this does not affect the exclusion restriction, it could raise ques- Imbens, & Rubin, 1996). tions regarding the monotonicity assumption of the instrument. Note, how- 26I control for weekend×hour fixed effects in order to allow weekend ever, that this will not create additional bias under the assumption that the hours to differ from weekday hours.

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measure deterrence without the simultaneity bias concerns in TABLE 4.—THE EFFECT OF POLICE PRESENCE ON DIFFERENT TYPES OF CRIMES the OLS estimates (if more police are present at locations and IV = Outside IV = Outside times with increased crime risks, this will result in a positive OLS Calls Ratiob Callsc  (1) (2) (3) bias on the estimated deterrence effect (β1)). The instrument allows me to focus on changes in police presence that were A. Dependent Variable = Violent Crimes (mean of dependent variable 0.065, SD 0.258) not a direct outcome of changes in perceived crime risks at Police Vehiclesa 0.005*** −0.094*** −0.098*** the given beat and hour. (0.0003) (0.017) (0.028) In column 2, when instrumenting for police presence with B. Dependent Variable = Public Disturbances the OCR instrument, I find a significant negative effect of (mean of dependent variable 0.053, SD 0.234) Police Vehicles 0.004*** −0.061*** −0.057** police presence on crime equal to −0.185 (0.032). While β1 (0.0002) (0.017) (0.025) in equation (4) represents the effect of an additional police C. Dependent Variable = Burglaries vehicle (P ) on crime, what is driving the estimate is the real- (mean of dependent variable 0.032, SD 0.181) bh Police Vehicles 0.003*** −0.030*** −0.026* ity that cars are often withdrawn from their patrol beat when (0.0002) (0.011) (0.014) assigned to an outside call. Accordingly, a real-world inter- D. Dependent Variable = Theft pretation of this effect is that removing 60 minutes of presence (mean of dependent variable 0.012, SD 0.109) Police Vehicles 0.001*** −0.006 0.003 from a given beat at a given hour results in a 123% increase (0.0001) (0.007) (0.008) × 0.185 . in crime 100 0.15 If I focus on average police presence Beat FE Yes Yes Yes per hour (36 minutes), a 10% decrease in police presence Month FE Yes Yes Yes − 27 Day of Week FE Yes Yes Yes implies a 7.4% increase in crime (elasticity of 0.74). I Weekend × Hour FE Yes Yes Yes estimate a similar deterrence effect when applying the OC First-Stage F-Statistic 321.73 40.81 instrument (column 3). Observations 2,017,676 2,017,676 2,017,676 Each observation is a beat and hour in 2009. Average police presence is 0.605 (SD 1.078). Standard Table 3 also provides information on how different weather errors in parentheses account for geographic clustering within a 10 km radius, and serial correlation of 5 and time characteristics have an impact on crime outcomes. hours. I include controls for temperature, precipitation, twilight, darkness, and whether it is a holiday. aThe number of police vehicles patrolling the beat at given hour (60 minutes of presence = 1 vehicle). I find that crime is more likely to occur during twilight. bThe OCR is a proxy for police activity outside the beat. It is calculated by dividing the weighted sum of outside unrelated calls by the weighted sum of officers assigned to patrol the sector where the call took Higher temperatures increase the occurrence of crime, and place. Unrelated calls are defined as those reporting incidents related to mental health, child abandonment, bad weather lowers the probability of crime. fire, animal attacks, dead people, suicides, abandoned property, fireworks, and drug houses. cOC is a weighted sum of 911 calls unrelated to crime occurring within the division outside the beat. In table 4, I separately examine the impact of police on This instrument is interacted with division in order to allow out-of-beat calls to have different effects in different divisions. different types of crimes (violent crimes, public disturbances, Significant at ∗10%; **5%; and ***1%. burglaries, and theft).28 I first report the measured effect of police presence in an OLS model that controls for month, day of week, weekend×hour, and beat fixed effects, as well similar estimates of the effect of police presence on pub- as temperature, precipitation, twilight, holiday, and darkness. lic disturbances and burglaries, it is more noisily measured In specifications 2 and 3, I report results when instrumenting when applying the OC instrument. I find that a 10% increase for police presence with the OCR and OC instruments used in police presence decreases public disturbances by 6% to in table 3.29 All crime types exhibit a significant positive 7% and burglaries by 5% to 6%. The effect of police pres- correlation between police presence and crime (see column ence on theft in Row D is much smaller and not statistically 1) that disappears when instrumenting for police presence significant from 0 when applying either of the instruments. with the OCR and OC (see columns 2 and 3). The estimated deterrence effect of police presence on vi- IV. A Closer Look at the Mechanisms of Deterrence olent crime after instrumenting for police presence with the OCR is similar to that of OC. These deterrence estimates of My estimates suggest that police presence at the beat level −0.094 (SE 0.017) and −0.098 (SE 0.028) translate to an can have a significant impact on crime. The next step is to elasticity of roughly 0.9.30 While both instruments provide understand the mechanism by which police presence changes behavior. What are patrol officers doing to prevent crime? Does police presence also affect noncrime-related incidents? 27This is calculated as 3.6 × 100 × 0.185 . 60 0.15 Are police officers more or less effective when allocated to 28I classify violent crimes as stabbings, shootings, robberies, assaults, kidnappings, and armed encounters. I classify public intoxication, illegal certain areas? Does an increase in police presence at this beat parking, suspicious behavior, prostitution, loud music, gunfire, speeding, displace crime to a neighboring beat? road rage, and panhandlers as public disturbances. Police officers engage in both active patrol (e.g., stops, 29Outside calls are defined in this paper as those reporting mental health, child abandonment, fire, animal attacks, dead people, suicides, abandoned questioning, frisks) and passive patrol (e.g., car patrol, pa- property, fireworks, and drug houses. perwork) when working a beat. In order to correctly interpret 30The deterrence impact on violent crimes was calculated by taking the my deterrence results, it is relevant to understand the extent to estimated impact of an additional police vehicle on violent crime (−0.094 (OCR)and−0.098 (OC)) relative to the average violent crime rate of 0.065. which outside calls affect active police patrol. This differen- Thus, the OCR (OC) instrument specification estimate implies that an addi- tiation is important for gaining insight into whether an empty tional police car results in a 144% (151%) decrease in violent crime. Since patrol car (or an officer who is simply filling out paperwork the average amount of police presence is 0.6, a 10% increase in police pres- ence requires dividing the full hour impact by 16.7. This calculation is also in his or her car) can have the same deterrence effect as an applied to all other crime types. officer actively patrolling the streets. I therefore use arrests

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TABLE 5.—THE IMPACT OF POLICE PRESENCE ON ARRESTS when police are present, I cannot rule out the possibility that IV = Outside Calls Ratiob IV = Outside Callsc some of this effect is driven by an arrest taking place before (2) (4) the individual had time to commit a crime. Police Vehiclesa 0.025 0.079** In 2009, DPD received over 10,000 911 calls related to (0.024) (0.035) fires, suicides, abandoned children, and drug houses. While Temperature 0.0003*** 0.0003*** these incidents require police involvement, we would not ex- (0.0001) (0.0001) Precipitation −0.001** −0.001** pect them to respond to changes in police presence. Thus, (0.0003) (0.0003) these call categories provide an opportunity for a placebo Twilight −0.002 −0.002 test to ensure that the deterrence estimates reported in tables (0.002) (0.001) Holiday 0.00001 0.005 3 and 4 are driven by changes in police presence. Table 6 (0.003) (0.004) illustrates that unrelated calls that should not be sensitive to Dark −0.004** −0.005** police officer patrol (suicides, abandoned children, fires, and (0.002) (0.002) Beat FE Yes Yes drug houses) are not significantly affected by police presence Month FE Yes Yes when applying both instruments. Day of Week FE Yes Yes If police presence affects crime by providing a visual re- Weekend × Hour FE Yes Yes First-Stage F-Statistic 321.73 40.81 minder of the costs of crime, I would expect larger beats, Observations 2,017,676 2,017,676 where officers are less likely to be seen, to be less affected Each observation is a beat and hour in 2009. The average arrest rate is 0.03 (SD 0.29), average police by losing a police vehicle than smaller beats. In table 7, I presence is 0.605 (SD 1.078). Standard errors in parentheses account for geographic clustering within a 10 km radius and serial correlation of 5 hours. split the data into three groups of roughly equal sizes: small aThe number of police vehicles patrolling the beat at given hour (60 minutes of presence = 1 vehicle). beats (less than 4.6 miles of roads), midsize beats (4.6 to 8 bThe OCR is a proxy for police activity outside the beat. It is calculated by dividing the weighted sum of outside unrelated calls by the weighted sum of officers assigned to patrol the sector where the call took miles of roads), and large beats (more than 8 miles of roads). place. Unrelated calls are defined as those reporting incidents related to mental health, child abandonment, fire, animal attacks, dead people, suicides, abandoned property, fireworks, and drug houses. I find that police vehicles have a smaller impact on crime in cOC is a weighted sum of unrelated 911 calls occurring within the division outside the beat. This instrument is interacted with division in order to allow out-of-beat calls to have different effects in different large areas versus midsized areas when using the OCR and divisions. OC instruments. Significant at ∗10%; **5%; and ***1%. When instrumenting for police presence with OCR, I find that each additional car reduces crime by 0.116 (0.035) in the larger beats versus 0.246 (0.060) in midsize beats as a proxy for active police presence and examine how they and 0.253 (0.075) in the smaller beats. Interestingly, this are affected by changes in police presence that are driven by implies that a 10% increase in police presence in either out-of-beat calls. a large or a midsized beat results in a 7.6% decrease Table 5 suggests that changes in police presence that are × . × −0.116 ∼ × . × −0.246 in crime 100 0 094 0.146 100 0 053 0.168 , driven by out-of-beat calls may affect arrests. The observed with a smaller marginal effect of 5.7% at smaller beats increase in arrests resulting from increased police presence × . × −0.253 32 100 0 034 0.152 . This similarity at the margin is stands in contrast to much of the literature on police hiring that driven by the significant difference in average police presence reports a decrease in crime without any observed increase in between beats of different size, where small beats average 20 arrests (see Owens, 2013). This raises the important question minutes of presence, mid-sized beats average 30 minutes of of whether an increase in police presence results in a change in presence, and large beats average 57 minutes of presence per behavior (deterrence) or, alternatively, incapacitation where hour. Differences in the baseline rate of police presence per the potential criminals are no longer available to commit the beat may also contribute to the size of the deterrence effect. In crime. other words, taking an officer away from a beat that averages Incapacitation seems especially relevant for an individual little to no police presence may be more detrimental to crime planning to commit multiple crimes in that beat at that exact control than taking an officer from a beat with relatively high unit of time but due to police presence was arrested after the levels of police presence. first attempt. If this is the mechanism through which inca- The question of deterrence versus geographic displace- pacitation immediately affects crime, then it is possible to ment is an important issue. My findings suggest that increas- measure a deterrence effect that is separate from incapac- ing the size of the patrol force would decrease crime (as itation by estimating equation (4) focusing on how police this could hypothetically allow an increase in police pres- presence (Pbh ) affects the probability of a crime as opposed ence in all locations). However, if increasing police pres- to the number of crimes. In this specification, I continue to ence in one location simply shifts crime to the next location, find a significant deterrence effect such that a 10% increase it could raise significant concerns about increasing police in police presence results in a 6.1% to 7% decrease in the 31 probability of crime. While this suggests that people may The average probability of crime per beat and hour is 0.14 (SD 0.3), and change their behavior due to the increased risk of penalty the average amount of police presence is 0.605 (SD 1.08). 32When splitting the data by beat size, the first-stage F-tests when using the OC instrument are below conventional levels for small and midsized 31 The estimated coefficient on Pbh is −0.163 (SE 0.028) when applying the beats. The measured deterrence effect for large beats is larger than that of OCR instrument and −0.141 (SE 0.034) when applying the OC instrument. the OCR instrument and statistically significant at the 1% level.

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TABLE 6.—THE EFFECT OF POLICE PRESENCE ON OTHER TYPES OF CALLS IV = Outside Calls Ratiob IV = Outside Callsc (1) (2) A. Dependent Variable = Suicide Reports (mean of dependent variable 0.001, SD 0.037) −0.001 −0.003 Police Vehiclesa (0.002) (0.003) B. Dependent Variable = Abandoned Child Reports (mean of dependent variable 0.001, SD 0.027) −0.003 −0.001 Police Vehicles (0.002) (0.002) C. Dependent Variable = Fire Reports (mean of dependent variable 0.002, SD 0.039) −0.001 0.0003 Police Vehicles (0.002) (0.003) D. Dependent Variable = Drug House Reports (mean of dependent variable 0.001, SD 0.037) −0.001 0.005* Police Vehicles (0.002) (0.003) E. Dependent Variable = Placebo Categories A-D (mean of dependent variable 0.005, SD 0.071) −0.005 −0.002 Police Vehicles (0.004) (0.006) Beat FE Yes Yes Month FE Yes Yes Day of Week FE Yes Yes Weekend × Hour FE Yes Yes First-Stage F-Statistic 321.73 40.81 Observations 2,017,676 2,017,676 The average crime rate is 0.15 (SD 0.4), average police presence is 0.605 (SD 1.078). Standard errors in parentheses account for geographic clustering within a 10 km radius and serial correlation of 5 hours. I include controls for temperature, precipitation, twilight, darkness, and whether it is a holiday. aThe number of police vehicles patrolling the beat at given hour (60 minutes of presence = 1 vehicle). bThe OCR is a proxy for police activity outside the beat. It is calculated by dividing the weighted sum of outside unrelated calls by the weighted sum of officers assigned to patrol the sector where the call took place. Unrelated calls are defined as those reporting incidents related to mental health, child abandonment, fire, animal attacks, dead people, suicides, abandoned property, fireworks and drug houses. cOC is a weighted sum of unrelated 911 calls occurring within the division outside the beat. This instrument is interacted with division in order to allow out-of-beat calls to have different effects in different divisions. Significant at ∗10%; **5%; and ***1%.

TABLE 7.—THE DETERRENCE EFFECT OF POLICE ON CRIME BY BEAT SIZE IV = Outside Calls Ratiob IV = Outside Callsc Small Medium Large Small Medium Large (1) (2) (3) (4) (5) (6) Police Vehiclesa −0.253*** −0.246*** −0.116*** 0.047 −0.278*** −0.152*** (0.075) (0.060) (0.035) (0.078) (0.099) (0.046) First-Stage F-Statistic 113.87 182.86 172.37 13.73 12.53 24.15 Mean Level of 0.342 0.527 0.943 0.342 0.527 0.943 Police Presence [0.615] [0.856] [1.474] [0.615] [0.856] [1.474] Mean Level of Crime 0.152 0.168 0.146 0.152 0.168 0.146 [0.404] [0.427] [0.395] [0.404] [0.427] [0.395] Observations 669,570 669,651 678,455 669,570 669,651 678,455 Beat FE Yes Yes Yes Yes Yes Yes Month FE Yes Yes Yes Yes Yes Yes Day of Week FE Yes Yes Yes Yes Yes Yes Weekend × Hour FE Yes Yes Yes Yes Yes Yes Each observation is a beat and hour in 2009. Standard errors in parentheses account for geographic clustering within a 10 km radius and serial correlation of 5 hours. Standard deviations are presented in brackets. All specifications also include controls for temperature, precipitation, twilight, dark (=1 after sunset), and holiday. Small, medium, and large beats are defined based on the miles of roads included within the beat. aThe number of police vehicles patrolling the beat at given hour (60 minutes of presence = 1 vehicle). bThe OCR is a proxy for police activity outside the beat. It is calculated by dividing the weighted sum of outside unrelated calls by the weighted sum of officers assigned to patrol the sector where the call took place. Unrelated calls are defined as those reporting incidents related to mental health, child abandonment, fire, animal attacks, dead people, suicides, abandoned property, fireworks, and drug houses. cOC is a weighted sum of unrelated 911 calls occurring within the division outside the beat. This instrument is interacted with division in order to allow out-of-beat calls to have different effects in different divisions. Significant at ∗10%; **5%; and ***1%.

presence in a specific beat. I therefore consider the impact of nificant at the 1% level.33 These estimates suggests that most police presence at larger geographic levels in table 8, where crimes do not easily displace to neighboring areas. I would expect to find a smaller impact of police presence on crime if criminals are shifting their activities to neighboring beats. V. Conclusion In Dallas, beats are grouped into sectors, with each sector While there exists an abundance of research and views re- comprising roughly seven beats. The measured effect of po- garding the deterrent effects of policing on crime, there has lice on violent crime and burglaries at the sector level when yet to be a detailed analysis using information on how the applying the OCR instrument is very similar to the estimates exact location of police officers affects behavior. In a sur- reported in table 4 from analyzing deterrence at the beat level. vey conducted in May 2010, 71% of city officials reported However, when applying this same instrument, I do not find a statistically significant effect of police presence on public 33The measured deterrence effects at the sector level when applying the disturbances at the sector level. When the analysis was run OC instrument are larger than those estimated at the beat level. Thus, they at the beat level, I measure an elasticity of −.7 which is sig- do not provide any evidence of a spatial spillover effect.

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TABLE 8.—THE IMPACT OF POLICE PRESENCE ON CRIME AT THE SECTOR LEVEL The results presented in this paper raise concerns that fre- IV = Outside Calls Ratiob IV = Outside Callsc quently assigning officers to out-of-beat 911 calls may have (1) (3) significant costs in terms of deterring future crimes. I esti- A. Dependent Variable = Violent Crimes mate that a 10% decrease in police presence at a given beat (mean of dependent variable 0.428, SD 0.707) and hour increases crime at that location by 7%. This esti- a *** *** Police Vehicles −0.107 −0.203 mate is especially relevant to 911 calls as my instruments (0.026) (0.073) B. Dependent Variable = Public Disturbances focus on shifts in police presence that are created because (mean of dependent variable 0.387, SD 0.689) officers are assigned to incidents outside their beat. This pa- Police Vehicles −0.027 −0.129** per asks. What happens when a police car leaves its allocated (0.019) (0.056) C. Dependent Variable = Burglaries area to fulfill other departmental duties? I find that shortening (mean of dependent variable 0.214, SD 0.478) response times may have a direct impact on the deterrence Police Vehicles −0.035*** −0.065*** effect of patrol officers. This problem will only increase as (0.014) (0.028) D. Dependent Variable = Theft fewer police officers are hired. (mean of dependent variable 0.079, SD 0.284) Despite the concern that deterrence is negatively affected Police Vehicles −0.011 −0.004 by the assignment of officers to out-of-beat calls, the flip side (0.008) (0.012) Sector FE Yes Yes of this finding is that the thin allocation of officers across large Month FE Yes Yes areas (which is driven by the rapid-response philosophy) can Day of Week FE Yes Yes have crime prevention benefits. The prevalent assumption that Weekend × Hour FE Yes Yes First-Stage F-Statistic 260.28 21.08 there is a tension between the rapid-response philosophy and Observations 304,420 304,420 deterrence is not borne out by my research. In other words, Each observation is a sector and hour in 2009. Average police presence is 4.014 (SD 3.194). Standard the fact that the movement of these allocated officers affects errors in parentheses account for geographic clustering within a 10 km radius and serial correlation of 5 hours. I include controls for temperature, precipitation, twilight, darkness, and whether it is a holiday. crime implies that allocating officers in an effort to provide aThe number of police vehicles patrolling the sector at given hour (60 minutes of presence = 1 vehicle). bThe OCR is a proxy for police activity outside the sector. It is calculated by dividing the weighted sum fast response times can be wedded to a deterrence policy. of outside unrelated calls by the weighted sum of officers assigned to patrol the sector where the call took While the allocation of officers to beats may be driven by place. Unrelated calls are defined as those reporting incidents related to mental health, child abandonment, fire, animal attacks, dead people, suicides, abandoned property, fireworks, and drug houses. the demands of providing fast response times, in reality, the cOC is a weighted sum of unrelated 911 calls occurring within the division outside the sector. This instrument is interacted with division in order to allow out-of-beat calls to have different effects in different presence of these cars reduces the probability of crime. This divisions. may imply that police executives can “have your cake and eat Significant at ∗10%; **5%; and ***1%. it too” but does not rule out the possibility that stronger deter- rence may be achieved by a hot-spots versus rapid-response decreases in the number of police personnel in order to deal allocation strategy. Either way, my results highlight the cau- with budget cuts resulting from the economic downturn.34 tion that must be taken in order to maximize the deterrence With lower budgets, police departments are being forced to benefits of a rapid-response system. While arriving quickly at make tough decisions regarding police activities and deploy- the scene of an incident may help to lower the expected ben- ment. Understanding how these deployment techniques af- efit of committing a crime (see Blanes i Vidal & Kirchmaier, fect crime is key for optimizing outcomes given the current 2018, and Mastrobuoni, 2019), it can also disrupt preemptive budgets. police activity. Police department performance measures are often a func- My results suggest that optimizing the impact of policing tion of crime rates, arrests, response times, and clearance rates on crime requires weighing the costs and benefits of assigning (the proportion of crimes reported that are cleared by arrests). officers to out-of-beat calls. But what is the aggregate impact Some deterrence programs may take time to develop and see of outside calls on crime? If beats where 911 incidents occur results. Thus, a police department that is very involved in gain the minutes lost at the assigned officer’s patrol beat, we neighborhood-based crime reduction activities may get little might expect a decrease in crime that matches the increase at reward for its effort in terms of decreased crime rates. Addi- the abandoned beat and no aggregate effect of outside calls tionally, as crime rates and clearance rates are influenced by on crime. However, this does not take into consideration the outside factors and their outcomes are an imprecise reflection commuting time lost, as well as the fact that an officer re- of investment, departments may prefer to focus on shortening sponding to an incident may not be as visible as an officer response times, an easily measured police activity.35 Indeed, on general patrol. Additionally, losing an officer assigned to the Dallas Morning News reported in 2013 that after criti- patrol a beat that he or she is familiar with may have a very cism of rising response times to 911 calls, the Dallas Police different effect from the added presence of a new officer in Department “temporarily reassigned dozens of officers who a possibly unknown environment. Indeed, recent research on normally spend much of their time targeting drug activity to increases in patrol-surrounding areas where crime occurred duties where they respond to 911 calls” (Eiserer, 2013). has shown limited deterrence effects (see Blanes i Vidal & Mastrobuoni, 2018, and Blattman et al., 2018). In addition to providing a measure of the crime costs of de- 34Information released in U.S. Department of Justice (2011). 35See Davis (2012) for a more in-depth discussion regarding police out- creasing police force size throughout the United States, this comes and outputs (police investment). paper provides insight into the mechanism through which

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police reduce crime. My outcomes are particularly interest- Di Tella, Rafael, and Ernesto Schargrodsky, “Do Police Reduce Crime? ing given recent studies that imply that policing is effective Estimates Using the Allocation of Police Forces after a Terrorist 36 Attack,” American Economic Review 94:1 (2004), 115–133. only when focused at specific high-crime locations. One Draca, Mirko, Stephen Machin, and Robert Witt, “Panic on the Streets of interpretation of my results is that police do not need to be London: Police, Crime, and the July 2005 Terror Attacks,” American micromanaged, and simply assigning them to a fairly large Economic Review 101 (2011), 2157–2181. Eck, John E., and Edward Maguire, “Have Changes in Policing Reduced geographic area (beats average 1.7 square miles) will reduce Violent Crime? An Assessment of the Evidence,” in Alfred Blum- crime. However, the Dallas Police Department is known to stein, ed., The Crime Drop in America 207 (Cambridge: Cambridge follow a directed patrol data–driven strategy that attempts to University Pres.2000). Eiserer, Tanya, “Dallas Police Shift More Manpower, Money to 911 Calls,” direct patrol specifically to hot-spot areas (street blocks with Dallas Morning News, June 1, 2013. very high crime rates). Thus, within the beat, allocated police Evans, William N., and Emily G. Owens, “COPS and Crime,” Journal of may be focused on specific hot-spot areas that they are forced Public Economics 91 (2007), 181–201. Gould, Eric D., and Guy Stecklov, “Terror and the Costs of Crime,” Journal to abandon when answering a call. of Public Economics 93 (2009), 1175–1188. This paper attempts to shed light on what police are doing Kelling, George L., and Mark Harrison Moore, “The Evolving Strategy in order to lower crime. 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Mayo-Wilson, “Police Strategies to Reduce Illegal Pos- where crime decreases because a criminal is arrested before session and Carrying of Firearms: Effects on Gun Crime,“ Campbell he or she can commit multiple offenses.37 However, as this Systematic Reviews 8 (2012), 1–53. effect occurs immediately (within the same hour), it also sug- Larson, Richard C., “What Happened to Patrol Operations in Kansas City? A Review of the Kansas City Preventative Patrol Experiment,” Jour- gests a separate deterrence channel where increased police nal of Criminal Justice 3 (1975), 267–297. visibility has a direct impact on crime outcomes. Levitt, Steven D., “Using Electoral Cycles in Police Hiring to Estimate the Effect of Police on Crime,” American Economic Review 87 (1997), 270–290. ——— “Using Electoral Cycles in Police Hiring to Estimate the Effects 36See works by Weisburd et al. 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