Police levels and crime

Abstract

Researchers have long examined the relationship between police levels (officers or spending per capita) and crime, yet consistent findings remain elusive due to the variety of methodological approaches employed. We present the results of a systematic review and meta-analysis of published and unpublished longitudinal macro-level police levels-crime research in order to ascertain the empirical status of this relationship. Twenty-four studies met the criteria for systematic review; 12 met the criteria for meta-analysis. Findings from a vote-counting procedure reveal mixed evidence of policing’s effect on crime; however, results from the meta-analysis suggest there is a small, inverse association between police levels and crime at the macro-level.

Keywords

crime rates meta-analysis police levels

During or after crime surges, police agencies routinely embark on hiring binges in an effort to improve public safety (e.g. Andrews and Smith, 2014). When hiring is not possible, existing resources are strategically deployed. And during or after crime drops, less demand exists for increased spending and hiring. Whether such fluctuations in the police presence ultimately affect crime, however, has been a subject of intense empirical scrutiny. Indeed, generations of researchers have reached a bewildering array of conclusions about the effects of policing on crime.

Studies of focused policing strategies have yielded encouraging findings that certain policing interventions can (if only temporarily) reduce specific crime types (e.g. Sherman and Rogan, 1995a) and/or crime in specific locales (e.g. Braga et al., 2012). By contrast, there is no consensus as to the effects of straight-up police hiring or spending on crime. Some researchers have found strong associations between the police presence and crime (e.g. Marvell and Moody, 1996), others have found modest associations (e.g. Governmental Accountability Office, 2005) and still others have found none whatsoever (Worrall and Kovandzic, 2007).

The main reason for a lack of consensus in this second line of research concerns the variety of methodological approaches employed. Since Ehrlich’s seminal work in 1973, researchers have invoked a wide range of novel or underutilised statistical approaches to ascertain the police-crime relationship, ranging from cross-sectional (e.g. Hakim, 1980) and time-series designs (Corman and Mocan, 2000) to panel data modelling (Evans and Owens, 2007) and Granger causality tests (Kovandzic and Sloan, 2002). Still others have utilised creative instruments in a two-stage least squares context (Levitt, 1997, 2002) or capitalised on the availability of natural experiments (DiTella and Schargrodsky, 2004; Klick and Tabarrok, 2005).

Lim et al. recently took stock of and attempted to summarise this literature. After conducting a systematic review of 256 findings in 58 macro-level studies, they were unable to draw ‘…firm conclusions on the deterrent impact of increased police levels on crime rates…’ (2010: 1). They did, however, find more inverse associations between police levels and crime than positive or negative associations. In the same year, Worrall also summarised this macro-level police levels-crime literature, concluding that ‘…a police presence matters’ (2010: 48).

Like Lim et al. (2010) and Worrall (2010), we present a systematic review of the police-levels crime literature. We go a step further, however, and invoke formal meta-analytic techniques to draw general conclusions concerning the effects of police levels on crime.

Meta-analysis has become increasingly popular throughout the criminological literature, having recently entered the realm of policing scholarship. Braga et al. (2012) in a recent examination of hot-spots interventions concluded that they are associated with ‘small but noteworthy’ crime reductions. We continue in their footsteps, extending meta-analysis to the macro-level policing/crime literature in an effort to clear up the seemingly conflicting findings presented in dozens of studies published over the past several decades.

Literature review

Two strains of police-crime research are relevant in this context. The first calls into question the relative strengths and weakness of various police strategies, from routine patrol to targeted initiatives in micro places. The second concerns the effects of police hiring or spending on crime.

Patrol and its limitations

The Kansas City (MO) Preventive Patrol Experiment, conducted in 1972 and 1973, called into question a long-standing assumption that random, preventive patrol can reduce crime. Kelling et al. (1974) found that (1) the level of patrol had no effect on suppressible crimes and (2) citizens did not notice the differing levels of patrol within each beat type. The findings were met with some criticism (e.g. Fienbert et al., 1976; Larson, 1975), but there is now a good deal of consensus in the policing literature that random, preventive patrol is limited in its deterrent effect.

Findings from the Kansas City experiment were at least partially responsible for a number of subsequent developments in policing practice and scholarship. Proactive policing strategies (e.g. Zimmer, 1990) were born of a realisation that simple patrol has its limitations. Likewise, directed patrol interventions, whether of hot spots or for specific crime types (e.g. Sampson and Cohen, 1988; Sherman et al., 1989; Sherman and Rogan, 1995b; Wilson and Boland, 1978), were considered improvements over outmoded, standard patrol tactics (Sherman, 1990). Even the popular broken-windows approach to law enforcement (Wilson and Kelling, 1982) parted ways with traditional patrol and instead focused on the intersection of disorder and criminality. Subsequent quality-of-life policing interventions did the same (e.g. Katz et al., 2001). A key driving force behind the community policing movement was citizen disenchantment with traditional police services, including simple patrol (Kelling, 1996). The same also holds for problem-oriented policing (Goldstein, 1979, 1990), third-party policing (Buerger and Mazerolle, 1999) and even more recent developments, such as SMART policing (see, for example, http://www.smartpolicinginitiative.com/).

Effects of policing on crime: Macro-level research

Researchers have employed at least seven distinct methodological approaches in their efforts to gauge the effects of police levels on crime at the macro-level: cross-sectional designs, time-series designs, panel designs, Granger causality tests, instrumental variables/two-stage least squares estimation, natural experiments and studies of the effects of federal police grant programmes on crime.

Cross-sectional designs were most common in early studies of police levels and crime (e.g. Carr-Hill and Stern, 1973; Greenwood and Wadycki, 1973). Authors of these studies either explored associations between police levels and crime at one point in time or pooled their data over several years and then more or less ignored the time dimension within them. Marvell and Moody (1996) reviewed much of this literature and uncovered an array of mixed findings.

Time-series studies came on the heels of cross-sectional studies (e.g. Fujii and Mak, 1980; Wolpin, 1978) and remain somewhat popular in this literature even today. For example, Corman and Mocan (2000: 584) found ‘robust evidence for the deterrent effects of arrests and police on most categories of serious felony offenses’. Panel designs have become quite popular in recent years. Unfortunately, though, the findings from this research have also proven quite mixed (e.g. Cornwell and Trumbull, 1994; Greenberg and Kessler, 1982; Greenberg et al., 1983). No consensus has emerged concerning the effects of police levels or spending on crime.

Marvell and Moody (1996) and Kovandzic and Sloan (2002) utilised a Granger causality testing approach to identify the police levels–crime relationship. This line of research has also revealed that crime and police are strongly interrelated. For example, Marvell and Moody (1996: 640) concluded that ‘[r]ising crime rates elevate police levels, but the magnitude of the impact is small despite high significance levels. Higher police levels reduce most types of crime, particularly at the city level. The size of the impact is often substantial’.

Researchers have also employed two-stage least squares (and similar instrumental variables techniques) to unpack the police level–crime relationship. Instruments researchers have selected include mayoral and gubernatorial elections (Levitt, 1997), municipal firefighters (Levitt, 2002) and various forms of federal policing hiring spending (e.g. Evans and Owens, 2007; Government Accountability Office, 2005; Worrall and Kovandzic, 2010). Much of this research has found modest inverse associations between police levels and crime.

On the subject of grant spending, a number of researchers have also sought to determine whether federal COPS spending led to reductions in crime. Others have studied different federal grant programmes, such as Local Law Enforcement Block Grants (Worrall, 2008). Some of these researchers have ignored the simultaneity issue and found either that such grants reduce crime (Zhao et al., 2002; Zhao and Thurman, 2001) or have no effect on it (Worrall and Kovandzic, 2007). Others have used COPS spending as instruments in various police-levels crime questions and, as above, detected modest inverse associations between police levels and crime (e.g. Evans and Owens, 2007; Government Accountability Office, 2005; Worrall and Kovandzic, 2010).

Finally, some researchers have availed themselves of natural experiments in order to determine whether police levels affect crime. DiTella and Schargrodsky (2004) examined the effect of police presence on crime stemming from the July 1994 terrorist attack in a Jewish area of Buenos Aires, Argentina. The attack led to a surge in the police presence around all Jewish institutions. Klick and Tabarrok (2005) used terror alert levels in the mall area of Washington, DC, to explore the police levels–crime relationship. Both research teams found large reductions in various crime types following the surges.

Objectives

This study explores macro-level empirical research concerning the effects of police levels on crime. It also considers the extent to which prior studies have controlled for possible simultaneity in the police-crime relationship. Consistent with prior research, police levels are defined as either the number of sworn officers per capita or some measure of spending per capita (such as grant funds or expenditures per officer).

We begin with a systematic review of published and non-published studies that have examined the macro-level police levels–crime relationship. In order to overcome the limitations of systematic review, we also present the results of a meta-analysis of the police levels–crime relationship.

Methods

Criteria for inclusion and exclusion of studies

Eligible studies were selected based on factors such as design, variables included, and the type of results and summary statistics presented. A detailed account of the criteria used to select studies is discussed below.

Types of studies

Inclusion in this review was largely dependent on the research question(s) examined. All eligible studies explicitly addressed the relationship between police levels and crime. It was also required that all studies examine this relationship over time. This is primarily due to the well-established reciprocal nature of the police-crime relationship. Although many studies attempt to account for this simultaneity bias through the use of instrumental variables and other strategies (Lim et al., 2010; Marvell and Moody, 1996), it is imperative that longitudinal data be used to establish causal order properly (Shadish et al., 2002); thus, cross-sectional studies were excluded from this review. As a result, selected studies used panel designs, time series or multiple time series (MTS).

Additionally, in order to calculate an effect size for the meta-analysis, it was required that all data necessary for calculating an effect size be supplied in the study. There are many different methods for calculating an effect size (Wilson, 2010), but this meta-analysis chose to use the standard difference of means (Cohen’s d). In most cases, studies simply supplied t-statistics/F-statistics and sample sizes, or regression coefficients, standard deviations and sample sizes, which were then used to calculate Cohen’s d. However, some studies failed to include one or more of these components.¹ Any study that failed to include the proper information for calculating Cohen’s d (sample size, for example) was deemed ineligible and was excluded.

Units of analysis

Based on the aggregate nature of the data, there was no specific unit of analysis required for inclusion in this review. The units of analysis varied across studies, but were generally limited to cities, counties or states. Table 1 shows the number of studies within each area.

Table 1.

Number of studies per unit of analysis.

4	Law enforcement agencies
15	Cities/Suburbs
4	Counties
2	States
1	Dutch areas

*Two of these studies included multiple units of analysis (for example, cities and states).

Measures of police levels

The first measure of police levels was the number of sworn police officers per capita. These data were typically derived from agency-level police employment data (e.g. Kovandzic and Sloan, 2002). The second measure of police levels consisted of either policing expenditures per capita, policing expenditures or grants used for hiring purposes. Besides overall police spending, the following eight expenditure/grants were also included in the systematic review: COPS MORE, COPS Hiring, Innovative, Spending, Local Law Enforcement Block Grant (LLEBG), Byrne Discretionary, State Criminal Alien Assistance Program (SCAAP), Violence Against Women Act (VAWA) and Weed & Seed.²

Outcome measures

Studies were required to include an outcome measure of crime at the macro/aggregate level. These data were typically reported as the crime rate per 100,000 people for index crimes³ generated by the FBI’s Uniform Crime Report (UCR). This review analysed data based on crime type, so there was no specific requirement as to how the crime variable was presented. Some studies relied on one measure for all index crimes (Benson and Rasmussen, 1998; Cornwell and Trumbull, 1994; Ren et al., 2008); however, others classified crime as either property or violent crime (van Tulder et al., 1992). Still others further categorised the crime variable based on individual crime types (for example, murder, burglary, motor vehicle theft) (e.g. Corman and Joyce, 1990; Kim, 2007; Kovandzic and Sloan, 2002; Lilley and Boba, 2009; Marvell and Moody, 1996; Worrall and Kovandzic, 2010). We thus made an effort to include all useable data that examined the police levels–crime rate relationship, regardless of how the crime variable was presented. The only additional requirement was that all data necessary for calculating the effect size (i.e., Cohen’s d) be included.

Search strategies for identification of studies

We incorporated the following search strategies to identify eligible studies:

searches of online journals and databases (e.g. Social Science Citation Index, Criminal Justice Abstracts and NCJRS)

forward and backward citation searches

searches of past systematic reviews (e.g. Lim et al., 2010; Marvell and Moody, 1996)

suggestions from experts in the field.

The police levels–crime literature is quite vast. The search terms⁴ returned several hundred studies within a variety of databases.⁵ Many studies did not fit the scope of the review. Forward and backward citation reviews of bibliographies and suggestions from experts proved much more fruitful in terms of identifying studies specifically concerned with the police levels–crime relationship.

Given the long history of research that examines the police-crime relationship, this review searched as far back as possible. The main limitation with older studies was their tendency to use cross-sectional data. We were thus limited to including studies from 1983 to present.⁶

Statistical procedures

The systematic review was conducted first to provide a broad overview of the police level-crime relationship. This was important in that it allowed for the inclusion of studies that were otherwise excluded due to the strict selection criteria of the meta-analysis. For example, studies that omitted data necessary for calculating an effect size were still eligible for inclusion in the systematic review.

The systematic review relied on vote counting analysis to assess the relationship between police levels and crime. This simply generated a count of studies that found support for the hypothesis that more police led to less crime versus those that did not. Although the review was able to examine more studies than the meta-analysis, there were several limitations that affected its findings. Primarily, the systematic review focused on statistical significance testing rather than the size or direction of the police level effect on crime. This is problematic in that it is largely dependent on sample size and is typically biased toward significant findings. The meta-analysis attempts to correct this issue by focusing on the magnitude and direction of the effect.

Meta-analyses are also better equipped to find obscure relationships, protect against over-interpreting findings, and are more capable of handling large numbers of studies (Lipsey and Wilson, 2001). The key component of the meta-analysis is the effect size, which standardises the findings across studies for the purpose of drawing comparisons. There are multiple types of effect size and each has a variety of methods for calculation. The most common type of effect size, the standardised mean difference effect size (i.e., Cohen’s d), was used for this study.

The standardised mean difference effect size is used to compare two continuous groups on one or more dependent variables (Lipsey and Wilson, 2001; Wilson, 2010). The methodology used in this review to calculate effect sizes was as follows: Cohen’s d was calculated using the Campbell Collaboration’s online effect size calculator. In most cases, t-statistics, F-values and regression coefficients were obtained from the studies and converted to Cohen’s d using the online calculator. Excel formulas outlined by Lipsey and Wilson (2001) were used for all other calculations.

Independence of findings

Several studies included in this review presented results from both aggregate and individual macro-level crime measures. Studies included models for total crime, violent crime, property crime and each of the seven individual index crimes, resulting in a total of 10 separate outcome measures that were analysed. Many of these outcomes stemmed from the same sample, thus resulting in statistically dependent outcomes. To overcome this issue, separate meta-analyses were calculated for each outcome measure so that only one effect size was recorded per study for each meta-analysis. This is further discussed in the meta-analysis section below.

Findings

Selection of studies

The search strategies summarised above yielded 68 relevant studies. These were carefully scrutinised based on the aforementioned criteria for selection. Ultimately, a total of 24 studies met all of the criteria for the systematic review. Only 12 of these met the criteria for the meta-analysis.⁷

Characteristics of studies

The 24 studies varied on factors such as design type, units of analysis and whether they accounted for simultaneity bias. Approximately half of the studies included used a panel design, while eight used time series and four used multiple time series designs. Similarly, the majority of these studies used Ordinary Least Squares (OLS) regression to analyse the police levels–crime relationship. Some studies invoked a two-stage least squares (2SLS) approach instead. Finally, two studies used GMM, or the generalised method of moments.

Thirteen of these studies focused on the effect of police levels on crime at the city-level, while four focused on counties, three on states and four on law enforcement agencies. One study examined the police levels–crime relationship using data from across the United States and another was limited to Dutch areas. Of these 24 studies, two focused on more than one area (for example, cities and states).

More than half of the studies accounted for simultaneity bias (15). Of these 15 studies, six used an instrumental variable, while four used the Granger Test and four used lags. Table 2 illustrates the characteristics of all studies included in this review.

Table 2.

Characteristics of studies included in the review.

Studies	Unit of analysis	Design	Sample size	Analysis	Addressed simultaneity bias
Greenberg et al. (1983)	269 cities, 252 suburbs	Panel	269, 252	OLS	Lag
Kim (2007)	58 large cities, 408 small cities, 173 counties	Panel	464 (LC), 3,264 (SC), 1384 (Co.)	FD-GMM	Lag
GAO (2005)	4,247 agencies	Panel	9,797,096	OLS	Instrumental Var.
Kovandzic and Sloan (2002)	57 FL counties	TS	1,025	OLS	Granger Test
Marvell and Moody (1996)	56 cities, 49 states	TS	1029, 980	OLS	Granger Test
Corman and Joyce (1990)	NYC	TS	189	VAR	Granger Test
Corman and Mocan (2000)	NYC	TS	300	OLS	Lag
Corman and Mocan (2005)	NYC	TS	300	OLS	Lag
Corman et al. (1987)	NYC	TS	174	VAR	Granger Test
Cornwell and Trumbull (1994)	NC counties	TS	630	2SLS	Instrumental Var.
Ren et al. (2008)	85 US cities	Panel	935	OLS	None
Benson and Rasmussen (1998)	67 FL counties	TS	335	OLS	None
van Tulder et al. (1992)	32 Dutch areas	TS	189	OLS	None
Lin (2009)	51 states	TS	1409	OLS, 2SLS	Instrumental Var.
Zhao et al. (2002)	6,100 city police agencies	Panel	36,605	2SLS	None
Lilley and Boba (2009)	11,559 US jurisdictions	Panel	91, 323	OLS	None
Worrall and Kovandzic (2010)	5199 cities	Panel	47,901	GMM	Instrumental Var.
Worrall and Kovandzic (2007)	189 US cities	Panel	2,079	2SLS	None
Boba and Lilley (2009)	10,371 US jurisdictions	Panel	55,917	OLS	None
Liu and Bee (1983)	Youngstown	TS	48	OLS	None
Evans and Owens (2007)	2,074 US cities	Panel	23,335	2SLS	None
Levitt (2002)	122 US cities	Panel	2,005	2SLS	Instrumental Var.
Levitt (1997)	59 US cities	Panel	1,136	2SLS	Instrumental Var.
Deutsch et al. (1990)	48 states	TS	528	OLS	None

Vote counting results

According to the systematic review conducted by Lim et al. (2010), there is still some question as to whether increased police levels are associated with crime rates. They found that although the majority of studies that examined this relationship found a negative relationship between police levels and crime, these findings were not always significant. Furthermore, the authors found that because of methodological issues pertaining to factors such as simultaneity bias, no firm conclusion could be drawn as to the overall effect of police levels on crime.

A simple vote count of the studies used in this review suggests that police levels are associated with reductions in crime rates, but like Lim et al. (2010), the results were mixed as well. Out of the studies reviewed in this study, approximately half found a significant inverse relationship between police levels or police spending and crime rates (e.g. Evans and Owens, 2007; Kovandzic and Sloan, 2002; Marvell and Moody, 1996; Ren et al., 2008; Worrall and Kovandzic, 2010). Others, however, found little to no relationship between police levels and crime rates (e.g. Corman et al., 1987; Cornwell and Trumbull, 1994; Greenberg et al., 1983; Kim, 2007; Worrall and Kovandzic, 2007).

Meta-analysis results

Due to the use of multiple outcomes per study and the inconsistent use of those outcomes across studies, several separate meta-analyses were conducted. For each study, a single effect size was calculated for each different crime outcome and then weighted according to sample size. From here, separate meta-analyses were conducted for each crime outcome. This was necessary to ensure that all calculated effect sizes were statistically independent.

The weighting of effect sizes required that standard errors be reported by each study. Consequently, this became the final criterion for a study’s inclusion in the meta-analysis. Although standard errors are not necessary to calculate an effect size, they are critical to the weighting process. Therefore, any study that omitted standard errors was dropped from the meta-analysis. This limited the number of selected studies to 12.

First, a meta-analysis was conducted using overall index crime as the outcome variable. The Q-statistic (Q = 1.11, df = 5) indicates that the effect sizes were distributed homogenously. A fixed effects meta-analysis model was thus used to calculate the mean effect size for all studies. The mean effect size of sworn police officers on index crime was small (−0.242),⁸ but statistically significant (Z = −4.686, p < 0.001). This indicates that there is a slight negative relationship between police levels and overall index crime rates.

Fixed effects meta-analysis models were also conducted using violent crime (Q = 0.586, df = 4) and property crime (Q = 1.49, df = 4) as the outcome variables. The number of police officers had a very small effect (−0.030) on violent crime, and nearly an identical effect on property crime (−0.029), neither of which were statistically significant. The standard mean difference effect sizes, standard errors, inverse variance weights and 95% confidence intervals for all aggregate crime outcomes are presented in Table 3.

Table 3.

Meta-analysis of the effect of sworn police officers on aggregate crime.

Study	Effect size	Std. err.	Inverse variance weight	Confidence interval (lower)	Confidence interval (upper)
Overall index crime
Cornwell and Trumbull	0.0873	0.617	2.627	−0.205	0.3796
Kim (2007)	−0.03	0.241	17.217	−0.1587	0.0987
Ren et al. (2008)	−0.2544	0.053	355.999	−0.3831	−0.1257
Meta-analysis (weighted)	−0.242*
Violent crime
Evans and Owens (2007)	−0.042	0.631	2.511546837	−0.0676	−0.0162
Greenberg et al. (1983)	0.005	0.105	90.70294785	−0.2421	0.2517
Kim (2007)	0.0048	0.306	10.67965312	−0.1647	0.0927
Levitt (2002)	−0.1727	0.231	18.74027848	−0.2347	0.1106
Lin (2009)	−0.2561	0.74	1.826150475	−0.3303	−0.182
Meta-analysis (weighted)	−0.030
Property crime
Evans and Owens (2007)	−0.023	2.6	0.147928994	−0.0482	0.0031
Greenberg et al. (1983)	0.0058	0.087	132.1178491	−0.2411	0.2527
Kim (2007)	−0.042	0.259	14.90735081	−0.1707	0.0867
Levitt (2002)	−0.252	0.235	18.10774106	−0.0867	0.0363
Lin (2009)	−0.3014	0.925	1.168736304	−0.3757	−0.2272
Meta-analysis (weighted)	−0.029

Many of the studies that examined the effect of police levels on aggregate crime outcomes also assessed the impact that increased police levels have on individual crime types. The seven index crimes (excluding arson) were used as outcomes for separate meta-analyses. The Q-statistic for the effect of police officers on rape (Q = 10.82, df = 4, v = 0.086) was distributed heterogeneously; therefore, a random effects meta-analysis model was conducted. Fixed effects meta-analysis models were estimated for the remaining crime types.

The mean effect size of sworn officers on homicide (0.016) and rape (0.184) were small and not statistically significant. The mean effect size of police officers on robbery (−0.07), assault (−0.149), burglary (−0.037), larceny (−0.075) and motor vehicle theft (−0.128) were small and they were not statistically significant. Tables 4 and 5 illustrate the standard mean difference effect sizes, standard errors, inverse variance weights and 95% confidence intervals for individual crime outcomes.

Table 4.

Meta-analysis of the effect of sworn police officers on individual violent crimes.

Study	Effect size	Std. err.	Inverse variance weight	Confidence interval (lower)	Confidence interval (upper)
Homicide
Lilley and Boba (2009)	0.006	0.035	816.3265306	−0.0085	0.0205
Lin (2009)	−0.1505	1.31	0.582716625	−0.2244	−0.0765
Worrall and Kovandzic (2010)	0.0267	0.035	816.3265306	0.0087	0.0446
Meta-analysis (weighted)	0.016
Rape
Kim (2007)	1.5091	0.454	3.428047662	1.3633	1.655
Levitt (1997)	−0.404	0.77	9.556645247	−3.5326	−3.2752
Lilley and Boba (2009)	0.0405	0.103	1.440932094	0.0261	0.055
Lin (2009)	−0.1303	0.78	1.473849713	−0.2042	−0.0564
Worrall and Kovandzic (2010)	0.002	0.138	10.39455334	−0.0159	0.02
Meta-analysis (weighted)	0.184
Robbery
Kim (2007)	−0.036	0.361	7.673360395	−0.1647	0.0927
Levitt (1997)	−0.4233	0.79	1.602307323	−0.5064	−0.3401
Lilley and Boba (2009)	0.0267	0.967	1.069416922	0.0122	0.0411
Lin (2009)	−0.03	1.12	0.797193878	−0.1039	−0.0438
Worrall and Kovandzic (2010)	0.0239	0.763	1.717714272	0.006	0.0419
Meta-analysis (weighted)	−0.071
Assault
Evans and Owens (2007)⁹	−0.0249	0.466	4.604984435	−0.0505	0.0008
Kim (2007)	0.0781	0.486	4.233771952	−0.0506	0.2068
Levitt (1997)	−0.6407	0.73	1.876524676	−0.725	−0.5564
Lilley and Boba (2009)	0.0479	1.258	0.631885977	0.0334	0.0623
Lin (2009)	−0.5722	0.72	1.929012346	−0.6475	−0.4968
Worrall and Kovandzic (2010)	0.025	1.55	0.416233091	0.0071	0.043
Meta-analysis (weighted)	−0.149

Table 5.

Meta-analysis of the effect of sworn police officers on individual property crimes.

Study	Effect size	Std. err.	Inverse variance weight	Confidence interval (lower)	Confidence interval (upper)
Burglary
Kim (2007)	−0.006	0.244	16.79656006	−0.1347	0.1227
Levitt (1997)	−0.014	0.9	1.234567901	−0.962	0.0682
Lilley and Boba (2009)	0.0453	2.063	0.234964117	0.0308	0.0597
Lin (2009)	−0.4041	0.8	1.5625	−0.4787	−0.3295
Worrall and Kovandzic (2010)	0.0254	2.775	0.129859589	0.0074	0.0433
Meta-analysis (weighted)	−0.037
Larceny
Kim (2007)	−0.0621	0.254	15.500031	−0.1908	0.0666
Levitt (1997)	−0.062	1.01	0.980296049	−0.1443	0.0202
Lilley and Boba (2009)	0.0518	5.826	0.029461784	0.0374	0.0663
Lin (2009)	−0.2193	1	1	−0.2934	−0.1453
Worrall and Kovandzic (2010)	0.0066	8.502	0.013834319	−0.0114	0.0246
Meta-analysis (weighted)	−0.075
Motor vehicle theft
Kim (2007)	−0.1788	0.534	3.50685239	−0.3077	−0.0499
Levitt (1997)	−0.1404	0.8	1.5625	−0.2227	−0.058
Lilley and Boba (2009)	0.0216	1.845	0.293769875	0.0071	0.036
Lin (2009)	−0.5542	1.82	0.301895906	−0.6295	−0.479
Meta-analysis (weighted)	−0.128

A random effects meta-analysis model was used to estimate the effect size for police expenditures/grants on homicide (Q = 6.03, df = 2, v = 0.002). A fixed effects meta-analysis model was used to calculate the mean effect size for police expenditures/grants on all other crime types (see Table 6 for a complete list of Q-statistics, degrees of freedom and p-values, which were used to determine the type of analysis – i.e. fixed effects versus random effects meta-analyses – based on effect size distribution within each meta-analysis). The mean effect sizes of police expenditures/grants on rape (0.012) and motor vehicle theft (0.005) were trivial. The impact of expenditures/grants on all other crime types was also very small (homicide = −0.011, robbery = −0.01, assault = −0.011, burglary = −0.028, larceny = −0.004). Furthermore, none of these effects was statistically significant. The standard mean difference effect size, standard errors, inverse variance weights and 95% confidence intervals for the meta-analysis of police expenditures/grants on violent and property crimes are presented in Tables 7 and 8.

Table 6.

Distribution of effect sizes.

Outcome variable	Independent variable	Q-statistic	Degrees of freedom	P-value
Overall index crime	Sworn police officers	1.11	2	p > 0.25
Overall violent crime	Sworn police officers	0.59	4	p > 0.25
Overall property crime	Sworn police officers	1.15	4	p > 0.25
Homicide	Sworn police officers	0.19	2	p > 0.25
Homicide	Expenditures/Grants	6.026*	2	p = 0.05
Rape	Sworn police officers	10.82*	4	p = 0.05
Rape	Expenditures/Grants	0.02	2	p > 0.25
Robbery	Sworn police officers	0.24	4	p > 0.25
Robbery	Expenditures/Grants	0.005	2	p > 0.25
Assault	Sworn police officers	1.13	5	p > 0.25
Assault	Expenditures/Grants	0.007	2	p > 0.25
Burglary	Sworn police officers	0.23	4	p > 0.25
Burglary	Expenditures/Grants	0.001	2	p > 0.25
Larceny	Sworn police officers	0.02	4	p > 0.25
Larceny	Expenditures/Grants	0.0002	2	p > 0.25
Motor Vehicle Theft	Sworn police officers	0.09	5	p > 0.25
Motor Vehicle Theft	Expenditures/Grants	0.001	2	p > 0.25
All Crime Outcomes	Sworn police officers	4.57	9	p > 0.25

*Statistically significant Q-statistics indicate that the distribution of effect sizes is heterogeneous and a random effects meta-analysis is warranted (as opposed to a fixed effects meta-analysis).

Table 7.

Meta-analysis of police expenditures/hiring grants on individual violent crimes.

Study	Effect size	Std. err.	Inverse variance weight	Confidence interval (lower)	Confidence interval (upper)
Homicide
GAO (2005)	−0.0532	0.028	0.089146415	−0.0541	−0.0523
Lilley and Boba (2009)	0.019	0.009	561.4823133	0.0045	0.0335
Worrall and Kovandzic (2007)	0.0085	3.349	402.5764895	−0.0841	0.1011
Meta-analysis (weighted)	−0.011
Rape
GAO (2005)	0.018	0.075	177.7777778	0.0171	0.0189
Lilley and Boba (2009)	0.001	0.103	94.25959091	−0.0143	0.0146
Worrall and Kovandzic (2007)	0.0871	3.931	0.064713354	−0.0067	0.181
Meta-analysis (weighted)	0.012
Robbery
GAO (2005)	−0.068	1.07	0.873438728	−0.0689	−0.0672
Lilley and Boba (2009)	0.036	0.967	1.069416922	0.0215	0.0504
Worrall and Kovandzic (2007)	0.0061	134.609	5.51889E−05	−0.0865	0.0987
Meta-analysis (weighted)	−0.011
Assault
GAO (2005)	−0.03	1.08	0.85733882	−0.0309	−0.0291
Lilley and Boba (2009)	0.0154	1.258	0.631885977	0.001	0.0299
Worrall and Kovandzic (2007)	0.0061	127.937	6.10953E−05	−0.0865	0.0987
Meta-analysis (weighted)	−0.011

Table 8.

Meta-analysis of police expenditures/hiring grants on individual property crimes.

Study	Effect size	Std. err.	Inverse variance weight	Confidence interval (lower)	Confidence interval (upper)
Burglary
GAO (2005)	−0.054	1.33	0.565323082	−0.0549	−0.0531
Lilley and Boba (2009)	0.0337	2.063	0.234964117	0.0193	0.0482
Worrall and Kovandzic (2007)	0.0313	180.388	3.07316E−05	−0.0616	0.1241
Meta-analysis (weighted)	−0.028
Larceny
GAO (2005)	−0.0104	3.05	0.107497984	−0.0113	−0.0095
Lilley and Boba (2009)	0.021	5.826	0.029461784	0.0066	0.0355
Worrall and Kovandzic (2007)	0.0019	453.892	4.85395E−06	−0.091	0.0948
Meta-analysis (weighted)	−0.004
Motor vehicle theft
GAO (2005)	−0.068	3.44	0.084505138	−0.0689	−0.0672
Lilley and Boba (2009)	0.0263	1.845	0.293769875	0.0118	0.0408
Worrall and Kovandzic (2007)	0.0232	198.962	2.52615E−05	−0.0696	0.1161
Meta-analysis (weighted)	0.005

Robustness checks

One potential issue is the failure of studies to account for simultaneity bias. All but one of the studies included in the meta-analyses accounted for simultaneity bias. To determine if that one study had an influence on the mean effect size for each crime outcome, each meta-analysis was reanalysed using only those studies that accounted for simultaneity bias. This resulted in slightly stronger effect sizes for all crime types. However, no effect size became statistically significant as a result of this change.

Other possible issues might arise from differences in units of analysis and study design. To account for these differences, each meta-analysis was revised to include only one type of unit of analysis or one type of design. Over half of the studies included in the meta-analyses focused on the police level–crime relationship at the city level. Therefore, analyses were conducted using only studies that used city-level data. This resulted in very little change in size and no change in direction or statistical significance.

Due to the large number of studies that used panel designs (10 out of the 12 studies), another set of analyses was conducted using only studies that used a panel design. Again, the results were very similar, with only minor changes in size and no changes in direction or statistical significance. Based on these studies, it does not appear as though the unit of analysis or study design had any noticeable impact on the results.

To assess the sensitivity of analysing each crime outcome as a separate meta-analysis, a single meta-analysis of the effect of police officers on all crime outcomes combined (e.g. homicide, rape, robbery, burglary, larceny, etc.) was conducted. Unlike the overall crime index, which represents an actual variable presented in many of the studies included in this paper, this analysis effectively used the mean effect sizes from each meta-analysis (i.e. one for each crime outcome included in this paper) and conducted an additional meta-analysis. The Q-statistic (Q = 22.12, df = 9) indicated that the effect sizes were heterogeneously distributed. A random effects meta-analysis model was therefore used to calculate the mean effect size of police officers on all crime outcomes. The mean effect size was very small (−0.054) and was not statistically significant. These findings are supportive of those derived from separate crime outcomes.

Conclusion

The findings from this study suggest that there is a small, inverse association between police levels and overall index crime. However, when this relationship is examined across individual crime types, the effect decreases in magnitude, loses statistical significance and, in some cases, changes direction. This could be due to problems with selection bias.

Although a large number of studies have examined the relationship between police levels and crime, many did not meet the selection criteria outlined in this study and were ultimately excluded from the analyses. Moreover, it is plausible that some of the studies that were included in these analyses were methodologically flawed, leading to the calculation of inaccurate effect sizes. Additionally, any study that was not published or that the authors were unable to find might have contributed to the overall findings as well.

Still, the meta-analysis of studies that were selected is superior to other methods of review (Lipsey and Wilson, 2001), which gives some weight to the findings. Yet, to understand truly the police levels–crime relationship, futures studies will need to supply detailed summary statistics in addition to their overall findings. For now, we can conclude that if there is an effect of police levels on crime, it is small.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

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