Conservative government, which included agencies such as Her Majesty’s Inspector of Constabulary HMIC and the Audit Commission, and the introduction of various public
charters, including the Citizen’s Charter and the Victim’s Charter for a discussion, see Stephens, 1994; Sullivan, 1998.
This comprehensive review resulted in various publications concerned with efficiency in the service and included Audit Commission 1990, Home Office 1993, Police Research
Group 1993, and the report by Sheehy 1993, which led to recommendations included in The Police and Magistrates’ Courts’ Act of 1994. One of the main recommendations of the
Sheehy report was to change the nature of police management from a public to a business- oriented organization and to introduce efficiency targets that were coordinated with local
police authorities. Sullivan 1998 argues that the police reform of the 1990s led to the managerialism of the service. That is, “managerialism referred to the belief that all state
services do better when reconceived and restructured in terms of the business community’s values of efficiency and effectiveness” p. 307. The government’s concept of “value for
money” in the police service has led us to posit a socioeconomic model of the modern police force. That is, we introduce a methodology that is based on the reorganization of the police
force that was begun in the ThatcherMajor government’s reforms but that is set within the concept of the economics of the firm.
The new Labour government has carried on this agenda of ensuring efficiency in the police force Home Office Inspectorate of Constabulary, 1998. The report reiterated the
previous Conservative government’s efficiency drive in the police service with the HMIC arguing that, “police managers need to work harder to ensure that VFM [value for money]
is achieved, for competitive pressure has to be created internally. The costing of activity with subsequent measurement and comparison of performance provide the means by which such
encouragement is given” p. 8, paragraph 10.
This article utilizes data envelopment analysis DEA to estimate the relative efficiency of the English and Welsh police forces. To determine whether there are categorical size effects
in policing, we also utilize multiple discriminant analysis MDA. To the authors’ knowl- edge, this is the first article to examine the relative efficiency of the English and Welsh police
forces. The article is organized as follows. In Section 2, we discuss the methodology utilized in our DEA analysis of police forces and provide details on the variables and data sources.
Section 3 presents the results of the DEA efficiency rankings together with a discussion of how certain forces have fared over the 1992–1993 to 1996 –1997 sample period. In Section
4, we undertake MDA tests to discover whether there are categorical size effects that can discriminate between police forces in the sense that one size of force is likely to be more
efficient than another. We conclude the article with Section 5.
2. Methodology and data
The term DEA was coined by Charnes et al. 1978 and is a linear-programming technique for constructing extremal, piecewise frontiers that were originally developed by Farrell
1957. The constructed relative efficiency frontiers are nonstatistical or nonparametric in the
54 L. Drake, R. Simper International Review of Law and Economics 20 2000 53–73
sense that they are constructed through the envelopment of the decision-making units DMUs with the “best practice” DMUs forming the nonparametric frontier.
DEA is a leading analytical technique for measuring relative efficiency and has been widely used by both academics and practitioners in evaluating the efficiency of DMUs within
an organization or industry in terms of converting resourcesinputs into outputs. The tech- nique was originally developed to determine performance measures in non-profit-making
organizations where the usual monetary criteria of return on assetscapital, for example, were not appropriate. Hence, DEA has been widely used for relative performance measurement in
public sector services such as education Chalos Cherian, 1995; Sarrico et al., 1997, health services see SalinasJime´nez Smith, 1995, for an example assessing primary-care
performance in the English Family Health Service Authorities, and Thanassoulis et al., 1996, for an example using data concerned with prenatal care in England, and criminal courts see
PedrajaChaparro SalinasJime´nez, 1996, for an example of Spanish court efficiency. Although DEA is ideally suited to the examination of the relative efficiency of law enforce-
ment units, to our knowledge, this is the first study to apply this technique to the analysis of relative police force efficiency.
A particular advantage of nonparametric techniques such as DEA, relative to statistical or parametric techniques such as stochastic frontier analysis Drake Weyman-Jones, 1996;
Ferrier Lovell, 1990, is that the latter must assume a particular functional form that characterizes the relevant economic production function or cost function. Hence, any result-
ant efficiency scores will be partially dependent on how accurately the chosen functional form represents the true production relationship i.e., the relationship between inputs
resources and outputs. As DEA is nonparametric and envelops the inputoutput data of the DMUs under consideration, the derived efficiency results do not suffer from this problem of
functional form dependency.
The use of DEA is not confined to public sector enterprises, however. DEA can be applied to any organizationindustry in which a reasonably homogenous set of DMUs use the same
set of resources, possibly in different combinations, to produce an identifiable range of outputs or “deliverables,” again possibly in different combinations. In this context, DEA has
been applied to the analysis of individual building societies and banks within the U.K. financial sector Drake Weyman-Jones, 1992, 1996; Drake, 1997, to the relative effi-
ciency of hotels within a hotel chain Johns et al., 1997, and to the analysis of the relative efficiency of the individual bank branches of a U.K. clearing bank Drake Howcroft,
1994.
2.1. Measuring relative efficiency using DEA Within the methodological framework of DEA it is possible to decompose the relative
efficiency performance of DMUs into the categories initially suggested by Farrell 1957, and later elaborated on by Banker et al. 1984 and Fare et al. 1985. Farrell’s categories are
best illustrated, for the single-outputtwo-input case in the unit isoquant diagram Fig. 1 where the unit isoquant yy shows the various combinations of the two inputs x
1
, x
2
that can be used to produce one unit of the single output y. The firm at E is productively or
overall efficient in choosing the cost-minimizing production process given the relative input
55 L. Drake, R. Simper International Review of Law and Economics 20 2000 53–73
prices represented by the slope of WW’. A DMU at Q is allocatively inefficient in choosing an inappropriate input mix, while a DMU at R is both allocatively inefficient in the ratio
OPOQ and technically inefficient in the ratio OQOR because it requires an excessive amount of both inputs, x, compared with a firm at Q producing the same level of output, y.
The use of the unit isoquant implies the assumption of constant returns to scale. However a firm using more of both inputs than the combination represented by Q may experience
either increasing or decreasing returns to scale so that, in general, the technical efficiency ratio OQOR may be further decomposed into scale efficiency, OQOS, and pure technical
efficiency, OSOR, with point Q in Fig. 1 representing the case of constant returns to scale. The former arises because the firm is at an input-output combination that differs from the
equivalent constant returns-to-scale situation. Only the latter pure technical efficiency rep- resents the failure of the firm to extract the maximum output from its adopted input levels
and, hence, may be thought of as measuring the unproductive use of resources. In summary,
productive efficiency 5 allocative efficiency 3 scale efficiency 3 pure technical efficiency OPOR 5 OPOQ 3 OQOS 3 OSOR.
1 Due to the difficulties in accurately measuring all input prices in public sector services such
as the police force, this article does not consider allocative efficiency. Hence, concentrating on overall technical efficiency, Farrell 1957 suggested constructing, for each observed
DMU, a pessimistic, piecewise, linear approximation to the isoquant, using activity analysis applied to the observed sample of DMUs in the organizationindustry in question. This
produces a relative rather than an absolute measure of efficiency because the DMUs on the
Fig. 1. Farrell efficiency. 56
L. Drake, R. Simper International Review of Law and Economics 20 2000 53–73
piecewise, linear isoquant constructed from the boundary of the set of observations are defined to be the efficient DMUs.
Subsequent developments have extended this mathematical linear-programming approach. If there are n DMUs in the industry, all the observed inputs and outputs are represented by
the n-column matrices X and Y. The input requirement set, or reference technology, can then be represented by the free disposal convex hull of the observations, i.e., the smallest convex
set containing the observations consistent with the assumption that having less of an input cannot increase output. We do this by choosing weighting vectors, l one for each firm, to
apply to the columns of X and Y to show that firm’s efficiency performance in the best light.
For each DMU in turn, using x and y to represent its particular observed inputs and outputs, pure technical efficiency is calculated by solving the problem of finding the lowest
multiplicative factor, u, which must be applied to the firm’s use of inputs, x, to ensure that it is still a member of the input requirements set or reference technology. That is, choose
u, l to min u, such that u
x l9X l
i
0, l
i
5 1,
y l9Y i 5 1, . . . , n.
2 To determine scale efficiency, we solve the technical efficiency problem 2 without the
constraint that the input requirements set be convex; i.e., we drop the constraint Sl
i
5 1. This permits scaled-up or down-input combinations to be part of the production possibility
set of the DMUs. Fig. 2 illustrates this for the case of a single input and a single output. In Fig. 2, the production possibility set under constant returns to scale is the region to the
right of the ray, OC, through the leftmost input-output observation. Any scaled-up or
Fig. 2. SE and PTE. 57
L. Drake, R. Simper International Review of Law and Economics 20 2000 53–73
scaled-down versions of the observations are also in the production possibility set under this assumption of constant returns to scale. Imposing the convexity constraint Sl
i
5 1 ensures that the production possibility set is the area to the right of the piecewise linear frontier VV’,
which does not assume constant returns to scale, but allows for the possibility of increasing returns to scale at low output levels and decreasing returns at high output levels. The
resulting overall technical and pure technical efficiency ratios, AQAR and ASAR, are illustrated for one of the observations. Scale efficiency is the ratio of the two results.
In the case of program 2, the efficiency ratios with and without the convexity constraint may be labeled u
p
and u
o
, and scale efficiency u
s
is then u
o
u
p
. In the subsequent results, we refer to overall technical efficiency as OE, pure technical efficiency as PTE, and scale
efficiency as SE. As explained above, it follows that: OE 5 PTE 3 SE, and SE 5 OEPTE
Using DEA to derive a measure of OE, but also to decompose the results into the components of PTE and SE, allows us to examine not only the effectiveness of the use of resources in
policing PTE but also to gain an insight into the relationship between efficiency and the size of police forces SE. All economic organizations that use resources to produce outputs are
prone to output ranges that display, first, increasing, then constant, and finally decreasing returns to scale. Obtaining this type of information about English and Welsh police forces
may enable us to shed some light on the optimal size and structure of police forces from the perspective of economic efficiency, although it is recognized that there will be many other
factors that inevitably impinge on the size and structure of forces.
2.2. The identification of inputs and outputs in policing The measurement of the police force in its actions and activities is complex because it
involves many accountable and nonaccountable services. For example, Redshaw et al. 1997 argue that policing consists of the “prevention and detection of crime and the maintenance
of public order, but it also embraces a social service role such as welfare and the prevention of crime” p. 284. Byrne et al. 1996 differentiate between two main police functions:
traditional law enforcement, which includes the prevention and repression of crime; and public service duties, including the regulation of noncriminal activities. However, the
complications of measurement rest not with the inputs of the police but with their outputs. That is, the former can be grouped as if the service was a firm and, therefore, include labor
and various capital costs.
In our model, we break down the inputs of each police force into four distinct categories, as outlined in the Chartered Institute of Public Finance and Accountancy Police Force
Statistics. The first input in our estimation methodology is employment costs. This is the total cost of the employed staff of each police force, which includes all police officer ranks, traffic
wardens, civilian staff, and other staff development expenses that occur on a daily basis. We have included civilian staff in the summation of police staff costs because the demarcation
between the police function and the civilian involvement in policing has become ever more blurred. In a recent report by Her Majesty’s Inspectorate for the Constabulary 1998, for
example, the employment of civilian staff was thought to lead to an enhancement of
58 L. Drake, R. Simper International Review of Law and Economics 20 2000 53–73
“efficiency and effectiveness,” and the report revealed that civilian staff represented approx- imately 30 of total staff employed in the service in 1995–1996. Furthermore, the report
argues that “the classification of roles into policecivilian was in itself a redundant concept. Instead, it would be more appropriate to shift the focus to the actual cost of delivering a
service function. . .” HMIC, 1998, p. 55, paragraph 2.48. We believe, therefore, that a total labor cost variable should be utilized as an input, as many of the functions once wholly
undertaken by the police are now beginning to be undertaken by civilian staff.
The second input is premises-related expenses, which is the sum of all premises expenses and covers the general daily running costs including repair and maintenance. The third input
is transport-related expenses, which includes the running costs and repairs of police vehicles. Finally, the fourth input is capital and other costs. This latter variable includes capital-
financing costs and all those costs associated with equipment bought for internal use such as information technology, communications, and furniture, and also includes contracted-in and
contracted-out services. This variable has been noted as one that could lead to greater pressure on future capital expenditure due to the need to update information technology
facilities so that police forces have the latest equipment. In total, the average annual per capita expenditure of all forces in England and Wales on capital equipment has increased
from £67 in 1987–1988 to £123 in 1995–1996 HMIC, 1998.
A major problem inherent in measuring the efficiency of the police service is how to quantify the role of the police in society. There have been many different measurable outputs
that have been advanced as useful in compiling efficiency rankings. The first relate to surveys, where some authors have argued that surveys on the evaluation of police perfor-
mance “provide more easily quantified measures that dominate HMIC requirements and that. . .can lead to improvements in policing” Redshaw et al., 1997, p. 284.
It also has been argued, however, that it would be incorrect to survey the public about police service actions as this would introduce bias when using qualitative judgments on how
well the police service operates. For example, Shaw Williamson 1972 argued that young people and the working class rated the service lower than did older people and the middle
classes. Recently, Waddington Braddock 1991 found that white and Asian youths had mixed views of how the police operate, whether as “guardians” or “bullies,” but that black
youths tended “to favour the ‘bullies’ perception” p. 39. The authors concluded that “what distinguishes the races is not the absence of some whites and Asians who regard the police
as ‘bullies,’ but the virtual absence amongst their black counterparts of any conception of police as ‘guardians’” p. 39. These problems and socioeconomic stereotypes imply that
surveys could lead to a misinterpretation by the public of police functions.
It is for the above reasons that in addressing the issue of the use of survey data as possible performance indicators of police functions, the HMIC 1998 report “What Price Policing?”
concluded that “surveys are an imperfect measure and are affected by sample size, survey methodology and the nature of the population targeted” p. 85, paragraph 2.167. Skogan
1996 also argued that local surveys were fraught with difficulties because there are inter-area differences. In a Greater Manchester police survey across 13 districts, for example,
Skogan found “that the percentage of residents rating ‘burglary and theft’ the ‘single most serious problem’ in their area ranged from 2 to 22. The range for ‘street crime’ was from
59 L. Drake, R. Simper International Review of Law and Economics 20 2000 53–73
less than 1 to 22, car crime 13 to 28, and ‘young people hangingdrilling around’ from 5 to 24” p. 427.
In addition, a study by Redshaw et al. 1997 surveyed police officers, neighborhood watch coordinators, and members of the public and found that when asked to rank 37 jobs
that the police are asked to perform, they responded by ranking the top three as 1 respond immediately to emergencies, 2 detect and arrest offenders, and 3 investigate crime, all three
of which relate to the classification of a reactive police force variable. However, the authors note that “even where activities appear to have no immediate ‘crime control’ payoffs, there
is widespread acceptance that the British tradition of local, community-based, service- oriented, policing needs to be preserved” p. 300. It is hoped that in future research we will
be able to include in our model a variable that can proxy this all-important function of policing.
1
For the above reasons, and because of the lack of quantifiable data on other police functions, we use traditional outputs associated with responsereactive policing.
The responsereactive methodology of measuring policing can be found in a number of studies, including Todd Ramanathan 1994 and Byrne et al. 1996, who argue that even
though half of the police’s community work cannot be modeled, a production function can still be estimated. They break down police activities into crime prevention “where crime is
contemplated but not committed,” and crime repression, where the “crime has occurred,” and they use an argument from Schmidt Witte 1984 that any criminal is likely to assess the
probability of getting caught after committing a crime. Todd Ramanathan 1994 also state that outputs should be a measure of activity, such as the number of arrests made, and that
“employee allocations are explained marginally better by background demand for services, . . .” p. 131.
2
Hence, the probability of arrest is linked to the number of arrests in a police force and, in particular, to the number of convictions. For this reason we feel that the clear-up
rate used in this study is a good proxy for the preventive methods used by the police. We also note the criticisms of Walker 1992 in using clear-up rates as an output variable
and have, therefore, split our sample police forces into Metropolitan English, Welsh, and the Metropolitan and London police forces, and into four size groupings.
3
This will allow comparisons of forces that are closely linked by geographic circumstance and economic size,
1
Jackson 1992 found, using data from the United States, that a sizeable proportion of the cost of policing could be attributed to other factors, such as the decline in the demographic and socioeconomic bases of many
cities. Most importantly, these factors, even when held constant, still led to increases in fiscal expenditure as the “police are called upon to manage the social threats that rise from the ashes of social decay” p. 202.
2
O’Brien 1996 has argued that there is some level of police discretion in reporting or recording criminal incidences. Hence, instead of using recorded crime statistics for a variety of crimes, it would be better to consider
serious crimes such as murder, where there is evidence a body and with which, therefore, the assessment of police productivity can be better assessed. This methodology is not used in our estimation because it would
exclude a considerable number of other crimes, which constitute a higher proportion of crime in the United Kingdom than in the United States, as represented by the study of O’Brien.
3
Walker 1992 believes that clear-up rates can be misleading and forcibly argues that they “should not be commended as performance indicators by which to judge the policing service delivered to the public. Compar-
isons between forces in these rates are invidious, and they may lead to inefficient and even possibly corrupt practices” p. 305.
60 L. Drake, R. Simper International Review of Law and Economics 20 2000 53–73
and will mitigate any possible bias in our analysis of police forces and the results presented in Section 4.
The second output variable is the total number of traffic offenses that the police and contracted civilian staff such as traffic wardens deal with in a year, which includes
prosecutions, the number of written warnings, and fixed-penalty fines. This is an important variable as it measures the effect on policing of the 6 increase in registered vehicles from
21.6 million in 1988 to 22.9 million in 1995–1996 and the associated increased traffic problems encountered by the police. Furthermore, in line with the responsereactive meth-
odology it would be expected that increases in the number of recorded traffic offenses would, ceteris paribus, tend to reduce the per capita number of traffic offenses.
In recent years, the government has implemented a strict drunk-driving campaign, which can take up police time with respect to performing breathalyzer test on drivers. In fact, there
has been a 76 increase in breathalyzer tests since 1988, and the 781,100 tests carried out by police in 1996 –1997 is the largest number of tests since breathalyzer tests were intro-
duced in 1967 source: Home Office. We would expect that, as more people have breatha- lyzer tests administered to them, serious road accidents would be likely to drop, thereby
freeing up more police time for other activities. As mentioned above, we would also expect that increased administration of breathalyzer tests would act as a deterrent to drunk driving
and, hence, should, ceteris paribus, ultimately reduce the level of per capita drunk-driving offenses. Following the methodology of Byrne et al. 1996, this action can be classified as
a reactive approach to reducing car accidents, and so, the total number of breathalyzer tests constitutes our final output variable. The next section discusses the results from the DEA and
