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
MDA using the methodology outlined above.
3. DEA results
The DEA results for OE, PTE, and SE for the English and Welsh police forces are detailed in Tables 1, 2, and 3. The corresponding results for the London and Metropolitan police
forces are given in Tables 4, 5, and 6. It is important to note, however, that all the efficiency scores were derived by contrasting each police force with all its peers, although we elected
to summarize the results separately for the English, Welsh, and Metropolitan police forces. As can be seen from the tables, we produce DEA relative efficiency scores for each year from
1992–1993 to 1996 –1997 and also provide details of the mean efficiency scores for each police force over these years.
With respect to the DEA efficiency results, the ratios discussed previously typically produce efficiency scores of unity for efficient DMUs and less than unity for inefficient units.
We choose to use a score of 100 for efficient units, however, as this permits a ready interpretation of the degree of inefficiency in percentage terms. In Table 1, for example,
Surrey appears to have the least efficient force with an average OE score of 62.39 over the 5-year period and with individual year scores ranging from 43.12 in 1992–1993 to 81.43 in
1993–1994. The interpretation of these results is that, on average, the Surrey force is around 38 less efficient than its efficient reference set forces those forces that form the relevant
frontier and have scores of 100 in terms of translating its available resources into the
61 L. Drake, R. Simper International Review of Law and Economics 20 2000 53–73
specified outputs. Furthermore, in 1992–1993 this relative degree of inefficiency was as high as 57. If we analyze the PTE and SE results for Surrey, we can gain some insight into the
source of this level of inefficiency. The mean PTE score is 69.34, for example, while the mean SE score is 89.27. This suggests that the bulk of the inefficiency is not caused by a
failure to operate under constant returns to scale. In fact, the SE score in most years is over 90, suggesting that the Surrey force is not too far removed from the constant returns region
Table 1 DEA of English and Welsh police forces OE results
a
1992–1993 1993–1994
1994–1995 1995–1996
1996–1997 Mean
Non-metropolitan England Avon and
Somerset 93.46
95.31 77.45
81.95 83.83
86.40 Bedfordshire
100 80.58
88.12 82.04
100 90.15
Cambridgeshire 100
100 100
90.26 96.07
97.27 Cheshire
78.81 76.35
69.59 83.88
81.18 77.96
Cleveland 100
100 100
100 100
100 Cumbria
88.97 86.7
79.43 95.76
85.71 87.31
Derbyshire 85.94
100 95.61
96.85 100
95.68 Devon and
Cornwall 89.65
78.89 91.9
96.65 93.53
90.12 Dorset
100 100
100 100
100 100
Durham 64.08
84.59 82.05
77.07 60.85
73.73 Essex
87.21 88.02
NA
b
NA 81.15
85.46 Gloucestershire
100 91.41
91.06 98.42
100 96.18
Hampshire 87.54
89.65 86.38
100 100
92.71 Hertfordshire
98.54 88.37
80.40 82.68
88.55 87.71
Humberside 60.39
64.56 72.02
90.82 78.14
73.19 Kent
74.75 80.61
79.39 77.92
75.81 77.70
Lancashire 66.91
82.77 73.89
87.12 100
82.14 Leicestershire
100 100
100 100
100 100
Lincolnshire 77.48
100 NA
100 100
94.37 Norfolk
93.34 77.47
78.09 74.47
87.65 82.0
Northamptonshire 100
100 100
100 98.98
99.80 North Yorkshire
71.15 78.93
70.82 69.79
75.37 73.21
Nottinghamshire 68.79
100 100
100 100
93.76 Staffordshire
87.33 92.83
83.33 93.62
100 91.42
Suffolk 79.08
80.33 72.90
100 85.79
83.62 Surrey
43.12 81.43
62.15 65.36
59.89 62.39
Sussex 94.69
93.93 79.14
87.69 96.01
90.29 Thames Valley
100 100
100 87.15
84.98 94.43
Warwickshire 76.17
77.17 83.28
97.49 93.94
85.61 West Mercia
83.13 86.72
81.93 83.31
78.66 82.75
Wiltshire 78.85
87.59 75.25
98.41 79.12
83.84 Wales
Dyfed-Powys 75.99
82.45 76.10
83.66 87.81
81.20 Gwent
72.11 100
100 100
100 94.42
North Wales 86.80
97.14 100
81.69 83.41
89.81 South Wales
92.70 100
100 100
100 98.54
a
Data for the Essex 1994 –1995 and 1995–1996, and Lincolnshire 1994 –1995 police forces were unavail- able.
b
NA, not available. 62
L. Drake, R. Simper International Review of Law and Economics 20 2000 53–73
of operation. The mean PTE score of 69.34, however, suggests that the main factor behind the observed low overall efficiency levels is a failure to utilize resources effectively.
Specifically, the mean figure of 69.34 suggests that the Surrey force should be able to reduce their use of resources by around 31, on average, across the range of inputs without
adversely affecting the capacity of the force to deliver the observed outputs. It is possible to make this type of assertion because the DEA results tell us that, in comparison with the
Table 2 DEA of English and Welsh police forces PTE results
a
1992–1993 1993–1994
1994–1995 1995–1996
1996–1997 Mean
Non-metropolitan England Avon and
Somerset 100
100 82.73
83.03 85.00
90.15 Bedfordshire
100 95.19
100 93.56
100 97.75
Cambridgeshire 100
100 100
96.56 100
99.31 Cheshire
81.61 77.11
69.88 84.72
84.49 79.56
Cleveland 100
100 100
100 100
100 Cumbria
98.59 97.15
94.60 100
100 98.07
Derbyshire 94.58
100 97.58
100 100
98.43 Devon and
Cornwall 96.78
87.54 100
98.98 94.59
95.58 Dorset
100 100
100 100
100 100
Durham 88.94
84.59 82.25
78.41 78.07
82.45 Essex
89.42 90.68
NA
b
NA 81.48
87.19 Gloucestershire
100 100
100 100
100 100
Hampshire 97.24
96.77 100
100 100
98.80 Hertfordshire
99.97 88.81
81.96 83.57
88.87 88.64
Humberside 61.92
69.02 72.19
92.61 78.60
74.87 Kent
79.45 80.66
83.78 89.00
94.03 85.38
Lancashire 75.00
82.79 76.69
91.72 100
85.24 Leicestershire
100 100
100 100
100 100
Lincolnshire 88.72
100 NA
100 100
97.18 Norfolk
96.34 82.61
80.58 77.52
88.81 85.17
Northamptonshire 100
100 100
100 99.06
99.81 North Yorkshire
80.21 83.48
80.15 77.90
83.65 81.08
Nottinghamshire 69.23
100 100
100 100
93.85 Staffordshire
95.90 92.89
83.34 94.15
100 93.26
Suffolk 90.16
92.66 91.48
100 100
94.86 Surrey
61.86 83.46
66.77 68.92
65.68 69.34
Sussex 100
100 86.09
91.17 96.23
94.70 Thames Valley
100 100
100 87.99
91.61 95.92
Warwickshire 94.40
98.71 100
100 100
98.62 West Mercia
84.00 88.15
81.99 83.40
80.18 83.54
Wiltshire 90.55
97.71 91.19
100 100
95.89 Wales
Dyfed-Powys 100
100 100
100 100
100 Gwent
100 100
100 100
100 100
North Wales 90.27
98.04 100
89.34 88.57
93.24 South Wales
100 100
100 100
100 100
a
Data for the Essex 1994 –1995 and 1995–1996, and Lincolnshire 1994 –1995 police forces were unavail- able.
b
NA, not available. 63
L. Drake, R. Simper International Review of Law and Economics 20 2000 53–73
Surrey force, other forces with similar input and output configurations are using, on average, 31 fewer inputs to deliver similar output levels.
If we turn now to Tables 4, 5 and 6, we see that the observed OE levels of the Metropolitan police force require a different interpretation. Table 4 indicates that the Metropolitan force
has a mean OE score of only 57.52, which is the lowest of any force in the sample. With the exception of 1993–1994, the figures range from 30.56 in 1992–1993 to 62.06 in 1994 –1995.
Table 3 DEA of English and Welsh police forces SE results
a
1992–1993 1993–1994
1994–1995 1995–1996
1996–1997 Mean
Non-metropolitan England Avon and
Somerset 93.46
95.31 93.62
98.69 98.63
95.94 Bedfordshire
100 84.65
88.12 87.69
100 92.09
Cambridgeshire 100
100 100
93.47 96.07
97.91 Cheshire
96.57 99.01
99.59 99.01
96.08 98.051
Cleveland 100
100 100
100 100
100 Cumbria
90.24 89.24
83.96 95.76
85.71 88.98
Derbyshire 90.86
100 97.98
96.85 100
97.14 Devon and
Cornwall 92.63
90.12 91.90
97.64 98.88
94.24 Dorset
100 100
100 100
100 100
Durham 72.05
100 99.76
98.29 77.94
89.61 Essex
97.53 97.07
NA
b
NA 99.59
98.06 Gloucestershire
100 91.41
91.06 98.42
100 96.18
Hampshire 90.02
92.64 86.38
100 100
93.81 Hertfordshire
98.57 99.50
98.10 98.94
99.64 98.95
Humberside 97.53
93.54 99.76
98.07 99.41
97.66 Kent
94.08 99.94
94.76 87.55
80.62 91.39
Lancashire 89.21
99.98 96.35
94.98 100
96.10 Leicestershire
100 100
100 100
100 100
Lincolnshire 87.33
100 NA
100 100
96.83 Norfolk
96.89 93.78
96.91 96.07
98.69 96.47
Northamptonshire 100
100 100
100 99.92
99.98 North Yorkshire
88.70 94.55
88.36 89.58
90.10 90.26
Nottinghamshire 99.36
100 100
100 100
99.87 Staffordshire
91.06 99.94
99.99 99.44
100 98.08
Suffolk 87.71
86.69 79.69
100 85.79
87.98 Surrey
69.71 97.57
93.08 94.83
91.181 89.27
Sussex 94.69
93.93 91.93
96.18 99.771
95.30 Thames Valley
100 100
100 99.05
92.77 98.36
Warwickshire 80.689
78.18 83.28
97.49 93.94
86.72 West Mercia
98.96 98.38
99.93 99.89
98.10 99.05
Wiltshire 87.079
89.64 82.52
98.41 79.12
87.35 Wales
Dyfed-Powys 75.99
82.45 76.10
83.66 87.81
81.20 Gwent
72.11 100
100 100
100 94.42
North Wales 96.156
99.08 100
91.41 94.17
96.17 South Wales
92.70 100
100 100
100 98.54
a
Data for the Essex 1994 –1995 and 1995–1996, and Lincolnshire 1994 –1995 police forces were unavail- able.
b
NA, not available. 64
L. Drake, R. Simper International Review of Law and Economics 20 2000 53–73
It would be inappropriate to label the Metropolitan as a highly inefficient police force, however, as Table 5 indicates that the corresponding PTE scores are 100 in each year of the
study. This suggests that, given the scale of the Metropolitan’s operations, it is a highly efficient police force with no obvious inefficiencies in resource utilization. In contrast, Table
6 reveals an average SE score of only 57.52, confirming that all of the observed OE is associated with scale effects. Given that the Metropolitan is the largest force in the country,
this result strongly suggests that there are significant diseconomies of scale at work with respect to large police force operations. As in other large organizations, this is probably
attributable to the extra bureaucracy and layers of management structure that tend to accompany large scale operations.
Further statistical examination of the relative efficiency results is undertaken in Section 4, but it is interesting to note from Table 7 that the mean SE levels for the largest and smallest
police forces 86.99 and 85.85, respectively are considerably lower than those of the intermediate-size forces, staff group 2 95.11 and staff group 3 96.23. This is not
surprising because we would expect that a large proportion of staff group 1 forces would exhibit increasing returns to scale, while the majority of staff group 4 forces would exhibit
Table 4 DEA of London and Metropolitan police force OE results
1992–1993 1993–1994
1994–1995 1995–1996
1996–1997 Mean
Metropolitan Greater
Manchester 90.32
100 100
100 100
98.06 Merseyside
69.33 66.75
60.87 76.01
72.64 69.12
South Yorkshire 74.61
76.68 69.66
72.99 78.70
74.53 Northumbria
73.41 60.96
69.76 73.21
76.05 70.68
West Midlands 18.23
74.54 68.68
71.58 74.28
61.46 West Yorkshire
65.49 69.65
70.99 74.51
77.08 71.54
London City
100 100
75.00 73.21
71.22 83.89
Metropolitan 30.56
99.35 62.06
42.24 53.41
57.52
Table 5 DEA of London and Metropolitan police force PTE results
1992–1993 1993–1994
1994–1995 1995–1996
1996–1997 Mean
Metropolitan Greater
Manchester 100
100 100
100 100
100 Merseyside
81.64 71.55
87.74 92.00
74.50 81.49
South Yorkshire 81.21
82.48 74.72
76.85 79.16
78.88 Northumbria
80.65 61.07
80.79 82.74
78.09 76.67
West Midlands 18.82
74.54 82.05
100 100
75.08 West Yorkshire
78.73 69.73
77.40 100
100 85.17
London City
100 100
100 100
100 100
Metropolitan 100
100 100
100 100
100 65
L. Drake, R. Simper International Review of Law and Economics 20 2000 53–73
diseconomies of scale. Hence, both sets of police forces would have SE scores well below 1. In contrast, staff groups 2 and 3 would be expected to be operating much closer to, if not
at, the constant-returns region of the production relationship and would, therefore, have SE scores at, or closer to, unity. The fact that staff group 3 exhibits the highest mean SE score
96.23, with by far the lowest standard deviation 4.04, strongly suggests that police forces in this size band and staff group are close to the optimum in terms of scale efficiency.
Clearly, this type of information could prove highly informative in the context of any proposed restructuring of police forces such as the merging of forces or the redrawing of
police force boundaries, etc.
Interestingly, Table 7 indicates that the smallest forces those in staff group 1 appear to be the most technically efficient, with a mean PTE score of 99.64 and a standard deviation
of only 1.30. Furthermore, the mean PTE scores appear to decline with size as the scores for
Table 6 DEA of London and Metropolitan police forces SE results
1992–1993 1993–1994
1994–1995 1995–1996
1996–1997 Mean
Metropolitan Greater
Manchester 90.32
100 100
100 100
98.06 Merseyside
84.92 93.29
69.38 82.62
97.50 85.54
South Yorkshire 91.87
92.97 93.23
94.98 99.42
94.49 Northumbria
91.02 99.82
86.35 88.48
97.39 92.61
West Midlands 96.86
100 83.71
71.58 74.28
85.29 West Yorkshire
83.18 99.89
91.72 74.51
77.08 85.28
London City
100 100
75 73.21
71.22 83.89
Metropolitan 30.56
99.35 62.06
42.24 53.41
57.52
Table 7 Group descriptive statistics and the test for equality of group means between different staff groups,
1992–1993 to 1996 –1997 Dependent variable
Independent variables Sample
size SE
PTE OE
Group means Staff group 1
85.85 99.64
85.56 19
Staff group 2 95.11
91.73 87.43
101 Staff group 3
96.23 90.57
87.17 53
Staff group 4 86.99
88.36 76.13
39 Total
93.07 91.52
85.12 212
Standard deviations
Staff group 1 11.02
1.30 11.23
19 Staff group 2
6.61 10.44
12.73 101
Staff group 3 4.04
9.72 10.24
53 Staff group 4
16.87 15.49
18.89 39
Total 10.12
11.24 14.01
212 66
L. Drake, R. Simper International Review of Law and Economics 20 2000 53–73
staff groups 2, 3, and 4 are 91.73, 90.57, and 88.36, respectively. This suggests that, leaving aside the issue of the scale of operations, effective resource usage and cost control are easier
to accomplish in smaller police forces than in larger ones. Hence, we appear to have an interesting dichotomy in the sense that levels of PTE appear
to decline with police force size, but there is clear evidence of an inverted U-shaped relationship with respect to scale efficiency. The latter is suggestive of the classic U-shaped
average-cost curve that is typically attributed to increasing, and eventually decreasing, returns to scale. Indeed, it is interesting to note that the mean SE scores support the notion
of a “saucer-shaped” average cost curve for policing in the sense that there appear to be substantial increasing and decreasing returns to scale in evidence at the extreme ends of the
size spectrum, but a relatively large region of constant returns or modest economies diseconomies of scale at intermediate size ranges. Although this is a very common finding
in economic studies of industrial production, it is a particularly interesting result to find that the same economic production relationship appears to hold good in public sector services
such as policing.
Clearly, the apparent tradeoff between PTE and SE presents particular problems in the context of decisions over police force management and structure, and it warrants further
research and investigation. A simple way of characterizing the problem is to think of the SE results and the corresponding notional average cost curve as revealing the minimum level
of average costs that could be attained for any given scale of output, provided that all resources are used effectively. Furthermore, this information reveals the relationship between
size and efficiency, or size and unit costs. Economists frequently refer to this as revealing the minimum efficient scale of operation, i.e., the minimum level of output that exhausts all
economies of scale. Our results suggest that this would be at staff group 2 or 3.
As Liebestein 1966 pointed out, however, these notional minimum costs at each given scale of operation are not always realized due to various factors such as managerial
inefficiency, for example. He referred to this failure to realize the minimum possible unit costs as “X-inefficiency” and the DEA analog to this is our PTE results, which show whether
resources are being used at their maximum efficiency for any given scale of output. Clearly, a failure to utilize resources at their maximum efficiency would result in unit costs exceeding
their potential minimum. Our finding that PTE declines with the scale of output has powerful implications because it suggests that X-inefficiency increases with size and, hence, that the
wedge between minimum and actual unit costs will be increasing, while at the same time minimum unit costs are actually declining with size up to a point.
Our results suggest, therefore, that to enhance the overall efficiency of the English and Welsh police forces two approaches are necessary. First, consideration must be given to
some structural reorganization such that individual forces are operating closer to the mini- mum efficient scale, which appears to be staff groups 2 to 3. Second, the apparent problem
of worsening X-inefficiencies must be investigated and tackled in larger police forces. While DEA can provide valuable insights into the reductions in inputs necessary to achieve PTE for
given output levels using comparisons with police forces that have efficient reference sets, it seems likely that a review of management and staffing structures in the larger police forces
may be required. It is interesting to note in this respect that only three police forces, Cleveland, Dorset, and Leicestershire, are consistently efficient in terms of both SE and PTE
67 L. Drake, R. Simper International Review of Law and Economics 20 2000 53–73
and, necessarily, OE. Hence, these forces will tend to form part of the efficient reference set of police forces for a large number of inefficient forces, and a detailed comparison of
these “best-practice” forces with the less efficient units could provide very useful information in any reorganizationrestructuring process.
So far we have not addressed the issue of the statistical significance of the differences in our efficiency scores across staff size groups. We rectify this in the next section using
analysis of variance ANOVA and discriminant analysis techniques.
4. MDA results
