Abstract In this paper, we evaluate the efficiency of state
police services in the continental United States using a
multiple-stage data envelopment analysis model. Using multiple
inputs and multiple outputs to characterize police service
provision, technical and scale efficiency are calculated for the 49
continental states. Given the complex nature of service provision,
we allow for environmental factors of production and control for
these non- discretionary inputs. Our results indicate that most
states are technically efficient, but nearly half are operating at
less than optimal scale size. 3
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Previous studies(1/2) AuthorInputOutput Drake & Simper
(2005)Burglaries, vehicle crimes and robberies, total budget
Civilian days lost, aggregate offenses cleared Diezticio &
Mancebon (2000)Total man power, vehicles, the inverse of population
Clear up rate, property crime offenses Carrington et al.
(1997)Sworn officers, civilian employees, police cars Offences,
arrests, summons, automobile accidents, vehicle travel distance Sun
(2002)The same as above Gyimah-Brempong (1987)Sworn police wages,
civilian police wages,, police fleet value Index of personal
crimes, robbery, burglary, larceny, motor vehicle theft, population
4
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Previous studies(2/2) AuthorInputOutput Gyapong & Gyimah-
Brempong (1988) The same as above + Physical units of inputs
(rather than costs) The same as above Nyhan and Martin (1999)Total
crimes, response time, crime clear up rate Total department cost,
total staff 5
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Objective 6 We assess police efficiency of all US states using
an expanded set of DMUs and a broader set of inputs and outputs,
with improved three-stage DEA techniques to account for multiple
environmental variables.
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Methodology(1/4) First Stage 7
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Methodology(2/4) Second Stage-regression 8
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Methodology(3/4) Third Stage 9 Forth Stage
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Methodology(4/4) Fifth Stage 10 Sixth Stage
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Empirical application Collect data from 1. US Department of
Justice 2. Bureau of Justice Statistics 3. US Federal Bureau of
Investigation Uniform Crime Reporting 4. US Bureau of Census DMUs
are selected from 49 state police force from year 2000 in US.
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Empirical application Output for crime type Murders Other
violent crimes Total property crimes Discretionary input The number
of sworn officers The number of other employees The number of
vehicles 12
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Empirical application Environmental factor The percent of
single mother The poverty rate The percent of individuals in the
labor force Population Population per square mile 13
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Empirical application 1. Use the outputs and discretionary
input in first-stage. 2. To decomposed the effect, use second-stage
where the index from first-stage regressed on the environmental
variables. 3. Calculate CI(cost index), the overall cost of
providing police services. 4. Then solving fifth-stage, allows
calculate SE(scale efficiency). 14
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Empirical application An improved policing environment for more
dense populations. High correlation (0.59) between the poverty rate
and the percent of single mothers. The percent of single mothers is
positively correlated with the population and the population per
square mile. 15 In particularRegression Result Single
motherNegative coefficient PopulationNegative coefficient
PovertyNegative coefficient Positive coefficient Population/mi le
AmbiguousPositive coefficient Labor forcePositive coefficient
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Empirical application 16
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Empirical application 123 17
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Empirical application -Efficient states California, Florida,
Illinois, Michigan, New York, Ohio, Pennsylvania, and Texas have
the largest cost indices and, with the exception of Texas, are
technically efficient. Illinois and Texas are observed operating on
the increasing returns to scale portion of the production frontier.
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Empirical application -Inefficient states Arizona, Arkansas,
Colorado, Delaware, Kansas, Kentucky, Louisiana, Maryland,
Minnesota, Missouri, Nebraska, New Mexico, Oklahoma, Tennessee, and
Texas from a diverse cross section of population and landmass size
and geographic regions, but tend to be of larger landmass with
fewer major cities. Arizona and Kentucky are operating at
increasing returns of scale. 19
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Conclusions Most of the states are technically efficient and
that the location of the frontier depends crucially on
environmental factors beyond the control of the states. To
inefficient SKUs There are opportunities for cost reduction via
contraction of observed input usage. To Arizona and Kentucky There
are opportunities for lowering average costs by changing the level
of inputs. 20
