Evaluating US state police performance using data envelopment analysis

Outline 2 Abstract Previous studies Objective Methodology Empirical application Conclusions

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

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

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

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.

Methodology(1/4) First Stage 7

Methodology(2/4) Second Stage-regression 8

Methodology(3/4) Third Stage 9 Forth Stage

Methodology(4/4) Fifth Stage 10 Sixth Stage

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. 11

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

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

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

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

Empirical application 16

Empirical application

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. 18

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

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