Scale Economies & Police Scale Economies & Police Department Consolidation: Department Consolidation:

Evidence From Los Angeles Evidence From Los Angeles

By Miles Finney By Miles Finney

Sara Sutachan Sara Sutachan

SummarySummaryAuthor: Miles Finney – CSLA ProfessorAuthor: Miles Finney – CSLA ProfessorTests for scale economies of a Tests for scale economies of a public good: police services.public good: police services.Methodology modeled after Gyimah-Brempong Methodology modeled after Gyimah-Brempong study of Florida police departmentsstudy of Florida police departmentsTranslog cost function is used to test for scale Translog cost function is used to test for scale relationship in police outputrelationship in police outputNull Hypothesis: Police output is produced under Null Hypothesis: Police output is produced under increasing returns.increasing returns.The main goal: to find that LA county consolidation The main goal: to find that LA county consolidation of police services is justified by efficiencyof police services is justified by efficiency

Intergovernmental Arrangement Intergovernmental Arrangement FactsFacts

Degree of Intergovernmental Sharing of Degree of Intergovernmental Sharing of Police Services is High in Los Angeles Police Services is High in Los Angeles County:County:– 45% of LA jurisdictions provide police 45% of LA jurisdictions provide police

services through intergovernmental services through intergovernmental agreementsagreements

– Over 90% of Over 90% of incorporatedincorporated (since 1954) Los (since 1954) Los Angeles jurisdictions engage in Angeles jurisdictions engage in intergovernmental arrangements (39 out of intergovernmental arrangements (39 out of 43)43)

Another Question RaisedAnother Question Raised

Would it be economically efficient for Would it be economically efficient for suburban police jurisdictions to suburban police jurisdictions to consolidateconsolidate or to engage in or to engage in intergovernmental arrangementsintergovernmental arrangements with the with the Los Angeles County Sheriff’s Dept?Los Angeles County Sheriff’s Dept?

Variables Used in AnalysisVariables Used in Analysis

2 Separate Output Measures2 Separate Output Measures– Intermediate Good of Arrests Intermediate Good of Arrests – The Inverse of the Crime Rate (Safety) The Inverse of the Crime Rate (Safety)

5 Input Measures5 Input Measures– Price of Uniformed Police LaborPrice of Uniformed Police Labor– Price of Civilian Police LaborPrice of Civilian Police Labor– Measure of CapitalMeasure of Capital– Inverse of the Poverty RateInverse of the Poverty Rate– % of Owner Occupied Homes% of Owner Occupied Homes

Socioeconomic

Factors

Variable Data SourcesVariable Data Sources

Safety (inverse of Crime Rate=FBI major crime Safety (inverse of Crime Rate=FBI major crime index/jurisdiction population) and Arrests – index/jurisdiction population) and Arrests – California Department of Justice & California DOFCalifornia Department of Justice & California DOFAverage Salaries for Police officers and civilians – Average Salaries for Police officers and civilians – US Dept of CommerceUS Dept of CommerceCapital – price of the average police automobile: Capital – price of the average police automobile: Chevrolet CapriceChevrolet CapriceExpenditures by Department – California Office of Expenditures by Department – California Office of State ControllerState ControllerNumber of Police and civilian personnel by dept – Number of Police and civilian personnel by dept – California Dept of JusticeCalifornia Dept of Justice

Expenditure & Salary DataExpenditure & Salary DataIn Real Terms (1979 base Year)In Real Terms (1979 base Year)

Variable Mean Standard Deviation

Police Expenditure 15350233 20972377Arrests 6356 9357Crime Rate 0.0658 0.0195Police Salary 50310 5608Civilian Salary 29655 5044Capital Price 15330 215Police Share 0.50 0.0972Civilian Share 0.12 0.0342Capital Share 0.38 0.0883Population 96474 98718Poverty Rate 0.1411 0.0634% Homeownership 0.4736 0.1148

Table 1Summary Statistics for Dependent and Independent Variables

Economic Model Used in Economic Model Used in AnalysisAnalysis

Zellner’s Seemingly Unrelated Regression Zellner’s Seemingly Unrelated Regression (SUR)(SUR)– Utilizes information from the correlation Utilizes information from the correlation

between equation 1 and the independent between equation 1 and the independent input cost share in order to increase input cost share in order to increase estimation efficiency.estimation efficiency.

F-statistics are analyzed in lieu of F-statistics are analyzed in lieu of RR² in ² in this analysisthis analysis

Translog Cost FunctionTranslog Cost FunctionEquation 1Equation 1

Where: Where: TC= Total CostTC= Total CostQ = OutputQ = OutputWW11 = Price of Police Output = Price of Police Output

SSmm = Unpriced Socioeconomic input = Unpriced Socioeconomic input mmββ= Parameter Estimates= Parameter Estimates

Translog Cost Function - Translog Cost Function - PropertiesProperties

Must be Must be homogeneous of degree onehomogeneous of degree one in input in input pricesprices

Symmetric second order cross effectsSymmetric second order cross effects

Allows for fairly complete characterization of Allows for fairly complete characterization of substitution patterns among inputs – data need substitution patterns among inputs – data need not fit pre-specified patternnot fit pre-specified pattern

Format incorporates input prices in a flexible Format incorporates input prices in a flexible way in order to control for input prices. Thus way in order to control for input prices. Thus making returns to scale more reliablemaking returns to scale more reliable

Returns to Scale - DefinitionReturns to Scale - Definition

Economies of scale or increasing returns Economies of scale or increasing returns to scale - output increases more than to scale - output increases more than proportionately to inputs proportionately to inputs

Constant returns to scale - output Constant returns to scale - output increases in the same proportion as inputs increases in the same proportion as inputs

Diseconomies of scale or decreasing Diseconomies of scale or decreasing returns to scale - output increases less returns to scale - output increases less proportionately to inputs. proportionately to inputs.

Scale Economies in Police Scale Economies in Police DepartmentsDepartments

Economies of Scale or Increasing Returns:Economies of Scale or Increasing Returns:– Provide incentives for consolidation of police Provide incentives for consolidation of police

services and would be justified by enhancing services and would be justified by enhancing efficiencyefficiency

Decreasing Returns:Decreasing Returns:– Consolidation of police departments would not Consolidation of police departments would not

be efficientbe efficient

Returns to ScaleReturns to Scale

Measurement of Returns to Scale is 1 Measurement of Returns to Scale is 1 minus minus output elasticityoutput elasticity::

1-1-∂∂ln(TC)/ln(TC)/∂∂ln(Q)ln(Q)Output ElasticityOutput Elasticity is calculated through is calculated through equation 2.equation 2.

Output Elasticity Output Elasticity (Equation 2)(Equation 2)

Equation 2 = Output ElasticityEquation 2 = Output Elasticity

Measurements of Returns to Scale = 1-Equation 2Measurements of Returns to Scale = 1-Equation 2

ResultsResults

Translog Cost Function Parameter EstimatesTranslog Cost Function Parameter Estimates

Model 1 – Model 1 – Output is the Output is the Inverse of Inverse of the Crime the Crime Rate (Safety)Rate (Safety)

Model 2 – Model 2 – Output is Output is ArrestsArrests

Standard Errors in Standard Errors in parenthesisparenthesis*significant at the *significant at the 5% level5% level**significant at the **significant at the 10% level10% level

Variable

Q 2.6599* (0.7590) 1.125* (0.4983)W1 -0.0203 (0.2870) 0.159 (0.2820)W2 0.0262 (0.1080) -0.033 (0.1175)W3 0.994* (0.3380) .874* (0.3403)W1W1 0.5102** (0.2900) 0.35 (0.2796)W1W2 -0.0011 (0.0210) -0.008 (0.0220)W1W3 -0.5091** (0.2910) -0.342 (0.2784)W2W2 0.0743 (0.1090) 0.126 (0.1168)W2W3 -0.0731 (0.1140) -0.118 (0.1186)W3W3 0.5823 (0.3460) 0.46 (0.3373)W1Q -0.1823* (0.0480) -.061* (0.0201)W2Q 0.0078 (0.0220) 0.004 (0.0103)W3Q 0.1744* (0.0580) .056* (0.0256)S1Q -0.6903* (0.2640) -.298** (0.0173)S2Q 0.6903* (0.2640) .298** (0.0173)W1S1 -0.00005 (0.0010) -0.00004 (0.0011)W1S2 0.00005 (0.0010) 0.00004 (0.0011)W2S1 0.000008 (0.0005) 0.000002 (0.0005)W2S2 -0.000008 (0.0005) -0.000002 (0.0005)W3S1 -0.0308 (0.1730) -0.3 (0.1917)W3S2 0.0308 (0.1730) 0.3 (0.1917)F - ValueF Prob-ValueN = 56

Table 2Translog Cost Function Parameter Estimates

Model 1 Model 2

14.69 14.700.0001 0.0001

Study Findings – w/r/t SafetyStudy Findings – w/r/t Safety

Parameter Estimates indicate that the Parameter Estimates indicate that the average department’s costs would rise by average department’s costs would rise by 11.3% if safety was increased by 10%*11.3% if safety was increased by 10%*

LA suburban jurisdictions produce LA suburban jurisdictions produce safetysafety with an average -0.125 returns to scale*with an average -0.125 returns to scale*

* 5% Significance Level* 5% Significance Level

Study Findings – w/r/t ArrestsStudy Findings – w/r/t Arrests

Parameter Estimates indicate that the Parameter Estimates indicate that the average department’s costs would rise by average department’s costs would rise by 26.6% if arrests were increased by 10%*26.6% if arrests were increased by 10%*

LA suburban jurisdictions produce LA suburban jurisdictions produce arrestsarrests with an average -1.65 returns to scale*with an average -1.65 returns to scale*

* 5% Significance Level* 5% Significance Level

SUR for both models 1 and 2 show highly SUR for both models 1 and 2 show highly significant F-Statisticssignificant F-Statistics

The F-statistic of approximately 14.7 suggest The F-statistic of approximately 14.7 suggest that one would that one would reject the null hypothesisreject the null hypothesis that that police outputs in suburban areas operate under police outputs in suburban areas operate under increasing returns at any level of significanceincreasing returns at any level of significance

Results indicate police departments produce Results indicate police departments produce safety and arrests under safety and arrests under decreasing returnsdecreasing returns

Study FindingsStudy Findings

Study Findings (cont’d)Study Findings (cont’d)

Per capita expenditure for the 14 sampled jurisdictions Per capita expenditure for the 14 sampled jurisdictions in 1992 was $177.36in 1992 was $177.36If these jurisdictions consolidated: Per capita If these jurisdictions consolidated: Per capita expenditures to produce the same # of arrests in the expenditures to produce the same # of arrests in the same time period would have been $472.78. same time period would have been $472.78. For LA jurisdictions that contracted with the LA County For LA jurisdictions that contracted with the LA County Sheriff’s Dept, the per capita expenditures in the same Sheriff’s Dept, the per capita expenditures in the same year was $77.32year was $77.32

Cost Savings of Intergovernmental Arrangements nearly Cost Savings of Intergovernmental Arrangements nearly $400 per capita.$400 per capita.

ConclusionConclusion

Since the analysis infers that police Since the analysis infers that police services are operating under decreasing services are operating under decreasing returns to scale, consolidation is therefore returns to scale, consolidation is therefore inefficient. inefficient.

Finney found that intergovernmental Finney found that intergovernmental arrangements with the Los Angeles arrangements with the Los Angeles County Sheriff’s Department are County Sheriff’s Department are economically efficienteconomically efficient

Improvements to the Study?Improvements to the Study?

Study did not directly account for fixed Study did not directly account for fixed costs such as computer equipment.costs such as computer equipment. – In analyzing a total cost function, not In analyzing a total cost function, not

accounting for fixed costs could generate accounting for fixed costs could generate misleading resultsmisleading results

Improvements to the Study? Improvements to the Study? (cont’d)(cont’d)

Small Sample: 14 jurisdictions Small Sample: 14 jurisdictions over 4 yearsover 4 years– Analyze surrounding suburban Analyze surrounding suburban

areas such as the San areas such as the San Bernardino/Riverside areaBernardino/Riverside area

– Analyze similar cities to Los Analyze similar cities to Los Angeles, with same crime and Angeles, with same crime and populationpopulation

– Extend the time period analyzed.Extend the time period analyzed.– Make some assumptions on the Make some assumptions on the

missing wage data instead of missing wage data instead of omittingomitting

Improvements to the Study? Improvements to the Study? (cont’d)(cont’d)

Divergent definitions of police Divergent definitions of police output output

Safety as an output definitionSafety as an output definition– Finney states the input data Finney states the input data

“Safety” to be qualitative and “Safety” to be qualitative and elasticity output produced more elasticity output produced more of a “returns to quality” as of a “returns to quality” as opposed to a returns to scale opposed to a returns to scale figure.figure.

– Defining police output is Defining police output is challengingchallenging