1. Scale Economies & Police Department Consolidation: Evidence From Los Angeles By Miles Finney Sara Sutachan

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

3. Intergovernmental Arrangement Facts Degree of Intergovernmental Sharing of Police Services is High in Los Angeles County: –45% of LA jurisdictions provide police services through intergovernmental agreements –Over 90% of incorporated (since 1954) Los Angeles jurisdictions engage in intergovernmental arrangements (39 out of 43)

4. Another Question Raised Would it be economically efficient for suburban police jurisdictions to consolidate or to engage in intergovernmental arrangements with the Los Angeles County Sheriff’s Dept?

5. Variables Used in Analysis 2 Separate Output Measures –Intermediate Good of Arrests –The Inverse of the Crime Rate (Safety) 5 Input Measures –Price of Uniformed Police Labor –Price of Civilian Police Labor –Measure of Capital –Inverse of the Poverty Rate –% of Owner Occupied Homes Socioeconomic Factors

6. Variable Data Sources Safety (inverse of Crime Rate=FBI major crime index/jurisdiction population) and Arrests – California Department of Justice & California DOF Average Salaries for Police officers and civilians – US Dept of Commerce Capital – price of the average police automobile: Chevrolet Caprice Expenditures by Department – California Office of State Controller Number of Police and civilian personnel by dept – California Dept of Justice

7. Expenditure & Salary Data In Real Terms (1979 base Year)

8. Economic Model Used in Analysis Zellner’s Seemingly Unrelated Regression (SUR) –Utilizes information from the correlation between equation 1 and the independent input cost share in order to increase estimation efficiency. F-statistics are analyzed in lieu of R² in this analysis

9. Translog Cost Function Equation 1 Where: TC= Total Cost Q = Output W 1 = Price of Police Output S m = Unpriced Socioeconomic input m β= Parameter Estimates

10. Translog Cost Function - Properties Must be homogeneous of degree one in input prices Symmetric second order cross effects Allows for fairly complete characterization of substitution patterns among inputs – data need not fit pre-specified pattern Format incorporates input prices in a flexible way in order to control for input prices. Thus making returns to scale more reliable

11. Returns to Scale - Definition Economies of scale or increasing returns to scale - output increases more than proportionately to inputs Constant returns to scale - output increases in the same proportion as inputs Diseconomies of scale or decreasing returns to scale - output increases less proportionately to inputs.

12. Scale Economies in Police Departments Economies of Scale or Increasing Returns: –Provide incentives for consolidation of police services and would be justified by enhancing efficiency Decreasing Returns: –Consolidation of police departments would not be efficient

13. Returns to Scale Measurement of Returns to Scale is 1 minus output elasticity: 1-∂ln(TC)/∂ln(Q) Output Elasticity is calculated through equation 2.

14. Output Elasticity (Equation 2) Equation 2 = Output Elasticity Measurements of Returns to Scale = 1-Equation 2

15. Results

16. Translog Cost Function Parameter Estimates Model 1 – Output is the Inverse of the Crime Rate (Safety) Model 2 – Output is Arrests Standard Errors in parenthesis *significant at the 5% level **significant at the 10% level

17. Study Findings – w/r/t Safety Parameter Estimates indicate that the average department’s costs would rise by 11.3% if safety was increased by 10%* LA suburban jurisdictions produce safety with an average -0.125 returns to scale* * 5% Significance Level

18. Study Findings – w/r/t Arrests Parameter Estimates indicate that the average department’s costs would rise by 26.6% if arrests were increased by 10%* LA suburban jurisdictions produce arrests with an average -1.65 returns to scale* * 5% Significance Level

19. SUR for both models 1 and 2 show highly significant F-Statistics The F-statistic of approximately 14.7 suggest that one would reject the null hypothesis that police outputs in suburban areas operate under increasing returns at any level of significance Results indicate police departments produce safety and arrests under decreasing returns Study Findings

20. Study Findings (cont’d) Per capita expenditure for the 14 sampled jurisdictions in 1992 was $177.36 If these jurisdictions consolidated: Per capita expenditures to produce the same # of arrests in the same time period would have been $472.78. For LA jurisdictions that contracted with the LA County Sheriff’s Dept, the per capita expenditures in the same year was $77.32 Cost Savings of Intergovernmental Arrangements nearly $400 per capita.

21. Conclusion Since the analysis infers that police services are operating under decreasing returns to scale, consolidation is therefore inefficient. Finney found that intergovernmental arrangements with the Los Angeles County Sheriff’s Department are economically efficient

22. Improvements to the Study? Study did not directly account for fixed costs such as computer equipment. –In analyzing a total cost function, not accounting for fixed costs could generate misleading results

23. Improvements to the Study? (cont’d) Small Sample: 14 jurisdictions over 4 years –Analyze surrounding suburban areas such as the San Bernardino/Riverside area –Analyze similar cities to Los Angeles, with same crime and population –Extend the time period analyzed. –Make some assumptions on the missing wage data instead of omitting

24. Improvements to the Study? (cont’d) Divergent definitions of police output Safety as an output definition –Finney states the input data “Safety” to be qualitative and elasticity output produced more of a “returns to quality” as opposed to a returns to scale figure. –Defining police output is challenging