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Slide 1
Estimating Marginal Costs for
Cost-Benefit Analysis in Criminal Justice
February 23, 2011
Christian Henrichson, Senior Policy Analyst, Cost-Benefit Analysis Unit
Valerie Levshin, Policy Analyst, Cost-Benefit Analysis Unit
Slide 2
Estimating Marginal Costs for
Cost-Benefit Analysis in Criminal Justice
Valerie Levshin
Christian Henrichson
Slide 3
The Cost-Benefit Knowledge Bank for Criminal Justice (CBKB) is a
project of the Vera Institute of Justice funded by the U.S.
Department of Justice’s Bureau of Justice Assistance.
• Website (cbkb.org)
• CBA Toolkit
• Snapshots of CBA Literature
• Podcasts, Videocasts, and Webinars
• Roundtable Discussions
• Community of Practice
Slide 4
Today’s Agenda
Introduction and Housekeeping 5 minutes
Overview of Cost-Benefit Analysis 10 minutes
Understanding Marginal Costs 15 minutes
Estimating Marginal Costs 25 minutes
Wrap Up 5 minutes
Slide 5
Housekeeping items
Questions
Use the chat feature to send us your
questions at any time during the webinar.
We will address your questions after
each section of the presentation.
Slide 6
Housekeeping items
Webinar support and troubleshooting
Call: (800) 843-9166
Email: [email protected]
Handouts
This webinar is being recorded
The recording and all materials will be posted to cbkb.org
Slide 7
Preview of today’s webinar
You will learn:
• The difference between marginal and average costs.
• An approach to reading CBA reports.
• Questions to ask while reading CBA reports.
Slide 8
Overview of
Cost-Benefit Analysis in
Justice Policy
Slide 9
What is Cost-Benefit Analysis (CBA)?
• A tool to assess the pros and cons of policies and programs
• A method for finding out what will achieve the greatest net benefit to society
• An approach to policymaking
Slide 10
Added Value of CBA
• Monetizes costs and benefits
• Assesses the economic impact over the long term horizon
• Future costs and benefits are discounted to the present
• Includes both tangible and intangible costs/benefits
Slide 11
The CBA Process
• Determine the Impact of the initiative
• Determine whose perspectives matter
• Measure costs and benefits (outcomes)
• Compare costs and benefits
• Test results
Slide 12
Measuring Costs and Benefits
• Measure costs
• quantity × unit cost
• e.g.: number of program participants × cost per participant
• Measure benefits (in dollars)
• quantity × unit cost
• e.g.: number of people who will be incarcerated × cost of incarcerating one person
Slide 13
Measuring Costs and Benefits
• Measure costs
• quantity × unit cost
• e.g.: number of program participants × cost per participant
• Measure benefits (in dollars)
• quantity × unit cost
• e.g.: number of people who will be incarceration × cost of incarcerating one person
The accuracy of the unit costs affects the
accuracy of the cost benefit results.
Slide 14
Marginal Costs and Policy Decisions
―There is certain to be some budgetary benefit. It costs $44,563 (the average for the U.S. is $28,817) to incarcerate a prisoner for a year in California — nearly the same price as a year at Harvard University with room and board.‖
The Fiscal Times, Runaway Prison Costs Trash State Budgets, Adam Skolnick, Feb. 9, 2011.
• True: The average cost of incarceration and the average cost of Harvard are about the same.
• False: The savings that would be generated if the prison population declined by one inmate would be sufficient to send one person to Harvard.
Slide 15
Marginal Costs and Policy Decisions
―At present, it costs an average of $46,000 per year to house an inmate in the MA DOC [Massachusetts Department of Corrections]. But there is more to this figure than one might realize. This cost changes with the inmate’s security level, medical needs and other factors. What is less known is that, on average, the cost associated with one inmate’s specific needs is about $9K per year – this covers stuff like food, clothing, and other incidentals that we pay for on an inmate-by-inmate basis.‖
Taunton Daily Gazette, Addressing the prison’s budget and population. Paul Heroux, Feb. 17, 2011
Slide 16
Questions
Slide 17
Understanding
Marginal Costs
Slide 18
• Programs and policies can create costs or cost-savings (benefits) to government agencies
• Example: a corrections department decides to expand a
reentry program that decreases recidivism rates. How much
will it cost to serve more people in the program? How much
will the program save by reducing recidivism rates and,
therefore, prison costs?
• To accurately measure the costs or savings from initiatives, determine the marginal costs of government operations.
Marginal Costs and CBA
Slide 19
Marginal versus Average Costs
• Marginal costs describe how the cost of an operation changes when workload changes by a small amount.
• Synonymous with incremental
• Borrowed from economics
• Average costs include both marginal and fixed costs.
• Fixed costs do not change as workload changes.
Slide 20
Marginal versus Average Costs
• Example:
• 1,000-bed prison
• Inmate population goes from 900 to 850
• Prison system saves on food, clothing (marginal costs)
• Does not save on electricity, building maintenance, warden salary (fixed costs)
• The average cost may be $46,000, but this cost includes both the marginal and the fixed cost
• This small reduction in the inmate population will not save $46,000
Slide 21
Marginal versus Average Costs
When policies have a small effect on agency operations, using average costs, instead of
marginal costs, will overstate costs/savings.
Slide 22
Step-Fixed Costs
• But what if the inmate population decreases from 900 to 700?
• Then add step-fixed costs to marginal costs to determine the long-term marginal costs.
• Step-fixed costs describe how the cost of an operation changes with significant changes in activity.
Quantity
Cost
Slide 23
Marginal Costs
Warden Guards Inmates
If the inmate
population
decreases by 5
people, the prison
system can save on
food and clothing
(marginal costs).
Marginal cost:
$5,000
Housing
Area 1
Housing
Area 2
Housing
Area 3
Note: only 3 housing areas are depicted, most prisons have
many more.
Slide 24
Long-Term Marginal Costs
Warden Guards Inmates
If the inmate
population
decreases by 20
people, the prison
system can save on
food, clothing
(marginal costs) and
staff salaries (step-
fixed costs)
Long-term marginal
cost: $20,000
Housing
Area 1
Housing
Area 2
Housing
Area 3
Note: only 3 housing areas are depicted, most prisons have
many more.
Slide 25
Average Costs
Housing
Area 1
Warden Guards Inmates
If the inmate
population
decreases by 600
people, the prison
can be closed,
eliminating all prison
expenses.
Average cost:
$60,000*
Housing
Area 2
Housing
Area 3
Note: only 3 housing areas are depicted, most prisons have
many more.
This cost still
excludes some fixed
costs like the cost of
the central
corrections office.
Slide 26
Which Costs to Use in CBA?
• Magnitude of the costs depends on the policy’s impact on the system
Small reduction in the inmate population?
Prison wings closed? A whole prison closed?
New reentry program?
• Based on the impact, use marginal, long-term
marginal, or average costs
Slide 27
Questions
Slide 28
Estimating Marginal Costs
Slide 29
Several Approaches
1) Ask government agencies
2) Review budget and workload documents
3) Consider capacity reductions
4) Use estimates from other organizations or states
5) Conduct regression analysis
Slide 30
• How: contact local/state budget offices and fiscal departments of criminal justice agencies
• Agency fiscal offices
• Executive budget offices
• Legislative fiscal staff
Ask agencies:
• Do you have marginal or incremental costs?
• How would a change in inmate population (or probation workload, etc.) affect agency funding?
1. Ask Government Agencies
Slide 31
Example: a spreadsheet showing marginal cost by levels of change in the inmate population at a hypothetical jail.
• Pro: estimates likely reflect actual spending patterns.
• Con: agencies may not have marginal cost estimates.
1. Ask Government Agencies
Type of Cost 1-100
inmates
101-600
inmates
600+
inmates
Corrections personnel n/a $16,700 $52,145
Other personnel n/a $5,575 $15,300
Supplies and materials $1,300 $1,550 $1,550
Total Marginal Cost $1,300 $20,000 $72,000
See Handout for additional detail:
Jail Marginal Cost per Inmate per Year
Slide 32
• How: review budget documents to identify marginal costs.
• Example:
2. Review budget and workload documents
Marginal Cost of a Prison
Item Estimate Source/Calculation
Inmates per staff 2.5 Budget documents
Staffing ratio (staff per inmates) 0.4 1 / 2.5
Annual Salary $29,000 Sunshinereview.org
Personnel cost per inmate $11,600 $29,000 x 0.4
Supplies & materials per inmate $7,000 Estimate
Marginal Cost $18,600 $11,600 + $7,000
Slide 33
2. Review budget and workload documents
• Pro: budget documents are usually readily available
• Salaries aren’t secrets!
• Con: can be difficult to determine what is a variable and what is a fixed cost; estimates may not reflect actual spending decisions
Salary Data in North Carolina from
sunshinereview.org
Please see Handout #2 Government Employee Salaries:
A Sample Page from Sunshinereview.org
Slide 34
• How: review budget documents and consult with criminal justice agencies to determine whether there has been a recent capacity reduction.
• Example:
From the New York State Budget:
“The parolee population is projected to decline by nearly 1,500; therefore, fewer parole officers are needed. …Savings are estimated at $3.7 million.‖ (New York State Budget Presentations 2010)
Marginal cost = $3.7 million / 1,500 = $2,466 per parolee
3. Consider Capacity Reductions
Slide 35
3. Consider Capacity Reductions
• Pro: reflects actual savings from past experience.
• Con: previous capacity reductions may represent unique situations that may not occur in the future, so marginal cost estimates may not hold in the future.
e.g., if a previous capacity reduction involved a closure of a outdated facility that was expensive to maintain, these savings might not be indicative of savings in newer prisons.
Slide 36
4. Use Estimates From Other States or Organizations
• How :
• review reports and studies for marginal cost estimates
• adjust these estimates for cost-of-living differences across states and inflation, if applicable.
• [or] determine the marginal/average cost ratio in another state, then apply the ratio to determine the marginal cost in your state.
Slide 37
4. Use Estimates From Other States or Organizations
• Example 1: unit cost estimates from a WSIPP report:
Please see Handout #3, Marginal Operating Costs, Washington State
Criminal Justice System
Slide 38
4. Use Estimates From Other States or Organizations
Marginal Cost in WA Estimate Source
Average Cost - WA $4,182 WSIPP report
Marginal Cost - WA $670 WSIPP report
Marginal/Average cost 16% $670 / $4,182
Average Cost - NC $3,110 police expenditures / arrests
$1,358,211,000 / 436,676
BJS
Marginal Cost in NC $498 $3,110 x 16%
• Example 2: Calculating North Carolina marginal cost
of law enforcement using data from WSIPP and the
Bureau of Justice Statistics (BJS).
Slide 39
• Pro: information is generally available.
• Con: estimates may not accurately reflect local costs.
4. Use Estimates From Other States or Organizations
Slide 40
5. Conduct Regression Analysis
• How: conduct regression
analysis using historical
spending and population data.
• What is regression analysis?
• Technique used to understand how changes in
one or more variables (or factors), affect
changes in a variable of interest.
Slide 41
5. Conduct Regression Analysis
• Example:
Washington State Institute for Public Policy (WSIPP)
uses police expenditures and arrest data to estimate
the marginal cost of policing.
• Pro: reflects changes in actual spending vs. workload.
• Con: spending may change for other reasons; long-term data on costs and workloads may not be available.
Slide 42
Recap of Estimation Approaches
1) Ask government agencies
2) Review budget and workload documents
3) Consider capacity reductions
4) Use estimates from other organizations or states
5) Conduct regression analysis
Slide 43
Key Takeaways
• Marginal costs represent a more accurate measure of
costs and cost-savings associated with new programs
and policies
• There are several ways to estimate marginal costs.
Pick one that is right for you.
• Work with government staff to develop marginal cost
estimates and build relationships.
Slide 44
Questions
Slide 45
Wrap-Up
Slide 46
Recap of Today’s Webinar
You learned:
• The difference between marginal and average
costs.
• Why marginal cost are necessary in a credible
cost-benefit analysis.
• 5 methods to estimate the marginal costs at
criminal justice agencies.
Slide 47
Follow-up
Please complete the evaluation form as you leave this training.
To receive information and notifications about upcoming webinars and other events
• Visit the Cost-Benefit Knowledge Bank for Criminal Justice at http://cbkb.org
• Subscribe to receive updates from CBKB.
• Follow us on Twitter at http://www.twitter.com/CBKBank
The next webinar will be on March 24th. Elizabeth Drake from the Washington State Institute of Public Policy (WSIPP) will discuss the role of evaluation in CBA.
Slide 48
This project is supported by Grant No. 2009-MU-BX K029 awarded by the Bureau of
Justice Assistance. The Bureau of Justice Assistance is a component of the Office of
Justice Programs, which also includes the Bureau of Justice Statistics, the National
Institute of Justice, the Office of Juvenile Justice and Delinquency Prevention, and
the Office of Sex Offender Sentencing, Monitoring, Apprehending, Registering, and
Tracking. Points of view or opinions in this document are those of the author and do
not represent the official position or policies of the United States Department of
Justice.
Slide 49
Contact Information
Christian Henrichson
(212) 376-3161
Valerie Levshin
(212) 376-3062
http://www.cbkb.org
Slide 50
Thank you!
