Dynamic Drivers of Successful
Social Impact Bonds
Robert J. White mu , David N. Ford, Ph.D., P.E2
Zachry Department of Civil Engineering, Texas A&M University
3136 TAMU, College Station, TX 77843-3136
Telephone: 979.845.3759
Facsimile: 979.845.6554
robertjwhite@ tamu.edu; davidford@ tamu.edu
Abstract
Public goods and services, such as prisons, are often underfunded compared to private goods and
services. Social Impact Bonds (SIB) are a new financial vehicle to increase the use of private
funds for public good. SIB use a pay for performance structure to change a critical reinforcing
loop from a vicious cycle of decay to a virtuous cycle of improvement. A a case study model of
the Her Majesty’s Prison (HMP) Peterborough SIB is developed and analyzed to understand the
roles of high leverage parameters and feedback loops in the SIB success or failure for the two
primary participants (HMP system and SIB investors). Program effectiveness and unit program
costs are found to be two high leverage SIB design characteristics. The analysis and model are
used to make recommendations for both the owners and investors conceming SIB design.
Keywords: public goods, finance, prisoner rehabilitation, Social Impact Bond, Recidivism,
Rehabilitation, Program Finance, Pay for Performance, Peterborough, project finance
Introduction
Public goods and services tend to be underfunded compared to private goods and
services. This is partially because they are often non-excludable and non-rival. Services are non-
excludable when they cannot be restricted when in use. Services are non-rival when one party’s
use does not impact its use by others. Street lights are a simple example of such a public good.
They are non-excludable because everyone sees the objects they light up, and they are non-rival
because one person’s use of the street lights does not impair or hinder another’s use of the light.
‘PhD Student, Zachry Department of Civil Engineering, Texas A&M University. robertjwhite@ tamu.edu
? Associate Professor and Urban/Beaver Development Professor, Zachry Department of Civil Engineering, Texas
A&M University. davidford@ tamu.edu
Page 1 of 24
Some people (free-riders) prefer excludable or rival goods and services, leading them to
undervalue and therefore underfund public goods and services(Gruber 2011). This is a problem
when the social benefit for public goods are greater than the, excludable or rival, private goods
(Marwell and Ames 1981). Prison systems are non-excludable and non-rival and often
experience underfunding due to the free-rider problem (Marvell and Moody 1998).
Prisons measure performance in multiple dimensions. One measure is the population of
prisoners held in prisons. Assuming the correct population is being held, a lower population
indicates more success. This objective is partially reflected in the prison’s recidivism, the
fraction of released prisoners that are reconvicted (Disley, Rubin, Scraggs, Burrowes, & Culley,
2011; Moynihan, 2008). Prisons also measure performance using cost (e.g. dollars per prisoner-
year). Like in many systems, these performance measures create tradeoffs. Rehabilitation
programs can lower the recidivism rate for a prison system, but increase the cost per
prisoner(Loder, et al. 2010, Mulgan, et al. 2011). Therefore efforts to limit cost can prevent the
initiation and use of rehabilitation programs. Thus rehabilitation programs are likely to be
underfunded when cost per prisoner is the performance metric. Therefore, a major challenge for
prisons systems is how to fund rehabilitation programs with little public funding (Moynihan D.
P., 2008; Loder et al., 2010; Mulgan et al., 2011). Donald Moynihan (2008) describes the
Alabama Department of Corrections (ALDOC) as an example of this dilemma. ALDOC was
underfunded, requiring it to operate at almost 200% capacity (Britt 2012). Single guards were
responsible for 200 prisoners, forcing them to stand back and try to prevent full scale riots (Britt
2012). Under such circumstances funds for rehabilitation programs could not even be considered.
Social Impact Bonds (SIB)
Social Impact Bonds (SIB) are one potential solution for using private funds to develop and
support public goods, such as prisoner rehabilitation programs. Social Impact Bonds are a new*
and innovative form of performance-based contracting that integrates the provision of public
services, the “do good for others” altruism of non-government organizations (NGO), and the
profit motive of private capital markets. In a SIB private sector investors and a public sector
agency agree that investor retums will be contingent upon the creation of specific social
3 The term “Social Impact Bond” was coined by the Y oung Foundation in 2008 (Loder et al., 2010)
Page 2 of 24
outcomes by an NGO that result in tangible savings to the public sector. A portion of these
savings are paid to the investors if, and only if, specific improvement targets are met. Therefore,
a SIB links investor returns to monetized outcomes. See Mulgan et al., (2011), Social Finance
(2009, 2011b), and Y oung Foundation (2010) for more on Social Impact Bonds.
Figure 1 shows a portion of the feedback structure of a prisoner rehabilitation program.
When operating as a vicious cycle of decay reinforcing loop 1 (R1) degrades prison system
performance by reducing rehabilitation programs and thereby increasing recidivism as budgets
are reduced, which increases reconvictions, prison populations and costs, thereby reducing funds
for rehabilitation programs farther. Figure 1 also illustrates how the challenge described above
can be initiated if the total prison budget (Figure 1, center) is constrained, requiring a tradeoff
between the operating and discretionary budgets. A reduction in the total budget of a prison
system operating in a steady state can reduce the discretionary budget enough to initiate the
vicious cycle of decay.
+
New prisoner —F operaioa
conviction rate Prison
+. Population
Operating Operations savings
a budget ho Fpuclget surplus)
ff
patie Total RD
ecidivism ison
Pdget +
B1 : = Prison syetem Investor
a Available discretionary account
Recidivism Recidism Change udget
Gap Rehabilitation +
—— FRR ation
Minimum
Recidivism
Legend of Loops
R1 - Paid-from-Success rehabilitation loop: Prison budget funds program which reduces population and
generates savings which are used to pay for the program
R2 - Social Impact Bond loop: SIB invests in rehabilitation program, reducing population and creating
savings, part of which are paid to investors as returns
B1 — Limits to Improvement loop: Decreased recidivism reduces improvement available, which limits the
amount of future recidivism reduction
Figure 1: Partial Feedback Structure of a Prison Rehabilitation Program
Financed with a Social Impact Bond
Page 3 of 24
However, reinforcing loop 1 (R1) in Figure 1 also describes a potential solution if the
reinforcing loop operates as a virtuous cycle of improvement instead of a vicious cycle of decay.
In this behavior mode loop R1 depicts the use of a paid-from-savings approach in which a
rehabilitation program reduces recidivism and then reconvictions, thereby reducing a prison’s
population and operating costs. This increases operating savings, which can be used to continue
to fund the rehabilitation program. These improvements are limited by the minimum recidivism
that the rehabilitation programs can create (Figure 1, loop B1). Changing the behavior mode of
this reinforcing loop into a virtuous cycle of improvement is the primary objective of a Social
Impact Bond applied to prisoner rehabilitation. A SIB can solve this financing problem by
having its investor provide the required funds to start and initially operate a rehabilitation
program and be repaid (with profit) from the operating savings (Figure 1, loop R2). Thus a SIB
can change the prison budget dynamics from tradeoffs among alternative uses or a vicious cycle
of decay to the use of savings from reduced recidivism to continuously improve the prison
system’. After the SIB ends the prison system can operate the rehabilitation program in
perpetuity with its share of the savings generated by the SIB-funded program and future savings.
In addition, after the SIB has ended the investors can continue this dynamic by reinvesting in a
larger or different rehabilitation programs (Disley et al., 2011). See Strickland (2010), Loder et
al. (2010), Mulgan et al. (2011), and von Glahn and Whistler (2011) for detailed descriptions of a
SIB for prisoner rehabilitation.
Traditional bonds and public private partnerships (P3) are common forms of funding for
public programs. SIBs are similar to public private partnerships (P3) in that investor returns
depend on performance. However, the risk and reward structure of SIBs distinguish them from
public private partnerships and traditional bonds. Mulgan et al., (2011) suggest four categories of
program risk that can be used to compare SIBs to traditional bonds and P3:
Performance risk’ is the risk that the public agency may not experience the
improved outcomes and capture the anticipated savings. For example, ina
prisoner rehabilitation program performance risk reflects the possibility that
released prisoners will be convicted of additional crimes.
“ However, there are natural limits to growth (Senge, 1990) such as minimum recidivism fractions and maximum
retums, not included for clarity. These are included in the formal model but not in the causal loop diagram for
clarity.
= Mulgan et al., (2011) refer to performance risk as basis risk.
Page 4 of 24
e Measurement risk is the risk that the measures of performance may not accurately
and equitably depict the outcomes. For example, in a prisoner rehabilitation
program measurement risk reflects the possibility that recidivism may not
adequately describe prison system population and operating cost changes.
e Execution risk is the risk that programs may not scale up from a pilot stage. For
example, in a prisoner rehabilitation program execution risk reflects whether a test
program for short term offenders at one prison can generate the same results if
used for other prisoner types and prisons.
e Unintended consequences are the risks of creating policy resistance that will
defeat the program objectives. For example, one unintended consequence in a
prisoner rehabilitation program could be the reduction of prison budgets as
savings are captured, thereby providing inadequate funds to maintain the
rehabilitation program.
In a traditional bond for a public sector program the owner (e.g. public prison system)
commits to paying the investor specified retums regardless of the performance of the program.
Therefore, the owner holds all four of these types of risk in a traditional bond. In a public private
partnership much of the performance, measurement, and execution risks are transferred to the
investors and developers of the project, and the unintended consequences risks are shared. For
example, a toll road developer typically takes the traffic volume (performance), toll collection
(measurement), and scale (execution) risks, but would only bear some of the unintended
consequence risk (e.g. lower traffic due to higher tolls but not regulation changes). A SIB differs
from the traditional bond risk / reward structure by having the investors assume the performance
risk and measurement risks (like in a P3). But, like a traditional bond, the SIB owner holds the
execution risk (due to the limited and specified scale of the SIB) and the more of the unintended
consequences risk than in a P3 (Mulgan et al., 2011; Miraftab, 2004; Hatry, 2006). SIB investors
would be expected to require a higher investment retum rate than traditional bond investors for
bearing the additional risks (Loder et al., 2010; Mulgan et al., 2011), but (presumably) less than
the returns of a P3 (ceteris paribus). Notably, the bearing of the performance risk by the SIB
investor creates an incentive for investors to actively participate in the program (Mulgan et al.,
2011).
Due to the delayed feedback structure of a SIB (e.g. Figure 1) the system dynamics
methodology (Sterman, 2000; Forrester, 1964) can provide valuable insight to the drivers of SIB
success or failure through the SIB structure’s impacts on the risks and rewards of its two primary
stakeholders (Damnjanovic & Ford, 2011). Modeling a SIB-financed system can potentially
improve the design and management of SIBs and their applications. These insights and
Page 5 of 24
improvements would accelerate the development if SIBs as a new financing vehicle, increase
SIB investor confidence, and thereby accelerate its widespread adoption. The current work
develops, analyzes, and uses a system dynamics model of the only known operating SIB and
draws conclusions for SIB development and use.
The HMP Peterborough Social Impact Bond
In 2010 the United Kingdom (UK) initiated the first SIB through the Ministry of Justice
(MOJ). The six-year SIB is designed to reduce the recidivism of released short term offenders
from the Her Majesty’s Prison (HMP) Peterborough (Strickland, 2010; Disley et al., 2011; Cave,
Williams, Jolliffe, & Hedderman, 2012) by reducing the reoffending rate of the released
offenders (Strickland, 2010; Cave et al., 2012). The program is operated by NGOs that consist of
organizations with proven track records but insufficient funds to operate on a scale as large as the
Petersboro SIB. Savings are expected due to reductions in the number of arrests, convictions, and
prison terms, all which impose costs on HMP Petersboro.
The Petersboro SIB potentially addresses at least two major challenges to the success of
rehabilitation programs: lack of adequate resources, and overly aggressive implementation
schedules (Loder et al., 2010). The Bridges to Life rehabilitation program (Bridges To Life,
2011, Maybield-Geiger and Rudnicki, 2007) is an example of how successful a program can be
if these two challenges are addressed. The SIB addresses the resources issue by incentivizing
investors to provide adequate funds to allow success. The SIB addresses the implementation
schedule challenge by structuring oversight of the program by investors, who will seek to keep
the program slow enough to allow for its success.
The Petersboro SIB investors provided £5 million across six years paid through a special
purpose vehicle (SPV) to the NGOs (Strickland, 2010). To measure performance the
Peterborough SIB specifies four cohorts of released prisoners. Each of the first three cohorts has
a maximum of 1000 prisoners in each. The fourth is an accumulation of the first three cohorts
(Cave at al., 2012). If the program reduces recidivism by 10% for any of the first three cohorts,
or 7.5% for the fourth (cumulative) cohort, then the MOJ pays a portion of the savings to the
Page 6 of 24
investors(Strickland 2010)°. However, if the reconviction targets are not met, then the investors
receive no performance payments for the failed cohort.
If successful, the Peterborough SIB will provide the investors with an attractive return
and the MOJ with three practical benefits. First, HMP Peterborough would have a sustainable
program able to fund its own rehabilitation programs. Second, the sustainable program could be
replicated in similar prisons for similar offenders, thereby further improving the HMP system.
Third, the HMP Peterborough SIB case could serve as a model for expanding SIBs beyond the
domain of prison systems, to other public services and infrastructures. Understanding the
feedback structure of the Petershoro SIB is critical to explaining its performance and success or
failure.
Research A pproach and Model Structure
The system dynamics modeling methodology (Sterman, 2000; Forrester, 1964) was used
because of its ability to formally describe and simulate the impacts of feedback structures in
managed system. The current study developed a formal model of the Petersboro SIB for
rehabilitation, analyzed the model to identify high leverage system components, and used those
results to investigate SIB design issues as them impact performance outcomes of the SIB
investors (IRR) and owners (prison population reduction).
The Peterborough SIB model has three sectors, depicting the prison system, the
performance measurement, and SIB finances. In general, the prison system structure models the
flow of prisoners through the system and the effects of the SIB on prison population
dynamics(Strickland 2010). The performance measurement sector compares the prisoners in the
Peterborough cohorts and a comparison group of prisoners to assess the performance of the SIB
(Cave et al., 2012). The SIB finances sector use the performance assessment to simulate the
financial returns to investors according to the SIB (Strickland, 2010; Disley et al., 2011; Cave et
al., 2012).
5 Returns to the Petershoro SIB investors are also ined by mini and i interest paid on the
invested funds. See Cave et al. (2012) for details. These constraints are incorporated in the model.
Page 7 of 24
The prison system structure provides a simplified view of how people move in, out, and
around the prison system’. New offenders are incarcerated from the general population (Figure 2,
upper left). In the model released prisoners unknowingly one of two stocks, those who function
within the norms of society (rehabilitated offenders) or those who will recommit (undiscovered
reoffenders). At the time of release the actual prison system does not know what fraction of
released prisoners will recommit, be arrested and convicted again, and reenter the prison. But the
model distinguishs these stocks and their related flows and uses Stickland’s (2010) historical
value of 75% re-offending fraction to initialize the model. Rehabilitated prisoners A fter their
release, prisoners are reintroduced to society where they either (i.e. are rehabilitated, Figure 2,
top center) or recommit crimes (i.e. are unrehabilitated, Figure 2, left) and will eventually re-
offend, be arrested and convicted, and returned to prison (Figure 1, bottom) (Disley et al., 2011).
The model simulates these two types of released prisoners separately. Rehabilitated prisoners
leave the system after the one-year probation period (Figure 2, upper right). Those that will
recommit and be reconvicted remain under the same probation period until they are reconvicted.
Once reconvicted, a prisoner retums to the prison for the duration of their holding, where they
are again released into the same system (some being rehabilitated and the rest unrehabilitated).
The prison system has a structure of stocks and flows similar to the rework cycle in most system
dynamic project management models (see Lyneis and Ford, 2007) with work being replaced by
prisoners, the fraction requiring rework being replaced by the recidivism fraction, and the quality
assurance function replaced by the probation period. Similar to how improved work quality
reduces rework in project models, reducing the recidivism of first time offenders can greatly
reduce the magnitude of repeat offenders(Langan and Levin 2002).
7 The model retains all prisoners, so that none are lost, e.g., to crime escalation or death. Therefore the model is
accurate as long as these anomalies remain insignificance (Cave at al., 2012). The limit of insignificance is
determined by Cave et al., (2012). .
Page 8 of 24
New offender First time-rehabilitated Offenders coming
incarceration rate offenders release rate off probation rate
holding-first <<
7 offers | |__offendes |
untehabilted Repeat- rehabilitated
offender release rate Repeat. offenders release
unrehabilitated re
offender release rate |
Untisonva. holding-repeat
offenders
Repeat offender
arrest rate
Figure 2: Petersboro SIB Model: Prison Sector Stock and Flow Structure
To assess SIB performance the performance measurement sector compares the prisoners
in the four Peterborough cohorts to four parallel cohorts in a comparison group of prisoners at
other UK prisons. The effects of large scale factors such as a national decline in crime do not
influence program performance because prison reconviction is compared to concurrent prisoner
cohorts. Recidivism is used as the performance measure (Cave et al., 2012). Success is defined
as a reduction in recidivism of 10% or more than the recidivism change in the comparison cohort
for each of the three 1000 prisoner (maximum) cohorts at Petersboro or a reduction in recidivism
of 7.5% or more than the recidivism change in the comparison cohort for the fourth (combined)
Petersboro cohort. If the performance meets either of these targets the MOJ pays the SIB
investors a specified® fraction of the savings captured by the MOJ.
The SIB financial sector uses the assessments of success from the performance
measurement sector to simulate payments to investors and calculate returns. Investors providing
funds for program operations and expenses create outflows of investor cash. Loder et al. (2010)
and Mulgan et al. (2011) describe the costs of the program, including the overhead for the special
purpose vehicle used to structure and operate the SIB. If the program is successful the MOJ
makes payments based on savings captured to the SIB investors, creating cash inflows to the
investors. The benefits of the program used to determine payments are the savings in
reconvictions and re-incarceration (Strickland, 2010; Mulgan et al., 2011; Cave et al., 2012). The
modelers assumed (consistent with the SIB intent) that if the program is successful the MOJ will
use its savings (including those that were used to pay SIB investors) to continue to operate the
5 The fraction is specified in the SIB contract but has not been made public.
Page 9 of 24
rehabilitation program. This closes the “big” feedback loop from funding from the SIB through
the prison system, performance measurement and finances, and back to funding the program (by
the MOJ after the SIB), and the shifting of dominance from loop R2 in Figure 1 (SIB-based
success) to loop R2 (internally supported success). If, in contrast, the program is unsuccessful the
MOJ makes no payments to the SIB investors and the program closes out after the investment
period. Standard formulas with an assumed discount rate are used to estimate internal rate of
return (IRR) and the net present value (NPV) of the SIB for the investor.
Model Calibration, Typical Behavior, and Validation
Model Calibration
The model was calibrated to the Peterborough SIB case using publicly available literature
as referenced above. Langan & Levin (2002), Loder et al. (2010), Strickland (2010), Mulgan et
al. (2011), Disley et al. (2011), and Cave et al., (2012) describe the program impact, costs,
assessment process and timing, and magnitude. Mulgan et al. (2011) and Loder et al. (2010)
describe the expected impact of the rehabilitation program as well as various costs added to the
assessment. Strickland (2010) identifies the value of investment and limits of the investment.
Disely et al. (2011) also provide results of a preliminary assessment of the SIB in terms of
magnitude and affect. Model values coincide with the information on the SIB and program found
in this literature. Values that were not described in the literature were estimated and the model
initially set to steady state conditions. For example, Disely et al. (2011) noted that about 315 new
offenders entered HMP Peterborough in just over six months and the steady state model uses
about 317 in a similar time frame. Cave et al. (2012) noted that the normal reconviction rate for
HMP Peterborough was 1.64 persons per month for data collected up to one year after the close
of the cohort. The calibrated model calculates about 1.53 persons per month in a similar time
frame.
Typical Model Behavior
Typical model behavior is illustrated by two performance variables of the SIB investors and
MOJ. Although recidivism is the metric used in the SIB, a (perhaps the) primary performance
measure of the MO] is the reduction in the Peteresboro population. Figure 3 shows the simulated
behavior over time of this variable for the calibrated model.
Page 10 of 24
40
Prison Population Reduction (%)
~
8
0
0 20 40 60 80 100 120 140 160 180 200
Time (Month)
Base Case
Figure 3: Typical Model Behavior - HMP Petersboro Prison Population Reduction
After a period of steady state operations (months 0-20) the program begins and more prisoners
are rehabilitated in the Peterboro system, reducing the prison population (months 20-60).
However, as available funds decrease, so does the number of prisoners allowed to enter the
program, slowing the rate of improvement (months 30-60) and eventually reversing the progress
and causing an increase in prison population when SIB funds have been depleted (months 60-
75). After the completion of the program funded by the SIB the rehabilitation program is
continued by the MOJ (consistent with van Golahn and Whistler, 2011), initially using the
savings generated by the SIB funded program. This causes the prison population to reduce again,
approaching a steady state at its maximum which is controlled by a minimum recidivism (months
75-200). We later describe the potential dangers of the temporary increase in prison population
and use the model to investigate the causes and a possible solution.
The primary performance measure of the SIB investors is their retum, reflected in the internal
rate of return. Figure 4 shows the internal rate of return for SIB investors for the calibrated model
case.
Page 11 of 24
xe
a
°
o
Internal Rate of Return (fraction)
: S
a
a
on
an
a
25 35 45 55 65 75 85 95 105
Time (months)
Base Case Behavior Validation
Figure 4: Typical Model Behavior - HMP Petersboro SIB Internal Rate of Return
The SIB-funded program starts in month 20, paying startup and operating costs. Until retums are
paid to the investors the IRR is -100%. The success or failure of the first cohort occurs after the
first assessment period, when (for the base case) success reduces recidivism and creates savings.
This initiates the first payment by the MOJ to the SIB investors (month 57), consistent with Cave
et al. (2012) and Mulgan et al. (2011). Similarly, the second and third successful cohorts are paid
starting in months 75 and 92, each increasing the IRR. In the actual Petersboro case and the
calibrated model used for the base case the IRR is limited to 8.25% (months 100-200). Model
analysis results are used later to investigate performance without this limit.
Model Validation
The model contains a total of 141 variables consisting of 23 basic stocks and 24 flows
(with five arrays), and 29 exogenous variables. The model structure is based upon the extensive
literature specifically about the Petersboro SIB case referenced in the model structure description
above. Of the 29 exogenous variables 14 used values taken from the literature specifically about
HMP Petersboro or HMP system. The values of four of the remaining exogenous variables were
supported from other literature but that literature provided inconsistent values. These ranges
were used in extreme conditions testing. Four more were supported by other literature. The
Page 12 of 24
remaining seven were used to establish steady state conditions (e.g. initial values of stocks) or
estimated by the modelers.
The model generated reasonable behavior when each of the 29 exogenous variables were
set to extreme values. More specifically, each exogenous variable was tested for its impact on
several outcome variables, including SIB investor IRR, offender release rate, and the
reconviction fraction. For example, when the Normal Recidivism Discovery Time (average time
to discover that a released prisoner has re-offended) was set to a relatively high value (twelve
months’) the SIB investor IRR decreases because there are fewer reconvictions for every
unrehabilitated prisoner and therefore less savings and reduction in recidivism. See the
supporting documents for details on the extreme conditions testing and results.
The Petersboro SIB has not progressed adequately to provide actual behavior data for use
in model validation. However, the literature describes the expected behavior for the case,
including Disely et al. (2011) reviewing the expectations for both how investors eam money as
well as how the SIB financially functions, Cave et al. (2012) describes how the third party
assessor of performance defines the limits among the different cohorts and determines cohort
success, Langan and Levin (2002) describing how the prison system creates a perpetual cycle of
offences, and Mulgan et al. (2011) describing the transfer of risk, cost savings to the MOJ, and
flows of capital between key stakeholders. The models behavior is consistent with the expected
behavior for financial and other performance measures. For example, Disely et al. (2012)
describes the increase in investor returns due to either a decrease in reconvictions, or an increase
in the investors’ share of the total savings. By varying these two parameters the model also
simulates this increase in returns (Figure 5), building confidence in the ability to generate “the
right behavior for the right reasons”.
5 The prisoners targeted by the program are limited to those with short (12 months or less) sentences and the average
sentence served was about three months. Therefore twelve months for discovering a re-offense is relatively long.
Page 13 of 24
Se
a
o
Intemal Rate of Return (fraction)
S
a
is
0 20 40 60 80 100 120 140 160 180 200
Time (months)
High recidivism reduction
Low redicivism reduction
Figure 5: Behavior Validation Test of SIB Return based on Recidivism Reduction
As another example of model behavior validation the model successfully reflects the
expectation that the government would continue a successful program, as described by Glahn
and Whistler (2011). The model’s behavior is consistent with what would be expected in the
operation of the actual SIB at HMP Petersboro.
Based on these model validation tests the Petersboro SIB model is considered valid for
investigating the impacts of SIB design parameters on system behavior and performance.
Model Analysis
Model analysis to identify and describe high leverage parameters was performed in two
steps. First statistical screening (Taylor, Ford, and Ford, 2010; Ford and Flynn, 2005) was used
to identify high leverage parameters for one performance measure for the MOJ (prison
population reduction) and for one performance measure for SIB investors (IRR). Statistical
screening is a simple, structured, and user-friendly means of identifying high leverage model
parameters based on model behavior. Statistical screening quantifies parameter influence
throughout simulation, thereby describing the evolution of exogenous impacts on behavior. In
addition, statistical screening provides modelers with the objective model analysis results
required to generate clear behavior distinctions. Consistent with the application of statistical
Page 14 of 24
screening (Taylor et al., 2010), the time frame after the SIB is completed (months 100-165) was
chosen as the focus of the analysis. The results of the statistical screening analysis were used to
identify two of the highest leverage parameters that could be influenced by SIB designers. These
were then described with univariant sensitivity analysis. See the model analysis supporting
documentation for details on these analyses.
Figure 6 shows the results of the statistical screening analysis the most influential
exogenous variables that impact the prison population reduction. The analysis results show the
relative influence of the four exogenous parameters with the most impact on the prison
population reduction. Correlation coefficient values farther from zero indicate more influence.
Positive values indicate movement in the same direction and vice versa. The results indicate that,
after the SIB is over, the reduction in recidivism, maximum cohort size, reference (pre-program)
recidivism fraction, and unit program cost (per participant) are most influential on the prison
population reduction (in decreasing order of influence). The reduction in recidivism after the SIB
is particularly important because it is a metric of program effectiveness, something that SIB
designers can influence through their choice, design, and management of the rehabilitation
program. Similarly, the unit program cost can also be influenced by SIB designers and managers.
Correlation Coefficient:
S
te
I
h
I
I
20 30 40 50 60 70 80 90 100 10 120 130 140 150 160
Time (months)
—Normal recidivism fraction --~Maximum cohort size
— + Unit program cost Reduction in recidivism
Figure 6: Statistical Screening Model Analysis Results:
Prison Population Reduction
Page 15 of 24
Figure 7 shows the results of the statistical screening analysis for the four most influential
exogenous variables that impact the SIB investor IRR. The analysis results show that, in
decreasing order of influence, the relative influence of the four exogenous parameters with the
most impact on the SIB investor internal rate of return. The results indicate that, after the SIB is
over, the reduction in recidivism, unit program cost, unit cost of conviction, and investor
discount rate are most influential on SIB investor IRR.
Correlation Coefficient
20 30 40 50 60 70 80 90 100 110 120 130 140 150 160
Time (months)
— —Unit cost of conviction — Investor Discount Rate
+ Unitprogramcost, tte Reduction in recidivism
Figure 7: Statistical Screening Model Analysis Results:
SIB Investor Internal Rate of Return
The results of the two statistical screening analyses indicate that reduction in recidivism
and unit program cost are two of the highest leverage parameters for both the MOJ and SIB
investors that SIB designers can influence. Consistent with model analysis using statistical
screening (Taylor et al., 2010), the model structure is used to link these parameters to potential
drivers of system behavior and performance (e.g. feedback loops, delays, accumulations). Both
variables have a direct impact on the strength of core feedback loops in the Petersboro SIB.
Increasing the program effectiveness and thereby the reduction in recidivism (Figure 1, left side)
reduces reconvictions, prison population (a MOJ performance metric), operating costs, and
thereby savings that generate return for SIB investors (Figure 1, Paid-from-Success rehabilitation
loop R2). As described above, strengthening this loop drives the Social Impact Bond loop
Page 16 of 24
(Figure 1, loop R1) that allows the MOJ to operate the rehabilitation program on a self-sustaining
basis. This demonstrates the critical role of understanding and managing these two feedback
loops.
However, knowing what system parameters and feedback loops have the most influence
does not provide operational recommendations to system designers and managers because the
amount of benefits derived from changes, limits of change, difficulty of change, cost of change,
and other factors impact the attractiveness of change alternatives. Knowing the relative amounts
of leverage that each of these parameters have on performance can facilitate SIB design.
Therefore, univariant sensitivity analysis, initially using the calibrated model as a base case, was
performed to better describe their impacts. Figure 8 shows the relative impacts of these two
variables on prison population reduction. These results indicate that the reduction in recidivism
has an equal or larger impact on prison population than the unit program cost and that reducing
the unit cost below a specific value (40% above the base case cost in these simulations) does not
reduce the prison population. This latter lack of impact is due to the program having achieved the
maximum possible reduction in recidivism.
——— Unit
4.2 program
cost
WA oa in
ie recidivism
Percent Variable Change from Base Case
Base Case
Prison Population Reduction (fraction of
Figure 8: Results of Univariant Sensitivity Analysis with Base C ase:
Prison Population Reduction
Figure 9 shows the results of the univariant sensitivity analysis for the impacts of the
reduction in recidivism and unit program cost on the SIB investor internal rate of return.
Page 17 of 24
7. 5 a — nit program
0.9: cost
0.02 — Reduction in
recidivism
Internal Rate of Return (fraction:
N¢
|
-50 0 50. 100
Percent Variable Change from Base Case
eb
S
Ss
Figure 9: Univariant Sensitivity Analysis Results with Base Case:
SIB Investor Internal Rate of Return
SIB investor IRR increases as the final recidivism reduction increases from a loss of all
invested funds if recidivism reductions are not adequate and no cohorts are successful to the
calibrated reduction values, after which they remain constant at 8.25% (Figure 9, top). This limit
is because the Petersboro SIB and the model include a maximum retum regardless of
performance. Similarly, SIB investor IRR increases as the program cost per participant decreases
from 2.27% when costs are double the Petersboro costs (Figure 9, lower right) to a return of
8.25% at the calibrated costs (Figure 9, upper left). Returns fall to -100% because there are no
successful cohorts if there is inadequate reduction in recidivism (Figure 9, lower left) or 2.37%,
the minimum return for successful cohorts in the SIB, if unit costs are very high (Figure 8, lower
right). As shown by similar slopes in Figure 9 near the base case conditions, reductions in
recidivism and unit program cost have similar amounts of leverage near the base case conditions
and less influence with increased variance from base case conditions. To better understand
performance for other possible SIB designs the model was altered to remove the 8.25%
maximum allowed retum and 2.37% minimum return on successful cohorts!°. The univariant
sensitivity analysis was repeated and the results are shown in Figure 10.
1° The results of the univariant sensitivity analysis for prison population reduction do not change if the limits on the
SIB investor retums are removed.
Page 18 of 24
—§— : ————
— unit program
-100 po ar ee cost
o4 —Reduction in
recidivism
1
Percent Varlable Change
Internal Rate of Return (fraction)
Figure 10: Univariant Sensitivity Analysis Results with Unlimited Return:
SIB Investor Internal Rate of Return
Note the different vertical scale in Figure 10 when compared to Figure 9. Results indicate
that a reduction in recidivism that is twice as large as the base case (i.e. if the program is very
effective) can generate much larger returns when retums are unrestricted (23.49% vs. 8.25%).
Similarly, retumms can increase from 8.25% to 11.61% if program costs are cut to at least 80% of
the calibrated costs if returns are not limited. However, unconstrained returns can fall to -12.1%,
well below the minimum retum of 2.37% (Figure 9) with high costs. This illustrates how the SIB
investor traded away the opportunity for a higher reward if the program was very successful to
gain some protection with a minimum retum in case costs were high.
Model Use
The dynamics of the Petersboro SIB provide insights into the challenges for SIB design.
The model was used to investigate potential solutions to those challenges. First, from the MOJ
perspective, the temporary increase in prison population at the end of the SIB funded program
(Figure 3) could cause HMP managers to believe that the rehabilitation program cannot succeed
without SIB funding. They might then refuse to use the savings to continue the program, thereby
causing a retum of the prison population to its pre-program level and loss of social benefits. We
hypothesize that this “worse before better” scenario may be because of an intuitive but
misguided funding delay. In the model the MOJ does not start funding the program from savings
until well after the program begins to limit participation due to funding. The reason is that the
Page 19 of 24
MO] is (reasonably) waiting until the program has been assessed. This delay creates a 15 month
(base case) period of no funding and therefore reduced or no program participation. We used the
model to test this hypothesis by starting MOJ funding of the program at a series of times starting
nine months earlier than the base case and ending six months after the based case. The results
(Figure 11) support our hypothesis by showing that reducing the delay nine months keeps the
prison population reduction above 32% instead of letting it drop to a 25% reduction (base case)
and that increasing the delay by six months allows the reduction to drop to almost 20%.
40
: 35
i
:
& 30
z
&
5
2 25
20
25 45 65 85 105 125 145 165
Time (Month)
Base_Case 6 months early
3months ealy, —-—- 6 months late
IOLA Le 9 months early
Figure 11: Decrease in Prison Population based on MOJ Funding Start Time
Perhaps more important, the Petersboro SIB design may prevent one of the key aspects of
SIBs from being implemented. One of the objectives of shifting performance risk to SIB
investors is to make them active managers of intervention to improve their retums (e.g. see
Loder et al., 2010). This change from traditional bonds can activate management and other
expertise in the private sector to improve performance of changes in public goods. In the
Petersboro case the SIB investors do not receive returns, and thereby financial information, on
the performance of their investment until 2.5-4 years after their first investment and until after
Page 20 of 24
the second or third cohort has been funded. Therefore they receive feedback on their financial
performance too late to change the program to improve it and thereby improve their return. In
feedback terms this is the delay between “Operations savings (budget surplus)” and “Investor
account” in Figure 1 being too large to allow feedback loop R2 to provide continuous SIB
funding or signal that program changes are required. SIB designers would like SIB-funded
programs to be long enough that investors can actively work to make programs successful,
thereby increasing the social benefits, returns to investors, and attractiveness of SIB investments
for continued, future, or other public good improvements. Assuming some time is required to
assess financial and operational performance, and to design and implement intervention changes,
future SIB designs may be improved by having SIB investors funding extend until significantly
after initial returns are (or are not) paid by owners.
Conclusions:
A system dynamics model of the only known operating Social Impact Bond to fund a
prisoner rehabilitation program at the Petersboro prison in the United Kingdom was developed
and validated. The model was analyzed using statistical screening to identify high leverage
parameters for one important performance metric for both the owner and investors. Univariant
sensitivity analysis was then used to describe the impacts of the two highest leverage parameters
that can be used in SIB design. The analysis results were used to investigate two SIB design
issues.
The highest leverage parameters for the final reduction in the prison population (MOJ
performance metric), in decreasing order of influence, were found to be the fractional reduction
in recidivism, maximum cohort size, reference (pre-program) recidivism fraction, and unit
program cost (per participant). The highest leverage parameters for final SIB investor returns
were found to be the fractional reduction in recidivism, unit program cost, unit cost of
conviction, and investor discount rate. These high leverage parameters influence the strength of
the feedback loops that control the prison population and savings captured by the MOJ and
partially paid to investors. To maximize SIB performance designers and managers must
understand and influence the strength of this feedback loop.
Page 21 of 24
The two parameters shared by the performance measures identified with statistical
screening analysis are also two parts of the system that SIB designers can influence: program
effectiveness (reduction in recidivism) and unit program cost. The univariant analysis revealed
that the constraints built into the SIB agreement controlled the relative effectiveness of these
parameters on performance, particularly return limits on investor performance. Univariant
analysis without those constraints indicate that program effectiveness has equal or more
influence on MOJ performance (prison population) and investor performance (IRR) than unit
program cost. This suggests that SIB designers should focus on developing and selecting highly
effective interventions, with less regard for costs (which also might decline over time due to
learning curve effects).
The work also identified two potentially fatal characteristics of the Petersboro SIB
design. First, the delay between the end of investments in the program and information feedback
to investors (through the first returns) about performance could prevent the program from
becoming self-sustaining by creating a temporary increase in the prison population. Reducing the
delay by having the MOJ start funding the program before the testing of the SIB is a
counterintuitive policy that can address this challenge. Second, ending investor funding before
they receive feedback on SIB financial performance may prevent the SIB investors from being
active participants by effectively influencing the system intervention for improved performance
and higher returns. This challenge can be addressed in future SIB-funded programs with longer
SIB-investor funding and should improve as a track record of performance is established.
The current work can be extended with additional analysis of SIB design principles using
the model. It can also be used as the basis for modeling other planned and operational application
of the SIB approach. Finally, the model can be used to model the application of SIBs to other
systems that generate savings from improvements, such as sustainability improvements to built
infrastructure. Continuing to improve the understanding of the dynamics of the application of
Social Impact Bonds will provide the basis for better design and management, leading to
increased benefits from public goods and increased returns for investors.
Page 22 of 24
References
(BTL), Bridges To Life. Goals, Outcomes, and Evaluation. 2011.
http://www. bridgestolife.org/index.php?option=com_content&view=article&:id=7&Itemid=67 (accessed May 09,
2013).
Britt, Bill. "Alabama's Prison Dilemma." Alabama Political Reporter. April 30, 2012.
http://www.alreporter. ives/2011-di ber/832-alab prison-dil html
Cave, Sion, Tom Williams, Darrick Jolliffe, and Carol Hedderman. "Peterborough Social Impact Bond: an
independent assessment." J ustice.gov.uk. May 16, 2012.
http://www justice.gov.uk/downloads/publicati id
bond-assessment.pdf (accessed August 20, 2012).
lysis/moj peterborough-social-impact-
Damnjanovic, Ivan D., and David N. Ford. "Social Impact Bonds for SustainabilityImprovement in Built
Infrastructures." College Station: White Paper, July 08, 2011.
Disley, Emma, Jennifer Rubin, Emily Scraggs, Nina Burrowes, and Dierdre Culley. Lessons learned from the
planning and early implementation of the Social Impact Bond at HMP Peterborough. Research Series, Ministry of
Justice, 2011.
Ford, David N., and Durward K. Sobek. "Adapting Real Options to New Product Development by Modeling the
Second Toyota Paradox." IEEE Transactions on Engineering Management, 2005: 175-85.
Glahn, Drew von, and Caroline Whistler. "Translating Plain English: Can the Peterborough Social Impact Bond
Construct A pply Stateside?" Investment Review, 2011: 58-70.
Gruber, Jonathan. Public Finance and Public Policy. New Y ork: Worth Publishers, 2011.
Hatry, Harry. Performance Measurement: Getting Results. 2nd. Washington, D.C.: The Urban Institute, 2006.
Langan, Patrick A., and David J. Levin. "Recidivism of Prisoners Released in 1994." Federal Sentencing Reporter,
2002: 58-65.
Loder, John, Geoff Mulgan, Neil Reeder, and Anton Shelupanov. Financing Social Value: Implementing Social
Impact Bonds. Working Paper, The Y oung Foundation, 2010.
Lyneis, James M., and David N. Ford. "System dynamics applied to project management: a survey, assessment, and
directions for future research." System Dynamics Review, 2007: 157-89.
Marvell, Thomas B., and Carlisle E. Moody. "The impact of out-of-state prison population on state homicide rates:
displacement and free-rider effects." Criminology, 1998: 513-36.
Marwell, Gerald, and Ruth E. Ames. "Economists Free Ride, Does Anyone Else?" Journal of Public Economics,
1981: 295-310.
Mayfield-Geiger, Sue, and Jean West Rudnicki. "Remarkable Men!" Change Magazine, June 2013: 16-8.
Miraftab, Faranak. "Public-Private Partnerships: The Trojan Horse of Neoliberal Development?" Journal of
Planning Education and Research, 2004: 89-101.
Moynihan, Donald P. The Dynamics of Performance Management: Construction Information and Reform.
Washington D.C.: Georgetown University Press, 2008.
Page 23 of 24
Mulgan, Geoff, Neil Reeder, Mhairi Aylott, and Luke Bo'sher. "Social Impact Investment: the challenges and
opportunity of Social Impact Bonds." The Young Foundation. March 2011. http://www.youngfoundation.org/social-
impact-i jovember-2010 (accessed January 18, 2012).
Osborne, David, and Peter Hutchinson. "Budgeting for Outcomes." Government Finance Review 20, no. 5 (2004):
10-4.
Senge, Peter M. The Fifth Discipline: The Art & Practice of The Learning Organization. New Y ork: Doubleday,
1990.
Social Finance Limited. "Peterborough Social Impact Bond." Social Finance. 2011.
http://www.socialfinance.org.uk/sites/default/files/SF_Peterborough_SIB.pdf (accessed September 15, 2012).
Sterman, John D. Business Dynamics: Systems Thinking and modeling for a Complex World. New Y ork: Irwin
McGraw-Hill, 2000.
Strickland, Pat. "Social impact Bonds - the Pilot at Peterborough Prison." Parliament.uk. November 12, 2010.
www.parliament.uk/briefing-papers/SN05758.pdf (accessed February 15, 2012).
Taylor, TRB, Ford, DN and Ford, A. “Improving model understanding using statistical screening”. System
Dynamics Review. Vol. 26, No. 1. Pp. 73-87. Jan.-March, 2010
Young Foundation “Social Impact Bonds In Health” Oct., 2010). http://www.youngfoundation.org/social-impact-
bonds-health. accessed May 26, 2011.
Page 24 of 24
