economics series swp 2016/2 towards an internal ......1" " towards an internal market...

Faculty of Business and Law Department of Economics

ECONOMICS SERIES

SWP 2016/2

Towards an Internal Market Based Approach to Cost-Benefit Analyses of the Criminal

Justice System

Andrew Torre

The working papers are a series of manuscripts in their draft form. Please do not quote without obtaining the author’s consent as these works are in their draft form. The views expressed in this paper are those of the author and not necessarily endorsed by the School or IBISWorld Pty Ltd.

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Towards an Internal Market Based Approach to Cost-Benefit Analyses of the Criminal Justice System.

Andrew Torre.1

March 2016.

Abstract.

Shadow prices are required for social impact studies when there is an absence of a market or a market failure. Absolute general and incapacitation deterrence, which is produced by the criminal justice system, satisfies this criterion, since it is a non-traded public good that generates positive externalities. Estimating the dollar value of both types of deterrence necessitates shadow pricing the externalised cost of avoided crimes, or what is the same thing, the value of crime prevention services. The present practice for doing this is to use either a combination of contingent valuation and revealed preference methods, or to import outside estimates of crime externalised costs into the analysis. This article suggests a variation on this theme, which avoids some of the objections to the traditional methods, and is well grounded in microeconomic and the economic theory of institutions. It is based directly on revealed preference estimates of the police and judiciary, and indirectly on persons’ willingness to pay to avoid mortality risks. The former are determined in an internal market like setting with the intervention of defence lawyers, hence the title of this paper. Analytically our analysis yields a ‘supply curve’ of absolute general and incapacitation deterrence, or value of crime prevention services curve. As an example, the methodology is then applied to estimate the value of crime prevention services produced by SA prisons in 2007. Tentatively, these are found to be substantial.

1 Department of Economics. Deakin University. The author is grateful to Dr. Ching-jen Sun, Dr. Cong Pham for fruitful discussions in the preparation of this paper, and to Dean Vogdanos who read and provided valuable comments on an earlier version of this work from a legal perspective. Any errors and omissions are the sole responsibility of the author.

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1. Introduction.

The criminal justice system (CJS) is costly to run. For example in 2013-14, total real recurrent government expenditure in Australia was $13.3 billion: $10.182 billion was spent on police services (68.2%); $767 million on the criminal courts (5.1%) and $3.369 billion on corrective services (22.6%) (Productivity Commission, 2015).2 Since criminal justice is part of the not for profit non-market sector, its services are valued at the cost of supply by the Australian Bureau of Statistics (ABS).3 Consequently using this metric the industry produced approximately $13.318 billion worth of services at an equivalent cost, and therefore just broke even in 2013-14. While this fact is not very informative on its own it does give rise to several interesting economic issues, which include the valuation of the system’s final output and the social returns generated from the relatively large amount of expenditure on the three sectors of the criminal justice industry. Assessing these and related matters necessitates a careful economic evaluation that is well grounded in the relevant economic, institutional and criminological theory. There are numerous cost-benefit analyses of the industry, and a comprehensive and contemporary overview of the issues and methodological problems that arise from these is provided by Dominguez and Raphael (2015). Extant studies suggest that prisons are the least cost effective sector, and as a consequence, it is usually inferred that their operation worsens social welfare.

An example of the current approach to the analysis of CJS institutions is provided by Donohue 111’s (2009) economic appraisal of prisons based on the review of a large number of studies that are supplemented with his own estimates of the marginal social benefits (MSB) and marginal social cost (MSC) of imprisoning one extra offender. A value for MSB is derived by computing the number of deterred crimes multiplied by their social cost. Crimes avoided are estimated using a deterrence elasticity, which is defined as:

C

P*

P

Ce

∂

∂=

C is the number of crimes and P the number of prisoners. The elasticity estimates, which can be computed as aggregates of all crime types or as crime-specific, are ‘obtained by regressing the crime rate on the state prison rate (either once lagged or contemporaneous to the crime variable)’.4 The marginal effectiveness of imprisonment is found by setting P∂ = to 1 (one additional prisoner) and solving the expression for C∂ (one additional crime). This yields C/P)(eC =∂ . Sometimes the expression is adjusted for non-reported crime:

C∂− =P

C*

R

e

R is the fraction of crimes reported. This expression is then multiplied by the average social cost (ASC) of each prevented crime, to find the MSB of prison, which is:

2 Table C.1. 3 For profit prisons, which are becoming more popular in Australia are not discussed, although their presence does not fundamentally change the analysis. 4 04.

3

)P

C*

R

e(ASCMSB =

MSB is then compared with the short run marginal social cost of incarceration (MSC); if MSB > MSC, then there is a net social gain from imprisoning the last offender; conversely if MSB < MSC, there is a net social cost. If MSB = MSC net gains are maximised and the system is operating optimally in the short run.5

On the basis of extensive simulations utilising his methodology, Donohue 111 demonstrated that in the case of low social cost crimes, too many persons had been incarcerated since MSC > MSB; conversely too few people had been imprisoned after being convicted of high social cost crimes, since MSB > MSC.6 He concluded that: ‘based on which figures one adopts for the elasticity of crime with respect to incarceration, the cost of crime and the marginal cost of an added prisoner, one could justify essentially any conclusion about incarceration, from massive reductions in the number of inmates to dramatic increases.’7 Two main problems have been identified with current methodological practices:

first, for a given elasticity the computation is very sensitive to the term P

Cin the expression for MSB.

This is because if prisoners increase at a much faster rate than crimes, then the number of these that are prevented will become continuously smaller. Second, three valuation issues relating to the availability and quality of data arise: the econometric estimation of the deterrence elasticity, the estimation of the social cost of each crime and the computation of the marginal social cost of an additional prisoner.

Abrams (2014) has reached virtually the same results about the effectiveness of incarceration, following his estimates of the social benefits and costs of a 1 percent increase in all serious crime prison sentences, where the net annual benefit of doubling sentence lengths is given by:

Net Benefit = η crime * ‘Crime’ * C crime – C prison * ‘Prisoners’8

η crime is the total elasticity of crime and is equal to: Inc

life

0SDGD ηdsent(sent)fηη ++ ∫ .

The total elasticity consists of three partial elasticities:

GDη is the elasticity of crime with respect to sentence length due to general deterrence,

SDη is the elasticity of crime with respect to sentence length due to specific deterrence;

5 As a practical illustration consider homicide. The social cost of murder has been estimated to be $2.7 million in 2011 dollars (Smith et. al., 2014. Page 15). On the assumption of a deterrence elasticity of -0.5, no unreported offences, 20 reported murders and 100 prisoners, the MSB of one extra prisoner would appear to be equal to:

$270,000.)100

20*0.5(2,700,000 =− This seems very low and would certainly be less than the MSC of

incarcerating the offender for the effective court sentence. 6 Table 9A.3, Page 319. The parameter values underpinning these calibrations are: -0.05 to -0.4 for the elasticity values, and $25,797 to $80,000 for the marginal social cost of imprisoning an extra offender. The avoided social cost of a crime, as a consequence of deterrence (MSB of imprisonment), is defined as the sum of (i) costs suffered by the victim such as pain and suffering, (ii) the lost productivity of incarcerated prisoners and (iii) the criminal justice system costs that accompany the crime. (Page 290). The dollar values are obtained from other studies and Donohue 111’s own estimates. 7 Page 305. 8 Page 82.

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Incη is the incapacitation elasticity;

Ccrime is the exogenously determined cost of the mean crime;

Cprison is the cost of a year of prison;

‘Crime’ is the number of crimes committed annually;

‘Sent’ is the sentence length, and

‘Prisoners’ is the number of offenders incarcerated.

Abrams concluded that: ‘at the low end, assuming a total elasticity of 0.25 and a low cost of the average crime, the cost of a one percent sentence increase would exceed the benefits by over $900 million. At the other extreme, using the high cost of crime value and the high range of elasticity estimates, implies that the sentence increase would yield a net benefit of almost $2.5 billion’.9 In both of these studies, estimates of crime externalised costs were based on external studies by Cohen and Piquero (2009), Miller, Cohen and Wiersema (1996) and Cohen, Rust, Steen and Tidd (2004), supplemented with the researchers’ own estimates.

The objective of this article is to supplement these methodologies using an alternative framework. Specifically, we theoretically derive the supply curve of criminal justice system (CJS) services from first principles by carefully defining final output, using the internal valuations of the key system decision makers. In other words, just as managers in a firm decide how much output to produce given their objective of input cost minimisation or profit maximisation, the police and judges similarly make decisions about how much deterrence to supply, in a non-profit setting. Instead of profit maximisation or input cost minimisation, their objective is akin to output maximisation, or externalised cost minimisation.10 Deterrence is the final output of the CJS, not for example, the number of arrests, committals to the higher courts or people imprisoned, which are really inputs into the production of deterrence. Valuing CJS final output therefore necessitates estimating the avoided externalised costs of crime. Usually these are inferred using outside or exogenous estimates of crime negative externalities, as in the studies by Donohue and Abrams, or alternatively by estimating the community’s WTP for crime prevention, using methods discussed in the last section of this paper. We analyse and solve the problem differently, obviating the need for independent costings or gauging community preferences, by using the assessments of the police and judiciary of the relative harm from crime, which they must make implicitly in their capacity as agents of the government and wider society. Our analysis has implications for cost-benefit methodology for the entire CJS sector, as well as for each of its component parts. To our best knowledge, these issues have not yet been systematically addressed in the literature in a unified framework.

9 Page 85. In the calibration exercise, the parameter values used by Abrams were: ;η 10.0GD − SDη between -0.05

and -0.30 and Incη -0.10. The total elasticity from a 1 percent increase in sentence length ranged from -0.25 to -0.5. The number of crimes committed annually in the USA in 2005 and adjusted for underreporting was 28,892,802, which was used for the ‘crime’ parameter, and in 2006 the mean prison sentence length was 37.2 months. A total incarceration cost per prisoner of $38,600 a year was used, which consists of direct costs + cost of foregone wages + the disutility from lost freedom + the impact on family and friends + capital costs. 10 This is equivalent to sales maximisation in the marginalist economic theory of the firm.

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2. The Supply Curve of Crime Prevention Services.

It is common knowledge that the supply curve for a traded good can be derived directly from the firm’s

profit function or indirectly from its production function. In the former situation, if the firm’s profit

function is given by π = PY – W L (P), where Y = output, W = the wage rate and L = labour input, or

more simply π = R – C, i.e. profit = revenue minus cost, then differentiation of the profit function with

respect to output price P, yields the firm’s supply function. Consequently the supply curve is given by:

P

LWY

P ∂

∂−=

∂

∏∂ (Hazari and Tran-Nam 1991). Alternatively, for a short run Cobb-Douglas

production function: 1/2L2/1

KX−

= , where K

2XL = and short run marginal cost = −

K

xw2, the supply

curve is equal to: −=

K

xwxP

*2 (Binger and Hoffman 1998). These solution techniques obviously cannot

be applied to a non-traded, non-excludable and non-rival in consumption, public good.

Bagaric (2001), who provides a detailed analytical discussion of sentencing theory and practice, identifies four different types of deterrence: specific, general, absolute general, and incapacitation11. The first two are respectively achieved, when offenders do not reoffend as a consequence of their punishment, and when increasing the quantum of penalty reduces the prevalence of the offence. Since it is unlikely that these objectives are attained in practice, specific and general deterrence are not considered to constitute part of the final output of the criminal justice system. Absolute general deterrence measures the impact of punishment on those individuals who are at the margin of lawful and unlawful behaviour. While the number of these potential offenders is not observable at any point in time, the operation of the criminal justice system must continuously deter some of them. The basis for this claim is that if for example, the heavily sanctioned crimes against the person and terrorist offences against the state were legalised, thereby effectively abolishing the penalties they attract, then one could confidently predict that the number of these activities would increase. Absolute general deterrence was also recognised in the classical Roman law as being an appropriate objective of punishment. According to the Roman jurist Gaius:

‘The Principal end of some Sanctions…is…the deterrence of future wrongdoers by exemplary punishment of a past offender (Mendelson, 2014).’12

Incapacitation deterrence arises because incarceration reduces the number of crimes committed given that some prisoners will re-offend upon release. Since prisons physically confine recidivists during the period of their court imposed sentence, we attribute the production of incapacitation deterrence to these institutions. By assuming that the only sanction used by the courts is imprisonment, we are restricting our analysis to the more serious crimes dealt with by the higher criminal courts and excluding Magistrates’ courts.

When the police make decisions about how much effort and how many resources to put into investigating offences, judges consider the type and severity of penalties to impose on convicted

11 General deterrence is also known as marginal deterrence. 12 Page 14.

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offenders, and prison administrators house recidivists, they are all producing deterrence. At the same time, the police and judges are implicitly valuing the externalised cost of crime.

The concept of the value of a statistical life (VSL) is used extensively in economic and social policy analysis, for example in the evaluation of health programs and natural disaster interventions. In both of these policy areas there is a risk of serious injury and death, which necessitates valuing lives saved. Similarly, many crimes result in substantial harm to the person, and in the worst case scenario of murder, actual death of the victim. Therefore as we discuss subsequently, the appropriate estimate of the externalised cost of murder in our framework is the VSL, which is not determined by the police or judiciary. Rather, its source is peoples’ willingness to pay for reductions in mortality risk. In our analysis murder is therefore the numeraire offence, and this forms the basis for converting combined police and judicial valuations of all other crime externalised costs to dollar values. Formally the police, judiciary and prisons jointly maximise the total value of deterrence or output (TVD), or what is the same thing, minimise the externalised cost of crime.13

TVD = VSL [H (O (Ps, P2, Xs, I)) - Ps P2 XS, I (O (Ps, P2, XS, I))] (1)

Where:

TVD = Total value of deterrence.

VSL = Value of a statistical life.

H = The externalised costs of crime.

O = The number of offences.

PS = Pmurder/Poffence, i.e. the standardised offence clearance rate where P is the probability of

apprehension following commission of the offence.

P2 = The probability of imprisonment.

Xs = The standardised sentence in years and is equal to [(X/Ps)*(1/XM)], where X is the mean sentence

for the offence and XM is the mean sentence for murder.

I = The number of prisoners.

In words (1) states that the total value of deterrence or output consists of the total avoided externalised crime costs from apprehending and punishing convicted offenders (the first term), minus the value of the imputed value of the externalised costs of the offenders’ actual committed crimes (term 2).

Expressions for ascertaining decision makers’ valuations of an additional unit of deterrence or output by using calibration techniques, are found by optimising (1). It is set equal to zero and partially differentiated with respect to each of its main arguments, Ps, P2, Xs and I.14

Each of the first order conditions are:

13 Strictly speaking prison administrators do not directly determine their output levels. This is done by the judiciary who decide how often to use the prison sanction. In this sense, prisons can be thought of as agents of the courts. 14 Full derivations are provided in the appendix.

7

0ISX2PO

SP

OI

SX2PSP

SP

O

O

H

SPDTV

=+∂

∂−

∂

∂

∂

∂=

∂

∂ (2)

0IS

XSPO2P

OI

SX2PSP

2P

O

O

H

2PD

TV=+

∂

∂−

∂

∂

∂

∂

∂

∂= (3)

0I2PSPO

SxO

ISX2PSP

SxO

O

H

sXDTV

=+∂

∂−

∂

∂

∂

∂=

∂

∂ (4)

0sX2PS

POIO

ISX2PSPI

OO

HIDTV

=+∂

∂+

∂

∂

∂

∂=

∂

∂ (5)

These are re-arranged, simplified and then multiplied by the VSL to convert them into dollar values.

]ISX2PSP

1e-

ISX2PSP

[VSLsP

MV += (6)

]ISX2PSP

2e-

ISX2PSP

[VSL2P

MV += (7)

]ISX2PsP

3e-

ISX2PsP

[VSLsX

MV += (8)

]ISX2PsP

4e-

ISX2PsP

[VSLI

MV += (9)

In (6) to (9):

MVPs = value of an additional unit of police absolute general deterrence.

MVP2 = value of an additional unit of criminal court absolute general deterrence.

MVXs = value of an additional unit of criminal specific or marginal court deterrence.

MVI = value of an additional unit of incarceration deterrence.

8

The negative elasticities are defined as follows: 0;OsP

sP

O1e <

∂

∂= 0

O2P

2P

O2e <

∂

∂= ; 0

OsX

sX

O3e <

∂

∂= ;

0O

I

I

O4e <

∂

∂= .15

We have already noted the almost unanimous consensus that criminal courts are unlikely to produce ‘marginal’ or specific deterrence, since increasing jail time for an offence does not reduce crime prospectively, consequently, in our analysis, it is not considered to contribute towards the total value of deterrence, and expression therefore (8) becomes redundant.16 The first term of (6), (7) and (9) is negative, given the sign on the deterrence elasticities e1, e2 and e4.17 The transmission mechanism for police absolute general deterrence is individuals’ ex-ante perceptions of the probability of being apprehended, and for court absolute general deterrence, the probability of subsequent punishment by imprisonment, if convicted. Prisons are more problematical. The source of their MVI is that they disrupt the criminal careers of recidivists, and in so doing reduce the overall expected externalised cost of crime. If it was certain that the additional incarcerated offender would not engage in further crime in the time frame equal to the jail sentence, then his or her imprisonment would unequivocally lower social welfare.18 While the marginal social cost of imprisonment would be positive, incarceration deterrence would be effectively zero, and the outcome would be a net social cost. The second term of (6), (7) and (9) is the imputed externalised cost of the offender’s committed crime, as valued by the police and judiciary. Since it is not deterrable, it does not constitute part of the MV of deterrence and is subtracted.19

Since (6), (7) and (9) trace out a trajectory of optimal values, they constitute part of the supply of criminal justice services (absolute general and incapacitation deterrence) curve. However to complete this construction we require a function that maps each of the deterrence variables into the value of the saved externalised costs, and exhibits diminishing returns to deterrence. The following concave function TS satisfies our requirements. Its relationship to (6), (7) and (9) is as follows.

1/2]1/2I4b1/22

P2

b1/2s

P1

b[Is

X2

Ps

PVSLTS ++= (10)

In the bracketed part of expression (10) the deterrence variables Ps, P2 and I impact positively on harm through the number of prevented offences, internally valued by the police and judiciary. The first term of (10) imports into the TS curve these internal valuations of crime externalised costs. The strength of the deterrence is captured in the parameters b1, b2 and b4, and these are the link between the deterrence elasticities in (6), (7) and (9) and output. Plausible values of these can be gleaned from a knowledge of empirical estimates of each of the elasticities e1, e2 and e4 since the relationship between b1, b2 b4, offences, and e1 e2 and e4 is given by:

15 These are easily interpreted. For example e1 the police deterrence elasticity measures the percentage change in offences divided by the percentage change in police offence clearance rates. A value of -0.5 means that a one percent increase in offence clearance rates results in a 0.5 percent decrease in offences. 16 Bagaric (2001) discusses the empirical literature on this point. See also Wan et. al. (2012) discussed subsequently. 17 The first term is the reduction in the externalised cost of crime that follows from clearing, prosecuting and then punishing upon conviction, one additional offence. 18 Unfortunately the committed crime cannot be deterred. It is a sunk externalised cost. 19 Being positive in value it is in effect subtracted from the first term.

9

1/2sP

O1e21b = , 1/2

2P

O2e22b = , ,

2/1I

O4e24b = where O, Ps, P2 and I are evaluated at their mean values.20

Since police, courts and prisons deterrence are generated independently, (10) is additively separable and can be rewritten to give the supply curves of the component parts of the CJS: SPs = VSL Ps P2 Xs I [b1 Ps

1/2]1/2 (11) SP2 = VSL Ps P2 Xs I [b2 P2

1/2]1/2 (12) SI = VSL Ps P2 Xs I [b4 I1/2]1/2 (13) The value of an extra unit of police S*Ps, court S*P2 and prison deterrence S*I is found by differentiating (11) to (13) using a combination of the product and chain rules.

IsX2PVSL1/2]1/2sP1b[]75.0

s4P

5.01b[IsX2PsPVSLPs*S

sPsP

S+==

∂

∂ (14)

IsXsPVSL1/2]1/22P2b[]75.0

24P

5.02b[IsX2PsPVSLP2*S

2P2P

S+==

∂

∂ (15)

2PsXsPVSL1/2]1/2I4b[]0.754I

5.04b[IsX2PsPVSLI*SI

IS +==∂

∂ (16)

While (14) to (16) appear to be complicated expressions, they are easily diagrammed in two dimensional saved externalised costs (output) and deterrence space. The supply curve of a public good is generally presented in the economics literature as an increasing marginal social cost curve that reflects increasing opportunity cost, i.e. additional resources allocated to supplying the public good mean that less are available for alternative uses. Sometimes a horizontal constant cost line is used instead. In these models, the socially optimal or efficient supply of the public good occurs where the collective demand curve found by summing individual demand curves vertically to give total willingness to pay, equals the MSC of supply (Samuelson, 1954; Bergstrom and Goodman; Abelson, 2012).21 If in addition to the MSC line our supply function is introduced, the socially optimal quantity of police, courts and prisons deterrence would be diagrammed as follows:22

20 The proof is as follows. O = b1 Ps

1/2 + b2 P21/2 + b4 I1/2. The apprehension probability elasticity is defined as: e1

= O

sP

sP

O

∂

∂. This is given by

O

sP*11/2

sP1b2

1

sP

O −=

∂

∂, therefore 1/2

sP

O1e21b = . The court probability of imprisonment

elasticity is defined asO

2P

2P

O2e

∂

∂= .This is given by

O

2P*11/2

2P2b2

1 −, therefore 1/2

2P

O2e22b = . The incapacitation

elasticity is defined as:O

I

I

O

4e

∂

∂= . This is given by .

O

1/2-I4b

2

1

O

I*

1-1/2I4b

2

1= Therefore b4 = 1/2

I

O4e2 .

21 Page 189. 22 The WTP of the median voter is a common alternative for representing the demand side in the case of a public good.

10

Ps

ASC

SPs*

WTP (median voter) P*s

P2

ASC Sp2*

WTP (median voter) P*2

$

$

11

The social optima P*s, P*2 and I* are found by equating marginal social benefits (WTP), ASC and S*. It is important to note the distinction between ASC and S* in our formulation of the problem at hand. ASC is the traditional increasing opportunity cost of provision, while S* is the internally valued marginal output measure (absolute general and incapacitation deterrence) of the CJS. What is missing in the usual textbook treatment of the optimal supply of a public good is a final output indicator; instead a cost function is superimposed on the demand function of the median voter, or a collective demand function obtained by vertically summing the preferences of individuals in the community. Ideally all three functions are required. The problem of course is that measurement of intangibles is notoriously difficult, so that intermediate outputs are often used as proxies. Nevertheless in our case, we have measured protection against crime directly using decision makers’ preferences, whom we assume are acting in the public interest and therefore making optimal choices.

The demand curve of the median voter in figure 1 is interpreted as the WTP to reduce the externalised costs of crime, or what is the same thing, for crime protection. The median voter theory of the demand for a public good assumes that the government will provide crime prevention services as long as the median voter is willing to pay the tax price. This is the amount of tax T that is sufficient to cover the average cost of provision, which is why we label the upward sloping cost curve on the left hand side of the back to back diagrams in figure 1 as ASC rather than MSC. The interpretation of figure 1 is straightforward. As an example, the bottom panel would be interpreted as follows. The surplus to society and hence the contribution to social welfare of imprisoning the first offender I1 is $c – $b, since prevented crime costs = $a, the median voter’s maximum WTP is $c and the ASC of incarceration is $b. In figure 1 it is considered optimal to supply an extra unit of deterrence if the median voter’s maximum WTP > the ASC (tax price). However, if instead of taking cognisance of the median voter’s preferences, the government makes decisions about resource allocations to the CJS independently of the electorate, then the median voter’s WTP construct is irrelevant. Under these circumstances, the social welfare maximising decision rule involves comparing S*I with ASC. If S*1 > ASC, it is optimal to imprison an additional offender, and conversely if S*1 < ASC. This seems a more likely scenario given that taxpayers are likely to be more responsive to taxation levels rather than the precise composition of services that they finance. In figure 2 below, given the objective of output maximisation, the optimum is I*s since the surplus from incapacitation deterrence is maximised at this point, i.e. the

b

c

a

I1 I

ASC

SI*

WTP (median voter) I*

Figure 1

$

12

total value of prevented crime ABI*s0 equals the total short run social cost of running the prison system ABI*s0.

3. Police and Judicial Shadow Internal Market Based Pricing of the Externalised Cost of Crime.

The proposition that the police and judiciary provide a combined independent, implicit valuation of the externalised cost of a crime through their own resource allocation decisions and recourse to sentencing law and principles respectively, is consistent with the economic theory of criminal justice system institutions as explicated by Nagin, 1978; Easterbrook, 1983 and Adelstein, 1979. According to this literature, these are to be interpreted as structures designed to evaluate the externalised costs of proscribed behaviour and activities, and then to exact from offenders a roughly equivalent punishment price. These prices are determined in a market like setting by the interaction of police, prosecutors, defence lawyers and defendants engaging in ‘charge bargaining’, and judges imposing personalised and sometimes discounted sentences. An analogy can be drawn with the view of the firm that interprets it as an institution that supersedes the price mechanism, and thereby corrects a market failure, by internalising high transaction cost activities that would otherwise be mediated through the market (Coase, 1937). In the case of the criminal justice system as noted by Adelstein, the market failure is missing markets in negative externalities ‘that would allow victims of crime and wider society to reveal and value all of the economic and other costs imposed upon them’. Instead this task is given to criminal justice system institutions.

Possible internal measures of crime severity are the legislatively prescribed maximum penalty, court determined ‘tariffs’ for specific offences, or the average prison sentence, which is ‘the best proxy for offence seriousness’ (Bagaric, 2015).23 An important underlying basis of court customised pricing of

23 Page 19. Bagaric documents that in relation to the first, the courts have indicated that this is a poor indicator of offence seriousness (Elias v The Queen (2013) 87 ALJR 895; and that in relation to the second, the courts do not adopt uniform pricing of offence types. Furthermore, ‘public opinion is not relevant to offence severity.’

I

$

Figure 2

S*I

ASC

I*s 0

A B

13

crimes is the legal principle of proportional sentencing, which in theory should ensure that judicial sentences, bear a strict relationship to the perceived harm from the offence.24

The proportionality doctrine is enshrined in both the common and statute law. In Hoare v The Queen, the High Court of Australia put the matter in these terms:

A basic principle of sentencing law is that a sentence of imprisonment imposed by a court should never exceed that which can be justified as appropriate or proportionate to the gravity of the crime considered in light of its objective circumstances.25

‘Proportionality also has a statutory foundation in most Australian jurisdictions’ (Bagaric et. al. (2011).26

To reiterate, one of the current practices for shadow pricing crime is to use exogenous or ‘outside’ estimates derived using either ‘bottom up’ or ‘top down’ costing techniques. Bottom up approaches purport to value the harm from a particular crime by identifying and aggregating all of the relevant costs. For example, in the case of rape, victim costs would be medical and mental health care, lost productivity and pain and suffering; while broader community costs would include: criminal justice system costs, avoidance and fear costs by non-rape victims, who take taxis at night, and any costs to the offender’s family (Cohen, 2010). While estimates of victim costs are reasonably obtainable, most of the community costs are not. The top down approach to costing a rape offence would ‘attempt to estimate the total cost from one source only’ (Cohen, 2010). An example of bottom up costing in Australia, is the estimate provided by Rollings (2008) of the cost of one murder in 2005, of $1,915,000. This figure comprises: medical costs $1,740; lost output $1,449,000 and intangible losses $464,000.

We have noted that we equate the externalised cost of murder with the VSL. The standard economic approach to valuing a human life is based on willingness to pay to avoid fatality risk.27 This assumes that reductions in the probability of death due to accident or illness should be valued according to what an individual is willing to pay to achieve the reductions, or is willing to accept in compensation to forgo them. The most common techniques for estimating willingness to pay in this context, are by examining data ‘on the purchase of devices that improve safety’ or ‘the estimation of a hedonic wage model where the dependent variable is the wage, and one of the key explanatory variables is fatality risk’ (Doucouliagos et. al, 2012)28. The authors explain that in relation to the second technique: ‘Labour market studies involve the estimation of a hedonic wage model where the dependent variable is the wage and one of the key explanatory variables is fatality risk. The coefficients on the fatality risk variable are then used to derive the VSL estimates.’29 In their thorough analysis of 39 hedonic wage equation estimates from 37 comparable studies corrected for publication bias, the authors’ most conservative estimate of a VSL in terms of Australian dollars in the year 2,000 was $3.59 million (95% confidence interval $Aus. 1.7 to $Aus. 5.47 million), which was ‘for the typical worker in the entire research literature with sample average income in 2,000.’30

24 In practice, strict proportionality is not attained. Analysis is provided in Bagaric (2015 & 2001). 25 (1989) 167 CLR 348, 354. Extracted from Bagaric et. al. (2011). 26 ‘Crimes Act (1914) (Cth) s 16(A) (2)(k); Crimes (Sentencing) Act 2005 (ACT), s7(1)(a); Crimes (Sentencing Procedure) Act (NSW) 1999, s3(A)(a); Sentencing Act (NT) s5(1)(a); Penalties and Sentences Act 1992 (Qld) s9(1)(a); Criminal Law (Sentencing) Act 1988 (SA) s10(1)(k); Sentencing Act 1991 (Vic), ss5(1)(a), 5(2)(c), s6D(b); Sentencing Act 1995 (WA), s6(1)(a)’. 27 This includes willingness to forego a desirable experience or activity such as skydiving. 28 Page 199. 29 Page 199. 30 Page 204. ‘$3.59 million AUD = $2.74 million US ($US1.3 to $US4.18 million, 95% confidence interval), using purchasing power parity rates’. The OECD PPP adjusted exchange rate is 1.31, which is the number of $US

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For our analysis we adopt a VSL of $16,760,000 million, which is considerably above the upper bound estimate emanating from the Doucouliagos et al. study. The justification for this is that these scholars derived their values from correcting, re-interpreting and re-calibrating a number of studies obtained from workers’ perceptions of workplace fatality risk. However murder, which is a particularly gruesome and unnatural end, is in a very different category. Consequently Abelson (2007), who has recommended a benchmark of $3.5 million 2007 dollars for Australian project evaluations, argues that the VSL is likely to be higher in the case of painful deaths. In a survey based study in America, Cohen and Piquero (2009) estimated a WTP to avoid the social cost of a murder to be $11.8 million in 2007 US dollars = $AUD 16.76 million. This estimate has not been screened for publication and other biases. These are possible, since Cohen and Piquero document that typically, respondents are asked to value a 10% reduction in crime on the assumption that their estimates encompass ‘fear, expected costs of victimisation, anticipated reductions in personal expenditures or avoidance behaviours’ and perhaps somewhat unrealistically ‘criminal justice and offender productivity savings.’31

4. Some Empirics. We have presented and then contrasted the traditional median voter model of public good provision with our ‘internal valuation’ alternative that involves comparing the value of crime prevention with the ASC of providing it. In this section we present some empirical estimates of aspects of the second approach, in order to give readers a feel for the magnitudes of the key model parameters. While the data requirements for calibrating SPs; SP2, SI and S*Ps; S*P2 and S*I appear parsimonious, unfortunately consistent criminal justice data bases across all of the Australian states are not available to produce state by state estimates of the contribution of the police, courts and prisons towards crime prevention. Even though the ABS (2015) collects comprehensive data on the criminal courts for each state annually, comparable police clearance rates are not available. Similarly, econometric estimates of deterrence elasticities are sparse. The relatively few Australian studies of these are usually obtained from regression models where the dependent variable is criminal activity and the independent variables measure deterrence and other drivers of crime. The most recent ones are by Wan et. al (2012) on police and court, and Weatherburn et. al. (2006) on incapacitation deterrence. The former authors obtained estimates of short and long run deterrence elasticities for property and violent crime, by examining data from 153 NSW local government areas over the period 1996 to 2008. They found that the deterrent effect of a one percent increase in the arrest rate and probability of imprisonment on property crime took at least 1.8 years to come to fruition, while in the case of violent crime it was about 2.5 years.32 Their short run police and court elasticity estimates were -0.14533 and -0.1034 respectively.35 Increasing sentence length had no impact, which is, as we have documented, consistent with zero marginal or general deterrence, and implying MVXs in (8) equals zero. Weatherburn et. al. (2006) estimated an incapacitation elasticity of -0.20 for burglary in NSW. Relatively recently, Donohue 111 (2009) has documented and critically examined values of the incapacitation elasticities from what he considers to be the most reliable American studies, and has concluded that ‘the elasticity of crime with respect to incarceration is perhaps most likely to be between -0.10 and -0.15, but it is conceivably within the broader interval between -0.05 and -0.40’.36 Cherry and List (2001) estimated police (probability of arrest) and court (probability of imprisonment) elasticities for aggregate crime of -0.355 and -0.173 respectively.

that would be needed in Australia to buy the same representative basket of goods and services that would cost $100 US in the United States. 31 Page 35. Further methodological detail is provided in Cohen et. al. (2004). 32 Page 14. 33 This is an average of the short run elasticities for each offence category: property offences and violent crime. 34 This is an average of the short run elasticities for each offence category: property offence and violent crime. 35 The police elasticity was measured using the probability of arrest for an offence and the court elasticity using the probability of imprisonment. 36 Page 283.

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Supplementing and then re-engineering information collected by the South Australian Office of Crime Statistics and Research in 2007 with a range of plausible values of the incapacitation deterrence elasticity, makes it possible to estimate the prisons’ supply of crime prevention services in SA.37 Using Donohue’s work, our simulation strategy is to choose -0.4, -0.15, -0.10 and -0.05 as our elasticity values and apply these uniformly across all offence groupings.38 Parameter values and calibration results are presented in Tables 1 to 4, with extensive footnotes providing details about sources and definitions. Table 4 provides the combined police and judicial average monetary valuations of the externalised cost of an offence in each of the stipulated categories; for example the average externalised cost of a fraud offence was considered to be $1,297,224, while the total externalised cost of serious crime in SA in 2007 was jointly valued at approximately $28 million. Table 1: Parameter Values.

Offence Sentence39 Ps40 XS P2

41 O42 I43 b444

b445 b4

46 b447

Murder 14.44 1 1 1 14 10 0.44 0.88 1.32 3.54 Against the person 2.45 1.43 0.12 0.49 201 79 2.26 4.52 6.78 18.09 Sexual offences 3.28 1.60 0.14 0.62 192 74 2.23 4.46 6.69 17.85 Robbery/extortion 3.22 2.86 0.08 0.64 115 46 1.69 3.39 5.08 13.56 Criminal trespass 2.46 6.01 0.03 0.47 241 74 2.80 5.60 8.40 22.41 Fraud 1.58 2.25 0.04 0.86 13 6 0.53 1.06 1.59 4.24 Larceny/receiving 1.16 5.65 0.014 0.42 35 22 0.74 1.49 2.23 5.96 Property damage 1.61 6.29 0.017 0.35 27 6 1.10 2.20 3.30 8.81 Against good order 0.84 1.38 0.042 0.26 107 24 2.18 4.36 6.55 17.47 Drugs 1.83 1.00 0.13 0.29 285 71 3.38 6.76 10.14 27.05 Other 0.78 1.19 0.045 0.36 20 8 0.70 1.41 2.12 5.65

37 No subsequent years of data have been forthcoming. 38 Donohue used incapacitation elasticity values between -0.5 and -0.4 and Abrams -0.10, in their simulations. 39 This is the mean prison sentence (non-parole period) in years imposed by the court. Table 3.12. SA Office of Crime Statistics. 40 The probability of apprehension is measured as the clearance rate of offences in 2007 recorded in 2007. The clearance rate for murder is set equal to 1. The clearance rates for each offence group in Table 1 were: 0.70; 0.62; 0.35; 0.17; (Table 4.1). 0.44; 0.18; 0.16 ((Table 4.9). 0.73 (Table 4.19); 0.99 (Table 4.15); 0.84 (Table 4.20). The Tables in parentheses refer to the relevant source in the SA Office of Crime Statistics publication. 41 Percentage of offenders sentenced to immediate imprisonment. Tables 3.12 and 3.13. SA Office of Crime Statistics. 42 Total number of persons charged and dealt with in the higher courts. Table 3.1. SA Office of Crime Statistics. The actual number of offences per person is not available so this proxy will be an underestimate. 43 Number of convicted offenders sentenced to immediate imprisonment. Table 3.12. SA Office of Crime Statistics.

44 1/2I

O4e24b = . e4 = -0.05. In the calibration exercise the absolute value of each elasticity is used.

45 e4 = -0.10. 46 e4 = -0.15. 47 e4 = -0.40.

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Table 2: Estimates of the Supply of Incapacitation Deterrence SI.

Offence S148 SI

49 SI50 SI

51 TSCI52

Murder $197,697,124 $279,585,954 $342,421,464 $560,758,216 $16,606,000 Against person 498,979,179 705,651,809 864,243,434 1,411,693,859 22,258,250 Sexual offences 754,407,163 1,066,892,841 1,306,671,536 2,134,383,633 27,912,800 Robbery/extortion 382,208,772 541,323,831 662,657,555 1,082,647,663 17,033,800 Criminal trespass 515,805,851 729,459,630 893,401,941 1,459,244,876 20,934,600 Fraud 8,868,332 12,541,716 15,360,402 25,083,432 1,090,200 Larceny/receiving 22,821,490 32,383,313 39,616,907 64,766,625 2,934,800 Property damage 6,177,703 8,736,591 10,700,096 17,483,108 1,110,900 Against good order 19,809,250 28,014,510 34,336,849 56,077,190 2,318,400 Drugs 239,412,405 338,580,271 414,674,450 677,285,745 14,941,950 Other 3,637,035 5,161,881 6,329,456 10,332,911 717,600 Total 2,649,816,304 3,748,332,347 4,590,414,090 7,499,757,258 127,859,300

48 Using a value of b4 corresponding to e4 = 0.05. In effect each of the elasticities adopted are assumed to be averages of the offence group. 49 Using a value of b4 corresponding to e4 = 0.10. 50 Using a value of b4 corresponding to e4 = 0.15. 51 Using a value of b4 corresponding to e4 = 0.40. 52 Estimated at $115,000 a year multiplied by the unadjusted mean sentence and the number of inmates in columns 1 and 6 of Table 1, and based on: (i) direct operating cost/year of incarcerating an offender: $84,497 (Productivity Commission, 2008) and (ii) indirect costs of $35,000 a year based on Donohue 111. The indirect costs are the lost income and productivity of prisoners, the value of lost leisure time, the costs imposed on any family, post incarceration costs of a possible decline in labour market earnings and the deadweight loss from taxes used to finance prisons. Donohue 111 estimated lost productivity equal to $8,000 a year and $25,000 for intangibles in 2009. The full value of lost wages during incarceration are adjusted downwards since the disutility of work and the costs of feeding, clothing and housing the prisoner are avoided. The $8,000 cost includes the lost tax payments on legally earned income and expenditure to support others. (Pages 297, 300 and 301). According to the Australian Institute of Health and Welfare (2010) Australian prisoners have lower levels of educational attainment and poorer health (mental health problems, communicable diseases, alcohol misuse, smoking and illicit drug use) relative to the rest of the community. Seventy five percent had completed year 10 or less and 43% reported suffering a head injury that resulted in a loss of consciousness. These unfortunate and grim findings suggest that the typical Australian prisoner has a low opportunity cost of time during incarceration and dismal post release labour market prospects.

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Table 3: Estimates of the Value of an Extra Unit of Incapacitation Deterrence S*I. Offence S*I

53 S*I54 S*I

55 S*I56 MSCI = ASCI

57 Murder $13,896,658 $19,652,842 $24,069,717 $39,417,190 $1,660,600 Against person 2,648,205 3,745,128 4,586,826 7,492,326 281,750 Sexual offences 4,344,863 6,144,565 7,525,525 12,292,574 377,200 Robbery/extortion 3,988,075 5,648,327 6,914,358 11,296,655 370,300 Criminal trespass 2,970,685 4,201,183 5,145,378 8,404,242 282,900 Fraud 1,180,491 1,669,467 2,044,671 3,389,935 181,700 Larceny/receiving 598,722 849,577 1,039,351 1,699,155 133,400 Property damage 822,333 1,162,955 1,424,393 2,327,231 185,150 Against good order 466,137 659,218 807,991 1,319,569 96,600 Drugs 1,452,057 2,053,519 2,515,036 4,107,797 210,450 Other 337,905 479,574 588,050 959,998 89,700

Table 4: Combined Police and Judicial Estimates of the Externalised Cost of an Additional Crime.

Offence Externalised Cost Relative valuations58 Murder $16,760,000 66 Against the person 1,409,248 5.5 Sexual offences 2,327,629 9 Robbery/extortion 2,454,200 9.7 Criminal trespass 1,420,259 5.6 Fraud 1,297,224 5 Larceny/receiving 556,801 2.2 Property damage 627,251 2.48 Against good order 252,566 1 Drugs 631,852 2.5 Other 323,099 1.28 Total 28,060,129

5. Discussion and Conclusions.

Donohue and other authors such as Abrams have provided us with a valuable framework for considering the difficult problem of measuring the economic value of deterrence. Traditionally, this is achieved by importing into the analysis outside independent estimates of the externalised cost of different crimes by sociologists, criminologists and economists, and this technique is adopted by them. Our contribution to the subject is to supplement this methodology by clearly distinguishing between absolute general and incapacitation deterrence as final output concepts, measuring the value of these from the decisions of the police and judiciary, and then using these results to calibrate a public goods provision model that does not rely on the median voter principle, or on WTP estimates of the community to prevent crime. Table 3 suggests tentatively that in 2007 the prison sanction was underutilised in SA across all offence categories. The estimated value of total incapacitation deterrence is from approximately $2 to $7 billion (Table 2), which was produced at an estimated short run social cost of $127.8 million.59 Even though two of the key parameters require more careful measurement (in particular the incapacitation elasticity across offence categories and the social cost of imprisonment), the positive gap between the value of

53 Using a value of b4 corresponding to e4 = 0.05. 54 Using a value of b4 corresponding to e4 = 0.10. 55 Using a value of b4 corresponding to e4 = 0.15. 56 Using a value of b4 corresponding to e4 = 0.40. 57 The ASC is TSC divided by the number of inmates. 58 The least serious offence was considered to be offence against good order. Murder was considered to impose 66 times more harm on the community, offences against the person 5.5 times more harm etc. 59 The Productivity Commission (2008) gives the 2006-07 recurrent cost of running SA jails equal to $108,306,000. This is not an estimate of social cost, since it excludes the indirect costs discussed in footnote 52.

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crime prevention services produced by the SA prisons and short run social cost is significant.60 It is unlikely that our chosen values for elasticity and social cost diverge markedly from their true underlying average values, since these have been benchmarked against high quality studies to ensure their plausibility. Even though they are American empirical results, the socio-economic characteristics of prisoners including recidivism rates and post release prospects are unlikely to be very different.61 In fact our elasticity values imply very conservative estimates of crimes prevented during the average incarceration period. The implied averages can be found by reverse engineering the elasticities at the mean values of O and I in Table 1. For example in the case of murder, assuming an incapacitation

elasticity of -0.40, our upper bound estimate14

10*

ΔI

ΔO0.40 =− . Solving for

ΔI

ΔO yields -0.56.

Multiplying -0.56 by the average murder sentence of 14.44 years suggests that on average 8 murders are prevented as a consequence of imprisoning the average offender. Table 5 shows the corresponding estimates for the other offence groups and elasticity values.

Table 5: Average number of offences prevented implied by the incapacitation elasticities.

Offence e4 = -0.05 e4 = -0.10 e4 = -0.15 e4 = -0.40 Murder -1 -2 -3 -8 Against person -0.31 -0.62 -0.93 -2.5 Sexual offences -0.42 -0.85 -1.27 -3.4 Robbery/extortion -0.4 -0.8 -1.2 -3.2 Criminal trespass -0.4 -0.8 -1.2 -3.2 Fraud -0.17 -0.34 -0.51 -1.36 Larceny/receiving -0.09 -0.18 -0.27 -0.74 Property damage -0.36 -0.72 -1.08 -2.9 Against good order -0.22 -0.44 -0.67 -1.78 Drugs -0.36 -0.73 -1.10 -2.93 Other -0.098 -0.2 -0.3 -0.8

On the production side, the institutions of the criminal justice system constitute a complex and interdependent vertically integrated production process. The real final output of the CJS is a composite pure public good that is non-rival in consumption, non-excludable and generates significant positive externalities. It is common in the economic literature to analyse competitively supplied private goods in a demand and supply framework, and the history of economic thought provides fascinating insights into the development of the complex theory that underpins the derivation of these analytical tools. An example that thoroughly analyses the demand side from a historical and primal perspective is Creedy (1992). Sgro (1986) performs a similar feat, from the dual perspective, and then applies it to the pure theory of international trade. In the case of pure public goods, supply curves are generally taken to be equivalent to a constant (or upward sloping) marginal cost = average cost of provision function. We

60 In Australia, very little is known about the true MSC of processing a convicted offender through the criminal justice system. Research into appropriate costing methodologies for computing CJS enforcement and processing costs on a consistent basis across the states, is therefore essential, if CBA studies of the CJS in Australia are to advance further. A good starting point is the very recent costing of community justice centres by Morgan and Brown (2015). 61 See also footnote 56. Recidivism rates are high in Australia. From Table 3.26 of the SA Office of Crime Statistics, the percentage of offenders in each offence group who had one or more previous imprisonments was: (a) Against the person: 0.32; (b) Sexual offences: 0.22; (c) Robbery/extortion: 0.43; (d) Criminal trespass: 0.42; (e) Fraud: 0.15; (f) Larceny/receiving: 0.46; (g) Property damage: 0.37; (h) Against good order: 0.33; (i) Drugs: 0.24 and (j) Other: 0.55. No data is available on the average number of offences committed by a recidivist in each offence category. An exception is the Weatherburn et. al (2006) study that found that the career burglar commits on average 38 burglaries a year in NSW.

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have suggested an alternative but related way of modelling and valuing the supply of criminal justice system services.

Economic value is driven by willingness to pay and willingness to supply, or demand and supply prices, which are revealed in and determined by the market, in the case of a traded good or service. However when a service does not produce marketed output, recourse is made to non-market valuation techniques for gauging WTP. In the median voter model of public good supply, the median voter’s valuation of a marginal unit of deterrence determines its monetary value. More generally, demand prices reflecting voters’ preferences are gauged directly by asking them to identify their maximum willingness to pay; or indirectly by observing relevant aspects of their behaviour, such as purchasing decisions. The first method is known as contingent valuation (CV) and the second revealed preference.

It is well known and accordingly documented that when directly questioned about their preferences, individuals have incentives to misrepresent these. Subjective valuations based on ex ante willingness to pay or willingness to accept compensation, are subject to what Cohen (2010) calls ‘hypothetical bias.’62 The two possible reasons advanced for this are: ‘warm glow’ or ‘acting strategically’ in order to unduly influence outcomes.63 The former manifests itself when the respondent responds positively to improving a social ill, or proffers a high value because ‘people want to feel good about being altruistic’, or it is thought that ‘this is what the interviewer wants to hear.’64 The usual outcome of strategic behaviour is an overstated willingness to pay, since any relatively small fixed payments, usually extracted through the tax system, will ‘be independent of any stated bid’.65 Underpinning these concerns are three related matters. In relation to crime these are: whether or not the ‘public has adequate information about the risk and consequences of crime;’ ‘the advisability of using values based on ex ante stated preferences when people generally adapt to bad events ex post,’ and whether ‘crime or policies to reduce it’ should be valued.66

A type of hybrid of the CV and revealed preference methodologies is the life satisfaction survey technique. An example is provided by Ambrey et al. (2012) in which the authors study how property crime affects individuals’ life satisfaction. They estimate their implicit willingness-to-pay to decrease its level in their local government area, which is said to proxy the intangible cost of property crime. The claimed advantages of the methodology are that ‘it does not rely on housing markets being in equilibrium’ and rather than being asked to value an intangible bad, ‘individuals are asked to evaluate their life satisfaction, a less cognitively demanding task’67 Furthermore, ‘there is no reason to expect strategic behaviour or social desirability bias to influence valuations,’ and individuals are not required to reveal ‘stated fears of criminal victimisation’.68 Reservations about the approach include, inter alia the inclusion of absolute rather than relative income as an explanatory variable in life satisfaction regressions, the specification of the income variable as exogenous, when in fact it may be endogenous, and self-selection bias in the location decision.69

The final recognised technique for valuing willingness to pay is ‘the third party method, which uses a combination of estimates of cost-of-illness and civil jury awards’ (Roman, 2010). Since ex post victim compensation is based on willingness to accept and not willingness to pay, this technique is said to

62 Page 100. 63 Ibid. Page 101. 64 Idem. 65 Idem. 66 Ibid. Pages 103-104. 67 Idem. Page 4. 68 Idem. 69 Page 6. ‘The study found that the average implicit willingness-to-pay, in terms of annual household income, to decrease the level of reported property crime by one offence per 1000 residents in the LGA in the previous 12 months is $3,213 (90% confidence intervals of $765 to $5,661).’ (Page 15).

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violate ‘a fundamental assumption from price theory that choices about the use of scarce resources are based on expectations of utility, and thus precede the transaction.’70 In addition too much emphasis is placed on victims’ ‘current context’ in the compensation exercise, for example their employment status71; true social costs are not measured, and more generally, ‘while the resulting estimates are a useful metric for comparing policies or programs, the absolute values produced by these estimators are the product of an approach without any theoretical support.’72

Our figure 2, which resembles what Roman calls a market based approach to cost-benefit analysis obviates the need to utilise contingent valuation and voter revealed preference valuation techniques. Instead it substitutes police and judges’ revealed preferences as agents of the community whom they serve, through the provision of crime prevention services. These preferences are likely to be more consistent over time, and subject to minimal strategic behaviour and fewer of the biases identified in our brief literature review of CV and revealed preference techniques. Also definitional problems that continue to plague the concepts of social and externalised cost in the external cost of crime studies take on a different form.73 While Roman points out that ‘the third party’ method of valuation has no theoretical support, this is not the case with our proposed methodology. In addition decision makers’ revealed preferences determined in internal market like institutions are much more cost effective to obtain. Our analysis, which suggests that expenditure of about $127m generated social benefits of $2 to $7 billion is only the starting point for a true cost-benefit study. Further work is required for a full study. It would necessitate examining whether alternative uses of these funds could produce even higher social benefits by investing them in non-custodial based crime prevention programs. This inquiry is outside the scope of this study.

70 Page 194. 71 Page 194. 72 Page 198. 73 Donohue and Abrams each employed substantially different definitions of ‘the social costs of crime.” See footnotes 6 and 9 respectively. In our formulation of the problem, definitional issues are dealt with in sentencing law as developed, refined and applied by the judiciary. While Appeal Courts play an important part in reducing divergences between jurisdictions, Bagaric (2015) documents the inconsistencies in judicial pricing of offences.

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Wan, W, S. Moffatt, C. Jones and D. Weatherburn (2012). The effect of arrest and imprisonment on crime. Contemporary Issues in Crime and Justice. Number 93.

Weatherburn, D, J. Hua and S. Moffatt (2006). How much crime does prison stop? The incapacitation effect of prison on burglary. Contemporary Issues in Crime and Justice. Number 93.

23

Appendix.

TVD = VSL [H (O (PR, P2, Xs, I)) - PR P2 XS, I (O (PR, P2, XS, I))] (1)

0ISX2PO

RP

OI

SX2PRP

RP

O

O

H

RPDTV

=+∂

∂−

∂

∂

∂

∂=

∂

∂

ISX2PO)ISX2PRPO

H(

RP

O−=−

∂

∂

∂

∂

ISX2PRP

RP

O

ISX2PO

O

H+

∂

∂=

∂

∂

Multiplying each term by RPRP

ISX2PRPRPRP

RP

O

RPRP

ISX2PORPRP

O

H+

∂

∂=

∂

∂

Noting that MECOH=

∂

∂ is the marginal externalised cost of one additional crime and the

reduction in MEC due to deterrence is the marginal value of a unit of police deterrence MVPs:

ISX2PRP1e

ISX2PRPPs

MV +−

=

Where RP

O

ORP

1e

10;

ORP

RP

O1e ∂

∂=<

∂

∂=

I]SX2PRP1e-

ISX2PRP[VSLPs

MV +=


24

0IS

XRPO2P

OI

SX2PRP

2P

O

O

H

2PD

TV=+

∂

∂−

∂

∂

∂

∂=

∂

∂

ISXRPO)IsX2PRPO

H(

2P

O−=−

∂

∂

∂

∂

2P

O

IsXRPOIsX2PRPO

H

∂

∂

−=−

∂

∂

IsX2PRP

2P

O

IsXRPO

O

H+

∂

∂=

∂

∂

Multiplying each term by 2P2P

ISX2PRP2P2P

2P2P

2P

O

ISXROP2P2P

O

H+

∂

∂=

∂

∂

Noting that MECO

H=

∂

∂ is the marginal externalised cost of one additional crime and the

reduction in MEC due to deterrence is the marginal value of a unit of absolute general court deterrence MVP2:

I]SX2PRP2e-

ISX2PRP[VSLP2

MV +=

Where 2P

O

O2P

2e

10;

O2P

2P

O2e ∂

∂=<

∂

∂=

25


0I2PRPO

Sxo

ISX2PRP

SxO

O

H

sXDTV

=+∂

∂−

∂

∂

∂

∂=

∂

∂

I2PRPO)ISX2PRPO

H(

sX

O−=−

∂

∂

∂

∂

ISX2PRP

SX

O

I2PRPO

O

H+

∂

∂=

∂

∂

Multiplying each term by sXsX

IsX2PRPSXSX

SXSX

SX

OSXSXI2PRPO

O

H+

∂

∂=

∂

∂

IsX2PRP

sX

O

IsX2PRPsX

O

O

H+

∂

∂=

∂

∂

IsX2PRP3e

IsX2PRP

O

H+

−=

∂

∂

Where sX

O

OsX

3e

10;

OsX

sX

O3e ∂

∂=<

∂

∂=

Noting that MECOH=

∂∂ is the marginal externalised cost of an extra crime, and the reduction

in MEC due to deterrence is the marginal value of a unit of court sentence length deterrence MVXs:

I]SX2PRP3e-

ISX2PRP[VSLXs

MV +=

26


0sX2PR

POIo

ISX2PRPI

OO

HIDTV

=+∂

∂−

∂

∂

∂

∂=

∂

∂

sX2PRPO)ISX2PRPO

H(I

O−=−

∂

∂

∂

∂

ISX2PRP

I

Os

X2PRPO

O

H+

∂

∂=

∂

∂

Multiplying each term by I

I

IsX2PRPI

I

I

I

I

OI

Is

X2PRPO

O

H+

∂

∂=

∂

∂

IsX2PRP

I

O

IsX2PRPI

O

O

H+

∂

∂=

∂

∂

IsX2PRP4e

IsX2PRP

O

H+

−=

∂

∂

Where I

O

O

I

4e

10;

O

I

I

O4e ∂

∂=<

∂

∂=

Noting that MECOH=

∂∂ is the marginal externalised cost of an extra crime, and the reduction

in MEC due to deterrence is the marginal value of a unit of incapacitation deterrence MVI:

I]SX2PRP4e-

ISX2PRP[VSLI

MV +=

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