What does cost-benefit analysis add to decision making? Evidence from the criminal justice literature

What does cost-benefit analysis add to decision making?Evidence from the criminal justice literature

Kevin Marsh & Aaron Chalfin & John K. Roman

Published online: 12 April 2008# Springer Science + Business Media B.V. 2008

Abstract This paper asks whether undertaking a cost-benefit analysis providesadditional information to policy makers as compared to an analysis solely of theeffect of an intervention. A literature review identified 106 evaluations of criminaljustice interventions that reported both an effect size and measures of net benefit.Data on net benefit and effect size were extracted from these studies. We found thateffect size is only weakly related to net benefits. The rank order of net benefits andeffect size are minimally correlated. Furthermore, we found that the two analyticmethods would yield opposing policy recommendations for more than one in fourinterventions. These bi-variate findings are supported by the results of multivariatemodels. However, further research is needed to verify the accuracy of the standarderrors on net benefit estimates, so these models must be interpreted with caution.

Keywords Cost-benefit . Criminal justice interventions . Economic efficiency .

Economic evaluation . Decision making

Introduction

This study assessed the contribution that cost-benefit analysis can make to publicpolicy decision making. Specifically, it asked the following question: Doesundertaking a cost-benefit analysis provide additional information to policy makerscompared to an analysis solely of the effect of an intervention?

J Exp Criminol (2008) 4:117–135DOI 10.1007/s11292-008-9049-1

A. Chalfin : J. K. RomanUrban Institute, Washington, DC, USA

K. Marsh (*)Matrix Knowledge Group, Epworth House, 25 City Road, London EC1Y 1AA, UKe-mail: [email protected]

Why is cost-benefit analysis important?

Cost-benefit analysis (CBA) is concerned with both measuring the effectiveness ofan intervention and whether an intervention is efficient in that the benefits of theintervention are greater than the costs (Barnett and Escobar 1987; Dhiri and Brand1999; Cohen 2000; Welsh and Farrington 2000b; Roman and Butts 2005; Swaray etal. 2005). In a cost-benefit analysis, the effects—the outcomes of an intervention—are valued in standardized monetary units, such as the dollar or the pound, andcompared with the costs of the intervention’s inputs. This approach creates astandardized measure that allows a direct comparison of two or more interventions,even if those interventions vary in their goals and objectives and targetheterogeneous populations and outcomes.

Economists make a number of arguments in favour of analysing the costs andbenefits of criminal justice interventions. First, even though an intervention mayyield positive outcomes (such as desistance from crime and increases in pro-social behaviour), the cost of the intervention may, nevertheless, outweigh theintervention’s benefits. Moreover, an alternative intervention may achieve thesame outcomes for a lower cost. Second, whereas observational studies examineoutcomes one at a time, cost-benefit analysis considers all outcomes jointly,using the standardized (monetized) estimates of costs and benefits as weights thatgenerate a single measure of intervention effectiveness. Third, CBA allows thevaluation of hard-to-observe outcomes, such as fear, pain and suffering. Fourth,CBA has the potential to account for externalities—outcomes for individuals notdirectly involved in the intervention, but who are, nevertheless, affected by itsresults. Finally, since public resources are scarce, it is incumbent upon policymakers to choose the most efficient intervention, that is, the scheme where costsare minimized and benefits are maximized (Cohen 2000).

Despite the advantages of CBA, to date there have been few economicevaluations of criminal justice interventions. Cohen (2000) and Brown (2004)point out that, despite the widespread use of economic techniques in otherpolicy domains, economic evaluation tools have not been staples of the criminaljustice policy analyst’s tool kit. A number of authors have identified a dearth ofrigorous applications of economic analysis, including CBA, to interventions incriminal justice (Bushway and Reuter 2005; Cohen 2000; DiIulio 1996; Swaray etal. 2005).

Welsh and Farrington (2000b) identified 26 crime-prevention studies thatinclude a calculation of a benefit–cost ratio. A slightly more recent review ofcorrectional interventions identified nine cost-benefit analyses (Farrington et al.2001). Additionally, a recent review of sentencing options identified nine CBAsand 11 cost-effectiveness analyses (CEAs) (McDougall et al. 2003). A slightlylarger literature describes the costs and benefits of substance misuse-relatedintervention. The review by Simoens et al. (2006) of the pharmaco-economicliterature on community maintenance for opiate dependence between 1995 and2005 identified 12 cost-effectiveness or cost-utility analyses and six CBAs.Similarly, Cartwright (2000) identified 18 cost-benefit studies of drug treatmentinterventions.

118 K. Marsh et al.

What is economic efficiency and how might we expect it to vary from effect size?

This study empirically tested the hypothesis that cost-benefit analysis provides newinformation to inform decision making. Specifically, we tested the null hypothesisthat net benefits are equivalent to effect sizes. If the alternative hypothesis, that effectsizes and net benefits are not equivalent, is rejected, then the additional expense ofan economic analysis is unwarranted. It is useful to consider how effect size andmeasures of economic efficiency might be expected to vary. In general, the cost-benefit method measures cost effectiveness according to the following equation:CEjt ¼ Bjt � Cjt, where intervention j is cost-effective if CEjt>0, which occurs whenthe costs (Cjt)< benefits (Bjt).

Effect sizes (ESs) from an observational study are transformed into benefits byweighting the outcomes according to Bjt ¼

PESit Witð Þ1. That is, for each outcome

i=1.....n, the effect size is multiplied by a weight (wit), which is the monetized valueof a one-unit change in each outcome i (generally taken from extant empiricalliterature). The product of the weight and the effect size are then summed over eachobserved outcome. A similar strategy is used to estimate costs, except that the costsare observed for each input summed over all inputs. Thus, a costly intervention withlarge effects that have relatively small weights would generate large and positiveeffect sizes but would have small or negative net benefits.

There are then two factors that will influence the relationship between an effectsize and net benefits. First, given an observed effect size, and all else being equal,lower cost interventions will have greater economic efficiency. Second, if the cost ofthe intervention is held constant, as the value of the effect (the weight) increases, sowill the net benefits of the intervention. In this way, a programme that reducesrobbery will be more cost effective than a programme that reduces theft.

Variables that affect the relationship between effect size and net benefits

There is substantial variation in the methods used for valuing effect and measuringcost. The two main sources of variation are in the choice of a sampling frameworkthat determines whose costs and benefits are to be counted and the choice oftechnique for monetizing those effects. With respect to the former, choosing to focusonly on the outcomes for a single unit of government, for example, would yielddifferent results than if exactly the same study measured benefits to all of society.With respect to the latter, there are approximately ten extant estimates of the costs tothe victim associated with a single residential burglary, and the largest estimate(Cohen 2005) is approximately ten times the smallest estimate (Cohen 1988), evencontrolling for inflation. As a result, two studies which find the same reduction in themagnitude and type of offending can, nevertheless, report different values of thebenefits of the programme if they vary in the extant estimates used to monetize

1 Although not discussed here, time is added as a subscript because of the use of discounting in cost-benefit analysis, where future events have smaller values than current events. This is discussed in moredetail later in this section.

What does cost-benefit analysis add to decision making? 119

harms. For a specific intervention with an observed cost and effect, variation inwhose benefits are counted between studies will substantially influence therelationship between effect and economic efficiency.

Selecting a sampling frame—adopting a perspective

A key decision in undertaking an economic evaluation is to determine who hasstanding in the analysis, that is, whose costs and benefits will be included.2 Thechoice is whether the costs and benefits are to be calculated for all of society (the‘net social welfare’ perspective) or whether a more narrow perspective is to beadopted, such as one concerned only with costs and benefits to the government,which is often called the ‘public payer’ perspective (Cartwright 2000; Cohen 2000;Nagin 2001; Roman 2004). The advantage of the net social welfare perspective isthat all impacts are measured, including private costs, such as victimization. Theadvantage of the public payer perspective is that it answers the question of greatestimport to the intervention’s stakeholders (e.g. how will this intervention affect myagency’s budget?). For a given effect size, it is reasonable to expect that a societalperspective will produce a much different estimate of economic efficiency from thatof a public sector perspective.3 A related decision is whether to estimate both directand indirect costs—which are other public sector resources not directly funded bythe intervention (Dhiri and Brand 1999)—and whether to include both tangible(equipment, materials, money) and intangible (productivity loss/increase, experience,fear) costs (Vanagas et al. 2006). We show later in the paper that there is substantialvariation in sampling frames among economic evaluations.

Selecting a sampling frame—measurement of effects

While the choice of perspective informs who has standing in the analysis and hascosts and benefits that are to be counted, the choice of measurement strategy informswhich costs and benefits are estimated. Since the advantage of CBA is hypothesizedto be a function of the inclusiveness of the analysis, it is reasonable to presume thatanalyses that include more outcomes will be more likely to yield new information.At a minimum, most criminal justice cost-benefit analyses include the effect of theintervention on offending (Welsh 2000). Of course, a broader range of outcomesmay result from criminal justice interventions, including substance misuse,education, employment, health and family factors (Dhiri and Brand 1999; Welsh2000; Welsh and Farrington 2000b; Cartwright 2000; Simoens et al. 2006). Clearly,it is not possible for a CBA to consider every direct effect and externality, and, thus,some choices are required in every CBA.

2 See Trumbull (1990) for an interesting exposition on the topic of standing in CBA.3 The effect of this decision on the expected direction of the net benefits (positive or negative) isambiguous. For instance, cutting resources for a government-run programme will surely lower costs to thegovernment. Under a public payer perspective, this is likely to be cost effective. However, from a socialwelfare perspective, the resulting decrease in private benefits may not be cost effective.

120 K. Marsh et al.

Selecting a sampling frame—time

Another challenge to measuring the effect of an intervention is the short-termnature of effect studies compared with the longer-term nature of the effects ofinterventions (Cartwright 2000; French et al. 2000, 2002a, b; Harrell andRoman 2001; Roman and Butts 2005). Cartwright (2000) points out that short-running evaluation frameworks are inadequate for dealing with a long-runningproblem such as substance addiction. Clearly, both net benefits and effect size willbe affected by the choice of the length of the period of observation. For instance, a10% reduction in offending, measured after 5 years, will reflect a greater numberof avoided crimes than will a 10% reduction in offending measured after 6 months.Effect size calculations tend to be undifferentiated in time, but most CBAsaccount for time, by adjusting past events for inflation and, occasionally, bydiscounting the value of future events. This has critical implications in periods ofunusual inflation, since CBAs will value results in real terms (adjusting forinflation in prior periods), and effect sizes will be measured in nominal terms (withno adjustments), and, thus, the two approaches will have different results on thisbasis alone.4

Valuation of effects

Perhaps the most controversial aspect of CBA in the study of crime control policiesand programmes is the need to place a monetary value on intangible factorsassociated with criminal victimization, such as pain, suffering and lost quality of life(Dolan et al. 2005; Cohen 2000; Brown 2004; Rajkumar and French 1997). There isa substantial literature that addresses the moral and empirical issues surroundingmonetization of effects.5 There are several published studies of the costs to crimevictims that employ differing methods. As a result, there is substantial variationwithin these estimates, up to an order of magnitude within a single crime category(Cohen et al. 1994; Miller, Cohen and Wiersma 1996; Miller, Fisher and Cohen2001; Rajkumar and French 1997). This variation will influence the relationshipbetween estimates of effect and economic efficiency.

4 Some CBAs and effect size estimates predict future events, often associated with relatively predictableevents such as the length of expected incarceration. As a result of discounting, CBAwill tend to put moreweight on short-term events and, thus, value early impacts more than persistence of impacts This issomething of a curious phenomenon. Budget stakeholders are likely to adopt a similar perspective as CBAdoes and substantially discount future events. Intervention stakeholders, however, may place a premiumon persistence of effects and, thus, prefer effect size calculations. For a full discussion of discounting, seeViscusi (2006).5 For further discussion of the relative merits of monetary valuation methods see Cohen (2000) Nagin(2001) and Dolan et al. (2005).


Method

A review of impact and cost-benefit analyses was undertaken to identify estimates ofthe effect size and net benefit of criminal justice interventions. The review wasundertaken in three parts:

1. Studies were identified from three existing literature reviews of economicevaluations of criminal justice interventions: Welsh and Farrington (2000a);McDougall et al. (2003), and Cartwright (2000).

2. Those studies were supplemented by a review of the English language literaturefor the period 2000 to 2006. The following databases were searched: AppliedSocial Science Index and Abstracts (ASSIA), British Library Direct, CriminalJustice Abstracts, Dissertation Abstracts, International Bibliography of SocialSciences, National Criminal Justice Reference Service (NCJRS), PsycInfo,Social Care Online, Social Policy & Practice, Social Services Abstracts,Sociological Abstracts, and Web of Knowledge.6

3. A final search of the following databases was undertaken: Criminal JusticePeriodical Index, EBSCO Host, Educational Research Information Consortium(ERIS), Journal Storage (JSTOR), and NCJRS.7

A total of 112 studies that included an impact analysis and economic analysis ofcriminal justice interventions were identified. Those studies were included in theanalysis if they fulfilled two criteria. First, they had to, at minimum, measure thechange in offending, arrest or conviction resulting from an intervention. Second,they had to provide sufficient detail to allow the calculation of an effect size (basedon a measure of change in offending) and the net benefit per participant. Once theinclusion criteria had been applied, 106 estimates of the effect and net benefit ofcriminal justice interventions were identified. In each case, the effect size and thecost-benefit ratio were calculated on exactly the same set of outcomes. The dataextracted from the studies are reported in the Appendix.

Measuring effectiveness

Effect sizes were calculated on the offending outcomes and on those outcomes‘closest’ to the crime. That is, offending data were preferred over arrest data, whichwere preferred over conviction data. Effect sizes were calculated as the difference ofmeans, the difference of proportions, or the converted odds ratios, depending on thenature of the data reported in the study.

6 The following search terms were used to interrogate the databases: (crim* or offend* or re-offend* orrecidivis*) and (econ* or cost*) and (benefit*) and (intervention* or outcome*). A second search ofCriminal Justice Abstracts and Sociological Abstracts was carried out using the following terms: (costs orbenefits or cost-benefit or CBA) and (crime or offending or criminal justice or drug).7 The following search terms were used to interrogate the databases: (costs or benefits or cost-benefit orCBA) and (crime or offending or criminal justice or drug).

122 K. Marsh et al.

Depending on the nature of the effect data reported in the study, one of threeequations was used to calculate effect sizes. Equation (1) reports the function used tocalculate effect size based on a difference of means:

ES ¼ Me �Mc

, ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiSD2

eþSD2c

2

q; ð1Þ

where ESm is the estimated effect size for the difference between means; Me is themean number of offences for those who offend (or re-offend) for the experimentalgroup; Mc is the mean number of offences for those who offend (or re-offend) for thecontrol group; SDe is the standard deviation of the mean number of offences forthose who offend (or re-offend) for the experimental group; and SDc is the standarddeviation of the mean number of offences for those who offend (or re-offend) for thecontrol group.

Equation (2) reports the function used to calculate effect size, based on adifference of proportions.8

ESm pð Þ ¼ 2 � arcsinffiffiffiffiffiPe

p� 2 � arcsin

ffiffiffiffiffiPc

p; ð2Þ

where ESm(p) is the estimated effect size for the difference between proportions fromthe research information; Pe is the percentage of the population that offended (or re-offended) for the experimental or treatment group; and Pc is the percentage of thepopulation that offended (or re-offended) for the control or comparison group

Equation (3) reports the function used to calculate effect size from an odds ratio.

ESm oð Þ ¼ ln ORð Þ=1:81 ; ð3Þwhere ESm(o) is the estimated effect size derived by converting an estimate of theodds ratio, and OR is the odds ratio.

Study attributes

Table 1 presents the coding scheme for other variables that were available todescribe each of the 106 evaluations included in this study. A number of variableswere included to measure the different economic evaluation methods employed bythe studies. First, whether the valuation of benefits of the intervention included justoffending outcomes or a broader set of outcomes, such as improvements insubstance misuse and/or incomes levels. Second, the perspective adopted in valuingoutcomes—whether outcomes were valued from a societal or a public payerperspective. Third, an estimate of the cost of the intervention. Finally, since twometa-analyses contributed to the majority of studies, an indicator measures whether astudy was derived from meta-analytical data or a single study.

A measure of whether or not an intervention targeted juvenile offenders isincluded to identify whether this population had different outcomes (effect size andnet benefits), all else being equal. It is reasonable to presume that, given the higher

8 The arcsine method was employed, as this was the approach adopted by Aos et al. (2001), as the sourceof a number of effect size estimates used in the analysis. In order to be consistent with the calculations ofAos et al, effect sizes for the other studies were calculated in the same way.


average cost of juvenile interventions and the tendency for these interventions tohave longer time horizons, for a given effect size, the net benefit wouldsystematically differ from that of adult interventions. Year dummy variables capturesecular changes in net benefits over time, independent of effect size.

A number of other variables were coded, but they were excluded from theanalysis because data were missing for large numbers of the observations, includingthe source of the data used to estimate the monetary value of crime and the length ofthe follow-up period. We also attempted to code a more refined measure of theperspective of the economic analysis that would measure the scope of the estimate ofthe value of crime. That is, we investigated whether it was possible to code policecosts, probation costs, court costs, victims’ tangible costs and victims’ intangiblecosts, such as pain and suffering. However, again, those details were generally notavailable in the studies we reviewed.

Finally, the literature review identified interventions targeted at both individualoffenders, such as drug treatment, and geographical areas, such as closed circuittelevision (CCTV). As the relationship between effect size and net benefit for area-level studies is a function of the area or population being targeted, and these datawere not available in the studies, area-level studies (n=10) were removed from theanalysis. For instance, for a given reduction in the likelihood of being a victim of anoffence in an area, the benefit associated with this effect is dependent upon howmany people live in the area being studied.

Results

Three sets of analyses were run to compare measures of effect sizes and net benefits.First, we tested whether effect sizes and net benefits measures yielded results of thesame direction by running a cross-tabulation of whether effect was positive (areduction in crime) or negative, and whether net benefit was positive (benefitsgreater than cost) or negative. If policy makers are interested in choosing between anintervention and its alternative, effect size and net-benefit measures yielding resultsof the same direction would cause them to produce the same policy recommenda-tions. If the cross-tabulation suggests the results are in the same direction, this would

Table 1 Study attributes

Variable Description

Effect size×100 Standardized effect size of intervention multiplied by 100Juvenile Indicator variable; 1 if intervention focused on juvenile offenders, 0 if the

intervention focused on adult offendersPublic sectorperspective

Indicator variable; 1 if outcomes were valued using public payer perspective; 0if the outcome valuation adopted a societal perspective

Outcomes other thanoffending

Indicator variable; 1 if benefits were calculated using a broader range ofoutcomes than just offending; 0 if benefits were calculated based only onchanges in offending

Meta-analysis Indicator variable; 1 if the study was a meta-analysis; 0 if it was a single studyQuasi-experiment Indicator variable; 1 if the study employed a quasi-experimental design; 0 if notYear, 2000–2002 Indicator variable; 1 if study year was 2000–2002, 0 if notYear, 2003–2006 Indicator variable; 1 if study year was 2003–2006, 0 if not

124 K. Marsh et al.

suggest that we should reject the null hypothesis that cost-benefit analysis does notprovide any additional information to policy makers.

Second, the degree to which effect size and net-benefit measures rankedinterventions in the same way was tested by correlating the rankings of theinterventions using effect size and net benefit. The same policy recommendationwould result from effect size and net-benefit measures if they ranked interventionsthe same. If the correlations suggest that there is little relation between the rankingsof interventions based on effect sizes and on net benefit, we can reject the nullhypothesis that cost-benefit analysis does not provide any additional information topolicy makers.

Finally, whether effect size is a significant predictor of net benefit was tested bothby examining how the two measures co-vary at the bi-variate level and by examiningthe degree to which the bi-variate relationship holds when controlling for potentialconfounders in a multivariate analysis.

Descriptive statistics

Table 2 reports descriptive statistics for all relevant variables. The mean effect sizewas 0.15, indicating an average reduction in offending of 15%. On average, theinterventions yielded a per-participant net benefit of $13,711. Approximately one-quarter (24%) of studies focused on juvenile offenders, 8% of studies valuedoutcomes from a public payer perspective, and 8% of studies included outcomes inaddition to offending when calculating the benefit of the intervention.

The majority of studies were impact evaluations, where effects were estimated viameta-analytical methods (73%). The remainder were individual studies that employeda quasi-experimental design. Slightly more than half (52%) of the studies werepublished between 2000 and 2002, and 45% were published between 2003 and 2006.

Bi-variate analysis

Table 3 shows the results of the cross-tabulation that tested whether interventionshad consistent signs for the net benefits and effects size estimates. For the 96interventions with a positive effect (a reduction in offending), only 74 (77%) also

Variable Net Benefits Models

Mean S.D.

Net benefits $13,711 $46,485Effect size 0.1496 0.1463Juvenile 0.24 0.42Public sector perspective 0.08 0.28Outcomes other than offending 0.08 0.28Meta-analysis 0.73 0.45Year, 2000–2002 0.52 0.50Year, 2003–2006 0.45 0.50N 96 96

Table 2 Descriptive statistics


produced a positive net benefit. Of the ten interventions that had negative effects (anincrease in crime), only three (30%) had a negative net benefit. Overall, the directionof effect only predicts the direction of net benefit 73% of the time. Put another way,in 27% of instances, measurements of effect and measurements of efficiency wouldproduce contradictory policy recommendations.

While it is easy to explain why a positive effect size and a negative net benefit mightbe obtained (most likely due to the high costs of the intervention), explaining thefinding of a negative effect (an increase in crime) and a positive net benefit is lessobvious. One example of this scenario is the case of adult boot camps (Aos et al. 2001).The study in this analysis compares boot camp with prison. Aos et al. (2001) costedthese interventions at $14,271 and $23,136, respectively (1995 prices). In this casethe counterfactual (prison) has greater benefits than the test intervention (boot camp),and, thus, the effect size was negative. However, boot camps are much less costly tooperate, and, thus, those cost savings can be invested elsewhere and achieve a furtherbenefit. Thus, the extra spending for prisons is not as efficient, since these resourcescould have been invested elsewhere to achieve an even greater benefit.

A second means of testing our hypothesis is to compare how the two outcomes rankthe interventions. Once we have ranked the interventions from largest effect to smallesteffect for each of the two measurement strategies, the simple (pair-wise) correlation ofintervention rankings is 0.16 (P=0.101), indicating a modest but statisticallyinsignificant positive relationship between the ranks of effect sizes and ranks of netbenefits. However, a statistically significant positive relationship is found betweenranks of effect and ranks of efficiency when they are assessed with the Kendall rankcorrelation test (τ-b=0.1332, P=0.044), though the association is still only modest.

Table 4 presents the bi-variate correlations for each combination of variablesincluded in the multivariate analysis. The bi-variate correlation between effect size andnet benefits (0.07) is positive but both empirically small and statistically insignificant.

If cost-benefit analysis did not provide any additional information to policymakers when compared with effect size estimates, we would expect to find estimatesof net benefit and effect size yielding results in the same direction and there being astrong correlation between both effect sizes and net benefits and between the rankingof interventions based on effect sizes and net benefits. However, in 27% ofinstances, measurements of effect size and net benefit produce contradictory policyrecommendations, and there is only a very slight association between effect size andnet benefit and between the ranking of interventions on these measures. This wouldsuggest that policy decisions based on estimates of net-benefit would vary fromthose based on effect sizes, and that cost-benefit analysis is providing additionalinformation when compared with analysis of effect.

Effect Net Benefit

Negative Positive Total

Increased crime 3 7 10Reduced crime 22 74 96Total 25 81 106

Table 3 Cross-tabulation of ef-fect and efficiency

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Multivariate analysis

The bi-variate comparisons provide compelling evidence that net benefits and effectsizes yield different results. However, the bi-variate statistics do not allow for causalinference, and it is reasonable to presume that measures of association betweeneffect size and net benefit may be confounded by heterogeneity in the methodsemployed to measure net benefit between studies or by characteristics of the studiesthemselves. Given the small sample sizes and identification problems endemic inthis study, we employed multivariate analysis to investigate these issues, but we donot presume that these analyses will allow for causal inference. However,consistency between the bi-variate findings and the multivariate findings wouldlend further support to the rejection of the null hypothesis.

The form of the multivariate model is outlined in equation (4):

Yi ¼ β0i þ β1ESi þ X δ þ "i ; ð4Þwhere Yi is a measure of net benefit for intervention i, ESi represents the standardizedeffect size of intervention i and X is a vector of covariates theoretically associatedwith an intervention’s net benefits. An ordinary least squares (OLS) model wasspecified that regressed the continuous dependent variable, net benefit, on effect sizeand covariates.9

A key challenge facing the construction of the model outlined in equation (4) wasthe likelihood that the data were not identically distributed, causing some estimatesof net benefit to be more precise than others. This was due to the presence of datathat were extracted from both individual studies and meta-analytical studies.Variation in the precision of the studies meant that the independent and identicallydistributed (iid) assumptions underlying the OLS model were not met. This calledinto question the validity of the standard errors associated with the coefficientsproduced by the model. Furthermore, the true standard errors associated with the

9 A logistic regression with a dependent variable of whether the net benefit was positive or negative wasalso considered, but the small sample size ruled out this model. Furthermore, such a dichotomousdependent variable would be a less finely grained measure of efficiency. A Shapiro–Wilk test on thedependent variable used in the analysis, net benefits, determined that the variable was normallydistributed.

Table 4 Bi-variate correlations (parentheses indicative negative correlations)

Parameter NetBenefits

EffectSize

Quasi-experiment

Meta-analysis

OtherOutcomesIncluded

Juvenile PublicSectorPerspective

Effect Size 0.07Quasi-experiment 0.07 (0.33)***Meta-analysis 0.13 0.37*** (0.94)***Other outcomes included 0.04 0.00 0.35*** (0.40)***Juvenile 0.06 (0.05) 0.05 (0.06) (0.06)Public sectorperspective

0.03 (0.43)*** 0.45*** (0.43)*** (0.09) (0.08)

Year, 2000–2002 0.09 0.33*** (0.28)*** 0.33*** 0.08 0.18* (0.02)Year, 2003–2006 0.09 (0.25)*** 0.21** (0.23)** (0.13) (0.14) (0.02)

*P<0.10, **P<0.05, ***P<0.01


coefficients could be either larger or smaller than those generated by an OLSmodel.10 As a result of this problem, the interpretation of the OLS model onlyfocused on the coefficients produced and did not consider the standard errors or theirassociated P values produced.

Table 5 shows the output from the multivariate model estimating the impact ofeffect size on net benefit. The interpretation of the coefficient on effect size is thechange in net benefits associated with a 0.01 increase in effect size. Thus, a 0.01increase in effect size is associated with a $4,150 increase in net benefit. Thisvariation in net benefit with effect size can be considered in the context of net-benefit estimates included in the model ranging from −$63,001 to $253,337.

The coefficient on effect size was much smaller than the coefficient on the othervariables included in the model, which were at least a magnitude of 75-times greater thanthat for effect sizes and, in many cases, were magnitudes of over 1,000-times greater.

It is important to note that the relatively high R2 (0.43) value is misleading, as it ispredominantly the result of the inclusion of the constant. When the model was runwithout the constant, the R2 value fell to 0.03. That is, the constant represented ahigh portion of the mean value of net benefit, and the independent variablesexplained very little of the mean.

Discussion and conclusion

The analysis tested the hypotheses that CBA does not contribute new informationbeyond the effect size alone, by assessing whether effect size was a good proxy fornet benefit and whether effect sizes and net benefits produce similar policyrecommendations. This hypothesis was generally rejected by the analysis, whichsuggests that measures of intervention effect in isolation are insufficient to explainestimates of net benefit. That is, effect size is not strongly related to net benefit, andeffectiveness analysis and CBA lead to different policy outcomes.

If cost-benefit analysis did not provide any additional information to policymakers when compared with effect size estimates, we would expect to find thatestimates of net benefit and effect size would yield results in the same direction andthat there would be a strong correlation between both effect sizes and net benefitsand the ranking of interventions based on effect sizes and net benefits. However, in27% of instances, measurements of effect size and net benefit produce contradictorypolicy recommendations, and there is only a very slight association between effectsize and net benefit and between the ranking of interventions on these measures.

The relationship between effect size and net benefit was confounded by thedifferent methods employed to measure effect and efficiency. Multivariate analysiswas employed to try and isolate the effect of methodological variation. Thissuggested that a 0.01 increase in effect size is associated with a $4,150 increase innet benefit. However, this analysis was undermined by some important limitations.

10 In the light of this problem, a number of adjustments to the standard errors in the model wereconsidered: a model with robust (sandwich) standard errors, and a model with clustered standard errors.Both of these standard error adjustments would tend to increase the standard errors on model coefficientscompared to the standard OLS model. Thus, the adjustments would not overcome the problem of variationin the precision of the studies, as this variation can cause standard errors to be either too small or too large.

128 K. Marsh et al.

First, the standard errors estimated by the analysis were unreliable, as it is likely thatthe net benefits estimated in the studies included in the analysis varied in theirprecision. Second, effect size and the methods variables included in the modelexplained very little of the variation in net benefit.

Further research is required to ensure that the model is specified appropriately.First, further effort is required to measure the standard errors on the net-benefitestimates extracted from the studies. Before this can be done, it is necessary toimprove the methods employed by economists to measure the costs of interventions.Very few of the studies included in the analysis had measured costs in a way thatwould allow standard errors to be measured.

Second, measurements are required of more of the methods variables that confoundthe relationship between effect and net benefit. A number of variables were excludedfrom the models, due to limited data. For instance, length of follow-up is a keydeterminant of the measure of intervention benefit, but it was only reported by a smallnumber of studies. The offending history of the sample in each study could alsoinfluence measures of economic efficiency, but this influence is not necessarily reflectedin different effect sizes. For instance, homicide is a more costly crime than shoplifting,and the same effect size applied to homicides and shoplifting reflects quite differentavoided costs of crime. To some extent this was captured through the measurement ofwhether the intervention was targeted at juvenile or adult offenders, but there was likelyto be variation in offending patterns that was not captured by this variable.

A further limitation to the analysis was that it relied on estimates of effect andeconomic efficiency available in the existing literature. This not only limited thesample size available for the analysis, as there is a dearth of economic evaluations inthe criminal justice field, but it also created the possibility that the analysis would be

Variable Coefficient (Standard Error)

Effect size×100 $4,150($8,282)

Juvenile $316,749($276,312)

Public sector perspective $1,290,506**($493,223)

Outcomes other than offending $493,440($503,871)

Meta-analysis $4,667,302***($721,768)

Quasi-experiment $4,370,661***($684,823)

Year, 2000–2002 $2,700,008***($639,533)

Year, 2003–2006 $3,020,818***($596,117)

Intercept −$7,597,887***($806,985)

Model fit (R2) 0.493N 97

Table 5 Multivariate model(net-benefits models)

**P<0.05, ***P<0.01


subject to publication bias. With this in mind, it is reassuring that the reviewidentified studies that reported negative effect sizes and negative benefit-cost ratios.

Despite these limitations, this paper provides important insight into theinformation required by decision makers. The evidence suggests that measuringeffect size is insufficient to determine whether an intervention will have positive netbenefits or the extent of the net benefit produced by an intervention. Since effectsizes cannot be used to predict meaningfully the net benefit of an intervention, weconclude that the use of effect size as a proxy for the efficiency of an intervention ismisguided. Moreover, the decision rule often employed by researchers, whereby acost-benefit analysis of an intervention is foregone in the absence of a significanteffect size, may be misguided. While an intervention’s net benefit is ultimatelydependent on its effect size, by adding new information beyond what is available inthe effect size construct, cost-benefit analysis represents a fundamentally differentanalytical construct. It is important that policy makers use economic analysis toinform their decision making.

A list of studies included in the analysis is given in Table 6 in the Appendix

Appendix

List of studies included in the analysis

Table 6 Data extracted from studies (RCT randomized controlled trial)

Author Intervention Population Net Benefit EffectSize

EffectMethod

OutcomePerspective

Adamson 2005 Burglary reduction Adult $64,254 0.00 Quasi-experimental SocialAos et al. 2001 Nurse Home Visitation Adult $15,918 −0.29 Meta-analysis SocialAos et al. 2001 Early Childhood Education Adult $6,972 −0.10 Meta-analysis SocialAos et al. 2001 Social Development Project Adult $14,169 0.13 Meta-analysis SocialAos et al. 2001 Quantum Opportunities

ProgrammeAdult $16,428 −0.31 Meta-analysis Social

Aos et al. 2001 Mentoring Adult $4,524 −0.04 Meta-analysis SocialAos et al. 2001 National Job Corps Adult $1,719 −0.08 Meta-analysis SocialAos et al. 2001 Job Training Partnership Act Adult −$12,082 0.10 Meta-analysis SocialAos et al. 2001 Multi-Systemic Therapy Juvenile $131,918 −0.31 Meta-analysis SocialAos et al. 2001 Functional Family Therapy Juvenile $59,067 −0.25 Meta-analysis SocialAos et al. 2001 Aggression Replacement

TrainingJuvenile $33,143 −0.18 Meta-analysis Social

Aos et al. 2001 Multidimensional TreatmentFoster Care

Juvenile $87,622 −0.37 Meta-analysis Social

Aos et al. 2001 Diversion Project Juvenile $27,212 −0.27 Meta-analysis SocialAos et al. 2001 Diversion with Services Juvenile $5,679 −0.05 Meta-analysis SocialAos et al. 2001 Intensive Probation Juvenile $6,812 −0.05 Meta-analysis SocialAos et al. 2001 Intensive Probation Juvenile $18,854 0.00 Meta-analysis SocialAos et al. 2001 Intensive Parole Supervision Juvenile $6,128 −0.04 Meta-analysis SocialAos et al. 2001 Coordinated Services Juvenile $14,831 −0.14 Meta-analysis SocialAos et al. 2001 Scared Straight Juvenile −$24,531 0.13 Meta-analysis SocialAos et al. 2001 Family-Based Therapy Juvenile $30,936 −0.17 Meta-analysis SocialAos et al. 2001 Sex Offender Treatment Juvenile $23,602 −0.12 Meta-analysis SocialAos et al. 2001 Boot Camps Juvenile −$3,587 0.10 Meta-analysis SocialAos et al. 2001 In-Prison Therapeutic

CommunityAdult $2,365 −0.05 Meta-analysis Social

Aos et al. 2001 In-Prison TherapeuticCommunity

Adult $5,230 −0.08 Meta-analysis Social

Aos et al. 2001 Therapeutic Community Adult $15,836 −0.17 Meta-analysis SocialAos et al. 2001 In prison drug treatment Adult $7,748 −0.09 Meta-analysis Social

130 K. Marsh et al.

Table 6 (continued)


EffectMethod

OutcomePerspective

Aos et al. 2001 Drug Courts Adult $4,691 −0.08 Meta-analysis SocialAos et al. 2001 Drug treatment Adult $1,230 −0.03 Meta-analysis SocialAos et al. 2001 Community-based drug

treatmentAdult $5,048 −0.07 Meta-analysis Social

Aos et al. 2001 In prison drug treatment Adult $3,361 −0.05 Meta-analysis SocialAos et al. 2001 Sex Offender Treatment Adult $19,534 −0.11 Meta-analysis SocialAos et al. 2001 Intensive Supervision Adult −$384 −0.03 Meta-analysis SocialAos et al. 2001 Intensive Supervision Adult $5,520 −0.10 Meta-analysis SocialAos et al. 2001 Intensive Supervision Adult $6,386 0.00 Meta-analysis SocialAos et al. 2001 Boot camps Adult $10,011 0.00 Meta-analysis SocialAos et al. 2001 Boot camps Adult $3,666 0.00 Meta-analysis SocialAos et al. 2001 Moral Reconation Therapy Adult $7,797 −0.08 Meta-analysis SocialAos et al. 2001 Reasoning and

RehabilitationAdult $7,104 −0.07 Meta-analysis Social

Aos et al. 2001 Work Release Programmes Adult $2,351 −0.03 Meta-analysis SocialAos et al. 2001 Job Counselling/Search for

Inmates Leaving PrisonAdult $3,300 −0.04 Meta-analysis Social

Aos et al. 2001 In-Prison Basic Education Adult $9,176 −0.11 Meta-analysis SocialAos et al. 2001 In-Prison Vocational

EducationAdult $12,017 −0.13 Meta-analysis Social

Aos et al. 2001 Correctional industriesprogramme

Adult $9,413 −0.08 Meta-analysis Social

Austin 1988 Early release Adult $1,480 −0.14 Quasi-experimental Public sectorBarnoski and Aos 2004 Adult drug courts Adult $2,888 −0.02 Meta-analysis SocialBarnoski and Aos 2004 Functional family therapy Juvenile $20,348 −0.25 Quasi-experimental SocialBarnoski and Aos 2004 Aggression replacement

trainingJuvenile $7,939 −0.15 Quasi-experimental Social

Barnoski and Aos 2004 Co-ordination of services Juvenile $2,755 −0.13 Quasi-experimental SocialBayer and Pozen 2003 >State correction Juvenile -$6,044 −0.21 Quasi-experimental SocialBayer and Pozen 2003 County correction Juvenile $5,424 −0.09 Quasi-experimental SocialBayer and Pozen 2003 Private (non-profit)

correctionJuvenile $1,069 −0.20 Quasi-experimental Social

Belfield et al. 2006 High/Scope PerryPreschool Program

Juvenile $229,646 −0.33 RCT Social

Craddock 2004 Day reporting centres Adult $1,869 −0.35 Quasi-experimental Public sectorCraddock 2004 Day reporting centres Adult −$366 −0.15 Quasi-experimental Public sectorDaley et al. 2004 Drug treatment Adult −$44,865 −0.17 Quasi-experimental Public sectorDaley et al. 2004 Drug treatment Adult −$42,861 −0.39 Quasi-experimental Public sectorDaley et al. 2004 Drug treatment Adult −$39,840 −0.48 Quasi-experimental Public sectorFinigan 1995 Drug treatment Adult $7,524 −0.56 Quasi-experimental SocialFowles et al. 2005 Community-based

drug treatmentAdult $4,958 −0.12 Meta-analysis Social

Fowles et al. 2005 Intensive supervision Adult −$3,799 −0.16 Meta-analysis SocialFowles et al. 2005 Basic Education Adult $10,209 −0.25 Meta-analysis SocialFowles et al. 2005 Fines Adult $5,788 −0.20 Meta-analysis SocialFowles et al. 2005 Intensive supervision Adult $2,029 0.00 Meta-analysis SocialFowles et al. 2005 Drug treatment Adult $4,507 −0.16 Meta-analysis SocialFowles et al. 2005 Financial assistance on

leaving prisonAdult $8,082 −0.08 Meta-analysis Social

Fowles et al. 2005 Intensive supervision Adult −$6,458 −0.15 Meta-analysis SocialFowles et al. 2005 Correctional industries Adult −$2,610 −0.17 Meta-analysis SocialFowles et al. 2005 Sex offender treatment Adult −$26,014 −0.27 Meta-analysis SocialFowles et al. 2005 Boot camps Adult −$32,048 −0.01 Meta-analysis SocialFowles et al. 2005 In prison drug treatment Adult $4,306 −0.10 Meta-analysis SocialFowles et al. 2005 In-prison drug treatment Adult $4,313 −0.19 Meta-analysis SocialFowles et al. 2005 Sex offender treatment Adult $3,090 −0.08 Meta-analysis SocialFowles et al. 2005 Sex offender treatment Adult −$5,783 −0.18 Meta-analysis SocialFowles et al. 2005 Electronic Monitoring Adult $3,128 −0.14 Meta-analysis SocialFowles et al. 2005 In-prison vocational

educationAdult $6,002 −0.24 Meta-analysis Social

Fowles et al. 2005 Job counselling and search Adult $3,465 −0.05 Meta-analysis SocialFowles et al. 2005 Drug courts Adult $4,506 −0.32 Meta-analysis SocialFowles et al. 2005 In prison therapeutic

communityAdult $7,346 −0.04 Meta-analysis Social

Fowles et al. 2005 Life Skills programs Adult $10,171 −0.37 Meta-analysis Social


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Kevin Marsh is head of Economics at The Matrix Knowledge Group (TMKG). His research interestsinclude the economic evaluation of criminal justice and public health interventions. He completed his PhDin Economics at the University of Bath, specialising in monetary technique for valuing environmentalresources. Following a year at the Social Disadvantage Research Centre, Oxford University, Marsh joinedTMKG in 2003. At Matrix he is responsible for maintaining the quality of economic and statisticalmethods, advising on a range of projects across the crime and justice and health sectors. He has recentlyundertaken research in a number of areas of public policy, including: prisons, promoting physical activity,drug trafficking, reducing drug use among both adult and juvenile populations, human trafficking,reducing health inequalities, reducing social exclusion, and area-based regeneration.

Aaron Chalfin is a Research Associate at the Urban Institute’s Justice Policy Center, where his researchfocuses on evaluations of criminal justice programs, cost-benefit analysis and the economic and socialdeterminants of criminal activity. He has used statistical methods to evaluate programs designed to reducerecidivism and improve labor market outcomes and has developed full-information economic models toestimate social costs and benefits. His current research includes studies of individual and neighborhoodcharacteristics that predict fear of crime and methodological issues in cost-benefit analysis.

134 K. Marsh et al.

John Roman is a Senior Research Associate at the Justice Policy Center at the Urban Institute where hisresearch focuses on evaluations of innovative crime control policies and programs. Roman is directingstudies of the demand for community-based interventions with drug-involved arrestees, the use of DNA inburglary investigations, the reclaiming futures initiative and the cost of the death penalty. His priorresearch includes studies of specialized courts, the age of juvenile jurisdiction, prisoner reentry and cost-benefit methodology. He is the co-editor of Juvenile Drug Courts and Teen Substance Abuse and aforthcoming volume on Cost-Benefit Analysis and Crime Control Policies.

John Roman is a Senior Research Associate at the Justice Policy Center at the Urban Institute where hisresearch focuses on evaluations of innovative crime control policies and programs. Roman is directingstudies of the demand for community-based interventions with drug-involved arrestees, the use of DNA inburglary investigations, the reclaiming futures initiative and the cost of the death penalty. His priorresearch includes studies of specialized courts, the age of juvenile jurisdiction, prisoner reentry and cost-benefit methodology. He is the co-editor of Juvenile Drug Courts and Teen Substance Abuse and aforthcoming volume on Cost-Benefit Analysis and Crime Control Policies.


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What does cost-benefit analysis add to decision making? Evidence from the criminal justice literature