BuildingCriminalCapitalvsSpecificDeterrence:
TheEffectofIncarcerationLengthonRecidivism
DavidS.Abrams
December,2011
Abstract
Inevaluatingtheefficacyofmostmoderncriminaljusticesystems,avitalrelationshipto
understandisthatbetweenincarcerationlength(andlikelihood)andrecidivism.Because
mostpreviousattemptstoestimatethisrelationshipsufferfromomittedvariablesbias,
eventhesignisunknown.Inthispaper,Ibuildonpreviousworkidentifyingsubstantial
heterogeneityinattorneyabilityinapublicdefenderofficewithrandomcaseassignment.I
makeuseofthisvariationtoaddresstheomittedvariablesproblembyinstrumentingfor
sentencelengthandincarcerationrateusingtherandomlyassignedpublicdefender.A
negativerelationshipbetweenrecidivismandsentencelengthgoesawaywhen
instrumentingforsentence.Similarly,apositiveandstatisticallysignificantrelationship
betweenrecidivismandincarcerationbecomesinsignificantintheIVregressions.
Howevertheregressionresultsdonotrevealthefullstory,astherelationshipsarerather
nonlinear.Agraphicalexaminationrevealsanegativerelationshipbetweenrecidivismand
sentencelengthandalsorecidivismandincarcerationrate,particularlyforshorter
sentencesandlowerincarcerationrates.Inaddition,longersentencestendtoleadto
moreseverecrimesuponoffenderrelease.Puttogether,thesefindingsprovidesome
evidenceforamildspecificdeterrenteffect,butonethatrapidlydiminishes.
JELClassifications:J24,K14,K42

University of Pennsylvania Law School and Wharton. The author would like to thank Stephanos Bibas, Shawn Bushway, Philip Cook, John MacDonald, John Pfaff, and members of the Penn Junior Faculty Economics Workshop for helpful comments and encouragement. Emily Turner provided extraordinary feedback and discussion on the project. This paper would not be possible without a prior co‐authored work with Albert Yoon, to whom special thanks is due. Excellent feedback was provided by members of the Penn, Texas, Georgetown, Michigan, Northwestern, Harvard and Berkeley law school faculties, the NBER 2010 SI Crime Workshop, and 2010 CELS participants. Nancy Wang and especially Kathy Qian provided outstanding research assistance. Email: [email protected] 1 I.Introduction
ThegrowthinincarcerationrateintheUnitedStatesinthelastseveraldecadesof
the20thcenturyandearly21stcenturyiswellknown.Muchhasbeenwrittenaboutthe
efficacy,justice,andefficiencyofthisapproachtocrimefromamyriadofmethodological
perspectives.1InthispaperIattempttounderstandonepieceoftheincarcerationpuzzle:
theimpactofsentencelengthandlikelihoodofincarcerationonrecidivism,oftencalled
specificdeterrence.
Therelationshipbetweenincarcerationanddeterrenceisofinteresttoeconomists,
asitisoneofthecomponentsindeterminingthewelfareeffectsofincarceration.2Theend
goalistoanswerthequestion:Inwhatsituationsisincarcerationwelfare‐enhancing?This
projectmaybethoughtofasalargecost‐benefitcalculus,inwhichthecostsincludethe
capitalexpendituresonincarceration,thevalueoffreedom,andpotentialcriminogenic
effectsofimprisonment.Benefitsfromincarcerationincludecrimereductiondueto
incapacitation,generaldeterrence,andspecificdeterrence.3
Thispaperfocusesonthelastoftheserelationships,incarcerationandspecific
deterrence.ThequestionsIexploreare“Whatistheimpactofamarginalincreasein
incarcerationlengthonfuturerecidivism?”4and“whatistheimpactofamarginalincrease
inanindividual’slikelihoodofincarcerationonfuturerecidivism?”Whilesimpletostate,
1
Cite several background papers here. I have investigated the costs and benefits of other aspects of the criminal justice system elsewhere. This includes Abrams and Rohlfs (2010) on optimal bail‐setting and the value of freedom; Abrams (2010) on general deterrence; Abrams, Bertrand and Mullainathan (2011) on defendant race and sentencing. 3
One may also include retribution and rehabilitation in the calculus, although these are much harder values to estimate. 4
I will sometimes refer to the derivative of recidivism with respect to sentence length as the magnitude of specific deterrence or simply specific deterrence. 2
2 thereissubstantialcomplexityinthesequestions,andasIshowinthispaper,inthe
answers.
Definingrecidivismisahardenoughproblemthatasubstantialamountofworkhas
beendevotedjusttothistopic(Maltz,2001).Iengageinsomeofthecomplexityofthis
probleminseveralways.Iuseseveralalternativedefinitionsofrecidivism,including
binaryindicatorswithvaryingtimewindows,aswellascontinuousvariablesthatindicate
theseverityoftherecidivatingcrime.Iapplyhazardmodelsandadditionallyexaminethe
effectsonrecidivismofboththeintensiveandextensivemarginofincarceration.
Perhapsmostconfoundingtomuchpreviousresearchisthefactthatthereare
almostcertainlyunobservablevariablesthatarecorrelatedwithbothsentencelengthand
recidivism.Itmaybethecasethatdefendantswhoarerelatively“bad”inunobservable
waysaremorelikelytobothgetlongersentencesandrecommitoffenses.Underthis
model,aninabilitytocontrolfor“badness”willyieldupward‐biasedestimatesoftheeffect
ofsentencelengthonrecidivism.Alternatively,judgesmaybeinfluencedbythelikelihood
thatoffenderswillbeapprehended,andthusindividualssentencedtolongerdurationsof
incarcerationmayappeartohavelowerrecidivismratesinthecrosssection.Inprevious
work(egSpohnandHolleran,2002;Gottfredson,1999)attemptsweremadetoaccountfor
theseconcernsthroughsyntheticcontrolgroups,covariatebalancing,andothermatching
techniquesbasedonobservables.Butthereissubstantialliteratureineconomicsand
elsewherethatillustratesthedifficultiesinusingeventhemostsophisticatedmatching
techniques(Lalonde,1986;DehejiaandWahba,1998;Dehejia,2000).
3 Anotherchallengeposedbytheresearchquestionsisthattherelationships
investigatedarecomplicatedandmaynotbewell‐suitedtoasinglecoefficientasinanOLS
orprobitregression.IestimatebothOLSandIVregressionsinthispaper,usingdifferent
assumptionsaboutthesentencingdistribution.Dependingonthemodelforthesentencing
distribution,Ifindeitheranegativerelationship,butmorefrequentlynosignificant
relationshipbetweenrecidivismandsentencelength.Therelationshipbetweenthe
variablesisnotalwaysmonotonicandIfurtherexploreitthroughnon‐parametric
techniques.
IntheIVregressions,Ifindastatisticallyinsignificantrelationshipbetween
recidivismandsentencelength.Butthismasksanegativerelationshipforrelativelylow
sentencelengthsandaflatrelationshipthereafter.Usingtheinstrumentstopredictany
incarcerationalsoyieldsinsignificantcoefficients.Again,though,thereappearstobea
decliningrelationshipforlowprobabilitiesofincarcerationwhichflattensoutas
probabilityofincarcerationexceedsabout40%.
Whentakingseverityoftherecidivatingcrimeintoaccount,increasedsentence
lengthpredictsmoresevererecidivism.Takentogether,theseresultstellastoryofa
moderatedeterrenteffectofincarcerationandsentencelength,butonewiththeperverse
effectthatthefewerrecidivatingcrimestendtobemoresevere.Thesephenomenaare
quiteconsistentifcriminalsinclinedtocommitlesssevereoffensesarejustthosewhoare
moredeterred.
Theremainderofthepaperisorganizedasfollows.InSectionII,Ireviewsomeof
themorerecentcontributionsinthelongliteratureonincarcerationandrecidivism.
4 SectionIIIprovidesbackgroundinformationonthePublicDefender’sofficeinClarkCounty
anddescribesthedataset.InSectionIV,Ipresenttheempiricalspecificationsandthe
mainresults.SectionVconcludes.
II.BackgroundonIncarcerationandRecidivism
Understandinghowpunishmentaffectsrecidivismisessentialtoarationalcriminal
justicepolicy.Soitshouldnotbesurprisingthatanumberofattemptshavebeenmadeto
estimatethisrelationship.Alargefractionofthesestudiespotentiallysufferfromomitted
variablesbias,soIfocusprimarilyonrecenteconomicstudiesthatattempttoexplicitly
accountforit.Theydosowithavarietyofapproaches:matchingtechniques,regression
discontinuity,instrumentalvariables,naturalexperiments,andevenafieldexperiment.
Tworelativelyrecentreviews(Nagin,Cullen&Jonson2009;Bushway&Paternoster
2009)bothdiscussempiricalworkonrecidivismandspecificdeterrence(theformerisa
muchmoreextensivesurvey).Theycoverarangeofstudiesandbothnotethelackof
consensusonthetopic.Oneimportantreasonforthelackofconsensusisthatstudies
oftenseektoanswerslightlydifferentquestions.Thereisvariationinthedefinitionof
recidivism(re‐arrest,reincarceration,etc),whethertheintensiveorextensivemarginis
thefocus,thesizeofthepotentialrecidivismwindow,theinitiallawenforcementaction
whoseeffectisbeinginvestigated,andthegeographiclocale.
ArecentstudybyNieuwbeerta,Blokland,Nagin(2009)usesamatchingtechnique
toattempttodetecttheeffectoffirstincarcerationonrecidivismintheNetherlands.They
5 usepropensityscorematchingwithincriminaltrajectorygroupstosynthesizecontrol
groupsinordertoestimatethecausaleffectofincarceration.Theauthorsfindthatthe
experienceoffirstincarcerationsubstantiallyincreasesthelikelihoodoffuturecriminality
(overtwiceashighforsomeindividuals).Thetwoprimarycritiquesofthestudyarethe
standardcritiqueofmatchingapproaches(thepotentialthatomittedvariablesstilldrive
results)andthegeneralizabilitygiventhesubstantiallydifferentcriminaljusticesystemin
theNetherlands.
MuchotherrecentworkaddressestheOVBproblemmoresquarely,usingIVor
quasi‐experimentaltechniques.Kuziemko(2007)usestwoapproachestoestimatethe
magnitudeofspecificdeterrenceusingdatafromGeorgiastateprisons.Anatural
experimentthatledtothereleaseof901prisonersin1981providesthepotentialto
compareprisonerswithsimilarsentencesandvaryinglengthsoftimeserved,wherethe
variationisdeterminedexogenouslybywhentheirsentencesbegan.Theidentifying
assumptionhingessharplyontherebeingnotimetrendorotherdirectrelationship
betweendateofincarcerationandlikelihoodofrecidivism.Usingthisapproachand
anothermakinguseofprisonerriskassessmentsshefindsasubstantialnegativeeffectof
sentencelengthonrecidivism:a7%declineinrecidivismforeveryextramonthserved.
BushwayandOwens(2010)takeabehavioralapproachtounderstandingthe
impactofsentencelengthsoncrime.A2001lawchangeinMarylandprovidesthemwitha
naturalexperimentwherebyanaturalreferenceforsentencelengthischanged,butnotthe
actualsentences.Whilenotdirectlycomparabletootherstudiesexamined,theauthors
findthatshortersentencesrelativetoareferencepointleadtohigherrecidivismrates.
6 Drago,Galbiati,andVertova(2009)examineanaturalexperimentinItalywhereall
inmatesincarceratedin2006receiveduptoa3yearsentencecommutation.Whilethe
experimentisdramaticandsubstantialdeterrenceisdetected,theinterpretationis
difficult.Sinceprisonerswithlongersentencereductionsalsofacehigherpenaltiesupon
rearrest,theneteffectmustbeacombinationofspecificandgeneraldeterrence.If,as
someotherstudiessuggest,specificdeterrenceisnegative(lesscrimeafterlonger
incarceration)thengeneraldeterrencemustdominateheresincedefendentswhoreceived
greatercommutationshadlargerdropsinrecidivism.Anevenmorerecentpaperusinga
Europeannaturalexperiment(MaurinandOuss2010)usesthe1996BastilleDaypardon
inFrancetoestimatetheeffectofsentencereductionsonrecidivism.Theyfindthata
greatersentencereductionviathepardonleadstoanincreaseinexpectedfuture
recidivism.
Hjalmarsson(2009)usesaregressiondiscontinuityapproachmadepossiblebythe
WashingtonStatejuvenilesentencingguidelines.Shefindsthatjuvenileswhoare
incarceratedhavealowerprobabilityofrecidivismthanthosethatreceivealocal(non‐
incarceration)sanction.ThisisincontrasttothestudybyNieuwbeerta,etaldiscussed
abovewhichfoundapositiveeffectoffirstincarcerationonrecidivismintheNetherlands.
Fourrecentpaperstakeaninstrumentalvariablesapproachtothequestionof
specificdeterrence,threeofwhichuseverysimilarinstruments.Loeffler(2005)uses
judge‐specificsentencingtendenciesandrandomcaseassignmenttoobtainexogenous
variationinsentencelength.Thisstudy,usingdatafromEssexCounty,NJ,alsofocuseson
7 theextensivemarginandfindsthatincarcerationsubstantiallyreducesthelikelihoodof
recidivism.
AvirtuallyidenticalapproachtothatofLoefflerisadoptedbyBerubeandGreen
(2007)andGreenandWinik(2010).TheGreenco‐authoredpapersbothmakeuseofdata
fromtheDCsuperiorcourtandbothfindlittlerelationshipbetweensentencelengthand
recidivism.Theyfindanegativeandstatisticallysignificantrelationshipbetween
incarcerationlengthandrecidivismwhendoingordinaryleastsquaresregressions.But
thesignbecomespositiveandtheeffectstatisticallyinsignificantwhen2SLSorLIML
estimationisperformed(althoughthestandarderrorsarelarger).
TheclosestapproachtothatusedinthispaperisfoundinTurner(2009).Usingthe
ClarkCountydatasetusedhere,Turnerinstrumentsforsentencelengthusingrandom
assignmenttoattorneyandheterogeneityinattorneyperformance.Shefindsamostly
insignificantrelationshipbetweensentencelengthandrecidivism,althoughonethatvaries
somewhatbytherecidivismwindow.
Perhapsthemostsignificantcontributiontotheliteratureonspecificdeterrence
comesfromalittle‐knownfieldexperimentperformedbytheCaliforniadepartmentinthe
1970s(BerecocheaandJaman1981).Theauthorsrandomizeda6‐monthearlyrelease
amongfelonsservingtimein1970.Theycompareoneandtwoyearrecidivismrates
betweenthetreatmentandcontrolgroupsandfindnosignificantdifference.However,a
simplet‐testonthedataindicatesthattheearlyreleasegrouprecidivatedatasignificantly
higherrate,supportinganegativerecidivism‐sentencelengthrelationship.Takentogether,
8 thesestudiesshowthatthereisnotconsistentevidenceontheeffectofimprisonmenton
futurerecidivism. III.CriminalJusticeinClarkCounty,Nevada
Thedataforthispapercomesfromtwosources,bothinNevada.5Thefirstdata
sourceistheClarkCountyPublicDefender(CCPD)6andincludesdataondefendants
representedbytheCCPD’sofficefrom2001–2008.Theinitialdatasetwascollectedin
ordertoinvestigatetheimpactthatattorneyshaveoncaseoutcomes(Abrams&Yoon,
2007;Abrams&Yoon,2009).ThekeyfeatureoftheCCPDisthattheofficeusesrandom
assignmentofcasestopublicdefendersforalmostallcases7.Inthispaper,Iexploitthis
randomassignmentandthesubstantialvariationinpublicdefenderskilltoinstrumentfor
sentencelength.
TheCCPDisintheminorityofpublicdefenderofficesinthatitusesrandomcase
assignmentandalsomakesuseofverticalrepresentation.Thisensuresthatasinglepublic
defenderhandlesalmostallcasesfrombeginningtoend.Theofficeusesrandom
assignmentpartlyasarecruitingtool,toenticeambitiousyoungattorneyswiththe
prospectofhandlinginterestingcasesmuchmorequicklythaninotheroffices.Thesystem
isalsoseenasbeingmoreequitablethanthehierarchicaloneusedinmostoffices.Forthis
paper,whatisimportantisitsconsistentapplication.InAbramsandYoon(2007&2009)
itwasempiricallyverifiedthatobservablecasecharacteristicsappeartoberandomly
assignedacrosspublicdefenders.
5
The Nevada DOC data is still being collected. Las Vegas contains the vast majority of the population of Clark County. 7
There are several classes of exceptions, including public defenders in their first year, certain sex crimes, and capital murder cases. For further detail see Abrams and Yoon (2007). 6
9 TheseconddatasetcomesfromtheNevadaDepartmentofCorrections(NDOC)and
containsdataonprisonersheldinNevadafromJanuary,2006–October,2009.The
offenderinformationincludesdemographicinformationandmayincludebeginningand
enddatesoftheprisonterm.
Table1summarizestheCCPDdataset.Inadditiontotherandomlyassigneddata,a
substantialnumberofadditionalobservationsareincludedinordertocalculaterecidivism
rates.Theseobservations(whichbringtheinitialtotalto110,282observations)often
containmissingdata,butaretakenasindicatorsofrecidivismaslongasthedefendantis
identifiable.Besidestherecidivismrates,thedatainTable1refersonlytotherandomly
assignedcases(n=17,471),whichincludeonlythefirstappearanceofanoffenderinthe
dataset.Thisimpliesthatthemeansentencesusedwillbelowerthanthemeanofthefull
dataset.
InNevada,defendantsreceiveasentencerangefromthejudge,indicatinga
minimumandmaximum.Inpractice,thevastmajorityofdefendantsareincarceratedfora
periodoftimemuchclosertotheminimumsentencelengththanthemean.8Forthis
reason,theprinciplemeasureofsentencelengthIuseistheminimum.Themean
minimumsentencelengthis4.6months(includingzeroes),althoughabouthalfthe
sentencesarezero.Theinstrument,whenconstructedusingOLSinthefirststage,hasan
identicalmeanbyconstruction,butsubstantiallylowerstandarddeviation.Whenthefirst
stageisatobitregressionthemeanofthepredicted(minimum)sentenceisabithigher
thantheunderlyingmean.Theseareduetothenon‐normalityofthesentencing
8
In some cases, defendants may be paroled even before serving the minimum sentence length, since a 2007 legislative reform. See Chapter 525, Statutes of Nevada 2007. 10 distributionandinparticularitslongrighttail(Figure1).Thenon‐normalityistobe
expectedinpartduetotruncationatzero.Onesimplepotentialfixwouldbetoperforma
logtransformation,asthedistributionoflogsentenceismuchclosertonormal.However
thisnecessarilydiscardsallofthezerosentences,whichmakeupthemajorityofthedata.
Thiswouldinvalidatetheinstrumentasdatawouldbeselectedbasedontheoutcome.9For
mostofthespecifications,IusethemaininstrumentbasedonPublicDefenderidentity,and
thisdistributionmaybeseeninFigure2.
Duetothelargenumberofzerosentences,conditioningonthesentence10being
non‐zeroyieldsameanof9.3months,substantiallyhigherthantheunconditionalmean.
Bycomparisonthemeanunconditionalsentence(theaveragebetweentheminimumand
maximumsentencingrange)is8.5months.Only50%oftheoffendersinthedataset
receiveasentencewithsomelengthofincarceration.11
Demographically,thedefendantsresemblethoseinmanyothercriminaljustice
populations:heavilymaleandminority.80%ofthepopulationismale,with31%Black
and22%Hispanic(theseclassificationsarenotmutuallyexclusive).Theaverageoffender
ageinthedatasetisalmost33yearsold,butthereissubstantialvariation,ascanbeseen
inFigure3.
9
One potential way to use this technique may be to find a subset of data for which all defendants receive some sentence, and thus taking the log does not discard any data based on the dependent variable. However, it is likely that the untransformed data will be close to normally distributed for just such a subset, making the transformation unnecessary. 10
From here forward I use sentence to indicate the minimum sentence, unless otherwise noted. 11
Probation (or suspended sentences) is counted as a zero sentence length in this data set. 11 Crimetypeisbrokendownintofourcategories,withpropertycrimescomprising
thelargestcategory,containing40%oftheoffenders.12Drugcrimesmakeup24%ofthe
data,andviolentcrimeanadditional16%.Sexcrimesaccountfor2%ofthedataand19%
donotfallintoanyofthesecategories.
Recidivismistheprimarydependentvariableandisdefinedhereasreappearance
intheClarkCountyPublicDefenderdatasetwithinafixedamountoftimefromexpected
releasefromincarceration.Thismeasureofrecidivismissomewhatintermediatebetween
arrestandimprisonmentdata.Itindicatesthatprosecutionhasprogressedtothepoint
whereaPDhasbeenassigned,butmanycaseswillnotresultinincarcerationoreven
conviction.Theassumptionisthatthisisanunbiasedmeasureofcriminalactivity.
Specifically,thenyearrecidivismdummyvariableis1iftheoffenderappearsinthedata
withinthenyearperiodimmediatelyfollowingreleasefromincarcerationandzeroifthere
isnoappearancewithinthiswindow.Thedateofreleasefromincarcerationisestimated
asthecaserecorddataplustheminimumsentencelength.Inordertoavoidtruncation
effects,recidivismdummiesarenotcalculatedforoffenderswhosesentencesendwithinn
yearsoftheendofthedataset.
Therecidivismratesestimatedinthispopulationareinlinewiththosefound
elsewhere,althoughthepopulationsandmethodforcomputingrecidivismvary.Theone,
two,andthreeyearrecidivismratesforthesampleare21.2%,34.9%and47.5%,
respectively.Theseratesareabithigherthanthosefoundforfederalprisonersin(Chen&
Shapiro,2007)of16.4%,27.5%and37.0%.AnotherpointofcomparisonistheUnited
12
The property crime category is equivalent to the Embezzlement, Fraud, and Theft (EFT) category used in other crime datasets. 12 StatesSentencingCommissionFY1992RecidivismSampleforwhichthetwoyear
recidivismrateis22.1%(USSC2003).InthenextsectionIinvestigatetowhatextentthese
recidivismratesareaffectedbysentencelength.
IV.The(Complicated)RelationshipbetweenSentenceLengthandRecidivism
Ifirstinvestigatetherelationshipbetweensentencelengthandrecidivismby
runninganaïvecross‐sectionallinearprobabilitymodelasin(1):
(1)
Hererecidisadummyvariablethatis1ifdefendantdrecidivateswithinpyearsofrelease
fromincarceration,zeroifthedefendantdoesnotrecidivateinthiswindow,andnot
observedotherwise.Theindependentvariableofinterestissentencelengthtowhich
defendantdwasinitiallysentenced.Anarrayofcaseanddefendant‐specificcontrols,
includingjudge,casetype,defendantage,defendantrace,defendantsex,aswellasmonthly
timedummiesareincludedasregressors.Thisisalsoestimatedusingaprobit
specification,whereΦisthecumulativenormaldistribution.
(2)
Φ
Themainproblemwiththisapproachisthatsentencesarenotrandomlyassigned
todefendants.Infactitislikelythatjudgesdeterminesentencesbasedinparton
characteristicsunobservabletotheeconometricianthatarealsocorrelatedwithlikelihood
ofrecidivism.Thatis,E[εd|sentd]≠0andislikely>0.Themostlikelysuchcharacteristicis
someunderlyingcriminalpropensity,whichisorthogonaltoallobservablecontrol
variable,butdetectablebythejudgeandcorrelatedwithsentencelength.Criminal
13 propensitywillalsocertainlybepredictiveofrecidivism,andthusfailuretoaccountforit
willresultinanupwardbiasedcoefficientonsentencelength.
TherandomassignmentofPublicDefenderstocasesintheCCPDconstitutesa
naturalexperimentinsentencelengthassignment.SincePD’svarysubstantiallyin
individualability,andassignmentisrandom,defendantseffectivelyfaceapartiallottery
oversentencelengths.Iusethislotterytoobtainanunbiasedestimateoftheeffectof
sentencelengthonrecidivismusinganIVregression.
Animportantmethodologicalchallengestillremains:howtobestmodelthe
sentencingdistribution.Sentencingcanbemodeledasatwostageprocess,composedof
thedecisionofwhethertoincarcerateandthenwhatmagnitudesentencetoassign,for
thosethatarenon‐zero.Thistypeofprocessleadsnaturallytoconsideringsomesortof
censoreddistribution,likethetobit.Anderson,KlingandStith(1999)useazero‐inflated
negativebinomialmodeltocapturethefactthatsentencesusuallyarechosenasanintegral
numberofmonths.Inresultsnotreportedinthepaper,thezero‐inflatednegativebinomial
wasfoundtofitthesentencingdistributionsimilarlytothetobit,andsotheanalysiswas
runusingthelatterforsimplicity.
Forthefirststageregression,Iinstrumentforsentencelengthusingafullsetofpublic
defenderdummyvariables(PDa)asin(3):
(3)
Thesecondstageusesthepredictedvaluesofsentencelengthtogetexogenousvariationin
(4),relyingontheidentifyingassumptionthatE[νd|PDa]andE[εd|PDa]=0.
14 (4)
Table2reportsresultsfromtheOLSregressionsaswellasthefirststagefromthe
IVregression.Thefirstcolumnreportsresultsfromthebaselinearprobabilitymodel
describedinequation1.Thereisastatisticallysignificantandnegativecoefficienton
sentencelength,indicatingthatinthecross‐sectionanextramonthsentencelengthis
associatedwithadecreasedrecidivismrateofabout0.7percentagepoints.Figure5a
displaystherelationshipgraphically.Offthemean18%oneyearrecidivismratefoundin
Table1,thisisareductionofaround3.3%.Ofcourse,thisislikelytosufferfromomitted
variablesbias,asdiscussedbefore.BeforeIattempttoaddressthisconcern,Iexaminethe
relationshipofthecontrolvariablesandrecidivismaswellastheotherspecifications.
Thesecondspecificationusesaprobitmodelratherthanlinearprobability.The
reportedmarginaleffectof‐.0079isstatisticallyindistinguishablefromthecoefficientin
thelinearprobabilitymodel.Irunprobitversionsofalloftheothermodelsaswellandthe
resultsareallconsistentwiththelinearprobabilitymodel,sotheyareomittedfromthe
tables.
Oneofthemostdifficultempiricalchallengeswithdeterminingrecidivismratesis
howtoproperlycontrolforage.Itiswellknown(BushwayandPiehl2007)that
criminalitydeclinesovertime.Infactonecanseetrendclearlyinthisdataset,asinFigure
4.Thispresentsamajorchallengetotheeconometrician.Evenifavalidinstrumentis
foundforsentencelength,thetreatmentwillnecessarilyimplythatthosedefendantswho
arerepresentedbyworseattorneys(andhencegetlongersentences)willbeolderon
15 averageattimeofrelease.Thisthenhasadirectnegativeimpactonthemagnitudeof
recidivism.
Thuswenowhavereasonswhythenaïveestimatemaybeupwardbiased(omitted
variables)ordownwardbiased(thecriminalityageprofile,whichmayalsosimplybean
omittedvariable).Toaddresstheformerconcern,IusetheIVspecificationdescribedin
equations3and4above.Toaddressthelatter,Itakethreedifferentapproaches:First,I
controlforageatoffense.SinceIdonotknowtheexactreleasedatefromincarcerationin
theCCPDdataset,thisisatleastlikelytobestronglycorrelated.13SecondIusethe
estimatedreleasedate,calculatedastheinitialtrialdateplustheminimumsentence.
Finally,IusetheempiricalageprofileinFigure4tonormalizetherecidivismvariable.
Thusanobservationwithrecidivismwheretheoffenderis50willreceivesubstantially
moreweightthanwhentheoffenderis20.
Inthecross‐section,addingtheagecontrolsdoincreasethecoefficientonsentence
length,butonlyveryslightly(Table2,column3).Thepointestimatesaresomewhatlarger
inabsolutemagnitudeforthe2and3yearmeasuresofrecidivism,butasafractionofbase
recidivismratestheyareevensmaller,andlosestatisticalsignificanceforthe3yearrate.
Forthe3yearmeasurethecross‐sectionalregressionindicatesanapproximate3.5%
declineinrecidivismforamonthincreaseinminimumsentence(seeFigure6a).Sincethe
sentencingdistributionisveryskewed,thestandarddeviationisnotnecessarilyvery
informative.Stillusingthevalueof11.1monthstranslatestoasubstantial39%declinein
recidivismassociatedwithaonestandarddeviationincreaseinsentencelength.An
13
In future work incorporating Nevada DOC data I will know the exact date of release. 16 examinationofthecontrolvariablesindicateslittleconsistencythatisstatistically
significantacrossmostspecifications,exceptthatBlackandmaleoffenderstendtohave
higherrecidivismrates.
Table3presentsthemainregressionresultsfromtheIVstrategy,althoughasIwill
discussshortly,linearregressiontellsaveryincompletestoryinthiscontext.Theresults
fromthefirststage(column1)areunsurprising:maledefendantstendtoreceivelonger
sentences.Weakinstrumentsmaybeaconcerninthisdataset.Itestforthembylooking
atthechangeinR2whentheinstrumentsareaddedtotheregression(arelativelysmall1.5
percentagepoints).IalsorunanF‐testonthejointsignificanceoftheinstruments.The
valueofaround6islessthantherule‐of‐thumbthresholdof10.However,thesetestsmay
beinappropriategiventhenon‐normalityoftheerrors.
ThemainreasonthatIVisimportantinthiscontextistoavoidtheunobserved
variablesproblem.Iarguedabovethattheunobservedcriminalpropensityislikelytobias
thecoefficientonsentenceupwardinthiscontext.Incolumn2ofTable3wefindevidence
forthisargument,asthecoefficientonsentencelengthisalmosttwicethemagnitudeas
thatintheOLSregression,wherethefirststageisalinearmodel(seealsoFigure5b).14
Adjustingfortherecidivism‐ageprofiledoeslittletochangethecoefficient.Becauseofthe
potentialweakinstrumentsconcern,IalsoperformaLIMLIVregressionwhichshouldbe
consistentevenwithweakinstruments.Thepointestimatefromthisspecificationis
negative,butsmallerinmagnitudeandstatisticallyinsignificant.Whenlookingattwoor
threeyearrecidivism(seeFigure6b),thecoefficientremainsnegativeandlargerin
14
One ramification of using a linear model for the first stage is that predicted sentence can be negative. This leads to the unusual aspect of Figures 5b and 6b having some negative‐valued sentences. The slope of the curve is unaffected by axis scale and this is the parameter of interest. 17 magnitudethanOLS,andstatisticallyindistinguishablefromzero.AsintheOLS
regressions,offenderageissignificantlynegativelyrelatedtorecidivism.Blackandmale
offendershavehigherrecidivismratesaswell,whichwasalsoseenintheOLS.
Whenusingatobitmodelforthefirststage,theresultsdiffersomewhat,butare
consistentwiththeOLSfirststageresults.Thecoefficientonsentencelengthismore
positiveforeachofthethreetimewindowsexamined,butallarestillstatistically
insignificant.AnexaminationofFigures5canddand6cprovidesthevisualanalogofthese
regressions.WhiletheIVapproachiskeytogettinganunbiasedmeasureofspecific
deterrence,thecoefficientsarenotmeaningfuliftherelationshipbetweendeterrenceis
notlinear,ashasbeenassumedthusfar.Ratherthanattemptingamorecomplicated
parametricorsemi‐parametricapproach,thefiguresprovidemoreinformativenon‐
parametricevidence.
Figures5and6showacomplicatedrelationshipbetweenrecidivismandsentence
length,onethatisnotwell‐capturedinamonotonicregressionasreportedinTables2and
3.Thereisagenerallynegativerelationshipbetweenrecidivismandsentencelength,
althoughonethatdoesnotappearverylinear(whichmayexplaintheinsignificant
regressionresults).Bothfigures5cand6cseemtoindicatethatwhilelongersentences
mayreducerecidivismforshortsentencelengths,theeffectsrapidlypeterout.
Inextexaminetheextensivemargin:theeffectofachangeinlikelihood,ratherthan
length,ofincarcerationonfuturerecidivism.TheresultsarereportedinTable4and
Figures7aand7b.Aswiththeintensivemargin,theOLSresultsappeartobeupward‐
18 biased.Thisseemslikeanaturalramificationofjudgesbeingmorelikelytosentencethe
unobservablycrime‐pronetoincarceration.Herethepointestimatesforalltimeranges
arepositiveandstatisticallysignificantforOLS,butinsignificantforIV.Theremaystillbea
substantialpositiveimpactofincarcerationonrecidivismofupto10percentagepoints,
butthelargestandarderrorsintheIVspecificationsmakethisimpossibletodistinguish
fromanulleffect.
Tothispointallrecidivatingcrimeshavebeentreatedequally.Fromapolicy
perspective,onemaywanttoweightrecidivatingcrimesaccordingtotheirseverity.In
Table5andFigures8aand8b,Iperformthesameanalysis,butreplacethebinary
recidivismdependentvariablewiththeexpectedsentencelengthfortherecidivating
crime.Thisshouldbeareasonablemeasureoftheseverityoftherecidivatingcrime.The
resultsshowthatlongersentencesleadtoanincreasedseverityofrecidivatingcrime.The
regressioncoefficientsarenotstatisticallysignificant,althoughthestandarderrorsare
quitelarge.ThevisualevidenceinFigures8aand8bseemtosupportthepositive
relationship.
Sincealmostallfeloniesareincludedinthedataset,itispossiblethatsomeofthe
nullresultsareduetoheterogenouseffectsbycrimetype,crimeseverity,orother
characteristics.SincetherandomassignmentofcasestoPD’sisessentialtothe
identificationstrategy,itisnotpossibletoexaminesubsetsofthedatabyacharacteristic
likecrimeseverity(asmeasuredbysentencelength)thatisanoutcomeofthetrialprocess.
Butsincealltypesofcasesarerandomlyassigned,itispossibletoperformtheanalysisfor
aparticulartypeofcrime.Unfortunately,theonlyhomogenouscrimecategoryforwhich
19 thereispotentiallysufficientdataisdrugcrimes.ThisanalysisisreportedinFigures9a,
9b,and9c.Theregressionresultsareomitted,butconveythesameinformationasthe
figures:namelythatthereisnosignificantrelationshipbetweensentencelengthand
recidivismfordrugcrimes.Thefiguresconveythelackofpowerinthisanalysis,soevena
substantialcoefficientmightnotbedetectedbythisanalysis.
V.Conclusion
Seentogether,thedatatellsacomplicatedstory,butonethathelpstoexplainthe
divergenceofpreviousfindings.Loeffler(2005)reportsthatofthehandfulofpapersthat
havepreviouslytriedtoaddresstheomittedvariablesconcern,6reportednodeterrent
effectand4reportedapositiveeffect.Dependingonwhichpartofthedistributionone
focusesonandthemeasureofrecidivism,thispapercouldfindapositive,negative,orno
effect.
Onecontributionofthispaperistheabilitytoexaminetheeffectonrecidivismover
alargerangeofthesentencingandincarcerationdistributions.Almostallpreviouswork
hasfocusedeitheronanarrowsubset,orassumedahomogeneouseffect.Butan
examinationofthefiguresproducedhereshowthatthisassumptionisincorrect.This
paperfurthershowstheimportanceoftheIVapproachwhenthereisseriousconcern
aboutomittedvariables.
RunninganOLSorprobitofrecidivismonsentencelengthyieldsanegative
coefficientforalldurations,andonethatissignificantfor1yearrecidivism.AnOLSor
probitofrecidivismonprobabilityofincarcerationyieldsapositive,andstatistically
significantcoefficient.Itisstrikingthatthesignofthecoefficientisoppositethaton
20 sentencelength.IntheabsenceofOVB,thiswouldmeanthatgoingtoprisonmakesone
morelikelytorecidivate(perhapsevidenceforcriminalcapitalformation)butthelonger
spentinprisonmakesonelesslikelytorecidivate(perhapsexplainedbyupdatingof
prisonersastothelikelihoodofbeingsentencedtoprisonand/ortheunpleasantness
thereof).
Byinstrumentingforsentencelengthusingrandomlyassignedpublicdefenders,I
amabletoobtainacausalestimateoftheimpactofsentencelengthandincarcerationon
recidivism.TheseanalysesshowthattheOLSpointestimatesareupwardbiased,although
theIVresultsarestatisticallyinsignificant.Anexaminationofthefigures5‐7showsthat
thisislikelyduetothefactthattherelationshipisnonlinear.Whilelongersentencesmay
reducerecidivismforshortsentencelengths,theeffectsrapidlydiminish.
Theothermainresultsmakeuseoftheseverityofrecidivismasthedependent
variable.HereIfindthatlongersentencesincreasetheexpectedseverityofthe
recidivatingcrime.Thiscomplicatedrelationshiplendsatleastsomesupporttotheories
ofspecificdeterrence.Thecomplexityofthesefindingsisimportanttounderstandbetter
withaneyetowardmakingbetterpolicydecisions.
21 AppendixA:DataCleaningProcedure
Ibeginwithadatasetofover140,000charge‐levelobservationsfromtheClark
CountyPublicDefender’sOffice,butonlyafractionofthemaremadeuseofintheanalysis.
ThisAppendixdescribestheprocedureemployedtoproducetheusabledataset.
Approximately12,500observationsdonotcontainthenameoftheleadpublic
defenderonthecase.Lackingtheinstrument,theseobservationsaredropped.Theinitial
datasetcontainsmultiplechargespercase.Forsimplicity,onlythemostseverechargeis
examinedforeachcase,whicheliminatesapproximately24,000observations.Firstyear
publicdefendersdonotreceivecasesthroughtherandomassignmentprocessusedwith
otherPD’s,anddroppingtheircaseseliminatesabout20,500observations.
Thekeytotheidentificationstrategyinthispaperistherandomassignmentof
casestopublicdefenders.Sometimesmultipleattorneysmayworkonacase,makingit
difficulttoknowwhichonetoattributeacaseto.Thesecasesareeliminated,whichdrops
about44,500observations.Certaincasetypesarenothandledbyrandomassignment.For
example,probationviolationsareusuallyhandledbythesameattorneywhohandledthe
underlyingcase.Eliminatingtheseobservationsreducesthenumberbyabout13,000.
Finally,toensurethateachpublicdefenderhasaminimumof50totalcases,Ieliminate
about1,500caseshandledbythosePD’swithfewerthantheminimum.Thisleavesatotal
of28,803observationsforwhichthecasesarerandomlyassignedtopublicdefenders.
ThesecasesrepresentXdefendants.
22 FigureA1a(AlternativeReleaseDates)
1 Year Recidivism Rate vs. Predicted Sentence
.1
.15
Recidivism
.2
.25
.3
.35
First Stage Tobit
0
2
4
6
Predicted Sentence
8
10
FigureA1b(AlternativeReleaseDates)
2 Year Recidivism Rate vs. Predicted Sentence
.2
.3
Recidivism
.4
.5
First Stage Tobit
0
2
4
Predicted Sentence
23 6
8
FigureA2a(AlternativeReleaseDates)
1 Year Recidivism Severity vs. Predicted Sentence
2
Recidivating Sentence
4
6
8
10
First Stage Tobit
0
2
4
6
Predicted Sentence
8
10
FigureA2b(AlternativeReleaseDates)
2 Year Recidivism Severity vs. Predicted Sentence
2
Recidivating Sentence
4
6
8
10
First Stage Tobit
0
2
4
Predicted Sentence
6
8
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27 Figure1
0
1000
Frequency
2000
3000
Sentence Length Distribution
0
10
20
30
Minimum Sentence Length (months)
40
50
Figure2
PD Identity as an Instrument for Sentence Length (Tobit)
0
2
Frequency
4
6
8
10
Variation in Defendant Sentence by PD
0
2
4
PD Tobit Sentencing Effect (months)
6
28 Figure3
0
500
Frequency
1000
1500
Offender Age Distribution
20
40
60
Age at Offense
80
100
Figure4–ToReplace
.1
3 Year Recidivism Rate
.2
.3
.4
.5
.6
3 Year Recidivism-Age Profile
20
40
60
Actual Sentence
29 80
100
Figure5a
1 Year Recidivism Rate vs Actual Sentence
0
.1
Recidivism
.2
.3
.4
Cross Section
0
10
20
Actual Sentence
30
40
Figure5b
1 Year Recidivism Rate vs. Predicted Sentence
.1
.15
Recidivism
.2
.25
.3
First Stage OLS
-4
-2
0
2
Predicted Sentence
30 4
6
Figure5c
1 Year Recidivism Rate vs. Predicted Sentence
.1
.15
Recidivism
.2
.25
.3
.35
First Stage Tobit
0
2
4
Predicted Sentence
6
8
Figure5d
1 Year Recidivism Rate vs. Predicted Sentence
.1
.15
Recidivism
.2
.25
.3
.35
First Stage Tobit, Renormalized Ages
0
2
4
Predicted Sentence
31 6
8
Figure6a
3 Year Recidivism Rate vs Actual Sentence
.1
.2
Recidivism
.3
.4
.5
.6
Cross Section
0
10
20
Actual Sentence
30
40
Figure6b
3 Year Recidivism Rate vs. Predicted Sentence
.3
.4
Recidivism
.5
.6
.7
First Stage OLS
-2
0
2
Predicted Sentence
32 4
6
Figure6c
3 Year Recidivism Rate vs. Predicted Sentence
.3
.4
Recidivism
.5
.6
.7
.8
First Stage Tobit
0
2
4
Predicted Sentence
33 6
8
Figure7a
1 Year Recidivism Rate vs. Predicted Incarceration Rate
.1
.15
Recidivism
.2
.25
.3
First Stage Probit
0
.2
.4
.6
Predicted Incarceration Rate
.8
Figure7b
2 Year Recidivism Rate vs. Predicted Incarceration Rate
.2
.3
Recidivism
.4
.5
First Stage Probit
.2
.4
.6
Predicted Incarceration Rate
34 .8
Figure8a
1 Year Recidivism Severity vs. Predicted Sentence
2
Recidivating Sentence
4
6
8
10
First Stage Tobit
0
2
4
Predicted Sentence
6
8
Figure8b
3 Year Recidivism Severity vs. Predicted Sentence
2
Recidivating Sentence
4
6
8
10
First Stage Tobit
0
2
4
Predicted Sentence
35 6
8
Figure9a–DrugPossession
1 Year Recidivism Rate vs. Predicted Sentence
0
.1
Recidivism
.2
.3
.4
.5
First Stage Tobit
0
2
4
6
Predicted Sentence
8
10
Figure9b–DrugPossession
2 Year Recidivism Rate vs. Predicted Sentence
0
.2
Recidivism
.4
.6
First Stage Tobit
0
2
4
6
Predicted Sentence
36 8
10
Figure9c–DrugPossession
3 Year Recidivism Rate vs. Predicted Sentence
0
.2
Recidivism
.4
.6
.8
First Stage Tobit
0
5
10
Predicted Sentence
37 15
Table1
SummaryStatistics
Variable
Mean
Median Std.Dev.
Observations
SentencingCharacteristics
MinimumSentence(months)
PredictedMinSentence(tobit)
PredictedMinSentence(ols)
MeanSentence(months)
MinSentence(non‐zero)
Incarceration
4.59
5.7
4.59
8.5
9.3
0.50
0
5.7
4.8
0
6.0
0
11.1
2.9
2.7
22.3
14.3
0.50
17471
17310
17471
17471
8647
17471
OffenderCharacteristics
Ageatoffense
Black
Hispanic
Male
32.6
0.31
0.22
0.80
30.9
10.4
17471
17471
17471
17471
OffenseCharacteristics
Drugs
ViolentCrime
SexCrime
PropertyCrime(EFT)
Other
0.24
0.16
0.02
0.40
0.19
17471
17471
17471
17471
17471
0.212
0.349
0.475
4.15
13725
10243
7295
6113
RecidivismRates
Withinoneyear
Withintwoyears
Withinthreeyears
RecidivatingSentence
0.00
9.60
Summary Statisticsforoffender‐level dataobtained fromthe ClarkCountyPublic Defender forthe
years 2001 ‐ 2008.Offensecharacteristics reported forfirstoffense.Data includes81Public
Defenders, eachwithaminimumof50caseseach,and50judges. Recidivismisdefined as
reappearance asaPublicDefender clientwithinthe indicated timeafter release fromincarceration
(ifsentenced toincarceration).
38 Table2 OLSregressionresults
1YearRecidivism
VARIABLES
Sentence
Sex(1=male)
BlackOffender
HispanicOffender
DrugOffense
ViolentOffense
EFT
SexOffense
Constant
Observations
AdjustedR‐squared
**p<0.01,*p<0.05
(1)
(2)
Probit
Noage
control
Marginal
Effects
‐0.00706
(0.000580)**
0.0650
(0.00837)**
0.0365
(0.00828)**
‐0.0199
(0.00884)*
0.0138
(0.0140)
‐0.0283
(0.0148)
0.0227
(0.0134)
‐0.0227
(0.0269)
0.241
(0.0484)**
‐0.00785
(0.000736)**
0.0667
(0.00805)**
0.0360
(0.00821)**
‐0.0267
(0.00892)**
‐0.0501
(0.00930)**
‐0.0869
(0.00969)**
‐0.0380
(0.00914)**
‐0.0785
(0.0205)**
13573
0.030
13725
2YearRecidivism
3YearRecidivism
(3)
(4)
(5)
(6)
(7)
Recidivism‐
AgeProfile
Adjustment
Noage
control
Recidivism‐
AgeProfile
Adjustment
Noage
control
Recidivism‐
AgeProfile
Adjustment
‐0.00157
(0.00132)
0.0935
(0.0147)**
0.0790
(0.0132)**
‐0.0137
(0.0156)
0.00630
(0.0238)
‐0.0582
(0.0257)*
0.00477
(0.0223)
‐0.0136
(0.0464)
0.533
(0.0504)**
‐0.00168
(0.00134)
0.0952
(0.0149)**
0.0799
(0.0134)**
‐0.0243
(0.0156)
0.0126
(0.0243)
‐0.0632
(0.0259)*
‐0.000181
(0.0225)
0.0142
(0.0502)
0.518
(0.0500)**
7156
0.079
7146
0.074
‐0.00696
‐0.00533
‐0.00537
(0.000591)** (0.000899)** (0.000924)**
0.0648
0.0976
0.0992
(0.00848)** (0.0116)**
(0.0118)**
0.0354
0.0635
0.0622
(0.00841)** (0.0109)**
(0.0111)**
‐0.0263
‐0.0181
‐0.0292
(0.00882)**
(0.0123)
(0.0123)*
0.0171
0.0252
0.0307
(0.0142)
(0.0188)
(0.0191)
‐0.0299
‐0.0253
‐0.0281
(0.0148)*
(0.0201)
(0.0203)
0.0212
0.0374
0.0342
(0.0135)
(0.0179)*
(0.0180)
‐0.0100
‐0.0574
‐0.0419
(0.0288)
(0.0366)
(0.0393)
0.223
0.388
0.370
(0.0462)**
(0.0524)**
(0.0512)**
13557
0.028
10101
0.049
10087
0.045
Robuststandarderrorsinparentheses
Note:Offender‐leveldataobtainedfromtheClarkCountyPublicDefenderOfficefortheyears 2001‐2008.Monthlytimedummies
includedtoallow fortimevariationinoverallcrimerates.Sentenceistheminimumsentencemeasured inmonths,EFT=
embezzlement,fraud,theft.Dataincludes81PublicDefenders,eachwithaminimumof50casesand50 judges.Recidivismis
definedasreappearanceasaPublicDefenderclientwithintheindicatedtimeafterreleasefromincarceration (ifsentencedto
incareceration).
39 Table3
IVregressionresults
1YearRecidivism
FirstStageOLS
VARIABLES
(1)
FirstStage
Sentence
Length
Sentence
Sex(1=male)
BlackOffender
HispanicOffender
DrugOffense
ViolentOffense
EFT
SexOffense
AgeatOffense
Constant
Observations
AdjustedR‐squared
1.081
(0.123)**
0.0516
(0.110)
‐0.0235
(0.106)
0.896
(0.187)**
1.397
(0.233)**
1.631
(0.171)**
1.207
(0.361)**
0.000453
(0.00425)
‐0.884
(0.386)*
13573
0.165
(2)
Noage
control
FirstStage
Tobit
2YearRecidivism
IVLIML
3YearRecidivism
FirstStage FirstStage FirstStage FirstStage
OLS
OLS
Tobit
Tobit
(3)
(4)
(5)
(6)
Recidivism‐ Recidivism‐Age
Recidivism‐
AgeProfile
Profile
Controlfor
AgeProfile
Adjustment
Adjustment
ageatoffense Adjustment
(7)
Recidivism‐
AgeProfile
Adjustment
(8)
Recidivism‐
AgeProfile
Adjustment
(9)
Recidivism‐
AgeProfile
Adjustment
‐0.0148
(0.00519)**
0.0735
(0.0101)**
0.0369
(0.00831)**
‐0.0200
(0.00888)*
0.0199
(0.0145)
‐0.0169
(0.0165)
0.0357
(0.0158)*
‐0.0135
(0.0276)
‐0.0157
(0.00525)**
0.0744
(0.0103)**
0.0359
(0.00844)**
‐0.0265
(0.00886)**
0.0240
(0.0147)
‐0.0171
(0.0166)
0.0359
(0.0159)*
0.000429
(0.0294)
‐0.00478
(0.00425)
0.0624
(0.00965)**
0.0355
(0.00844)**
‐0.0261
(0.00887)**
0.0209
(0.0164)
‐0.0288
(0.0177)
0.0223
(0.0177)
‐0.00687
(0.0307)
‐0.00715
(0.00434)
0.0695
(0.00873)**
0.0338
(0.00744)**
‐0.0328
(0.0105)**
‐0.0530
(0.0149)**
‐0.0949
(0.0157)**
‐0.0437
(0.0167)**
‐0.0807
(0.0238)**
‐0.0126
(0.00741)
0.107
(0.0142)**
0.0622
(0.0111)**
‐0.0302
(0.0124)*
0.0392
(0.0210)
‐0.0160
(0.0237)
0.0468
(0.0220)*
‐0.0369
(0.0397)
0.00123
(0.00544)
0.0923
(0.0128)**
0.0622
(0.0111)**
‐0.0285
(0.0123)*
0.0217
(0.0228)
‐0.0402
(0.0246)
0.0215
(0.0235)
‐0.0481
(0.0411)
‐0.00757
(0.0103)
0.1000
(0.0171)**
0.0803
(0.0134)**
‐0.0246
(0.0156)
0.0214
(0.0288)
‐0.0533
(0.0311)
0.0113
(0.0302)
0.0202
(0.0512)
0.00514
(0.00824)
0.0901
(0.0161)**
0.0791
(0.0134)**
‐0.0251
(0.0157)
‐0.00385
(0.0330)
‐0.0796
(0.0337)*
‐0.0181
(0.0325)
0.00150
(0.0532)
0.233
(0.0485)**
0.214
(0.0463)**
0.230
(0.0461)**
0.271
(0.0174)**
0.363
(0.0514)**
0.375
(0.0510)**
0.514
(0.0504)**
0.519
(0.0500)**
13573
0.024
13557
0.022
13557
0.021
13725
0.022
10087
0.043
10087
0.042
7146
0.074
7146
0.074
**p<0.01,*p<0.05 Robuststandarderrorsinparentheses
Note:Offender‐leveldataobtainedfromtheClarkCountyPublicDefenderOfficefortheyears 2001‐2008.Monthlytimedummiesincludedtoallow fortime
variationinoverallcrimerates.Sentenceistheminimumsentencemeasured inmonths,EFT=embezzlement,fraud,theft.Dataincludes78PublicDefenders,
eachwithaminimumof50casesand51judges.RecidivismisdefinedasreappearanceasaPublicDefenderclientwithintheindicatedtimeafterreleasefrom
incarceration(ifsentencedtoincareceration).
40 Table4
RecidivismandIncarceration
1YearRecidivism
VARIABLES
Incarceration
Sex(1=male)
BlackOffender
HispanicOffender
DrugOffense
ViolentOffense
EFT
SexOffense
AgeatRelease
Constant
Observations
AdjustedR‐squared
**p<0.01,*p<0.05
(1)
OLS
0.0335
(0.00774)**
0.0543
(0.00836)**
0.0333
(0.00832)**
‐0.0272
(0.00901)**
0.00782
(0.0140)
‐0.0409
(0.0147)**
0.00654
(0.0134)
‐0.0254
(0.0270)
‐0.00159
(0.000340)**
0.296
(0.0490)**
13573
0.026
(2)
IV
2YearRecidivism
(3)
OLS
0.00396
0.114
(0.0437)
(0.0106)**
0.0574
0.0807
(0.00954)** (0.0115)**
0.0345
0.0565
(0.00839)** (0.0108)**
‐0.0257
‐0.0325
(0.00907)** (0.0124)**
0.00995
0.00777
(0.0186)
(0.0189)
‐0.0393
‐0.0443
(0.0188)*
(0.0201)*
0.00914
0.0115
(0.0191)
(0.0179)
‐0.0223
‐0.0510
(0.0309)
(0.0367)
‐0.00157
‐0.00288
(0.000340)** (0.000457)**
0.290
(0.0498)**
13540
0.025
0.487
(0.0535)**
10103
0.060
(4)
IV
0.0148
(0.0521)
0.0910
(0.0126)**
0.0591
(0.0109)**
‐0.0289
(0.0126)*
0.0161
(0.0259)
‐0.0393
(0.0261)
0.0192
(0.0257)
‐0.0500
(0.0407)
‐0.00282
(0.000460)**
0.467
(0.0546)**
10059
0.050
3YearRecidivism
(5)
OLS
(6)
IV
0.159
0.0889
(0.0131)**
(0.0804)
0.0777
0.0861
(0.0146)**
(0.0162)**
0.0706
0.0734
(0.0130)**
(0.0134)**
‐0.0311
‐0.0288
(0.0156)*
(0.0162)
‐0.0257
‐0.0358
(0.0238)
(0.0436)
‐0.0799
‐0.0959
(0.0254)**
(0.0403)*
‐0.0284
‐0.0405
(0.0222)
(0.0404)
‐0.0164
‐0.0337
(0.0466)
(0.0563)
‐0.00303
‐0.00294
(0.000575)** (0.000588)**
0.633
(0.0532)**
7156
0.100
0.608
(0.0545)**
7110
0.082
Robuststandarderrorsinparentheses
Note:Thistablereportsthe resultsofOLSand2SLS regressionsorrecidivism onabinaryincarcerationindicator.
Offender‐leveldataobtainedfromtheClarkCountyPublicDefenderOfficefortheyears 2001‐2008.Monthlytime
dummiesincludedtoallow fortimevariation inoverall crimerates. EFT=embezzlement,fraud,theft.Dataincludes
81PublicDefenders,eachwithaminimumof50casesand50judges.Atobitregressionisusedforthefirststageof
theIVregressionsreportedinthistable.
41 Table5
RecidivismSeverity
VARIABLES
Sentence
Sex(1=male)
BlackOffender
HispanicOffender
DrugOffense
ViolentOffense
EFT
SexOffense
AgeatRelease
Constant
Observations
AdjustedR‐squared
**p<0.01,*p<0.05
1Year
Recidivism
2Year
Recidivism
3Year
Recidivism
0.195
(0.159)
1.542
(0.296)**
‐0.292
(0.293)
‐0.673
(0.347)
‐0.736
(0.526)
0.443
(0.746)
‐0.357
(0.563)
‐1.874
(0.914)*
‐0.000828
(0.0138)
2.461
(1.261)
0.231
(0.175)
1.538
(0.311)**
‐0.168
(0.316)
‐0.560
(0.376)
‐1.008
(0.626)
0.363
(0.803)
‐0.519
(0.620)
‐1.639
(1.104)
0.000826
(0.0149)
2.404
(1.269)
0.0726
(0.218)
1.460
(0.357)**
‐0.385
(0.352)
‐0.526
(0.420)
‐1.027
(0.766)
0.775
(0.912)
‐0.0444
(0.764)
‐1.299
(1.230)
0.00533
(0.0168)
2.686
(1.290)*
5707
0.011
4950
0.011
4064
0.082
Robuststandarderrorsinparentheses
Note:Thistablereports2SLS regressionswhere theoutcomeistheexpected
sentenceoftherecidivatingcrime.Offender‐leveldataobtainedfromtheClark
CountyPublicDefenderOfficefortheyears 2001‐2008.Monthlytimedummies
includedtoallow fortimevariationinoverallcrimerates.Sentenceisthe
minimumsentencemeasured inmonths,EFT=embezzlement,fraud,theft.Data
includes81PublicDefenders,eachwithaminimumof50casesand50judges.A
tobitregressionisusedforthefirststageinalloftheregressionsreportedinthis
table.
42