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1 On the Impact of the NSW Crmnal Justce System on Crme * Dr Vasls Sarafds, Dscplne of Operatons Management and Econometrcs Unversty of Sydney * Ths presentaton s based on jont work wth Rchard Kelaher 1

2 Introducton Crme, orgnatng from the root of Latn cernō ( I decde, I gve judgement ) s the behavour judged by the State to be n volaton of the prevalng norms of socety. For offences deemed to be serous, crmnal justce systems have hstorcally mprsoned those responsble n the hope that a combnaton of deterrence and ncapactaton may lower the crme rate. More than 9.8 mllon people n the world are nsttutonalsed for punshment, half of whch are held n the U.S., Chna and the U.K. (Walmsley, 2000). Over the past 30 years the U.S. prson populaton has more than quadrupled, manly due to an ncrease n puntveness rather than an ncrease n the rate of crme (Raphael and Stoll, 2009). 2

3 NSW The ncarceraton rate n NSW has ncreased over 23% n the last 10 years and s currently hgher than that of Germany. The NSW prson system costs taxpayers more than $1 bllon per year. At the same tme crme rates have fallen or remaned relatvely stable, leadng some to declare such hgh rates of ncarceraton a polcy falure. How effectve s the crmnal justce system n deterrng crme? To what extent do changes n law enforcement rules nfluence the motvaton of ndvduals to engage n llegal pursuts? To address these questons n a constructve way and assst n formulatng polces to deter crme, one needs to understand the causes for such behavour. Durng the early part of the 20 th century, crmnal behavour was vewed as a type of socal llness. 3

4 The economc model of crme (Becker 1968) Becker (1968) argued that crmnals are ratonal ndvduals who engage n llegal actvty because the subjectve beneft exceeds the expected cost of dong so The key concepts/ngredents n hs theory are: The probablty of convcton (p ) The ncome or beneft flowng from llegal actvty (Y ) The collateral costs assocated wth crmnal charges (C ) The cost to the ndvdual of the sancton mposed as punshment (S ) The ncome from legal actvty (I ) The subjectve value of the benefts from llegtmate actvty (U NL ) and legal actvty (U L ) Expressed n mathematcal terms, Becker s (1968) theory mples that an ndvdual commts a crme whenever: p U NL NL L Y C S 1 p U Y U I 4

5 The economc theory of crme (Ehrlch 1975) E Ehrlch (1975) later expanded ths theory, argung that the probablty of punshment should be decomposed nto ts three component parts: the probablty of arrest (P A ), the probablty of convcton gven arrest, (P C A ) and the probablty of mprsonment gven convcton (P P C ) Expressed n mathematcal terms Ehrlch s (1975) model mples that the expected utlty (beneft) from crme E(U NL ) can be expressed as follows: NL NL NL NL U 1 P 1 A U Y P P U Y C P P U Y C S A C A A C A P C NL ' P P 1 P U Y C S. A C A P C 5

6 Key mplcatons of the theory The model just descrbed has two very mportant mplcatons: (1) Increases n the probablty of arrest (P A ), the probablty of convcton gven arrest (P C A ) and the probablty of mprsonment gven convcton (P P C ) should decrease the expected utlty (beneft) from crmnal actvty. (2) The margnal deterrent effects of the crmnal justce system are ordered, such that the effect of P A > P C A > P P C. In other words, ncreasng the probablty of arrest should have a larger mpact on crme than ncreasng the probablty of convcton gven arrest; AND Increasng the probablty of convcton should have a larger mpact on crme than ncreasng the probablty of mprsonment. 6

7 Testng the theory (1) If the theory has some emprcal relevance, one should be able to predct crme behavour and test the mplcatons of theory usng a statstcal model contanng terms reflectng The lkelhood of arrest; The lkelhood of convcton gven arrest; The lkelhood of mprsonment gven convcton; The expected length of the prson term; Other factors lkely to affect crme (e.g. unemployment & ncome) Indeed, a large emprcal lterature has emerged, tryng to nform publc polcy on the effect of the crmnal justce system on crme. Ths s well justfed gven the adverse effects that crme has on economc actvty, as well as on the qualty of one s lfe n terms of a reduced sense of personal and property securty. 7

8 Exstng evdence There s no research consensus on the mpact of the crmnal justce system on crme. For example, Hrsch (1998) argues: Estmates of the deterrent effect vary Further emprcal nvestgaton s necessary to gan a more accurate estmate of ts magntude Cornwell and Trumbull (1994) conclude: The ablty of the crmnal justce system to deter crme s much weaker than prevous results ndcate A fundamental flaw n each of the [prevous] studes s an nablty to control for unobserved heterogenety We argue that t ths lack of consensus s manly due to the nablty of prevous studes to overcome effectvely a number of problems encountered wth statstcal modellng of crme. The most mportant of these are: Smultanety Dynamc ms-specfcaton Omtted varable bas 8

9 Smultanety Smultanety arses when two factors, x and y nfluence each other. Typcally, we thnk of crme = a functon of arrest rate Or, crme = functon of mprsonment rate In both cases, there s an mplct assumpton that there exsts a un-drectonal cause-and-effect relatonshp between crme and the deterrence varables. Standard estmaton technques, such as Ordnary Least Squares, are not desgned to deal wth ths ssue. We deal wth ths problem usng a specal statstcal method of analyss called the GMM approach (the detals of whch h don t matter here). 9

10 Dynamc ms-specfcaton Past research has often assumed that the full effects of law enforcement polces occur almost nstantly Ths s unrealstc as t may take some tme for people to realse any changes n enforcement actvty n a partcular area, and of course humans often form ther decsons based on habt formaton and costs of adjustment. If we are to fully capture the effects of the crmnal justce system, we need to formulate a dynamc model that allows these effects to be dstrbuted over tme. 10

11 Omtted varable bas Omtted varable bas occurs when there exst factors omtted from the model, whch are correlated wth those ncorporated nto the model. The result of ths s that the true mpact of the omtted factors s lkely to then be absorbed by those ncluded nto the model, leadng to based nferences wth respect to the effect of the crmnal justce system on crme. It s rarely the case wth prevous studes that all varables prescrbed by theory are ncluded nto the model. Our paper shows that excluson of relevant deterrence varables can practcally lead to under-estmatng the true effect of polcng. 11

12 The model (don t panc) crm t crm t arr t conv t b b b b pop 1 ln t pop t crm t arr 0 ln 1 ln 2 ln 1 t b ln avsen b ln ncome b ln unemp e, e a d 4 t 5 t 6 t t t 3 t mpr ln conv u t t t The term ln just means the term n brackets s logged The equaton bascally says the crme rate at tme t = b 0 (crme rate at t-1) + b 1 (probablty of arrest at t) + b 2 (probablty of convcton at t) + b 3 (probablty of mprsonment at t) + b 4 (average sentence at t) + b 5 (ncome) + b 6 (unemployment) + e. The b s are called coeffcents and measure the sze and drecton of the expected mpact of the probablty of arrest, convcton, mprsonment, sentence length, ncome and unemployment on crme, all other thngs remanng constant. b 0 measures persstence,.e. the extent to whch habt formaton and costs of adjustment nfluence current behavour. 12

13 Our expectatons We expect b 1, b 2, b 3 and b 4 to be negatve and sgnfcant (*) because as the level of the deterrence varables ncreases, crme s lkely to decrease. We expect b 1 > b 2 > b 3 because our theory suggests changng the rsk of arrest should have a larger mpact on crme than changng the lkelhood lh of convcton, whch h n turn should have a larger effect than changng the lkelhood of mprsonment. We expect the coeffcent of unemployment to be postve and sgnfcant (*) because as unemployment ncreases, crme should go up. We expect the coeffcent on ncome to be negatve and sgnfcant (*) because as ncome goes up, crme should go down. 13

14 Testng the theory (2) To test the theory we obtaned annual data on volent and nonvolent crme n each of the 153 Local Government Areas n NSW over the 13 year perod from 1995/ We supplemented these data wth nformaton over the same perod n the same areas on: The proporton of people arrested The proporton of those arrested who were convcted The proporton of those convcted who were mprsoned The average prson term mposed on those who were mprsoned The unemployment rate The average wage for full-tme workers We then ftted our model to these data. 14

15 Results: descrptve statstcs Varable Type of Mean Standard 10 th 90 th Crme devaton percentle percentle Crme rate Probablty of arrest (b 1 ) Probablty of convcton (b 2 ) Probablty of mprsonment (b 3 ) Sentence length (days) (b 4 ) Total Non-volent Volent Total Non-volent Volent Total Non-volent Volent Total Non-volent Volent Total Non-volent Volent

16 Results: model effects Estmated Margnal Elastctes Total Crme Non-volent Crme Volent Crme Coeffcents Short-term Long-term Short-term Long-term Short-term Long-term Prob. of arrest (b 1 ) *** *** *** *** *** ** Prob. of convcton (b 2 ) *** *** ** *** *** *** Prob. of mprsonment(b 3 ) ** ** ** ** Sentence length (b 4 ) *** ** *** ** Income (b 5 ) ** *** *** ** Unemployment (b 6 ). 626 ***.962 ***.305 ***.481 ***.198 ***.554 ** Persstence.350 ***.366 ***.642 *** H0: b 1 >b 2 >b 3 YES YES NO The entres tell us the sze and drecton of the effect. The value of n the thrd row of the frst column, for example, means that a 1 per cent ncrease n the lkelhood of arrests, s expected to reduce total crme by 0.87 per cent n the short term and 1.3 per cent n the long-term. The value of.626 at the bottom of that row means that a 1 per cent ncrease n unemployment s expected to ncrease crme by and 0.96 per cent n the short- and long-term respectvely. 16

17 Summary of man results: Total Crme All estmated coeffcents are sgnfcant and have the expected sgn (- or +). The coeffcents assocated wth the rsk or apprehenson and convcton are much larger than those assocated wth the lkelhood and severty of punshment. Changng the lkelhood of mprsonment (gven convcton) appears to have a smlar effect wth that of changng sentence length, suggestng that crmnals respond to the expected length sentence as a sngle factor: e = prbmpr avsen. The effects of ncome and unemployment are large and statstcally t t sgnfcant. f The magntude of these effects dffer substantally, suggestng that n formulatng the crme-no crme decson ndvduals may consder more the level rather than the certanty of ther ncome. b 0 =.35 mples that t takes 2.5 perods for 90% of the total mpact of a change n a law enforcement actvty to be realsed. Restrctons mpled by theory are supported by the data. 17

18 Summary of man results: Non-volent & Volent Crme There are stark dfferences n the results obtaned for nonvolent and volent crme. The former resembles more closely the model for total crme, whch s not surprsng gven that about ¾ of total crme s non-volent. The hypothess of sequental orderng of the deterrence coeffcents s supported only for non-volent crme. Ths ndcates that ratonal behavour may apply only to ths type of crme. Ths s also manfested through the estmated coeffcents; for example, the effect of punshment, both n terms of lkelhood and severty, s statstcally sgnfcant only for non-volent crme and even so t appears to be small compared to the effect of ncreasng the rsk of apprehenson and convcton. Income and unemployment appear to have an apprecably smaller effect on volent crme. 18

19 Persstence (speed of adjustment) t) Volent crme s charactersed by hgher persstence. Whle t takes about 2.5 perods for 90% of the total mpact to be realsed for non-volent crme, volent crme requres about 6 perods for the same effect to occur 19

20 Concludng remarks Our fndngs suggest that the crmnal justce system can potentally exert much greater nfluence on crme than past estmates t suggest. From a polcy perspectve, t appears that targetng the rsk of apprehenson and convcton are more effectve strateges than ncreasng the severty of punshment. Volent crme appears to be more persstent and relatvely less responsve to changes n law enforcement polces compared to non-volent crme. Ths s to be expected snce volent crme s often commtted by people under the nfluence of alcohol or strong emotons such as anger or jealousy. 20

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