Mirta B. Gordon Pisa, April 17-18, Laboratoire TIMC-IMAG CNRS and Université de Grenoble

Transcription

1 Crime and Mirta B. Gordon Laboratoire TIMC-IMAG CNRS and Université de Grenoble Collaborators J. R. Iglesias, J-P. Nadal, V. Semeshenko Pisa, April 17-18, 2008

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3 : an old problem

4 : an old problem explanations deviance, anomia (before the 60 s) poverty inequality age gender social and urban segregation

5 : an old problem explanations deviance, anomia (before the 60 s) poverty inequality age gender social and urban segregation prevent - deter lex talionis an eye for an eye banishment England sent criminals to Australia in 18th century incapacitation imprisonment, execution punishment criminals may be rehabilitated

6 statistical data sources of data too aggregated (mostly at country level) systematic biases (under-reporting) no agreement on the types of s difficult to disentangle causes from effects ex: effect of probability of arrest on amount of vs. effect of amount of on probability of arrest

7 statistical data sources of data too aggregated (mostly at country level) systematic biases (under-reporting) no agreement on the types of s difficult to disentangle causes from effects ex: effect of probability of arrest on amount of vs. effect of amount of on probability of arrest individual data self-reports on criminality activity records of criminality activity compiled by the justice system (bias: only convicted persons included)

8 causes of rate = f(explicative variables) statistical studies regressions variables: income, inequality, % young males, education, probability of arrest,... choice of proxies guided by availability - homicide rates for rates, death penalty for punishment,... hypothesis not fully discussed - Fajnzylber et al (2002) correct the reported homicide rate yi,t of country i by a constant: y i,t = yi,t + ξ i - Deutsch et al (1992) assume that punishment is criminal s wealth -... lack of systematic studies - each author considers different explicative variables

9 quoting Fajnzylber et al (2002) - rate vs. expected punishment often contradictory Ehrlich (1973, 1975a) found that rates are sensitive to the expected size of punishment Archer and Gartner (1984) find no impact of capital punishment on murders in their cross-national study

10 quoting Fajnzylber et al (2002) - vs. average income often contradictory Fleisher (1966) and Ehrlich (1973) examined the effect of unemployment rates, income levels, and income disparities their findings on the effects of average income levels are contradictory

11 quoting Fajnzylber et al (2002) - vs. education often contradictory Tauchen and Witte (1994) find that in a sample of young men, going to work or school tends to reduce the probability of being involved in criminal activities. Ehrlich (1975b) finds a positive relationship between the average number of school years completed by the adult population and property s committed across the U.S. in 1960 ( education puzzle ).

12 recent studies - contradictions remain often contradictory Entorf and Spengler (2000) Socioeconomic and demographic factors of in Germany (data of 11 German Laender over , all types of ) higher income is associated with higher rates higher urbanization is associated with higher rates Fajnzylber et al (2002) What causes violent? (data of 45 countries over , homicide and robbery) average income is not correlated with (violent) higher urbanization is associated with higher robbery rates but not with homicide rates

13 some robust - is correlated with: explaining inequality (Ehrlich (1996), Hojman (2002)) probability of punishment, but not with punishment severity (Eide, 1999) age and gender: 7% of the US workforce were men under supervision of the criminal justice system in 1993 (Freeman, 1996)

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15 JUSSIM functional models A. Blumstein, 2002 developed by the Task Force on Science and Technology created in 1966 by the President s Commission on Law Enforcement and Administration of Justice, USA

16 JUSSIM functional models A. Blumstein, 2002 developed by the Task Force on Science and Technology created in 1966 by the President s Commission on Law Enforcement and Administration of Justice, USA - a model for evaluating the costs and required resources for a criminal case, by considering the flow through the justice system

17 economic models G. Becker (1968), Stigler(1974), Ehrlich (1975, 1996),... costs and benefits of social loss function social loss from offenses (number and produced harm) cost of deterrence factors (aprehension and conviction) probability of punishment per offense

18 economic models G. Becker (1968), Stigler(1974), Ehrlich (1975, 1996),... costs and benefits of social loss function social loss from offenses (number and produced harm) cost of deterrence factors (aprehension and conviction) probability of punishment per offense questions how many offenses should be permitted? how many offenders should go unpunished?

19 dynamical models Campbell,Ormerod (2000), Nuño,Herrero,Primicerio (2008) evolution: differential equations

20 epidemiology - three categories of individuals criminal C susceptible S non-susceptible N dynamical models Campbell,Ormerod (2000), Nuño,Herrero,Primicerio (2008) evolution: differential equations - flows between categories: social pressure against C contamination of S by C

21 epidemiology - three categories of individuals criminal C susceptible S non-susceptible N - flows between categories: dynamical models Campbell,Ormerod (2000), Nuño,Herrero,Primicerio (2008) social pressure against C contamination of S by C evolution: differential equations predator-prey - three kinds of individuals owners O are preys criminals C: predators of O guards G: predators of O, C - evolution of the populations efficiency of the guards G competition C vs. G

22 other models network models (Ballester,Calvó-Armengol,Zenou (2006)) network organization centrality of actors: key-player...

23 other models network models (Ballester,Calvó-Armengol,Zenou (2006)) network organization centrality of actors: key-player... multi-agents models (Epstein,Steinbbruner,Parker (2001)) idiosyncratic characteristics encounters network organization...

24 a preliminary multi-agents model

25 a preliminary multi-agents model aim initiate dialog with experts, set a basis for further developments

26 main elements a preliminary multi-agents model society composed of N heterogeneous individuals s (thefts) have a probability of punishment the fraction of punished criminals affects the law-abidingness of the population

27 main elements a preliminary multi-agents model society composed of N heterogeneous individuals s (thefts) have a probability of punishment the fraction of punished criminals affects the law-abidingness of the population monthly dynamics criminality rates, costs and earnings as a function of time

28 main elements a preliminary multi-agents model society composed of N heterogeneous individuals s (thefts) have a probability of punishment the fraction of punished criminals affects the law-abidingness of the population monthly dynamics criminality rates, costs and earnings as a function of time main result phase transition depending on the relative of important s

29 each individual i is characterized by a monthly wage W i details of the model individual characteristics

30 each individual i is characterized by a monthly wage W i details of the model individual characteristics drawn at random from an unequal distribution: 0, , , ,0 0 5 p W (W ) 0, W

31 each individual i is characterized by details of the model individual characteristics a (time-dependent) honesty level H i in [H min, H max ] (inclination to abide by the law) 0,0 5 p H (H ) drawn at random from an initial distribution: 0,0 3 % o f in itia l in trin s ic c rim in a ls s u s c e p tib le 0, H

32 criminal attempts details of the model monthly dynamics each month m there are A(m) criminal attempts A(m) decreases with the average honesty level A(m) increases with the number of intrinsic criminals

33 criminal attempts details of the model monthly dynamics each month m there are A(m) criminal attempts A(m) decreases with the average honesty level A(m) increases with the number of intrinsic criminals at each attempt a potential criminal k and a potential victim v are drawn at random among the (not imprisoned) population the is more likely to be committed the lower the honesty level H k and the wage W k of k

34 number of criminal attempts details of the model implementation 8 Hmax (m) H(m) >< 1 + r(m) c A N + N H(m) C (m) if H(m) H min, A(m) = >: 1 + r(m) c A N + 2 N C (m) if H(m) = H min. where 1 r(m) N (random) ensures A(m) 1 N c(m) is the number of intrinsic offenders (H i = 0) probability of we draw a random honesty value H U [H min, H max ] if H k < H U the is committed with probability p k = e W k /W another implementation: p k = e W k /W e H k /H (1)

35 details of the model and probability of punishment the criminal steals a random amount S proportional to the victim s v wage: S W v (or the victim s wealth K v if S > K v ) wealths are updated the victim s capital is decreased K v K v S the criminal s capital is increased K k K k + S

36 details of the model and probability of punishment the criminal steals a random amount S proportional to the victim s v wage: S W v (or the victim s wealth K v if S > K v ) wealths are updated the victim s capital is decreased K v K v S the criminal s capital is increased K k K k + S probability of punishment depends on the importance of the offense: π(s) = 1,0 π(s ) p p 1 0 = 0.4, p 1 = p 1 p 0,2 0 e p S/W p 0 = 0.3, p 1 = 0.5 p 0 0 = 0.3, p 1 = 0.6 0, p 0 0,8 0,6 0,4 W = 3 4 p 1 S

37 if criminal k is punished details of the model punishment prison: number of months stolen amount: 1 + S/W duty: returns a fraction f R S (f R < 1) to victim v pays a fine f D S (if capital K k is smaller than f D S, k contributes with K k )

38 if criminal k is punished details of the model punishment prison: number of months stolen amount: 1 + S/W duty: returns a fraction f R S (f R < 1) to victim v pays a fine f D S (if capital K k is smaller than f D S, k contributes with K k ) losses: contribution to taxes we set f R + f D 1: victim loses (1 f R )S criminal loses (f R + f D 1)S (or K k if f D S > K k )

39 details of the model honesty dynamics punished honesty levels of all but the criminal k increase: H i H i + δh criminal s honesty level does not change: H k H k

40 details of the model honesty dynamics punished honesty levels of all but the criminal k increase: H i H i + δh criminal s honesty level does not change: H k H k unpunished honesty levels of all but the criminal k decrease: H i H i δh criminal s honesty level decreases even more: H k H k 2 δh

41 free individuals monthly balance after the A(m) attempts wealths K i are updated wage W i is added monthly living costs are subtracted L i = W min + f (W i W min ), 0 < f < 1

42 free individuals monthly balance after the A(m) attempts wealths K i are updated wage W i is added monthly living costs are subtracted L i = W min + f (W i W min ), 0 < f < 1 inmates wealths K i do not change cumulated taxes are decreased by W min to account for the convicted living cost inmates having completed their conviction time are freed

43 - depend crucially on the probability of punishment 1,0 π(s ) p 0 0,8 0,6 0,4 0,2 0,0 as a function of time W = S p 0 = 0.4, p 1 = 0.9 p 0 = 0.3, p 1 = 0.5 p 0 = 0.3, p 1 = 0.6 p 1

44 - depend crucially on the probability of punishment 1,0 π(s ) p 0 0,8 0,6 0,4 0,2 0,0 as a function of time W = S p 0 = 0.4, p 1 = 0.9 p 0 = 0.3, p 1 = 0.5 p 0 = 0.3, p 1 = 0.6 s, convicted, inmates vs. time: phase transition p 0 = 0.3, p 1 = 0.5 p 0 = 0.3, p 1 = 0.6 p

45 as a function of time average wealth vs. time

46 as a function of time average wealth vs. time inequality: Gini coefficient 0,75 0,70 0,65 0,60 0,55 0,50 0,45 0, ,35 0, the Gini coefficient 0 G 1 increases with inequality

47 s, botty, taxes 0,8 at the end of 240 months vs. probability of punishment 0,6 0,4 0,2 0,0 0,2 0,4 0,6 0,8 1,

48 at the end of 240 months vs. probability of punishment s, botty, taxes 0,8 average wealth and Gini ,6 0,4 0,2 0,0 0,2 0,4 0,6 0,8 1, ,2 0,4 0,6 0,8 1, , ,7 0, ,5 10 0, ,2 0,4 0,6 0,8 1,0

49 probability of initial values: wealth distribution actual initial values: 0,0 2 0 p W (W ) 0, , , , W

50 probability of initial values: wealth distribution actual initial values: 0,0 2 0 p W (W ) 0, , , , W final distribution (p 0 = 0.3, p 1 = 0.5): final distribution (p 0 = 0.3, p 1 = 0.6):

51 probability of initial values: honesty index distribution actual initial values: 0,0 5 p H (H ) 50 % o f in itia l in trin s ic c rim in a ls 0,0 3 s u s c e p tib le 0, H

52 probability of initial values: honesty index distribution actual initial values: 0,0 5 p H (H ) 50 % o f in itia l in trin s ic c rim in a ls 0,0 3 s u s c e p tib le 0, H final distribution (p 0 = 0.3, p 1 = 0.5): all the population ends up with H i = 0

53 probability of initial values: honesty index distribution actual initial values: 0,0 5 p H (H ) 50 % o f in itia l in trin s ic c rim in a ls 0,0 3 s u s c e p tib le 0, H final distribution (p 0 = 0.3, p 1 = 0.5): final distribution (p 0 = 0.3, p 1 = 0.6): 500 all the population ends up with H i =

54 1,0 0,8 0,6 0,4 0,2 0, Crime and probability of initial values: honesty index distribution actual initial values: 0,0 5 p H (H ) 50 % o f in itia l in trin s ic c rim in a ls 0,0 3 0, H s u s c e p tib le - honesty dynamics for π = constant H(t + 1) (1 π)[h(t) δh] + π[h(t) + δh] H constant for π = 1/ final distribution (p 0 = 0.3, p 1 = 0.6): π(s ) W = p 0 S p 0 = 0.4, p 1 = 0.9 p 0 = 0.3, p 1 = 0.5 p 0 = 0.3, p 1 = 0.6 if p 0 < 1/2 then p 1 > 1/2 p

55 main assumptions - punishment has a deterrent effect on criminality honesty (law abidness) is independent of the income depends on the number of punished s small larcenies have lower probability of being punished - phase transition in the society s properties tolerance to small larcenies requires bigger efforts to cope with important s - drops in criminality have positive consequences increase the earnings of the population stabilization of inequality

56 open questions treatment of recidivism other laws for the probability of punishment consider criminals that choose victims according to the expected payoff effects of imprisonment time on honesty level consider networks of criminals...

57 Thank you!

58 [1] [2] [3] [4] [5] [6] [7] [8] [9]

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60 Horst Entorf and Hannes Spengler. Socioeconomic and demographic factors of in germany: Evidence from panel data of the german states. International Review of Law and Economics, 20:75 106, Pablo Fajnzylber, Daniel Lederman, and Norman Loayza. What causes violent? European Economic Review, 46: , Richard B. Freeman. Why do so many young american men commit s and what might we do about it? Journal of Economic Perspectives, 10:25 42, (1996). David E. Hojman. Explaining in Buenos Aires: the roles of inequality, unemployment, and structural change. Bulletin of Latin American Research, 21: , (2002).