This paper demonstrates that increasing the expected sanctions for a crime may increase this crime's prevalence, using a principal-agent model with different crimes. The intuition is that the policy change may increase the principal's expected payoff from crime by decreasing the information rent required by the agent.Crime, principal-agent relation, information rent

Tim Friehe

English

Research Papers in Economics

 
 
 
 
 
 
University of Konstanz 
Department of Economics 
 
Tempting Righteous Citizens? 
On the Counterintuitive Effects of 
Increasing Sanctions 
 
 
Tim Friehe 
 
 
 
http://www.wiwi.uni-konstanz.de/workingpaperseries 
                           Working Paper Series  
2011-09 Tempting righteous citizens?
On the counterintuitive eects of increasing sanctions
Tim Friehe
May 5, 2011
Abstract
This paper demonstrates that increasing the expected sanctions for a crime may increase
this crime's prevalence, using a principal-agent model with dierent crimes. The intuition is
that the policy change may increase the principal's expected payo from crime by decreasing
the information rent required by the agent.
Keywords: Crime, principal-agent relation, information rent
JEL-Code: K42, H23
University of Konstanz, Box D 136, 78457 Konstanz, Germany. Phone: 0049 7531 88 2534. E-mail:
tim.friehe@uni-konstanz.de. I would like to thank Florian Baumann, Eberhard Feess, Laszlo Goerke, and seminar
participants at the University of T ubingen for very helpful suggestions.
11 Introduction
The question addressed in this paper is whether higher punishment for a crime may increase the
crime's incidence. In criminal law scholarship, it is commonly understood that higher sanctions will
help deter crimes (e.g., Meares et al. 2004). We conclude that increasing the sanction for or the
detection probability of a crime may induce more of this crime.1
To explain how we have arrived at this conclusion, we sketch the framework we will analyze.
We consider organized crime undertaken by a principal-agent pair, since it is characteristic for or-
ganized crime groups to be hierarchical in structure (Kumar and Skaperdas 2009). In contrast to
other research on organized crime (such as Garoupa 2000, Garoupa 2007), we allow for asymmetric
information regarding the agent's crime choice. The principal and the agent prefer dierent crimes of
which one involves violence and the other does not. Examples would be robbery versus burglary, or
extortion versus fraud. The use of violence increases the detection probability relative to the other
crime, but also implies a status gain for the agent.2 The principal must grant an information rent to
the agent in order to incentivize the agent to choose the non-violent crime. If the expected sanction
for the violent crime is increased, the information rent decreases, since the agent's preference for the
violent crime over the other is weakened.3 As a result, the principal's expected payo from crime
may increase, inducing more principals to opt for crime.
Our argument relies on the conict of interests between the principal and the agent. Several
accounts show that this is an important factor in real-life criminal situations. For example, Levitt
and Venkatesh (2000, p. 781), in their description of the workings of a drug-selling gang, describe
how gang wars, which run counter to the gang's best interests, were repeatedly provoked by low-
level members seeking to build a reputation for toughness. Similarly, Anderson (1995) reports that
American maa leaders struggle to prevent members from engaging in activities that would endanger
1Note here the dierence to the marginal deterrence argument that increasing the sanction for or the detection
probability of a given crime may increase levels another crime (Stigler 1970, Shavell 1992).
2Violence is a considerable source of status in criminal subcultures (see, e.g., Anderson 1999, Dur and van der
Weele 2011).
3Recently, there have been moves to increase sanctions for violent crimes in Sweden, among other countries (\Sweden
to get tougher on violent crime", The Local, 28 January 2010).
2other members.
We will identify a relationship between expected punishment and crime using information rents,
which applies to both the level of the sanction and the detection probability. In a related paper,
Poutvaara and Priks (forthcoming) consider a principal-agent setup with hidden agent types to
study how a gang leader's demands on members in terms of crimes are aected by variations in the
unemployment level, where unemployment enters the gang member's optimization via their outside
option. In the literature, Andreoni (1991) and Feess and Wohlschlegel (2009) have argued that higher
sanctions may reduce deterrence, relying on the concept that jurors will become less likely to convict
a suspect if the punishment is severe.
2 Model and analysis
We consider a setup in which the population is split into two distinct groups. Type L individuals have
little human capital and both a legal income and a wealth level set at zero. Type H individuals are
paid their marginal product  when legally employed. There are at least as many type L individuals
as type H ones. Type H's marginal product comes from the interval [;  ] according to G(). Apart
from legal work, it is possible to earn income in the criminal sector.4 If a type H individual opts to
commit a crime, he may face a context in which both a property crime P and a violent crime V are
possible, or one in which only crime V is possible. The probability of the former (latter) contingency
is  (1   ). Type H individuals planning criminal activities hire a type L individual to commit the
act. In the situation with two possible types of crimes, there is asymmetric information regarding
the crime selected by the agent.5
We now characterize crimes P and V. The expected monetary payo is 
 irrespective of the type
of oense. P will be detected with probability pP and detection implies a non-monetary sanction with
a monetary equivalent for the principal (agent) of fPR (fA
P ). V will be detected with probability pV,
pV > pP, and detection implies a non-monetary sanction with a monetary equivalent for the principal
4We consider the empirically supported \crime as work" model (Grogger 1998, Williams and Sickles 2002).
5This assumption is also used, for example, in the literature on project selection (see, e.g., Bester and Kr ahmer
(2008).
3(agent) of fPR (fA
V ).6 The principal prefers crime P to V, when all else is equal. In contrast, the
agent prefers crime V to P, because the commission of V transfers a status of value s to the agent,
i.e., it holds that
s > pVf
A
V   pPf
A
P (1)
The timing of the game is as follows: (1) Type H individuals determine whether they want to
work in the legal or the criminal sector. (2) Principals learn whether only crime V or both crimes
are possible. (3) The principal oers a contract to a type L individual, consisting of transfers in
the detection and the no-detection state of the world. (4) Detection takes place. (5) Principals
pay agents according to the contract terms, because actual payment is required to maintain the
principal's credibility.
2.1 Stage 3
Crimes P and V possible: The principal who seeks to ensure the agent's selection of crime P
needs to guarantee that both the agent's participation and the incentive compatibility constraint
hold. Designating the transfer from the principal to the agent TPV(
) if the principal's (gross)
payo is 
 and both crimes are possible, we can state the participation, incentive compatibility, and
limited liability constraint of the agent as follows:
(1   pP)TPV(
) + pPTPV(
   f
PR)   pPf
A
P  0 (2)
(1   pP)TPV(
) + pPTPV(
   f
PR)   pPf
A
P  (1   pV)TPV(
) + pVTPV(
   f
PR) + s   pVf
A
V (3)
TPV(
); TPV(
   f
PR)  0 (4)
The principal tries to
max
TPV (
);TPV (
 fPR)
(1   pP)[
   TPV(
)] + pP[
   TPV(
   f
PR)   f
PR] (5)
subject to (2), (3), and (4). Since pP < pV, it is clear that setting T(
   fPR) = 0 serves this
objective. Furthermore, the principal will increase T(
) only enough to ensure that (3) holds with
6Thus, without our results depending on it, we presume that the sanction imposed on the principal does not depend
on the crime type.
4equality. We use this fact to arrive at an explicit expression for the transfer in the event the crime
is not detected
TPV(
) =
pPfA
P + s   pVfA
V
pV   pP
(6)
Using this expression in (2), we obtain
(1   pP)(s   pVf
A
V ) >  (1   pV)pPf
A
P (7)
that is, a strict inequality due to (1), which implies the principal's transfer of an information rent to
the agent to induce crime P. In summary, the principal obtains an expected payo of
PV = 
   (1   pP)TPV(
)   pPf
PR (8)
Alternatively, he could let the agent choose crime V. The agent participates in crime V if transfers
are such that his participation constraint is fullled. This constraint is given by
(1   pV)TV(
) + pVTV(
   f
PR) + s   pVf
A
V  0 (9)
and implies that paying
TV(
) =
pVfA
V   s
1   pV
(10)
and TV(
   fPR) = 0 is satisfactory. Due to (1), it follows that TPV(
) > TY(
). Allowing the
agent to choose crime V implies an expected payo for the principal of
V = 
   (1   pV)TV(
)   pVf
PR (11)
As a consequence, it will hold that the principal induces crime P if PV > V, that is, if
(pV   pP)f
PR > (1   pP)TPV(
)   (1   pV)TY(
) (12)
We assume that this condition is fullled. Inducing crime P instead of V implies that the principal is
sanctioned with probability pP instead of pV. However, this comes at the cost of having to transfer
TPV to the agent with probability 1   pP instead of TV with probability 1   pV.
Only crime V possible: The principal only needs to ensure that the participation constraint holds.
As a consequence, the principal pays TV(
) as specied in (10) and TV(
   fPR) = 0, and thereby
arrives at the expected payo V detailed in (11).
52.2 Stage 1
In the rst stage, type H individuals with marginal product  choose whether to work in the legal
or the criminal sector, and prefer legal work if
  PV + (1   )V (13)
We assume that there is a critical level c, at which the left-hand side in (13) is equal to the right-
hand side. As a consequence, the total crime level is given by G(c). An increase in c implies an
increase in the level of both crimes, given that there is a condition, in which crimes P and V are
possible but P is induced, and another condition, in which only crime V is possible and induced.
It is our assertion that an increase in punishment can result in an increase in crime. To understand
this, rst note that the critical level can be explicitly stated, using the denitions (6) and (10) from
above, as
c = 
   (1   pP)
pPfA
P + s   pVfA
V
pV   pP
  (1   )(pVf
A
V   s)   pVf
PR + (pV   pP)f
PR (14)
This allows derivation of our nding:
Proposition 1 (i) An increase in the sanction fA
V increases the level of crime if it holds that
 >
pV   pP
1   pP + pV   pP
= 1
(ii) An increase in the probability pV increases the level of crime if it holds that
 >
(pV   pP)2(fPR + fA
V )
(1   pP)[pP(fA
P   fA
V ) + s] + (pV   pP)2(fPR + fA
V )
= 2
Proof. Claims (i) and (ii) result from @c=@fA
V > 0 and @c=@pV > 0. Note that pP(fA
P  fA
V )+s > 0
due to (1) so that 1; 2 < 1.
The change in the enforcement policy weakens the agent's preference of V over P.7 This lowers
TPV and thereby increases PV. In the case of increasing pV, the principal is additionally negatively
aected by the higher probability of being sanctioned.
7We consider an exogenous status. Note, however, that, if harsher punishment were to increase status, this would
not necessarily put our qualitative ndings into question.
6References
Anderson, A., 1995. Organised crime, maa and governments. In: Fiorenti, G., Peltzman, S. (eds.).
The economics of organized crime. Cambridge: Cambridge University Press.
Anderson, E., 1999. Code of the Street: Decency, Violence, and the Moral Life of the Inner City.
New York: Norton.
Andreoni, J., 1991. Reasonable doubt and the optimal magnitude of nes: should the penalty t the
crime? Rand Journal of Economics 22, 385-395.
Bester, H., Kr ahmer, D., 2008. Delegation and incentives. Rand Journal of Economics 39, 664-682.
Dur, R., van der Weele, J.J., 2011. Status-seeking in criminal subcultures and the double dividend
of zero-tolerance. IZA Discussion Paper 5484.
Feess, E., Wohlschlegel, A., 2009. Why higher punishment may reduce deterrence. Economics Let-
ters 104, 69-71.
Garoupa, N., 2000. The economics of organized crime and optimal law enforcement. Economic
Inquiry 38, 278-288.
Garoupa, N., 2007. Optimal law enforcement and criminal organization. Journal of Economic Be-
havior and Organization 63, 461-474.
Grogger, J.T., 1998. Market wages and youth crime. Journal of Labor Economics 16, 756-791.
Kumar, V., Skaperdas, S., 2009. Organized crime. In: Garoupa, N. (ed.). Criminal law and eco-
nomics. Cheltenham: Edward Elgar.
Levitt, S.D., Venkatesh, S.A., 2000. An economic analysis of a drug-selling gang's nances. Quar-
terly Journal of Economics 115, 755-789.
Meares, T.L., Katyal, N., Kahan, D.M., 2004. Updating the study of punishment. Stanford Law
Review 56, 1171-1210.
Poutvaara, P., Priks, M., forthcoming. Unemployment and gang crime: Could prosperity backre?
Economics of Governance.
Shavell, S., 1992. A note on marginal deterrence. International Review of Law and Economics 12,
133-149.
7Stigler, G., 1970. The optimum enforcement of laws. Journal of Political Economy 78, 526-536.
Williams, J., Sickles, R.C., 2002. An analysis of the crime as work model: Evidence from the 1958
Philadelphia birth cohort study. Journal of Human Resources 37, 479-509.
8

Tempting Righteous Citizens? On the Counterintuitive Effects of Increasing Sanctions

http://www.wiwi.uni-konstanz.de/workingpaperseries/WP_Friehe-9-11.pdf

Tempting Righteous Citizens? On the Counterintuitive Effects of Increasing Sanctions

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics