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Using (im)perfect markets to catch criminals
Journal
of Economic
Behavior
and Organization
Using (im)perfect criminals*
21 (1993) 3141.
markets
North-Holland
to catch
Brian L. Goff Western Kentucky Unioersity, Bowling Green, KY, USA
Robert
D. Tollison
George Mason University, Fairfax, VA, USA Received
August
1991, final version
received
April 1992
We extend the use of rational choice models of criminal activity to examine operations. These operations are modeled as technological innovations in law influence the probability of detection/conviction of criminal activities. We operations have the same impact on the supply of criminal activity? We find are sensitive to the type of sting used and the competitiveness of the criminal the sting is used.
the use of ‘sting’ enforcement that ask: do all sting that such impacts market in which
1. Introduction Various authors have provided theoretical models and evidence of how criminal activities respond to incentives.’ We extend their work here by examining the use of so-called ‘sting’ operations to catch criminals. The general nature of these clandestine operations by law enforcement officials are well known, although the specific characteristics of stings may differ. We model sting operations as technological innovations in law enforcement that influence the probability of detection and/or conviction of criminal activities. We ask a simple question: do all sting operations have the same impact on the supply of criminal activity? From the standpoint of public policy the answer is that the characteristics of the stings and the markets in which they are used are of utmost Correspondence to: R.D. Tollison, George’s Hall, George Mason University, Fairfax, VA 22030, USA. *We acknowledge helpful comments from Robert Pulsinelli and Melvin Boreland. The usual caveat applies. ‘Some of the prominent contributions include Becker (1968), Becker and Stigler (1974), Ehrlich (1973, 1975), Block and Heineke (1975), and Block and Lind (1975). More recent contributions include McCormick and Tollison (1984), Viscusi (1986), Ehrlich (1987), Davis (1988), and Cover and Thistle (1988). Also see Marx (1983). 0167-2681/93/$06.00
0
1993-Elsevier
Science Publishers
B.V. All rights reserved
importance. If used predominantly as a passive monitoring device or as an ex post investigative tool where reasonable cause already exists in relatively competitive criminal markets, then stings almost certainly enhance welfare. However, as use of aggressive stings in relatively uncompetitive markets increases, the benefits of these operations diminish. 2. Criminal choice model We assume that agents choose consumption, legal labor supply, and criminal activity in order to maximize a Von Neuman-~orgenstern utility function as follows: jU(c, n, T)f(a) da,
(1)
where c =consumption units, n =labor supplied to legal activity, T = labor supplied to illegal activity, f(a) is the agent’s probability density function over the detection/conviction rate, and where U, >O, U,, U, ~0, U,, 50, and U,,, U,, < 0.* Consumption, labor and illegal activity possibilities are constrained by: c=c”+h(n)[l-u]+VT[l-a],
c,n,T~O,
(2)
where co is the initial consumption endowment; h(n) =production function transforming legal labor activity into consumption; I’= the value of criminal activity per offense; (I = the stochastic detection/conviction rate, and 0 5 a 5 1. This specification embodies a penalty to criminal activity equal to the value of foregone legal labor and criminal income based upon the probability of detection/conviction, Implicitly, this type of penalty specification requires a link between detection/conviction and legal income production due to imprisonment. While imprisonment does not necessarily follow conviction, most sting-related convictions lead to prison sentences. Eliminating this link would obviously decrease the expected costs of crime. The individuals decision is therefore determined by: IF’(n,T)=maxf n.T
U[n,T,c"+h(n)[l -a]+ VT[Il -a]]f(u)da.
(3)
Assuming that some illegal activity will occur, the first-order condition for a maximum is: E{U,[1/-h’(n)][l-u]-U,+Ur}=O.
(4)
20ur work is closely related to Block and Heineke, who highlight the assumptions about preferences and income that are necessary to generate unambiguous signs. Our main departure from their model is in the treatment of penalties for crime. Block and Heineke use a fixed-fine penalty. We use a variable penalty based upon foregone consumption possibilities. The results are not sensitive to this specification.
B.L. Gof,
Using markets
to catch criminals
33
For the subsequent analysis of criminal detection through stings, we are interested in two comparative static results. First, the marginal impact of a change in the initial consumption endowment upon criminal activity is: dT/dc’=E[U,,(V-h’(n))[l-a]-U,,+U,,]/U,,.
(5)
As Block and Heineke explain, the sign of (5) can only be determined from more detailed information about the agent’s attitude toward risk.3 If the agent displays decreasing absolute risk aversion, U,,, is positive. We will proceed under this assumption. In addition, a change in consumption can influence the sign of (5) through its impact on the agent’s ethical attitudes toward legal and illegal labor, U,, and U,,. We treat these effects as negligible. Under these conditions the sign of (5) depends on the marginal value of criminal activity on consumption versus the marginal impact of legal labor supply on consumption. When [V-h’(n)] is positive, eq. (5) is positive; criminal activity is a normal good. The rational choice model does not ignore the importance of ethical considerations, which are reflected in U,, U,, U,,. and U,, in eqs. (4) and (5). For any specific individual in society, these components may take on such large magnitudes as to make criminal activity highly unlikely under almost any realistic enticement. Our interest here, however, lies in the behavior of those individuals whose ethical qualms would not completely dominate monetary and consumption incentives.4 Consequently, we adopt the conditions of decreasing absolute risk aversion, marginal crime productivity relatively greater than marginal legal labor productivity, and small cross-preference effects. The second comparative static result of interest is the impact of a change in the value of criminal activity per offense on criminal supply. This relationship is: dT/dV=-EU,[l-al/U,, The sign of (6) is unambiguously even if (5) is negative so that
+T[l-a]dT/dc’.
(6)
positive as long as (5) is positive.S Also, crime is an inferior good, dT/d V will be
3Risk aversion alone, as implied by U,,O, or in the case that cov( .)=O. This follows from the nonnegativity of E(U,) and EC1 -a].
34
B.L. C&
Using markets IO catch criminals
positive as long as the income effect [the right-hand term in (6)] is smaller than the substitution effect represented by the left-hand term.
3. The impact of stings The term ‘sting’, encompasses a variety of undercover operations by enforcement agents, where the agents take on the guise of criminals. Most analysis of stings is normative in nature, although Marx (1988) is a notable attempt to analyze some of the positive aspects.6 Law enforcement officials engage in many diverse types of stings. Some of the most famous are the political bribery cases such as ‘Abscam’, where federal officials posed as wealthy Arabs seeking political favors from congressmen, and the more recent ‘Bubbagate’ where several members of the South Carolina legislature accepted bribes from undercover agents seeking political services. The underground activity of illicit drug transactions has been another place for sting operations against dealers and distributors as well as against law enforcement officials suspected of facilitating and profiting from these transactions. Possibly the most frequently used and ongoing sting method is the ‘fencing’ operations in which police pose as buyers and videotape the purchase of stolen property. We view stings as a detection/conviction technology which alters the detection/conviction density function.’ We use x to represent the intensity of a sting. It is a continuous index of the value of resources that police devote to stings. The index takes on higher values as police set up more sting locations, use additional labor or offer larger cash amounts to criminals. We are interested in changes in x which increase the expected conviction rate, Era]. To accomplish this, we include x as a part of a useful density function:
and where B ensures that fAf(a) = 1. Here, increases in x increase the expected detection/conviction rate.8 We consider the impact of this criminal enforcement technology in two situations: (I) where the sting has no impact upon the value per criminal 6The Fall of 1987 issue of the Journal of Social Issues is devoted to the discussion of the normative issues surrounding the use of stings. 7Stings are not the only technological factor capable of shifting the density function. Other factors include identification technologies (fingerprinting, blood-typing, DNA-prints, fiber analysis), as well as information technologies (data processing, data analysis, data banks). *The restriction on x ensures that a falls in [0,11. Given f(a), the expected conviction rate is E[a] =(fll +x)/(pl +fiJ. We are specifically interested in mean-altering, variance-preserving changes in x. This would require that dx=j3-/3,. We do not explicitly include this additional restriction because the implications of the model are not sensitive to it. For background on the properties of our density function, see Hastings and Peacock (1975).
35
B.L. Gaff, Using markets to catch criminals
offense, sting.
and (2) where
3.1. Detection-only
the value
per offense
increases
in the presence
of a
sting
If the sting operation only influences the probability of detection/ conviction, increases in the detection/conviction rate influence criminal labor supply directly through its impact on the density function as well as indirectly through its impact on consumption expectations. No impact upon the value of criminal activity is present so that dT/dV=O. If the sting increases the probability by x, then the impact of the sting upon criminal labor supply is (with x = 0): dT/dx = E[U,( V- h’(n))/U,,
-(vT+h(n))dT/dc’IClI(P, +Bz)l.
(8)
The sign of (8) will be unambiguously negative as long as criminal activity is a normal good, dT/dc’ >O, and the value per criminal offense is greater than the marginal productivity of legal labor on consumption, or [V-h’(n)] > 0. Again, even if crime is inferior, (8) will be negative so long as this impact is small relative to the direct impact on the density function as represented by the left-hand term. An increase in criminal enforcement technology reduces criminal supply. A low marginal productivity of labor enhances this effect. Such conditions are common among individuals engaging in petty crimes.
3.2. Detection-inducement
sting
One interesting characteristic of sting operations is that such operations go beyond pure monitoring or ex post investigation of criminal activities. Instead, law enforcement officials become actors in the criminal process. In addition, undercover information gathering is not the sole purpose of stings; offers and/or exchanges of cash, goods or services are used to obtain stolen property, drugs, political favors and the like. The result is that stings have an impact upon the value of criminal activity in addition to an impact upon the density function of detection/conviction. The nature of V becomes of primary importance in this case. To this point, we have treated I/ as exogenous. This sufficed as long as stings had no direct impact upon the value per criminal offense. To understand the possible behavior which stings can foster, we decompose I/ into smaller parts. In part, the value per offense depends upon the type of crime committed
36
B.L. Gaff, Using markets to catch criminals
and the manner in which the criminal makes use of the spoils of the offense. Consider first a criminal who either steals cash or consumes the stolen goods. In this case, the consumption benefit from the offense depends solely upon the human capital and preferences of the criminal with respect to the consumption of the stolen goods themselves or the goods/services purchased with the cash. We denote this part of I/ as V,. A second part of the value per offense depends upon the criminal marketplace. Criminals do not always steal cash and may only occasionally consume the stolen goods. Also, crimes extend beyond thefts. When engaging in thefts, criminals often sell the stolen property to some third party. The criminal benefits from the value of the stolen goods upon resale. Additionally, many crimes are committed on a contractual basis by individuals who are not the ultimate demanders of the criminal activity. The actual perpetrator is compensated by the ultimate demander on some pre-arranged basis. We denote this part of V by Vi. Vi is determined by factors in the marketplace for resale of criminal goods and criminal acts committed under contract. While various market forces may exert influence on Vi, we restrict our attention to two. Suppose
where E is the elasticity of demand for resold goods and contracted criminal acts in the market for such goods, and x is the law enforcement techology parameter driven by stings. The impact of the elasticity of demand upon V, is negative. In a very competitive market for criminal goods, perpetrators of criminal acts may be price-takers at the going market ‘price’ for such goods. In a less competitive market on the demand side, the perpetrator may search for the revenue-maximizing ‘price’. In addition to the demand elasticity, sting operations alter the value per offense by offering potential or suspected criminals compensation for stolen property. Other things equal, as the sting offers a greater reward to the potential criminal, the value per offense to the criminal increases. A specific parameterization of I/ is: v=v,+VJ(l-X/&),
X
O<&
(10)
The resale component of the value per offense approaches V, as the elasticity of demand approaches the polar extreme of a perfectly competitive market and is greater than I’, as the elasticity approaches the value of x. Other factors constant, x has a positive impact on the value per offense when the elasticity of demand is relatively small. For very large values of E, though, x has a negligible impact upon I/: This is an important feature of the model of I/: In a perfectly competitive market for criminal resale/contracts, the sting reward only represents one of many opportunities for the potential criminal.
31
B.L. Gaff; Using markets to catch criminals
An example may help to clarify this link between the value per offense and stings. Suppose a legislator can influence political outcomes and that explicit payments to the legislator are illegal. In the absence of well developed markets for such illegal payments, the legislator may have little information on the price which may be obtained. The legislator may, in fact, place a very low value on the expected price. The legislator is then approached by an undercover agent who offers a much higher than expected price. The sting offer has increased the value of committing the offense. Consider the impact of stings on the amount of criminal activity when the sting has the potential of altering the value per offense. Taking the derivative of T with respect to x and evaluating the result where x = 0 yields: dT/dx=E{[V-K(n)-(V,/s2)(1-&)I/&
-CM4+ f’T+(TV,h2)(l -Bl)l
x dT/dc’- [u,(~J~2)(1 -Bdllu,~
HMBI +&I).
(11)
The impact of making the value per offense endogenous to the demand elasticity and stings is seen by comparing eqs. (8) and (11). As the market demand approaches the perfectly competitive extreme, the right-hand side expression condenses to the expression found in (8). The sting operation has a negative impact upon the number of criminal acts committed. No additional crimes are induced by the sting. In contrast, if the market elasticity takes on a non-extreme value, the right-hand side of eq. (11) is larger than the right-hand side of eq. (8) even though it may still be negative in sign. Because of the sting, the value of criminal activity increases and thereby the amount of criminal activity increases relative to eq. (11). This increase affects all three terms to the right of the equal sign through some modification of the factor of V,( 1 --a)/~~. In the first two terms, the factor reduces the expression within the bracket. The last term is positive.’ Changes in the value per offense due to stings motivate behavioral changes through both the substitution and income effects. The increase in consumption possibilities increases the benefits to criminal activity. This income effect is seen in the second right-hand term in (11). In addition, the relative increase in return to criminal labor entices some substitution away from legal into illegal activity. The exact magnitude by which Vi is altered by a sting depends upon the details of the specific operation. In the case of drug stings and stings of public officials receiving bribes, where the amounts of money involved run into the thousands and hundreds of thousands of dollars, the impact on the equation may be substantial.
9An additional
restriction,
/I, < 1, is necessary
for the unambiguous
results above.
38
4. Applications
B.L. Gaff, Using markets
to catch criminals
and public policy
4.1. Applications Criminal markets most likely represent less than perfectly competitive markets. If nothing more, legal barriers restrict entry and exit.” Yet differences exist between the relative competitiveness of different criminal resale/contracting markets. Existing data on enforcement stings are sparse and primarily of the case study type. Some of the more detailed examinations of actual sting operations can be found in U.S. Department of Justice (1979), Klockars (1974, 1980), Wycott et al. (1980), and National Institute of Law Enforcement (1974). The most competitive market in which stings are used would appear to be the typical ‘fencing’ operation, at least in large metropolitan areas. The fencing operation is a guise in which police act as a broker in the receipt and payment for stolen property. In these circumstances, the police are almost certainly not the sole option for the would-be seller of stolen property. The sting’s impact on the value per offense would be small, so that the additional number of crimes induced due to the sting operation would also be small. In effect, the police set up a monitoring station and offer a market price to criminals who happen to choose this particular buyer for their transaction. A caveat to the result here is that the police are not necessarily constrained to act as profit-maximizing agents in the criminal fencing market. Hence, to detect criminals, the police might offer a premium for fenced goods. This makes the market less than perfectly competitive. But if criminals have rational expectations, the presence of premiums in their markets will be viewed with suspicion, thereby limiting the degree to which the police can quote above-market prices for fenced goods. A lower state of competition would appear to obtain in the case of drug stings. As in the fencing operation, the police very seldom represent the sole purchasing outlet for resale/contracting. The criminal will be searching for a purchasing outlet, and the police act as monitors of the market. However, due to the added amount of violence and in some cases the amount of physical capital (airplanes, weapons, and so on) involved in many drugrelated crimes relative to property theft crimes, one would expect the number of buyers and the market demand elasticity to be lower. Also, the police may actively seek to arrange deals rather than passively waiting as a competitive point of purchase or sales. Therefore, the model suggests that police sting operations in these markets will have a larger positive impact on the amount of criminal activity than in the case of the stolen property fencing operations. The least competitive case would appear to obtain in the case of political “Rubin (1973) and Reuter (1983) provide less than perfectly competitive.
support
for the assertion
that criminal
markets
are
bribery stings. In these situations, the potential suspects may or may not actively engage in criminal activity independently from the sting operation or search for resale/contracting outlets for their potential criminal activities. Also, the sting may represent one of only a few, if not the only, outlet for contracting for these criminal offenses. As a result, the demand elasticity will be smaller so that for any given value of x, the value per offense is higher than in markets with more competition. The increase in criminal activity due to the sting is largest in this case. The sting does not simply represent a passive monitoring of criminal activity; instead, it may actually induce a substantial increase in criminal acts.
4.2. Public policy Suppose that aggregate welfare, W, is a function of two variables: criminal acts, T, and enforcement costs, E. Enforcement technology acts as a parameter for both T and E, and we continue to use x to describe the impact of stings as an enforcement technology. We have: W= W(T,E;x),
(12)
where Wr, cl/i,< 0, and E, ~0, so that stings are treated as a cost-reducing technology.” As we have seen above, the impact of x upon T depends on the nature of the criminal market under consideration. First, we consider the case where TX< 0. Here, stings either have no impact upon the value per offense or the market for criminal resale/contracting is perfectly competitive. An increase in the utilization of stings by law enforcement olhcials unambiguously increases welfare by lowering both enforcement costs and the number of criminal actions. Criminals are caught with lower public resource expenditures, and the sting operations also act as a deterrent to further criminal activity. These are the two most obvious public policy rationales supporting the use of stings. Second, we consider the alternative case where TX> 0. Here, stings have an impact on the value per offense, and criminal resale/contracting markets are less than perfectly competitive. In this environment, an increase in the utilization of stings by law enforcement offtcials has an ambiguous effect upon welfare. Stings still decrease enforcement costs; however, they increase the number of crimes committed. The total impact on welfare will depend on the relative magnitude of these effects and the relative importance of
“Marx (1983) considers the possibility that stings do not always reduce costs. For instance, in Seattle, a fencing operation cost the city over !!4OO,OGO because third-party purchasers of the fenced items did not have to return the stolen property.
40
B.L.
Go& Using markets
LO
catchcriminals
enforcement costs and crimes in determining welfare. The welfare-maximizing quantity of stings would occur where:i2 [dW/dE][dE/dx]
=[dW/dT][dT/dx].
(13)
Finally, our analysis gives some economic meaning to the term ‘entrapment’. For example, an agent in our model who is approached in a sting operation with the offer of some reward for criminal acts could meaningfully accuse the enforcement process of inducing the criminal action under certain circumstances. This should come as no surprise to economists who readily accept the idea that demand curves slope downward. At some price, criminal activity could be induced in any individual (who has the means to commit the crime) with the exception of those with extreme preferences against such activity. Indeed, a legal defense could possibly be erected around an estimate of the elasticity of demand in the fenced market. “We have omitted the consideration of possibly important impacts of stings upon the distribution of criminal activities. If different crimes have different detection rates, stings may provide an undiscussed benefit. For example, a sting may result in a switch from one type of hard-to-detect criminal activity to a more easily detectable criminal activity. This aspect of stings would enhance welfare since no net increase in crime occurs, but more crime is detected.
References Becker, Gary S., 1968, Crime and punishment: An economic approach, Journal of Political Economy 76, 169-217. Becker, Gary S. and George J. Stigler, 1974, Law enforcement, malfeasance, and the compensation of enforcers, Journal of Legal Studies 3, l-l 8. Block, Michael K. and John M. Heineke, 1975, A labor-theoretic analysis of the criminal choice, American Economic Review 6.5, 3 14-325. Block, Michael K. and Robert C. Lind, 197.5, An economic analysis of crime punishable by imprisonment, Journal of Legal Studies 4, 479-492. Cooter, Robert and Thomas Ulen, 1988, Law and economics (Harper Collins, New York). Cover, James P. and Paul D. Thistle, 1988, Time series, homicide and the deterrent effect of capital punishment, Southern Economic Journal 55, 615-622. Davis. Michael L.. 1988. Time and punishment: An intertemnoral model of crime, Journal of Political Economy 96, 383-390. . Ehrlich, Isaac, t973, Parti~pation in illegal activities: A theoretical and empirical investigation, Journal of Political Economy 81, 521-565. Ehrlich, Isaac, 1975, The deterrent effect of capital punishment: A question of life or death, American Economic Review 65, 397-417. Ehrlich, Isaac and George D. Boower, 1987, On the issue of causality in the economic model of crime and law enforcement, American Economic Review 77, 99-106. Hastings, N.A.J. and J.B. Peacock, 1975, Statistical distributions (John Wiley and Sons, New York). Klockars, Carl, 1974, The professional fence (Free Press, New York). Klockars, Carl, 1980, Jonathan Wilde and the modern sting, in: Incarda and Taupel, eds., History and crime: Implications for criminal justice poicy (Sage Press, Beverly Hills, CA). Marx, Gary T., 1983, Who really gets stung?, in: G.M. Caplan, ed., Abscam ethics: moral issues and deception in law enforcement (Police Foundation, Washington, DC). Marx, Gary T., 1988, Undercover: Police surveillance in America (University of California Press, Berkeley, CA).
I
B.L. Gofl, Using markets to catch criminals
41
McCormick, Robert E. and Robert D. Tollison, 1984, Crime on the court, Journal of Political Economy 92, 2233235. National Institute of Law Enforcement, 1974, New York city anti-crime patrol (National Institute of Law Enforcement, Washington, DC). Reuter, Peter, 1983, Disorganized crime: Economics of the visible hand (MIT Press, Cambridge, MA). Soquist, David L., 1973, Property crime and economic behavior: Some empirical results, American Economic Review 63, 4399446. U.S. Department of Justice, 1979, What happened? (U.S.G.P.O., Washington, DC). Viscusi, W. Kip, 1986, The risks and rewards of criminal activity: A comprehensive test of criminal deterrence, Journal of Labour Economics 1, 317-340. Wycott, M.A., C. Brown and R. Petersen, 1980, Birmingham anti-robbery unit evaluation report (Police Foundation, Washington, DC).
of Economic
Behavior
and Organization
Using (im)perfect criminals*
21 (1993) 3141.
markets
North-Holland
to catch
Brian L. Goff Western Kentucky Unioersity, Bowling Green, KY, USA
Robert
D. Tollison
George Mason University, Fairfax, VA, USA Received
August
1991, final version
received
April 1992
We extend the use of rational choice models of criminal activity to examine operations. These operations are modeled as technological innovations in law influence the probability of detection/conviction of criminal activities. We operations have the same impact on the supply of criminal activity? We find are sensitive to the type of sting used and the competitiveness of the criminal the sting is used.
the use of ‘sting’ enforcement that ask: do all sting that such impacts market in which
1. Introduction Various authors have provided theoretical models and evidence of how criminal activities respond to incentives.’ We extend their work here by examining the use of so-called ‘sting’ operations to catch criminals. The general nature of these clandestine operations by law enforcement officials are well known, although the specific characteristics of stings may differ. We model sting operations as technological innovations in law enforcement that influence the probability of detection and/or conviction of criminal activities. We ask a simple question: do all sting operations have the same impact on the supply of criminal activity? From the standpoint of public policy the answer is that the characteristics of the stings and the markets in which they are used are of utmost Correspondence to: R.D. Tollison, George’s Hall, George Mason University, Fairfax, VA 22030, USA. *We acknowledge helpful comments from Robert Pulsinelli and Melvin Boreland. The usual caveat applies. ‘Some of the prominent contributions include Becker (1968), Becker and Stigler (1974), Ehrlich (1973, 1975), Block and Heineke (1975), and Block and Lind (1975). More recent contributions include McCormick and Tollison (1984), Viscusi (1986), Ehrlich (1987), Davis (1988), and Cover and Thistle (1988). Also see Marx (1983). 0167-2681/93/$06.00
0
1993-Elsevier
Science Publishers
B.V. All rights reserved
importance. If used predominantly as a passive monitoring device or as an ex post investigative tool where reasonable cause already exists in relatively competitive criminal markets, then stings almost certainly enhance welfare. However, as use of aggressive stings in relatively uncompetitive markets increases, the benefits of these operations diminish. 2. Criminal choice model We assume that agents choose consumption, legal labor supply, and criminal activity in order to maximize a Von Neuman-~orgenstern utility function as follows: jU(c, n, T)f(a) da,
(1)
where c =consumption units, n =labor supplied to legal activity, T = labor supplied to illegal activity, f(a) is the agent’s probability density function over the detection/conviction rate, and where U, >O, U,, U, ~0, U,, 50, and U,,, U,, < 0.* Consumption, labor and illegal activity possibilities are constrained by: c=c”+h(n)[l-u]+VT[l-a],
c,n,T~O,
(2)
where co is the initial consumption endowment; h(n) =production function transforming legal labor activity into consumption; I’= the value of criminal activity per offense; (I = the stochastic detection/conviction rate, and 0 5 a 5 1. This specification embodies a penalty to criminal activity equal to the value of foregone legal labor and criminal income based upon the probability of detection/conviction, Implicitly, this type of penalty specification requires a link between detection/conviction and legal income production due to imprisonment. While imprisonment does not necessarily follow conviction, most sting-related convictions lead to prison sentences. Eliminating this link would obviously decrease the expected costs of crime. The individuals decision is therefore determined by: IF’(n,T)=maxf n.T
U[n,T,c"+h(n)[l -a]+ VT[Il -a]]f(u)da.
(3)
Assuming that some illegal activity will occur, the first-order condition for a maximum is: E{U,[1/-h’(n)][l-u]-U,+Ur}=O.
(4)
20ur work is closely related to Block and Heineke, who highlight the assumptions about preferences and income that are necessary to generate unambiguous signs. Our main departure from their model is in the treatment of penalties for crime. Block and Heineke use a fixed-fine penalty. We use a variable penalty based upon foregone consumption possibilities. The results are not sensitive to this specification.
B.L. Gof,
Using markets
to catch criminals
33
For the subsequent analysis of criminal detection through stings, we are interested in two comparative static results. First, the marginal impact of a change in the initial consumption endowment upon criminal activity is: dT/dc’=E[U,,(V-h’(n))[l-a]-U,,+U,,]/U,,.
(5)
As Block and Heineke explain, the sign of (5) can only be determined from more detailed information about the agent’s attitude toward risk.3 If the agent displays decreasing absolute risk aversion, U,,, is positive. We will proceed under this assumption. In addition, a change in consumption can influence the sign of (5) through its impact on the agent’s ethical attitudes toward legal and illegal labor, U,, and U,,. We treat these effects as negligible. Under these conditions the sign of (5) depends on the marginal value of criminal activity on consumption versus the marginal impact of legal labor supply on consumption. When [V-h’(n)] is positive, eq. (5) is positive; criminal activity is a normal good. The rational choice model does not ignore the importance of ethical considerations, which are reflected in U,, U,, U,,. and U,, in eqs. (4) and (5). For any specific individual in society, these components may take on such large magnitudes as to make criminal activity highly unlikely under almost any realistic enticement. Our interest here, however, lies in the behavior of those individuals whose ethical qualms would not completely dominate monetary and consumption incentives.4 Consequently, we adopt the conditions of decreasing absolute risk aversion, marginal crime productivity relatively greater than marginal legal labor productivity, and small cross-preference effects. The second comparative static result of interest is the impact of a change in the value of criminal activity per offense on criminal supply. This relationship is: dT/dV=-EU,[l-al/U,, The sign of (6) is unambiguously even if (5) is negative so that
+T[l-a]dT/dc’.
(6)
positive as long as (5) is positive.S Also, crime is an inferior good, dT/d V will be
3Risk aversion alone, as implied by U,,
34
B.L. C&
Using markets IO catch criminals
positive as long as the income effect [the right-hand term in (6)] is smaller than the substitution effect represented by the left-hand term.
3. The impact of stings The term ‘sting’, encompasses a variety of undercover operations by enforcement agents, where the agents take on the guise of criminals. Most analysis of stings is normative in nature, although Marx (1988) is a notable attempt to analyze some of the positive aspects.6 Law enforcement officials engage in many diverse types of stings. Some of the most famous are the political bribery cases such as ‘Abscam’, where federal officials posed as wealthy Arabs seeking political favors from congressmen, and the more recent ‘Bubbagate’ where several members of the South Carolina legislature accepted bribes from undercover agents seeking political services. The underground activity of illicit drug transactions has been another place for sting operations against dealers and distributors as well as against law enforcement officials suspected of facilitating and profiting from these transactions. Possibly the most frequently used and ongoing sting method is the ‘fencing’ operations in which police pose as buyers and videotape the purchase of stolen property. We view stings as a detection/conviction technology which alters the detection/conviction density function.’ We use x to represent the intensity of a sting. It is a continuous index of the value of resources that police devote to stings. The index takes on higher values as police set up more sting locations, use additional labor or offer larger cash amounts to criminals. We are interested in changes in x which increase the expected conviction rate, Era]. To accomplish this, we include x as a part of a useful density function:
and where B ensures that fAf(a) = 1. Here, increases in x increase the expected detection/conviction rate.8 We consider the impact of this criminal enforcement technology in two situations: (I) where the sting has no impact upon the value per criminal 6The Fall of 1987 issue of the Journal of Social Issues is devoted to the discussion of the normative issues surrounding the use of stings. 7Stings are not the only technological factor capable of shifting the density function. Other factors include identification technologies (fingerprinting, blood-typing, DNA-prints, fiber analysis), as well as information technologies (data processing, data analysis, data banks). *The restriction on x ensures that a falls in [0,11. Given f(a), the expected conviction rate is E[a] =(fll +x)/(pl +fiJ. We are specifically interested in mean-altering, variance-preserving changes in x. This would require that dx=j3-/3,. We do not explicitly include this additional restriction because the implications of the model are not sensitive to it. For background on the properties of our density function, see Hastings and Peacock (1975).
35
B.L. Gaff, Using markets to catch criminals
offense, sting.
and (2) where
3.1. Detection-only
the value
per offense
increases
in the presence
of a
sting
If the sting operation only influences the probability of detection/ conviction, increases in the detection/conviction rate influence criminal labor supply directly through its impact on the density function as well as indirectly through its impact on consumption expectations. No impact upon the value of criminal activity is present so that dT/dV=O. If the sting increases the probability by x, then the impact of the sting upon criminal labor supply is (with x = 0): dT/dx = E[U,( V- h’(n))/U,,
-(vT+h(n))dT/dc’IClI(P, +Bz)l.
(8)
The sign of (8) will be unambiguously negative as long as criminal activity is a normal good, dT/dc’ >O, and the value per criminal offense is greater than the marginal productivity of legal labor on consumption, or [V-h’(n)] > 0. Again, even if crime is inferior, (8) will be negative so long as this impact is small relative to the direct impact on the density function as represented by the left-hand term. An increase in criminal enforcement technology reduces criminal supply. A low marginal productivity of labor enhances this effect. Such conditions are common among individuals engaging in petty crimes.
3.2. Detection-inducement
sting
One interesting characteristic of sting operations is that such operations go beyond pure monitoring or ex post investigation of criminal activities. Instead, law enforcement officials become actors in the criminal process. In addition, undercover information gathering is not the sole purpose of stings; offers and/or exchanges of cash, goods or services are used to obtain stolen property, drugs, political favors and the like. The result is that stings have an impact upon the value of criminal activity in addition to an impact upon the density function of detection/conviction. The nature of V becomes of primary importance in this case. To this point, we have treated I/ as exogenous. This sufficed as long as stings had no direct impact upon the value per criminal offense. To understand the possible behavior which stings can foster, we decompose I/ into smaller parts. In part, the value per offense depends upon the type of crime committed
36
B.L. Gaff, Using markets to catch criminals
and the manner in which the criminal makes use of the spoils of the offense. Consider first a criminal who either steals cash or consumes the stolen goods. In this case, the consumption benefit from the offense depends solely upon the human capital and preferences of the criminal with respect to the consumption of the stolen goods themselves or the goods/services purchased with the cash. We denote this part of I/ as V,. A second part of the value per offense depends upon the criminal marketplace. Criminals do not always steal cash and may only occasionally consume the stolen goods. Also, crimes extend beyond thefts. When engaging in thefts, criminals often sell the stolen property to some third party. The criminal benefits from the value of the stolen goods upon resale. Additionally, many crimes are committed on a contractual basis by individuals who are not the ultimate demanders of the criminal activity. The actual perpetrator is compensated by the ultimate demander on some pre-arranged basis. We denote this part of V by Vi. Vi is determined by factors in the marketplace for resale of criminal goods and criminal acts committed under contract. While various market forces may exert influence on Vi, we restrict our attention to two. Suppose
where E is the elasticity of demand for resold goods and contracted criminal acts in the market for such goods, and x is the law enforcement techology parameter driven by stings. The impact of the elasticity of demand upon V, is negative. In a very competitive market for criminal goods, perpetrators of criminal acts may be price-takers at the going market ‘price’ for such goods. In a less competitive market on the demand side, the perpetrator may search for the revenue-maximizing ‘price’. In addition to the demand elasticity, sting operations alter the value per offense by offering potential or suspected criminals compensation for stolen property. Other things equal, as the sting offers a greater reward to the potential criminal, the value per offense to the criminal increases. A specific parameterization of I/ is: v=v,+VJ(l-X/&),
X
O<&
(10)
The resale component of the value per offense approaches V, as the elasticity of demand approaches the polar extreme of a perfectly competitive market and is greater than I’, as the elasticity approaches the value of x. Other factors constant, x has a positive impact on the value per offense when the elasticity of demand is relatively small. For very large values of E, though, x has a negligible impact upon I/: This is an important feature of the model of I/: In a perfectly competitive market for criminal resale/contracts, the sting reward only represents one of many opportunities for the potential criminal.
31
B.L. Gaff; Using markets to catch criminals
An example may help to clarify this link between the value per offense and stings. Suppose a legislator can influence political outcomes and that explicit payments to the legislator are illegal. In the absence of well developed markets for such illegal payments, the legislator may have little information on the price which may be obtained. The legislator may, in fact, place a very low value on the expected price. The legislator is then approached by an undercover agent who offers a much higher than expected price. The sting offer has increased the value of committing the offense. Consider the impact of stings on the amount of criminal activity when the sting has the potential of altering the value per offense. Taking the derivative of T with respect to x and evaluating the result where x = 0 yields: dT/dx=E{[V-K(n)-(V,/s2)(1-&)I/&
-CM4+ f’T+(TV,h2)(l -Bl)l
x dT/dc’- [u,(~J~2)(1 -Bdllu,~
HMBI +&I).
(11)
The impact of making the value per offense endogenous to the demand elasticity and stings is seen by comparing eqs. (8) and (11). As the market demand approaches the perfectly competitive extreme, the right-hand side expression condenses to the expression found in (8). The sting operation has a negative impact upon the number of criminal acts committed. No additional crimes are induced by the sting. In contrast, if the market elasticity takes on a non-extreme value, the right-hand side of eq. (11) is larger than the right-hand side of eq. (8) even though it may still be negative in sign. Because of the sting, the value of criminal activity increases and thereby the amount of criminal activity increases relative to eq. (11). This increase affects all three terms to the right of the equal sign through some modification of the factor of V,( 1 --a)/~~. In the first two terms, the factor reduces the expression within the bracket. The last term is positive.’ Changes in the value per offense due to stings motivate behavioral changes through both the substitution and income effects. The increase in consumption possibilities increases the benefits to criminal activity. This income effect is seen in the second right-hand term in (11). In addition, the relative increase in return to criminal labor entices some substitution away from legal into illegal activity. The exact magnitude by which Vi is altered by a sting depends upon the details of the specific operation. In the case of drug stings and stings of public officials receiving bribes, where the amounts of money involved run into the thousands and hundreds of thousands of dollars, the impact on the equation may be substantial.
9An additional
restriction,
/I, < 1, is necessary
for the unambiguous
results above.
38
4. Applications
B.L. Gaff, Using markets
to catch criminals
and public policy
4.1. Applications Criminal markets most likely represent less than perfectly competitive markets. If nothing more, legal barriers restrict entry and exit.” Yet differences exist between the relative competitiveness of different criminal resale/contracting markets. Existing data on enforcement stings are sparse and primarily of the case study type. Some of the more detailed examinations of actual sting operations can be found in U.S. Department of Justice (1979), Klockars (1974, 1980), Wycott et al. (1980), and National Institute of Law Enforcement (1974). The most competitive market in which stings are used would appear to be the typical ‘fencing’ operation, at least in large metropolitan areas. The fencing operation is a guise in which police act as a broker in the receipt and payment for stolen property. In these circumstances, the police are almost certainly not the sole option for the would-be seller of stolen property. The sting’s impact on the value per offense would be small, so that the additional number of crimes induced due to the sting operation would also be small. In effect, the police set up a monitoring station and offer a market price to criminals who happen to choose this particular buyer for their transaction. A caveat to the result here is that the police are not necessarily constrained to act as profit-maximizing agents in the criminal fencing market. Hence, to detect criminals, the police might offer a premium for fenced goods. This makes the market less than perfectly competitive. But if criminals have rational expectations, the presence of premiums in their markets will be viewed with suspicion, thereby limiting the degree to which the police can quote above-market prices for fenced goods. A lower state of competition would appear to obtain in the case of drug stings. As in the fencing operation, the police very seldom represent the sole purchasing outlet for resale/contracting. The criminal will be searching for a purchasing outlet, and the police act as monitors of the market. However, due to the added amount of violence and in some cases the amount of physical capital (airplanes, weapons, and so on) involved in many drugrelated crimes relative to property theft crimes, one would expect the number of buyers and the market demand elasticity to be lower. Also, the police may actively seek to arrange deals rather than passively waiting as a competitive point of purchase or sales. Therefore, the model suggests that police sting operations in these markets will have a larger positive impact on the amount of criminal activity than in the case of the stolen property fencing operations. The least competitive case would appear to obtain in the case of political “Rubin (1973) and Reuter (1983) provide less than perfectly competitive.
support
for the assertion
that criminal
markets
are
bribery stings. In these situations, the potential suspects may or may not actively engage in criminal activity independently from the sting operation or search for resale/contracting outlets for their potential criminal activities. Also, the sting may represent one of only a few, if not the only, outlet for contracting for these criminal offenses. As a result, the demand elasticity will be smaller so that for any given value of x, the value per offense is higher than in markets with more competition. The increase in criminal activity due to the sting is largest in this case. The sting does not simply represent a passive monitoring of criminal activity; instead, it may actually induce a substantial increase in criminal acts.
4.2. Public policy Suppose that aggregate welfare, W, is a function of two variables: criminal acts, T, and enforcement costs, E. Enforcement technology acts as a parameter for both T and E, and we continue to use x to describe the impact of stings as an enforcement technology. We have: W= W(T,E;x),
(12)
where Wr, cl/i,< 0, and E, ~0, so that stings are treated as a cost-reducing technology.” As we have seen above, the impact of x upon T depends on the nature of the criminal market under consideration. First, we consider the case where TX< 0. Here, stings either have no impact upon the value per offense or the market for criminal resale/contracting is perfectly competitive. An increase in the utilization of stings by law enforcement olhcials unambiguously increases welfare by lowering both enforcement costs and the number of criminal actions. Criminals are caught with lower public resource expenditures, and the sting operations also act as a deterrent to further criminal activity. These are the two most obvious public policy rationales supporting the use of stings. Second, we consider the alternative case where TX> 0. Here, stings have an impact on the value per offense, and criminal resale/contracting markets are less than perfectly competitive. In this environment, an increase in the utilization of stings by law enforcement offtcials has an ambiguous effect upon welfare. Stings still decrease enforcement costs; however, they increase the number of crimes committed. The total impact on welfare will depend on the relative magnitude of these effects and the relative importance of
“Marx (1983) considers the possibility that stings do not always reduce costs. For instance, in Seattle, a fencing operation cost the city over !!4OO,OGO because third-party purchasers of the fenced items did not have to return the stolen property.
40
B.L.
Go& Using markets
LO
catchcriminals
enforcement costs and crimes in determining welfare. The welfare-maximizing quantity of stings would occur where:i2 [dW/dE][dE/dx]
=[dW/dT][dT/dx].
(13)
Finally, our analysis gives some economic meaning to the term ‘entrapment’. For example, an agent in our model who is approached in a sting operation with the offer of some reward for criminal acts could meaningfully accuse the enforcement process of inducing the criminal action under certain circumstances. This should come as no surprise to economists who readily accept the idea that demand curves slope downward. At some price, criminal activity could be induced in any individual (who has the means to commit the crime) with the exception of those with extreme preferences against such activity. Indeed, a legal defense could possibly be erected around an estimate of the elasticity of demand in the fenced market. “We have omitted the consideration of possibly important impacts of stings upon the distribution of criminal activities. If different crimes have different detection rates, stings may provide an undiscussed benefit. For example, a sting may result in a switch from one type of hard-to-detect criminal activity to a more easily detectable criminal activity. This aspect of stings would enhance welfare since no net increase in crime occurs, but more crime is detected.
References Becker, Gary S., 1968, Crime and punishment: An economic approach, Journal of Political Economy 76, 169-217. Becker, Gary S. and George J. Stigler, 1974, Law enforcement, malfeasance, and the compensation of enforcers, Journal of Legal Studies 3, l-l 8. Block, Michael K. and John M. Heineke, 1975, A labor-theoretic analysis of the criminal choice, American Economic Review 6.5, 3 14-325. Block, Michael K. and Robert C. Lind, 197.5, An economic analysis of crime punishable by imprisonment, Journal of Legal Studies 4, 479-492. Cooter, Robert and Thomas Ulen, 1988, Law and economics (Harper Collins, New York). Cover, James P. and Paul D. Thistle, 1988, Time series, homicide and the deterrent effect of capital punishment, Southern Economic Journal 55, 615-622. Davis. Michael L.. 1988. Time and punishment: An intertemnoral model of crime, Journal of Political Economy 96, 383-390. . Ehrlich, Isaac, t973, Parti~pation in illegal activities: A theoretical and empirical investigation, Journal of Political Economy 81, 521-565. Ehrlich, Isaac, 1975, The deterrent effect of capital punishment: A question of life or death, American Economic Review 65, 397-417. Ehrlich, Isaac and George D. Boower, 1987, On the issue of causality in the economic model of crime and law enforcement, American Economic Review 77, 99-106. Hastings, N.A.J. and J.B. Peacock, 1975, Statistical distributions (John Wiley and Sons, New York). Klockars, Carl, 1974, The professional fence (Free Press, New York). Klockars, Carl, 1980, Jonathan Wilde and the modern sting, in: Incarda and Taupel, eds., History and crime: Implications for criminal justice poicy (Sage Press, Beverly Hills, CA). Marx, Gary T., 1983, Who really gets stung?, in: G.M. Caplan, ed., Abscam ethics: moral issues and deception in law enforcement (Police Foundation, Washington, DC). Marx, Gary T., 1988, Undercover: Police surveillance in America (University of California Press, Berkeley, CA).
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B.L. Gofl, Using markets to catch criminals
41
McCormick, Robert E. and Robert D. Tollison, 1984, Crime on the court, Journal of Political Economy 92, 2233235. National Institute of Law Enforcement, 1974, New York city anti-crime patrol (National Institute of Law Enforcement, Washington, DC). Reuter, Peter, 1983, Disorganized crime: Economics of the visible hand (MIT Press, Cambridge, MA). Soquist, David L., 1973, Property crime and economic behavior: Some empirical results, American Economic Review 63, 4399446. U.S. Department of Justice, 1979, What happened? (U.S.G.P.O., Washington, DC). Viscusi, W. Kip, 1986, The risks and rewards of criminal activity: A comprehensive test of criminal deterrence, Journal of Labour Economics 1, 317-340. Wycott, M.A., C. Brown and R. Petersen, 1980, Birmingham anti-robbery unit evaluation report (Police Foundation, Washington, DC).