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Corruption and the optimal use of nonmonetary sanctions
International Review of Law and Economics 24 (2004) 219–225
Corruption and the optimal use of nonmonetary sanctions Nuno Garoupaa,b,∗ , Daniel Klermanc,1 a
Faculdade de Economia, Universidade Nova de Lisboa, Campus de Campolide, P-1099-032 Lisboa, Portugal b CEPR, London, UK c University of Southern California Law School, University Park MC-0071, 699 Exposition Blvd, Los Angeles, CA 90089-0071, USA
Abstract This article analyzes the effect of corruption on the use of nonmonetary sanctions such as imprisonment. It is a well-known result in the law enforcement literature that in the absence of corruption, social welfare maximization requires that nonmonetary sanctions should be imposed infrequently. We show that, in the presence of corruption, it is optimal to use (or at least threaten to use) nonmonetary sanctions more often. In addition, optimal nonmonetary penalties will usually be higher in a corrupt environment. Corruption transforms the socially costly nonmonetary sanction into a monetary bribe. Although corruption thus reduces deterrence, nonmonetary sanctions are still useful, because they allow officials to extract higher bribes, thus restoring some deterrence. © 2004 Elsevier Inc. All rights reserved. JEL classification: K4 Keywords: Nonmonetary sanction; Corruption
1. Introduction This article presents a model of nonmonetary sanctions with corruption. Corruption has been a key issue in the economic literature of law enforcement. In their seminal article, ∗ 1
Corresponding author. Tel.: +351 21 3801600; fax: +351 21 3871105. Tel.: +1 213 740 7973; fax: +1 213 740 5502. E-mail addresses: [email protected] (N. Garoupa), [email protected] (D. Klerman).
0144-8188/$ – see front matter © 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.irle.2004.08.006
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Becker and Stigler (1974) argued that it might be advantageous to extend private enforcement to the criminal law and other areas where the law is now enforced publicly. Their principal argument was that public enforcement creates incentives to bribery which undermine deterrence. If law enforcement were privatized, however, competitive private enforcers could be rewarded with the fines offenders paid and enforcers would have no incentive to take bribes. Until recently, however, Becker and Stigler’s concern with corruption was not generally taken up in the literature. Nevertheless, in the last few years, scholars have begun to pay more attention to corruption. Bowles and Garoupa (1997), Chang, Lai, and Yang (2000), Marjit and Shi (1998), Polinsky and Shavell (2001) model corruption under a regime of public enforcement. Garoupa and Klerman (2001) model corruption under a regime of private enforcement. A central conclusion of this literature is that corruption is usually socially undesirable, because it dilutes deterrence. As a consequence, it is usually optimal to expend resources to detect and penalize corruption. The optimal use of nonmonetary sanctions, such as imprisonment, has been considered by Polinsky and Shavell (1984), Shavell (1985, 1987). This literature concludes that, because nonmonetary sanctions are costly, (1) they should always be used in tandem with maximal monetary sanctions, and (2) they should be used when maximal monetary sanctions are low, as when offenders are poor. This article extends the theory of nonmonetary sanctioning to a context where there is corruption, that is where offenders can bribe enforcement agents not to prosecute. Corruption, in effect, transforms a nonmonetary sanction into a monetary bribe. Its primary effect is usually to reduce welfare by reducing deterrence. Nevertheless, this detrimental effect is partly offset by the benefit of replacing a costly, nonmonetary sanction with a socially costless, monetary sanction. In the absence of corruption, nonmonetary sanctions should be imposed infrequently. We show that, in the presence of corruption, it is optimal to impose (or at least threaten to impose) nonmonetary sanctions more often. In addition, it is usually optimal to set higher nonmonetary penalties. These results are somewhat surprising. One might have thought that nonmonetary sanctions would be futile in a corrupt environment, because corruption transforms nonmonetary sanctions into monetary ones.2 Nevertheless, because nonmonetary sanctions allow enforcers to extract higher bribes, the threat of nonmonetary sanctions enhances deterrence, even if nonmonetary sanctions are never imposed. In addition, since corruption means that the nonmonetary sanctions will not be imposed, the marginal cost of nonmonetary sanctions goes down. In Section 2, we discuss why a government might impose nonmonetary sanctions in the usual law enforcement model developed by Polinsky and Shavell (2000). We then extend the model to an environment where corruption is possible, that is, where law enforcement agents can be bribed not to prosecute. The article concludes with final remarks in Section 3.
2 In fact, Laffont and Tirole (1993, chapter 11) argue that in a corrupt environment, it is optimal to use less powerful incentive schemes. In the law enforcement context, the principal is the government and the agents are potential criminals, so subjecting agents to less powerful incentives would mean lower sanctions.
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2. The Model 2.1. Nonmonetary sanctions without corruption As in Becker (1968), we start by assuming that each risk-neutral individual chooses whether to commit an offense, for example, smuggling or theft.3 The criminal’s gain from committing the offense is b, which is distributed across the population according to a probability density function g(b) with support [0, ∞) and a cumulative density function G(b).4 Offenses are detected and punished with probability p. If detected and punished, the offender bears a penalty f + s, where f is a monetary penalty and s the opportunity cost of a nonmonetary penalty, such as imprisonment or the death penalty. In this setting, an individual commits an offense if and only if b ≥ p(f + s). The number of offenders in this economy is given by: n(p, f, s) =
1 p(f +s)
dG(b) = 1 − G(pf + ps)
In the optimal law enforcement literature, social welfare generally equals the sum of individuals’ expected utilities minus the harm caused by offenses minus expenditure on law enforcement:5 W=
1
p(f +s)
[b − h − pt(s) − ps] dG(b) − x(p)
where h is the harm caused by the offense and x(p) the cost function of law enforcement, where xp > 0 and xpp ≥ 0. The function x(p) represents the cost of catching and convicting offenders, but not of punishing them. As is conventional in the law enforcement literature, the monetary sanction is assumed to be socially costless to impose, but it costs the government money to impose the nonmonetary sanction. The function t(s) is the cost function of the nonmonetary sanction, where ts > 0 and tss ≥ 0. The parameter h can be greater than one (the harm is always greater than the offender’s gain) or smaller than one (the harm is sometimes smaller than the offender’s gain). The government sets the probability of detecting and punishing offenders and the sanction. From Polinsky and Shavell (1984), we know that for a social-welfare maximizing government the optimal monetary sanction is maximal. That is, the government should impose a fine equal to the offender’s entire wealth. When both sanctions are used together, it is 3 Our model follows Bowles and Garoupa (1997), Chang et al. (2000), Polinsky and Shavell (2001) rather than the Laffont and Tirole mechanism design approach (Laffont & Tirole, 1993, chapter 11). Our model, however, could be translated into the mechanism design framework. In our model, the principal is a benevolent government, the agents are the potential offenders, and the supervisors are the law enforcement officials. The agency costs are due to asymmetric information. The government cannot costlessly observe collusion between officials and offenders, and officials imperfectly observe whether or not potential offenders commit crimes. 4 For a general survey of the literature, see Garoupa (1997), Polinsky and Shavell (2000). 5 See Garoupa (1997), Polinsky and Shavell (2000). It is conventional in this literature to include all gains in social welfare. Some argue that the offender’s gains should be excluded for moral reasons.
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desirable to set the fine at its highest possible value and then to use the nonmonetary sanction to enhance deterrence. The intuition behind the result is that the marginal cost of a monetary sanction is zero, while the marginal cost of a nonmonetary sanction is strictly positive. The government maximizes the social welfare function in s and p, given f = F (the fine is maximal), subject to the constraint that the nonmonetary sanction s is upper bounded by the offender’s maximal opportunity cost S. This upper bound might be a maximal jail sentence, such as life in prison without parole.6 The first-order conditions of this problem are:7 Ws = [h + pt(s) − pF ]g(·)p − p(ts + 1)n ≥ 0
(1)
Wp = [h + pt(s) − pF ]g(·)(s + F ) − [t(s) + s]n − xp = 0
(2)
Let us assume that the cost function exhibits sufficiently large decreasing returns so that the objective function W is strictly concave in s. By evaluating (1) when s = 0, we can derive the necessary and sufficient conditions for nonmonetary sanctions. If so, an interior (strictly positive) solution is optimal when: h − pF > (ts (0) + 1)(1 − G(pF ))/g(pF )
(3)
As a consequence, the optimal nonmonetary sanction in the absence of corruption will be: (a) Zero, if the marginal cost of imposing a nonmonetary sanction is very high, that is, if h − pF ≤ (ts (0) + 1)(1 − G(pF ))/g(pF ). (b) Maximal (S), if the marginal cost of imposing a nonmonetary sanction is very low, that is, if h + pt(S) − pF ≥ (ts (S) + 1)(1 − G(pF + pS))/g(pF + pS). (c) Positive but not maximal, if otherwise. That is, if the marginal cost of imposing nonmonetary sanctions is intermediate (i.e. neither very high nor very low), the optimal nonmonetary sanction is between zero and S. More precisely, in this situation, the nonmonetary sanction will satisfy: h + pt(s) − pF = (ts (s) + 1)(1 − G(pF + ps))/g(pF + ps). 2.2. Nonmonetary sanctions with corruption Assume that an offender can bribe an enforcement agent not to prosecute. Suppose that the bribe is given by v(f, s) = β(f + s), where β represents the enforcement agent’s 6 The model thus implicitly assumes that offenders all have the same wealth and the same maximal opportunity cost. This assumption is common in the literature, see Polinsky and Shavell (2001). Chu and Jiang (1993), Levitt (1997) explore the implications of dropping these assumptions. For a more general survey, see Avio (1998). In order to simplify the analysis and focus on the effects of corruption, we have retained the assumption that all offenders have the same wealth and maximal opportunity cost. Our results hold as long as wealth is perfectly observable in every stage of the enforcement process even if it varies among individuals. For a discussion of the general implications of dropping this assumption, see Garoupa (1998), Polinsky and Shavell (1991). 7 As Kaplow (1990) notes, we must check the second-order condition since the objective function is not necessarily concave in s: Wss = p2 (2ts + 1)g(·) + [h + pt(s) − pF ]g (·)p2 − ptss n. As long as the cost function of the nonmonetary sanction exhibits sufficiently large decreasing returns to scale, the objective function is concave in s and we can proceed to consider an interior nonmonetary sanction. However, for example, if the cost function exhibits constant returns to scale (say t(s) = ts) and g(.) is a uniform probability density function, then the second order condition is p2 (2t + 1). In that case, as Kaplow (1990) demonstrates, the objective function is convex in s and nonmonetary sanctions should be zero for many acts.
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bargaining power and 0 < β < 1. For a bribe of this magnitude to be possible, it must be the case that v(f, s) ≤ F where F is the maximal monetary sanction, i.e. the offender’s total wealth.8 If v(f, s) ≥ F , then we assume that the bribe is the offender’s total wealth, F . In this situation, we say that the wealth constraint is binding. As a consequence, let us redefine v(f, s) = min{β(f + s), F }. Under the assumption of asymmetric Nash bargaining (or Rubinstein bargaining in continuous time), bargaining never breaks down. Thus, all offenders and enforcers engage in bribery if it is mutually beneficial.9 Taking into account corruption, the expected sanction is no longer p(f + s), but rather pv(f, s). The number of offenders in this economy is given by: n(p, f, s, β) =
1 pv(f,s)
dG(b) = 1 − G(pv(f, s))
In the presence of corruption, the government’s objective function (social welfare) is given by the sum of the expected utility of individuals plus the expected utility of enforcers minus the harm caused by offenses minus expenditure on law enforcement: ˆ = W
1
pv(f,s)
(b − h) dG(b) − x(p)
As in the previous section, the optimal fine is maximal (for the usual Beckerian reasons). The government maximizes the social welfare function in s and p, given f = F , subject to the constraint that the nonmonetary sanction s is upper bounded by the offender’s maximal opportunity cost S. The first-order conditions for this problem can be written as: ˆ s = [h − pv(F, s)]g(·)p ∂v ≥ 0 W ∂s ˆ Wp = [h − pv(F, s)]g(·)v(F, s) − xp = 0
(4) (5)
In (4) we have the marginal benefit of nonmonetary sanctions (deterrence) but no marginal cost (since nonmonetary sanctions are not actually applied).10 When the wealth constraint is not binding, increasing nonmonetary sanctions has benefits but no cost, so it is always optimal to set the maximal nonmonetary sanctions. When the wealth constraint is binding, nonmonetary sanctions equal to (1 − β)F/β allow enforcement agents to extract the offender’s entire wealth as a bribe. Thus, there is no benefit in setting nonmonetary sanctions 8 Bargaining between caught offenders and enforcement officers may bring about additional costs such as enforcing the bargaining outcome, and time and effort spent on bargaining. As in previous literature, we ignore these costs. These costs would increase the social cost of corruption which in this paper is the cost of undermining criminal deterrence. 9 When bribery is possible but not universal, the results we have presented in the paper are not as strong, because nonmonetary sanctions now sometimes impose real social costs. Nevertheless, it will still usually be true that nonmonetary sanctions will be set more often and that the optimal nonmonetary sanction will be higher than in a corruption-free environment. Proof on file and available by request. 10 Unlike the previous section, we now satisfy the second-order condition even when the technology does not exhibit large decreasing returns to scale.
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higher than (1 − β)F/β. On the other hand, there is no cost either, because bribery will always transform the (socially costly) nonmonetary sanction into a (socially costless) monetary bribe. Thus, when the wealth constraint is binding, the optimal nonmonetary sanction is any nonmonetary sanction in the range [(1 − β)F/β, S]. From this it follows that, in the presence of corruption, nonmonetary sanctions should be used more often than when there is no corruption. Whereas, as discussed in Section 2.1, it is sometimes optimal for a noncorrupt government to set zero nonmonetary penalties, it is always optimal for a corrupt government to set positive nonmonetary sanctions. In addition, when the wealth constraint is not binding, even when nonmonetary sanctions would be optimal in a corruption-free environment, corruption means that the sanctions should be increased, if they are not already maximal. That is, as discussed in Section 2.1, in a noncorrupt environment, nonmonetary sanctions are sometimes less than maximal. In a corrupt environment, however, maximal nonmonetary sanctions are always optimal. When the wealth constraint is binding, it is still optimal to increase nonmonetary sanctions, if they are not already maximal. Nevertheless, it might also, in some circumstances be optimal to lower the nonmonetary sanctions to (1 − β)F/β. That is, a corrupt government might set the optimal nonmonetary sanction to be (1 − β)F/β, while a noncorrupt government might set a higher or maximal nonmonetary penalty higher. More precisely, lower nonmonetary sanctions could be optimal in a corrupt environment when the following condition is satisfied: (1 − β)F (1 − β)F (1 − G(pF + p(1 − β)F/β)) h + pt − pF > ts +1 β β g(pF + p(1 − β)F/β) This condition identifies situations where the marginal cost for a noncorrupt government of imposing nonmonetary sanctions is low. In such situations, a noncorrupt government might find it beneficial to set nonmonetary sanctions higher than (1 − β)F/β and thus higher than a corrupt government. On the other hand, as pointed out above, since the marginal cost of setting (i.e. threatening) nonmonetary sanctions is zero for a corrupt government, a corrupt government might choose to set nonmonetary sanctions to their maximal amount (S) in all circumstances. Thus, even when the above condition is satisfied, a corrupt government might set nonmonetary penalties higher (or at least as high) as a noncorrupt government.
3. Final remarks The economic literature on law enforcement has generally shown that nonmonetary sanctions should be used infrequently, because they are socially costly. This article presents a possible motivation to use (or at least threaten to use) nonmonetary sanctions more often: corruption. Corruption makes nonmonetary sanctions more attractive, because it converts costly nonmonetary sanctions into socially costless monetary bribes. In absence of corruption, optimal law enforcement policy often suggests that offenders should pay a maximal monetary sanction and face a zero nonmonetary sanction. When corruption is present, a nonmonetary sanction should be used to make sure that the bribe takes approaches the value of the maximal monetary sanction.
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Acknowledgements We are grateful to David Friedman, A. Mitchell Polinsky, Steven Shavell, Matt Spitzer, and participants in the Stanford Olin Workshop and American Law and Economics Association 2000 Annual Meetings for helpful suggestions. Nuno Garoupa has been supported by a scholarship from FCT, Fundac¸a˜ o para a Ciˆencia e Tecnologia, Lisbon, Portugal, and John M. Olin Fellowship, Center for Law, Economics, and Business, Harvard Law School. The usual disclaimers apply.
References Avio, K. L. (1998). The economics of prisons. European Journal of Law and Economics, 6, 143–176. Becker, G. S. (1968). Crime and punishment: An economic approach. Journal of Political Economy, 76, 169–217. Becker, G. S., & Stigler, G. J. (1974). Law enforcement, malfeasance and compensation of enforcers. Journal of Legal Studies, 3, 1–18. Bowles, R., & Garoupa, N. (1997). Casual police corruption and the economics of crime. International Review of Law and Economics, 17, 75–87. Chang, J.-J., Lai, C.-C., & Yang, C. C. (2000). Casual police corruption and the economics of crime: Further results. International Review of Law and Economics, 20, 35–52. Chu, C. Y. C., & Jiang, N. (1993). Are fines more efficient than imprisonment? Journal of Public Economics, 51, 391–413. Garoupa, N. (1997). The theory of optimal law enforcement. Journal of Economic Surveys, 11, 267–295. Garoupa, N. (1998). Optimal law enforcement and imperfect information when wealth varies among individuals. Economica, 65, 479–490. Garoupa, N., & Klerman, D. (2001). Corruption and Private Law Enforcement, mimeograph. Kaplow, L. (1990). A note on the optimal use of nonmonetary sanctions. Journal of Public Economics, 42, 245–247. Laffont, J.-J., & Tirole, J. (1993). A theory of incentives in procurement and regulation. Cambridge, Massachusetts: MIT Press. Levitt, S. D. (1997). Incentive compatibility constraints as an explanation for the use of prison sentence instead of fines. International Review of Law and Economics, 17, 179–192. Marjit, S., & Shi, H. (1998). On controlling crime with corrupt officials. Journal of Economic Behavior and Organization, 34, 163–172. Polinsky, A. M., & Shavell, S. (1984). The optimal use of fines and imprisonment. Journal of Public Economics, 24, 89–99. Polinsky, A. M., & Shavell, S. (1991). A note on optimal fines when wealth varies among individuals. American Economic Review, 81, 618–621. Polinsky, A. M., & Shavell, S. (2000). The economic theory of public enforcement of law. Journal of Economic Literature, 38, 45–76. Polinsky, A. M., & Shavell, S. (2001). Corruption and optimal law enforcement. Journal of Public Economics, 81, 1–24. Shavell, S. (1985). Criminal law and the optimal use of nonmonetary sanctions as a deterrent. Columbia Law Review, 85, 1232–1262. Shavell, S. (1987). The optimal use of nonmonetary sanctions as a deterrent. American Economic Review, 77, 584–592.
Corruption and the optimal use of nonmonetary sanctions Nuno Garoupaa,b,∗ , Daniel Klermanc,1 a
Faculdade de Economia, Universidade Nova de Lisboa, Campus de Campolide, P-1099-032 Lisboa, Portugal b CEPR, London, UK c University of Southern California Law School, University Park MC-0071, 699 Exposition Blvd, Los Angeles, CA 90089-0071, USA
Abstract This article analyzes the effect of corruption on the use of nonmonetary sanctions such as imprisonment. It is a well-known result in the law enforcement literature that in the absence of corruption, social welfare maximization requires that nonmonetary sanctions should be imposed infrequently. We show that, in the presence of corruption, it is optimal to use (or at least threaten to use) nonmonetary sanctions more often. In addition, optimal nonmonetary penalties will usually be higher in a corrupt environment. Corruption transforms the socially costly nonmonetary sanction into a monetary bribe. Although corruption thus reduces deterrence, nonmonetary sanctions are still useful, because they allow officials to extract higher bribes, thus restoring some deterrence. © 2004 Elsevier Inc. All rights reserved. JEL classification: K4 Keywords: Nonmonetary sanction; Corruption
1. Introduction This article presents a model of nonmonetary sanctions with corruption. Corruption has been a key issue in the economic literature of law enforcement. In their seminal article, ∗ 1
Corresponding author. Tel.: +351 21 3801600; fax: +351 21 3871105. Tel.: +1 213 740 7973; fax: +1 213 740 5502. E-mail addresses: [email protected] (N. Garoupa), [email protected] (D. Klerman).
0144-8188/$ – see front matter © 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.irle.2004.08.006
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Becker and Stigler (1974) argued that it might be advantageous to extend private enforcement to the criminal law and other areas where the law is now enforced publicly. Their principal argument was that public enforcement creates incentives to bribery which undermine deterrence. If law enforcement were privatized, however, competitive private enforcers could be rewarded with the fines offenders paid and enforcers would have no incentive to take bribes. Until recently, however, Becker and Stigler’s concern with corruption was not generally taken up in the literature. Nevertheless, in the last few years, scholars have begun to pay more attention to corruption. Bowles and Garoupa (1997), Chang, Lai, and Yang (2000), Marjit and Shi (1998), Polinsky and Shavell (2001) model corruption under a regime of public enforcement. Garoupa and Klerman (2001) model corruption under a regime of private enforcement. A central conclusion of this literature is that corruption is usually socially undesirable, because it dilutes deterrence. As a consequence, it is usually optimal to expend resources to detect and penalize corruption. The optimal use of nonmonetary sanctions, such as imprisonment, has been considered by Polinsky and Shavell (1984), Shavell (1985, 1987). This literature concludes that, because nonmonetary sanctions are costly, (1) they should always be used in tandem with maximal monetary sanctions, and (2) they should be used when maximal monetary sanctions are low, as when offenders are poor. This article extends the theory of nonmonetary sanctioning to a context where there is corruption, that is where offenders can bribe enforcement agents not to prosecute. Corruption, in effect, transforms a nonmonetary sanction into a monetary bribe. Its primary effect is usually to reduce welfare by reducing deterrence. Nevertheless, this detrimental effect is partly offset by the benefit of replacing a costly, nonmonetary sanction with a socially costless, monetary sanction. In the absence of corruption, nonmonetary sanctions should be imposed infrequently. We show that, in the presence of corruption, it is optimal to impose (or at least threaten to impose) nonmonetary sanctions more often. In addition, it is usually optimal to set higher nonmonetary penalties. These results are somewhat surprising. One might have thought that nonmonetary sanctions would be futile in a corrupt environment, because corruption transforms nonmonetary sanctions into monetary ones.2 Nevertheless, because nonmonetary sanctions allow enforcers to extract higher bribes, the threat of nonmonetary sanctions enhances deterrence, even if nonmonetary sanctions are never imposed. In addition, since corruption means that the nonmonetary sanctions will not be imposed, the marginal cost of nonmonetary sanctions goes down. In Section 2, we discuss why a government might impose nonmonetary sanctions in the usual law enforcement model developed by Polinsky and Shavell (2000). We then extend the model to an environment where corruption is possible, that is, where law enforcement agents can be bribed not to prosecute. The article concludes with final remarks in Section 3.
2 In fact, Laffont and Tirole (1993, chapter 11) argue that in a corrupt environment, it is optimal to use less powerful incentive schemes. In the law enforcement context, the principal is the government and the agents are potential criminals, so subjecting agents to less powerful incentives would mean lower sanctions.
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2. The Model 2.1. Nonmonetary sanctions without corruption As in Becker (1968), we start by assuming that each risk-neutral individual chooses whether to commit an offense, for example, smuggling or theft.3 The criminal’s gain from committing the offense is b, which is distributed across the population according to a probability density function g(b) with support [0, ∞) and a cumulative density function G(b).4 Offenses are detected and punished with probability p. If detected and punished, the offender bears a penalty f + s, where f is a monetary penalty and s the opportunity cost of a nonmonetary penalty, such as imprisonment or the death penalty. In this setting, an individual commits an offense if and only if b ≥ p(f + s). The number of offenders in this economy is given by: n(p, f, s) =
1 p(f +s)
dG(b) = 1 − G(pf + ps)
In the optimal law enforcement literature, social welfare generally equals the sum of individuals’ expected utilities minus the harm caused by offenses minus expenditure on law enforcement:5 W=
1
p(f +s)
[b − h − pt(s) − ps] dG(b) − x(p)
where h is the harm caused by the offense and x(p) the cost function of law enforcement, where xp > 0 and xpp ≥ 0. The function x(p) represents the cost of catching and convicting offenders, but not of punishing them. As is conventional in the law enforcement literature, the monetary sanction is assumed to be socially costless to impose, but it costs the government money to impose the nonmonetary sanction. The function t(s) is the cost function of the nonmonetary sanction, where ts > 0 and tss ≥ 0. The parameter h can be greater than one (the harm is always greater than the offender’s gain) or smaller than one (the harm is sometimes smaller than the offender’s gain). The government sets the probability of detecting and punishing offenders and the sanction. From Polinsky and Shavell (1984), we know that for a social-welfare maximizing government the optimal monetary sanction is maximal. That is, the government should impose a fine equal to the offender’s entire wealth. When both sanctions are used together, it is 3 Our model follows Bowles and Garoupa (1997), Chang et al. (2000), Polinsky and Shavell (2001) rather than the Laffont and Tirole mechanism design approach (Laffont & Tirole, 1993, chapter 11). Our model, however, could be translated into the mechanism design framework. In our model, the principal is a benevolent government, the agents are the potential offenders, and the supervisors are the law enforcement officials. The agency costs are due to asymmetric information. The government cannot costlessly observe collusion between officials and offenders, and officials imperfectly observe whether or not potential offenders commit crimes. 4 For a general survey of the literature, see Garoupa (1997), Polinsky and Shavell (2000). 5 See Garoupa (1997), Polinsky and Shavell (2000). It is conventional in this literature to include all gains in social welfare. Some argue that the offender’s gains should be excluded for moral reasons.
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desirable to set the fine at its highest possible value and then to use the nonmonetary sanction to enhance deterrence. The intuition behind the result is that the marginal cost of a monetary sanction is zero, while the marginal cost of a nonmonetary sanction is strictly positive. The government maximizes the social welfare function in s and p, given f = F (the fine is maximal), subject to the constraint that the nonmonetary sanction s is upper bounded by the offender’s maximal opportunity cost S. This upper bound might be a maximal jail sentence, such as life in prison without parole.6 The first-order conditions of this problem are:7 Ws = [h + pt(s) − pF ]g(·)p − p(ts + 1)n ≥ 0
(1)
Wp = [h + pt(s) − pF ]g(·)(s + F ) − [t(s) + s]n − xp = 0
(2)
Let us assume that the cost function exhibits sufficiently large decreasing returns so that the objective function W is strictly concave in s. By evaluating (1) when s = 0, we can derive the necessary and sufficient conditions for nonmonetary sanctions. If so, an interior (strictly positive) solution is optimal when: h − pF > (ts (0) + 1)(1 − G(pF ))/g(pF )
(3)
As a consequence, the optimal nonmonetary sanction in the absence of corruption will be: (a) Zero, if the marginal cost of imposing a nonmonetary sanction is very high, that is, if h − pF ≤ (ts (0) + 1)(1 − G(pF ))/g(pF ). (b) Maximal (S), if the marginal cost of imposing a nonmonetary sanction is very low, that is, if h + pt(S) − pF ≥ (ts (S) + 1)(1 − G(pF + pS))/g(pF + pS). (c) Positive but not maximal, if otherwise. That is, if the marginal cost of imposing nonmonetary sanctions is intermediate (i.e. neither very high nor very low), the optimal nonmonetary sanction is between zero and S. More precisely, in this situation, the nonmonetary sanction will satisfy: h + pt(s) − pF = (ts (s) + 1)(1 − G(pF + ps))/g(pF + ps). 2.2. Nonmonetary sanctions with corruption Assume that an offender can bribe an enforcement agent not to prosecute. Suppose that the bribe is given by v(f, s) = β(f + s), where β represents the enforcement agent’s 6 The model thus implicitly assumes that offenders all have the same wealth and the same maximal opportunity cost. This assumption is common in the literature, see Polinsky and Shavell (2001). Chu and Jiang (1993), Levitt (1997) explore the implications of dropping these assumptions. For a more general survey, see Avio (1998). In order to simplify the analysis and focus on the effects of corruption, we have retained the assumption that all offenders have the same wealth and maximal opportunity cost. Our results hold as long as wealth is perfectly observable in every stage of the enforcement process even if it varies among individuals. For a discussion of the general implications of dropping this assumption, see Garoupa (1998), Polinsky and Shavell (1991). 7 As Kaplow (1990) notes, we must check the second-order condition since the objective function is not necessarily concave in s: Wss = p2 (2ts + 1)g(·) + [h + pt(s) − pF ]g (·)p2 − ptss n. As long as the cost function of the nonmonetary sanction exhibits sufficiently large decreasing returns to scale, the objective function is concave in s and we can proceed to consider an interior nonmonetary sanction. However, for example, if the cost function exhibits constant returns to scale (say t(s) = ts) and g(.) is a uniform probability density function, then the second order condition is p2 (2t + 1). In that case, as Kaplow (1990) demonstrates, the objective function is convex in s and nonmonetary sanctions should be zero for many acts.
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bargaining power and 0 < β < 1. For a bribe of this magnitude to be possible, it must be the case that v(f, s) ≤ F where F is the maximal monetary sanction, i.e. the offender’s total wealth.8 If v(f, s) ≥ F , then we assume that the bribe is the offender’s total wealth, F . In this situation, we say that the wealth constraint is binding. As a consequence, let us redefine v(f, s) = min{β(f + s), F }. Under the assumption of asymmetric Nash bargaining (or Rubinstein bargaining in continuous time), bargaining never breaks down. Thus, all offenders and enforcers engage in bribery if it is mutually beneficial.9 Taking into account corruption, the expected sanction is no longer p(f + s), but rather pv(f, s). The number of offenders in this economy is given by: n(p, f, s, β) =
1 pv(f,s)
dG(b) = 1 − G(pv(f, s))
In the presence of corruption, the government’s objective function (social welfare) is given by the sum of the expected utility of individuals plus the expected utility of enforcers minus the harm caused by offenses minus expenditure on law enforcement: ˆ = W
1
pv(f,s)
(b − h) dG(b) − x(p)
As in the previous section, the optimal fine is maximal (for the usual Beckerian reasons). The government maximizes the social welfare function in s and p, given f = F , subject to the constraint that the nonmonetary sanction s is upper bounded by the offender’s maximal opportunity cost S. The first-order conditions for this problem can be written as: ˆ s = [h − pv(F, s)]g(·)p ∂v ≥ 0 W ∂s ˆ Wp = [h − pv(F, s)]g(·)v(F, s) − xp = 0
(4) (5)
In (4) we have the marginal benefit of nonmonetary sanctions (deterrence) but no marginal cost (since nonmonetary sanctions are not actually applied).10 When the wealth constraint is not binding, increasing nonmonetary sanctions has benefits but no cost, so it is always optimal to set the maximal nonmonetary sanctions. When the wealth constraint is binding, nonmonetary sanctions equal to (1 − β)F/β allow enforcement agents to extract the offender’s entire wealth as a bribe. Thus, there is no benefit in setting nonmonetary sanctions 8 Bargaining between caught offenders and enforcement officers may bring about additional costs such as enforcing the bargaining outcome, and time and effort spent on bargaining. As in previous literature, we ignore these costs. These costs would increase the social cost of corruption which in this paper is the cost of undermining criminal deterrence. 9 When bribery is possible but not universal, the results we have presented in the paper are not as strong, because nonmonetary sanctions now sometimes impose real social costs. Nevertheless, it will still usually be true that nonmonetary sanctions will be set more often and that the optimal nonmonetary sanction will be higher than in a corruption-free environment. Proof on file and available by request. 10 Unlike the previous section, we now satisfy the second-order condition even when the technology does not exhibit large decreasing returns to scale.
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higher than (1 − β)F/β. On the other hand, there is no cost either, because bribery will always transform the (socially costly) nonmonetary sanction into a (socially costless) monetary bribe. Thus, when the wealth constraint is binding, the optimal nonmonetary sanction is any nonmonetary sanction in the range [(1 − β)F/β, S]. From this it follows that, in the presence of corruption, nonmonetary sanctions should be used more often than when there is no corruption. Whereas, as discussed in Section 2.1, it is sometimes optimal for a noncorrupt government to set zero nonmonetary penalties, it is always optimal for a corrupt government to set positive nonmonetary sanctions. In addition, when the wealth constraint is not binding, even when nonmonetary sanctions would be optimal in a corruption-free environment, corruption means that the sanctions should be increased, if they are not already maximal. That is, as discussed in Section 2.1, in a noncorrupt environment, nonmonetary sanctions are sometimes less than maximal. In a corrupt environment, however, maximal nonmonetary sanctions are always optimal. When the wealth constraint is binding, it is still optimal to increase nonmonetary sanctions, if they are not already maximal. Nevertheless, it might also, in some circumstances be optimal to lower the nonmonetary sanctions to (1 − β)F/β. That is, a corrupt government might set the optimal nonmonetary sanction to be (1 − β)F/β, while a noncorrupt government might set a higher or maximal nonmonetary penalty higher. More precisely, lower nonmonetary sanctions could be optimal in a corrupt environment when the following condition is satisfied: (1 − β)F (1 − β)F (1 − G(pF + p(1 − β)F/β)) h + pt − pF > ts +1 β β g(pF + p(1 − β)F/β) This condition identifies situations where the marginal cost for a noncorrupt government of imposing nonmonetary sanctions is low. In such situations, a noncorrupt government might find it beneficial to set nonmonetary sanctions higher than (1 − β)F/β and thus higher than a corrupt government. On the other hand, as pointed out above, since the marginal cost of setting (i.e. threatening) nonmonetary sanctions is zero for a corrupt government, a corrupt government might choose to set nonmonetary sanctions to their maximal amount (S) in all circumstances. Thus, even when the above condition is satisfied, a corrupt government might set nonmonetary penalties higher (or at least as high) as a noncorrupt government.
3. Final remarks The economic literature on law enforcement has generally shown that nonmonetary sanctions should be used infrequently, because they are socially costly. This article presents a possible motivation to use (or at least threaten to use) nonmonetary sanctions more often: corruption. Corruption makes nonmonetary sanctions more attractive, because it converts costly nonmonetary sanctions into socially costless monetary bribes. In absence of corruption, optimal law enforcement policy often suggests that offenders should pay a maximal monetary sanction and face a zero nonmonetary sanction. When corruption is present, a nonmonetary sanction should be used to make sure that the bribe takes approaches the value of the maximal monetary sanction.
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Acknowledgements We are grateful to David Friedman, A. Mitchell Polinsky, Steven Shavell, Matt Spitzer, and participants in the Stanford Olin Workshop and American Law and Economics Association 2000 Annual Meetings for helpful suggestions. Nuno Garoupa has been supported by a scholarship from FCT, Fundac¸a˜ o para a Ciˆencia e Tecnologia, Lisbon, Portugal, and John M. Olin Fellowship, Center for Law, Economics, and Business, Harvard Law School. The usual disclaimers apply.
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