Certainty, Severity, and Their Deterrent Effects Research Paper

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Severity of punishment without the credible threat of being detected and convicted “… is the sound of one hand clapping” (original quote: “Mediation without the credible threat of judicial determination is the sound of one hand clapping,” Genn 2010, p. 125). Theoretical and empirical analyses of general deterrence need to consider both certainty and severity of sanctions, that is, the intertwining activities of police, public prosecution, courts, and prison conditions. Many studies only rely on the probability of detection, that is, on police activity or efficiency, when discussing the role of expected sanctions. Other studies, in particular articles dealing with US data and thus motivated by the highly persistent upward trend in prisoner population, focus on the imprisonment rate and the severity of sanctions as crucial factors of deterrence (see the survey by Donohue 2009). The (brief) survey at hand summarizes the classical rational-choice fundamentals of modern deterrence theory and covers major theoretical and empirical findings on the interplay of certainty and severity of punishment as well as important underlying methodological problems since the early 1970s of the last century.

Any survey of the economics of crime would be incomplete without reminiscence of recent developments in behavioral economics of crime. The last few years seem to have witnessed a change in mainstream economics of crime. Rational-choice models are often criticized because they ignore that cognitive restrictions and emotional factors such as time pressure, peer group influence, or anger restrict the long-run optimality of individual decisions. Simon (1957) was the first to point out that the complexity of situations and limitations of both available information and cognitive capacity would lead to decisions under bounded rationality. Several recent papers focus on shortcomings and necessary extensions of the classical notion of certainty and severity of sanctions. This contribution discusses significant insights stemming from behavioral economics such as impulsiveness (myopia), prospect theory, and anger. Moreover, stigma effects (dynamic deterrence) and the distinction between objective and perceived threats of potential punishment will be addressed.

This survey contains the following subchapters: fundamentals of general deterrence theory, theoretical and empirical results concerning (a) the certainty of punishment and (b) the severity of sentences, limitations and extensions of the classical deterrence model, and, finally, the threat of punishment when trust in criminal law is absent. The paper concludes with remarks on future directions of research in deterrence.

Fundamentals Of General Deterrence Theory

General deterrence is the avoidance of crime by (deterrable) potential offenders through the credible threat of punishment. This definition entails (a) there is a threat in terms of a judicial system of appropriate sanctions and (b) this threat is credible, that is, there is a legal enforcement system of police, prosecutors, and judges which has the capability to realize a perceptibly high (strictly positive) probability of detection and conviction. The definition also requires that there is a nonempty group of compliers, that is, a deterrable subgroup of the population which can be correctly described as potential offenders because otherwise the theory of deterrence would be futile. The identification of deterrable and non-deterrable subpopulations is important but a rather neglected field in criminology.

The theoretical foundations of general deterrence are usually ascribed to Gary Becker’s (1968) seminal article, although the philosophical foundation of deterrence dates back to eighteenth century (Bentham (1781)). In a broader sense, the idea of general deterrence is related to rational-choice theory, which assumes that all individuals, irrespective of being criminal or not, respond to incentives, or as Becker puts it, “Some people become ‘criminals’ not because their basic motivation differs from that of other persons, but because their benefits and costs differ” (Becker 1968, p. 176). Though often disputed and criticized (see, among many others, McAdams and Ulen 2009), the importance of rational choice and general deterrence has also been acknowledged by criminologists and sociologists (as discussed in Rupp 2008, p. 6).

Becker’s theory on the supply of offenses is based on the comparison of (uncertain) expected utility from criminal activities to the (relatively certain) utility from not committing crimes. Thus, increasing the individual costs of crime by increasing the expected sentence would lead to a reduction of criminal behavior for rational offenders. Assuming additivity, the theory predicts that if the expected utility from committing a crime,

Certainty, Severity, and Their Deterrent Effects Research Paper

exceeds the expected utility from obeying the societal legal norms, ENC , a crime will be committed; otherwise individuals refrain from wrongdoing. Here p denotes the probability that the illegal act will be detected and punished, (1-p) is the probability of getting away with it, UC represents utility from crime, ENC is utility from noncrime, and CC captures disutility (cost) from being punished. Obviously, to make punishment effective, CC needs to be higher than UC . This condition fits Bentham’s (1781) “Principles of Morals and Legislation”: According to Rule 1 of “Of the Proportion Between Punishments and Offences,” “The value of the punishment must not be less in any case than what is sufficient to outweigh that of the profit of the offence” (Bentham 1781, p. 141).

Equation 1 can be expressed as the difference between the benefit from committing a crime and the expected sentence in case of detection, that is,

Certainty, Severity, and Their Deterrent Effects Research Paper

Equation 2 can be considered as the most parsimonious representation of severity and certainty of conviction. It is obvious that credibility of the threat of sanctions requires the expected sentence, that is, product pCC ; to be positive. As an example of the deterrence rationale, consider the choice between paying a certain amount of money, say, 3 Euros, for a short-term city parking space and not paying the amount and taking the risk of a fine of, say, 20 Euros. If on average every 10th free parking is detected, that is, p =0.1, then the utility from the illegal action, UC , would be 3 Euros, whereas the expected fine was 2 Euros. Hence the risk-neutral rational “offender” would decide against putting a coin into the parking meter and in favor of the illegal alternative. Of course, such reasoning may be ambiguous in case of risk preference, and as mentioned above, it requires that a nonempty subgroup is complying according to rational-choice rules, that is, a significant number of people belong neither to the group of always strictly norm-abiding citizens nor to the group of never law-abiding individuals. Thus, summarizing the standard rational-choice reasoning covered in Eq. 2, deterrence would not work either when the certainty of a sanction is zero or when sanctions lack severity. In both cases, the product pCC would be zero, that is, there would be no credible threat from expected sanctions for wrong doing.

Equation 2 also represents the basic foundation of Becker’s so-called supply of offenses, which is grounded on first-order conditions of the difference between illegal and legal sources of expected utility, EC-ENC . Taking derivatives with respect to the crucial impacting factors p, CC and ENC yield the behavioral equation

Thus, under standard neoclassical assumptions (see Becker 1968 for details), crime (C) would fall when the probability of detection and punishment increases or when potential offenders face the risk of higher costs from committing crimes. These disincentives to crime change in response to longer or tougher prison sentences, for example, in terms of tough-on-crime policies such as the Californian three-strikes law or the application of adult criminal law instead of juvenile criminal law (as discussed in Entorf 2012). Crime would also decrease when utility from noncriminal activities, ENC , increases, for instance, because of lower unemployment risk, or improving current and future legal income opportunities, which include the broad and lasting impact of education on crime. Of course, empirical models on crime would fail if only p, CC , and ENC were included as explanatory factors of crime. Thus, X represents further factors of which age, gender, alcohol and drug addiction, migration background, race, peer influence, and family background belong to the (incomplete) list of variables often (but not regularly) found in crime studies. An indeterminacy of statistical tests of deterrence models is the rather arbitrary choice of X. Indeed, a meta-study by Dolling et al. (2009, Table 5) reveals that the choice of control variables has a high influence on finding significance or nonsignificance of deterrence indicators in empirical studies: Dependent on the choice of the control variable, reported average t-values on deterrence variables range from -0.5 to -2.3. The problem of ad hoc specifications is discussed in more detail by Durlauf and Nagin (2010).

On The Impact Of Certainty

Early Contributions. The first empirical tests of Becker’s supply of offenses model have been conducted in the late 1960s and early 1970s of the last century. Early studies such as Tittle (1969) have found significant crime reducing effects in response to increasing certainty (p). However, these contributions were flawed by endogeneity problems and ignorance of incapacitation effects. Although follow-up papers such as Ehrlich (1973) used two-stage least squares techniques to account for simultaneity problems, identifications strategies such as use of lagged endogenous variables would be considered problematic from the current viewpoint of modern econometrics (see also Durlauf and Nagin 2010). Ehrlich’s (1973) results were intensively discussed, and not all studies agreed on the evidence in favor of the deterrence hypothesis. Many studies argue that the model is too simplistic and empirical findings are not reliable enough to draw any conclusion in favor or against the deterrence hypothesis. According to Rupp (2008), this criticism seems to be exaggerated, but the ambiguity of Ehrlich’s findings was and still is perhaps the main reason for the lasting debate on Ehrlich’s problematic contribution to the deterrence literature.

Ehrlich’s (1973) article also received prominent attention as a significant contribution to the theoretical literature. He modified Becker’s theoretical model by using a time allocation model. This framework widens the perspective because it includes leisure time as a source of utility besides utility from time spent on legal and illegal activities. This makes theoretical predictions less clear than in Becker (1968), where utility is achieved either from illegal or from legal activities. Ehrlich (1973, p. 530, footnote 13) draws attention to the point that the unambiguous negative sign of deterrence effects only holds when individuals are risk neutral or risk averse.

Survey of Surveys and Meta-studies. In the first three decades after Becker’s (1968) seminal article, several surveys on the economics of crime have been published. Rupp (2008) summarizes them in more detail. During the last few years, the frequency and number of surveys seems to accelerate. Surveys by Rupp (2008), Donohue (2009), Durlauf and Nagin (2010), and Ritchie (2011), to name only a selection of remarkable new publications, confirm what has been found by earlier studies, that is, that the deterrent effect of the certainty of sanctions far outweighs the severity of punishment.

Eide et al. (1994) is a good starting point in order to provide a sample of typical estimates of the deterrent effect of the certainty of sanctions. The authors summarize 20 international cross-sectional studies based on a variety of model specifications, types of data, and regressions. They find the median value of the 118 elasticity estimates of crime rates with respect to various measures of the probability of punishment to be about -0.7. The median of the somewhat fewer severity elasticities is about -0.4.

Donohue (2009) focuses on the effect of the imprisonment rate in six studies based on aggregate data and finds that most studies show a negative effect of incarceration rates on crime. However, the estimates of the elasticity of crime range considerably between -0.70 for robbery and results on all index crimes which suggest that marginal imprisonments would even increase crime. Donohue (2009, p. 17) admits that his best guess for the elasticity is “highly uncertain”, most likely being between -0.10 and -0.15 but “conceivably within the broader interval between -0.05 and -0.40”. Durlauf and Nagin (2010) discuss the papers of Donohue’s survey at some length. They criticize the statistical methodology employed in these studies and dismiss Levitt (1996) as the sole author of the survey who convincingly addressed the simultaneous interdependencies between crime and imprisonment rates. A further problem of studies relying on the imprisonment rate as the sole indicator of p is that it covers compound effects which might cause an omitted variable bias (see the subsequent subchapter on Decomposing the Certainty Effect).

Durlauf and Nagin (2010) consider studies based on police manpower more persuasive than those based on imprisonment rates. Their sympathy seems to be affected by the highly influential paper by Levitt (1997) and its critics on the choice of meaningful instruments. Durlauf and Nagin (2010) summarize the findings from these studies and further replication studies and mention an average elasticity of 0.3 for most estimates relating total crimes and police presence. However, given the high dependency of results on the type of crime under consideration (see below), such typical results covering the whole range of crime categories can hardly be considered useful for practical public policy purposes (which is in line with Donohue’s “uncertainty” about his best guess).

A recent extensive meta-analysis based on 700 empirical studies with 7,822 estimates of the crime-preventing effect of general deterrence (certainty or severity of sanctions) by Rupp (2008; see also Do¨ lling et al. 2009) reveals a large variation of effects depending on the choice of the deterrence variable. For instance, using the indicator ratio of convictions to reported crimes produces a highly statistical evidence in favor of the certainty of sanctions (median t-value =-3.5), whereas using the clearance rate would produce less significant results (median t-value=- 1.9; Dolling et al. 2009, Table 3). Results also differ with respect to the crime category under consideration. Rupp (2008), Table 3.43, p. 126 finds that among the offenses which have been in best accordance with the deterrence hypothesis are speeding (median t-value =-2.2), tax evasion ( -2.1), severe theft (-2.1), and fraud (-2.0), whereas sexual assault (- 0.5), manslaughter (0.0), and drug dealing (0.0) were only rarely found to be consistent with the deterrence hypothesis. Thus, very prominent in the group of consistent types of crimes are nonviolent crimes, while the discordant part seems to incorporate violent crimes and drug-related offenses.

Decomposing the Certainty Effect. Testing the theoretical prediction of p, that is, the certainty of sanction, requires empirical measurement of the joint probability of detection and subsequent punishment. Many empirical models are restricted to only one indicator such as clearance rates (Entorf and Spengler 2000) or number of police officers (Levitt 1996). However, variations in clearance rates may not change the threat of expected sentences when prior to judicial decisions cases are dismissed or discharged by the public prosecutor. Moreover, expected sentences differ in response to court decisions, which can be dismissal, unconditional imprisonment, probation, (financial) fine, or other sanctions such as educational measures. Thus, to improve the consistency of empirical models with their theoretical counterparts and in order to analyze the effectiveness of the various sources of deterrence, it is necessary to decompose the certainty effect p into its components. In its simplest way, this can be done by distinguishing between the probability of detection (clearance rate), pcl , and the conditional probability that a suspect is sentenced, ps|cl (probability of a sentence, conditional on detection), that is,

The variation of certainty effects becomes more transparent when changes in clearance or arrest rates are separated from the ones of courts and sentences. To fully understand such variations, changes in ps|cl can be further decomposed into changes of the indictment rate (driven by public prosecution), pcourt|cl (i.e., the probability that a suspect is brought to court), and those stemming from court decisions, ps|court (i.e., the probability that a suspect is convicted, given he or she is brought to court), eventually leading to ps|cl = pcourt|cl ps|court . In both the US and European legal systems, the (high) discretionary power of the prosecutor is to determine which case should be disposed of before trial either by dismissal of the charges or by imposing certain obligations on suspects in exchange for laying the file aside. The picture is still incomplete unless the risk of the most severe outcome conditional on detection has been covered, that is, the certainty of a (unconditional) prison sentence. After including ppris|s , that is, the probability of imprisonment given a conviction, the full decomposition of the probability of imprisonment (conditional on detection) looks as follows:

Not surprisingly, also empirical indicators of ppris|cl vary across time and space (see Entorf and Spengler 2013) Thus, to summarize, the probability of a sanction depends on the interplay of many factors, and all of them are far from being constant parameters.

Reasonable public policy analysis and recommendations should take the role of all key players and their decisions, that is, interplay of police, prosecutors, and courts, into account. Only few studies also cover the risk of convictions, for example, by the ratio of convictions to arrests. Cornwell and Trumbull (1994), who were among the first applying panel econometrics for testing general deterrence models, present exceptional work because of their comprehensive list of law enforcement variables containing the probabilities of arrest, conviction (conditional on arrest), and imprisonment (conditional on conviction) as well as the severity of sanctions. However, the overall impression is that only few studies are taking account of a comprehensive list of factors.

In particular, the interplay of conviction rates and sentence lengths, that is, the essential components of certainty and expected severity of punishment, has been neglected. However, it is obvious that components of general deterrence do not work independently of each other. Missing factors of the law enforcement system might cause severe omitted variable biases (Entorf and Spengler 2013).

On The Impact Of Severity

Death Penalty. The severity of punishment is the fundamental idea of capital punishment: “… if rational people fear death more than other punishment, the death penalty should have the greatest deterrent effect” (Ehrlich 1977, quotation found in Rupp 2008, p. 22). Although this statement is questionable, either because the expected sentence would be nil when there would be no (perceived) risk of detection or because “rational” suicide bombers expect going to paradise with the infamous 72 virgins, the focus of most studies in the aftermath of Ehrlich (1975) lies on the absolute deterrent effect of capital punishment. Most publications refer to US evidence, as can be seen from the fact that 71 out of 82 studies evaluated by Rupp (2008), p. 22, use US data and 5 are based on Canadian data. Ehrlich’s (1975, 1977) articles have fueled an ongoing debate about the effectiveness of the death penalty. His results have been criticized for data errors, misspecification problems, and other methodological problems. Numerous subsequent studies have rejected but also confirmed significance of the death penalty. Donohue and Wolfers (2005) summarize several studies on the death penalty in the United States. They conclude that all outcomes are too fragile and that the number of executions is too low to draw any noteworthy and robust conclusion. This result is in line with the meta-study on the significance of death penalties by Dolling et al. (2009, Table 10), where median t-values of effects range between 0.5 and +0.1, that is, below usual significance levels. This survey is not the right place to summarize all facets of the complex debate on the death penalty which is interesting for its methodological aspects, but most probably the large majority of scientists from industrialized countries outside the USA would not consider it a practical and ethically tolerable alternative to lifelong sentences.

Evidence on the Length of the Prison Sentence and Prison Conditions. According to the aforementioned meta-study (Dolling et al. 2009, Table 3), most results using the average length of served prison sentences as an indicator of the severity of sanctions do not show statistical significance (median t-value =- 0.6). This result is in line with the tenor of previous and recent surveys such as Eide et al. (1994), Durlauf and Nagin (2010), or Ritchie (2011). However, Durlauf and Nagin (2010) correctly state that most effects are measured as marginal effects in addition to already existing long sentences. Thus, more reliable evidence would be based on discontinuous jumps of severity. Levitt (1998) has found a significant drop in the offending of young adults when they reach the age of 18, that is, the age of jurisdiction for adult courts in Florida.

Other abrupt and unexpected changes of deterrence come from natural experiments. Maurin and Ouss (2009) and Drago et al. (2009) study the effect of external variations arising in response to collective pardons in France and Italy, respectively. Maurin and Ouss (2009) show that 5 years after release, those who have received a reduced sentence as a consequence of the pardon had a 12 % higher rate of recidivism than those who had received no reduction. In the case of the Italian clemency, inmates received a conditional reduction of prison sentences. In case of reoffending, they had to serve the remaining amount of their sentence (in addition to the new sentence). Drago et al. (2009) find that the threat of increased sanction continued after release: For every month the former prisoner would have to serve if convicted, there was a 1.2 % reduction in the propensity to recommit crimes. Both studies touch the problem of specific deterrence, that is, whether individuals would avoid future imprisonment because they are deterred by their own previous sentencing experience. However, in particular the study by Maurin and Ouss (2009) also tests the deterrent effects of longer prison sentences, though based on a subgroup of former inmates. In the case of Drago et al. (2009), the effect is a combination of certainty and severity because the threat of serving the remaining sentence also depends on the probability of detection and conviction.

Limitations And Extensions Of The Classical Deterrence Model

Predictions of the fundamental model (as presented in Section 2) are based on a static model under regular neoclassical assumptions. The classical rational-choice model needs to be reconsidered in the face of challenging recent findings of behavioral economics. In particular, the (objective) detection probability and the disutility from punishment need to be adjusted given insights from prospect theory, myopia, and dynamic deterrence:

The new elements of a behavioral supply of offenses model (Eq. 6) are to be introduced: Criminological research suggests that offenders have unusually high discount rates, that is, they place high value on immediate utility gains, whereas future events are strongly discounted, that is, they consider them as less important for current decisions than noncriminals. As consequences of criminal activities, if any, would have to be faced at some unknown time in the future, this so-called present bias (also called impulsiveness or myopia) leads to underestimation of expected future costs from punishment, CC:t+τ . In particular, adolescence, alcohol, or drug misuse (not to mention mental impairment) may lead to a very small personal weight of future consequences, that is, βc <<1.

The classical static deterrence model also neglects future consequences of illegal activities which a rational forward-looking individual would take into account. Given the person will be detected and punished, she would expect diminished reemployment chances, reductions in social capital, relational problems, etc. Thus, rational individuals would also be deterred by the potential future reduction of expected legal utility gains, that is, shrinking ENC:t+τ , in response to the stigma of a criminal record. This potential threat is also called dynamic deterrence.

A related but different deviation from classical rational-choice and general deterrence models is the existence of subjective probabilities of detection and punishment, π(p). These should be more precisely called decision weights because they do not satisfy the classical probability axioms. Allais (1953) was the first who criticized expected utility theory for its inconsiderate use of objective probabilities, that is, π(p) = p; in models of human behavior. Kahneman and Tversky (1979) developed an alternative model called prospect theory. They emphasized that “… people are limited in their ability to comprehend and evaluate extreme probabilities, highly unlikely events are either ignored or overweighted [.. .] Consequently, p is not well-behaved near the end-points” (Kahneman and Tversky 1979, pp. 282–283). Experiments show that individuals overweight low probabilities of gains, that is, (1-π(p))> (1 – p) in case of criminal gains, which implies π(p)<p, that is, underweighting the risk of being caught and punished. The overestimation of the criminals’ own ability to avoid any apprehension and sanction is also known as overconfidence in the behavioral economics literature (McAdams and Ulen 2009).

The perceived risk of detection of re-offenders is of particular importance because of the high share of crimes committed by recidivists. Piquero and Pogarsky (2002) argue that criminals behave according to the belief that “lightning won’t strike twice”: They underestimate the probability of being detected and convicted because they (erroneously) believe that the risk of being punished again is very low. Some further details and discussions on the perceived (instead of objective) risk of being punished can be found in McAdams and Ulen (2009) and Ritchie (2011).

The Threat Of Punishment When Trust In Criminal Law Is Absent

One of the stylized facts in empirical criminological research is the individual victim-offender overlap. A prominent explanation of the victim-offender overlap is the subculture-of-violence approach (Singer 1981), according to which individuals who attack others risk retaliations from former victims. Rational-choice theory seems to be generally questioned by such “irrational” retaliatory behavior of victims and criminals. However, retaliation can be seen as a rational deterrence strategy in a prelegal or pre-societal community. Given lacking access or trust in the public institution of criminal law systems in modern societies, victims might be tempted to take the law in their own hands. In particular in disadvantaged neighborhoods and subcultural societies where the retaliatory ethic of the code of the street (Anderson 1999) is used in lieu of criminal codes, the credible threat of punishing by strong retaliation might deter potential future perpetrators.

Rational-choice models are often criticized because they ignore that cognitive restrictions and emotional factors such as time pressure, peer group influence, or anger restrict the long-run optimality of individual decisions. As regards the overlap of victimization and offending, anger seems to be the major motivation of retaliatory behavior, as also stressed by many criminological and psychological research papers. Anger in response to perpetrated injury, frustration, and unfair treatment can be a triggering event that motivates striking back, not necessarily to the perpetrator himself but also to noninvolved bystanders and other available victims, also at some later point in time. Such behavior is often the consequence and origin of norms of honor and respect (or fear of dishonor and shame, respectively), prevailing and potentially escalating in subcultural societies (Anderson 1999) and serving as a deterrent factor when trust in criminal justice systems is absent. Such retaliatory behavior is not restricted to deprived subgroups: As suggested by findings in Fehr and G€achter (2002), punishing unkind behavior of others or negative reciprocity seems to be a social norm rooted in general human behavior. Participants in their experiments revealed some altruistic punishment behavior, that is, they punished defectors even when they had costly disadvantages from the retaliation. This so-called pro-social behavior has its origin in the notion of fairness as can be seen from the outcome of many ultimatum-game experiments: Responders often destroy any portion of their (guaranteed) gains when they perceive the proposal of the proposer as unfairly low. Thus, anger about unfair treatment is the individual motivation, but its social effect could be deterrence.

Future Directions

Certainty and severity of sanctions form the two cornerstones of general deterrence. This survey reveals that its underlying classical rationalchoice theory has been reconsidered by recent research, yielding important insights from bounded rationality and behavioral economics. Future research will continue to analyze the threat of punishment, but the focus will be on the role of hyperbolic discounting, overconfidence, perceived risk, ambiguity, prospect theory, and dynamic models, just to name only a few of many interesting fields. Also the empirical approach has changed dramatically during the last 10 years or so. Modern criminological research is often based on laboratory and (quasi) natural experiments (such as changes in legislation or clemencies) which create convincing external variations of deterrence variables. From a criminal policy point of view, the problem of cost-efficient use of deterrence instruments has a high potential for future research. Given the relatively small effect coming from the severity of sanctions, one might be tempted to shift resources from imprisonment to policing. Though certainly high on the political agenda, one should nevertheless be aware of the limited empirical evidence (mostly coming from the USA and dealing with marginal effects of already long sentences). Moreover, alternative (long-run) cost-benefit considerations such as shifting scarce resources to education and families should be taken into account, since both poor education and family background are identified as the major reasons of lacking legal opportunities over the life cycle and resulting criminal careers.


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