ECONOMICS OF CRIMINAL BEHAVIOR
Professor, Faculty of Law, University of Oslo
© Copyright 1997 Erling Eide
Models of criminal behavior, where a person is assumed to act rationally on thebasis of costs and benefits of legal and illegal opportunities, are presented. Mostof these models are similar to models of portfolio choice and of supply of labor.The empirical studies that are surveyed use various types of regression analysesand employ data from states and police regions down to campuses andindividuals. Most studies corroborate the hypothesis that the probability ofpunishment, and to a lesser degree also the severity of punishment, has adeterrent effect on crime. The effects of various economic factors are less clear,although unemployment seems to increase crime. Methodological problemsrelating to the assumption of rationality, to statistical identification of equations,to measurement errors, and to operationalization of theoretical variables arediscussed.
JEL classification: K42
Keywords: Crime, Punishment, Sanctions, Rational Choice
Theories of crime are abundant. Various mental, physical, developmental,economic, social, cultural, and other causes have been launched as explanationsof why people offend. Concepts like depravity, insanity, abnormality, devianceand deprivation are used to characterize those who commit crimes. During thelast 30 years economists have invaded the field using their all-embracing modelof individual rational behavior, where a criminal act is preferred and chosen if thetotal pay-off, including that of sanctions and other costs, is higher than that oflegal alternatives. Offenders are primarily not regarded as deviant individualswith atypical motivations, but rather as simple, normal persons like the rest of us.The theory of deterrence thus obtained is regarded as nothing but a special caseof the general theory of rational behavior under uncertainty. Assuming thatindividual preferences are constant, the model can be used to predict howchanges in the probability and severity of sanctions and in varioussocio-economic factors may affect the amount of crime. Even if most of thosewho violate certain laws differ systematically from those who abide by the samelaws, the former, like the latter, do respond to incentives, i.e. to sanctions andeconomic conditions. Empirical tests with increasing statistical rigour andrefinement have been carried out on the basis of this theory.
Whereas the general preventive effects of sanctions for a long time haveoccupied a main position in penal legislation and sentencing policy, such effectswere almost totally neglected in criminology and modern sociology until the late1960s. Criminologists have been more interested in rehabilitation and treatment,and many are still reluctant to accept studies of deterrence in general and modelsof criminal behavior based on rational choice in particular. However, scholarswho are reluctant to accept the assumption of rational choice, still find interestin the rather rigorous empirical studies in the economics of crime literature( Andenaes, 1975 ), and sociologists have in recent years been inspired to carryout similar research. Below, mainly studies made by economists are included.
Theories of criminal behavior based more or less on the assumption of rationalchoice were proposed by Beccaria and Bentham. Bentham (1843, p. 399 ) wrote that "... the profit of the crime is the force which urges man to delinquency:the pain of the punishment is the force employed to restrain him from it. If thefirst of these forces be the greater, the crime will be committed; if the second, thecrime will not be committed." From the beginning of this century interest in theirpoint of view dwindled as a plethora of other theories were developed. The mainidea of Bentham was vitalized and modernized in the pathbreaking article on Crime and Punishment by Becker (1968) , who suggests that "a useful theory ofcriminal behavior can dispense with special theories of anomie, psychologicalinadequacies, or inheritance of special traits and simply extend the economist'susual analysis of choice" (p. 170) . He argues that criminals are like anyone else,and assumes that an individual behaves as if he is a rational utility maximizer. Asthe total outcome of a criminal act is uncertain, Becker employs the usualassumption that people act as if they were maximizing expected utility, and alsothat utility is a positive function of income. The individual's expected utility E [ U ] from committing an offense is:
|E [ U ] = PU ( Y-f ) + (1- P ) U ( Y ),||(1)|
where U (.) is the individual's von Neumann-Morgenstern utility function, P is the subjective probability of being caught and convicted, Y is the monetaryplus psychic income (i.e. the monetary equivalent) from an offense, and f is themonetary equivalent of the punishment. The individual will commit the offenseif the expected utility is positive, and he will not if it is negative. The commonassumption of stable preferences provides a solid foundation for generatingpredictions about responses to various changes in parameters, and, accordingto Becker, prevents the analyst from succumbing to the temptation of simplypostulating the required shift in preferences in order to 'explain' all apparentcontradictions to his predictions. Analysis of comparative statics shows thatincreases in either the probability or the severity of punishment might changethe expected utility from being positive to being negative. For society as a wholeBecker introduces a "supply of offense function", where the two factors havean effect on the total amount of crime.
Whereas Becker considers the income and punishment equivalents of anoffense separated from other income, later authors, in accordance with Brownand Reynolds (1973) , take the individual's initial income position as a point ofreference. Expected utility becomes
|E [ U ] = PU ( W - f ) + (1- P ) U ( W + g ),||(2)|
where W is present income and g is gains from crime. Here, the crime will becommitted if the expected utility is higher than the utility of the initial income W .Furthermore, it is sometimes assumed that the offender in case of convictionmight retain some gain from the offense. Becker demonstrated that if theelasticity of the expected utility with respect to the probability of punishmentexceeded the elasticity of the expected utility with respect to conviction (bothin absolute values), the offenders were risk lovers. Empirical studies by Beckerand others corroborated this result. As shown by Brown and Reynolds (1973) equation (2), at variance with equation (1), does not imply such a conclusion.
Later, several types of economic models of crime have been developed, all ofwhich drawing on the theory of supply and the theory of behavior towards risk.The simplest one is very similar to models of portfolio choice, where a person'swealth is allocated between various risky and non-risky projects. In theeconomics of crime version of this model the illegal alternatives are consideredas risky mainly because of uncertainty about punishment. Allingham andSandmo (1972) , Kolm (1973) , and Singh (1973) have constructed such models fortax evasion, where the individual is confronted with the problem of decidingwhat proportion of income not to report to the tax authorities. At variance withBecker's model where the income of crime is a parameter, here the income ofcriminal activity is a function of the proportion of the exogenous income notreported.
Both the probability and the severity of punishment are found to deter crimefor a risk averse person. For risk lovers, the effect of the severity of punishmentis uncertain. An increase in the severity will have similar effects for illegalactivities as a wage decrease in labor supply models will have for legal activities.Two effects obtain: a substitution effect and an income effect. The substitutioneffect of a more severe punishment will consist in less crime. The sign of theincome effect will depend on individual attitude towards risk. For a risk lover theincome effect is positive, and the total effect on crime of a change in severitybecomes indeterminate. The effects of changes in gains from crime and inexogenous income depend on whether there is decrease or increase in the riskaversion or risk preference. For the common assumption of decreasing absoluterisk aversion an individual will allocate a larger proportion of his income to taxcheating the higher his exogenous income and the higher the gains from crime.
Heineke (1978) has presented a somewhat different type of model where theindividual allocates his time (and not his wealth or income) between legal andillegal activities. The individual's income is assumed to be equal to the sum ofthree elements: exogenous income, the monetary and monetized benefits andcosts of legal activities, and the monetary and monetized benefits and costs ofillegal activities. (Monetization implicitly takes place if an individual, having tochoose between actions involving non-monetary gains and losses, actsrationally according to certain axioms.) If convicted, this income is reduced bya factor that represents the monetary and monetized costs of crime. Here, someof the individuals may choose to specialize either legal or illegal activities,whereas others may choose a mix of the two. A marginal increase in theprobability or the severity of sanctions will affect the optimal mix of activities,whereas such an increase may be insufficient to have an effect on individualswho have specialized in one of the two activities. Assuming leisure time not tobe fixed, the same comparative statics results as for the portfolio choice modelare obtained. The reason for this similarity is the monetization of psychicbenefits, and the high degree of independence between the types of activities.In addition, for some attitudes towards risk, it turns out that an increase inreturns to legal activity increases time allocated to both types of activities.
Several authors, first and foremost Ehrlich (1973) , have studied the latter typeof model, but with the additional restriction that time allocated to leisure is fixed(and thus independent of returns and costs for legal and illegal activities). Theassumption of a fixed leisure time obviously requires that the time allocated tolegal and illegal activity changes in opposite direction (and with equal amounts),but the effects of changes in some of the parameters are also different from theprevious model. Whereas the effects on crime of changes in exogenous incomeand gains to crime are the same as above, the effects of changes in the severityof sanctions become inconclusive without further restrictions on someparameters.
The portfolio model of time allocation with non-fixed leisure time has beensomewhat extended by Wolpin (1978) and by Schmidt and Witte (1984) , whohave introduced four possible criminal justice states, each taking place with acertain probability. In these models the effects of changes in sanctions, and ingains and losses of crime become more ambiguous than in the previous models.Especially, and somewhat surprisingly, illegal activity will decrease withincreasing unemployment under the standard assumption of decreasing absoluterisk aversion. The explanation is that unemployment implies a lower income, andtherefore a higher risk aversion, and then again a lower expected utility of crime.Under risk neutrality time allocated to illegal activity is not affected by a changein the expected employment rate. Baldry (1974) introduces the assumption thata person has to choose between zero or a given number of hours of legal workper week. Transforming the Ehrlich model into a nonlinear programming model,he obtains unambiguous predictions of the effects on crime of changes insanctions and economic variables.
If one is not willing to accept the assumption that all psychic factorsassociated with legal and illegal activities can be monetized, one has to useutility functions where time allocations and their attributes are introducedexplicitly. Block and Heineke (1975a) have studied a model where a vector ofattributes of the penalty, interpreted as the length of sentence, is included in theutility function. In this model one obtains considerably more ambiguous resultsthan for the previous models. Unless one is willing to make strong assumptionsabout individual preferences, it is not possible to decide whether criminalactivity will decrease or increase as a result of changes in the probability ofpunishment, of changes in returns to legal and to illegal activity, and of changesin exogenous income.
Block and Heineke (1975a) have shown that changes in legal and illegalremuneration lead to changes in illegal activity that are composed of stochasticcounterparts of the substitution and income effects of traditional supply anddemand theory. But the similarity is not close. Even if one assumes that illegalactivity is inferior (i.e. that such activity is decreasing with income), it is notpossible to sign the relevant terms. Increasing the penalty, for instance, will notunambiguously deter crime.
Witte (1980, p. 59) and Schmidt and Witte (1984) have studied a simplifiedversion of their several sanctions model where time spent in legalincome-generating activity (work), time spent in illegal income-generatingactivity (theft, etc.), time spent in legal consumption activities, and time spentin illegal consumption activities (drug use, assaultive activities, etc.) are separatearguments in the individual's utility function. Here too, similar inconclusiveresults are obtained. When benefits and costs of legal activities are risky, evenmore ambiguous results are obtained.
The standard assumption that people maximize expected utility is appealingbecause it follows from the von Neumann-Morgenstern axioms of individualbehavior that many scholars regard as reasonable, or at least as a fruitfulhypothesis. However, many laboratory experiments have shown that people donot always choose in accordance with these axioms, in particular Lattimore et al.(1992) , who included burglaries in a set of risky prospects to choose between.As a result, various alternative forms of preference functions that are non-linearin the probabilities have been proposed. Eide (1995) has substituted theassumption of rank dependent expected utility for the ordinary expected utilityin various models of criminal behavior. In the latter study it is shown that thequalitative results of comparative statics analyses are the same for both typesof assumptions.
Summing up the comparative static results so far, an increase in theprobability of clear-up or arrest has, regardless of the sign of the attitudetowards risk, a negative effect on the supply of crime. The effect of an increasein the conviction rate, given arrest, is indeterminate without further assumptions,and the same holds true for an increase in the probability of imprisonment givenconviction. However, reasonable assumptions will produce the sameconclusions as for the unconditional probability of arrest or conviction. Theseresults constitute a certain support for the probability part of the deterrencehypothesis.
For any attitude towards risk in Beckers's model, an increase in the severityof punishment has a negative effect on the supply of crime. For the group ofportfolio choice models as a whole the severity part of the deterrence hypothesishinges upon the question of attitude towards risk. The effect of more severesanctions is especially uncertain for risk lovers, whereas risk averters in mostmodels offend less when sanctions increase. Furthermore, a positive shift inpunishment in the several-sanctions-model and in the labor supply model withnon-monetized attributes can cause an increase in crime for any attitude towardsrisk. In the latter model, the restriction necessary to generate this effect is thatthe income effects must be greater than the substitution effects. The laborsupply models with non-monetized attributes give inconclusive effects also forchanges in the other parameters that are studied. For the other models theeffects of changes in the gains to crime, in exogenous income, and in incomefrom legal activities depend on the individual's attitude towards risk.
As a whole, one may conclude that the effects of changes in the environmentdepend on the individual's attitude towards risk. If one is willing to stick to therather common assumption of decreasing absolute risk aversion, and also thatpsychic effects can be monetized, and that there is just one type of sanctions,the effects are clear: Crime is deterred by increases in the probability and in theseverity of punishment, and enhanced by increases in exogenous income, andin gains from both legal and illegal activities. The reason why increases invarious incomes and gains increases crime, is that punishment in the case ofdecreasing absolute risk aversion produces a smaller reduction in expected(total) income. For risk neutral people an increase in the probability or severityof punishment and a decrease in the gains to crime will reduce the supply ofcrime, whereas changes in exogenous income, and in the remuneration of legalactivity have no effect. Here, changes in the latter income components do notchange the bite of punishment.
A crucial assumption in the studies mentioned above seems to be theBernoulli distribution of the probability of punishment. Introducing a moregeneral distribution of risk into the Becker-type model of Block and Lind (1975) , Baldry (1980) concludes that the "standard" deterrence results cannot bederived.
A good survey of the main contributions to the development of theeconomic models of crime is found in Schmidt and Witte (1984) .
Various studies have elaborated on the benefits and costs of crime. The gainsand losses included in the economic models of criminal behavior are usuallymeant to represent all kinds of benefits and costs that have an effect on thepeople's decisions. People are assumed allocate time to criminal activity untilmarginal benefits equal marginal costs. For some people marginal benefits areprobably always lower than marginal costs, and we then have a law-abidingperson. Others will specialize in crime, whereas most of us possibly commit anoffense now and then.
The kinds of gains obtained from a criminal act vary, depending on the typeof crime and the individual criminal: Some are monetary, obtained from theft,robbery, insurance fraud, etc. Others are psychic, such as the thrill of danger,peer approval, retribution (bank robbery), sense of accomplishment, or "pure"satisfaction of wants (rape). For some property crimes the prices obtained onmarkets of stolen goods are of importance.
Among the costs one may distinguish between material costs (equipment,guns, vehicles), psychic costs (guilt, anxiety, fear, dislike of risk), expectedpunishment costs, and opportunity costs.
The punishment costs include all formal and informal sanctions, as well aspecuniary costs arising from lawsuits (lost income and lawyer's fee). The formalsanctions include fines, various forms of incarceration, etc. The more severethese sanctions are, the higher the cost. The informal sanctions include anypersonal inconveniences connected with arrest, suit, and conviction. Thesanctions related to the social stigma caused by arrest and formal sanctionsmust be added. The nuisance associated with appearing in court, and thereactions of employer, family and friends, might have a stronger effect thanformal sanctions.
The opportunity cost of crime consists of the net benefit (gross benefitminus cost) of the legal activity forgone while planning, performing andconcealing the criminal act. The lower an individual's level of income, the loweris his opportunity cost of engaging in illegal activity.
The amount a person can earn in the legal sector may depend upon age, sex,race, education, training, region, rate of unemployment, IQ, etc. People enableto earn only a rather low wage will have a low opportunity cost of crime, the costof giving up legal income. We would therefore expect that among criminals thereare more young people, men, blacks, low paid workers, etc. than in thepopulation at large. This is in fact what crime statistics tell us, but more refinedempirical studies are necessary to substantiate such relationships.
Many individual characteristics might have an effect on benefits and costs.Individual rates of discount might be important. The gains from crime oftenoccur immediately, whereas punishment is something that might come in thefuture, and stretched over a long period of time. A high discount rate willtherefore tend to increase crime. The probability of punishment will be differentfor different people. Some are more clever than others at concealing the offenseand eluding the police. There are also differences in abilities of defendingoneself in court, or in engaging good lawyers. The attitude towards risk will alsohave an effect.
A high rate of recidivism is in accordance with the model of rational choice.If for an offender preferences are stable and the opportunities available remainthe same, the degree of criminal activity will not tend to decrease after aconviction. Recidivism is thus not necessarily a result of erratic behavior or lackof self-control, but rather a result of rational choice. Moreover, several factorsthat count in favor of crime are increased by a imprisonment: additional criminalskills are acquired, and opportunities of legal income are reduced. If it wasrational to commit a crime in the first place, it is all the more so after havingserved a prison sentence. If the sentence has increased the criminal's evaluationof how probable or severe sanctions might be, or if he or she has obtained somebenefit of prison education schemes, the tendency to recidivism will becounterbalanced.
Exaggerating somewhat the differences between sociologists and economists,one may say that the first consider crime as deviant behavior whereas the latterconsider it as rational. Fig. 1 illustrates the main elements characterizing anindividual's choice situation according to the theory of rational choice. Theindividual has a feasible set of courses of action, some of which are illegal. Theenvironment, including sanctions and wages, determines the outcomes of thevarious courses of action. The individual is assumed to choose the course ofaction that best satisfies its preferences. Preferences include not only wants, butalso norms. The guilt of acting in conflict with norms is part of the costs ofcrime.
In theories of economics of crime, norms are seldom studied, or evenmentioned. Preferences as a whole are usually assumed to be constant, andauthors do not find it necessary, or do not feel competent to discuss norms.Traditional criminological theories, on the other hand, suggest that theindividual's environment has a significant impact on people's preferences,especially on norms, but also on wants. Theories about culture conflict, culturaldeviance, anomie and learning relate individual preferences to variouscharacteristics of the society. Other theories suggest that preferences areinherited or dependent on age, gender, race, intelligence and other personalcharacteristics. In the literature of economics of crime these various theories areoften neglected, and the main question studied is how the environmentproduces incentives to commit, or not to commit, crimes.
In a very broad sense a deterrent is any factor that exerts a preventive forceagainst crime. Sanctions may have an effect on crime either by causing fear orby influencing norms. The combination of these effects is in parts of theliterature on crime called "general prevention" ( Andenaes, 1975 ). In economicsof crime one focuses on the effects of law enforcement on the outcomes ofactions, and thereby on illegal behavior. This is the deterrence mechanism in thenarrow sense. The possibility that law enforcement or other aspects of theenvironment might affect individual norms and wants, e.g. by conditionedaversion as suggested by the behavioral perspective, is given less attention.
An interesting question is whether the model of rational choice is in conflictwith, a substitute for, a supplement to, or a general framework for other theoriesof crime. Carr-Hill and Stern (1979) emphasize that the economic andcriminological approaches should be seen as complementary rather thanconflicting. They maintain that the economic approach isolates the importanceof the probabilities and magnitude of reward and punishment, and shows howthey can be treated formally. The criminological approach takes these for grantedand indicates how different groups might view and react to these probabilities,rewards, and punishments.
These two approaches are related to the issue of opportunity vs. motivationas explanation of crime. Economists and others who focus on costs and benefitsof crime in a rational choice framework, also take into account that crimepresupposes potential victims. The better the opportunities of hitting valuableand low risk targets, the more crime there is. Those who more or less explicitlydismiss the theory of rational choice, often focus on the motivation ofindividuals, assuming that behavior is determined by individual characteristicsand by the norms of the groups to which they belong.
The opportunity approach is an element in the market models of crime, wherethe number of offenses is determined by the interaction of potential offenders,who are seeking the best targets, and potential victims, who by measures ofprivate protection seek to be less attractive or vulnerable to crime, cf Ehrlich(1981 , 1982 , 1996) , and Cook (1986) .
Several authors have discussed whether people have sufficient informationabout the environment and about outcomes of actions to make rational choices.Becker and others maintain that even if choices are based on subjective beliefsthat are wrong, the choices are meaningful from a subjective point of view, andbehavior can be explained and understood on this basis. One may argue that thisis not a satisfactory answer to the claim that people have cognitive limitations,and that they stick to "satisficing" and not to maximization. The studies of Carolland Weaver (1986) , Tunnell (1992) , and Nagin and Paternoster (1993) suggestthat Simon's theory of bounded rationality might be a better representation ofoffenders' behavior than the rational choice theory, a conclusion that issupported by Niggli (1994) .
It has also been argued that the simple rational choice theory is inadequatebecause people's behavior is determined by procedural rationality, in which anindividual is portrayed as a follower of rules established by history or socialrelations, or by expressive rationality, in which an individual, through symbolicacts, demonstrates to himself and others his self-conception and worth. Thereis disagreement about how serious such criticism is for the use of the rationalchoice theory in studies of crime. Ehrlich (1973, p. 532) maintains that "[s]incethose who hate need not respond to incentives any differently than those wholove or are indifferent to the well-being of others, the analysis ... would apply ...to crimes against the person as well as to crime involving material gains."
In a great number of empirical studies the theoretical models of criminal behaviorhave been tested, and the effect on crime of the probability and severity ofpunishment, and of benefits and costs of legal and illegal activities has beenestimated. The influence of norms, tastes, and abilities, corresponding toconstitutional and acquired individual characteristics, have in some cases beenstudied indirectly by including variables like age, race, gender, etc. A variety ofequation specifications and estimation techniques have been used, and thestudies have been based on data from countries and states down tomunicipalities, campuses, and individuals.
Analogously to the terms psychometric studies, cliometric studies, etc. itseems appropriate to introduce the term "criminometric studies" to characterizethis field of research. The subject matter is crime, and it gives the field asomewhat distorted and too limited range to call these studies econometric,although this is what is usually done. The studies are rooted in a general theoryof rational choice, and not in some rational choice theory presumably limited toeconomics.
In the framework of norm-guided rational behavior norms may depend on theenvironment. In most criminometric studies norms, as well as wants, are assumedto be constant, and often also equal among individuals. Becker (1976, p. 5) expresses a rather common attitude by stating that "[s]ince economists generallyhave little to contribute, especially in recent times, to the understanding of howpreferences are formed, preferences are assumed not to be very differentbetween wealthy and poor persons, or even between persons in differentsocieties and cultures." With this assumption it is relatively easy to test otherparts of the theory, such as hypotheses about the effect of sanctions, and ofgains and losses of legal and illegal activities. If preferences differ amongindividuals, estimates of the effects of sanctions will be relevant for an"average" person. The explicit assumption that individual preferences areconstant, distinguish criminometric studies from most other studies incriminology.
There are good reasons to carry out empirical studies of criminal behavior atthe individual level instead of an aggregated level. In the first place it is at bestcontroversial to posit that behavior is anything but individual. Second, thetheoretical models that are developed are based on individual rational choice.Third, as will be discussed below, studies based on aggregated data require anumber of additional assumptions of questionable validity. Forth, the statisticalidentification problem is less serious when individual behavior is studied. Usingaggregated data one faces the problem of distinguishing between the effect ofthe probability of arrest on the amount of crime and the effect of the amount ofcrime on the probability of arrest. In empirical studies at the individual level itcan reasonably be assumed that the probability and severity of punishment isdetermined without being influenced by the actions of a given individual. Thus,the deterrence variables can be considered to be exogenous to the individual'schoices, and the problem of simultaneity inherent in macro studies is absent.Unfortunately, empirical tests of these models by use of information onindividuals are few. The application of the theoretical models to empirical studiesis intricate ( Manski, 1978 ), and suitable data are scarce. The data we have, aremainly self-reports on criminal activity, and records of criminal activity compiledby the criminal justice system. The most serious problem with the latter type ofdata is that they do not constitute representative samples of the population, butare biased in the sense that only convicted persons are included. It is hardlypossible to test a general theory of rational criminal behavior by studying onlyone subgroup of the offenders. A related problem is that most available datasources include information only about choices made, and not about thoseavailable, but not chosen. It is difficult, if not impossible, to test a theory ofrational choice if the choice set in this way is limited. Whereas such data are oflimited interest for studies of general deterrence, i.e. of effects on people ingeneral, they are useful for studies of special deterrence, i.e. of effects on theindividuals that are punished.
The bulk of criminometric studies consists of cross section regressionanalyses based on macro data. Some of them are rather broad, including manytypes of regional areas, estimation techniques, and types of crime, whereasothers concentrate on particular types of crime, such as property crimes orhijacking. A few of them address special questions, such as the effect of police"aggressiveness" in patrolling, or the influence of income differentials. Timeseries studies are less numerous, and employ mostly data on total crime.
The majority of these empirical studies of crime have been evaluated invarious surveys. In an annotated bibliography Beyleveld (1980) reviews anumber of investigations of correlations between crime and deterrence variables,in addition to 35 cross-sectional and 31 time-series econometric studies of crime.A thorough review of the empirical evidence of general deterrence is also givenby Nagin (1978) , who comments on 24 correlation and econometric studies, allbut two also covered by Beyleveld. Taylor (1978) concentrates upon six majoreconometric studies, whereas Pyle (1983) reviews the same studies and about 15others. A shorter, but somewhat more up to date review is Cameron (1988) , anda more recent comprehensive survey is found in Eide (1994) . Reviews of certainparts of the literature are found in Passell and Taylor (1977) , Vandaele (1978) , Fisher and Nagin (1978) , Klein, Forst and Filatov (1978) , and Nagin (1978) .
(1) Empirical Effects of Punishment Variables. In empirical studies the measuresused to represent the probability of punishment include the probabilities ofarrest, of clearance, of conviction, and of conviction given arrest. The severityof punishment is represented by fines, by the length of sentence, or by timeserved. Witte (1980) and Schmidt and Witte (1984) have employed individualdata on post-release activities of a random sample of 641 men released fromprison in North Carolina. The effects on crime of measures of both theprobability and the severity of punishment are found to be more or less negative. Myers Jr. (1983) , using a sample of 2127 individuals released from US Federalprisons, finds that severity of punishment has a statistically significant negativeeffect on crime, whereas the probability measure (the ratio of previous prisoncommitments to previous convictions) has a positive effect. Higher wages arefound to reduce recidivism. Trumbull (1989) has used data on about 2000offenders released from prisons in North Carolina to study recidivism and specialdeterrence. He finds that none of the deterrence variables (probabilities of arrest,conviction and imprisonment, and length of sentence) are statisticallysignificant. Trumbull finds this result natural, since the sample consists only ofindividuals who, whatever the probability and severity of punishment, havechosen to engage in illegitimate activities. However, an increase in an offender'sown previous sentence length has a significant negative effect on crime, a resultthat corroborates the hypothesis of special deterrence. Higher earnings on thefirst job after release has a negative effect on crime. Quite unexpectedly, so hasunemployment. Viscusi (1986b) uses an approach common in labor economicsin the studies of hazardous jobs to estimate the risk/reward trade-off for illegalactivities. In labor markets increasing health risks are often rewarded by someamounts of money in addition to non-risk wages. Treating the probability andseverity of punishment in the same manner as the probability and severity ofinjury are treated in analyses of hazardous jobs, Viscusi is able to estimate theeffects of changes in these variables. A survey of 2358 inner-city minorityyouths from Boston, Chicago, and Philadelphia constitutes the data employed.Viscusi finds that the premiums obtained for criminal risks are strong and quiterobust. In his framework this is interpreted as a corroboration of the generaldeterrence hypothesis.
Studies of tax cheating based on individual data by Clotfelter (1983) , Witteand Woodbury (1985) , Slemrod (1985) , and Klepper and Nagin (1989) allconclude that both the probability and the severity of punishment have negativeeffects upon crime.
Many studies of correlation between crime rates and punishment based onaggregated data appeared in the late sixties and early seventies. Using mostlyUS data on the state or municipal level these studies indicate a negativeassociation between the certainty of arrest and the crime rate for different crimecategories. But crime rates are not generally found to vary with the severity ofimprisonment, although in some studies a deterrent effect is obtained forhomicide and a couple of other crime categories.
A necessary condition for interpreting the results of these correlationstudies, mostly carried out by sociologists, as estimates of deterrence is, ofcourse, that there is a one-way causation from punishment to crime, and nonein the opposite direction. The many subsequent cross section criminometricstudies allowed for a two-way causation by various specifications of the generalmodel
|C = f ( P, S, Z j ),||(3)|
|P = g ( C, R, Z k ),||(4)|
|R = h ( C, Z l ),||(5)|
where C = crime rate (No. of crimes per population), P = probability ofpunishment, S = severity of punishment, R = resources per capita of the CriminalJustice System (CJS), and Z j , Z k , Z l = vectors of socio-economic factors. Thecrime function (3) assumes that the crime rate is a function of the probability andthe severity of punishment; equation (4) assumes that the probability ofpunishment is a function of the crime rate and the resources allocated to the CJS;and equation (5) assumes that the resources allocated to the CJS is a functionof the crime rate. Various socio-economic factors are included as explanatoryvariables in all three equations. In some studies police resources is included asan explanatory variable in the crime function.
Among the first simultaneous regression analyses in this field we find Ehrlich(1972) , Phillips and Votey (1972) , and Orsagh (1973) . The first major cross sectionstudy appearing after Becker's theoretical article was Ehrlich (1973) . He studiesseven types of crimes in the US based on data for all states from 1940, 1950, and1960. He finds that the probability of imprisonment has a statistically significantnegative effect on all types of crime, and, except for murder, not less for crimesagainst the person than for other crimes. The severity of punishment has asimilar effect, but here only about half of the estimates are statisticallysignificant. Crime is also found to be positively related to median family income(presumably more assets to steal) and to income differentials. Ehrlich's study hasbeen thoroughly scrutinized by several authors, some of whom have given harshevaluations of his work. Revisions, replications, and extensions of Ehrlich'sstudies by Forst (1976) , Vandaele (1978) , and Nagin (1978) resulted in moremoderate deterrent effects of the probability and severity of punishment.Moreover, Forst found that by introducing variables thought to be correlatedwith the punishment variables, such as population migration and populationdensity, the punishment variables became statistically insignificant. Nagin foundthat incapacitation could explain a large part of the apparent deterrent effect. Ina fierce attack on Ehrlich's study Brier and Fienberg (1980) conclude an empiricalinvestigation of the Ehrlich type that no deterrence effect of sanctions werefound. A response to the criticism from these and other authors is found in Ehrlich and Mark (1978) . Despite critical remarks by various authors, there is nowa long list of studies similar to the one by Ehrlich.
The great majority of correlation studies and cross section regressionanalyses show a clear negative association between punishment variables andthe crime rate. Almost without exception the coefficients of the punishmentvariables (which usually are the elasticities of the crime rates with respect to thepunishment variables) are negative, and in most of the cases significantly so.Furthermore, the estimated elasticities have rather high values. Eide (1994) summarizes such estimates of 20 cross section studies based on a variety ofmodel specifications, types of data and regression techniques ( Ehrlich (1973) , Sjoquist (1973) , Swimmer (1974) , Danziger and Wheeler (1975) , Holtman and Yap(1978) , Phillips and Votey (1975 and 1981) , Forst (1976) , Chapman (1976) , Mathieson and Passell (1976) , Thaler (1977) , Vandaele (1978) , Wilson and Boland(1978) , Heineke (1978) , Mathur (1978) , Avio and Clark (1978) , Blumstein andNagin (1977) , Carr-Hill and Stern (1979) , Myers Jr. (1980 and 1982) , Furlong andMehay (1981) , Sesnowitz and Hexter (1982) , Willis (1983) , Schuller (1986) , Trumbull (1989) ). Eide finds the median value of the 118 estimates of elasticitiesof crime rates with respect to various measures of the probability of punishmentto be about -.7. The median of the somewhat fewer severity elasticities is about-.4. The rates of clearance by arrest are usually considered to be better measuresof the certainty of sanction than the rates of conviction ( Andenaes, 1975, p. 347 ).The median of the elasticities of arrest is found to be somewhat smaller than themedian of the elasticities of conviction, but the difference is not great.
Almost all criminometric time series studies give additional firm support tothe hypothesis that the probability of punishment has a preventive effect oncrime. The results concerning the effect of the severity of punishment issomewhat less conclusive. Wahlroos (1981) , using Finnish data, finds that theseverity of punishment has a statistically significant deterrent effect on larceny,but not on robbery. Cloninger and Sartorius (1979) , using data from the city ofHouston in the US, obtains a negative, but not statistically significant effect ofthe mean sentence length. Wolpin (1978) , using a time-series for England andWales in the period 1894-1967, finds that the estimates of the effects of thelength of sentences differ among types of crime, and are often not statisticallysignificant. Schuller (1986) on the other hand, using Swedish data, finds anegative effect of the average time in prison. In an international comparison ofcrime between Japan, England and the US Wolpin (1980) obtains firm supportfor the deterrent effect of the severity of punishment. These diverging results arenot surprising. The theories surveyed above tell us that if there is a significantproportion of risk lovers in the population, and/or if the income effect is greaterthan the substitution effect, and/or the effects of legal activities are risky, and/orhousehold protection expenditures are inversely related to the severity ofpunishment, an increase in the severity of punishment may well cause crime toincrease on the macro level. If, however, in spite of these crime increasingeffects, macro studies show that crime is reduced when punishment becomesmore severe, there is all the more reason to believe in a deterrent and/or a normformation effect of punishment.
Among the several empirical studies concentrating on just one type of crime,it is worth noticing that Landes (1978) obtained firm support for the deterrencehypothesis for hijacking. In a study of draft evasion in the US, Blumstein andNagin (1977) avoid four of the main objections against criminometric studies (seediscussion of objections below): draft evaders are likely to be well informedabout possible sanctions; data are relatively error free; as draft evasion canhappen only once, there is no danger of confounding incapacitation effects withdeterrence effects; simultaneity problems caused by over-taxing of the CriminalJustice System are unlikely because draft evasion was given priority in therelatively well staffed federal courts. The authors consider that their resultsprovide an important statistical confirmation of the existence of a deterrenteffect. They find, however, that the severity of the formal sanction has a modesteffect on draft evasion compared to the stigma effect of being arrested andconvicted.
The economic model of crime suggests that changes in benefits and costsof committing a particular type of crime might have effects on other types ofcrime. If, for instance, the probability of being convicted for robbery increases,some robbers might shift to burglary. One crime is substituted for another, justas people buy more apples instead of oranges when the price of oranges goesup. Such substitution effects between crimes have been estimated by Heineke(1978) , Holtman and Yap (1978) , and Cameron (1987) . A certain number ofstatistically significant effects are found, indicating that some crimes aresubstitutes whereas others are alternatives.
As a whole, criminometric studies clearly indicate a negative associationbetween crime and the probability and severity of punishment. The result maybe regarded as a rather firm corroboration of the deterrence explanation obtainedfrom the theory of rational behavior: an increase in the probability or severity ofpunishment will decrease the expected utility of criminal acts, and thereby thelevel of crime. It should be remembered, however, that in some studies the effectof an increase in the severity of punishment is not statistically different fromzero, and a statistically significant positive effect has also occasionally beenobtained.
(2) Empirical Effects of Income, Norm and Taste Variables. In accordance withthe theoretical models, most criminometric studies contain income variablesrepresenting some of the benefits and costs of legal and/or illegal activities.Looking first at the benefits of legal activities, the great variety of proxies appliedis striking: median family income, median income, labor income to manufacturingworkers, mean family income, mean income per tax unit, mean income per capita,etc. No systematic relationship appears between the income measures appliedand the estimates obtained. Although the hypothesis that an increase in legalincome opportunities decreases crime is not rejected in most of the studies,others would not reject the inverse hypothesis that an increase in legal incomeopportunities would increase crime. This ambiguity in results might be due tothe fact that the income measures used represent benefits not only of legalactivities, but also of illegal ones: Higher legal incomes (mostly wages) tend tomake work more attractive than crime, but to the extent that higher legal incomein a region produces a greater number of more profitable targets for crime, thesame empirical income measure may be positively correlated with criminalactivity. In addition, high legal incomes also mean high incomes foregone whenincarcerated, a cost of crime that will have a negative effect on crime. If thesemechanisms are at work simultaneously, and their relative strength notuniversally constant, it is not surprising that the results of various studies differ.The theory is not necessarily deficient, but the methods applied do notdistinguish between the two mechanisms. The main problem is that the incomesof legal and illegal activities are highly correlated, and that it is difficult (orimpossible?) to find empirical measures that with enough precision candistinguish between their effects. The impact of income is further obfuscated bythe fact that private security measures increase with income, while higher incomeprobably reduces the marginal utility of each piece of property, and thereforealso the measures taken to protect property. These problems of correlation arenot present in studies where individual data are employed, such as Witte (1980) and Myers Jr. (1980) .
The estimates of the effects of gains to crime underscore the problem offinding good empirical measures for theoretical variables. Whereas Ehrlich usesmedian family income as a measure of gains to crime , other authors use the samemeasure to represent legal income opportunities . A variety of other measuresof gains have been used, with diverse estimated effects on crime.
A large income differential may indicate that crime is a comparativelyrewarding activity for the very low income group (that may find a lot to stealfrom the very rich). Estimates of the effect on crime of income differentials alsovary across studies. It is interesting to note, however, that a study whichincludes variables of both legal and illegal income opportunities in addition toone of income differential ( Holtman and Yap, 1978 ), obtains significant estimatesof the expected signs for all three variables. Also Freeman (1995) finds thatwages from legitimate work and measures of inequality have the expected effectson crime.
Unemployment is usually included in criminometric studies as a proxy for(lack of) legal income opportunities. Unemployment will make crime moreattractive if the alternative is a life in poverty. The estimates of the effect ofunemployment on crime, however, are positive in some studies, and negative inothers. A comprehensive survey by Chiricos (1987) demonstrates thatunemployment in most studies seems to increase crime. He has reviewed 63aggregate studies published in major journals of economics, sociology, andcriminology containing 288 estimates of the relationship between unemploymentand crime. He finds that 31 % of the estimates were positive and statisticallysignificant, whereas only 2 % were negative and statistically significant. Mostof the non-significant estimates were positive. A similar conclusion is obtainedin a survey by Freeman (1995) . Chiricos finds little support for the hypothesisthat unemployment decreases the opportunity for criminal activity because offewer and better protected criminal targets, an hypothesis that has beenlaunched in order to explain why in some studies a negative relationship isobtained. Another explanation of such a negative association, suggested by Carr-Hill and Stern (1973) , is that unemployed fathers stay at home and keep aneye on their delinquent sons. Furthermore, differences in results might be thevariability in unemployment insurance schemes. In some places unemploymentinsurance is only slightly below ordinary legal income, and in addition, some ofthe formally unemployed receive income from short term jobs. According toeconomic models of crime, the number of offenses will then not increase whenunemployment increases. A decrease may even occur. But if unemployment hitspeople without such income opportunities, crime will increase.
According to criminal statistics the well-to-do are less likely to commit crimesthan the poor. Lott (1990) provides a survey of various explanations of this fact.In an empirical study of ex-convicts Lott (1992) finds that the reduction inincome from conviction is extremely progressive, a result that corroborates thehypothesis that an increase in the costs of committing crimes has a negativeeffect on the amount of crime.
(3)Effects of Norm and Taste Variables. In most studies varioussociodemographic variables have been included. Unfortunately, the reasons forincluding many of these variables are often not thoroughly discussed. Forinstance, an explanation of how differences in preferences (tastes) for legal andillegal activities may vary between groups of people are often lacking. Thevarious choices of empirical measures probably reflect the availability of data.
The estimated coefficients on the proportion of non-whites in the population areusually found to be positive. It is difficult to decide whether this result reflectsdifferences in norms, in tastes, in abilities, or in income opportunities. The highproportion of non-whites might also be the result of a tendency among thepolice to concentrate search for offenders to this group.
The predominance of young people among those arrested and convictedsuggest that age would be a very important factor in explaining crime. In manystudies such an effect is not found. One reason might be that there is notenough variability in the proportion of youth between statistical units toproduce precise estimates. Also possible, crime among young people is not aconsequence of their preferences (lack of socialization, etc.), but of their meagerlegal income opportunities that possibly is adequately represented by othervariables. Young people are perhaps not different, just poorer.
Population density is in most cases found to be a statistically significantexplanatory variable. Population density may reflect various phenomena, suchas differences in social control, psychic diseases, etc. The studies reviewed arehardly suitable for a discussion of which of these mechanisms may be at work.
Some studies use police expenditures or the number of police officers aspossible deterrent variables instead of measures of probability and/or severityof punishment. Many of these studies show that police activity has a negligible,and sometimes positive, effect on crime. On the other hand, Buck et al. (1983) ,including both police presence and arrest rates as explanatory variables, findthat the former rather than the latter has a deterrent effect. The studiesconcluding that police activities have a minor effect have tempted some authorsto dismiss deterrence as an efficient means against crime. It must be kept in mind,however, that in the theoretical models the deterrence variables are theprobability and the severity of punishment, and not the police. There are at leasttwo interpretations of the minor effect on crime of expenditures on the police.Either these expenditures do not have a noticeable effect on the probability ofpunishment, or such expenditures result in a higher proportion recorded ofcrimes, a fact that decreases the probability of punishment registered in the dataused.
In some studies routine activity and situational opportunity are included asmain explanations of crime, cf Cohen. Felson and Land (1980) . Chapman (1976) ,for instance, finds that the female participation rate in the labor market, a proxyfor the proportion of unguarded homes, has a significant positive effect.
It has been argued that the rational choice framework might be relevant forcertain property crimes, but not for violent crimes that are considered to be"expressive" and not "instrumental". Undoubtedly, the degree of"expressiveness" differs among crimes. Many empirical studies may beinterpreted as support for the view that threat of punishment also has apreventive effect on "expressive" crime. At least substantial elements ofrationality are revealed in a study of mugging by Lejeune (1977) , in a study ofrape and homicide by Athens (1980) , and in a study of spouse abuse by Dobashand Dobash (1984) . Although the effect of punishment may differ among typesof crime, evidence so far indicates that the rational choice framework is relevantfor all types of crime, and that analyses rejecting a priori that some particulartypes of crime are deterrable are inadequate.
Objections to economic studies of criminal behavior have been many andoccasionally fierce, see e.g. Blumstein et al. (1978) , Orsagh (1979) , Brier andFienberg (1980) , Prisching (1982) , and Cameron (1988) . In particular, studiesbased on aggregated data have been criticized. In addition to attacks on theassumption of rational behavior, the main criticism relates to interpretations ofempirical results, to statistical identification of equations and unobservedheterogeneity, to measurement errors, and to operationalization of theoreticalvariables.
(1) Interpretation of Empirical Results. It has been argued that many studiesdo not take into consideration that more certain or more severe punishment mayprevent crime by two different mechanisms: either directly as a cost, or indirectlythrough norm formation. A type of crime that is cleared up more and moreseldom, or sanctioned more and more leniently, will easily be considered as notvery serious by the population. Individual norms may adjust accordingly,people's crime aversion decrease, and consequently the level of crime increases.It seems true that in most empirical studies no effort is made to distinguishbetween this mechanism and the more direct deterrence effect of an increase inpunishment. Results are often interpreted as a deterrent effect, and not as ageneral prevention effect where also the indirect norm formation mechanism isincluded.
Can criminometric studies possibly distinguish between the twomechanisms? In cross section studies one can imagine that people living inregions where the clear-up probability is low tend to consider crime as lessserious than do people in other regions. If such differences in norm formationexist, they are probably more predominant the longer the distance between theregions that are compared, for instance in international comparisons, or instudies of states in the US. It is not probable that norm formation differ amongthe districts within a rather small region, especially if news about punishmentcan be assumed to be more or less the same, and mobility of people is high. Theeffect on crime of variation in the severity of punishment found in studies usingdata from rather small areas within a region can therefore hardly be explained bya norm formation mechanism. Where one obtains a negative relationshipbetween the crime rate and the clear-up probability when data representingcounties of only one state ( Chapman (1976) , Avio and Clark (1978) , and Trumbull(1989) ), or of police districts in a metropolitan area ( Mathieson and Passell(1976) , Thaler (1977) , and Furlong and Mehay (1981) ), one will have reason tobelieve that the norm formation mechanism must be of minor importance. Thesame holds true for some studies of substitution of crime which show that anincrease in punishment of one type of property crime will have a statisticallysignificant effect on the number of other property crimes. It is not probable thata higher probability of being punished for burglary has any effect on the normsregarding robbery. It is more reasonable to think that robbery is substituted forburglary because of a change in relative costs.
Even if the importance of each mechanism is regarded as uncertain, theestimates obtained in various studies are still of interest. Not only from a politicalpoint of view, but also from a scholarly one, it may be useful to know that theprobability of punishment has a certain negative effect on crime,notwithstanding the mechanism(s) involved.
Another possible uncertainty concerning the evaluation of results is thatthere might exist an underlying phenomenon, unknown and/or not studied, aphenomenon that at the same time produces a low crime rate and a highprobability of punishment. Individual norms may create such a relationship. Ifpeople in one region appreciate each others' welfare more than on average, theywill both have a relatively strong aversion against criminal infringements againstothers, and a high interest in clearing up crimes in order to decrease crime ingeneral. If such differences in norms exist, they must be rooted in culturaldifferences of some kind. Possibly, such differences can develop if regions aresituated far from each other, or if distance in time is substantial. For the smallerregions, such differences seem less realistic.
Theories of criminal behavior show that a whole series of "causes" may beinvolved, and that recorded differences in crime between regions, gender, races,drug abuse, etc. might be related to more fundamental explanations of crime,involving norms, wants, opportunities and circumstances. The intricacy ofrelationships shows the difficulty in interpreting the estimates of the effects oncrime of such variables.
(2) Identification and Unobserved Heterogeneity. If, in an empirical study, onefinds that crime rates and probabilities of punishment are negatively correlated,one cannot easily distinguish between the hypothesis that higher probabilitiesof punishment cause lower crime rates (eq. 3), or the hypothesis that highercrime rates cause lower probabilities of punishment (because of policeoverloading, eq. 4). If such a simultaeneity exists it is not acceptable to use themethod of ordinary least squares (OLS) to estimate each equation. Using theHausman test Layson (1985) and Trumbull (1989) have for homicide found thatsimultaneity was not a problem in their data, and OLS could be applied. Ifsimultaneity is present, the standard procedure to identify the first relation, thecrime function, consists of introducing exogenous variables that have an effecton the probability of punishment, but not on the crime rate. In an excellentdiscussion of the (im)possibility of identifying the crime function in macrostudies Fisher and Nagin (1978, p. 379) declare that they know of no suchvariables. The consequence of this view is that all attempts of identification inempirical macro studies are illusory. The equations may be technically identified,but by false assumptions. Using panel data for police districts Aasness, Eideand Skjerpen (1994) claim to have solved this problem. In studies based onindividual data, the question of identification is much less serious, cf above.
It is interesting to note that in the cross-section studies reviewed by Eide(1994) the method of ordinary least squares tend to give smaller estimates of theelasticities of crime with respect to the probability and severity of sanctions thando the methods of 2 stages least squares, full information maximum likelihood,and other more advanced methods. This is what might be expected if asimultaneous equation bias is present. The difference in estimates is, however,not great.
Cornwell and Trumbull (1994) point to the fact that aggregate cross-sectioneconometric techniques do not control for unobserved heterogeneity.Addressing this problem by use of a panel dataset of North Carolina counties,they obtain more modest deterrent effects of the arrest and conviction rates thanthose obtained from cross-section estimation.
(3) Measurement Errors. Since a substantial part of all crimes is not registeredby the police, one may have serious doubts about the results of empiricalstudies based on official statistics. However, the problem of underreporting isnot damaging to empirical research if the rate at which actual crimes are reportedis constant across regions (in cross section studies) or over the years (in timeseries studies). This seems to be an implicit assumption in most studies. Blumstein et al. (1978) explain how differences in "dark numbers" betweenobservational units create a spurious negative association between the recordedcrime rate and the probability of clearance. Aasness, Eide, and Skjerpen (1994) introduce, in addition to the recorded crime rate, a latent variable for the realcrime rate, and relates the latter to the former by a linear function and astochastic term. By this procedure measurement errors are given an explicitstochastic treatment, that allows for a distribution of "dark numbers" amongpolice districts.
The existence of a substantial "dark number" of crime, has fostered a certaininterest in using victimization studies to obtain more reliable data. These studiesgive more or less similar results as those based on recorded crimes. A prominentexample is Goldberg and Nold (1980) who find that the reporting rate, and thusthe probability of clearance, has a great impact on the amount of burglaries.Another comprehensive study is Myers Jr. ( 1982) , who obtains almost the sameestimates of the effects of sanction variables by correcting crime rates byvictimization data.
(4) Wrong Beliefs. If people have wrong beliefs, one may also question thevalidity of estimates of the effects of punishment variables and varioussocio-economic factors. Presumably, the true risk of sanction is not known to theindividual. Empirical studies suggest that people tend to overestimate theaverage risk, while at the same time believing that the risk they themselves runis lower than average. Offenders, however, seem to be better informed. Wilsonand Herrnstein (1985, p. 392) refer to a study where over two thousand inmatesof jails and prisons in California, Michigan, and Texas were interviewed abouttheir criminal careers. The study revealed a close correspondence between theactual and perceived risk of imprisonment in Michigan and Texas, whereas asomewhat weaker correspondence was found in California. The study furthercorroborated the theoretical result that an increase in the probability ofimprisonment will decrease crime.
Even if beliefs to some extent are wrong, macro studies might still be of somevalue. It may well be that some persons do not observe a given change, and alsothat they have been mistaken in their beliefs. But the gradual change from verylenient to very harsh punishment will certainly be registered by at least a part ofthe population, and behavior will change, more or less, as already explained.
(5) Various Operationalisations. Many studies give weak arguments for thechoice of theoretical variables (e.g. of variables of punishment, benefits andcosts), and of their empirical measures. Orsagh (1979) argues that the greatdiversity of variables in empirical criminology shows that no good theory exists,and that macro studies of the usual kind have little interest. The objection iscertainly relevant, but the consequence is not necessarily that such analysesshould be avoided. Problems of operationalisation do not make a theoryirrelevant. Better than to drop such studies is to continue the theoreticaldiscussion about determinants of crime, and produce more empirical studies, inorder to improve the foundation for choosing acceptable measures of theoreticalconstructs. If various operationalisations produce similar results, there is reasonto believe that the theory is robust to such differences. Then, one might evenconclude that the theory is quite good, despite the fact that each and everyformal test of significance is of limited value.
The studies reviewed above reveal quite consistent results as far as the signof effects of the punishment variables is concerned. The insensitivity of theseresults to various operationalisations is comforting. The effects of incomevariables are less consistent, a result that might either imply that economicfactors do not have a uniform effect on crime or that some, or all, of theoperationalisations tried so far are unacceptable.
Several measures of punishment variables have been employed. When onlyone type of sanctions is included, one would expect that the effect assigned tothis variable really includes effects of punishment variables correlated with theone included. A better alternative is to use several sanctions simultaneously, asproposed and employed by Witte (1980) and others.
The reasons why people are more or less law-abiding are manifold. Thenorm-guided rational choice framework seems to provide a suitable frameworkfor discussing various theories of crime, including characteristics of individualsand circumstances ( Cornish and Clarke, 1986, p. 10 ). The framework allows fora simultaneous consideration of many possible determinants of crime. Theabstract model is a means of gaining insight into the elements of rationalbehavior, and it permits filling bits of information into a broader context. Incriminometric studies it might be useful to distinguish between norm variables(representing desires for various courses of action), want (or taste) variables(representing preferences for various outcomes), ability variables (representingintellectual, psychic and physical characteristics), punishment variables(representing the probability and severity of punishment), individual economicvariables (representing legal and illegal income opportunities), andenvironmental variables (other than punishment and economic variables). Asurvey of variables used in various empirical studies of crime organizedaccording to this typology is given in Eide (1994) . Variation in crime amongindividuals are traditionally related to gender, age, race, etc. A deeperunderstanding must be sought in variations in norms and wants, in abilities, andin the opportunities, rewards and costs determined by the environment.Variation in crime among individuals may be caused by differences in all theseelements of the rational choice framework. Certain individuals may have morecrime prone (or less crime averse) norms than others. The special norm structuremay be a result of genetic, biological or psychological characteristics, an effectof lack of socialization, or a consequence of cultural conflict, cultural deviance,or anomie. Inherited or acquired abilities may restrict legal activities more thanillegal ones. In an empirical study of college students Nagin and Paternoster(1993) found that both individual differences (poor self-control) and the costsand benefits of crime were significantly related to crime. The formidable task forthe future may be found in a proposition for social science research by the NobelPrize Winner Niko Tinbergen (who should not be confused with J. Tinbergenwho has won the Nobel Memorial Prize in economics) that four levels of analysisshould be put together: the biological (genetical), the developmental (how anindividual is socialized), the situational (how the environment influencesbehavior), and the adaptive (how a person responds to the benefits and costsof alternative courses of action).
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