VATT-KESKUSTELUALOITTEITAVATT-DISCUSSION PAPERS

244

MODELLINGCRIME ANDPUNISHMENT

Virn Matti *

Valtion taloudellinen tutkimuskeskusGovernment Institute for Economic Research

Helsinki 2000

* 20014 University of Turku, Finland, and Bank of Finland, P.O.Box 160, 00101Helsinki, Finland. E-mail: matti.viren@bof.fi. I am grateful to the Academy ofFinland and the Yrj Jahnsson Foundation for financial support, TuomoNiskanen from Statistics Finland for help in collecting the data and JukkaVirtanen for research assistance. I would also like to thank Erkki Koskela forhelpful comments. This paper was written in 1998 while the author worked in theGovernment Institute for Economic Research (VATT, Helsinki). This paper willappear in Applied Economics.

ISBN 951-561-350-7

ISSN 0788-5016

Valtion taloudellinen tutkimuskeskus

Government Institute for Economic Research

Hmeentie 3, 00530 Helsinki, Finland

Email: matti.viren@bof.fi

Yliopistopaino

Helsinki, December 2000

VIRN MATTI: MODELLING CRIME AND PUNISHMENT. Helsinki,VATT, Valtion taloudellinen tutkimuskeskus, Government Institute forEconomic Research, 2000, (C, ISSN 0788-5016, No 244). ISBN 951-561-350-7.

Abstract: This paper provides an extended supply of labour model which allowsfor different intensities of legal and illegal (criminal) activities and in whichcriminal activities may be considered both as work and leisure. Heterogeneity ofindividuals is also taken into account. The model is estimated from Finnishaggregate time-series data, pooled Finnish municipalities data and pooledinternational cross-country data. With the Finnish aggregate data, a volume indexof crime is constructed and then used in testing the model. All empirical resultsgive strong support to the hypothesis that apprehension and punishment areimportant deterrents of crime. By contrast, the role of sosioeconomic anddemographic variables turns out to be of little importance.

Key words: Crime, index theory, crime deterrenceJEL classification code: 916

VIRN MATTI: MODELLING CRIME AND PUNISHMENT. Helsinki,VATT, Valtion taloudellinen tutkimuskeskus, Government Institute forEconomic Research, 2000, (C, ISSN 0788-5016, No 244). ISBN 951-561-350-7.

Tiivistelm: Tutkimus perustuu laajennettuun tyvoimantarjontamalliin, jossasallitaan sek laillisen ett laittoman (rikollisen) toiminnan harjoittaminen. Mal-lissa sallitaan mys se, ett rikollinen toiminta voi olla luonteeltaan joko tyttai vapaa-aikaa. Mys ihmisten erilaisuus (heterogeenisuus) otetaan mallia ra-kennettaessa huomioon. Malli estimoidaan Suomea koskevasta aggre-gaattiaikasarja-aineistosta, Suomen kuntia koskevasta paneeliaineistoa ja kan-sainvlisest (maittaisesta) paneeliaineistosta. Suomea koskevan aineiston avullakonstruoidaan rikollisuuden volyymi-indeksi, jota mys kytetn mallin tes-tauksessa. Kaikki empiiriset testitulokset tukevat voimakkaasti hypoteesia, jonkamukaan kiinnijmisriski ja rangaistusten ankaruus ovat trkeit tekijit rikolli-suuden torjunnassa. Sen sijaan sosioekonoomisten ja demograafisten tekijidenmerkitys osoittautuu toissijaiseksi.Asiasanat: Rikollisuus, indeksiteoria, rikollisuuden torjuntaJEL luokittelukoodi 916

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 An Occupational Choice Model of Criminal Behaviour . . . . . . . . . . . . . . . . 22.1 Individual Choice Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Aggregate Criminal Activity and Empirical Analysis . . . . . . . . . . . . . 5

3 The Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.1 Presentation of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.2 Interpretation of the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

11 For an extensive survey of the relevant literature, see eg Heineke (1978), Taylor (1978), Brier

and Fienberg (1980), Cameron(1988) and Dnes (1996). In general, the results have been quitemixed, although it might be safe to say that the overall evidence gives some weak support to theeconomics of crime model. Unfortunately, most of the evidence concerns the United States only.Very few studies have been carried out in other countries. For some of the few exceptions, seeWolpin (1980), Withers, G. (1984) and Virn (1990, 1993).

1 Introduction

Beginning with Becker (1968) and continuing through Ehrlich (1973) and Blockand Heineke (1975), among others, economists have produced a succession oftheoretical models of individual criminal behaviour. These models hypothesizethat all individuals, criminals and non-criminals alike, respond to incentives. Morespecifically, by taking the individual's "taste for crime" as a datum, if the costs andbenefits associated with an action change, the agent's choices are also likely tochange. Describing criminal behaviour in the same way as conventional economicbehaviour enables one to relate criminal behaviour to observable deterrencevariables, such as the apprehension rate and severity of punishment. Moreover,propositions of microeconomic theory can be used to produce predictions of theeffects of various exogenous variables on illegal activity.

Existing models of criminal behaviour1 are based on the notion of arepresentative agent who faces a time allocation decision in which some availableactivities are legitimate and others criminal. These models can be criticized at leaston the grounds that they do not account for different forms of specialization incriminal activities: some individuals participate only in illegal activities, some inboth legal and illegal activities and most people only in legal activities. Obviously,one needs to explain this heterogeneity. In explaining it, one may considerdifferences in individual productivity as the main distributional variable.Alternatively, one may utilize the possibility that the time spent in criminalactivities is also considered as leisure, depending on valuation schemes, which inturn may be different for different individuals and which obviously can explaindifferent levels of criminal activities.

The empirical applications of existing models of criminal behaviour areperhaps even more deficient. Analyses based on aggregate data use very crudemeasures of crime and punishment. Crime is measured with simple sumaggregates which do not take into account changes in the nature and structure ofcrime. Thus, a minor crime (eg petty theft) and a more serious crime (bankrobbery) are each counted as one unit of crime. As for punishment, most studiesuse the average length of prison sentence as the main indicator. Because thepunishment menu is actually much wider and changes over time, this approachmay produce completely erroneous results. Thus, we try to overcome theseproblems by constructing indices which account for structural changes.

The theoretical framework for the comparative statics is presented in section2, and empirical results are reported in section 3. Finally, there is a briefconcluding section.

22 Although taxes are not explicitly dealt with here, this does not mean that they are unimportant. In

fact, they are potentially very important because they lower the return from legal (but not illegal)activity. Thus, as shown in eg Koskela and Virn (1993), increases in income (as well ascommodity) taxes tend to increase crime.3 This definition assumes that given apprehension the time spent in criminal activity (the

amount of crime committed) can be found out and the punishment is related to this finding. Inpractice, this can be seen as an approximation only. Here we have the well-known problem thatfines cannot exceed total income which creates one additional restriction to the maximizationproblem. In the empirical analysis, we have, however, a more general punishment variable (whichalso includes other types of punishments) which partially circumvents this problem.

2 An Occupational Choice Model of CriminalBehaviour

In the spirit of Ehrlich (1973) we extend the conventional labour-leisure model soas to distinguish between different forms of labour, some of which society labelscriminal. We start by characterizing individual non-criminal and criminalbehaviour in section 2.1. In section 2.2, we analyse aggregate criminal activity andderive the estimating equations which are used to test the main implications of theextended economies of crime model.

2.1 Individual Choice Problem

The basic assumptions of our model are:

1) An individual can allocate his or her time to leisure, legal activity, e, or illegal(criminal) activity, h. The return from legal (illegal) activity is w (r). Bothrates are assumed to be constant. There are no taxes in the model, thoughobviously one can consider w to be the after-tax return, which depends oncertain tax parameter(s).2

2) Utility depends positively on leisure and consumption (in fact, we alsoassume that both are normal goods). The time allocated to criminal activitymay also be comparable to leisure, depending on a valuation partner . Thetotal leisure time now equals {conventional leisure + *(time spent incriminal activities)}. If = 1, time spent in criminal activities is equivalent toconventional leisure and if > 1, it is more onerous than conventionalleisure. Finally, if = 0, it is equivalent to working time (in legal activity) inwhich case we would have problems in explaining crime which does notproduce any economic reward.

3) The amount of punishment (if the person is caught) depends on the level ofcriminal activity h. To simplify things, we assume that it does not depend onincome from legal activity. All punishments are reduced to a commondenominator and expressed in money terms, ie in fines. Thus, the punishmentis expressed as s#h, where s indicates the severity of punishment.3

34 These assumptions are clearly not in accordance with the stylized facts from various countries.

Thus, for instance, in Finland a so-called daily fine was determined in the sample period by asimple rule: one daily fine in FIM = max {20, [(monthly gross salary/90) 8*number ofdependents in the family]}. A punishment is measured in daily fines. To assume that thepunishment does not depend on the level of income from legal activity is to emphasize the fact thatthe main determinant of punishment is the crime not the income. The assumption that transferincome does not depend on crime is also something which is not universally true for all countries.Thus, criminals may lose all benefits so that indeed transfer income may be zero if the individualpursues criminal activity and is caught. In essence this means that transfer income operates as somesort of additional punishment scheme. In several countries, as in Finland, criminal activity is notconsidered a reason for cancelling social security benefits. By contrast, various social programmeswhich intend to break criminal habits may even increase benefits. Here, this assumption is usedbecause we deal mainly with Finnish data and for the cross-country analysis we have no data (fromother countries) on alternative transfer systems.

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4) There is no difference between apprehension and conviction. Although thisassumption simplifies the analysis it also causes some problems because inthe cross-country setting it creates some measurement problems (and surelysome measurement errors).

5) An individual obtains some transfer income, A, irrespective of his or herbehaviour. Thus, also criminals get transfer payments.4

Criminal actions are actions taken under uncertainty. Uncertainty arises from thefact that there is some probability (p) that an individual pursuing criminal activitywill be caught and if so a fine sh must be paid. If only legal activity is pursued,there is obviously no fine, and we are back in the standard supply of labour model(ie, p does not matter). The probability p is here assumed to be constant, whichmeans that it does not depend on h, for instance. Obviously, this may not be true.Instead, one could specify p so that p = p(h,P) where P is some economy-widereference value for the apprehension rate. Here, we however adopt the simplerapproach with p fixed because we cannot subsequently estimate the moresophisticated model with our aggregate and semiaggregate data.

In line with the literature, we model the decisionmaking as the maximizationof expected utility as follows:

where u(.,.) is a strictly quasi-concave utility function which is strictly increasingin its arguments: total leisure l = (1e(1)h) and consumption c. Preferencesare thus linear in probabilities (see eg Hirsleifer and Riley 1992).

The first order conditions for the maximization of expected utility are:

and

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where 1 = 0u[1e(1)h, A+rh+we]/0[1e(1)h], u1 = 0u[1e(1)h,A+rh+wesh]/0[1e(1)h] and so on. If we allow p to depend on h, the first-order conditions would include p1 + p1 terms, which would, ceteris paribus,lower the optimal value of h because increasing time in criminal activity wouldalso increase the probability of being caught.

Assuming that the second-order condition holds, the first-order conditionsindirectly determine criminal and legal labour supply in terms of exogenousparameters, ie h = h(, A, w, r, p, s) and similarly e = e(, A, w, r, p, s).

Obviously, there are some important corner solutions which deservecomment. The most important case is where h is zero (no criminal activity). If thatwere the case, we would end up with the conventional consumption-leisure choicecondition u1 = wu2. It is easy to see that this case is obtained when = 0 (timespent in criminal activity is just "work" not leisure and w is high in relation tor but not necessary higher unless s or p = 0. By contrast, e may also be zero withh > 0 (individual becomes a full-time criminal). If 1 and r > w, this possibilitybecomes relevant. (The exact conditions are omitted here for space reasons.)

Alternatively, one might assume that the legal labour supply, e, is given foran individual either because of social custom (eg working-hours agreement) orbecause of a binding labour supply constraint (unemployment). If e could beassumed to be fixed, say s, this would simplify the analysis considerably. Onecould then simply concentrate on the first-order condition for h and, using this as apoint of departure, derive the following comparative statistics results with respectto the relevant parameters (assuming all the time an interior solution for h):

where the signs correspond to the signs of the respective comparative static effects(an appendix containing the derivation is available upon request from the author).The signs of the effects are quite intuitive and in accord with earlier theoreticalanalyses. Thus, we find that the price terms w, r, p and s which make legal activity(crime) more profitable have a negative (positive) effect on the amount of crime.Also, the effects of the "taste for crime" parameter are intuitively acceptable: ifcrime becomes more like other leisure, this obviously tends to increase crime. Bycontrast, if crime becomes more like work, utility decreases and less effort isdevoted to criminal activity.

An increase in transfer income tends to decrease criminal activity. The reasonis the same as in the standard supply of labour model: increased lump-sum incomeleads to lower labour supply. Finally, an increase in (exogenous) legal laboursupply tends (unambiguously) to decrease crime (and vice versa, as a part ofincreased "legal" leisure is used in criminal activities). Thus, an increase in

55 To model the effects on unemployment is somewhat difficult because one cannot make use of the

representative agent framework and relate unemployment directly to s. Rather, one must assumethat a fraction of individuals, say un, faces a constraint s = 0, while for the rest, 1un, s = e= > 0.Obviously 0H/0un g 0H/0(1-e=), although both are positive. To model the effects of un, one needsa more detailed specification of the transfer system and the wage distribution.

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unemployment, for instance, should indeed cause more crime, as is often arguedby sociologists.5

One may illustrate the nature of the solution by using a simple separableutility function u = al + cb where a and b are constant parameters. Using anapproximation 2 2, which is true when s = 0, one ends up with the followingclosed-form solution for h, given

66 Notice here that, ceteris paribus, the distribution function f(w) also determines the number of

corner solutions. Thus, the number of non-criminals (with h=0) may depend on f(w) and hence alsoon income inequality.

7 It is noted in the published reports that due to some technical difficulties part of the data for 1955

was not available.

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country setting. Thus, in addition to demographic variables an income equalitymeasure might be a good explanatory variable for aggregate crime because itmight give information on the distribution function, f(w).6 In the subsequentempirical analysis we do not have data for all relevant distributional measures.Obviously, when we deal with aggregated data we face severe difficulties inconstructing them. Therefore, we also use panel data for Finnish municipalities asa separate piece of analysis which may help to identify the effects of thesedistributional measures.

Next, we discuss briefly the question of how to derive the estimatingspecification for aggregate (property) crime. Basically, the solution is quitestraightforward: we take a (log) linear approximation of the supply function (6). Inpractice, that is not so simple because already such closed form solutions as (5)create some problems in linearization (to illustrate this point, the linearized formof (5) is reported in the Appendix). We tried to overcome these problems partly bycarrying out some numerical simulations which illustrate the relative effects ofdifferent variables/parameters (the results are available upon request from theauthor). Using the comparative statistics results and the numerical simulations as apoint of reference, we specified the aggregate empirical equation in the followingway:

where the symbols have the same meanings as above except that they now refer toaggregate (average) values. Thus, p is the apprehension rate (probability of beingcaught), s the sentence (severity of punishment), e working time, w return fromlegal activity, r return from illegal activity and A income transfers. Variable J heredenotes the the error term and x the (possible) demographic variables, which areincluded to account for aggregation and/or the omitted taste for crime parameter.

The set of socioeconomic indicators include: rate of unemployment,population aged 1524 and urban population, the last two in relation to totalpopulation. In addition, a dummy variable for 1955 is included. The residualsensitivity analysis (including tests for outlier observations) suggested that thisobservation is actually an outlier. On the other hand, there is reason to believe thatthe basic data are somewhat deficient for this year. Thus, a dummy variable, D55,is introduced.7

The model obviously represents some sort of long-run relationship and henceit may not account well for short-run changes in the respective variables.Therefore, we must deal with the dynamic specification as well. To obtain thisspecification, we take two alternative routes: first, a standard partial adjustment/habit persistence specification (8) and second, an error correction cumcointegration model (9). In the latter case, we use model (7) as the long-run

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cointegrating model and hence J is used as the cointegrating vector, which in turnis substituted for the error correction term.

where EC denotes the error correction term and u the error term. denotes thefirst backward differencing operator.

83 The Data

The empirical analysis consists of three parts. The first is an aggregate time seriesanalysis of property crime in Finland over the period 19511995. The second partis a panel data analysis of 460 Finnish municipalities over the period 19831995.The third part makes use of international cross-country (panel) data for 13countries over the period 19791994. Thus, in all cases the data are annual.

As for other details, the following comments may suffice. Property crime, H,is measured by the number of offenses known to the police during the year(expressed in log per capita terms, i.e. as log(H/N) where N denotes population).Property crime includes both theft, aggravated theft, petty theft, auto theft androbberies. Individual crime categories (and substitution between them) are notanalysed in this paper (see Heineke 1978c and Koskela and Virn 1995 for suchanalysis). Attempted thefts (in these categories) are included. In most of theanalysis a simple sum aggregate (per capita) is used for H. In the case of Finnishaggregate time series data, also a volume index of crime is constructed, byweighting the time series of different crime categories by a measure of theseriousness of crime. The seriousness of crime is in turn measured by the relativepunishment rates for 1975, ie using constant weights. The index is analogous tothe monetary indices introduced by Barnett (1980). Both the simple sum aggregateand the volume index are displayed in Figure 1. One can see that both indicespoint in the same direction although the relative scales are different and theestimation results with these two measures turn out to be somewhat different.

Figure 1. Property crime in Finland

98 In 1992 a major change took place in Finnish criminal law. Before that, individual sentences were

handed down for all crimes and punishments were later combined into a final sentence. After 1992just one combined sentence was given to a criminal who had committed several criminal actions.Obviously, it is very difficult to compare the period 19921995 with the earlier years and clearlythere is the danger of measurement errors. The comparison here is done by comparing sentencesthat apply only to single criminal actions.

Figure 2. Punishment and apprehension

As for the explanatory variables, p is measured as the ratio of persons captured andindicted to the total number of offenses known to the police. The punishment rate,s, is measured in terms of unconditional prison sentences using different weightsfor different forms of punishment. Thus, a weight of one was given tounconditional prison sentences, 0.33 to conditional prison (probation), 1.33 tounconditional penitentiary (ie prison with stricter conditions, which was used inFinland until the early 1970s), 0.44 to conditional penitentiary, 0.25 to daily fines(0.17 for 19511976). The weights are partly based on criminal law; otherwisethey were derived by interviewing a group of experts in the police and juridicalsystem. The punishment rates are computed for all subcategories of propertycrime. These are then aggregated by using either fixed 1975 weights (number ofoffenses known to the police) or by using variable weights (ie actual number ofoffenses known to the police each year).8 Figure 2 contains graphs for both p and s(s computed with fixed weights).

In the case of Finnish municipal data, we have no cross-section data forpunishments. Hence, the whole variable was omitted. With the cross-country data,we do not have precise and comparable indicators of the punishment rate. Hencewe have to rely on two crude proxies for this variable: First, we use the number ofprisoners (including jail inmates) / total population. Secondly, we use the average

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9 The main data source for Finland is the Finnish Crime Statistics (Statistics Finland, Helsinki). For

the international data, the main data source is the International Crime Statistics (Interpol, Lyon). Inaddition, we have used the Prison Information Bulletin (Council of Europe, Strassburg). Alsonational data sources have been used. The data for the economic variables come from FinnishNational Accounts (Statistics Finland, Helsinki) and the OECD National Accounts (OECD, Paris).A more complete description of the data and data sources (as well as a printout of the data) areavailable upon request from the author.

length of the prison sentence.9 Both of the these indicators are related to allcategories of crime, not only property crime. The number of prisoners/populationvariable suffers also from the problem that it does not take into account the effectof increased crime on the number of convicts. The unconditional prison sentencevariable is in turn equally deficient because it represents only one form ofpunishment. Thus, if fewer and fewer people are sentenced to prison, it may wellhappen that the average prison sentence even increases for the remaining convictseven though the "expected" severity of punishment for a typical property crimeclearly decreases. Needless to say, both of the above-mentioned measures can givea misleading impression of the developments of overall severity of punishmentand therefore the related results should be interpreted with caution. Even in thiscase, most empirical studies use such simple proxies for punishment rates. Alsothe amount of crime is measured very roughly using only the simple sumaggregate.

Finally, some comments on the rate of return variables merit note. In fact, weneed to find empirical proxies for r, w and s (assuming that e is exogenous). It isrelatively easy to measure s and w but quite difficult, if not impossible, to measurer. We may only hypothesize that r is related to income or consumption, for thesimple reason that higher income and consumption means more opportunities fortheft and robberies. The problem is then that we have basically the same variable,say consumption or income, to account for the conflicting effects of return fromlegal and illegal activity. Then we have to interpret the coefficient of this variableas some sort of net effect of increased standard of living. Clearly, an increase inthe standard of living shows up in both increased return from legal activity andincreased opportunities of crime. The sign of the net effect is obviouslyambiguous. The working-hour variable, s, is here measured as the averageworking time in Finnish industry. However, when we use the two panel data sets,this variable is not available and we must therefore abstain from measuring thecorresponding crime effect. Also with the transfer income variable, A, there wereserious measurement problems and we could not include the variable in theestimating specification(s).

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4 Estimation Results

4.1 Presentation of Results

Before estimating the final specification, we look at the results from the co-integration analysis. First, we analysed the time series properties of the key timeseries, H, c, p, s and w, using the set of tests proposed, for instance, by Engle andGranger (1987). This analysis clearly showed that all of these series are I(1),which may not be very surprising given the time series graphs in Figures 1 and 2(to save space we refrain from reporting these tests results here; they are, however,available on request from the author). Next, we estimated a cointegration model,which turned out to be a stochastic version of equation (1) except that thesocioeconomic variables were not included. The relevant estimation results arealso presented in Table 1. The relatively high values of the DurbinWatsonstatistic (not to mention other cointegration test statistics; see eg Engle and Yoo1987 and Kremers et al 1992) are clearly in accordance with the null ofcointegration. Hence, the error-correction form (8) appears to be consistent withthe data.

OLS estimation results from the error-correction and partial adjustment habitpersistence models are reported in Table 1. The OLS estimator may not beappropriate here because of simultaneity between pt and Ht (possibly also betweenst and Ht). Thus, the apprehension rate may indeed deter crime but it may also bethe case that crime crucially affects the efficiency of law enforcement activitiesand thus also the apprehension rate; see Ehrlich and Brower (1987) for a moredetailed treatment of this issue. Here we try to take this problem into account byusing the instrumental variable estimator to eliminate the simultaneity bias withrespect to pt. Table 2 in turn includes results with pooled international cross-country data. In this case, the estimating equation is the standard partialadjustment/habit persistence specification, which takes the following form:

where the Di's denote individual country intercepts (the number of countries is 13and the sample period is 19791994). Equation (10) is estimated using the OLSestimator, the variance components estimator, and an instrumental variableestimator to correct the possible simultaneity bias in terms of pt and Ht.

Finally, with the pooled Finnish municipalities data, we use a model which isin essence similar to equation (10). As pointed out earlier, we have no data on theseverity of punishment and hence the respective variable has to be deleted,although some sosio-economic variables may give us indirect evidence of the roleof this variable. By contrast, we have several socioeconomic and demographicvariables included in the model. Those variables are related to public expenditure(at the municipality level, exp), the unemployment rate (un), population density(dens), the share of votes for socialist parties (sos), population aged below 15 andabove 65 (A15 and A65), the municipality tax rate (tax) and total population(pop). The model is estimated in the same way as equation (9), with international

12

10 Because of deficient data (especially international cross-country data), this result should be

treated with some caution. We should however point out that if the equations(s) are estimated sothat the apprehension rate, p, is replaced by the number of cases which are solved by the police SP(and so easing the simultaneity problem) we end up with results which are qualitatively verysimilar to those with the apprehension rate variable. The instrumental variable estimate for thecoefficient of log(SP/N) (corresponding to equation 1 in Table 1) turned out to be .427 (2.14).Moreover, if p was replaced by the number of police log(NP/N) the respective coefficient turnedout to be .624 (2.64).

cross-country data, but in this case we also use the least absolute deviations (LAD)estimator to account for some possible outlier observations. Some of the 460municipalities (eg small islands) are clearly so different that a check for robustnessis required.

4.2 Interpretation of the Results

The results can be easily summarized. With all data sets the model performsstrikingly well. The coefficients of the apprehension and punishment ratevariables, p and s, are of the expected (negative) sign and magnitude and moreoverthe coefficients can be estimated very precisely. In addition, the results appear tobe very robust. Thus, changes in dynamic specification, proxy variables andestimators leave the main results practically unchanged. Also, the standard partialadjustment specification produces results that are very similar to the resultsobtained from the errorcorrection model. Finally, the instrumental variableestimation results, which are very similar to the OLS results, suggest that thecausality problem in terms of crime and apprehension (cf. eg Ehrlich and Brower1987) may not be of crucial importance.10

The coefficients of pt and st suggest that criminal policy should influence bothapprehension and punishment. It not obvious which instruments should be stressedmore: the importance depends on the measurement of crime and punishment andon the time horizon. The values of the coefficient estimates favour theinterpretation that the apprehension rate is more important. This shows up if wetake log transformations of both p and s and compare the respective (constant)elasticities. In the case of the apprehension rate it is 0.43, for the punishment rate0.21. If the log transformation applies only to s, the elasticity is .24 while thesemi-elasticity for p is 1.11 (a one percentage point increase in the apprehensionrate reduces crime by about one per cent; the corresponding elasticity notsemi-elasticity at the sample mean value is 0.46).

Estimation results also show that these variables cannot be combined into anexpected penalty variable (p*s). The corresponding F test statistic F(1,29) = 12.54,which clearly exceeds all critical levels. If, however, the log transformation ismade for both p and s, the "only expected penalty matters" hypothesis cannot beclearly rejected. The test statistic F(1,29) = 2.93, which only exceeds the 10 percent critical level. All in all, the results seem to suggest that criminals cannot becharacterized as risk-neutral but rather as risk lovers, as already suggested byBecker (1968).

The most important fact however is that the results support the existence ofdeterrence effects from both the apprehension rate and the severity of sentencing.

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11 Notice that we deal here with a completely static (theoretical) model and ignore all life-cycle

considerations, which are probably very important (cf. eg Witte 1980). Thus, eg for youngcriminals, the fact they are caught (and from then on known by the police) may be much moreimportant than the punishment. One would obviously need panel data for individuals to get greaterinsight into the importance of the dynamic effects. Recall also the distinction betweenapprehension and conviction which is bypassed in our model.

12 There are various explanations for this somewhat puzzling result. In particular, one may refer to

the fact that income and consumption may already capture the effects of cyclical changes inunemployment. Cyclical behavior of different crime categories may also differ (see eg Cook andZarkin (1988)). It may also be that unemployment affects crime not only via the opportunitychannel but also via criminal motivation channel (see eg Land et al (1995)). Thus interpreting thecyclical behavior of aggregate crime is quite difficult. Finally, measurement problems in terms ofun ought to be mentioned. For further discussion, see eg Lester (1995) and Borooah and Collins(1995).

Moreover, the corresponding effects are quite well in line with those obtained inprevious studies (see eg Dnes 1996).11

After these general comments, we ought to make some specific comments onthe different tables and data sets. First, considering Table 1, we might point outthat both estimating specifications indicate that there is not much differencebetween short- and long-run results and, accordingly, the speed of adjustment israther high. Thus, the equilibrium is reached in almost one year. In other words,changes in relevant policy parameters may rather quickly affect criminalbehaviour.

Second, leisure time (average working time denoted by e) appears indeed tobe an essential ingredient in the supply of property crime equation. The coefficientsuggests that a decrease in annual working hours from the current 1640 to about1500 would increase crime by more than 20 per cent quite a substantial increase.The effect of consumption on crime is positive, suggesting that an increase in thestandard of living shows up predominantly in increased crime opportunities thusleading to increased crime (for similar findings, see eg Cohen et al (1980)). Theshort-run effect (see the estimate for the error correction model) is howevernegative, although very unprecise. Thus, changes in income and consumption maymainly affect crime via the return on legal activity while the long-run (level) effectshows up more in the crime opportunities and in the corresponding returns.

What is however somewhat surprising is the fact that unemployment is not animportant determinant of crime (at least in Finland). Thus, if this variable isintroduced into the estimating model, the coefficient turns out to be negative.12Also the other additional variables that correspond to demographic andsocioeconomic developments perform rather poorly with the aggregate time seriesdata. Only the urbanization variable (urban population/total population) has acoefficient which is of correct sign and reasonable magnitude (the t-ratio is 1.40).

The sign of the coefficient of unemployment variable is negative also in thepooled data for Finnish municipalities (see Table 3). The coefficient cannot beestimated very precisely but even then one can pretty affirmatively conclude thatunemployment has not been a major factor in Finnish criminality. By contrast, onemay conclude that urbanization may indeed have played a role (see the densityvariable). As for the soc variable, as well as the demographic variables, one mayexplain the results by the "taste for crime" parameter which in Finland may reflectthe difference between the more religious and conservative Finnish country-side

14

and more liberal urban southern Finland. Thus, in fact, soc may also reflect(inversely) the severity of punishment, which we cannot observe/measure nor thusinclude in the model.

Finally a couple of comments might be made on the results from internationalcross-country data reported in Table 2. Because the quality of the data is muchmore deficient than with the Finnish data, one must accept the fact that the resultsare not as precise and robust as with the Finnish data sets. Still, all the results pointin the right direction and the coefficients are of reasonable magnitude (especiallyafter correcting the simultaneity bias in terms of the apprehension rate). Thus, bothapprehension and severity of punishments deter crime while income (which is aproxy for the rate of return variables and the leisure variable) has a positive effecton crime. At least one can say that the results with Finnish data do not represent aclear exception of a general pattern.

15

13 For a more general perspective of the empirical results obtained in this paper see eg Muncie et al

(1996).

5 Conclusions

The results give strong support to predictions of our model and in more generalthey give support to models which emphasize the role of deterrence effects andopportunity structures of crime rates.13 There may be several reasons for thisperformance. A couple of them may be recalled here. First, the model gives animportant role to the allocation of time between legal and illegal activities, and itseems that crime also depends on the available amount of leisure time at least tothe extent that we are dealing with part-time criminals. The second reason has todo with the data. Particularly Finnish data are reasonably good and are constructedin the proper way. There would therefore seem to be a good case for using betterdata and testing methodology to revisit the empirical tests of the economics ofcrime model in other countries as well. Obviously, the results also have importantpolicy implications. At least they show that crime is not exogenous, ie completelyunaffected by policy actions. By contrast, quite straightforward and reasonablepolicy measures have a significant impact on property crime.

16

Table 1. Estimation results with Finnish time-series data

(1) (2) (3) (4) (5) (6) (7) (8)

Const.

Ht1/ECt1

pt

st

stct

d55

R2100$SEEDWLM1

2.601(3.51)

.344(3.51).789(3.63).032(2.50)2.150(3.70)

.287(2.33).183(3.40)

.9964.981.8800.309

3.949(5.44)

1.090(4.75).038(2.78)3.504(6.92)

.450(3.46).238(4.01)

.9955.701.536

..

.025(2.30).807(5.71)1.212(3.19).057(2.64)1.490(2.55).120(0.49).159(4.53)

.6394.641.681

..

5.567(5.18)

.194(1.68)1.383(4.92).079(4.81)2.049(3.27)

.163(1.23).247(3.90)

.9955.671.9870.047

6.901(9.44)

1.659(7.18).093(6.78)2.678(5.26)

.209(1.60).286(4.81)

.9945.741.879

..

.013(1.22).829(5.21)1.585(3.60).059(2.42)2.531(3.76)

..

.208(5.00)

.6285.431.874

..

2.609(3.51)

.327(3.24).886(3.51).032(2.55)2.121(3.64)

.305(2.43).186(3.43)

.9954.991.866

..

5.257(4.57)

.229(1.84)1.236(3.63).076(4.49)2.045(3.26)

.143(1.06).240(3.73)

.9945.691.985

..

Dep.varEstimatorForm

sum

OLSlevel

sum

OLSlevel

sum

OLSdif

indexOLSlevel

indexOLSlevel

indexOLSdif

sum

IVlevel

indexIV

level

Numbers inside parentheses are (unadjusted) t-ratios (heteroskedasticity adjusted t-ratios werepractically identical). The number of observations is 43. c denotes aggregate consumption (which isused as a proxy for the rate of return variables), and d55 is a dummy variable for 1955. LM1 isGodfrey's test statistic for first-order autocorrelation in the presence of a lagged dependent variable.sum = sum aggregate of all kinds of larcenies and robberies, index = volume index of larcenies androbberies. Level = level form equation (in which case the lagged dependent variable Ht1 is introduced)and dif = an errorcorrection model in first log differences (in which case the error correction term ECt1is introduced it has been derived from the respective cointegrating equation). In the case of theinstrumental variable (IV) estimator, the set of instruments includes pt-1, NP = number of police andNR = number of prisoners. All level variables are expressed in per capita form.

17

Table 2. Estimation results with pooled cross-country data

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Ht1

pt

st

yt

R2DW100$SEE

.495(9.70).022(7.86)

.160(1.69)

.9911.1547.86

.514(4.40).022(3.68).046(0.60)

.189(1.42)

.9911.1727.85

.486(4.93).026(4.49).094(0.90)

.156(0.76)

.9871.1406.31

.523(4.36).020(3.40).020(1.99)

.175(1.46)

.9921.1927.79

.504(5.20).025(4.39).036(1.98)

.056(0.43)

.9891.1815.96

.885(33.19).003(1.76).086(2.96)0.171

(2.71)

.984

..

10.75

.868(34.38).003(2.13).027(4.61)

.154(2.76)

.988

..

9.50

.667(8.79).011(2.48).100(1.86)

.287(2.58)

.9911.3548.04

.690(4.36).009(1.07).031(2.27)

.231(2.00)

.9911.4008.02

Def of sEstimator

..

OLSNR

OLSNR

WeightAS

OLSAS

WeightNRVC

ASVC

NRIV

ASIV

Numbers in parentheses are t-ratios (which are heteroskedasticity adjusted according to thebootstrapping method of MacKinnon and White 1985). The number of observations is 169. Thedependent variable is the log of larcenies and robberies per capita. NR = number of prisoners andAS = average length of prison sentence. Weight means that the data are weighted by the squareroot of population. VC denotes the variance components estimator. In both cases the fixed effectmodel outperformed this random effects model according to Hausman test statistic. In the case ofthe OLS and IV estimators, the model also includes country dummies (which are not reportedhere). In the case of IV estimation, the list of instruments includes the lagged apprehension rateand the alternative proxies for st.

Table 3. Estimation results with pooled Finnish municipalities data

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Const.

Ht1

pt

yt

exp

dens

soc.

A15

A65

unt

R2SEEDW

14.870(0.98)

.800(40.43)7.986(2.15)

.963(8.58)

.111(0.46)

.207(3.94)

.261(3.53).104(0.24)

.336(0.95).210(1.36)

.75346.41

1.786

11.500(3.64)

.789(83.87)7.808(2.37)

.986(9.90)

.246(1.18)

.206(7.34)

.197(3.70).258(1.79)

.76846.96

..

12.865(1.69)

.792(154.24)5.760(2.58)

.723(16.20)

.338(2.67)

.309(16.38)

.245(6.99).839(3.63).411(2.70).297(3.76)

.75146.79

1.776

6.902(0.22)

.847(34.32)18.568

(2.72).105

(0.56)2.470

(4.24).046

(1.77).335

(2.71).604(0.67).454(0.68)1.278(4.11)

.89743.24

1.877

17.126(0.80)

.802(22.62)7.267(1.49)1.338

(6.14).723

(2.35).303

(3.72).391

(4.12).384(0.60).061(0.12).388(2.03)

.79559.97

1.778

32.056(7.63)

.792(89.27)3.965(0.91)1.450

(11.20).934

(3.45).296

(8.07).376

(5.33).469(2.47)

.81060.34

..

16.983(6.60)

.843(162.16)8.811(3.01)

.838(14.81)

.539(3.34)

.484(19.60)

.403(9.13).371(3.68)

.79260.56

1.784

33.30(2.71)

.816(15.97)47.961

(2.71).529

(1.75)4.213

(4.98).082

(2.22).692

(3.56)

1.625(4.27)

.91561.20

1.833

7.270(1.05)

.714(65.00)70.168

(5.41)1.145

(8.89).267

(1.14).261

(7.32).238

(3.78).201(1.34)

.68255.42

1.832

9.652(1.28)

.783(80.88)59.149

(4.91)1.347

(8.73).930

(3.34).351

(8.08).440

(5.68).441(2.47)

.77165.66

1.816

EstimatorDep.var.

OLSL

VCL

LADL

WeightL

OLSL&R

VCL&R

LADL&R

WeightL&R

IVL

IVL&R

Numbers in parentheses are t-ratios (which are heteroskedasticity adjusted according to the bootstrapping method by MacKinnon and White 1985). The numberof observations is 5520. L = larcenies and L&R (all kind of) larcenies and robberies. y = income, exp = public expenditure (both per capita), dens = populationdensity, soc = percentage of votes obtained by socialist parties, A15 (A65) population under 15 (above 65)/total population and un = the unemployment rate.Weight means that the data are weighted by the square root of population. VC denotes the variance components estimator. In all cases the fixed effect modeloutperformed this random effects model according to Hausman' test statistic. The list of instruments with the IV estimator include the lagged apprehension rate,tax, exp, pop, A15 and A65.

19

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21

(A1)

(A2)

Appendix

Linearization of (5)If the closed-form solution (5) is linearized by Taylor approximation around c =(cr, cA, cw, ce, cp, cs) we obtain

where R1 is the residual. This can be further simplifyed (by taking into accountthat the coefficients also the term inside brackets consist of constant termsonly):

which is, in fact, of the same form as equation (7) in text.Simulating both equation (5) and the corresponding approximate form (A1)

produced very similar partial effects for different variables suggesting that theapproximation is indeed reasonable good (simulation results are available uponrequest from the author).

VATT-KESKUSTELUALOITTEITA 244AbstractContents1 Introduction2 An Occupational Choice Model of Criminal Behaviour2.1 Individual Choice Problem2.2 Aggregate Criminal Activity and Empirical Analysis

3 The Data4 Estimation Results4.1 Presentation of Results4.2 Interpretation of the Results

5 ConclusionsTablesTable 1. Estimation results with Finnish time-series dataTable 2. Estimation results with pooled cross-country dataTable 3. Estimation results with pooled Finnish municipalities data

ReferencesAppendix