Assessing Substitution and Complementary Effects

Eur J Crim Policy Res DOI 10.1007/s10610-013-9196-4

Assessing Substitution and Complementary Effects Amongst Crime Typologies Claudio Detotto & Manuela Pulina

# Springer Science+Business Media Dordrecht 2013

Abstract This paper aims at assessing how offenders allocate their effort amongst several types of crime. Specifically, complementary and substitution effects are investigated amongst the number of recorded homicides, robberies, extortions and kidnapping, receiving stolen goods, falsity and drug-related crimes. Furthermore, the extent to which crime is detrimental for economic growth is also analysed. The case-study country is Italy, and the time span under analysis is from the first quarter of 1981 to the fourth quarter of 2004. A Vector Error Correction Mechanism (VECM) is employed after having assessed the integration and cointegration status of the variables under investigation. Empirical findings show that, in the long run, an increase in the overall welfare has a negative impact on the most serious crimes. In addition, the long-run elasticities reveal symmetric results in terms of positive and negative relationships amongst types of crime. In the short run, the crossdeterrence elasticities highlight a complementary effect between more serious crimes (i.e. robberies, extortions and kidnapping) and milder crimes (i.e. drug-related crimes and falsity) and a substitution effect amongst all other types of offences. Policy implications are drawn. Keywords Crime . Substitution and complementary effects . Enforcement . Legal economy . Crowding-out effect

Introduction Since Becker’s report (1968), the standard economic model of crime has primarily been concerned with the criminal’s choice between legal and illegal activities. In this framework, the criminal is a rational agent who maximises his/her utility given his/her budget constraint. In the real world, however, the criminal not only must choose the optimal allocation of effort between legal or illegal activities, but he/she may allocate his/her effort between several crime offences. A general crime model has to assume that payoffs and sanctions in one crime C. Detotto (*) : M. Pulina Department of Economics (DiSEA) and CRENoS, University of Sassari, Via torre tonda, 34, Sassari (Sardinia), Italy e-mail: [email protected]

C. Detotto, M. Pulina

may affect the level of activity in other crimes. Hence, the relationships between the different “submarkets of crime” (Jantzen 2008) have to be taken into account in order to explain criminals’ behaviour. Although this is not a new topic, it is still well under-researched, especially from an economic point of view. In the 1990s, crime economic research began to focus on the relationship existing amongst different types of crime. For example, Enders and Sandler (1993), within the terrorism economics literature, find that threats and hoaxes are complementary with skyjackings, hostagings and assassinations. Mativat and Tremblay (1997), within the credit-card counterfeiting market, use a displacement-induced crime-wave model where it is assumed that changes in crime opportunities will motivate a significant subset of offenders to engage in similar crime-switching adaptations. The crime wave is also associated with a concomitant decrease in other related offences. Koskela and Viren (1997) show that an increase in enforcement, or arrest rates, makes criminals switch to more profitable criminal activities. The paper presented here, which stems from this strand of research, further expands the theoretical model, inserting one extra criminal activity that is assumed to be a perfect complement to one of the other two criminal activities. Empirically, the objective is to test for either a complementary or substitution relationship amongst several types of crime. The crime typologies considered in this paper are the number of recorded voluntary homicides, robberies, extortions and kidnapping, receiving, falsity and drug-related crimes. The analysis is linked to an economic framework by including the real per capita Gross Domestic Product (GDP) as an additional variable. This investigation fits into the current debate by both testing the effects that economic growth produces on criminal activity and highlighting possible crowding-out effects running from illegal activity to legal economic activity. In fact, crime disrupts legal business and diverts resources from legal activities, thus reducing the economic growth in the short and long run (Detotto and Otranto 2010). Via a Vector Error Correction Mechanism (VECM), it is possible to explore multiple economic correlations both in the short and long run. A set of dummy variables is included in order to capture the impact of important policy measures such as pardons and amnesties on crime rates. To this end, given data availability, quarterly Italian data over the first quarter 1981 to the fourth quarter 2004 (1981:1–2004:4) are employed. Italy can be considered an interesting case study for several reasons. Firstly, an unprecedented increase in total crime offences has been observed over the last 25 years, going from 39.3 per 1,000 inhabitants in 1979 to 50.7 in 2004 (+35.7 %). If the time span from 1993 to 2007 is considered, the number of total crime offences increased by 29.8 %, in contrast with many other Western countries such as the USA (−20.4 %), Canada (−15.8 %), the UK (−10.9 %), France (−7.5 %) and Germany (−6.9 %) (Eurostat 2009). In a recent research conducted by Aebi and Linde (2010), a different pattern of growth is identified in western Europe from 1988 to 2007. Their results indicate that property offences and homicide have been decreasing since the mid-1990s, whereas violent and drug-related crimes have increased during the same time span. From this perspective, the study reported here makes an important contribution to exploring the causes of crime fluctuations in Italy by considering the relationship between the different types of crime and between crime and economic growth. The Italian crime pattern is, in fact, characterised by a prevalence of property crimes (73.4 % of total crime offences), which are better explained by economic motivations. Furthermore, several types of criminal activities under investigation are often committed by criminal organisations. Hence, this study allows one to indirectly investigate the allocation of the organised-crime criminal effort. A promising field of research has developed around the estimation of the social cost of crime. It is well known that crime generates significant negative externalities, causing

Assessing Substitution and Complementary Effects

tangible, intangible, direct and indirect costs for the community. A recent paper by Detotto and Vannini (2010) gauges the social cost of crime in Italy by analysing a subset of offences, such as street crimes, robbery, fraud and homicide. Their findings show that in 2006, the estimated total social cost was about € 40 billion, which represented 2.6 % of Italian GDP. It is evident that in Italy, criminal activity has a significant impact on legal activities and has important policy implications. The rest of this paper is organised as follows. The “Literature Review” section presents a literature review on crime economics related to time series analysis. The “Theoretical Model and Data Description” section describes the economic model adopted and data used. The “Empirical Methodology and Results” section explains the methodology and presents the results. The final section presents the main conclusions of this study.

Literature Review This section is aimed at giving an account on crime economic literature related to the time series analysis (Table 1). There are several econometric approaches that have been employed to analyse the social costs of crime expressed in terms of the relationship between economic opportunities, level of enforcement and crime. Vector Autoregressive (VAR) and VECM specifications are the most commonly used time series frameworks. Masih and Masih (1996), for example, estimate the relationship between different crime types and their socioeconomic determinants within a multivariate cointegrated system for the Australian case (1960–1993). Within a Granger test framework, the authors establish the direction of the temporal causation between the variables showing the criminal activity positively responds to urbanisation and bad economic conditions, but they fail to find a crime impact on the socioeconomic variables under study. Luiz (2001) explores the effect that economic performance may have on crime levels by using a VECM. The case-study country is South Africa and the empirical findings show that total offences per capita are negatively associated with income per capita, whereas murder per capita is negatively related to the conviction rate and the repression index. Chen (2009) implements a VAR model to examine the long-run and causal relationships amongst unemployment, income and crime in Taiwan (1976–2005). The results indicate the presence of long-run relationships amongst unemployment, income and theft and amongst unemployment, income and economic fraud. Moreover, Chen shows the presence of a long-run level equilibrium relationship amongst unemployment, income and total crime. The Granger causality tests depict a neutral relationship amongst unemployment, income and all crime categories used. Shoesmith (2010) examines the pattern of violent and property crimes in the United States during 1970 and 2003. The author employs a VECM where four factors are included: arrest rates for each of type of crime, disposable income per capita, proportion of criminal justice resources devoted to drug offences and alcohol consumption. The findings reveal a close link between crime rates and the percentage of prison resources devoted to drug crime. From our literature review, it emerges that the Autoregressive Distributed Lags (ARDL) model is less commonly used. Using an Australian data set (1964–2001), Narayan and Smyth (2004) examine within an ARDL model the relationship amongst unemployment, real wages and seven different crime categories: homicide, motor-vehicle theft, fraud, break and enter, robbery, stealing, serious assault. The authors found that, in the short run, robbery and stealing Granger cause real income, whereas robbery and motor-vehicle theft Granger cause unemployment. In the long run, income is Granger caused by unemployment, homicide and motor-vehicle theft, whereas fraud is Granger caused by real income and

Journal

American Political Science Review

Applied Economics

Applied economics

Social Indicators Research

Economics Letters

Applied Economics

The 66th International Atlantic Economic Conference

International Journal of Social Economics

Journal of Chinese Economics and Business Studies

Authors (year)

Enders and Sandlers (1993)

Masih and Masih (1996)

Koskela and Viren (1997)

Luiz (2001)

Funk and Kruger (2003)

Narayan and Smyth (2004)

Jantzen (2008)

Habibullah and Baharom (2009)

Chen (2009)

VAR

ARDL model

VAREC

ARDL model

VAR

VECM

Cointegration error-correction form

Cointegration

VAR

Method

Taiwan (1976–2005; annual data)

Malaysia (1973–2003; annual data)

New York City (US) (1960–2006; annual data)

Australia (1964–2001; annual data)

Switzerland (1984– 1992; quarterly data)

South Africa (1960– 1993; Annual data)

Finland (1951–1992; annual data)

Australia (1963–1990; annual data)

USA (1968–1988; quarterly data)

Data

Table 1 Crime economics literature review (time series analysis)

3) unemployment, income and fraud

2) unemployment, income and theft

1) unemployment, income and total crime

There exists a long-run level equilibrium relationship among:

Long-run causal effect in all cases runs from economic performance to crime rates and not vice versa

Real Gross National Product and different crime offences Unemployment, income and crime (total crime, theft, violent assault and economic fraud)

Robbery, burglary, larceny, auto theft have a long-run relationship. Robbery, larceny and auto theft seem to be complementary but burglary a substitute.

In the short run, robbery and stealing impact real income whereas robbery and motor-vehicle theft impact unemployment. In the long run, income is affected by unemployment, homicide and motor-vehicle theft, whereas fraud is affected by real income and unemployment.

An increase in the enforcement activity for mild offenses reduces both mild and severe offenses

Whilst total offences are negatively associated with income per capita, disaggregated crime series do not always yield cointegrating vectors

An increase in punishment or arrest rate makes criminals switch to more profitable activities

Urbanization and economic variables impact crime rates. No effect of crime on socioeconomic variable

Threat and hoax events are complementary with skyjackings, hostagings and assassinations

Results

Murder, robbery, aggravated assault, burglary, larceny, auto theft

Crime, unemployment and real wages

Crime, socioeconomic determinants and deterrence

Income per capita; police officers per capita; conviction rates; political instability

Robberies, auto thefts

Crime, socioeconomic determinants

Skyjackings, hostage, assassinations, threats and other incident types

Variables


Applied Economics

Journal of Applied Statistics



Shoesmith (2010)

Saridakis (2011)

Fallahi et al. (2012)

Halicioglu (2012)

ARDL

ARCH - VECM

VECM

VECM

Method

Turkey (1965–2009; annual data)

USA (1976–2004; quarterly data)

England and Wales (1960–2000; annual data)

USA (1970–2003; annual data)

Data

Nonviolent crime (property, burglary, auto theft, fraud etc.); violent crime (homicide, assault, kidnapping etc.) unemployment rate, divorce rate, public security expenditure and urbanisation rate

Burglary, larceny, auto theft, robbery and unemployment rate

Violent crime per capita, conviction rate, imprisonment rate, male unemployment rate, poverty rate and beer consumed by the people aged 16–74

Disposable income per capita, crime (violent crime arrest rate, property crime arrest rate, drug arrests, drug offenders, alcohol) and consumption per capita

Variables

2. Unemployment, divorce, urbanisation and security expenditures

1. Crime variables and income

There exists a long-run level equilibrium among:

The unemployment rate and its volatility are only cointegrated with burglary and auto theft

Long-run level equilibrium amongst aggravated crime and economic variables

Long-run level equilibrium amongst economic and crime related variables

Results

VAR Vector Autoregressive, VECM Vector Error Correction Mechanism, ARDL Autoregressive Distributed Lags, VAREC Vector Autoregressive Error Correction

Journal

Authors (year)

Table 1 (continued)



unemployment. Habibullah and Baharom (2009), applying an ARDL model to the Malaysian case (1973–2003), analyse the relationship between real Gross National Product (GNP) and different crime offences. Results indicate that in all cases, the long-run causal effect runs from economic variables to crime rates and not vice versa. More recently, Saridakis (2011) investigated the long-run impact of economic conditions, beer consumption and various deterrents on different categories of recorded violent crime in England and Wales (time span 1960–2000). By applying an ARDL, the author shows that, although there does not appear to be empirical evidence of long-run models for serious crimes of violence, aggravated assault declines in response to an increase in conviction and imprisonment rates, which supports the deterrence hypothesis; an increase in male unemployment rates, poverty rates and beer consumption causes a rise in aggravated assault in the long run. Fallahi et al. (2012) performed an ARDL, with data at a quarterly frequency (1976:1–2004:4) for the USA to analyse the relationship between economic instability (i.e. unemployment) and crime (i.e. burglary, larceny, motor-vehicle theft and robbery). From their findings it emerges that a stable labour market would provide an environment that more effectively controls certain types of crime. Halicioglu (2012) analysed the dynamics of crime and a set of socioeconomic variables (i.e. health, income, divorce, urbanisation and security expenditure). The case-study country is Turkey, and the time span under investigation is 1965–2009. The findings emerging from the ARDL model reveal that, in the long run, income is the main factor in determining both violent and nonviolent crime rates. A common theme in the aforementioned studies is the investigation of crime in the context of separate and independent submarkets. They specify a different econometric model for each type of crime without considering possible relationships that may exist amongst various illegal activities. First attempts at closing this gap can be seen with the use of crosssectional techniques (Holtmann and Yap 1978; Hakim et al. 1984; Cameron 1987). In general, these studies find the presence of a positive cross-effect of imprisonment and arrest rates amongst several property crimes. Koskela and Viren (1997), for example, propose a theoretical choice model of crime switching that analyses the occupational behaviour of a representative rational agent between one legal activity and two criminal ones. These authors test the model within a cointegration and error-correction framework using annual data from Finland for robberies and vehicle thefts between 1951 and 1992. The findings show the presence of substitution between the two types of crime: namely, an increase in punishment or arrest rates makes criminals switch to more profitable activities. Funk and Kruger (2003) employ a VAR to investigate the dynamic interrelationship between larceny–theft, burglary and robbery in Switzerland from 1984 to 1998. They find that an increase in the less severe crimes, namely theft, leads to the more severe crimes, i.e. burglary and robbery. Moreover, an increase in the enforcement of milder crimes not only deters minor offenses but reduces more severe crimes as well. The authors link such findings to the “broken window theory1”, which speculates that a rise “in disorder and minor crimes sends a signal that ‘no one cares’ and thereby creates an environment conducive for more severe crimes to occur” (Funk and Kruger 2003; p.292). Jantzen (2008) employs a Johansen’s cointegration method to estimate the long-run equilibrium relationship existing between several crime types, namely, murder, assault, “Social psychologists and police officers tend to agree that if a window in a building is broken and is left unrepaired, all the rest of the windows will soon be broken. This is as true in nice neighbourhoods as in rundown ones. Window-breaking does not necessarily occur on a large scale because some areas are inhabited by determined window-breakers whereas others are populated by window-lovers; rather, one unrepaired broken window is a signal that no one cares, and so breaking more windows costs nothing.” Wilson and Kelling (2000, p. 2). 1


robbery, burglary, larceny and vehicle theft. Augmented Granger causality tests are also conducted to identify the direction of causality between variables. Results indicate the existence of a long-run equilibrium relationship between property crimes. Besides, they are Granger caused by violent crimes such as murder and assault. An interesting case study relates to the analysis of the substitution effect stemming from the economics of terrorism. By implementing a VAR model, Enders and Sandler (1993) study the behaviour of rational terrorists to measure the relationships between various terrorism attack modes, namely, skyjackings, incidents involving a hostage, assassinations, threats and hoaxes and all other incident types. A set of dummy variables are included to capture the effect of exogenous policy interventions, such as the installation of metal detectors in airports or the retaliatory raid on Libya. The authors find that threats and hoaxes events are complementary with skyjackings, hostagings and assassinations. Moreover, they show the impact effects of policy intervention on each terrorism series. From this literature review, it emerges that the relationship between crime and economic variables, such as GDP and unemployment, has been extensively studied, especially within a time-series framework. On the whole, ARDL models have been employed given the use of low frequency data due to the availability of relatively short-span data sets. Furthermore, there is great focus on investigating the temporal relationship between legal and illegal activity via the standard Granger causality test. Overall, a rather mixed evidence emerges on the type of temporal causality existing between the analysed variables, depending on the econometric approach used and the country analysed. However, scarce attention has been given to investigating the extent to which offenders, regarded as rational individuals, allocate their efforts between legal and illegal activities, as well as amongst different types of crimes. To date, only a few studies exist on these specific economic issues. The study we report here, stemming from this latter strand of research, can be regarded as novel because a set of deterrence variables is controlled for. Funk and Kruger (2003), for example, employ a more limited number of enforcement variables. Also, possible substitution and complementary effects amongst several types of offence will be investigated within a multivariate framework and at a quarterly frequency.

Theoretical Model and Data Description The Economic Framework In this subsection, an economic model of crime switching is presented in which a rational agent can allocate his/her time in different criminal and legal activities. This model directly stems from Koskela and Viren (1997), in which individuals can choose between one legal activity, two criminal substitute activities and leisure. In our study, one extra criminal activity is included in the model, and it is assumed to be a perfect complement to one of the other two criminal activities. According to Koskela and Viren (1997), individual preferences can be described by an additively separable utility function, as follows: U ¼ ð1 pa Þð1 pb Þð1 pc ÞC1 þ pa ð1 pb Þð1 pc ÞC2 þ ð1 pa Þpb ð1 pc ÞC3 þð1 pa Þð1 pb Þpc C4 þ pa pb ð1 pc ÞC5 þ pa ð1 pb Þpc C6 þ ð1 pa Þpb pc C7 ð1Þ þpa pb pc C8


where pa, pb and pc are the probabilities to be detected in each crime category. Ci are the level of consumption associated with the different state of nature: C1 ¼ ta h þ minðtb k; tc rÞ þ td y C2 ¼ C1 qa ta h C3 ¼ C1 qb tb k C4 ¼ C1 qc tc r C5 ¼ C1 qa ta h qb tb k C6 ¼ C1 qa ta h qc tc r C7 ¼ C1 qb tb k qc tc r C8 ¼ C1 qa ta h qb tb k qc tc r

ð2Þ

ta þ tb þ tc þ td ¼ 1

ð3Þ

with

where ta, tb, tc and td indicate time allocated to the three illegal activities and the legal activity, respectively; h, k, r and y are the return of the three illegal activities and the legal activity, respectively; qa, qb e qc are the penalties associated with the three crime types. Notably, the first two categories (b and c) are perfect complements, whereas a and b and a and c are perfect substitutes. The intuition behind this model is the following: On the one hand, some types of crime are profitable only if they are jointly perpetrated; for example, drug-related crimes and robberies can be complements because the latter can be a source of income for the drug user. On the other hand, other types of crime can be substitutes, and criminals can switch from one crime to the other according to their expected revenues. The perfect complement relationship between b and c implies in equilibrium the following condition: tc* ¼

tb* k r

ð4Þ

indicating that, in equilibrium, the higher the value of k (r), the lower the time dedicated to the crime activity of type b (type c). Substituting Eq. (4), which represents the set of vertices of the Leontief relationship between b and c, into Eq. (2) allows one to solve the utility function maximisation. The linearity of the utility function in ta, tb and td implies that we can have only corner equilibria; by comparing the coefficients of ta, tb, and td, the following criminal/not-criminal specialisations are found2 Given the perfect linearity of the utility function, we can have only corner equilibria. Comparing the different possible equilibria, it is possible to identify the thresholds of each type of crime specialisation, as shown in Eqs. (5), (6) and (7).: 1. If y > kr ð1 pb qb pc qc Þ and y > hð1 pa qa Þ; then t* ¼ 1 and t* ¼ t* ¼ t* ¼ 0 d a b c kþr ð5Þ 2

Solving Eq. (1) by substituting Eq. (2), and given Eqs. (3) and (4), we find: ta hð1 pa qa Þ þ tb k ð1 pb qb pc qc Þ þ td y

Given the perfect linearity of the utility function, we can have only corner equilibria. Comparing the different possible equilibria, it is possible to identify the thresholds of each type of crime specialisation as shown in solutions (5), (6), and (7).


2. If hð1 pa qa Þ >

kr ð1 pb qb pc qc Þ and hð1 pa qa Þ > y; kþr

then t*a ¼ 1 and t*b ¼ t*c ¼ t*d ¼ 0

ð6Þ

3. If

kr kr ð1 pb qb pc qc Þ > hð1 pa qa Þ and ð1 pb qb pc qc Þ > y; kþr kþr then t*b ¼

r k ; t* ¼ and t*a ¼ t*d ¼ 0 kþr c kþr

ð7Þ

In order to understand the switching effect between the different types of crime, we focus on case 3. Precisely, in line with Koskela and Viren (1997), we hypothesise that the crime return of type b, namely k, varies across criminals with a uniform distribution in the range [k; k þ λ ] with λ>0. If the return of legal activity, y, is sufficiently low, there exists a critical level of b k that divides the criminals into two groups: the first group, b k k , is specialised k þ λ , is specialised into the two into type a criminal activity; the second group, k b complementary crimes, namely, types b and c. The critical threshold b k is given by the following equation: b k¼

hrð1 pa qa Þ ½rð1 pb qb pc qc Þ hð1 pa qa Þ

Notably, an increase in b k in the complementary crimes in these two crime activities. per criminals, the aggregate calculated as follows:

ð8Þ

leads to a reduction in the number of criminals involved b and c; conversely, a reduction in b k causes an increase Assuming that ta, tb and tc indicate the number of crimes level of crime offences, Na, Nb and Nc, can easily be

R bk Na* ¼ k ta* dk R kþλ * ð9Þ Nb* ¼ t dk b b Rkkþλ * * tc dk Nc ¼ bk By taking the partial derivative of Eq. (9), namely, Ni* ¼ f ðp1 ; p2 ; p3 ; q1 ; q2 ; q3 ; h; k; rÞ with i=a, b, and c, we can understand how the independent variables, treated as exogenous, interact with the number of offences within the three crime groups, as follows: 1.

@Na* @N * @N * @N * @N * @N * @N * @N * < 0; a > 0; a > 0; a < 0; a > 0; a > 0; a > 0; a < 0; @pa @pb @pc @qa @qb @qc @h @k and

@N*a < 0; @r

ð10Þ


2. @Nb* @N * @N * @N * @N * @N * @N * @N * > 0; b < 0; b < 0; b > 0; b < 0; b < 0; b < 0; b > 0; @pa @pb @pc @qa @qb @qc @h @k and

@N*b > 0; @r

ð11Þ

3. @Nc* @N * @N * @N * @N * @N * @N * @N * > 0; c < 0; c < 0; c > 0; c < 0; c < 0; c < 0; c > 0; @pa @pb @pc @qa @qb @qc @h @k and

@N*c > 0; @r

ð12Þ

Hence, an increase in the probability of being arrested in the substitute criminal activity leads to a rise in the number of crime offences of types b and c, whereas a rise in pb (the probability to be caught in the complementary crime activity) and pc reduces (increases) the number of offences of types b and c (type a). An increase in the penalty of the substitute activity decreases b k , causing a rise (decrease) of types b and c (a) offences. The opposite occurs when the qb and qc rise. Finally, the rate of return of the substitute crime activity is positively correlated with b k : hence, an increase in the returns of ta displaces the two complementary crime activities b and c, whereas a rise in the returns of b and c activities decrease (increase) the number of criminals involved in type a (b and c) activity(−ies) and the associated number of offences. This economic framework allows one to understand the cross-relationship between different types of crime in the presence of substitute and complementary activities. Precisely, we focus on the cross-effects of the probability of detecting each type of crime on the level of crime activities, namely Na* ; Nb* , and Nc* . Data Description In this paper six crime typologies are employed: the number of recorded attempted or committed intentional homicides (H); the number of recorded robberies, extortions and kidnapping (R); number of receiving—or dealings with—stolen property (e.g. archaeological goods) (RE); number of recorded falsity—such as fraud using altered or false documentation (F); and number of recorded drug crimes (DR). All these variables are defined per 100,000 inhabitants. Table 2 provides detailed definitions of the crime variables used in this study. As further variables, the per capita real GDP, the enforcement for homicides (EH), robberies, extortions and kidnapping (ER), receiving of stolen goods (ERE), falsity (EF) and drug crimes (EDR) are also employed. Quarterly Italian data from the Italian National Institute of Statistics (ISTAT) over the time span 1981:1 to 2004:4, were collected. The empirical analysis has a twofold aim: firstly, to assess for either a substitution or complementary relationship amongst the different crime typologies and, secondly, to pick up possible crowding-out effects between crime and economic growth. Given that one does not impose any a priori belief on the underlying relationship between the crime typologies and does not select a specific subset of variables—as, for example, in Koskela and Viren (1997)—it is possible to employ the largest number of crime typologies according to data availability.

Assessing Substitution and Complementary Effects Table 2 List of crime variables (number of recorder crimes per 100,000 inhabitants) Name

Definition

Homicide

Voluntarily committed homicide

Robberies, extortions and Robberies, extortions and kidnapping kidnapping

Code H R

Receiving

RE A receiving offence is committed when a person who intentionally handles, receives, retains or disposes of stolen goods, knowing or having reasonable grounds to believe they have been stolen

Falsity

F A falsity offence regards counterfeit of credit cards and currency, false seals (e.g. brand counterfeit, falsification of stamps or passports of the state) and falsifying documents (e.g. alteration of official documents and certificates)

Drug

Offence of possession, production and trade of drugs

Deterrence

EH The enforcement variables are measured as the ratio of the number of recorded offences committed by known offenders over the total crime ER recorded per each type of crime; this is a proxy of the police efficiency. ERE The expected sign is negative. EF

DR

EDR H intentional homicides, R robberies, RE receiving/dealing with stolen property, F falsity, DR drug crimes, EH homicide enforcement, ER robbery/extortion/kidnapping enforcement, ERE receiving stolen goods enforcement, EF falsity enforcement, EDR drug-crime enforcement

The variables under study have been transformed into a natural logarithmic specification (L), assuming the existence of a nonlinear relationship. A graphical representation of the moving trend proposed by Hodrick and Prescott> (calculated using Eviews 4.0) helps identify the general trend of each series, as shown in Figs. 1 and 2. An upwards trend characterises receiving (LRE) and falsity (LF), though the latter shows a reverse pattern at the end of the 1990s. LR and LDR depict an upwards trend until the beginning of the 1990s and thereafter show a more stable path of growth. Homicides are characterised by a cyclical pattern, with a peak reached in the second half of the 1980s, and a recrudescent of this crime type occurred in 2000. Looking at Fig. 2, the enforcements for robberies, extortions and kidnapping (LER) and drug crimes (LEDR) show a positive trend, whereas LERE presents a downwards slope. Finally, LEH and LEF depict an inverted U-shaped curve. Main descriptive statistics of the variables used are provided in Table 3.

Empirical Methodology and Results Long-run Elasticities The function under investigation is the following: LGDP ¼ f ðLH; LR; LRE; LF; LDRÞ

ð13Þ

where LGDP, LH, LR, LRE, LF and LDR are the aforementioned variables. Additionally, five exogenous variables are added into the system, one for each crime typology, namely LEH, LER, LERE, LEF, LEDR. It is worthwhile pointing out that these deterrence variables are treated as exogenous. From a preliminary unrestricted equation investigation, it turned

C. Detotto, M. Pulina 0.0

3.6

4.5

-0.2

3.4

4.0

3.2

3.5

3.0

3.0

2.8

2.5

2.6

2.0

2.4

1.5

-0.4 -0.6 -0.8 -1.0

1.0

2.2

-1.2 1985

1990 LH

1995

1985

2000

1990 LR

HPLH

1995

1995

2000

HPLRE

8.6

3.6

4.4

1990 LRE

HPLR

4.0

4.8

1985

2000

8.5

3.2 8.4

4.0 2.8

8.3

3.6 2.4

3.2

8.2

2.0 1.6

2.8 1985

1990 LF

1995 HPLF

2000

8.1 1985

1990 LDR

1995 HPLDR

2000

1985

1990 LGDP

1995

2000

HPLGDP

Fig. 1 General logarithmic (L) trend. LH homicide, LR robberies, LRE receiving/dealing with stolen property, LF falsity, LDR drugs, LGDP Gross Domestic Product, HP Hodrick–Prescott trend

out that the coefficients of these variables at time t were not statistically significant, implying that crime and deterrence do not appear to be simultaneously determined. Lags for the

Fig. 2 General logarithmic (L) trend of enforcement (E). LEH homicide, LER robberies, LERE receiving/ dealing with stolen property, LEF falsity, LEDR drugs, HP Hodrick–Prescott trend

Assessing Substitution and Complementary Effects Table 3 Descriptive statistics of crime variables and GDP Name

Mean

Standard deviation

Minimum

Maximum

H

0.456

0.081

0.307

0.664

R

23.703

5.099

10.351

24.444

RE

25.763

18.082

4.134

64.288

F DR

47.838 23.724

23.341 9.947

18.127 7.125

93.846 36.336

EH

0.120

0.025

0.071

0.166

ER

0.042

0.009

0.061

0.024

ERE

0.110

0.049

0.047

0.205

EF

0.062

0.018

0.032

0.095

EDR

0.065

0.030

0.006

0.126

GDP

4,537.945

580.968

3,562.989

5,343.211

H intentional homicides, R robberies, RE receiving/dealing with stolen property enforcement, F falsity, DR drug crimes, EH homicide enforcement, ER robbery/extortion/kidnapping enforcement, ERE receiving stolen goods enforcement, EF falsity enforcement, EDR drug-crime enforcement, GDP Gross Domestic Product

deterrent variables are hence used at time t-1, mathematically defined as follows: 2 3 LGDPt 2 3 2 i A10 A11 6 LHt 7 k 6 i 6 7 7 X A 6 LRt 7 6 20 7þ 6 A21 6 7¼6 6 LREt 7 4 . . . 5 i¼1 4 . . . 4 LF 5 t A60 Ai61 LDRt 2 þ

Bj11 j 6 B21 4 ... Bj61

k 6 X j¼1

Bj12 Bj22 ... Bj62

t-2, t-3 and t-4. The multivariate system is

2 3 3 LGDPti ... 6 LHti 7 7 76 ... 7 76 6 LRti 7 5 . . . . . . . . . 6 LREti 7 4 LF 5 ti Ai62 . . . Ai66 LDRti 2 3 2 3 LEHti j 3 "1t . . . B15 6 7 LER ti 7 6 6 7 . . . Bj25 7 76 LEREti 7 þ 6 "2t 7 7 4...5 . . . . . . 56 4 LEFti 5 j "6t . . . B65 LEDRti Ai12 Ai22

Ai16 Ai26

ð14Þ

where [A1],…,[Ak] and [B1],…,[Bk] are the 6×6 and 6×5 matrices , respectively, of parameters to be estimated; k is the number of lags considered in the VAR; εt is the 1×6 vector of the disturbance terms that are assumed to be uncorrelated with their own lagged values and uncorrelated with all of the right-hand-side variables. The methodological framework employed to investigate the relationship amongst these variables consists of three steps: The first is to test the order of integration. Table 4 gives the results of the augmented Dickey–Fuller (ADF), the Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) and Phillips–Perron (PP) test statistics. These tests are used to detect the presence of a unit root for the individual time series and their first differences. Overall, all test statistics are congruent and indicate that the series are integrated of order I(1) in the level form but I(0) in their first differences (e.g. Engle and Granger 1987). Nevertheless, there is some discrepancy regarding the order of integration for LR. Application of the ADF test yields the unit root is rejected when applied to its first difference, but there is no evidence when the test is applied to its level. KPSS suggests the series is I(1). Hence, overall, there are grounds to treat LR as stationary in its first difference. Some incongruence is also found for LER and LEF when applying the KPSS, though the ADF and PP suggest for I(1).

C. Detotto, M. Pulina Table 4 Unit roots test on dependent and explanatory variables (sample: 1981:1–2004:4) Variables

Status

ADF

Lags

KPSS

Lags

PP

Lags

LGDP

c,t - I(1)

−1.96

4

0.23***

7

−1.68

5

DLGDP

c,t - I(0)

−4.39***

3

0.07

5

−6.72***

4

LH

c - I(1)

DLH LR

c - I(0) c,t - I(0) or I(1)

−1.74 −17.20*** −3.05**

1

0.12*

0 2

0.08 0.26***

7

−3.88**

4

16 6

−17.70*** −3.88**

1 4

DLR

c - I(0)

−9.82***

1

0.19

2

−14.40

2

LRE

c,t - I(1)

−1.07

6

0.20**

7

−1.05

3

DLRE

c - I(0)

−3.66***

5

0.11

3

−9.88***

3

LF

c - I(1)

−1.13

0

1.15**

7

−1.06

2

−10.90***

c - I(0)

LDR

c,t - I(1)

−1.12

DLDR LEH

c - I(0) c - I(1)

−8.33*** −1.86

2 11 11

0.36

7

−1.95

6

9

0.22

6

−3.50**

2

LEH

c - I(1)

−1.86

DLEH

c - I(0)

−3.17**

0

0.11

2

3

0.25***

7

−10.90***

DLF

0.23 0.36

49 7

−2.77 −15.58*** −1.95

1 3 27 6

LER

c,t - I(1)

−2.37

6

0.18**

7

−2.86

5

DLER

c - I(0)

−4.98***

5

0.16

5

−3.69***

3

LERE

c - I(1)

−1.89

11

0.92***

7

−1.73

DLERE

c - I(0)

−3.00**

11

0.12

4

−3.79**

11

LEF DLEF

c - I(1) c - I(0)

−1.63 −3.44**

11 9

0.31 0.19

7 5

−1.64 −2.77*

5 0

LEDR

c - I(1)

−1.74

4

0.81***

7

−2.07

DLEDR

c - I(0)

−5.05***

5

0.04

2

−3.99***

4

1 10

Number of lags in the ADF test is set upon AIC criterion, whereas KPSS and PP test are set upon Newey– West bandwidth D first-difference operator, L logarithmic, E enforcement, GDP Gross Domestic Product, H intentional homicides, R robberies, extortions and kidnapping, RE receiving—or dealings with—stolen property, F falsity, DR drug crimes, c,t constant and linear trend included upon a trend coefficient statistically significant, ADF augmented Dickey–Fuller, KPSS Kwiatkowski, Phillips, Schmidt, and Shin, PP Phillips–Perron, AIC Akaike Information Criteria ***, ** indicate statistical significance at the 1 % and 5 % levels, respectively

Given the unit root results, the second step is to use the VAR approach that Johansen (1988) and Johansen and Juselius (1990) implemented to investigate the existence of a common long-run equilibrium amongst I(1) variables. The joint F test and the Akaike (AIC), Schwartz (SC) and Hannan–Quinn (HQ) Information Criteria are used to select the number of lags required in the unrestricted VAR to ensure that residuals are white noise. The F-test and the information criteria suggest a four-lag system (e.g. Garratt et al. 2003). The cointegration test results are presented in Table 5. The maximum likelihood (max) suggests at least a single significant cointegrating vector. Hence, there is empirical evidence that all variables are cointegrated and related in each model. Table 6 reports long-run elasticities calculated from the Johansen cointegration analysis. These figures shed light on co-movements amongst the different crime typologies, as well as the possible crowding-out effects on the Italian economy (i.e. on LGDP). As far as the

Assessing Substitution and Complementary Effects Table 5 Johansen cointegration trace test LGDP, LH, LR, LRE, LF, LDR sample: 1981:1–2004:4–4 lags - constant H0:rank