Economics Letters 79 (2003) 291–298 www.elsevier.com / locate / econbase

Dynamic interactions between crimes Patricia Funk, Peter Kugler* Department of Economics, University of Basel ( WWZ), Petersgraben 51, Basel 4003, Switzerland Received 14 September 2001; received in revised form 23 October 2002; accepted 28 October 2002

Abstract This paper investigates dynamic interrelationships between crimes of different severity. With Swiss quarterly time series data we find that an increase in minor crimes dynamically triggers more severe crimes without the reverse being true. As far as enforcement is concerned, a tougher enforcement of mild offenses not only reduces minor crimes, but also dynamically deters more severe offenses, as claimed by the ‘broken-windows-theory’.  2003 Elsevier Science B.V. All rights reserved. Keywords: Dynamics between crimes; Broken windows theory; Crime policy JEL classification: C32; K42

1. Introduction The economic model of crime posits that criminals react to changes in incentives, such as governmental deterrence or legal and illegal earning opportunities (Becker, 1968). As for the empirical support of the economic model of crime, it seems that favourable labour market conditions and harsher governmental deterrence indeed have a negative impact on crime.1 While empirical research focused on explaining different types of crimes independently of each other, hardly any attention has been directed to the interrelationships between the different crimes. By contrast, recent crime policy in America has been enormously influenced by Wilson and Kelling’s (1982) ‘broken windows’-article, which describes interrelationships between different types of crimes. Wilson and Kelling’s vision behind the evolution of crime is one of a broken window, which—if left unrepaired—causes the other windows to be broken soon. As far as crimes of different * Corresponding author. Tel.: 141-61-260-1264; fax: 141-61-260-1266. E-mail addresses: [email protected] (P. Funk), [email protected] (P. Kugler). 1 See Levitt (2001) for an overview of the literature on deterrence and Grogger (1998) and Raphael and Winter-Ebmer (2001) for recent studies on the impact of labour market conditions on crime. 0165-1765 / 03 / $ – see front matter  2003 Elsevier Science B.V. All rights reserved. doi:10.1016 / S0165-1765(03)00002-8

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severity are concerned, it is claimed that an increase in disorder and minor crimes (unless sharply checked) sends a signal that ‘no one cares’ and thereby creates an environment conducive for more severe crimes to occur (‘broken windows theory’). The broken windows theory calls for a crime policy which places more weight on fighting disorder and minor crimes, because thereby, an environment that would encourage more severe crimes can be avoided. In the early 1990s, New York’s police department began to implement such a policy by combating misdemeanors and minor crimes with ‘zero tolerance’. Other American states followed and even Europe has been affected by the ‘broken windows theory’ and the therefrom derived ‘zerotolerance-strategy’ (see e.g. the guideline of CDU’s crime policy, one of the major German political parties (www.cdu.de / politik)). The general support of this new crime-policing paradigm is astonishing in view of the fact that it is based on very weak empirical grounds (Harcourt, 2001). Wilson and Kelling (1982) originally supported their ‘theory’ by a single experiment (conducted by Zimbardo, 1973), which showed that an automobile without a license plate (‘broken window’) was quicker attacked by some vandals than the same car with a license plate in a region with similar crime. It took nearly two decades until the relationships between disorder and crime were examined in a more systematic way (Skogan, 1988). By regressing various crimes (like theft, rape, robbery etc.) on contemporaneous variables of social disorder (public drinking, vandalism, gang activity etc.), Skogan (1988) was able to detect a positive impact of social disorder on robbery crimes committed. However, his regression estimates turned out to be sensitive to the omission of variables accounting for both, disorder and crime (Harcourt, 1998). Furthermore, Skogan’s study does not necessarily test the broken-windows-theory, because the theory postulates a dynamic (and not static) relationship between disorder / misdemeanors and (more severe) crimes. In this paper, we for the first time investigate dynamic interrelationships between crimes of different severity. With a time-series analysis of Swiss quarterly crime data (from 1984–1998), we are able to provide a rigorous test of whether an increase in minor crimes dynamically fosters the occurrence of more severe crimes, as postulated by the broken windows theory.

2. Data and econometric model The range of offenses we consider are larceny-theft, burglary and robbery. Since in Switzerland, economic conditions as well as the political situation in foreign (mostly East-European) countries seem to account for the trend in the offenses, we incorporate the number of unemployed, the average hourly real wage, per capita income as well as the number of persons applying for political asylum as exogenous variables (see Appendix A for a visual inspection of the series). A formal test (Johansen Cointegration Test) confirms that the offenses are indeed cointegrated with these exogenous variables. From the cointegrating vectors (see Appendix B), it can be seen that there exists the following long-run relationship between economic conditions and crime: a favourable economic environment (low unemployment and high wages) tends to lower crime, whereas an increase in the number of asylum seekers and an increase in per-capita income exerts a positive effect on the amount of property crime committed.

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Since we are primarily interested in the dynamic interrelationships between the offenses and their enforcement, we estimate a partial VAR of the following type:

Ob K

Oit 5 ai 1

k 51

iik ? Oit 2k 1

O Ob K

ijk ? Ojt2k 1

j, j ±i k 51

O d ? EM 1 O z K

K

ik

k51

t2k

k 51

Og ? A 4

ik ? ES t2k 1

in

nt

1 eit ,

n51

(1) with E(e ) 5 0, E(ee 9) 5V and i 5 1 . . . 3. Oi denotes the (per capita) number of an offense i, which depends on the lagged number of the own offense i, the lagged number of the two other offenses committed as well as two enforcement measures. We approximate the harshness of enforcement of milder crimes (EM) by the conviction rate for theft offenses (including burglary) and the harshness of enforcement of more severe crimes (ES) by the conviction rate for robbery.2 A 1 to A 4 denote the four exogenous variables asylum, unemployment, real wage and per capita income; all variables are in logs. Since we observed quite a distinctive seasonality for most variables, we seasonally adjusted them by the census 311 method. Finally, K is set to 2, which is optimal according to the Akaike Criterion.

3. Results We content ourselves with the discussion of the most relevant impulse response functions, which can be obtained from the VAR-estimates by placing enough restrictions e.g. on the contemporaneous relationships between the endogenous variables. We employ the frequently used Choleski-Decomposition, which describes the contemporaneous relationships between the endogenous variables by a lower triangular matrix (see Sims, 1980). However, our results are driven by the dynamics of the system rather than our identifying assumptions; the impulse response functions look similar for all possible orderings of the variables in the Choleski matrix (the different graphs are available upon request). Furthermore, due to the relatively small sample size, we compute the standard errors by Monte Carlo simulations, since the standard errors derived from asymptotic distributions may be downward biased. Fig. 1 depicts the dynamic interactions between the crimes. As can be seen from column 1, there are highly significant dynamic effects of a shock in the less severe crime theft on the more severe crimes burglary and robbery (pictures with bold frame). Note further that we do not observe any similar strong and significant effects from the ‘severe’ offenses burglary and robbery on theft offenses (only for burglary, we observe a minor positive impact on theft). As such, there seems to exist a progression from mild offenses to more severe offenses without the reverse being true.3 As far as crime policy is concerned, Fig. 1 reveals that being tougher on milder crimes not only 2

The conviction rate is calculated as the number of convictions divided by the number of offenses committed. A look at the variance decomposition further reveals that the impact of a (one standard deviation) shock from minor offenses on more severe offenses is substantial. Shocks from theft offenses explain roughly 40% of the burglary’s and robbery’s variance of forecast error. On the contrary, only a small proportion of the variance of the theft’s forecast error can be explained by burglary and robbery shocks. 3

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Fig. 1. Estimation results.

deters minor offenses but dynamically reduces more severe crimes as well (see bold picture last column).

4. Discussion In this study, we investigated dynamic interrelationships between crimes of different severity. Our estimation results show that a shock in the minor crime theft triggers a substantial increase in subsequent more severe crimes like burglary and robbery. A similar effect from severe to mild crimes cannot be observed. As for the impact of law enforcement, we find that harsher prosecution of minor crimes not only deters mild offenders, but also reduces later occurrence of more severe crimes.

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Our results clearly confirm that there are important dynamic relationships of the kind postulated by the broken-windows-theory. However, the observed evolution from mild to severe offenses could equally reflect a life-cycle pattern of criminal careers, where a shock in mild offenses goes along with an increase in the number of ‘beginners’, who start committing mild crimes and later move on to more severe crimes (e.g. due to ‘learning-by-doing’). These life-cycle effects can best be disentangled from broken-windows effects by looking at the coefficient estimates of the partial VAR (see Eq. (1)). For instance, if an increase in mild offenses results in more intense prosecution and a proportional increase in the convictions for these crimes (so that the conviction rate remains constant), the signal that ‘no one cares’ seems to be weak and the broken-windows-theory does not necessarily predict a later increase in potentially more severe crimes. The estimated coefficients of the partial VAR with endogenous variables theft, burglary, robbery, conviction rate theft and conviction rate robbery (see Appendix C), show that: • an increase in theft offenses has a positive impact on later robbery offenses even if enforcement of mild offenses is controlled for (see bold values last column, first two rows). This result indicates that an evolution from mild offenses to severe offenses occurs independent of a varying degree of enforcement activity (or objective signal that ‘no one cares’), which seems to be compatible with the life-cycle-theory; • an increase in the enforcement activity for mild offenses has a crime-reducing impact on subsequent severe offenses even if the level of mild offenses (as well as enforcement of severe offenses) is controlled for (bold values last column, rows seven and eight). This effect can hardly be explained by the life-cycle-hypothesis, because the life-cycle-hypothesis predicts no impact of harsher enforcement of minor crimes on severe crimes if not by a changed level of mild offenses. However, it corresponds to the broken-windows claim after which a strong signal of keeping order and being tough on misdemeanors and minor crimes inhibits an environment conducive for more severe offenses to occur. It seems that an increase in minor crimes dynamically triggers more severe crimes not only due to an increased signal of being tolerant of crime (broken windows theory), but also due to other mechanisms such as possibly life-cycle patterns of criminal careers. However, our main result that there is an evolution from mild to severe offenses (without the reverse being true) is interesting per se, irrespective of the exact underlying cause. Important policy implications remain in any case: a crime policy succeeding in deterring mild offenses holds an additional benefit in the form of dynamically reducing more severe crimes as well.

Acknowledgements We would like to thank various participants of the 2001 annual conference of the Swiss Society of Economics and Statistics in Geneva as well as an anonymous referee for helpful comments. Financial support of the Swiss National Science Foundation is gratefully acknowledged.

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Appendix A. Graph of the series (in logs)

Note: theft and burglary offenses are measured per 1000 inhabitants, robbery offenses per 100,000 inhabitants. Asylum corresponds to the total number of requests for political asylum and unemployment to the total number of people asking for unemployment benefits. Income reflects real per capita income (in million Swiss Francs) and wage stands for the average hourly real wage. EM and ES reflect the enforcement measures defined as follows: enforcement mild offenses (EM)4 5(number of convictions for theft or burglary) /(number of theft and burglary offenses committed), enforcement severe offenses (ES)5(number of robbery convictions) /(number of robbery offenses committed). All the series are in logs. Appendix B. The cointegrating vectors We tested the exogenous variables with respect to cointegration with the different crimes. The 4

There is a change in the registration of convictions for mild offenses after the beginning of 1995. Accounting for this structural break doesn’t alter the results.

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Johansen Cointegration test points to one cointegrating vector between the three crimes and the exogenous variables. The values of the cointegrating vectors are the following (standard errors in parentheses). For: theft, unemployment, asylum, per-capita income, real wage:

b 5 [1, 2 0.12 (0.02), 2 0.15 (0.03), 2 2.6 (0.85), 7.1 (0.9)] For: burglary, unemployment, asylum, per-capita income, real wage:

b 5 [1, 2 0.19 (0.02), 2 0.13 (0.04), 2 3.6 (0.98), 8.01 (1.08)] For: robbery, unemployment, asylum, per-capita income, real wage:

b 5 [1, 2 0.29 (0.07), 2 0.27 (0.03), 2 4.9 (1.6), 9.7 (1.66)]

Appendix C Coefficient estimates of the reduced form VAR

Theft (21) Theft (22) Burglary (21) Burglary (22) Robbery (21) Robbery (22) Conviction rate theft (21) Conviction rate theft (22) Conviction rate robbery (21) Conviction rate robbery (22)

Theft

Burglary

Robbery

0.56 (0.2) 20.33 (0.19) 0.39 (0.16) 20.04 (0.13) 20.07 (0.08) 0.16 (0.08) 0.03 (0.12) 20.13 (0.13) 20.02 (0.04) 0.02 (0.05)

0.53 (0.21) 20.2 (0.2) 0.2 (0.17) 0.29 (0.14) 20.15 (0.09) 20.009 (0.09) 20.07 (0.12) 20.07 (0.14) 20.03 (0.04) 20.02 (0.05)

1.03 (0.33) 0.33 (0.3) 0.14 (0.27) 21.02 (0.22) 0.34 (0.13) 0.42 (0.14) 20.28 (0.19) 20.65 (0.21) 0.3 (0.07) 0.03 (0.08)

Note: standard errors in parentheses, exogenous variables not listed.

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