The uneven but non-random distribution of crime rate over space has been observed for a long time. Social scientists have developed different theories and techniques to explain such phenomenon. Anselin et al. (2000) has given a relatively comprehensive review on relevant theories methodologies. As summarized in their article, early sociological theories investigating the relationship between place and crime can be traced back to the middle of the 19th century: Guerry (1833, cited in Anselin et al.
2000) and Quetelet (1833, 1842, cited in Anselin et al. 2000), when they attempted to explain the differences in community crime levels with the social conditions of the resident population. Later on, such research made remarkable progress in the early 20th century thanks to the enormous contribution of the Chicago School. They obtained the record of each juvenile offender with their age, sex and home address and plotted on a map of Chicago. Based on the distribution of these juvenile offenses, Shaw and Mckay (1942) found a negative relationship between juvenile crime and the distance from central business districts.
More recent researches on crime distribution over space have greatly benefited from the invention of the Geographic Information Systems (GIS), which have made computerized mapping and spatial statistics possible. Adopting this technique, Curry and Spergel (1988) has found that delinquency is strongly correlated with poverty, while gang homicide, however, is predicted by the ethnic-race composition of local
community based on the data from the U.S. Cohen et al. (1998) has also utilized the GIS system and investigated the distribution of gangs. They found that gangs are normally concentrated in neighbourhoods dominated by ethnic minorities. In addition, the “underclass”, such as living in poverty and being unemployed, have also been positively correlated with gang activities.
Large proportion of papers analysing the distribution of crime rate have all, by some extend, benefited from two broadly cited theories, namely the routine activity theory and the social disorganization theory. The routine activity theory was initially developed in Cohen and Felson (1979) and later refined in Felson (1986, 1994).
Brantingham and Brantingham (1993) have extended this theory to explain the distribution of crime. Instead of emphasizing the characteristics of offenders, this theory focuses on the circumstances in which they commit crimes. It argues that each successful offense requires the convergence in both time and space dimensions of three minimal elements: 1) an offender with both the intention to violate the law and the ability to carry out such action; 2) a person or object providing a suitable target;
and 3) the absence of guardians capable to prevent such violation. Accordingly, the probability that an offense will occur at any specific time and place should be a function of the convergence of the three necessary elements. Any social conditions that affect the convergence of the three basic elements could possibly explain the variations in crime rate.
Place is essential in this theory in two ways. First, the physical features of a place can reduce the supervision effect that pedestrians could have. Newman (1972) has offered an example of this type. Public housings can increase population density in a building
which could provide guardians against illegal activities, as the probabilities of people watching each others’ back is higher in high-intensity estates. At the same time, however, because people are living vertically in public housings, such distribution can actually reduce the monitoring effect on each floor and weaken the informal social control among neighbours. Second, criminal activities are more likely to take place in target-rich environment. For example, thefts in a shopping mall, auto thefts from a large car park, or robberies in concentrated commercial areas (e.g. Engstad 1975;
Brantingham and Brantingham 1982). In addition, certain activities such as alcohol consumption seem to be positively correlated with violent crimes (Roncek and Bell 1981); and abandoned buildings could attract illegal drug dealers. Based on the routine activity theory, therefore, it is not surprising that crime rate is not randomly distributed over space and certain crime types of crime tend to concentrate on certain places, namely crime hot spots.
The social disorganization theory is another one trying to explain the relationship between crimes and their occurring locations. It was developed in Shaw and McKay (1942), as they were attempting to establish a positive relationship between delinquency and the communities unable to conform to common values and to solve problems for the residents. The paper argues that delinquency is not a unique response of unique individuals; it is normal reaction by normal individuals to abnormal conditions. If a community cannot provide adequate protection for its residents and their properties and has to depend on outside agencies, some individuals will take the opportunity to conduct illegal activities at their will. In their empirical analysis, Shaw and McKay tried to explain the level delinquency rate with community-level economic conditions, ethnic heterogeneity and population turnover. Such
explanatory factors are incorporated in hope to capture the instability and insecurity of communal environment. Their analysis proposes a spatial distribution pattern that juvenile delinquency rate is highest in inner-city areas and is decreasing with the distance away from city centre. As the analysis was carried out for the period of 1900-1933, large number of immigrants entered United States during that time and urban areas were the only places they could afford to live. Such fact implies that higher degrees of residential instability, ethnic diversity and social-economic deprivation are positively associated with the degree of urbanization and, hence, positively correlated with delinquency rate. Additionally, within inner-city areas, the probability of becoming an offender is associated with one’s interpersonal network involving his family, gangs, and the neighbourhood. Finally, the degree of social and economic deprivation, population turnover and ethnic heterogeneity are all associated with social disorganization and hence, with crime.
The social disorganization theory has been followed by many latter papers. The degree of social disorganization is normally represented by five factors, namely, demographic, economic, social, family disruption and urbanization. Each of these factors can be measured by specific variables. For examples, economic status can be measured by various income levels; demographic conditions can be measured by the ethnic composition; family disruption can be measured by the percentage of single parent family; urbanization can be measured by population density and so on. Harries (1995) has found that poverty provides the strongest explanatory power for crime.
Cahill and Mulligan (2003) has used ethnic composition, education, population density and other variables to measure the degree of social disorganization and tested their effects on violent crime. The results are generally consistent with expectation
that higher degree of social disorganization is positively correlated with crime rate.
One exception is that the population density does not exhibit significant effect as expected.
One common feature shared by the routine activity theory and the social disorganization theory is that they both attempt to explain the spatial variations in crime rates. More specifically, they seek to answer why the crime rates of certain areas are persistently higher than other areas? Instead of studying the behaviour of offenders, both theories focus on the characteristics of crime-prone locations. The aforementioned assumption by panel data analysis is that the crime rates of different areas are affected by specific features of those areas, but are independent from the features of neighbouring areas. Whereas, according to arguments presented above, crime rates could have spill-over effect across neighbouring areas. The crime rate of one area should, therefore, be affected by not only local relevant factors, but also such factors of neighbouring areas as well as neighbouring crime rates.
Fabrikant (1979) has developed a theoretical model which aims to derive an optimal allocation of police manpower when taking into consideration the possible spill-over effect of crime rate between neighbouring communities. This paper was motivated by two opposite opinions. On the one hand, Gylys (1974) suggests that “the residents of each political area have a positive marginal rate of substitution between another area’s consumption of police services and the goods that it consumes itself”. In other words, an increase in the police manpower in one area will not only reduce the local crime level, but also benefit the neighbouring areas. On the other hand, Press (1970) and Mehay (1977) oppose Gylys’s argument by providing empirical analyses suggesting
that the increased law enforcement personnel in one area motivate criminals to spill over into adjacent areas. Having considered the opinions from both sides, Fabrikant (1979) tries to establish a theoretical model that is able to explicitly derive the effect of increased police manpower in one area on the crime rates of neighbouring areas.
The theoretical framework is constructed by incorporating the criminal spill-over effect into the theory of rational choice as developed in Becker (1968) and Ehrlich (1973). Potential criminals are assumed to be economically rational and attempt to maximize their expected utilities subject to their constraints. Thus, by allowing for people to commit crimes in both “home” and neighbouring areas, potential criminals will evaluate the expected punishment (subject to the probabilities of detection, conviction and imprisonment) and potential gain of illegal activities from not only the
“home” area, but also evaluate these factors for neighbouring areas. Additionally, they need to evaluate the cost of travel in committing crimes in neighbouring areas.
Potential criminals will be motivated to commit crimes in neighbouring areas by the expected gain over what they can get in their own areas, net the travelling cost and relative risk of committing crimes in neighbouring areas. The criminal spill-over equation between communities i and j can be derived by solving a system of supply-of-offenses and demand-for-control equations and expressed by the following function.41
(5.1) The dependent variable is the aggregated number of offenses committed in community j by offenders residing in community i. The independent variable represents the costs of committing crimes in community j when the
offenders are residing in community i. Such costs include the travel expenses and the time spent on travelling and carrying out the offenses. As it is difficult to exactly measure , it can be approximated by the distance the offender has to travel.
represents the ratio between the potential gain from committing crimes in community j and that from committing crimes in community i. This variable measures how attractive committing crimes in community j is when the offenders are living in community i. is defined as the ratio between and which represent the clear-up rates in community j and i respectively. For someone living in community i, higher ratio represents relatively greater risk of getting detected in community j which will be less attractive as a result. The last independent variable is represented by the ratio between the number of potential offenses in community j and that in community i and measuring the relative competition pressure between communities j and i. The rationale is that higher number of potential offenses in a given community implies more fierce competition between offenders and thus lower marginal gain for an additional offense. When the competition pressure is higher in community j relative to that in community i, committing offenses in community j becomes less attractive with other variables being equal.
Given the definitions of the independent variables, their associations with aggregated offenses committed in community j by offenders from community i can be derived accordingly.
, , and .
The above relationships suggest that the number of offenses spilling over to a
spillovers of offenses into a neighbouring area is negatively correlated with the travelling expenditure (usually measured by travelling distance), positively correlated with the relative potential gain from neighbouring area, negatively correlated with the relative risk of detection of neighbouring area, and negatively correlated with the relative competition pressure (measured by the number of potential offenses) of neighbouring area.