This study analyzes the effect of income on repeat criminal victimization in Brazil using data from the 2009 National Household Sample Survey and its special supplement on victimization and access to justice. Two count-data models were estimated for four types of crime: theft, robbery, attempted theft/robbery, and physical assault. A positive nonlinear effect of income on repeat victimization for the three types of property crimes and a negative nonlinear effect of income on physical assault were observed.

Analisamos o efeito da renda na vitimização criminal repetida utilizando dados da PNAD 2009 e do seu suplemento especial sobre vitimização e acesso à justiça no Brasil. Foram estimados dois modelos de dados de contagem para quatro tipos de crime: furto, roubo, tentativa de furto/roubo e agressão física. Concluímos que há uma relação não-linear positiva entre renda e vitimização repetida para crimes contra a propriedade, e uma relação não-linear negativa para agressão física.

In the criminal universe, phenomena rarely follow a normal distribution. It is rather a universe governed by “concentrations.” A small part of the territory tends to accumulate a large proportion of crime (hot spots). A small number of criminals tend to commit a disproportionate amount of crime (predators). Victimization also follows this trend, considering that a small group of victims is usually the preferred target of a disproportionate amount of offenders.

Situational criminology suggests that these concentrations are explained by a combination of excessive risk factors and the absence of protective factors. Unmonitored areas with intense circulation of people and goods, low visibility, and signs of disorder become more attractive for crime. Low-weight infants living in homes with unmarried teenage mothers and children raised by lone parents or who drop out of school early are more likely to become criminals. Unmarried young people, who often tend to leave their home unguarded, to consume alcohol, and to be careless with their fancy cell phones are preferred prey for criminals.

From the standpoint of public crime prevention policies, these concentrations are advantageous, as they make it possible for resources to be allocated to areas and populations at risk through focused interventions, reducing risk factors and increasing protective factors. Hot spots that are appropriately identified can be more protected by police or cameras, better lighting, better cleaning services. Tertiary prevention programs – designed for people already involved with the criminal justice system – can focus on strengthening educational and therapeutic treatments for young offenders. Police departments can develop courses, booklets and guidelines on preventive measures that could be taken by owners of establishments that are attacked often. The problem is that it is difficult, or even impossible, to change many risk factors. You can improve the surveillance of an area, but a central shopping promenade might be always used for the same purposes and activities, implying risk. You can improve the employability of young offenders, but you cannot modify their age, gender, IQ, or their past involvement in crime. Victims can change risk behaviors and install security equipment, but there are intrinsic characteristics related to location, lifestyle, and architectural design, among others, which cannot be modified. That is why increasing the number of protective factors can shift some crimes to other areas or victims, but some of them will inevitably remain concentrated in the same locations and targets.

Many previous studies analyzed why some locations are more attractive to criminals than others and why certain types of crimes tend to concentrate in other locations ( Tseloni et al., 2003 and Tseloni et al., 2004 ), while other studies investigated risk factors associated with the criminal history of repeat offenders. Very little has been written, however, about the phenomenon of repeat victimization (being victim of more than one crime of the same type). Which variables could help us understand why victimization mainly affects a small percentage of victims, even though it is a relatively rare phenomenon?

Repeat victimization has some known characteristics. Most people are not victimized at all, but those who are remain at a high risk of being victimized again. Thus, prior victimization is one of the best indicators of future victimization. Moreover, recurrence can be rapid. In repeat victimization, the same type of criminal incident is experienced by the same victim or target within a specific period of time, as within a year, for example. Thus, repeat victimization refers to the total amount of offenses experienced by a victim or target, including the initial offense and subsequent ones.

Previous evidence of the causes of repeat victimization in Brazil was uniquely found by Carvalho and Lavor (2008) using data from a national survey carried out in 1988. The focus of their study was particularly on the effect of income inequality on property crime (composed of theft and robbery). Our study is focused on empirical advances in the modeling of causes of repeat victimization. In particular, the main objective of this paper is analyzing the effect of income on repeat criminal victimization by types of crime from an economic perspective.

Victimization is a complex process and, consequently, one that is difficult to be modeled empirically. There is no single well-structured theory to guide empirical analyses in this field. Studies have usually been based on two approaches that consider victims as objects of study, highlighting the importance of their “lifestyle” and the creation of “opportunities” for criminals to commit their crimes. Empirical analyses have been mainly based on the theoretical framework proposed by Cohen et al. (1981) . Using data from some previous studies, these authors expanded and formalized a sociological theory (which they refer to as the “opportunity model of predatory victimization”) to explain victimization risk. According to this approach, there are five factors strongly related to risk: exposure, proximity, guardianship, target attractiveness, and definitional proprieties of specific crimes.

Some factors with a bearing on repeat victimization can have a different effect according to the type of crime in question, especially if the nature of the crime is considered, i.e. property crimes or crimes against a person. In particular, income is widely debated in the literature. We are accustomed to associating crime with poverty, which is true in connection with homicides and other violent crimes against a person. Thus, a negative relationship between income and victimization is plausible. In the case of property crimes, however, its effect is ambiguous. On the one hand, higher income reduces the propensity to engage in crime, but on the other it produces more attractive targets, as property crimes are primarily crimes of opportunity. The higher the income, the more goods a victim has, the greater the criminal opportunities. But this relationship is not necessarily linear: low-income individuals or places are less attractive, but after a certain threshold a higher income tends to lead to the adoption of more defensive measures against crime through strategies and equipment designed to “block opportunities,” such as video cameras, alarms, and security devices. In short, wealthier individuals are on the one hand more economically attractive to criminals, but on the other they have stronger reasons and more money to spend on their own security, especially after being victimized for the first time. Therefore, the effect of income on repeat victimization is ambiguous, but its net effect can be observed empirically.

We believe that the sociological approach cited above is also helpful as a framework to understand the process of repeat victimization, i.e. why some people are victims of the same type of crime two or more times. Our analysis is also based on a simple victimization model proposed by Gaviria and Pagés (2002) , where an individual's wealth is the focus. In particular, the hypotheses tested here are: (i) income has a positive nonlinear effect on the number of times an individual was victimized by property crimes, and (ii) income has a negative nonlinear effect on crimes against a person.

The main improvements made here in relation to the previous empirical study are the following ones: the most recent victimization data from a nationwide sample survey carried out in Brazil were used; estimations for four types of crimes (theft, robbery, attempted theft/robbery, physical assault) were performed separately. We emphasize that physical assault is an aggravated physical aggression against a person and the three other crime types are property crimes; and the design of complex surveys was taken into account, since the actual variance tends to be underestimated when the sample design is ignored.

The next section presents a brief description of a useful theoretical framework for discussing the effect of income on repeat victimization. Section 3 provides details about the empirical modeling, while results are discussed in Section 4 . Concluding remarks are presented in Section 5 .

Gaviria and Pagés (2002) proposed a simple victimization model that, together with the approach proposed by Cohen et al. (1981) , is very useful for the empirical modeling that we will do in the next section and for understanding the results presented in Section 4 .