Introduction

Cargo theft is one of the major concerns of logistics systems worldwide in that it is costly to businesses and economies either directly through shrinkage (Bailey 2006) or indirectly through the cost of prevention measures and/or insurance (Alstete 2006), which may be swift in crippling small and medium businesses.

In the year 2019 alone, the median value of economic losses due to cargo theft ranges from $100,000 in South America to about $11,000 in Asia (BSI 2020). Such cost is internalized by businesses and compensated in the price paid by final consumers in the legal market, thus, distorting market conditions – reduced supply of goods due to shrinkage; increased cost due to crime prevention measures, and, consequently; higher price to final consumers in the legal market, whereas different prices are practiced in the black market (Bailey 2006; Guthrie and Guthrie 2006; Burges 2012; Johns and Hayes 2003). Besides direct economic costs, cargo theft also spawns indirect costs which are often many times higher compared to the direct costs (U.S. General Accounting Office 1980). Moreover, in certain regions, cargo thefts are very lethal crimes committed by fierce criminal organizations that resort to the use of heavy weapons, violence and, occasionally, the kidnap or death of innocent truck drivers (Oliveira and Martins 2014; Justus et al. 2018; BSI 2018).

There is unanimous evidence in the literature that the supply chain of cargos transported by trucks is the most disrupted compared to other freights worldwide and that a majority of these crimes happen in-transit (Burges 2012; Ekwall and Lantz 2015; SCIC 2018; BSI 2020). The literature is also in consensus that cargo theft is essentially economically motivated since the target is mostly products that are stolen from trucks, distributed, and sold through illegal channels to transform them into money (Burges 2012). These products are defined as hot products because they are CRAVED – concealable, removable, available, enjoyable, and disposable – especially in the black market (Clarke and Webb 1999; Burges 2012). In some cases, stolen products return to the legal market through flea markets, pawnshops, or second-hand stores (Johns and Hayes 2003). Apart from economic attractiveness, which is the major cause of cargo theft, the criminological literature suggests that locational opportunities are crucial to cargo thefts, whereby locations with a higher circulation of cargos tend to have higher cargo thefts and theft locations tend not to be randomly distributed (Tobler 1970; Cohen and Felson 1979). The situational approach also suggests that social flaws and structures such as, for example, unemployment and inequality create potential criminals (Merton 1938) who can be deterred by proper guardianship or policing (Becker 1968; Cohen and Felson 1979).

The main objective of this study is to provide empirical evidence on some causes of cargo theft, addressing geographical, economic, social structure, and deterrence factors. Specifically, the space-time dynamic of cargo theft is identified; the role of economic attractiveness on cargo theft is investigated using market factors such as sales and prices; the role of the unemployment rate (a proxy for social flaw and structure) on cargo theft is assessed, and, last but not least important; the effect of policing (a proxy for deterrence) on cargo theft is identified. The hypotheses put forward regarding these objectives are

  • H1: space-time dynamics hypothesis – cargo thefts are intertwined across locations and proximity influences spatial links;

  • H2: economic attractiveness hypothesis –higher sales and prices in the legal market increases cargo theft;

  • H3: social structure hypothesis – a higher unemployment rate increases cargo theft, and;

  • H4: deterrence hypothesis – a greater presence of police on the streets reduces cargo theft.

These hypotheses have been tested regarding other crimes such as robbery, theft, and homicide rates but the empirical evidence regarding cargo theft is still modest in the literature. This study resorts to the Brazilian context to test these hypotheses because this modality of crime is most severe in South America (BSI 2018; SCIC 2018), whereby Brazil takes the lead with about 22.200 incidences in the year 2018 alone, incurring a loss of about 1.47 billion reais (R$) to the economy (NTC and Logistics 2019). About 85% of these occurrences were registered in the Southeast of the country, where the states of São Paulo and Rio de Janeiro were responsible for about 39% and 41%, respectively. This position and the reliability and completeness of the database on cargo theft in São Paulo makes this state a relevant case to the national and international literature on the topic.

São Paulo is the richest Brazilian state and has the largest commercial and industrial center in South America. This state is responsible for about one-third of the Brazilian GDP and is leading in terms of the consumer market, infrastructure, human capital, population size, etc (IBGE 2018). Apart from the exceptional road quality, this state also bears locational advantage to businesses for having the largest and most modern port (Harbor of Santos) and the largest cargo terminal which receives and dispatches international cargo (Justus et al. 2018). The economic and geographic relevance of São Paulo state is what makes it an attractive location for cargo theft and also a relevant case study to the literature on the topic.

The geography of São Paulo state is divided into 645 municipalities, which is classified into three groups in this study following Justus et al. (2018), namely, the capital São Paulo, the great São Paulo (GSP), i.e., the large metropolitan area excluding the capital, and the inland municipalities that are the non-metropolitan areas (Fig. 1).

Fig. 1
figure 1

The geography of São Paulo state. Source: Elaborated by the authors

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Cargo theft is expected to naturally correlate in geographic space following the flow of cargos from one location to another. This technically implies that cargo theft series of a location is expected to cointegrate with that of other locations, respecting Tobler's first law of geography – "everything is related to everything else, but near things are more related than distant things." (Tobler 1970). Judging by the geography of São Paulo state (Fig. 1), cargo theft of the Capital is expected to be more correlated with that of the GSP, and this should be more correlated with that of inland municipalities.

Given the understanding that cargo theft is essentially economically motivated, the inflation and sales indexes are tested as economic predictors of the rate of cargo theft. The price indicator (inflation index) is considered a potential predictor of cargo theft since it is directly reflected in the value of the transported products and, consequently, the perceived reward by cargo thieves. Cargos are stolen, especially, to be transformed into money through sales (Burges 2012). Therefore, the demand for products in the trade sector is a potential predictor of how “hot” products are both in the legal and illegal market. For this reason, indexes for the volume and revenue from sales of the trade sector are included in the empirical model. Since some cargos are, in many cases, stolen together with trucks (Ceccato 2015; Justus et al. 2018) this control was further specified by including indexes for the volume and revenue from the sales of vehicles and automobile parts.

The rate of unemployment is tested as a social structural determinant of crime as suggested by Merton (1938) and as a seasonal predictor of property crimes as suggested by Falk (1952). Besides, unemployment is also a proxy indicator of the level of deprivation in the state.

Police activity is the major law enforcement measure adopted in fighting crime. Justus and Kassouf (2013) used the quarterly data on searches or identification of persons as an indirect measure of police activity. However, unlike homicide rates and robbery aggravated by death that have quarterly data since the mids 1990s, quarterly data on cargo theft are only available from the year 2005 and, consequently, the sample size is not as desirable for time series analysis. Therefore, this study resort to another police activity measure that reflects the indirect activity of the police and also the outcome – police apprehension in the act. This measure combines the number of offenders pursued by the police or caught practicing any criminal offense with or without violence or serious threat.

This study is structured into six sections. Following this introductory section, Section 2 presents the theoretical background and Section 3 presents the structure of the model and empirical tests and specifications. The results obtained from the models are presented in Section 4 and discussed in Section 5 and Section 6 concludes the study.

Theoretical background

The causes of cargo theft, like other thefts, are mostly explained by using the modern versions of the classical criminological theories: rationality, deterrence, and criminological economics theories as classified by Rasche (1998). From the perspective of these theories, cargo theft happens due to human rational choices which could be persuaded either by changing the decision-making factors or consequences of the crime in terms of punishment.

Rational choice is the essence of the criminological economic theory proposed by Becker (1968), whereby crime becomes attractive if the reward from an offense exceeds the cost of committing it and the rewards from alternative sources. Also drawing from the rational choice perspective, the routine activity theory proposed by Cohen and Felson (1979) explains that crime is an aftermath of the intersection of a motivated offender, a motivated target (e.g., cargo), and the absence of a capable guardian. Both the criminological economic and routine activity theories acknowledge the possibility of crime prevention by increasing the probability of crime failure and deterrence measures. Sharing the rationality perspective, the situational crime prevention approach proposed by Clarke (1983) is widely adopted to reduce crime opportunities and deter offenders by using strategies such as, for example, guardianship (or policing), target hardening, surveillance, and access control. This prevention approach is practical against cargo theft since the responsibility of prevention is not entirely on the police but also on private entities such as transport and insurance companies.

The importance of location, which is critical to cargo theft, is explicit in the routine activity and situational crime prevention perspectives. Cargo theft is a mobile crime since both the motivated offenders and the target are in movement. This implies weak geographical boundaries and, consequently, complexity in the explanation of the geography of cargo theft. Crime mobility is the core of the theory of crime displacement which states that crime prevention in an area may have an unintended effect on the crime level of other areas (Reppetto 1976). This framework is rooted in the assumption that, apart from being rational, opportunistic criminals are more elastic to prevention measures while professional criminals are less elastic (Reppetto 1976). Besides, perpetrators have mobility, although limited, in terms of time, place, method, and type of offense (Reppetto 1976; Hesseling 1994). According to Ekwall (2009b), “crime displacement is one probable explanation as to why the criminal pattern changes in a certain system”.

Deprivation measures are also theoretically identified as causes of crime in social structural theories, whereby crime is not a rational choice but a response to societal flaws such as poverty, unemployment, inequality, etc (Merton 1938). Falk (1952) discussed two theories that explain the seasonality of violent crimes (aggression) and property crimes. This author explained that aggressions follow weather temperatures and that the peak is observed in midsummer and drop in winter. Conversely, property crimes are high during fall and winter and often follow trends of seasonal unemployment and poverty. The crime motivations and seasonal patterns suggested by Falk (1952) for both types of crimes were upheld by Gorr et al. (2003).

Bearing on the social disorganization theory of crime, cargo theft has also been explained by the level of internal and external management quality of transport companies, whereby companies with weak management experience more theft (Smith et al. 2000). In this approach, motivated offenders take logistics infrastructure into account to determine their probability of crime success. Internal management flaws of companies occur especially through information leakage to external perpetrators concerning the transported cargo (Ekwall 2009a).

This study also bears on the fundamental concept of geography endorsed by Tobler (1970) that “everything is related to everything else, but near things are more related than distant things”. Therefore, given the importance of location for cargo theft, spatial correlation and dependence are naturally expected to surface in the empirical model of this study.

Method

The hypotheses of this study are tested using time series methods. The first step is the presentation of the basic vector autoregression model (VAR), which lag structure is specified using statistic methods and regressors chosen based on the literature. The data for all the regressors are plotted to identify trends, seasonal patterns, and outliers. Outliers are removed and replaced by mean values as described in Wilcox (2010) and regressors with seasonal trends are deseasonalized using the X-13-Arima-seats procedure detailed in (Sax and Eddelbuettel 2018). Both the dependent and dependent variables are transformed by applying logarithm, following the Box-Cox procedure (Box and Cox 1964) to obtain the elasticities of regressors and to reduce data discrepancies.

Prior to these data treatments, the Augmented Dick-Fuller (ADF) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) unit root tests are performed on all variables to ensure that they are stationary and suitable for time series analysis (Dickey and Fuller 1979; Kwiatkowski et al. 1992). Given that some of the variables are found to be stationary while others are not, the Bounded Autoregressive-Distributed Lag (ARLD-bound) estimation approach proposed by Pesaran et al. (2001) is used to test for stationarity and cointegration, and the long and short-run associations are obtained using this method as an alternative to the usual vector autoregressive (VAR) and vector error correction (VEC) estimation approaches that require either stationarity or non-stationarity of the regressors. The results obtained from the ARDL models are tested for serial correlation, heteroskedasticity, normality, and misspecification using the Breusch-Godfrey/Box-Ljung test, Breusch-Pagan test, Shapiro-Wilk, and Ramsey RESET test, respectively. Lastly, the stability of the long-run estimates is verified using the cumulative recursive residuals (CUSUM) and its square (CUSUMSQ).

Details regarding the tests, transformations, and estimation procedures and methods are provided in Sections 3.2 and 3.3.

Model structure

Based on the principles of the routine activity theory (Cohen and Felson 1979) and the organized characteristic of cargo theft (Tarnef 2013), it is reasonable to expect that cargo thefts are serially correlated. Therefore, the starting point of the analysis of cargo theft time series is the estimation of an autoregression vector model (VAR), which consists of a set of K endogenous variables yt = (y1t, …, ykt, …, yKt). The basic VAR(p) process is represented as

$${\boldsymbol{y}}_{\boldsymbol{t}}={\boldsymbol{A}}_1{\boldsymbol{y}}_{t-1}+\dots +{\boldsymbol{A}}_p{\boldsymbol{y}}_{t-p}+{\boldsymbol{u}}_t,$$
(1)

where Ai are the (K × K) coefficient matrices for i = 1, …, p and ui is a K-dimensional process with E(ui) = 0 and time-invariant positive definite covariance matrix \(E\left({\boldsymbol{u}}_{i},{\boldsymbol{u}}_t^{\prime}\right)={\sum}_{u}.\) This basic model will be developed based on the course of statistical tests and extended to contain regressors.

The stationarity of time series, which is required to estimate the vector autoregressive model presented in Eq. 1, is violated if its mean, variance, and autocorrelation structure vary over time. Time-dependent variance, however, can be stabilized by transforming the data. This study resorts to the Box-Cox transformation procedure (Box and Cox 1964) which consists of the estimation of parameter λ that represents a family of transformations calculated using the maximum likelihood method, whereby the transformed data is expressed as y∗ = (yλ − 1)λ if λ ≠ 0 and y∗ = log(yt) if λ = 0, t = 1, …, T. Assuming that data are not independent and identically distributed, the Box-Cox analysis shows that the natural logarithm can be applied to all the series to stabilize data variance. An additional advantage of logarithm transformation is that the estimated coefficients represent elasticities. Therefore, this transformation is performed on all the series before testing for unit root, i.e., stationarity.

In addition to the logarithm transformation, all the variables are seasonally adjusted using the X-13arima-seats procedure (Sax and Eddelbuettel 2018) to filter time-specific effects and to isolate the relationship between the variables.

Table 1 presents the regressors specified in the model alongside their sources and Fig. 2, 3, 4, 5 show the evolution of these series alongside a Lowess smoothing line to enable easy detection of time trends as suggested by Cleveland (1981).

Table 1 Definition and sources of time series (in logarithm), São Paulo, January/2005 – December/2018
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Fig. 2
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The number of cargo thefts (hypothesis 1), São Paulo city, great São Paulo, inland municipalities, from January to December 2018. Source: Elaborated by the authors using the data refrenced in Table 1

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Fig. 3
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Economic attractiveness (hypothesis 2), São Paulo state, from January 2005 to December 2018. Source: Elaborated by the authors using the data refrenced in Table 1

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Fig. 4
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Social structure (hypothesis 3), São Paulo state, from January 2005 to December 2018. Source: Elaborated by the authors using the data refrenced in Table 1

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Fig. 5
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Deterrrence (hypothesis 4), São Paulo state, from January 2005 to December 2018. Source: Elaborated by the authors using the data refrenced in Table 1

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The average number of cargo theft is higher in the São Paulo city (capital) compared to the greater metropolitan area of São Paulo (gsp) and non-metropolitan areas (inland). The temporal trajectory of cargo theft in the gsp was relatively stable around an average value until around the year 2016 but reached higher average levels in subsequent years. A similar trajectory was observed in the capital city, except that the number of incidences plunged significantly after the increase observed around the year 2016. The average number of cargo theft in the non-metropolitan areas (inland) was stable roughly from the year 2005 to 2008 but, thence, continuously increased until around the year 2018. Such a trend may engender non-stationarity to series and has been suspected by Justus et al. (2018) to have expressively reduced the cargo theft gap between non-metropolitan areas and the Great São Paulo. As shown in Justus et al. (2018), the number of cargo theft in the non-metropolitan areas reached similar levels of the gsp around the years 2017 and 2018, indicating possible convergence (Figs. 6, 7, 8, 9).

Fig. 6
figure 6

Logarithm and deseasonalized series of cargo thefts (hypothesis 1), São Paulo city, great São Paulo, inland municipalities, from January to December 2018. Source: Elaborated by the authors using the data refrenced in Table 1

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Fig. 7
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Logarithm and deseasonalized series for economic attractiveness (hypothesis 2), São Paulo state, from January 2005 to December 2018. Source: Elaborated by the authors using the data refrenced in Table 1

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Fig. 8
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Logarithm and deseasonalized series for social structure (hypothesis 3), São Paulo state, from January 2005 to December 2018. Source: Elaborated by the authors using the data refrenced in Table 1

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Fig. 9
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Logarithm and deseasonalized series for deterrrence (hypothesis 4), São Paulo state, from January 2005 to December 2018. Source: Elaborated by the authors using the data refrenced in Table 1

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The rate of unemployment reduced significantly from the year 2005 until around the year 2014 but regained a positive trend and increased until the year 2018. The seasonal unemployment discussed by Falk (1952) is noticeable in the time series but there is no apparent association with the trends of cargo theft. Nevertheless, the temporal direction of the rate of unemployment is inversely mirrored by the series of the volume and revenue from the sale of vehicles and automobile parts.

The volume of sales and revenue of the overall trade sector showed a seasonal trend throughout the analysis. However, the volume of sales stabilized in terms of growth around the years 2014 and 2018 but the revenue from the same sector continued increasing. The price index shows that consumer prices were less volatile and increased continuously throughout the period. The police activity measure shows that the rate of apprehension of offenders in the act increased significantly over the period, especially, from the year 2013 to 2014 but plunged from the year 2016 to 2018. It is noteworthy to point out that the series of police activity has a similar trend compared to the cargo theft rate of the capital city, especially from the year 2016 to 2018.

The periodicity of the cargo theft series promted the concern of monthly seasonality as observed by Falk (1952) regarding property and violent crimes. Such an attribute invalidates the regular time series tests and estimation if not properly addressed. For this reason, the Fig. 11 (Annex) illustrates the monthly plot of the cargo theft rate series of the capital, gsp, and inland to verify the presence of monthly seasonality. This plot shows the evolution and mean of cargo theft rate for each month of the year over time. Given that each label on the x-axis represents the months of the year, it is observable that the average rate of cargo theft rate per month is stable in the capital throughout the year; slightly increasing from January to December in the inland, and; more unstable in the gsp from January through December – the month of highest and lowest cargo theft rate in the gsp is March and September, respectively. It is important to highlight that the months of high and low cargo theft rates reported by Justus et al. (2018) for São Paulo state as a whole coincides with and, therefore mostly attributed to, that observed for the gsp. Nonetheless, the monthly plot is convincing that the monthly seasonality of cargo theft across the three locations is subtle. Still, this study opts to transform these series to eliminate possible seasanal pattern in order to better identify and isolate the empirical associations of interest.

Unit root test

The literature is consolidated regarding the temporal pattern of economic time series such as growth, unemployment, etc., but little is known about crime series. There is evidence in the literature regarding the non-stationarity of the time series of violent crimes as in homicide rates (Saridakis 2011; Justus and Kassouf 2013) and property crimes as in burglary, robbery, and property theft (Deadman and Pyle 1994; Gorr et al. 2003) but none on crime against trading such as cargo theft. Therefore, an unprecedented contribution of this study is to provide stationarity tests of the time series of cargo theft that may guide future empirical studies that use time-series methodologies.

The existence of a unit root, i.e. non-stationarity, in the stochastic process that generates the time series data is tested by using the ADF (Dickey and Fuller 1979) and KPSS (Kwiatkowski et al. 1992) tests. The null hypothesis of a unit root (H0 : d = 1) is tested against the alternative hypothesis of no unit root (HA : d = 0) in the ADF test, whereas these hypotheses are inverted in the KPSS test (H0 : d = 0 and HA : d = 1).

Bearing on Enders (2008), the ADF and KPSS tests were first performed on models with both constant and trend as deterministic regressors and then reduced to constant-only models if non-stationarity is concluded and further reduced to models without constant and trend if the non-stationarity conclusion is sustained. Table 2 presents the statistics and critical values of the tests which were analyzed at 5% of significance. The ADF and KPSS confirmed stationarity for the three cargo theft series and non-stationarity for other regressors (see Table 2). Following the steps of Almi (2014) and Dube et al. (2018) by performing the ADF and KPSS unit root tests on the differenced series of those that were non-stationary, the series are concluded to be difference-stationary. Therefore, cargo theft series are I(0) but other series are I(1).

Table 2 ADF and KPSS unit root tests
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ARDL Bounds cointegration test and model identification

Cointegration is a broadly applied econometric approach to investigate the short-run dynamics and long-run associations between time series in various academic fields (Justus and Kassouf 2013; Alimi 2014; Dube et al. 2018) using, especially, the methods developed by Engle and Granger (1987) or Johansen (1988). Although these methods are very effective, they both require that all the series in a model must be integrated in the same order, which is not always the case as shown in Table 2 and observed by Afzal et al. (2010), Alimi (2014) and Dube et al. (2018). This challenge, however, is solved in the bounded Autoregressive Distributed Lag (ARDL) cointegration approach developed by Pesaran et al. (2001) which allows series contained in a model to be a mix of level and first-differenced stationary variables, i.e., I(0) and I(1). Therefore, given the results presented in Table 2, this study uses the ARDL Bounds test. This method has been applied by recent studies from diverse areas of research namely, Timilehin et al. (2019), Tursoy (2019), and Algaeed (2020). Apart from specification flexibility, the ARDL Bounds test produces unbiased long-run estimates and is also more efficient for small and finite sample (Harris and Sollis 2003).

The cointegration exercises performed throughout this study are carried out using the ‘dLagM’ statistical package developed by Demirhan (2019) for the R software.

Although all the series described in Table 1 could be tested for cointegration, this study focuses only on the ARDL equations for cargo theft, which are represented as follows for the capital city

$$\varDelta \;ln \;capita{l}_t={\beta}_{01}+{\alpha}_{11}\mathit{\ln}\;{capital}_{t-1-i}+{\alpha}_{21}\mathit{\ln}\;{gsp}_{t-1}+{\alpha}_{31}\mathit{\ln}\;{inland}_{t-1}+{\alpha}_{41}\mathit{\ln}\;{unemp}_{t-1}+{\alpha}_{51}\mathit{\ln} vehicles.{v}_{t-1}+{\alpha}_{61}\mathit{\ln}\; vehicles.{r}_{t-1}+{\alpha}_{71}\mathit{\ln} trade.{v}_{t-1}+{\alpha}_{81}\mathit{\ln}\; trade.{r}_{t-1}+{\alpha}_{91}\mathit{\ln}\;{inpc}_{t-1}+{\alpha}_{10,1}\mathit{\ln}\;{police}_{t-1}+{\alpha}_{11,1}\mathit{\ln}\;{trucks}_{t-1}+{\alpha}_{12,1}\mathit{\ln}\;{population}_{t-1}+\sum_{i=1}^p{\beta}_{1i}\varDelta\ \mathit{\ln}\;{capital}_{t-1-i}+\sum_{i=1}^q{\beta}_{2i}\varDelta\ \mathit{\ln}\;{gsp}_{t-i}+\sum_{i=1}^q{\beta}_{3i}\varDelta \;ln\;{inland}_{t-i}+\sum_{i=1}^q{\beta}_{4i}\varDelta \;ln\;{unemp}_{t-i}+\sum_{i=1}^q{\beta}_{5i}\varDelta \;ln \;vehicles.{v}_{t-i}+\sum_{i=1}^q{\beta}_{6i}\varDelta \;ln \;vehicles.{r}_{t-i}+\sum_{i=1}^q{\beta}_{7i}\varDelta \;ln \;trade.{v}_{t-i}+\sum_{i=1}^q{\beta}_{8i}\varDelta \;ln \;trade.{r}_{t-i}+\sum_{i=1}^q{\beta}_{9i}\varDelta \;ln\;{inpc}_{t-i}+\sum_{i=1}^q{\beta}_{10,i}\varDelta \;ln \;polic{e}_{t-i}+\sum_{i=1}^q{\beta}_{11,i}\varDelta \;ln{trucks}_{t-i}+\sum_{i=1}^q{\beta}_{12,i}\varDelta \;ln\;{population}_{t-i}+{\varepsilon}_t$$
(2)

for the greater São Paulo thusly

$$\Delta \textrm{ln}{gsp}_t={\beta}_{02}+{\alpha}_{12}\ln {gsp}_{t-1-i}+{\alpha}_{22}\ln {capital}_{t-1}+{\alpha}_{32}\ln {inland}_{t-1}+{\alpha}_{42}\ln {unemp}_{t-1}+{\alpha}_{52}\ln vehicles.{v}_{t-1}+{\alpha}_{62}\ln vehicles.{r}_{t-1}+{\alpha}_{72}\ln trade.{v}_{t-1}+{\alpha}_{82}\ln trade.{r}_{t-1}+{\alpha}_{92}\ln {inpc}_{t-1}+{\alpha}_{10,2}\ln {police}_{t-1}+{\alpha}_{11,2}\ln {trucks}_{t-1}+{\alpha}_{12,2}\ln {population}_{t-1}+\sum_{i=1}^p{\beta}_{1i}\Delta\ \ln {gsp}_{t-1-i}+\sum_{i=1}^q{\beta}_{2i}\Delta\ \ln {capital}_{t-i}+\sum_{i=1}^q{\beta}_{3i}\Delta \textrm{ln}{inland}_{t-i}+\sum_{i=1}^q{\beta}_{4i}\Delta \textrm{ln}{unemp}_{t-i}+\sum_{i=1}^q{\beta}_{5i}\Delta \textrm{ln} vehicles.{v}_{t-i}+\sum_{i=1}^q{\beta}_{6i}\Delta \textrm{ln} vehicles.{r}_{t-i}+\sum_{i=1}^q{\beta}_{7i}\Delta \textrm{ln} trade.{v}_{t-i}+\sum_{i=1}^q{\beta}_{8i}\Delta \textrm{ln} trade.{r}_{t-i}+\sum_{i=1}^q{\beta}_{9i}\Delta \textrm{ln}{inpc}_{t-i}+\sum_{i=1}^q{\beta}_{10,i}\Delta \textrm{ln} polic{e}_{t-i}+\sum_{i=1}^q{\beta}_{11,i}\varDelta ln{trucks}_{t-i}+\sum_{i=1}^q{\beta}_{12,i}\varDelta ln{population}_{t-i}+{\varepsilon}_t$$
(3)

and, lastly, for the inland municipalities

$$\Delta \textrm{ln}{inland}_t={\beta}_{03}+{\alpha}_{13}\ln {inland}_{t-1-i}+{\alpha}_{23}\ln {capital}_{t-1}+{\alpha}_{33}\ln {gsp}_{t-1}+{\alpha}_{43}\ln {unemp}_{t-1}+{\alpha}_{53}\ln vehicles.{v}_{t-1}+{\alpha}_{63}\ln vehicles.{r}_{t-1}+{\alpha}_{73}\ln trade.{v}_{t-1}+{\alpha}_{83}\ln trade.{r}_{t-1}+{\alpha}_{91}\ln inpc.{v}_{t-1}+{\alpha}_{10,3}\ln {police}_{t-1}+{\alpha}_{10,3}\ln {trucks}_{t-1}+{\alpha}_{10,3}\ln population+\sum_{i=1}^p{\beta}_{1i}\Delta\ \ln {inland}_{t-1-i}+\sum_{i=1}^q{\beta}_{2i}\Delta\ \ln {capital}_{t-i}+\sum_{i=1}^q{\beta}_{3i}\Delta \textrm{ln}{gsp}_{t-i}+\sum_{i=1}^q{\beta}_{4i}\Delta \textrm{ln}{unemp}_{t-i}+\sum_{i=1}^q{\beta}_{5i}\Delta \textrm{ln} vehicles.{v}_{t-i}+\sum_{i=1}^q{\beta}_{6i}\Delta \textrm{ln} vehicles.{r}_{t-i}+\sum_{i=1}^q{\beta}_{7i}\Delta \textrm{ln} trade.{v}_{t-i}+\sum_{i=1}^q{\beta}_{8i}\Delta \textrm{ln} trade.{r}_{t-i}+\sum_{i=1}^q{\beta}_{9i}\Delta \textrm{ln}{inpc}_{t-i}+\sum_{i=1}^q{\beta}_{10,i}\Delta \textrm{ln} polic{e}_{t-i}+\sum_{i=1}^q{\beta}_{11,i}\varDelta ln{trucks}_{t-i}+\sum_{i=1}^q{\beta}_{12,i}\varDelta ln{population}_{t-i}+{\varepsilon}_t$$
(4)

where ln(.) is the logarithmic transformation discussed in Section 4.3.1, Δ is the first difference and εt are the error terms. Note that Eq. 2-4

are general representations of the ARDL models which contain the short and long-run associations that are represented in differences and levels, respectively (Pesaran et al. 2001).

The long-run association between the series (henceforth, co-integration) is confirmed if the null hypothesis of the F-test, which states that the lagged series in level are jointly equal to zero (i.e. H0 : α1i = α2i = α3i = α4i = α5i = α6i = α7i = α8i = α9i), is rejected. Two critical values were provided by Pesaran et al. (2001) for the F-test; one for level-stationarity (lower bound, F(0)) and another for first-difference stationarity (upper bound, F(1)). The F-test result is only conclusive if cointegration is confirmed for both bounds, i.e., F-test > F(0) and F(1). The optimal lag order of the ARDL equations that are chosen based on the Akaike Information Criterion (AIC), F-statistics, and critical values are presented in Table 3. The test values show that three cargo theft series are cointegrated within the ARDL bounds.

Table 3 ARDL bounds test results for Cointegration
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The models indicated as best fit by the AIC are tested for autocorrelation using Breush-Godfrey and Box-Ljung tests; homoskedasticity using the Breusch-Pagan test; normality using the Shapiro-Wilk test, and; model specification error using the Ramsey RESET test (Table 4). The test statistics and the p-values of these diagnostic measures are presented in Table 5. At 5% level of significance, the calculated values indicate that the three models reject the null hypothesis of autocorrelation, heteroskedasticity, absence of normality of residuals, and misspecification. Therefore, the models chosen based on the AIC can be used for analyses.

Table 4 Model diagnostics
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Table 5 Estimates for the long-run Granger causality
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The stability of the long-run estimates obtained from the best fit models is tested using the cumulative sum of recursive residuals (CUSUM) and its square (CUSUMSQ) as suggested by Pesaran and Pesaran (1997). The plots of the CUSUM and CUSUMSQ illustrated in Fig. 10 shows that the residuals are within stable ranges at the level of significance of 5%, i.e., the long-run estimates are stable.

Fig. 10
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Average cargo theft rates per month for the Capital, GSP, and Inland locations

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Results

The lag orders indicated by the AIC are used to specify the long-run models for cargo theft in the capital city of São Paulo (capital), Great São Paulo (gsp), and non-metropolitan municipalities of São Paulo state (inland) as presented in Eq. 2-4, respectively. The coefficients obtained for these models are presented in Table 4, focusing on the coefficients that indicate significant long-run Granger causality.

The significance of lncapitalt − 1 in the equation for capital shows evidence of long-run Granger causality of cargo theft in São Paulo city by the preceding rates of the same city. Similar evidence is observed in the models for the gsp and inland. This implies that cargo theft is serially correlated in the three geographic units of São Paulo state and that the present and future rates of cargo theft can be predicted by previous ones. The negative sign of this autoregressive parameter indicates that the increase of cargo theft in a particular period is followed by a reduction in subsequent periods.

Apart from the temporal association, the models also show evidence of the geographical association of cargo thefts. The models for the three geographic locations show that cargo theft in the gsp has a positive Granger-effect on that of the capital and inland cities, i.e., an increase in cargo theft in the gsp in a particular period increases cargo theft in the capital and inland in the subsequent period. The model for gsp shows that an increase in the cargo theft of the capital also increases that of the gsp, i.e., the long-run causality between cargo theft in the gsp and capital is bi-lateral. The effect of the gsp on both the capital and inland indicates the relevance of gsp as the middle ground of the geography of cargo theft. This is reasonable given the geography of the three locations as shown in Fig. 1.

The effect of the economic (vehicle, trade, inpc) and socioeconomic (unemp) conditions vary significantly between the capital, gsp, and the inland, indicating the differences in the economic, and socioeconomic dynamics of these locations. The rate of unemployment only Granger-causes cargo theft in the gsp, whereby its effect is positive. It is, however, important to recall that the unemployment rate available and used in this study is that of the metropolitan area of São Paulo that includes both the gsp and capital. Therefore, in the long run, a higher unemployment rate in the metropolitan are increases cargo theft in the gsp. The long-run Granger-effect of revenue from the sales of vehicles and automobile parts is negative in the inland. The volume of sales of vehicles and automobile parts, however, has a negative and significant Granger-effect on the cargo theft series in the capital but the effect is positive and significant in the inland.

The long-run Granger-effect of the overall trade sector is only significant in the equation for capital, whereby the effect of revenue and volume of sales is positive and negative, respectively. The Granger-effect of the price index (a proxy for inflation) on cargo theft is negative in the gsp. The police activity variable has a positive Granger-effect in the capital city in the long run but a negative effect in the gsp. The control for the circulation of trucks showed no impact on cargo theft in any of the locations and the control for population size is only significant in the equation for the capital city.

The residuals obtained from the long-run cointegration models in Eq. 2-4 are used to correct the short-run associations between the variables which are represented by the lagged differences of the equations (Pesaran et al. 2001). The models estimated from such a correction is called the Vector Error Correction Model (VECM) and the results are presented in Table 6.

Table 6 Estimates of the Vector Error Correction Model (VECM) for short-run associations
Full size table

The relationship between the incidences of cargo thefts across locations in São Paulo state is also observed in the short-run models. Similarly to the long run, the spatial link between the gsp and capital is positive and bi-lateral, and the effect from the capital to the gsp is both from contemporary and lagged cargo thefts. Cargo thefts from the inland did not affect that of the gsp and capital. However, contrary to the sign observed for the long run, a higher number of cargo thefts in the gsp reduces cargo thefts in the inlands in the short run. The comparison of the models for the three locations indicates a bilateral relationship of cargo thefts between the gsp and the capital, and the inland locations are crime receivers both in the short and long run.

Similarly to the result for the long-run associations, the short-run models show that the effects of economic and socioeconomic conditions on cargo theft very expressively across locations in the state of São Paulo.

A positive and significant effect of unemployment on cargo theft is observed in the gsp in the short run, i.e., a higher unemployment rate causes an increase in the cargo theft rate of the gsp. The lagged variations of the volume and revenue from the sales of vehicles and automobiles affect the cargo theft rate in the capital city, whereby an increase in the revenue from these sales reduces cargo theft, and an increase in the volume of sales increases cargo theft. The volume of sales of the overall trade sector also has a positive lagged effect on cargo theft in the capital. None of the sales variables have a significant effect on cargo theft in the gsp. As for the inland, a contemporary increase in the revenue from the sales of vehicles and automobile parts reduces cargo theft, and a contemporary increase in the volume of these sales increases cargo theft, although this latter effect is mitigated by lagged shocks.

There was no significant effect of inflation shocks on cargo theft rate in any of the locations in the short run.

The police variable, which is a control for the presence of law enforcement, reduces cargo theft rate in the gsp and inland in the short run. This implies that an increase in the rate of apprehension of offenders in the act reduces cargo theft in both locations. The significant effect of the police on cargo theft rate in the gsp is contemporary, whereas the effect is only observed in the inland for lagged shocks.

The contemporary effect of the circulation of trucks on cargo theft is positive in the inland but its lagged effect is negative in the gsp.

Discussions

The empirical results indicate that the short and long-run dynamics of cargo theft rate are strongly determined by temporal and spatial associations. The effect of socioeconomic and economic conditions varies across locations and that of law enforcement is more emphasized in the short run.

The temporal dependency indicated by the results implies that the current rates of cargo theft depend on past ones, thus, enabling predictability over time rather than the seasonality suggested by Falk (1952) – higher frequency of property crimes during fall and winter. This temporal dependency is observed for all locations in the São Paulo state in the long run, implying that cargo theft may be more opportunistic in the short run as suggested by Repetto (1976).

Although the seasonal variation of cargo theft is higher in the Great São Paulo, there was no overt sign of monthly seasonality comparable to that overtly observed in previous studies for days of the week, hours of the day, and specific months of the year (Burges 2012; Ekwall and Lantz 2015; Ceccato 2015; Justus et al. 2018). Specifically, Justus et al. (2018) reported that cargo thefts are more frequent between March to May and between October and December in São Paulo state. The results presented here adds the seasonality reported by these authors is mostly linked to the greater São Paulo rather than other regions.

The evidence of the interdependence of cargo theft rates between locations in São Paulo state supports the evidence from Justus et al. (2018) that cargo thefts follow a spatial clustering pattern as observed for the state of Minas Gerais by Queiroz et al. (2008) and the state of Rio de Janeiro by Ruediger et al. (2018). Apart from being clustered in big cities and around main highways of São Paulo state, Justus et al. (2018) observed that the clustering pattern also follows urbanization rate and the level of economic activities of the region, especially of port and other freight operations that are also strategically clustered in space. Apart from the cluster of the economic opportunity, the spatial dependence of cargo theft, according to Repetto (1976) and Ekwall (2009b), may be caused by the inherent mobility of cargo thefts and by the displacement provoked by crime prevention measures. Not surprisingly, stronger correlations were observed between locations in the short run compared to the long run. The results showed the importance of location proximity on the spatial correlation as highlighted by Hesseling (1994). This study showed that, in the short and long run, the greater São Paulo acts as the bridge between the capital city and inland cities. Moreover, the spatial link between the great São Paulo and the Capital is positive and bi-directional, whereas the link between the great São Paulo and inland municipalities is positive in the long run, negative in the short run, and uni-directional– from the former to the latter.

The effect of the economic (inflation and trade variables) and socioeconomic (unemployment) conditions on cargo theft rates vary and were barely significant across the models. Therefore, the results regarding these variables should be interpreted with caution. According to Justus and Kassouf (2018), the non-significance of economic conditions in time series’ models of crime has been discussed in the literature and is mostly attributed to the time necessary for individuals to adjust their decisions to economic and socioeconomic conditions in the short run. The results show that the unemployment rate significantly explains the cargo theft rate both in the short and long run in the great São Paulo. Specifically, the immediate effect of a higher unemployment rate is the increase in cargo theft rate as observed by Falk (1952).

Based on the results from Burges (2012), it was expected that a higher revenue and volume of sales in the trade sector will increase cargo thefts since the economic attractiveness and the opportunity is increased, respectively. However, the results for the short run indicate that the revenue from sales in the legal market reduces cargo theft rates while the volume of sales increases cargo theft rates, especially in the capital. This result may be plausible since the higher revenue from sales in the legal market implies lesser disruption of the supply chain by theft or lesser competition with the illegal market. However, the positive effect of the volume of trade on cargo theft is expected since it implies that more goods are in circulation and, therefore, more crime opportunities as suggested by the routine activity theory (Cohen and Felson 1979). Nonetheless, the relationship between the legal trade sector and cargo theft requires more investigation.

Similarly to revenue, inflation is expected to increase the economic attractiveness of cargo theft as indicated by John and Hayes (2003). However, the results show no evidence of association both in the short and long-run.

Goertzel and Kahn (2009) and Goertzel et al. (2013) observed that the growth dynamics of crime are not always determined by social and economic problems but rather by police activity and better law enforcement. The results found here show that police activity as in presence in the streets is effective in reducing cargo theft in the great São Paulo and inland areas. This result supports that found by Justus and Kassouf (2013) regarding the effect of arrests on lethal crimes in São Paulo city.

Conclusions

This study tests the hypotheses of the effect of geographic dependence, economic attractiveness, social structure or flaw, and deterrence on cargo theft. This objective is achieved by using the bounded Autoregressive Distributed Lag modeling approach (ARDL bounds) and resorting to one of the most severe context of cargo theft worldwide in terms of the number of incidences – São Paulo, Brazil. Significant results are found regarding the temporal and geographic dynamics of cargo theft rates, but economic and socioeconomic conditions struggled in explaining cargo theft rates in São Paulo. Such a challenge has been reported by previous studies that investigate crime in São Paulo using a similar method at the aggregate level.

Regarding the first specific objective of this study – the space-time dynamics hypothesis, the empirical results do not reject the hypothesis that cargo theft are intertwined across locations and that proximity plays a crucial role in the strength of this link.

Cargo theft rates are autoregressive in the capital city, inland, and the large metropolitan area, i.e., current and future rates are influenced by preceding rates. This autoregressive characteristic is observed for all locations in the São Paulo state in the long run but not in the short run. This may be indicative that cargo thefts are opportunistic in the short run in São Paulo state. Therefore, police patrol, surveillance, and other situational prevention measures that indicate the active presence of law enforcement along distribution channels on highways and roads may go a long way in reducing cargo theft in São Paulo state.

The high concentration of cargo theft in the capital city of São Paulo makes spatial spills to neighboring locations inevitable. The cargo theft rates of the capital city only affect that of the great São Paulo in the short and long run, emphasizing the role of proximity. This effect is positive and bi-directional between the capital and the greater São Paulo. Still, on the geographic spill, higher incidences of cargo theft in the greater São Paulo cause increase in the number of incidences in inland municipalities. Therefore, in the short and long run, the greater São Paulo acts as the bridge of cargo theft between the capital and inland areas. These spatial links imply that the cargo theft rate of a location can be predicted using the rates of neighboring locations. The policy implication of this finding is that cargo theft prevention measures such as, for example, road and transport policing, should not be concentrated in specific locations and designed with too rigid borders to control crime displacement.

As to the second specific objective – the economic attractiveness hypothesis, the empirical evidence found varies across locations and, therefore, there is not enough evidence to sustain the hypothesis that higher sales and prices in the legal market increase cargo theft. These economic conditions do not appear to have the same effect on cargo thefts in the capital, large metropolitan area, and inland areas of São Paulo state. Therefore, the associations found in this study for these variables are inconclusive and should not be generalized.

The results indicate that, in the short run, higher revenue from sales in the legal market reflects fewer incidences of cargo theft, whereas a higher volume of trade increases cargo theft opportunity, especially in the capital. This implies that the circulation of higher volumes of goods should be followed by more crime prevention measures. On one hand, this could be achieved by private logistics companies by increasing providing security escorts, more surveillance, and tracking system for a higher volume of goods. On the other hand, more policing could be allocated during seasons of higher circulation of goods such as, for example, the Christmas season.

The empirical evidence of this study permits to sustain the third hypothesis regarding the effect of social structure on cargo theft only for the greater São Paulo, i.e., a higher unemployment rate increases cargo theft in the greater São Paulo both in the short and long run, but there is no evidence of this effect in the capital or inland municipalities. This implies that economic growth and development policies designed to reduce unemployment will have a mitigating effect on cargo theft in the greater São Paulo in the short and long run.

Regarding the fourth hypothesis – the deterrence hypothesis, the empirical findings sustain the hypothesis that a greater presence of the police on the streets reduces cargo theft in the greater São Paulo and in the inland municipalities. No evidence is found regarding this effect in the capital city.

Cargo theft is a complex crime to investigate due to mobility, whereby both the economic target and the offender are in movement. Despite the coherent results obtained regarding the space-temporal dynamics of cargo theft, the results regarding the economic determinants are not as stable and consistent as desired. This may be due to the vast economic and socioeconomic differences among the geographic units considered or the modifiable area unit problem. Therefore, future studies on cargo theft in Brazil should consider investigating the determinants of cargo theft at smaller geographic units such as the municipality. Moreover, the spatial correlation hinted in this study could be further investigated by identifying the clusters of cargo theft in São Paulo. As to the international literature, this study recommends the test of the hypotheses put forward here in contexts of less severe cargo theft since the Brazilian is extreme compared to many other countries and may be more linked to national-specific factors or criminal organizations.

This study only considered the frequency of cargo theft and not the value of the goods per se. This may be misleading since, for example, the theft of a few cargos carrying medications may engender higher economic loss compared to the theft of many cargos of food items.

Despite these limitations, this study expands the evidence in the literature regarding the space-temporal dynamics of cargo theft in São Paulo state.