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This paper deals with the spatial analysis of crime in 2016 across the 113 NUTS 3 (Nomenclature of Units for Territorial Statistics) regions of the Czech Republic, Hungary, Poland and Slovakia (known as the V4, i.e. Visegrad 4, countries). The analysis is based on a total number of crimes per 1000 persons and includes conduction of an exploratory spatial data analysis (ESDA) and spatial econometric modelling. Both the box plot and box map of the distribution of the crime are presented. To investigate the spatial effects, the global Moran's I statistic together with the Moran scatterplot were employed. The presence of statistically significant positive spatial autocorrelation (based on queen case contiguity weight matrix) was confirmed. The local indicators of spatial association (LISA) were used to identify the local clusters. Since the statistically significant high-high clusters were confirmed for the 7 Hungarian regions, the low-low clusters occur across the 18 regions of the Czech Republic, Poland and Slovakia. The spatial outliers are represented by 2 Polish regions. Finally, the spatial econometric models were employed to assess the impact of location as well as of some economic and demographic indicators (GDP per capita, rate of employed persons and population density) on crimes in concrete region.
ABSTRACT
This paper deals with the spatial analysis of crime in 2016 across the 113 NUTS 3 (Nomenclature of Units for Territorial Statistics) regions of the Czech Republic, Hungary, Poland and Slovakia (known as the V4, i.e. Visegrad 4, countries). The analysis is based on a total number of crimes per 1000 persons and includes conduction of an exploratory spatial data analysis (ESDA) and spatial econometric modelling. Both the box plot and box map of the distribution of the crime are presented. To investigate the spatial effects, the global Moran's I statistic together with the Moran scatterplot were employed. The presence of statistically significant positive spatial autocorrelation (based on queen case contiguity weight matrix) was confirmed. The local indicators of spatial association (LISA) were used to identify the local clusters. Since the statistically significant high-high clusters were confirmed for the 7 Hungarian regions, the low-low clusters occur across the 18 regions of the Czech Republic, Poland and Slovakia. The spatial outliers are represented by 2 Polish regions. Finally, the spatial econometric models were employed to assess the impact of location as well as of some economic and demographic indicators (GDP per capita, rate of employed persons and population density) on crimes in concrete region.
Keywords: Crime, Regions, Spatial econometric analysis, V4 countries
(ProQuest: ... denotes formulae omitted.)
1. INTRODUCTION
The increasing development of spatial data analysis and spatial econometric modelling has encouraged researchers from different areas (criminology, economy, psychology and sociology) to deal with place-based theories of crime as well as with analysis of some socio-economic crime determinants. As pointed out by Messner et al. (1999), Anselin et al. (2000) and Ratcliffe (2010), the pioneering work in research on crime and place was presented by social ecologists in France during the middle of the 19th century followed by some studies of the Chicago School in the early 20th century. Nowadays it exists a broad range of studies analysing crime from different points of view using different approaches. Becker (1968) provided the economic analysis of crime and punishment based on costs of crime to society in order to determine optimal policies to combat illegal behaviour. The central role of place in crime determination was stressed by the routine activity theory (Cohen and Felson, 1979), by the rational choice theory (Cornish and Clarke, 1986), and crime pattern theory (Brantingham and Brantingham, 1993). These theories strongly confirm that crime is not randomly distributed over space (Anselin et al., 2000 and Ratcliffe, 2010) and thus their findings can have the potential policy implications exploiting the advantage of the Tobler's first rule of geography, that "Everything is related to everything else, but near things are more related than distant things" (Tobler 1970: 234). During the recent years, the significant software improvements1 and popularization in the area of spatial modelling has led to publication of plenty studies dealing with identification of spatial patterns in crime based on use of exploratory spatial data analysis (ESDA) as well as on estimation of spatial econometric models (for a detailed survey see e.g., Anselin et al., 2000, Lee et al., 2009 and Ratcliffe, 2010). Messner et al. (1999), Almeida et al. (2003) and Penchev (2014) analysed and identified spatial patterns of crime across different regions based on the ESDA techniques. Cracolici and Uberti (2008) dealt with the analysis of the geographical distribution of crime in Italian provinces by estimating of various cross-sectional spatial econometric models. Lee et al. (2009) used a mixed geographically weighted regression (GWR) approach in the analysis of determinants of crime incidence in Korea, Delbecq et al. (2013) studied the crime in Chicago using spatial panel econometrics. The aim of this paper is to explore the spatial patterns of crime and to estimate the appropriate econometric models of crime (both non-spatial and spatial) for the crosssectional data of 113 NUTS 3 regions of the Visegrad 4 (V4) countries2. The analysis is based on a total number of crimes per 1000 persons with consideration of following determinants of crime: GDP per capita (defined at current market prices in PPS3), rate of employed persons and population density. Regarding the spatial econometric modelling, the paper deals with the impact of above mentioned determinants on crime as well as with the assessment of potential spatial spillovers among neighbouring regions. The paper is organised as follows: after introduction in section 1, section 2 deals with the methodology, section 3 describes data and the empirical results and section 4 contains concluding remarks and suggestions for further research.
2. METHODOLOGY
In order to assess the impact of location on number of crimes in a concrete region it is useful to start with the data visualisation based on graphs and maps and to conduct the ESDA detecting the presence of spatial dependence, patterns of spatial clusters and spatial outliers. Furthermore, ESDA includes testing for the presence of spatial autocorrelation4 both on the global and local level. While the global statistics (given as a single value for the whole data set) measure the global spatial autocorrelation, i.e. how strong the spatial association is across neighbouring regions, its local versions enable to assess the spatial autocorrelation for one concrete region. The LISA (Local Indicators of Spatial Association) presented by Anselin (1995) can be used to determine the existence of local spatial clusters. There are various types of these statistics available (Moran's I, Geary C, Getis-Ord), in the empirical part we will use the global and local Moran's I statistics5 and present the Moran scatterplot capturing both the measures. To analyse the spatial interactions among analysed set of regions it is necessary to specify an appropriate spatial weight matrix W of dimension ( n x n ), where n is the number of regions in the data set. There are various possibilities how to specify the spatial weights, literature usually distinguishes two types of spatial weights: contiguity-based weights and distance-based weights. The contiguity matrix W is usually a binary one made up of ones for contiguous neighbours and zero for all others. Since there are various possibilities how to define the contiguous neighbours, the most common is to use the analogy as in the game of chess - the rook case, the bishop case and the queen case (for more information see e.g. Furková, 2016). By convention the diagonal elements of the matrix W are set to zero. Another approach is to use the distance-based weight matrix W based on distances between regions or travel time between regions. It is useful to bear in mind that the specification of the weight matrix W should not to strictly follow some mechanical rules, but to consider neighbours in context of the practical problem being analysed (Getis, 2010, Viton, 2010).
The empirical analyses are usually provided with the use of an appropriate software which enables also to create a spatial weight matrix (usually its row-standardized form). The impact of various determinants of crime on number of crimes in a concrete region can be analysed by estimation of econometric models. In general, literature distinguishes two approaches to estimation: classical approach (specific-to-general approach) and Hendry's approach (general - to-specific approach). In line with Florax et al. (2003), who proved that the classical approach outperforms the Hendry's approach and provides for better inference, we will follow the classical specific-to-general approach. As the first step it follows the estimation of the classic linear regression model by the ordinary least squares (OLS) method, i.e.
... (1)
where the dependent variable (crime) is a function of explanatory variables (gdp - GDP per capita, emp - rate of employed persons and dens - population density), β0, β1, β2 and β3 are unknown parameters and ui represents an error term.
It follows testing for the presence of the spatial autocorrelation among the regression residuals by calculation of the spatial diagnostic test statistics (e.g. the Moran's T). In case that the presence of the spatial autocorrelation is confirmed, the Lagrange Multiplier (LM) tests can be used in order to decide whether a spatial autoregressive (SAR) or a spatial error (SEM) model of spatial dependence is the most appropriate. If both statistics are significant, robust modifications of these statistics should be used (Anselin and Florax, 1995). Both SAR and SEM models can be estimated by the maximum likelihood method (ML) - for more details see e.g. Fischer and Wang (2011). Next, we present only the formulation of the SAR model because the SEM model will not be used in the empirical part of this paper. Model SAR is also known as a spatial lag model, the main feature of which is that the dependent variable (crime) depends on the values of this variable in the neighbouring regions. The extension of the linear model (1) to the SAR model can be written as follows:
... (2)
where p is the spatial autoregressive parameter, wij are the elements of matrix W describing the structure and intensity of spatial effects and all other terms were previously defined.
Besides the SAR and SEM models, very popular is the use of the spatial Durbin model (SDM) which is the SAR model augmented with the spatial lags of the explanatory variables. Similarly, as SAR and SEM models, also SDM model can be estimated based on ML method. In general, the SDM model occupies an interesting position in the spatial econometric literature, since it is possible to derivate from it many other models (see e.g. LeSage and Pace, 2009; Fischer and Wang, 2011). The formulation of the SDM model including the spatial lags of both dependent and explanatory variables is as follows:
... (3)
where parameters γ1, γ2 and γ3 measure the impact of explanatory variables from neighbouring regions on the dependent variable.
3. DATA AND EMPIRICAL RESULTS
The analysis in this paper is based on a total number of crimes per 1000 persons in 2016 across regions of V4 countries (Czech Republic, Hungary, Poland and Slovakia). However, it was quite problematic to gain the data, since the Eurostat database (General and Regional Statistics) contains only historical data (2008-2010) for crimes recorded by the police. The data for analysis - number of registered crimes in 2016 - were retrieved from different sources: Police of the Czech Republic (http://www.policie.cz/docDetail.aspx?docid=22346473&docType= ART), Hungarian Central Statistical Office (https://www.ksh.hu/docs/eng/xstadat/xstadat _annual/i_zji001b.html), Statistical Yearbook of the Regions - Poland 2017 (https://stat.gov.pl/en/topics/statistical-yearbooks/statistical-yearbooks/statistical-yearbook-ofthe-regions-poland-2017,4,12.html) and from the DATAcube. database of the Statistical Office of the Slovak Republic (http://datacube.statistics.sk/#!/view/sk/VBD_SK_WIN/sk3003rr/ Kriminalita%20pod%C4%BEa%20z%C3%A1kladn%C3%BDch%20skup%C3%ADn%20tre stn%C3%BDch%20%C4%8Dinov%20%5Bsk3003rr%5D). To calculate the total number of crimes per 1000 persons in concrete regions, the total number of crimes was divided by the Eurostat data on average annual population to calculate regional GDP data (thousand persons) by NUTS 3 regions in 20156 (http://ec.europa.eu/eurostat/web/rural-development/data /database). Furthermore, the crime determinants used in our analysis - GDP per capita defined at PPS for 2015, employed persons (in thousand persons) in 20157 and population density (inhabitants per km2) in 2016 were retrieved from the Eurostat (http://ec.europa.eu /eurostat/web/rural-development/data/database). The Visegrad group is formed from 4 countries and contains 114 NUTS 3 regions (14 Czech regions, 20 Hungarian regions, 72 Polish regions and 8 Slovak regions). With regard to the data from a Hungarian region Zala giving 26 593 registered crimes in 2016 in comparison to 6 222 registered crimes in 2015, we decided to exclude this region from analysis and to provide the research for a reduced set of 113 NUTS 3 regions. The spatial analysis was carried out in software GeoDa (https:// geodacenter.asu.edu/software/downloads). The shapefile (.shp) for the European regions with regard to NUTS 2013 classification was downloaded from the web page of Eurostat (http://ec.europa.eu/eurostat/web/gisco/geodata/reference-data/administrative-units-statisticalunits) and adequately modified in GeoDa. Figure 1 illustrates both the box plot and box map for the total number of crimes per 1000 persons in 2016 (denoted as cri16obyv) across individual NUTS 3 regions of V4 countries in order to visualise the unequally distribution of crimes over space with considerable differences across regions inside the analysed countries. Especially high concentration of criminality was detected in 4 regions - in Prague region (44.68 crimes per thousand persons), Budapest (37.75) and Pest (37.44) regions and the city of Wroclaw (36.27) while the mean value was about 19.24 crimes per thousand persons. Since no lower outliers were detected, the lowest criminality was detected across 7 out of 8 Slovak regions, 3 Czech regions and 18 Polish regions.
Figure 1 shows that the regions with similar number of crimes tend to be located together. However, the box map does not give any information about statistical significance/insignificance of clustering. In order to investigate if location affects the number of crimes, we have to test for spatial autocorrelation. The spatial neighbourhood was based on the queen case definition of spatial weights (two regions are considered as neighbours if they share any part of a common border). To find out how strong is the spatial association among neighbouring regions we used the global Moran's I statistic and to identify the statistically significant clusters the local Moran's I was employed. Figure 2 contains the Moran scatterplot and LISA cluster map for the number of crimes per 1000 persons in 2016. Moran scatterplot enables to identify regions with positive spatial autocorrelation (high-high - hot spots, low-low - cold spots) and negative spatial autocorrelation (i.e. spatial outliers of high-low and low-high type). The value of the global Moran's I, 0.2950, is larger than the expected value E(I) = -1/(n -1) = -1/112 = -0.0089 which indicates the positive spatial autocorrelation (Fischer and Wang, 2011). The LISA statistic, the local Moran's I, enables to assess the impact of individual region to the magnitude of the calculated global Moran's I. The corresponding LISA cluster map shows only regions with statistically significant (significance level 0.05) local Moran's I statistic colour coded by the type of spatial autocorrelation. Regions with high-high and low-low relationships, i.e. hot spots and cold spots, indicate the similar crime rate as their neighbours, while regions with the low-high and high-low relationships, i.e. spatial outliers, indicate different crime rates in comparison to their neighbouring regions. As it can be seen in Figure 2, there are 7 Hungarian regions representing the hot spots and 18 cold spots regions situated in the Czech Republic, Poland and Slovakia.
The analysis revealed 2 spatial outliers in Poland (1 of low-high type and 1 of high-low type) indicating dissimilar crime rates as their neighbours.
The second part of the empirical analysis is devoted to the estimation of spatial econometric models which are employed to assess the impact of location as well as of some crime determinants (GDP per capita, rate of employed persons and population density8) on a crime rate in a concrete region. The variable GDP per capita as a measure for income is expected to have a negative impact on crime. Similarly, with the rising rate of employed persons we will expect the downward trend in the number of crimes. Regarding the population density, areas with higher concentration of inhabitants are supposed to be more attractive for committing a crime due to high anonymity. Following the classical specific-to-general approach, the analysis starts with estimation of model (1) via OLS method. Estimation results are in Table 1 (Column 1 - Linear model). Although all the estimated parameters were statistically significant, the diagnostic statistics - Moran's I applied on regression residuals and the LM tests indicated that we can clearly reject the null hypothesis of non-spatial dependence. The LM specification tests led to the estimation of SAR model (2). The estimation results of SAR model (based on application of the ML method) are in Table 1 (Column 2 - SAR). All the estimated parameters were statistically significant and concerning the employment rate and population density the estimated parameters have expected signs. However, in case of GDP per capita the estimated sign is positive. This result is in line with Cero and Meloni (2000) who based on Becker's model proved a strong socio-economic effect on the crime rate in Argentina (unemployment rate and income inequality with positive effect on crime rate), as well as with explanations of Fajnzylber et al. (2002). Furthermore, the statistical significance of spatial parameter p confirms the significant positive spatial autocorrelation, i.e. presence of spatial effects across neighbouring regions. The crime rates in neighbouring regions can affect the crime rate of a region under study. The statistical adequacy (no remaining spatial autocorrelation) of the SAR model was proved by the value of the LR statistics. The necessity to incorporate the spatial component into econometric analysis was also clearly confirmed.
In order to investigate the spatial spillovers among regions generated by the explanatory variables, we considered their spatial lags and estimated model (3) without the term ... crimei with the use of OLS (Column 3 - Linear model). Concerning the statistical significance of parameters γ1, γ2 and γ3 it was proved that only employment rates in neighbouring regions can affect the crime rate of a region under study. However, it is necessary to mention that this interpretation is not adequate since the diagnostic test results clearly confirm the necessity of spatial lag specification. In the next step, the SDM model (3) was estimated (for estimation results see Table 1: Column 4 - SDM). Since the parameters of the spatially lagged explanatory variables were not statistically significant, we will not pay attention to these estimation results.
4. CONCLUSION
This paper was focused on the spatial analysis of crime in 2016 across the 113 NUTS 3 of V4 countries. The analysis of crime rates based on ESDA instruments clearly confirmed the significant positive spatial autocorrelation and revealed the statistically significant clusters of hot spots (7 Hungarian regions), cold spots (18 regions of the Czech Republic, Poland and Slovakia) and spatial outliers corresponding to 2 Polish regions. Thereafter follows the estimation of models with consideration of space. Overall, the estimation results imply that the crime rate is determined not only by the economic and demographic indicators (GDP per capita, rate of employed persons and population density) of the analysed region, but also essentially by the number of crimes in neighbouring regions. The inclusion of a spatially lagged crime variable should also be inevitably part of the econometric model in order to avoid misleading conclusions. Furthermore, the results imply that the higher GDP per capita and higher population density lead to increasing crime rates. On the other hand, the increasing rate of employed persons indicates the decline of crimes. However, one of the limitations of our paper (because of data unavailability) is the investigation of the total number of crimes.
For further research it would be interesting to distinguish the different types of crime (murders, thefts, etc.) and to provide the analysis for the regions of all the EU countries. To analyse impact of another socio-economic and demographic indicators on the crime rates builds another challenge for the future research.
ACKNOWLEDGEMENT: This work was supported by the Grant Agency of Slovak Republic - VEGA grant No. 1/0248/17 "Analysis of Regional Disparities in the EU based on Spatial Econometric Approaches".
1 GeoDa, R, SAS, MatLab, etc.
2 The Czech and Slovak Federative Republic (CSFR), Hungary and Poland created in 1991 in Visegrad a group - Visegrad group. Since the dissolution of the CSFR in 1993, the group has had four members - the Czech Republic, Slovakia, Poland and Hungary, which are often denoted as V4 countries.
3 Purchasing Power Standard
4 Spatial autocorrelation is something more complicated than temporal autocorrelation. Since in case of temporal autocorrelation the dependence is always in one direction, i.e. what happens at one time can be influenced only by what has happened in the past. In case of spatial autocorrelation there is dependence in all directions, i.e. what happens at any point in time can be influenced by both the past and the future (Viton, 2010; Spurná, 2008).
5 Mathematical formulas can be found e.g. in Getis (2010).
6 Since the data for 2016 were not available for Polish regions, we used the data for 2015.
7 In order to be included into the analysis this variable was transformed to an employment rate which was calculated as a ratio of employed persons to the average annual population to calculate regional GDP data (both in 2015).
8 Box-maps of these indicators are available from the author upon request.
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