Introduction 4 CHAPTER I: LITERATURE REVIEW 5 1. Overview of The Crime Index 5 2. Factors affecting The Crime Index 5 3. Research overview 7 3.1. Theories related to factors affecting crime rate 7 3.2. Relevant published research 8 CHAPTER II: METHODOLOGY, MODEL SPECIFICATION AND DATA 10 1. Methodology 10 2. Model specification 10 3. Variables, measure, and data source 11 CHAPTER III: ESTIMATION, MODEL TESTING AND STATISTICAL INFERENCE 12 1. Statistical description of variables 12 1.1. Summary of variables 12 1.2. Correlation matrix of variables 13 2. Quantitative analysis 14 2.1. Selecting the proper model 14 2.2. Testing violations 15 2.3. Fixing and finalizing the model 17 CHAPTER IV: RECOMMENDATIONS AND SOLUTIONS 19 CHAPTER V: CONCLUSION 19 References 21 Appendix 22 Introduction The Crime Index is one of the most effective indexes used in determining the stability of a nation. It is used to describe the overall level of crime in a given country in a period of time. The index indicates that a low Crime Index would result in a low overall level of crime, a stable economy, a solid political foundation and a high development level while a high Crime Index would result in a high overall level of crime, an unstable economy, a weakened political regime and a low development level.
LITERATURE REVIEW
Overview of The Crime Index
The Crime Index measures the overall crime level in a city or country, categorizing it as very low (below 20), low (20 to 40), moderate (40 to 60), high (60 to 80), or very high (above 80).
Each year, the Federal Bureau of Investigation (FBI) gathers and publishes crime statistics nationwide, resulting in the Crime Index, also known as the National Uniform Crime Report This index outlines a specific list of crimes that are measured and reported annually.
Factors affecting The Crime Index
Population density measures the number of individuals within a specific area, calculated by dividing the total population by the area in square kilometers This metric is typically expressed as the number of people per square kilometer and represents an average figure.
In simple terms, population density refers to the number of people living in an area per square kilometer or other unit of land area.
The formula of calculating population density is:
Population Density = Number of People / Land Area
Population density is believed to have a positive relationship with crime rate This
Net National Income (NNI) represents the total income generated by a nation's residents, calculated by subtracting the depreciation of fixed capital assets—such as buildings, machinery, transport equipment, and infrastructure—from the gross national income This measure accounts for the wear and tear and obsolescence of these assets, providing a clearer picture of a country's economic health.
The formula of calculating Net National Income is:
NNI = Gross National Income - Depreciation of Fixed Capital Assets
The net national income is anticipated to inversely affect the crime rate; as a nation's wealth increases, so do living standards This rise in living standards is likely to deter potential criminal activities, leading to a reduction in the overall crime rate.
The Gini Index, or Gini Coefficient, quantifies income, wealth, or consumption inequality within a nation or social group It assesses how income is distributed across a population, serving as a key indicator of economic disparity The coefficient ranges from 0 to 1, where 0 indicates perfect equality and 1 signifies complete inequality.
The Gini Index is derived from the Lorenz Curve, which illustrates the cumulative income distribution of a population It is calculated by measuring the area between the Lorenz Curve and the line of perfect equality, then dividing this area by the total area under the line of perfect equality.
The formula for calculating the Gini Index is:
Where A is the area between the Lorenz Curve and the line of perfect equality, and
B is the area under the Lorenz Curve.
Research indicates that income inequality significantly influences crime rates, often serving as a more accurate predictor than poverty levels A study by The AAF highlights that areas with greater income disparity tend to experience higher crime rates, reinforcing the connection between inequality and criminal activity.
The number of years of education indicates the total academic years an individual has completed in formal educational programs, including those offered by elementary and secondary schools, universities, colleges, and other recognized post-secondary institutions.
Research indicates that increased years of education are inversely related to crime rates Higher education levels significantly reduce the likelihood of criminal behavior for two main reasons: first, education improves living standards, which in turn discourages criminal activity; second, it shapes the personality and mindset of individuals, making them less inclined to engage in unlawful acts.
Research overview
3.1 Theories related to factors affecting crime rate
Various theories explore the factors influencing crime rates across countries, including Psychological, Social Class, Criminology, and Socioeconomic factors theories Notably, Socioeconomic factors theories are particularly pertinent to our research The Economic theory of crime, formalized by Nobel Laureate Gary Becker in 1968, is a micro-theory that suggests individuals seeking to maximize welfare allocate resources based on relative returns, thereby connecting socioeconomic conditions to the relative returns of legal versus illegal activities.
Strain theory, rooted in the work of Émile Durkheim and further developed by scholars such as Robert King Merton, Albert K Cohen, and others, posits that societal pressure compels individuals to pursue socially accepted goals, such as achieving higher economic or class status This pursuit can create significant strain, particularly for those residing in areas characterized by high inequality.
Research by Lance Lochner and Enrico Moretti (2004): The Effect of Education on Crime: Evidence from Prison Inmates, Arrests, and Self-Reports
The study analyzes individual-level incarceration data from the Census and state-level arrest data from the FBI Uniform Crime Reports to assess the impact of education on crime rates It utilizes self-reported criminal activity data from the National Longitudinal Survey of Youth to ensure that the findings reflect changes in crime rather than differences in arrest probabilities By applying Ordinary Least Squares and Instrumental Variable Estimates, the research concludes that increased schooling significantly lowers criminal activity Specifically, a one-year rise in average education is linked to an 11 percent reduction in arrest rates, and a 1-percent increase in high school completion among men aged 20–60 could save the U.S up to $1.4 billion annually in crime-related costs.
Research by Morgan Kelly (2000): Inequality and crime
This research uses data on crime taken from the FBI Uniform Crime Reports for
In 1991, research indicated a strong correlation between violent crimes and inequality, as measured by the Gini coefficient, with significant elasticities exceeding one for both income and education disparities Conversely, property crimes showed minimal influence from inequality The study highlights that individuals from disadvantaged backgrounds are more likely to commit crimes in regions with high inequality due to increased pressures and incentives.
Research by Mohamad Kassem, Amjad Ali, and Marc Audi (2019): Unemployment Rate, Population Density and Crime Rate in Punjab (Pakistan): An Empirical Analysis
This study analyzes crime determinants in Punjab, Pakistan, from 1981 to 2017, focusing on factors such as unemployment, remittances, industrialization, social infrastructure, and population density The research, utilizing the Augmented Dickey-Fuller (ADF) Test, reveals that a 1 percent increase in population density correlates with a 0.249320 percent rise in the crime rate Additionally, the unemployment rate also significantly influences crime, with a 0.142692 percent increase per 1 percent rise These findings highlight a strong relationship between population density and crime rates in Punjab.
Research by Dullah Muloka, Mori Kogidb, Jaratin Lilyc, and Rozilee Asidd (2016): The Relationship between Crime and Economic Growth in Malaysia: Re-Examine Using Bound Test Approach
The study investigates the link between crime and economic growth in Malaysia from 1980 to 2013, utilizing the ARDL bound test method to identify long-run relationships and causation directions Contrary to the common belief that improved economic conditions lead to reduced crime, the findings reveal a positive and statistically significant long-term impact of economic growth on crime rates Additionally, a significant bidirectional causation between crime and economic growth was observed in the short run.
METHODOLOGY, MODEL SPECIFICATION AND DATA
Methodology
We developed a linear regression model to analyze the relationship between the Crime Index (crime) and four independent variables: population density (PD), average years of education (educ), adjusted net national income (NI), and Gini index (gini) This analysis utilized data from 117 observations across 13 European countries from 2012.
2020 from trustworthy statistical databases (Worldbank, Statista, Numbeo, Global Data Lab) The data collected was then organized by Microsoft Excel and analyzed by STATA 16
Method we used to derive the model: Theoretical basis, Statistical model,Mathematical model.
Model specification
In order to analyze the influence of different factors on crime index, our group has chosen the following linear regression model:
Crime = 𝜷𝟎 + 𝜷1PD + 𝜷𝟐 educ + 𝜷𝟑 NI + 𝜷𝟒 gini + 𝒖i
𝜷 j (j = 1,2,3,4) : the regression coefficient of corresponding independent variables
Ui: The population random error, representing other factors affecting crime index but are not mentioned in the model
Variables, measure, and data source
Variable Meaning Unit Expected sign Data source
Crime Estimation of the overall level of crime in a country o Number
PD Midyear population divided by land area People/km 2 (+) Worldbank educ Mean years of schooling in each country Year (-) Global Data
NI Adjusted net national income
US$ (-) Worldbank gini Gini index o (+) Worldbank,
ESTIMATION, MODEL TESTING AND STATISTICAL INFERENCE
Statistical description of variables
Variable Obs Mean Standard deviation Min Max crime 117 38.61966 8.011793 21.2 56.7
From the summary table, we can conclude that:
crime: the average crime index in 13 European countries from 2012 to 2020 was
38.61966, with a standard deviation of 8.011793, a minimum of 21.2 and a maximum of 56.7
PD: the average number of people per square kilometer in 13 European countries from 2012 to 2020 was 112.1037, with a standard deviation of 55.85698, a minimum of 8.744145 and a maximum of 238.0173
educ: the average years of education in 13 European countries from 2012 to 2020 was 11.76485, with a standard deviation of 1.155001, a minimum of 9.511 and a maximum of 14.13
From 2012 to 2020, the average adjusted net national income (NI) across 13 European countries was approximately US$832.14 billion, exhibiting a standard deviation of US$969.28 billion The income figures ranged from a minimum of US$41.78 billion to a maximum of US$3,387.08 billion.
gini: the average GINI index in 13 European countries from 2012 to 2020 was
32.26068, with a standard deviation of 4.732972, a minimum of 20.9 and a maximum of 41.3
1.2 Correlation matrix of variables crime PD educ NI gini crime 1
r (crime, PD) = -0.2732 => There is a relatively low correlation with a negative relationship between crime index and population density
r (crime, educ) = -0.3681 => There is a relatively high correlation with a negative relationship between crime index and years of education
r (crime, NI) = 0.0923 => There is a low correlation with a positive relationship between crime index and adjusted net national income
r (crime, gini) = 0.1914 => There is a relatively low correlation with a positive relationship between crime index and GINI index
Quantitative analysis
Our group use STATA 16 in order to select the proper model
First, we use the command xtset to set the panel variable and time variable: xtset code Year a Test for random variables (Breusch and Pagan Lagrangian multiplier)
H0: The model does not contain random variable ai
H1: The model contains random variable ai
Using the command xttest0 after xtreg crime PD educ NI gini, re, we got the following result chibar2(01) = 233.56
Because p-value = 0.0000 < 0.05, we can reject hypothesis H0 and confirm that the model contains ai b Test for correlation between ai and Xi (Hausman test)
H0: ai doesn’t correlate with Xi
Using the command for the Hausman test hausman fe re, sigmaless
We got the following result chi2(4) = 14.01
Because p-value = 0.0073 < 0.05, we can reject hypothesis H0 and confirm that ai correlate with Xi, therefore we will use the fixed effect model
H0: The model doesn’t exist multicollinearity
Using the command vif, we got the following result:
Because the mean VIF = 1.73 < 10, we can’t reject H0 => The model doesn’t exist multicollinearity b Heteroskedasticity
Using the command xttest3, we got the following result:
Modified Wald test for groupwise heteroskedasticity in fixed effect regression model
H0: sigma(i)^2 = sigma^2 for all i chi2 (13) = 274.95
Because p-value = 0.0000 < 0.05, we can reject H0 => The model exist heteroskedasticity c Serial correlation
H0: The model doesn’t exist serial correlation
H1: The model exist serial correlation
Using the command xtserial, we got the following result:
xtserial crime PD educ NI gini
Wooldridge test for autocorrelation in panel data
Because p-value = 0.0002 < 0.05, we can reject H0 => The model exist serial correlation d Cross-section correlation
H0: The model doesn’t exist cross-section correlation
H1: The model exist cross-section correlation
Using the command xtcsd, we got the following result:
Pesaran's test of cross sectional independence = -0.544, Pr = 0.5863
Average absolute value of the off-diagonal elements = 0.437
Because p-value = 0.5863 > 0.05, we can’t reject H0 => The model doesn’t exist cross-section correlation
2.3 Fixing and finalizing the model
From the above tests, we concluded that our model has heteroskedasticity and serial correlation, therefore we use the command:
xtreg crime PD educ NI gini, fe cluster (code)
*These value are significant at 5% significance level
From the result of the significant model, we can conclude:
The overall model is significant at 5% significance level with p-value = 0.0001
3 out of 4 variables are significant at 5% significance level
CHAPTER IV: RECOMMENDATIONS AND SOLUTIONS
The rising crime rate is a global concern, affecting even developed regions in Europe, where it threatens societal development and the safety of residents Therefore, it is crucial for everyone to take action in reducing crime rates.
For the government, the following measures should be taken to better maintain their security, order and to protect their citizens.
Providing education to all is essential for raising public awareness about the threats posed by crime, ultimately fostering better citizenship and contributing valuable resources to society By enhancing the existing education system, governments can help individuals recognize the importance of crime prevention European countries have already begun investing in education through initiatives such as the Socrates program I and II in 1995 and 2000, the Lifelong Learning Program in 2007, and the Erasmus+ program.
In 2014, enhancing facilities, developing teachers' skills, and incorporating more vocational training into the education system can significantly benefit citizens by providing them with valuable skills and experience.
Addressing income inequality is crucial, as many regions in Europe still experience significant disparities between the wealthy and the impoverished This unequal distribution of income and wealth often results in poor living conditions for those at the lower end of the economic spectrum Interestingly, countries with higher net incomes can still face elevated crime rates, indicating a positive correlation between adjusted net income and crime To mitigate this issue, governments should focus on reforming and enforcing tax systems while investing in essential infrastructure, such as housing and healthcare, to support lower-income populations.
Despite advancements in income, quality of life, and culture in developed regions of Europe and the world, a significant issue persists: the rising crime rate, which poses a threat to societal development.
This research paper analyzes the statistical relationship between crime rates in 15 European countries and factors such as years of education, population density, net income, and income distribution Using STATA for analysis, the study finds that years of education and the GINI index show expected correlations with crime rates Surprisingly, adjusted net income correlates positively with crime rates, while population density shows a negative correlation This indicates that countries with stronger economies or lower population densities may not necessarily experience the lowest crime rates.
While our research may have limitations due to the focus on only four variables, the findings remain reliable and valuable for future studies To enhance this research, it would be beneficial to incorporate a larger dataset, extend the time frame, include additional independent variables, or explore alternative models to better understand the impacts.
1 Gary S Becker; Crime and punishment: An economic approach, JSTOR
Available at: https://www.jstor.org/stable/1830482
2 Robert K Merton; Social Structure and Anomie, JSTOR
Available at: https://www.jstor.org/stable/2084686?origin=crossref
3 Lance Lochner and Enrico Moretti (2004); The Effect of Education on Crime: Evidence from Prison Inmates, Arrests, and Self-Reports, ResearchGate
Available at: https://www.researchgate.net/publication/
4901649_The_Effect_of_Education_on_Crime_Evidence_from_Prison_Inmates_Arre sts_and_Self-Reports
4 Morgan Kelly (2000); Inequality and crime, ResearchGate
Available at: https://www.researchgate.net/publication/24095661_Inequality_And_Crime
5 Mohamad Kassem, Amjad Ali, and Marc Audi (2019); Unemployment Rate, Population Density and Crime Rate in Punjab (Pakistan): An Empirical Analysis, Bulletins of Business and Economics
Available at: https://bbejournal.com/index.php/BBE/article/view/148
6 Dullah Muloka, Mori Kogidb, Jaratin Lilyc, and Rozilee Asidd (2016); TheRelationship between Crime and Economic Growth in Malaysia: Re-Examine https://www.researchgate.net/publication/
309737921_The_Relationship_between_Crime_and_Economic_Growth_in_Malaysia_ Re-Examine_Using_Bound_Test_Approac
Country Year crime PD educ NI gini code
To import data from an Excel file into Stata, use the command `import excel "D:\Download\DATA.xlsx", sheet("main") firstrow` This command reads the first row as variable names and sums the variables: crime, PD, educ, NI, and gini Next, set the panel data structure with `xtset code Year`, followed by running a random effects regression with `xtreg crime PD educ NI gini, re` To test for random effects, use `xttest0`, and store the results with `est store re` Finally, perform a fixed effects regression using `xtreg crime PD educ NI gini, fe`.