Crime and the Likelihood of Being Caught - Essay Example

Crime and the likelihood of being caught: Introduction: The level of crime in a given year will depend on a number of factors, one of the most important factors include population density, level of unemployment, number of law enforcers, income, law enforcement expenditure, and the population. This paper estimates a model that helps explain what determines crime levels in an area, we expect from the model that the higher the level of unemployment then the higher the level of crime, also the higher the population density the higher the crime level. Other important factors include the number of police officers, we expect that the higher the number of police officers then the lower the crime rate, law enforcement expenditure is also important in that the higher the expenditure the lower the crime rate. We analyze the relationship of these variables using the classical linear regression model and analyze the significance of the estimated coefficients. In the second part of the paper we estimate a model that helps us determine the effect of previous cleared up crimes on the present year crime rate, this model will help us determine the effect of the likelihood of being caught and sentenced on crime rate, we further analyze the significance of the model and its parameters. Eviews software is used to estimate the models and also to analyze their significance. Data: Data used in analysis of the first model is data for the US year 1982 and 1987 regarding crime and this data comprises data from 92 US cities, the second model is estimated using Norway data for 53 police district for the year 1972 and 1978. Relationship between Crimes, population, per capita income, officers and year: Model 1: Data: We use data for the US from the year1982 and 1987, we estimate a model that will help estimate the crime levels, and the table below summarizes the correlation coefficient of the data: CRIMES D87 OFFICERS PCINC POP CRIMES 1 0.052176 0.864896162 0.04067988 0.89009431 D87 0.052175977 1 0.027533087 0.769528693 0.01553976 OFFICERS 0.864896162 0.027533 1 -0.065973538 0.8690456 PCINC 0.04067988 0.769529 -0.065973538 1 0.04727217 POP 0.890094313 0.01554 0.869045604 0.047272174 1 The correlation coefficient is a measure of the strength of the relationship that exists between two variables; it also shows the nature of the relationship that exists between two variables. From the table there is a very strong relationship between officers and crime, as the number of police officers increase the level of crime also increases, it is also evident that there is a strong relationship between the population and crimes. However it is evident that there is a weak relationship between per capita income and crime. we state the models and also determine the signs expected after estimation, in the first model we estimate the model that crime depends on the number of officers, income and population, in this case we expect that as the number of officers increase then the level of crime will reduce, also when per capita income increases we expect the level of crime to reduce, finally when the population increase we expect crime rates to increase, we state our model as follows. Crime = a + b1 d87+ b2 officers + b3 pcinc + b4 pop Where d87 is the year dummy variable, officers 9is the number of officers, pcinc is per capita income and pop is the population size. Results: Using eviews we estimate the above model using the data provided and the following are the results: Dependent Variable: CRIMES Method: Least Squares Sample: 1 92 Included observations: 92 Variable Coefficient Std. Error t-Statistic Prob.   C -4251.295 7483.085 -0.568121 0.5714 D87 270.1819 4332.814 0.062357 0.9504 OFFICERS 15.02688 3.743916 4.013679 0.0001 PCINC 0.491786 1.004124 0.489767 0.6255 POP 0.064538 0.011282 5.720609 0.0000 R-squared 0.827944     Mean dependent var 39663.53 The above results show that our estimated model is as follows: Crime = -4251.295 + 270.1819 d87+ 15.02688 officers + 0.491786 pcinc + 0.064538 pop We can explain the results of this model as follows, if we hold all factors constant and the value of all the independent variables is equal to zero then the crime level is 4251.295, if we hold all other factors constant and increase d87 by one unit then the level of crime will increase by 270.1819 units, if we hold all other factors constant and increase the number of officers by one unit the level of crime will increase by 15.02688 units, if per capita income increases by one unit holding all other factors constant the level of crime increased by 0.491786 units, finally if we hold all factors constant and increase the population level by one unit then crime will increase by 0.064538 units. It is evident that if the slope dummy variable for year is 1 then crime increases by 270.1819, on income it is evident that if income increases by one unit then crime rate increases by 0.491786 and finally is population increases by one unit then crime will increase by 0.064538. Correlation of determination for this model is 0.827944, this means that 82.79% deviations of the dependent variable are explained by the independent variables; regarding statistical significance of the estimated coefficients the following table summarizes the results: t-Statistic t critical null hypothesis C -0.56812 + or - 1.95996 accept D87 0.062357 + or - 1.95997 accept OFFICERS 4.013679 + or - 1.95998 reject PCINC 0.489767 + or - 1.95999 accept POP 5.720609 + or - 1.96000 reject From the above table it is evident that when we formulate the hypothesis that the coefficients are equal to zero and accept the null hypothesis then the coefficient is not statistically significant, the officer and population coefficient is statistically significant while the other coefficients are not statistically significant at 95% level of test. We test for the general significance of the model, in this case we test the null and alternative hypothesis, and we state them as follows: Null hypothesis: H0: b1 = b2 = b3= b4 = 0 Alternative hypothesis: Ha: b1 ≠ b2 ≠ b3 ≠ b4 ≠ 0 Where b1, b2 and b3 are coefficients of d78, officers, pcinc and pop respectively, we perform this test using the F table where alpha is 0.10, after calculations the F statistics value in this case is 104.6621, we determine the denominator and numerator degrees of freedom, the denominator has n-k degrees of freedom while the numerator has k-1 degrees of freedom, the F statistics is 2.6049, the F statistics is less than the F calculated we reject the null hypothesis that b1 = b2 = b3= b4 = 0, therefore the model is statistically significant. This model help us determine the effect of crime officers on crime, however the relationship portrayed in this model is not in line with our theory that states that the higher the number of crime officers then the lower the crime rate, however a different sample can be used to estimate the model which may produce a more appropriate model. Crime and clearing up of crime: Model 2: In this case we analyze the relationship between crime and clearing up of crime, estimation of this model is used using Norway data for 53 police district for the year 1972 and 1978, the sample size n= 1106 and we include only 4 variables to estimate the model. The following table summarizes an analysis of the correlation coefficient: CRIME CLRPRC1 CLRPRC2 D78 CRIME 1 -0.62073 -0.61863 0.182563 CLRPRC1 -0.62073 1 0.757217 -0.27803 CLRPRC2 -0.61863 0.757217 1 -0.35363 D78 0.182563 -0.27803 -0.35363 1 The table above summarizes the correlation coefficient, a relatively strong negative relationship exists between the clear up for one year and crime and also clear up for the past two years and crime, for the other variables there is a weak relationship between the variables and the crime variable. We now estimate the second model which will be used to determine the effect of cleared up crimes on the present year crime rate, it will also help determine the effect of the likelihood of being caught and sentenced on crime rate, and we estimate the model of the form: Crime = C + b1 CLRPRC1 + b2 CLRPRC2 + b3 D78 Where C is a constant, D78 is the year dummy variable, CLRPRC1 is the crimes cleared up in the previous year, CLRPRC2 is the crimes cleared up in the past two years, the following table shows the eviews output: Dependent Variable: CRIME Method: Least Squares Sample: 1 106 Included observations: 106 Variable Coefficient Std. Error t-Statistic Prob.   C 43.54963 3.475590 12.53014 0.0000 CLRPRC1 -0.309299 0.098105 -3.152731 0.0021 CLRPRC2 -0.313606 0.100586 -3.117804 0.0024 D78 -1.004602 1.747983 -0.574721 0.5667 R-squared 0.438885     Mean dependent var 17.51538 From the table above our estimated model takes the following form: Crime = 43.54963 - 0.309299 CLRPRC1 - 0.313606CLRPRC2 - 1.004602D78 From the above estimated model it is evident that is we hold all factors constant and all the independent variables are equal to zero then the crime level will be 43.55, if we hold all other factors constant and increase the number of cleared up crimes in the previous year by one unit then the level of crime will reduce by 0.09299, if we hold all other factors constant and increase the level of cleared up crime in the past two years by one unit then the level of crime will reduce by 0.3136 units, finally if the dummy variable d789 is increased by one unit holding all other factors constant then the crime rate will reduce by 1.0046. From the above discussion therefore the level cleared up crimes will affect the present levels of crime, this means that the more the level of cleared up crimes then the lower the levels of crime, therefore there is need to Correlation of determination for this model is 0.438885, this means that 43.88% deviations of the dependent variable are explained by the independent variables; regarding statistical significance of the estimated coefficients the following table summarizes the results: Variable t-Statistic t critical null hypothesis C 12.53014 + or - 1.95996 reject CLRPRC1 -3.15273 + or - 1.95997 reject CLRPRC2 -3.1178 + or - 1.95998 reject D78 -0.57472 + or - 1.95999 accept When we formulate the hypothesis that the coefficients are equal to zero and accept the null hypothesis then the coefficient is not statistically significant, in this case only the year dummy variable d78 is not statistically significant at 95% level of test. We test for the general significance of the model, in this case we test the null and alternative hypothesis, and we state them as follows: Null hypothesis: H0: b1 = b2 = b3 = 0 Alternative hypothesis: Ha: b1 ≠ b2 ≠ b3 ≠0 Where b1, b2 and b3 are coefficients of d78, CLRPRC1 and CLRPRC2 respectively, we perform this test using the F table where alpha is 0.10, after calculations the F statistics value in this case is 26.59367, we determine the denominator and numerator degrees of freedom, the denominator has n-k degrees of freedom while the numerator has k-1 degrees of freedom, the F statistics is 2.30259, because the F statistics is less than the F calculated we reject the null hypothesis that b1 = b2 = b3 = 0, therefore the model is statistically significant. Discussion: From the above discussion the first model estimated was Crime = -4251.295 + 270.1819 d87+ 15.02688 officers + 0.491786 pcinc + 0.064538 pop, this model shows that the number of police officers does not affect the level of crime, this means that the number of police officers does not deter crime, however in our second model there estimated model which is Crime = 43.54963 - 0.309299 CLRPRC1 - 0.313606CLRPRC2 - 1.004602D78 shows that there is an effect on the level of cleared crimes and the level of crime, when the levels of crimes in the past and past two years are cleared up then we expect the level of crimes in the present year to decline. The correlation coefficient in the first set of data is strong, however for the second series data used the correlation coefficients depict relatively a weaker relationship between the variables, in the second model the variables used especially the clear up for the first year and the clear up for the second year show a negative relationship between the variables and the crime variable. F tests for both model shows that they are statistically significant and therefore both models are appropriate to undertake forecasting and predictions. Despite the results of these models the correlation of determination in the first model shows a very strong relationship between the dependent variables and the independent variable, the second model shows a weak relationship between the dependent and the dependent variable, Conclusion: Crime rate depend on a many factors, some the factors discussed in this model include number of police officers, population density, and previous years clear up, income, year and region. From the paper it is evident that when crimes clear up in the previous year increases then the crime rate in the present year reduces. The first model shows that the number of police officers does not affect the level of crime rate negatively and therefore this model is not in line with our stated hypothesis that as the number of police officers increases crime rates reduce, this model also shows that by increasing the number of police officers crime rate will not be reduced. However the second model clear shows that increasing the level of clearing up of previous crimes will definitely reduce crime rate. Therefore from the above discussion it is evident that the models depict the relationship between the variables and crime, the higher the clear up in the past then the lower the crime levels, therefore crime rates can be reduced by improving on the ability of the police force to apprehend and charge criminals in court, unsolved crime will not deter crime and from the first model increasing the number of police officers will not automatically reduce crime levels, our model depicts that there is a positive relationship between crime and number of officers. Therefore the best way to reduce crime is increasing clear up and increasing the likelihood of being caught and sentenced. References: Isaac Ehrlich (1973) Participation in Illegitimate Activities: A Theoretical and Empirical Investigation, Journal of Political Economy, Volume 81, No page 521 to 565 J. Wooldridge (2006) Introductory Econometrics, McGraw Hill Press, New York Norway crime data 1972 and 1978 US crime data 1982 and 1987 Read More