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Draft: Violence Symposium, 3rd November 2011 Page | 1 Modeling violent crim e in The Bahamas Yan Lyansky School of Mathematics, Physics and Technology College of the Bahamas Abstract Our goal is to find the best pred ictors of the violent crime rate (violent crimes divided by population). We assume that the government will be able to ch ange policy to lower the crime rate if it knows the determining factors that influence crime. We compare unemployment, GDP, and population to the violent crime rate using linear models. We proceed to investigate nonlinear and multi-variable models. Only population and GDP were f ound to be related to crime; increases in population increased crime, wh ile increases in GDP decreased crime. Background Crime has been an escalating problem in the Caribbean. In Crime in the Caribbean: Provisional Evidence by McElroy and Roccanti (2005) question the sustainability of economic systems based on tourism given the large increase in crime. In The Bahamas, the general public perceives crime as a problem that it is out of control. Each week newspapers run murder, armed robbery, and/or stabbing stories. The number of murders continues to grow as well as the level of gun crime (Hanna, 2011). Criminals are becoming more brazen with their armed robberies as evidenced by the First Caribbean Bank assault (Smith, 2010 ) and an eco-tour attack (Thompson, 2009). According to sentiments expressed on local radi o and television, it is cl ear that the Bahamian people believe it is time for a solution before th ings get worse. The police commissioner is under
Draft: Violence Symposium, 3rd November 2011 Page | 2 pressure to find a solution to the problem (Blac k, 2011). The purpose of this study is to examine macro-level factors which may influence crime in The Bahamas, and so allow government to set policies which would be expected to reduce crime. We define violent crime as crime against anot her individual. This includes murder, attempted murder, manslaughter, serious wounding, rape, attemp ted rape, indecent assa ult, incest, unlawful sexual intercourse, burglary, armed robbery, r obbery, attempted robbery, and other sexual advances. The Bahamas gross domestic produc t (GDP), and populati on data are publicly available (World Bank, n.d.). Violent crime data from 1963 is also publicly available from the Royal Bahamas Police Force headquarters in Nassau. Unemployment data were available from two sources; the International La bor Organization (ILO) and the De partment of Statistics. The data are presented in Appendix 1. Method Our data allowed us to hypothesize that unemployment, population and GDP would be associated with crime. We ran single and multi-variable regressions on the data. F-tests were used to determine which factors were usef ul predictors (Blackwell, 2008). The main requirements to use a regression ar e: the predictor variables must be linearly independent, and the data is homoscedastic (the variance of the erro r is constant). The coefficient of determination, R2, gives the predictive ability of the model (the percentage of th e variability which is accounted for by the model.
Draft: Violence Symposium, 3rd November 2011 Page | 3 Results The GDP and population are independent. The labour data had a low correlation with crime, 0.053 (using ILO data) and 0.23 (using data from the De partment of Statistics ), to the crime rate. As the unemployment data from the Department of Statistics had a higher correlation to the crime rate, these data were used in our calculations. Initially, we begin with linear models We used Minitab to calculate the R2 for every combination of one, two, and three variable linear regressions. We also ra n F-tests that evaluated which variables are good predictors of the violent crime rate. The general results for the predictors of the crime rate (number of crimes/population) are below. Linear regressions comparing the crime rate to one other variable Crime vs unemployment (ILO data) gave R2=.003 which implies this variable explains less than .3% of the data. Crime rate vs unemployment using government data had R2=.053, hence it could explain 5.3% of the data (Figure 1). Running an F-test we found that th e p-value is .304 which implies it is not a good predictor of the crime rate. Using population alone we found R2=0.542, and the p-value was clos e to zero. Consequently, the population variable is a useful predictor of crime rate (Figure 2). It explains 54% of the variation in the crime rate data. Using GDP, R2=0.329 and the p-value was also near zero (Figure 3). Hence, the GDP is also a good predictor of cr ime rate. It explains 32.9% of the variation in the data.
Draft: Violence Symposium, 3rd November 2011 Page | 4 Linear regressions comparing the crime rate to several variables Including both population and GDP in the model resulted in R2=0.775 with a p-value near zero, consequently adding GDP accounted for an additi onal 43.5% of the variati on in the data being accounted for. Adding unemployment to the regression resulted in a lower R2. This is may be caused by a reduction in the amount of informa tion available for the model as unemployment only has 22 data points, most of which came from 1986 onwards. Polynomial regressions The scatterplot of GDP appeared to have a sec ond degree variable. As a result, we examined second degree polynomials for both variables. Models with polynomial regressions with both first and second degree population and GDP terms we re used. The initial regression resulted in R2=90.2%. However, this required five variables a nd all of them were usef ul predictors (p>0.05) of the crime rate. Using a backward elimina tion process, resulted in two variables: GDP2 and population2 as useful predictors (p<0.05) (Figure 4). This resulted in a R2=86.3% which was the highest R2attained with only two variable s; this model using population2 and GDP2 explained 86.3% of the variation in the crime rate data. We concluded that the square of the population a nd the square of GDP are useful predictors of the violent crime rate. The regression equation was: crime rate = 0.00313 .000000000270GDP2 + 0.000000000000188population2.
Draft: Violence Symposium, 3rd November 2011 Page | 5 These coefficients are rather small (because the da ta are large), so using normalized data (zero mean and unit variance), the equation becomes: crime rate =0.004790.00395(GDP2-11281671)/14629972+ 0.00534(population258494105117)/28445081033. Note the mean of GDP2=11281671 and population2=58494105117. The standard deviation of GDP2=14629972 and population2=28445081033 Discussion The coefficient of population2 in our model is positive and so an increase in population is associated with an increase the crime rate. This in dicates that as the popula tion rises, the rate of crime rises, that is, the number of crime is disproportionate to the population. This suggests that as the population increases, government may need to invest an ever greater proportion of its resources in dealing with crime as the number of crimes increase. However GDP2 has a negative coefficient; hence, a hi gher GDP is associated with lower crime rates. Consequently, as the wealth of the nati on increases, this should suppress crime. Clearly, government policies should be designed to increa se the prosperity of th e nation, but what these data show is that when the country cannot positi on itself to compete or ca nnot cope with external shocks, then crime would be expected to rise. C onsequently, recessions shoul d be expected to be associated with rises in crime. Unemployment failed to be a good predictor of the crime rate. The reduced number of data points for unemployment meant that the analysis including this variable had less information
Draft: Violence Symposium, 3rd November 2011 Page | 6 from which to estimate the parameters and so would be expected to result in less precise estimates. The fact that the two sources of unemployment data disagreed with each other suggests that there may be inhere nt reliability issues with th e data, or differences due to definitions. Analyses with more data may yet identify relationships which were not apparent the current information. Alternatively, unemployment may not be simply associated with crime, as people may live off their savings when first une mployed, so weakening the association through a time lag, or unemployment in cert ain industrial groups may have disproportionate consequences for crime. Such subtleties would not be evident at this global level. GDP2 is linear with respect to Population2, the relationship is defined via GDP2 = .00069629Population2, hence a change in Population2 by one person would require GDP2 to change to increase by 696 dolla rs. At the current population of 341,713 an increase in population of 1,000 people would require GDP to increase by 26.38 million to keep the crime rate constant.
Draft: Violence Symposium, 3rd November 2011 Page | 7 References Bahamas Population.(n.d.). World Bank, World Development Indicators Google Public Data Retrieved June 10, 2011, from http://www.google.com/publicdata?ds=wbwdi&met=sp_pop_totl&idim=country:BHS&dl=en&hl=en&q=bahamas population Black, S. (n.d.). Major Police Operation or PR Stunt?. Bahamas B2B: Complete Guide to the Islands of The Bahamas BahamasB2B.com Retrieved October 23, 2011, from http://www.bahamasb2b.com/news/2011/ 01/major-police-operation-or-pr-stunt5812.html Blackwell, M. (2008, December 3). Multiple Hypothesis Testing: The F-test. Matt Blackwell Research Retrieved June 10, 2011, from http://www.mattblackwell.org/files/teaching/ftests.pdf McElroy, J., & Roccanti, A. (2005). Crime in the Caribbean: Provisional Evidence. Insula 14.2 32-37. Statistics by Country (n.d.). LABORSTA Internet (E) Retrieved June 10, 2011, from http://laborsta.ilo.org/STP/guest Smith, I. (2010, July 29). Bank Robbers At Large. The Bahama Journal p. 1. Thompson, T. (2009, November 21). 18 Tourists in Shotgun Terror. The Tribune p. 1. World Bank, World Development Indicators-Goog le Public Data Explorer GDP (n.d.). Google Retrieved June 21, 2011, from http://www.google.com/publicdata?ds=wbwdi&met=sp_pop_totl&idim=country:BHS&dl=en&hl=en&q=bahamas%20population# ctype=l&strail=false&bcs=d&nselm=h& met_y=ny_gdp_mktp_cd&scale_y=lin&ind_y=f alse&rdim=country&idim=country:B HS&ifdim=country &hl=en&dl=en
Draft: Violence Symposium, 3rd November 2011 Page | 8 Figure 1: A scatterplot depicting the limited corr elation between crime rate and unemployment. 22.5 20.0 17.5 15.0 12.5 10.0 7.5 5.0 0.011 0.010 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 unemploymentcrime rateScatterplot of crime rate vs unemployment Figure2: A scatterplot depicting the correla tion between crime ra te and population
Draft: Violence Symposium, 3rd November 2011 Page | 9 350000 300000 250000 200000 150000 100000 0.010 0.008 0.006 0.004 0.002 0.000 populationcrime rateScatterplot of crime rate vs population Figure 3: A scatterplot depicting the co rrelation between crime rate and GDP ) 8000 7000 6000 5000 4000 3000 2000 1000 0 0.010 0.008 0.006 0.004 0.002 0.000 GDPcrime rateScatterplot of crime rate vs GDP
Draft: Violence Symposium, 3rd November 2011 Page | 10
Draft: Violence Symposium, 3rd November 2011 Page | 11 Figure 4: A scatterplot depicting a large correlation between cr ime rate and population2 and GDP2 ) 60000000 4 0000000 0.000 0.005 20000000 0.010 3.00 00E+10 6.0000E+100 9.0000E+10 1.2000E+11 crime rate GDP squared population squared3D Scatterplot of crime rate vs GDP squared vs population squared
Draft: Violence Symposium, 3rd November 2011 Page | 12 Appendix 1: Data on crime, employment, population and GDP from 1960-2007 Year Number Crimes IOL data UnemploymentPopulation Population/crimes Crimes/population GDP 1960 109644 169.802 1961 115284 190.096 1962 121327 212.253 1963 115 1276441109.9478260870.0009009432 237.743 1964 142 134072944.16901408450.0010591324 266.664 1965 140 1404701003.35714285720.0009966541 300.392 1966 197 146813745.24365482230.001341843 340 1967 217 153068705.38248847930.0014176706 390.196 1968 233 159082682.75536480690.0014646534 444.902 1969 232 164679709.82327586210.0014088014 528.137 1970 243 169744698.53497942390.0014315675 538.423 1971 328 174197531.08841463410.0018829257 573.4 1972 376 178097473.66223404260.0021112091 590.9 1973 506 6.74 181655359.00197628460.0027855 670.9 1974 748 185165247.54679144390.0040396403 632.4 1975 583 17.87 21.2188851323.92967409950.0030870898 596.2 1976 611 192774315.50572831420.0031695146 642.1 1977 548 19.42 20.7196889359.28649635040.0027832941 713 1978 694 201181289.8861671470.0034496299 832.4 1979 933 11.33 205601220.36548767420.0045379157 1140 1980 1114 13210109188.60771992820.0053020099 1335 1981 1192 214732180.1442953020.0055511056 1427 1982 1093 219482200.80695333940.0049799072 1578 1983 1234 224280181.75040518640.005502051 1733 1984 1145 229019200.01659388650.0049995852 2041 1985 1077 233626216.92293407610.0046099321 2321 1986 1107 13.5 12.2238054215.0442637760.0046502054 2473 1987 1142 242338212.20490367780.0047124264 2714 1988 1691 13.7 11246593145.82672974570.0068574534 2818 1989 1718 14.91 11.7250977146.08672875440.0068452488 3062 1990 1994 255603128.18605817450.0078011604 3166 1991 2049 16.03 12.3260507127.13860419720.0078654316 3111 1992 2144 20 14.8265633123.8959888060.0080712863 3109 1993 2391 17.95 13.1270885113.29360100380.0088266238 3092 1994 2831 19.1 13.327612397.53549982340.0102526772 3259 1995 2106 15.59 10.9281241133.54273504270.0074882396 3429 1996 2911 16.87 11.528621398.32119546550.010170747 3609 1997 2375 14.68 9.8291059122.55115789470.0081598576 4205
Draft: Violence Symposium, 3rd November 2011 Page | 13 Year Number Crimes IOL data UnemploymentPopulation Population/crimes Crimes/population GDP 1998 2243 12.14 7.8295771131.86402139990.0075835697 4714 1999 2089 12.29 7.8300354143.7788415510.0069551263 5150 2000 1591 304812191.58516656190.0052196108 5528 2001 1310 11.33 6.9309133235.9793893130.0042376582 5659 2002 1740 15.28 9.1313319180.06839080460.0055534455 5912 2003 1608 18.83 10.8317407197.39241293530.0050660508 5942 2004 1626 17.99 10.2321453197.69557195570.0050582822 6032 2005 1502 18.18 10.2325496216.70838881490.004614496 6509 2006 1594 13.83 7.6329551206.74466750310.0048368841 6876 2007 2041 14.62 7.9333609163.45369916710.0061179405 7234