Black Homicide (Arrests) & Unemployment
Blandon Casenave
12/11/2016
ABSTRACT
The purpose of this analysis is to determine if there is a relationship between homicide and unemployment in the US among the general population, and comparatively among its Black/African-American population. Using observational time-series data, collected between 1960-2015 for the general population, this analysis couldn’t reject the null hypothesis at a 99%, 95% or 90% confidence level (p-value = .17). However, the null hypothesis could be rejected when measuring the linear relationship between Aggravated Assault and Homicide (p-value = .0001).
In contrast, the data set for Black/African-American Violent Crime from 1980-2012 yielded results that allows the rejection of the null hypothesis that unemployment and homicide are not connected (p-value = .00). Also, within the same model the null hypothesis for aggravated assault’s relationship to Black homicide was rejected (p-value = .00). An extended data set that included 2013-2015, yielded almost identical results.
METHODOLOGY
Dependent Variable
For the purposes of this analysis, “Murder and nonnegligent manslaughter” Arrests as recorded by the FBI Uniform Crime Reports (UCR) data is our dependent variable, that operationalizes “Murder”. The murder rate per 100,000 is calculated by dividing the murder count by the population, and then multiplying by 100,000. The murder rate for the general population, as well as other violent crimes were calculated by the FBI UCR in two separate studies\(^1\), that were combined into one data table that was then trended data from 1960 - 2015 for this analysis.
Independent Variables
National unemployment rates were extracted from the Bureau Labor & Statistics\(^2\) and added to the above crime table to produce one data frame.It’s worth noting that the Participation Rate, Civilian Labor Force divided by the Civilian noninstitutional population is relatively even between Blacks and Whites in the US\(^3\). Given that we are concerned with the incidence of violent street crime for this analysis, considering an overall unemployed population size that includes persons that are already institutionalized, and no longer capable of committing additional street crime, isn’t applicable for this analysis. Therefore, we proceeded with unemployment rate as defined by BLS as our metric to generally capture the phenomenon of unemployment.
Violent crimes besides Homicide collected by the FBI UCR were also included in our data set, they are: Rape, Robbery & Aggravated Assault. For the crime of rape, a new definition was created in 2012 (Forced Rape). However, for the purposes of our analysis only the legacy definition was used for the years 2012-15.
Multicolinearity - Using the full set of violent crime presented problems of multicolinearity for two reasons. The overall Violent Crime Rate is an actually composite of the other violent crimes, making it directly related to the discrete crime types listed in our data, therefore this variable had to be excluded from our model. Also, interrelationships between crimes presented problems with the remaining variables. The common warnings of multicolinearity were present - unexpected coefficient signs, and near perfect R\(^2\) values.
Black/African-American Data Set
The initial data sets collected for this analysis were the homicide victim counts as reported by the FBI National Crime Victim Survey (NCVS). However, the only complete data sets by race went through the year 2008\(^4\). It wasn’t clear where to find newer data sets, or what population estimate had been used previously in order to replicate for the years 2009-2015.However the data set made available by Snyder and Wangota, in the BJS Data Analysis Tool that spanned 1980-2012, filtered on race and violent crime, provided the most complete data set available at this time\(^5\). Finally, the BLS started tracking Black Unemployment monthly in 1972\(^6\), that data set was merged with Violent Crime data spanning the years of 1980-2012, to created the blackdata table utilized for this study.
A manual calculation was performed using the “Black Alone” racial category from the Census/ACS counts for 2013\(^7\) and 2014-15\(^8\). To replicate the murder rates published in the Snyder & Wangota study, the Black population percentages from the Census/ACS 2013\(^9\), 2014\(^{10}\) and 2015\(^{11}\) studies, were applied to the FBI UCR Population Estimates, and then applied to the Murder Rate per 100,000 equation. These manually extended estimates for 2013-15, were pulled into a separate data frame (blackadd), and then combined with the original blackdata table, to form the data frame blackdata2015.
[Black Data] Multicolinearity The same issues that were observed in the general population data set, were also present in the Black/African-American data set, and were remedied in similar fashion.
[Black Data] Categorical Dummy Variable - A custom categorical variable was created to account for years when the actual count of Homicide arrests of Blacks, exceeded the number of arrests of whites (Yes=1, No=0).This variable was added to the data tables that contains time series data for black violent crime arrests and unemployment.
## Warning in read.table(file = file, header = header, sep = sep, quote
## = quote, : incomplete final line found by readTableHeader on 'https://
## raw.githubusercontent.com/Misterresearch/CUNY-Projects/master/
## blackdataadd.csv'*DATA SET - SUMMARY & INDIVIDUAL & VARIABLE DISTRIBUTION** General Population Crimetable
## Year Population Violent Rate Murder Rate
## Min. :1960 Min. :179323175 Min. :158.1 Min. : 4.400
## 1st Qu.:1974 1st Qu.:211006750 1st Qu.:383.3 1st Qu.: 5.475
## Median :1988 Median :243393950 Median :475.9 Median : 7.100
## Mean :1988 Mean :247445102 Mean :470.7 Mean : 7.105
## 3rd Qu.:2001 3rd Qu.:285981650 3rd Qu.:576.5 3rd Qu.: 8.850
## Max. :2015 Max. :321418820 Max. :758.2 Max. :10.200
## Rape Rate Robbery Rate Assault Rate National Unemployment
## Min. : 9.40 Min. : 58.3 Min. : 85.7 Min. :3.500
## 1st Qu.:25.55 1st Qu.:128.7 1st Qu.:212.0 1st Qu.:5.050
## Median :31.30 Median :168.8 Median :282.7 Median :5.750
## Mean :28.71 Mean :167.6 Mean :267.3 Mean :6.089
## 3rd Qu.:35.92 3rd Qu.:217.1 3rd Qu.:326.6 3rd Qu.:7.100
## Max. :42.80 Max. :272.7 Max. :441.9 Max. :9.700Original Blackdata
## Year Homicide Rape Robbery
## Min. :1980 Min. :12.50 Min. :13.60 Min. :132.5
## 1st Qu.:1988 1st Qu.:17.20 1st Qu.:22.20 1st Qu.:166.5
## Median :1996 Median :29.20 Median :38.50 Median :261.9
## Mean :1996 Mean :27.25 Mean :38.67 Mean :244.9
## 3rd Qu.:2004 3rd Qu.:36.70 3rd Qu.:56.00 3rd Qu.:316.1
## Max. :2012 Max. :41.90 Max. :60.40 Max. :352.4
## Aggravated.Assault Black.Unemployment Black.Higher
## Min. :306.7 Min. : 7.60 Min. :0.0000
## 1st Qu.:381.7 1st Qu.:10.10 1st Qu.:0.0000
## Median :435.4 Median :11.50 Median :1.0000
## Mean :461.3 Mean :12.31 Mean :0.6667
## 3rd Qu.:560.4 3rd Qu.:14.60 3rd Qu.:1.0000
## Max. :637.7 Max. :19.50 Max. :1.0000Extended Blackdata through 2015
## Year Homicide Rape Robbery
## Min. :1980 Min. :12.50 Min. :13.40 Min. :127.3
## 1st Qu.:1989 1st Qu.:16.88 1st Qu.:19.88 1st Qu.:159.8
## Median :1998 Median :26.80 Median :34.05 Median :204.7
## Mean :1998 Mean :26.14 Mean :36.71 Mean :235.6
## 3rd Qu.:2006 3rd Qu.:35.50 3rd Qu.:55.33 3rd Qu.:315.6
## Max. :2015 Max. :41.90 Max. :60.40 Max. :352.4
## Aggravated.Assault Black.Unemployment Black.Higher
## Min. :300.7 Min. : 7.60 Min. :0.0000
## 1st Qu.:365.6 1st Qu.:10.10 1st Qu.:0.0000
## Median :425.6 Median :11.50 Median :1.0000
## Mean :448.6 Mean :12.22 Mean :0.6944
## 3rd Qu.:557.2 3rd Qu.:14.38 3rd Qu.:1.0000
## Max. :637.7 Max. :19.50 Max. :1.0000
Based on the histograms and scatter plots, the explanatory variables that were used in the final linear model have a near normal distribution:
Crimetable[Murder] = bimodal Crimetable[Rape] = left skew (dropped) Crimetable[Robbery] = nearly normal (dropped) Crimetable[Aggravated Assault] = nearly normal Crimetable[Unemployment] = nearly normal
Blackdata[Murder] = unimodal Blackdata[Rape] = unimodal (dropped) Blackdata[Robbery] = bimodal (dropped) Blackdata[Aggravated Assault] = nearly normal Blackdata[Unemployment] = nearly normal, bimodal
Blackdata diagnostic applies to Blackdata2015. REGRESSION RESULTS & DIAGNOSTICS**
General Population Crimetable Regression Summary
##
## Call:
## lm(formula = `Murder Rate` ~ `National Unemployment` + `Assault Rate`,
## data = crimetable)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.6674 -1.5764 0.2094 1.2634 3.1819
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.091835 1.045691 3.913 0.000262 ***
## `National Unemployment` 0.136891 0.150071 0.912 0.365808
## `Assault Rate` 0.008154 0.002369 3.443 0.001132 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.72 on 53 degrees of freedom
## Multiple R-squared: 0.2107, Adjusted R-squared: 0.1809
## F-statistic: 7.074 on 2 and 53 DF, p-value: 0.001892General Population Crimetable Residual Plot 
Below are the genral populatio “crimetable”" correlations between the independent variables that remained in the final linear regression model, notice that the correlation is weak: \ National Unemployment & Assault Rate
## [1] 0.1688369Below are the general populatio “crimetable”" correlations between the independent variables that were removed and National Unemployment: \ National Unemployment & Robbery Rate
## [1] 0.2894432National Unemployment & Rape Rate
## [1] 0.2856348Assault Rate & Rape Rate
## [1] 0.9620128##
## Call:
## lm(formula = Homicide ~ Black.Unemployment + Aggravated.Assault,
## data = blackdata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.0234 -2.9675 -0.2485 2.6235 12.3226
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -32.330178 6.018617 -5.372 8.16e-06 ***
## Black.Unemployment 1.694637 0.290486 5.834 2.22e-06 ***
## Aggravated.Assault 0.083945 0.008697 9.652 1.04e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.912 on 30 degrees of freedom
## Multiple R-squared: 0.7809, Adjusted R-squared: 0.7663
## F-statistic: 53.46 on 2 and 30 DF, p-value: 1.288e-10
\ 
\ 
Below are the Black/AA “blackdata” correlations between the independent variables in the final model, notice that there’s no strong correlation: \ Black Unemployment & Aggravated Assault Arrests
cor(blackdata$Black.Unemployment, blackdata$Aggravated.Assault)## [1] -0.23066Below are the Black/AA “blackdata” variables that were removed (Robbery & Rape), and there correlations to the explanatory variables that remained (Unemployment & Assault) \ Black Unemployment & Robbery Arrests
cor(blackdata$Black.Unemployment, blackdata$Robbery)## [1] 0.4467175Black Unemployment & Rape Arrests
cor(blackdata$Black.Unemployment, blackdata$Rape)## [1] 0.4440861Black Aggravated Assaults & Rape Arrests
cor(blackdata$Aggravated.Assault, blackdata$Rape)## [1] 0.5316729##
## Call:
## lm(formula = Homicide ~ Black.Unemployment + Aggravated.Assault,
## data = blackdata2015)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.0879 -2.9239 -0.2347 2.8318 12.2214
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -30.707199 5.254242 -5.844 1.53e-06 ***
## Black.Unemployment 1.630743 0.274898 5.932 1.18e-06 ***
## Aggravated.Assault 0.082286 0.007657 10.747 2.59e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.781 on 33 degrees of freedom
## Multiple R-squared: 0.8012, Adjusted R-squared: 0.7891
## F-statistic: 66.5 on 2 and 33 DF, p-value: 2.655e-12
As we’re able to see from the summary tables, plots and graphs the residuals for all three tables are nearly normally distributed, the variance from the regression line is equal. However, the assumption of linearity might be weak, but it’s also important to note that a clear non-linear pattern doesn’t emerge either.
REGRESSION ANALYSIS RESULTS \ Based on the observational data that has been collected, we cannot reject the null hypothesis for the general population data set that unemployment and homicide are not related. The reported p-value in our final linear regression model for National Unemployment was .37, beyond the threshold for a 99%, 95% or 90% Confidence Interval.
However, in the case of the Black/African-American observational data set, the final linear regression model leads to rejecting the null hypothesis that unemployment and murder are not related. The final model for the original Black data set that spanned 1980-2012, shows a positive coefficient (as expected) between Black unemployment and Black arrests rates for murder, and p-values below .00000226. The intercept in this case has no real tangible meaning, asserting that there would be a rate of -32.33 murder arrests among Blacks. However, the slope coefficient suggests that for every one percentage increase in the Black unemployment rate, there’s an increase of 1.7 in the arrests made of Blacks murder suspects.
In both data sets, multicolinearity - as evidenced by unexpected coefficient signs and nearly perfect R-squared values, prevented the full data set from being used. However, what’s also very interesting as that it appears that the same variables produced multicolinearity, resulting in the same model for the general population and the black data set:
Y\(_{Homicide Arrest Rate}\) = b\(_0\) + b\(_{Unemployment}\) + b\(_{Assault}\).
(Aggravated Assault met the statistical threshold to reject the null hypothesis at a 99% CI in both data sets)
Finally, although the regression models included the same variables for both groups - the R-squared values were vastly different. The linear regression model for the general population “crimetable” has an r-squared value of .21, for the original “blackdata” set it’s .79…and for the 2015 manually extended black data set it’s .80.
In other words, 80% of the variability in Black homicide arrests can be explained by unemployment and assault, while among the general population unemployment wasn’t observed to be a factor at all - leaving only assault, which would explain 21% of the variation in homicide arrests.
There are several other directions that could be pursued with this data, such as expanding the crime types to include non-violent offenses related to drug arrests. Perhaps the relationship between unemployment and homicide (arrests), is the result of participation in a street-level drug economy that is often more deadly. Again, more data and more advanced analytical methods are needed to expose bidirectional relationships between the variables identified here - as well as others that were excluded from this analysis. ADDENDUM: BAYESIAN ANALYSIS
## Loading required package: coda## Loading required package: Matrix## ************
## Welcome to BayesFactor 0.9.12-2. If you have questions, please contact Richard Morey (richarddmorey@gmail.com).
##
## Type BFManual() to open the manual.
## ************## Bayes factor analysis
## --------------
## [1] Black.Unemployment : 1.473024 ±0%
## [2] Aggravated.Assault : 198251.7 ±0.01%
## [3] Black.Unemployment + Aggravated.Assault : 2627976768 ±0%
##
## Against denominator:
## Intercept only
## ---
## Bayes factor type: BFlinearModel, JZSA quick look at applying the Bayesian regression out final data model of black crime and unemployment, it also confirms the output of the linear regression model. The output here confirms that alternative hypothesis that the slopes are non-zero\(^{12}\). It further illustrates that the most robust model that explains Black Homicide Arrests, is the one includes Unemployment & Aggravated Assault - that it’s 2.6B more likely than the intercept only model (no explanatory variables)\(^{13}\). Sources:
[1] National Violent Crime Trend: BJS 1960 - 2012, BJS 1996 - 2015. Revised Rape definition in 2012. Legacy definition used for this analysis.
[2] National Unemployment Trend Source:BLS Unemployment 1940 - 2015
[3] http://www.bls.gov/emp/ep_table_303.htm
[4] Black Violent Crime Trend (Victim): 1980 - 2008, Homicide Trends in the United States. http://www.bjs.gov/index.cfm?ty=pbdetail&iid=2221
[5] Authors: Howard N. Snyder, Ph.D., Joseph Mulako-Wangota, Ph.D. BJS Arrest Data Analysis Tool (Homicide by Race 1980 - 2012): http://www.bjs.gov/index.cfm?ty=datool&surl=/arrests/index.cfm#
[6] Black Unemployment Trend: BLS, monthly data Jan 1972 - Oct 2016. Data was averaged to derive annual rate through 2015. http://beta.bls.gov/dataViewer/view/timeseries/LNS14000006
[7] (Used for 2009-2013 Race Estimate) Black Population - Annual Social and Economic (ASEC) Supplement to the Current Population Survey (CPS): http://www.census.gov/population/race/data/black.html
[8] (Used for 2014 -2015 Race Estimate) Annual Estimates of the Resident Population by Sex, Single Year of Age, Race, and Hispanic Origin for the United States: April 1, 2010 to July 1, 2015: http://factfinder.census.gov/faces/nav/jsf/pages/guided_search.xhtml
[9] 2013 FBI Homicide Arrests by Race (Table 43): https://ucr.fbi.gov/crime-in-the-u.s/2013/crime-in-the-u.s.-2013/tables/table-43
[10] 2014 FBI Homicide Arrests by Race (Table 43): https://ucr.fbi.gov/crime-in-the-u.s/2014/crime-in-the-u.s.-2014/tables/table-43
[11] 2015 FBI Homicide Arrests by Race (Table 43): https://ucr.fbi.gov/crime-in-the-u.s/2015/crime-in-the-u.s.-2015/tables/table-43
[12]Richard D. Morey,BayesFactor https://cran.r-project.org/web/packages/BayesFactor/BayesFactor.pdf, p45.
[13]Navarro, Daniel - Learning statistics with R: A tutorial for psychology students and other beginners, p580. Notes: The following sources were also consulted to provide baselines for the expected values,but were not used in the final data sets.
2009 FBI Homicide Arrests by Race (Table 43): https://www2.fbi.gov/ucr/cius2009/data/table_43.html
2010 FBI Homicide Arrests by Race (Table 43): https://ucr.fbi.gov/crime-in-the-u.s/2010/crime-in-the-u.s.-2010/persons-arrested
2011 FBI Homicide Arrests by Race (Table 43): https://ucr.fbi.gov/crime-in-the-u.s/2011/crime-in-the-u.s.-2011/persons-arrested/persons-arrested
2012 FBI Homicide Arrests by Race (Table 43): https://ucr.fbi.gov/crime-in-the-u.s/2012/crime-in-the-u.s.-2012/tables/43tabledatadecoverviewpdf