A Statistical Analysis: Is the Homicide Rate of the United States Affected by the State of the Economy?

Transcription

1 Modon 1 A Statistical Analysis: Is the Homicide Rate of the United States Affected by the State of the Economy? Michael Modon 1 December 1, 2007 Abstract This article analyzes the relationship between the annual number of homicides per 100,000 Americans and the state of the United States economy between 1950 and Multi-variable analysis is used in order to examine the correlation between the homicide rate, year over year Gross Domestic Product change, and unemployment rate. Graphs and correlation values are included. 1 Junior, The University of Akron; Finance, Economics Major; Expected Graduation: May 2010

2 Modon 2 Introduction Over the course of American history, the United States economy has affected various other aspects of the nation. A normative statement could be made saying The U.S. economy and the homicide rate are inversely related. That is to say: the better the American economy, the lower the homicide rate will be. While this statement might see logically correct, it has not been proven that this correlation between economy and homicide is statistically significant. Between 1950 and 2006, the economy has experienced many prosperous eras, but has also seen a fare share of recessions. Likewise, homicide rates have also climbed and fallen multiple times over the 56 year period. Homicide rates of the United States are reported two different ways. The annual number of homicides is reported, but not necessarily a good variable to examine when analyzing a time-series trend that spans over fifty years. Because the population of the Untied States increases every year, it would be rational in concluding that, all other variables held constant, the number of homicides each year will increase solely due to the fact that there are more people living in the U.S. Therefore, the Federal Bureau of Investigation reports a rate of homicides based on every 100,000 people in the nation. Table 1 of the Appendix displays rates from 1950 to 2006 of homicide rates in the U.S. per 100,000 people. The unemployment rate is a good indicator of the condition of the national economy. Every year, many Americans are surveyed about this current employment. The classification of unemployed entails that the individual is in fact looking for a job;

3 Modon 3 however, they cannot find one due to the current economic situation. Every year this data is reported to the U.S. Department of Labor through the Bureau of Labor Statistics. Please see Table 2 in the Appendix to view the annual unemployment rate from 1950 to The Gross Domestic Product (GDP) is another reflective number for the national economy. GDP is affected by a number of variables, including consumption and the trade balance. However, due to inflation, annual nominal GDP figures are adjusted to all reflect values from the same year. These figured represent annual real GDP numbers. Growth values are determined by taking the percentage of the difference between consecutive years and dividing it by the total GDP of the initial year. 2 The Bureau of Economic Analysis reports the year over year growth. Real GDP growth numbers from 1950 to 2006 are illustrated in Table 3 of the Appendix. Data and Results The SAS program was used to analyze all three variables of the data. By following the written computer code, the SAS software was able to display simple summary statistics as well as correlation coefficients. From there, two-dimensional graphs comparing GDP growth to the unemployment rate, GDP growth to the homicide rate, and unemployment rate to the homicide rate were created. The actual SAS code used in obtaining the statistics and graphs can be viewed in the Appendix. 2 The mathematical equation to determine real GDP growth is: (Real GDP n+1 Real GDP n ) / Real GDP n, where n represents the current year.

4 Modon 4 By viewing the MEANS Procedure in the SAS data, one can determine that the average unemployment rate over the last 56 years is 5.66%, the average real GDP growth is 3.49%, and the average homicide rate per 100,000 Americans is 7%. Out of the three variables, unemployment rate tends to be the most stable of the three variables and has the smallest distribution. The standard deviation for the unemployment rate is 1.48, compared to GDP growth of 2.34 and the homicide rate of Also, the range of the homicide rate is the smallest, with a maximum of 10.2 in 1980 and minimum of 4 in The change is GDP growth is the most varied. The range between maximum and minimum is over a 10% difference, and its standard deviation is the highest. The detailed summary statistics can be found in the appendix. The values of the Pearson correlation coefficients help indicate the relationship between two different variables. The coefficients are calculated by using the CORR Procedure in SAS. By looking at the correlation coefficients, the relationship between the homicide rate and the unemployment rate is the strongest, having a value of.572. This indicates that there exists a positive relationship between the two variables. As the unemployment rate increases, the homicide rate per 100,000 people increases as well. The graph displaying unemployment rate vs. homicide rate per 100,000 shows this correlation, as the data points are either in the bottom left or top right of the graph. A best-fit line with positive slope can be eyeballed, and it becomes apparent that the unemployment and homicide rates are related to one another.

5 Modon 5 The next strongest correlation between variables is the GDP growth and unemployment rate variables. The correlation value is This indicates that there is a negative relationship between real GPD percentage change and the unemployment rate. While this relationship would seem strong if there is more unemployment in the U.S. then one would assume that the GPD would be less statistically it is not as powerful as the relationship between the unemployment rate and the homicide rate. When examining the graph, one can tell that the relationship between variables is negative and not positive. But, the data points are more spread out, making it harder to determine the strength of the relationship between GDP growth and unemployment.

6 Modon 6 The correlation between GDP growth and homicide rate is not very strong. The correlation value given by SAS is only This indicates that these two variables are less related than the GDP growth with unemployment. Also, the correlation is negative, indicating that as GDP growth increases, the homicide rate per 100,000 Americans decreases. When analyzing the graph, it is very hard to determine if the data points are in some sort of arrangement. Instead, the graph shows a jumbled scatter plot.

7 Modon 7 Conclusion After analyzing the data and graphs, it is most apparent that there exists a relationship between the homicide rate in the U.S. and the state of the American economy. It can also be determined that there are multiple ways to measure the strength of the economy, and that these different variables can be utilized to manipulate the set of data. While many would agree that both the GDP yearly growth and unemployment rate are factors that help analyze the strength of the economy, the statistical analysis of each variable compared to the homicide rates from 1950 to 2006 show that the two variables are extremely different. The correlation coefficient for comparing unemployment to the homicide rate is twice as large as the coefficient for comparing GDP growth to the homicide rate. If the unemployment rate and GDP growth are similar indicators of how the economy is doing, then it would make sense that each variable s relationship toward the homicide rate would be similar. Instead, the difference between coefficient values is quite drastic. Therefore, assuming that unemployment rate is the variable used to indicate how the economy is doing, it can be said that there is a strong relationship between the homicide rate and the state of the United States economy.

8 Modon 8 Appendix Table 1: Homicide Rates Homicide Rate Per Year 100K Source: Department of Justice : Table 2: Unemployment Year Unemployment Rate

9 Modon Source: Bureau of Labor Statistics Table 3: Real GDP Real GDP percent Year change Source: Bureau of Economic Accounts

10 Modon 10 References Bureau of Economic Accounts. (2007). Gross Domestic Product. Retrieved December 2, 2007, from U.S. Deptartment of Justice Web site: index.htm#gdp Bureau of Justice Statistics. (2007, January 17). Homicide victimization, Retrieved December 2, 2007, from U.S. Department of Justice Web site: Bureau of Labor Statistics. (2007, February 6). Retrieved December 2, 2007, from U.S. Department of Labor Web site: