2005 State Murder Rates

Noel Somarriba

Eco 328

December 11, 2007 2

Table of Contents

Abstract……………………………………………………………………………………….pp. 1

Introduction…...……………………………………………………………………………...pp. 2

Literature Review…………..………………………………………………………………...pp. 4

Model...... ………………………………………………………………………………….pp. 9

Main Hypothesis...... …………………………………………………………………………pp.13

Econometric Issues…………………………..……………………………………………….pp.14

Data………………...…………………………………………………………………………pp.16

Data Problems…………………….…………………………………………………………..pp.18

Descriptive Statistics…….…………………..………………………………………………..pp.19

Empirical Results ………………...…………………………………………………………..pp.20

Initial Regression..……………………………………………………………………………pp.20

Corrections for Econometric Issues…………….…………………………………………….pp.24

Final Regression Output……………….……………………………………………………..pp.28

Conclusion...………………………………………………………………………………….pp.29

References……………………………………………………………………………………pp.31 3

Abstract

For decades sociologists and economists have attempted to better understand the underlying socioeconomic factors that explain murder rates. These studies have differed immensely throughout the last couple of decades. For instance, some have explained the variance in the murder rates as simply a matter of location, while others have found relationships with unorthodox factors such as the abortion rate. This cross-sectional study attempts to explain the

2005 murder rates of the 50 states. These murder rates are set to be explained by six independent variables; poverty, educational attainment, black population, certainty of punishment, severity of punishment, and the effective abortion rate. In this study, the results show that the variable with the largest impact on the state murder rate in 2005 was severity of punishment. Regressions indicate that if a state has the death penalty, its murder rate will be 33% higher than that of states without the death penalty, all else held constant. The second largest impact on the 2005 state murder rate was experienced through a change in poverty. This study shows that a 1% increase in the proportion of the state population that is living in poverty in 2005 will increase that state’s murder rate by 4% in 2005. 4

Introduction

This study attempts to explain the murder rate for each state in 2005 through the use of six socioeconomic independent variables. Although murder is known to be an unpredictable act, my interest in the subject lies within the ability to explain these state murder rates through measurable factors. The most common applicable factors seem to be socioeconomic ones. This is due to the fact that these are the factors that portray the living circumstances that all members of a certain state experience daily. The socioeconomic independent variables included within this study are poverty, educational attainment, black population, certainty of punishment, severity of punishment, and the effective abortion rate. The main question to be answered within this study is which socioeconomic variable generates the largest effect on the murder rate. Another question I would like to explore is whether the Death Penalty really works. In other words, does having the Death Penalty really result in lower murder rates?

Past studies have varied both in form and results throughout the past. Gibbs (1969) conducted a time-series study and found that certainty of punishment had a deterrent effect on the murder rate. Tittle’s (1969) study of different crime rates found that severity of punishment has a deterrent effect exclusively on the murder rate. Although these studies seem practical, other studies were not. For instance, Gastil(1971) and Hackney (1969) attributed higher murder rates to a states “southerness”, or southern location. In an analysis of these studies, Loftin and Hill

(1974) found that there was omitted variable bias. Therefore, Gastil and Hackney did not include all relevant variables. As a result, Loftin and Hill (1974) developed a “structural poverty index” that explained a larger variance of the murder rates and caused location variables to become insignificant. Then, Blau and Blau (1982) tested the whether poverty or income inequality was to blame for higher murder rates. Blau and Blau (1982) found that income inequality caused 5 poverty rate variables to become insignificant. Also, even more peculiar was Donohue and

Levitt’s (2001) time-series study that concluded that the legalization of abortion in the 1970s led to the decrease in crime rates in the 1990s.

In order to encompass most of the previous studies I will attempt to use the most relevant variables from each study. The data for these variables will be collected from several sources.

The main sources include the Census Bureau, Federal Bureau of Investigation crime statistics, and the Death Penalty Information Center. These sources seem to be dependable and trustworthy.

My study showed that the variable with the largest effect on a state’s murder rate in 2005 was the SOP variable. This variable indicated that states with the Death Penalty have a murder rate 33% higher than that of states without the death penalty, all else held constant. This proved that the Death Penalty does not have a deterrent effect on the murder rate. Although this was not the expected effect, it makes sense. States with the Death Penalty are usually those that need it the most. In other words, those states tend to have higher murder rates. Unfortunately, the results found for the effective abortion rate and the certainty of punishment variables were not similar to that of previous studies. Both led to increases in the murder rate, this was not the expected relationship. However, certainty of punishment was insignificant and was later dropped from the regression. The socioeconomic variable with the largest impact on the 2005 state murder rate was poverty. This study shows that a 1% increase in the proportion of the state population that is living in poverty in 2005 will increase that state’s murder rate by 4% in 2005. This variable was also significant. Therefore, within my model, poverty is the socioeconomic factor with the largest effect on a state’s murder rate. 6

Literature Review

The determinants of murder rates have been studied for decades. The interest in this statistical study seems to lie in the relatively high homicide rate of the United States compared to the rest of the “modernized world” (Gastil, 1971). Throughout my research for empirical studies

I have found that punishment and structural poverty have been the most significant factors in explaining the variations within the homicide rate. However, it seems as though every study has used a different methodology in defining these variables.

One of the most widely studied determinants of the murder rate has been punishment.

Common belief is that fear of punishment will deter a person from engaging in deviant activities.

However, even though this is a commonly held assumption, previous studies have shown mixed results. One form of punishment within our judicial system almost exclusively reserved for murder is capital punishment; or the death penalty. It is because of this that most studies focus on the relationship between capital punishment and the homicide rate.

Karl F. Schuessler (1952) analyzed the murder and execution rates for U.S. states from

1925 to 1949 in order to determine “whether differences in use of the death penalty correspond to differences in the relative occurrence of murder” (pp. 54) and “whether fewer murders occur in places where murder is punishable by death” (pp. 54). Schuessler first observed that executions between 1930-1939 and 1940-1949 dropped proportionately to the drop in the total number of murders. Between the decades, there was a 29% drop in executions and a 27% drop in total murders (Schuessler, 1952, pp. 57). Consequently, Schuessler concluded that since “capital punishment policy and practice in this country was fairly stable in the period 1924-1949; consequently, the movement of the murder rate…cannot be attributed to changes in the use of the death penalty…the death penalty and the murder rate are unrelated except in the circular 7 circumstance that more murders involve more death penalties” (pp. 57). Schuessler continued exploring these findings by controlling for “social circumstance”. He did so by pairing up states with similar population, racial composition, and location with only differences lying within death penalty policies. Schuessler concluded that in states with similar social circumstances, but differing death penalty laws, there is no significant difference in the murder rate.

On the other hand, studies that support deterrent theories do not simply rely on the existence of capital punishment within a state to determine its effect on the homicide rate. Two studies were conducted in the same manner within close periods of time. Gibbs’ (1969) study was based on the certainty and severity of punishment’s effect exclusively on the homicide rate for each state from 1959 to 1960. Tittle (1969) based his research on the certainty and severity of punishment’s effects on different crime rates for every state from 1959 to 1963. In these studies, certainty of punishment was defined as the proportion of crimes known to the police that result in imprisonment. Each index was adjusted for the certain crime it was observing. Severity of punishment was defined as the “mean sentence served by prisoners for homicide” (Tittle,

1969, pp. 413). Both Tittle and Gibbs concluded that severity and certainty of punishment have a negative, or deterrent, effect on the murder rate. Tittle (1969) concluded that “for homicide-and homicide only-the greater the severity of reaction, the lower the offense rate” (pp. 417). In other words, the more severe a punishment or the increased length of prison sentences for murder, the lower the murder rate. Furthermore, Tittle (1969) concluded that homicide also had “the higher mean certainty ratio (.471) and the lowest rate of offense (.00005)” (pp. 417), meaning the higher the possibility of getting caught, the lower the murder rate.

The term “structural poverty” was introduced by Loftin and Hill (1974). This study mainly examined the thesis developed by Hackney (1969) and Gastil (1971) which concluded 8 that the main indicator of the murder rate was a states location. Gastil (1971) used a “southerness index” and Hackney (1969) used a confederate state dummy variable to measure a state’s relative location. Both studies concluded that the “southern” sub-culture of violence was to blame for higher murder rates. However, Loftin and Hill criticized the Gastil-Hackney measurements of culture as measuring only regional location and not sufficiently controlling for the other socioeconomic factors that influence culture in a particular area. This led to the development of

“structural poverty index” in order to capture more of the socioeconomic variance within the homicide rate. The “structural poverty index” was designed to capture the percent of the population who are “at the lowest levels with respect to socioeconomic variables” (Loftin and

Hill, 1974, pp. 719). This was done due to the strong theoretical evidence that people at these low levels of social standing tend to have experience higher crime rates in comparison to people in other levels (Loftin and Hill, 1974, pp. 717). The “structural poverty index” included “the infant mortality rates, percent of persons 25 years or older with 5 years or less of school, percent of the population illiterate, percent of families with income lower than $1000, armed forces mental test failures, and the percent of children living with one parent” (Loftin and Hill, 1974, pp. 719).

The results were astonishing. The regression model improved tremendously with the addition of other socioeconomic factors, primarily the structural poverty index. For instance,

“goodness of fit” improved dramatically; in Hackney’s (1969) model the adjusted R square is .52 compared to a similar model (using same confederate state regional variable) produced by Loftin and Hill (1974) where the adjusted R square was .92 (pp. 722). The same magnitude of results was seen in comparison to Gastil’s (1971) model. However, probably the most important difference between the models was that the strongest indicator of homicide rates was the 9 structural poverty index, and not either of the regional indices. Furthermore, the regional indices were found to be statistically insignificant (Loftin and Hill, 1974, pp.722).

Blau and Blau (1982) set out to find the effects of income inequality on violent crime.

Blau and Blau (1982) used Data on the 125 largest American metropolitan areas(SMSAs) in order to study this relationship. As a measure of inequality for each SMSA, Blau and Blau

(1982) used the Gini coefficient for family income. The Gini coefficient is used to measure the inequality of income distribution; it a ratio with values varying from zero to one. The closer to one a Gini coefficient is, the higher the level of income inequality; a zero would indicate perfect equality. Their main reason for including this variable was to build upon similar past studies that attributed much of violent crime to simply to poverty levels. Furthermore, Blau and Blau held the assumption that “a specific form of inequality is more likely to engender pervasive conflict, which finds expression in a high incidence of violence” (Blau and Blau, 1982, pp.117). In their results, Blau and Blau (1982) found income inequality to be statistically significant. Even more important, the income inequality’s coefficient when explaining the variance in the murder rate was “atleast three times its standard error” (Blau and Blau, 1982, pp. 123), indicating its high level of significance.

Donohue and Levitt (2001) sought out to explain the sudden decline in crime rates in the

United States within the 1990s through the development of a time series model. Their first assumption was that rising levels of police and imprisonment sentences were ongoing for that last thirty years and, thus, could not be responsible for explaining the “recent abrupt improvement in crime” (Donohue and Levitt, 2001, pp. 380). Therefore, Donohue and Levitt

(2001) took a more radical approach. They decided to explore the relationship between the legalization of abortion in the early 1970s and the lower crime rates in the 1990s. Donohue and 10

Levitt (2001) explained that there may be deterrent effect on crime rates due to the ability to abort. In essence, their main reasoning was that women will use abortion to choose the optimum time for child-bearing; or the optimum time in which the may raise a child adequately. Thus, those most likely to abort are those most likely to give birth to a child that they cannot adequately care for. Furthermore, these children are at a higher risk of growing up in adverse conditions and, as a result, are more likely to engage in criminal activity. Consequently,

Donohue and Levitt (2001) assumed that those “children born after abortion legalization may on average have lower subsequent rates of criminality…” (Donohue and Levitt, 2001, pp. 381).

Subsequently, Donohue and Levitt (2001) developed an effective abortion rate. Donohue and Levitt defined the effective abortion rate as:

Effective Abortion Rate = Σ Abortion Ratiot-a*(Arrestsa/Arreststotal)

Where;

a: the age of the offender

t: the time period of the offense

Abortion ratiot-a: represents the number of abortions per live birth in t minus a time period.

In other words, if the offender is 18, and the period in which the offender is

arrested is 2005, they relevant abortion ratio would be that of 1987.

Arrestsa: the number of arrests for a certain crime of the offender of age a

Arreststotal: the total number of arrests for a certain crime

In essence, the effective abortion rate served as a weighted average to account for the age of the offender and the year in which the relevant abortion ratio applies. The ages used within this model were 18-24, which were considered to be “peak criminal age” by Donohue and Levitt 11

(2001). Moreover, Donohue and Levitt’s (2001) results showed that this relationship between the murder rate and the effective abortion rate was negative when properly lagged. In other words, the higher the abortion ratio of the appropriate previous time period, the lower the murder rate in the concurrent time period. However, in comparison to other types of crime, the effective abortion rate did not carry the largest coefficient, “One additional abortion is associated with the reduction of .23 property crimes, .04 violent crimes, and .004 murders…” (Donohue and Levitt,

2001, pp. 405). Furthermore, the most significant reduction in the number of murders was seen by increases in prison sentences and the number of police.

The dependent variable for this regression model is the murder rate. The murder rate will be represented in the model by the symbol Mi. The Uniform Crime Reporting Program defines murder and non-negligent manslaughter “as the willful (non-negligent) killing of one human being by another” (fbi.gov). The murder rate is the proportion of murders known to police relative to the population of a given state in the year 2005 per 100,000 people. The dependent variable will be determined by six independent variables; poverty, certainty of punishment, severity of punishment, educational attainment, effective abortion rate, and black population.

The first independent variable used is the proportion of the states population in 2005 that was “living in poverty”. This variable will be represented by the symbol Ρi in this model. “Living in poverty” was determined by poverty thresholds. Poverty thresholds are the dollar amounts that the Census Bureau uses to determine poverty status. For example, for a person who is less than

65 years old with no living relatives under the age of 18, their poverty threshold for 2005 was

$10,160. Therefore, any person who meets these criteria and has an annual money income of less than $10,160 is considered to live in poverty. It is my expectation, due to my research of 12 previous studies, that the poverty variable will have a positive relationship to the murder rate. In other words, the higher the poverty rate for a certain state, the higher the murder rate will be within that state. Furthermore, I expect the poverty rate to be one of the most significant determinants of the variance within the murder rate. Loftin and Hill (1974) used a variable which measured poverty within their structural poverty index to explain a larger variance of the murder rate. The comparison was made to studies conducted by Gastil (1971) and Hackney (1969) that did not include this index. Some form of this index continues to be used in many studies following Loftin and Hill’s (1974).

The second independent variable used within this regression model is an educational attainment variable. The educational attainment variable will measure the percentage of people

25 years of age or older within the population of a state for 2005 that are not high school graduates. This educational attainment variable will be represented by the acronym NHSGi, standing for not a high school graduate. It is my expectation, due to my research of previous studies, that the educational attainment variable will have a positive correlation with the murder rate. In other words, the larger the 2005 percentage of the state population 25 years of age or older that are not high school graduates, the higher the state murder rate in 2005. Educational attainment was also a factor within the structural poverty index created by Loftin and Hill

(1974). Furthermore, Loftin and Hill (1974) also found a strong positive correlation between their educational attainment variable and the murder rate. Their educational attainment variable was measured as the percent of the population with 5 years or less of education. However, for my study it seems more convenient and appropriate to use graduation of high school as a measurement of educational attainment due to the low proportion of the U.S. population who 13 receive less than 5 years of education. Also, I was unable to find a statistic measuring such a variable.

The third independent variable in this model is the effective abortion rate. This variable will be represented by the acronym EARi within this model. The effective abortion rate is defined as the abortion ratio in 1987 multiplied by the proportion of total arrests for murder in 2005 that were 18 years old. In some respect, this is a lagged variable. A lagged variable is a variable from a previous time period. J.J. Donohue and S.D. Levitt (2001) conducted a study in which they found that the effective abortion rate was a significant determinant of the decrease in crime rates.

This lag time between the abortion ratio and murder rate variable was about 18 years. This was done due to the assumption held by Donohue and Levitt that people aged 18-24 are considered to be in the “peak of criminal age” (Donohue & Levitt, 2001). Furthermore, the statistics for 2005 showed that this is the age group that accounted for the largest proportion of total murders.

Therefore, it is my expectation that there will be a negative relationship between the abortion occurrence rate and the murder rate. In other words, as the abortion rate increases for a state in

1987, the murder rate for that state in 2005 will be lower. This is due to Donohue and S.D.

Levitt’s (2001) assumption that people who were most likely to be aborted are those most likely to be involved in criminal behavior.

The fourth independent variable within this model is certainty of punishment. This variable will be represented within the model by the symbol COPi. This variable is measured by the total number of arrests made for murder within a certain state for the year 2004 divided by the total number of murders known to police in a state for 2004. For example, if there are 10 murders known to police and 8 arrests for murder, there is 80% certainty. Furthermore, this is also lagged variable. Gibbs (1969) developed a certainty of punishment variable by using the 14 number of admissions to state prison for the years 1959-1963 divided by the number of crimes known to police for the years 1958-1962. Gibbs (1969) then used this ratio as the certainty of punishment ratio for 1963. As a result, Gibbs (1969) created a lagged variable to account for the lag in time our judicial process causes in order to incarcerate a criminal. The measurement of certainty of punishment within my model is computed by using arrests instead of admission to prisons and only consists of one year’s observations. This is due to the fact that I could not find prison admissions for murder data for my study and arrests by state prior to 2004. Moreover, this certainty of punishment variable would then measure the probability of getting arrested for murder within the state for the year 2004. This variable can be used as a measure of deterrence because it is a lagged variable. In other words, a person is more likely to know the historical probability of being arrested for murder than the current probability. It is my expectation that the certainty of punishment variable will have a negative relationship with the murder rate. In other words, as the probability for being arrested for murder in a state for the year 2004 increases, the murder rate of 2005 will decrease for a state.

The fifth independent variable in this model is the severity of punishment variable. This variable will be represented by the acronym SOPi within my model. The severity of punishment variable is a dummy variable where SOP equals one when a state has the death penalty and SOP equals zero when it does not. This will attempt to gauge the deterrent effect of the death penalty on the murder rate. Although previous studies have found this variable to be insignificant,

Chiricos and Waldo (1970) and Gibbs (1969), I will attempt to gauge its effect in more modern settings. It is my expectation that the severity of punishment variable will be negatively related to the murder rate. In other words, if a state has the death penalty, I expect their murder rate to be lower. 15

The sixth independent variable used in this model is the racial composition variable. This variable will be represented by the symbol Bi. This variable will measure the percentage of a state’s population in 2005 that were black. Statistics show that the majority of people on death row for murder are black, 41.7% (Death Row, 2007). Furthermore, Blaus and Blaus (1982) found a statistically significant relationship between the percent of the population who were black and the murder rate. Thus, it is my expectation that the coefficient for this variable will be positive. In other words, the higher the percentage of the population that is black in 2005, the higher the murder rate will be for that state.

The mathematical representation of my model is as follows:

Mi = ß0 + ß1P i + ß2 NHSG i - ß3 EAR i - ß4COPi - ß5 SOP i+ ß6Bi +i

Where:

Mi: state murder rate per 100,000 people

P i: percent of state’s population “living in poverty”

NHSG i: state percentage of population 25 or older not a high school graduate

EAR i: effective abortion rate by state

COPi: state certainty of punishment for the year 2004

SOP i: severity of punishment, dummy variable where SOP=1 if state has a death penalty

and D=0 if state does not

Bi: percent of a state’s population that is black in 2005

Main Hypothesis

The main hypothesis test for my regression model is to determine which socioeconomic factor has the largest effect on the state murder rate in 2005.

Hypothesis tests for each independent variable can be set up as the following: 16

Ho: ß1≤0 I expect the coefficient of poverty to be positive.

Ha: ß1>0

Ho: ß2≤0 I expect the coefficient of educational attainment to be positive.

Ha: ß2>0

Ho: ß3≥0 I expect the coefficient of the effective abortion rate to be negative.

Ha: ß3<0

Ho: ß4≥0 I expect the coefficient of the certainty of punishment ratio to be negative.

Ha: ß4<0

Ho: ß5≥0 I expect the coefficient of the severity of punishment ratio to be negative.

Ha: ß5<0

Ho: ß6≤0 I expect the coefficient of the racial composition variable to be positive.

Ha: ß6>0

Econometric Issues

The first econometric issue that I might experience with my model is that of choosing the correct functional form. In my model I have used linear variables, lagged variables, and a dummy variable. Historically, some studies have used a left side log: Loftin and Hill (1974),

Blaus and Blaus (1982), and Donohue and Levitt (2001). However, others have explained linear relationships; Gibbs (1969) and Tittle (1969). Consequently, there is no guarantee that a left-side log functional form will be the correct functional form within this particular sample. In order to determine the correct functional form I will conduct a Ramsey Reset test to determine whether there are any specification errors.

In predicting the variance for a dependant variable such as the murder rate it is logical to expect some form of omitted variable bias. This is due to the fact that there are many other 17 variables that contribute to the occurrence of murder. Some of the variables I suspect that may possibly cause omitted variable bias within my model are age, income inequality, gun availability, and location. I had planned on using a racial inequality variable to measure the differences in per capita income between races since it was found to be significant by Williams

(1984) and Blau and Blau (1982). However, I was unable to find the data necessary. This also occurred for other variables that could explain the murder rate more accurately. For instance, the volume of missing or stolen fire arms has proven to be a significant variable in determining the violent crime rates in previous studies. Unfortunately, the Bureau of Justice statistics only has data regarding registered weapons, and even this data is only present for some large cities.

Another econometric issue that is possible is Multicollinearity. In other words, some of my independent variables might share linear functional relationships with each other. For instance, is the level of poverty and educational attainment related? It seems logical that those who live in poorer areas tend to achieve less, educationally speaking. Or, is low educational attainment the cause of poverty among certain states? It is unclear what the true relationship is at this point.

Heteroskedasticity is also a possibility within my model. Heteroskedasticity implies that

Classical Assumption V has been violated. This assumption stipulates that the observations of the error term are drawn from a distribution that has a constant variance. This issue is likely within my cross-sectional study of the states due to the high variances of my variables across the different states.

Impure serial correlation will be tested for using the Durbin-Watson test. However, due to the fact that this a cross-sectional study, impure serial correlation is not likely. As a result, it is only analyzed briefly. 18

The dependent variable within this regression model is the murder rate for each state in

2005. This variable is represented by the symbol M in this model and will be logged within the regression. Murder, as defined by the Uniform Crime Reporting Program (UCR), is “the willful killing of one human being by another” (Crime in the United States, 2006). Murders, as used within this model, are those known to police. The UCR tabulates the amount of murders as reported by several state agencies. Moreover, the murder rate is defined as the amount of murders known to police per 100,000 people. This data was collected from the FBI website within the “Crime in the United States 2005” report.

The first independent variable used is poverty in 2005 for each state. This variable will be represented by the symbol Ρ in this model. The poverty variable is the proportion of the population that lives in poverty. “Living in poverty” was determined by poverty thresholds as mentioned in the Model section of this paper. This data was collected from the U.S. Census

Bureau website. The Census Bureau reports poverty estimates from different national surveys and programs. These surveys and programs include the Current Population Survey (CPS),

American Community Survey, Survey of Income and Program Participation (SIPP), and Small

Area Income and Poverty Estimates.

The second independent variable used is an educational attainment variable. The educational attainment variable measures the proportion of the state population 25 years of age and older that do not have a high school diploma in 2005. This variable will be represented by the acronym NHSG within the regression model. This data was collected from the U.S. Census

Bureau website. The U.S. Census Bureau also collects educational attainment estimates from 19 many surveys and programs. These surveys and programs include the Current Population Survey

(CPS) and American Community Survey (ACS) Estimates.

The third independent variable used is the black population within each state for 2005.

This is measured as a proportion of the population that is one race; black. This was computed by taking the Census Bureau’s estimates of the black population in each state in 2005 and dividing it by the total population for that state in 2005. This variable will be represented by the symbol B within the model. This data was collected from the Census Bureau website. The Census Bureau’s estimates are based from the Current Population Survey (CPS).

The fourth independent variable used is the effective abortion rate (Levitt, 2001). The effective abortion rate is a weighted average abortion ratio. This variable is represented within the regression model by the acronym EAR, denoting the effective abortion ratio. It is computed by multiplying the number of abortions per 1000 live births in 1987 times the proportion of people arrested for murder 18 years old for each state in 2005. This method was used in accordance to J.J. Donohue and S.D. Levitt (2001).

Effective abortion rate = Abortions per 1000 live births1987 x (persons under 18

arrested for murder2005/total number of arrests for murder2005)

The arrests data was collected from the FBI website within the “Crime in the United

States 2005” report. The number of abortions per 1000 live births for 1987 was collected from the Wm. Robert Johnson archive, which collects abortion statistics from several state agencies.

The fifth independent variable used is certainty of punishment. This variable is represented by the acronym COP within the model. This variable is the number of arrests for murder in 2004 divided by the number of murders known to police in 2004. This variable was used to measure the probability of being attained for murder. It was used as a lagged variable in 20 accordance with empirical studies. This data was also collected from the FBI website within the

“Crime in the United States 2004” report.

The sixth independent variable used is severity of punishment. This variable is represented by the acronym SOP within the model. This variable is used in an attempt to explain the deterrent effect the death penalty may have on murder. Therefore, this variable was used as a dummy variable where if SOP equals one if the state has the death penalty and SOP equals zero if the state does not have the death penalty. The information regarding whether a state has the death penalty was collected from the Death Penalty Information Center (DPIC.com).

Data Problems

There were a couple of problems throughout the data collection process. Certainty of punishment does not follow the same methods as used in empirical studies. Certainty of

Punishment is defined as number of arrests for murder in 2004 divided by the number of murders known to police in 2004 within the model. Gibbs (1968) defined it as the number of prison admissions for murder divided by the number of murders known to police. However, the prison data needed was unavailable by state classification in 2004. Therefore, the best alternative was to measure this using arrest data for 2004. However, within the arrest data there are also discrepancies. First, the form in which it is collected does not take into account the amount of people arrested for murder. Instead, it counts the number of times a person was arrested for murder. Also, it is unknown whether a person committed more that one murder or whether one murder was committed by several people. Furthermore, several agencies may not have reported.

For instance, New York’s number of arrests did not include New York City and Illinois murders were based simply on Chicago. This causes major differences between the actual COP of those states. 21

Also, the severity of punishment variable was also not measured in accordance with empirical methods. Within this model, SOP is defined as whether a state has a death penalty or not in 2005. Gibbs (1969) defined it as the median number of months served under a homicide sentence by all persons in the relevant year. This data was also unavailable by state classification for 2005. Therefore, the death penalty was the best available alternative to measure the severity of punishment for committing murder.

Descriptive Statistics

There were no major discrepancies within the summary statistics for all the data sets. The mean murder rate is 4.714. The states with the highest murder rates in 2005 were Louisiana and

Maryland; the lowest was North Dakota. However, the highest effective abortion rate was

Nevada. I did not expect this. Also, the smallest black population was Montana with .38%. This was extremely low.

Descriptive M P NHSG B COP SOP EAR Statistics Mean 4.714000 12.09000 13.33200 10.36471 0.658280 0.740000 29.91263 Median 4.700000 11.70000 12.95000 7.182400 0.667296 1.000000 23.71685 Maximum 9.900000 20.10000 21.80000 36.94520 1.388889 1.000000 118.7509 Minimum 1.100000 5.600000 7.300000 0.380800 0.135417 0.000000 0.000000 Std. Dev. 2.366347 3.010000 3.878851 9.702563 0.286596 0.443087 27.11409 Skewness 0.253978 0.406723 0.452224 1.071719 0.340910 -1.094306 1.208782 Kurtosis 2.135364 3.025228 2.320466 3.247093 2.732035 2.197505 4.493818

Jarque-Bera 2.095027 1.379857 2.666232 9.698718 1.118092 11.32087 16.82521 Probability 0.350809 0.501612 0.263654 0.007833 0.571754 0.003481 0.000222

Sum 235.7000 604.5000 666.6000 518.2352 32.91398 37.00000 1495.631 Sum Sq. 274.3802 443.9450 737.2288 4612.847 4.024719 9.620000 36023.52 Dev.

Observations 50 50 50 50 50 50 50 22

Empirical Results

The first regression output used the Ordinary Least Squares method (OLS) and was a left- side log function. I have chosen a left-side log because more recent empirical studies have shown that this is a superior functional form when attempting to explain the variance of the murder rate. The resulting estimated equation was:

Log(Mi) = -0.209444+ 0.040245P i + 0.037030NHSG i + 0.004840EAR i + 0.017067COPi

+ 0.331172SOPi + 0.022025Bi + εi

Initial Regression Output Dependent Variable: LOG(M) Method: Least Squares Date: 12/08/07 Time: 22:12 Sample: 2 51 Included observations: 50 Variable Coefficien Std. Error t-Statistic Prob. t C -0.209444 0.284352 -0.736567 0.4654 P 0.040245 0.027351 1.471417 0.1485 NHSG 0.037030 0.021124 1.752974 0.0867 B 0.022025 0.006526 3.375029 0.0016 EAR 0.004840 0.002073 2.335233 0.0243 COP 0.017067 0.179518 0.095070 0.9247 SOP 0.331172 0.121154 2.733474 0.0091 R-squared 0.692419 Mean dependent 1.400168 var Adjusted R-squared 0.649501 S.D. dependent var 0.590067 S.E. of regression 0.349338 Akaike info 0.863621 criterion Sum squared resid 5.247578 Schwarz criterion 1.131304 Log likelihood -14.59052 F-statistic 16.13343 Durbin-Watson stat 2.152512 Prob(F-statistic) 0.000000

Given the preceding results, each interpretation is as follows; 23

Pi : For every one percent increase in the percentage of people who live in poverty,

the murder rate per 100,000 people would increase by 4%, all else held constant.

This was the expected sign for this coefficient. My corresponding hypothesis test was:

Ho: ßP≤0

Ha: ßP>0

Therefore, with a t-statistic for my poverty variable of 1.47, and a one-sided p-value of .

074, I can reject the null hypothesis with 90% confidence and conclude that the coefficient for poverty is significantly greater than zero. This was expected because previous studies have found that higher murder rates seem to be more likely in areas with higher poverty.

NHSGi: As the percentage of the population 25 years or older that are not high

school graduates in 2005 increases by one percent, the murder rate will increase

by 3.7%, all else held constant.

This sign for the NHSG coefficient was also expected. The corresponding hypothesis test used was:

Ho: ßNHSG≤0

Ha: ßNHSG>0

Therefore, with a t-statistic for my educational attainment variable of 1.75, and a one- sided p-value of .04, I can reject the null hypothesis with 95% confidence and conclude that the coefficient for NHSG is significantly greater than zero.

Bi: As the percent of a state’s total population that is black increases by one percent,

the murder rate will increase by 2.2%, all else held constant.

This sign was also expected for the coefficient of the Black population variable. The corresponding hypothesis test used was: 24

Ho: ßB≤0

Ha: ßB>0

Therefore, with a t-statistic for my black population variable of 3.375, and a one-sided p- value of .0008, I can reject the null hypothesis with 99% confidence and conclude that the coefficient for B is significantly greater than zero.

EARi : As the effective abortion rate for 1987 increases by one percent, the murder rate

per 100,000 people in 2005 will increase by .48%, all else held constant.

This was not the expected sign of the coefficient for EAR. The corresponding hypothesis test used was:

Ho: ßEAR≥0

Ha: ßEAR<0

Therefore, with a test statistic for the effective abortion rate of 2.33, and a one-sided p- value of .012, we fail to reject the null hypothesis and conclude that the coefficient for EAR is not significantly less that zero. The positive coefficient and positive test-statistic indicated that the number of murders per 100,000 will increase with increased abortion. There are a couple of possible culprits for this flipped sign. First, this could be a case of omitted variable bias. As I mentioned in the model section, the unavailability of some data caused me to exclude important variables. These exclusions may be biasing the EAR variable upwards. Second, the effective abortion rate takes into account the number of arrests for 18 year old for murder in 2005. As mentioned before, this data are skewed due to collection methods.

COPi: As the certainty of punishment for 2004 increases by one percent, the murder rate in 2005 will increase by 1.7%, all else held constant. 25

This was not the expected sign for this coefficient. The corresponding hypothesis test used was:

Ho: ßCOP≥0

Ha: ßCOP<0

Therefore, with a test statistic for the certainty of punishment of .095, and a one-sided p- value of approximately .48, we fail to reject the null hypothesis and conclude that the coefficient for COP is not significantly less that zero. This test also proved that the COP variable is insignificant. This could be due to the problems within the data for arrests that were discussed before.

SOPi: As a state’s severity of punishment increases or, a state has the death penalty, the murder rate per 100,000 people in 2005 will increase by 33%.

This was also not the expected sign for the SOP coefficient. The corresponding hypothesis test used was:

Ho: ßSOP≥0

Ha: ßSOP<0

Therefore, with a test statistic for the certainty of punishment of 2.73, and a one-sided p- value of .00045, we fail to reject the null hypothesis and conclude that the coefficient for SOP is not significantly less that zero. Although I expected the death penalty to have a deterrent effect on the murder rate, it was not so. As mention earlier in this study, empirical evidence showed that, historically, the death penalty did not have a deterrent effect on the murder rate.

Furthermore, this study proves that this still holds true for 2005.

The first regression output was a good start. There was an adjusted R square of .649, which is relatively decent. Furthermore, the model was significant according to the F-test, where; 26

Ho: β P= β NHSG= β B= β SOP= β COP= β EAR=0

Ha: Ho is not true.

The F-statistic for this model was 16.13 with a tiny p-value of 0.000. Therefore, with 99%

confidence, I can reject the null hypothesis and conclude that my model is statistically significant

overall.

Corrections for Econometric Issues

Though the first model was a good start, there are some econometrical issues that needed

to be explored. These issues are specification errors, multicollinearity, and heteroskedasticity.

Serial correlation, although not prevalent within cross-sectional studies, was examined briefly.

Multicollinearity was a non issue within the model. A simple correlation table showed

decent correlations with the dependant variable and no significant issues between the

independent variables. The only issue that may exist is the high correlation between the poverty

variable and the educational attainment variable; which was a relatively high .74. However, this

relationship seems logical due to the reality that people with lesser educational attainment tend to

make less money than others. Therefore, if a state has a high percentage of individuals without a

high school degree it is more likely that a higher proportion of their population will be living in

poverty.

Simple M P NHSG B EAR COP SOP Correlation M 1.000000 0.553209 0.672358 0.732914 0.221509 -0.049777 0.445379 P 0.553209 1.000000 0.740766 0.436460 -0.262440 -0.138224 0.206118 NHSG 0.672358 0.740766 1.000000 0.542922 0.010691 -0.107611 0.243615 B 0.732914 0.436460 0.542922 1.000000 0.168764 -0.131666 0.313745 EAR 0.221509 -0.262440 0.010691 0.168764 1.000000 0.051242 0.030673 COP -0.049777 -0.138224 -0.107611 -0.131666 0.051242 1.000000 0.120829 SOP 0.445379 0.206118 0.243615 0.313745 0.030673 0.120829 1.000000 27

Furthermore, in order to determine the severity of multicollinearity between P and

NHSG, I produced variance inflation factors (VIF) for each. Each VIF was computed by making the variable in question a function of all other independent variables. Then, I ran an ordinary least squares regression for this function. Also, I used the R squared of the corresponding regression in the equation:

2 VIF (βi) = 1/(1-Ri )

A VIF greater than five would indicate severe multicollinearity. For P, the VIF was 2.72.

For NHSG, the VIF was 2.696. These two VIFs indicate that there is no severe case of multicollinearity between these two variables.

Specification errors also needed to be examined. There were two main questions regarding specification errors within this model. First, is the functional form correct? Second, are there omitted variables? In order to examine these possibilities, I ran a Ramsey Reset test. This test uses polynomial forms of the dependent variable as proxies for possible omitted variables or incorrect functional forms. If the F-test shows that the overall “fit” of the model is significantly different between the Ramsey model and my original model, than there is evidence that some sort of specification error exists. 28

Ramsey RESET Test: F-statistic 4.427854 Probability 0.008852 Log likelihood ratio 14.33742 Probability 0.002480

Test Equation: Dependent Variable: LOG(M) Method: Least Squares Date: 12/08/07 Time: 22:39 Sample: 2 51 Included observations: 50 Variable Coefficien Std. Error t-Statistic Prob. t C 4.219139 4.771898 0.884164 0.3819 P -0.307282 0.358984 -0.855977 0.3971 NHSG -0.316633 0.331959 -0.953831 0.3459 B -0.166041 0.196682 -0.844211 0.4036 EAR -0.041470 0.043123 -0.961659 0.3420 COP -0.065174 0.226250 -0.288063 0.7748 SOP -2.818511 2.950910 -0.955133 0.3452 FITTED^2 10.49715 9.634084 1.089585 0.2824 FITTED^3 -4.671285 4.372059 -1.068441 0.2917 FITTED^4 0.686460 0.707974 0.969612 0.3381 R-squared 0.769099 Mean dependent 1.400168 var Adjusted R-squared 0.717146 S.D. dependent var 0.590067 S.E. of regression 0.313822 Akaike info 0.696872 criterion Sum squared resid 3.939360 Schwarz criterion 1.079277 Log likelihood -7.421807 F-statistic 14.80380 Durbin-Watson stat 1.825393 Prob(F-statistic) 0.000000

The Ramsey Reset test concluded that there is no evidence of significant specification errors. To begin with, the F-statistics for both the Ramsey regression and my initial regression are not significantly different. This means that the model has not been improved by the addition 29 of proxy omitted variable terms. Moreover, this conclusion is reemphasized through the Ramsey test statistic of 4.4278, and a p-value of 0.00852.

Next, we tested for heteroskedasticity using the White test without cross terms due to the high number of variables.

White Heteroskedasticity Test (intitial): F-statistic 1.361231 Probability 0.230831 Obs*R-squared 14.13304 Probability 0.225719

The test showed that there was no evidence of heteroskedasticity. The critical value for

11 slope coefficients is 17.28 at the lowest level of significance.

Although most of the econometric issues have been addressed, my regression still has a major problem; three flipped signs. The expected relationships between the effective abortion rate, certainty of punishment, and severity of punishment with the murder rate were negative; however, they all turned out to be positive within this sample. The only thing left to do was to drop the insignificant variables.

There was one insignificant variable; certainty of punishment. In retrospect, I believe that this variable was not well-defined. As discussed above, the proper form of defining this variable was not used due to the unavailability of certain data. Also, the data used were skewed due to collection methods. Therefore, the decision was made to drop COP from the model due to lack of theoretical support and proper definition. 30

Final Regression Output Dependent Variable: LOG(M) Method: Least Squares Date: 12/02/07 Time: 23:33 Sample: 2 51 Included observations: 50 Variable Coefficien Std. Error t-Statistic Prob. t C -0.197293 0.251132 -0.785616 0.4363 P 0.040080 0.026987 1.485163 0.1446 NHSG 0.037038 0.020885 1.773472 0.0831 B 0.021946 0.006399 3.429692 0.0013 EAR 0.004848 0.002047 2.368045 0.0223 SOP 0.333249 0.117818 2.828511 0.0070 R-squared 0.692354 Mean dependent 1.400168 var Adjusted R-squared 0.657395 S.D. dependent var 0.590067 S.E. of regression 0.345381 Akaike info 0.823831 criterion Sum squared resid 5.248681 Schwarz criterion 1.053274 Log likelihood -14.59577 F-statistic 19.80433 Durbin-Watson stat 2.156254 Prob(F-statistic) 0.000000

The removal of the certainty of imprisonment variable did not significantly change the model. All coefficients remained relatively the same and the adjusted R square increased.

Consequently, the insignificant change of this model shows that COP was not a relevant variable.

In this regression there still exists the issue of flipped signs of the effective abortion rate variable and the severity of punishment variable. First, severity of punishment is not defined in direct accordance with previous studies. The SOP variable tells us that there is an increase of 31

33% on the 2005 state murder rate if a state has the death penalty. Intuitively, we realize that this is true. States with higher murder rates tend to have the death penalty. However, higher murder rates are not the result of having the death penalty, instead, higher rates cause the death penalty to be needed. Second, one reason EAR has a flipped sign could be that abortion rates no longer hold deterrent effects on the future murder rates. Another reason could be that the variable is not lagged correctly and could be better suited for a time-series model.

Furthermore, the SOP variable and the EAR variables are statistically significant within the model. Therefore, even though the expected relationship was not found, I made the decision to leave those variables in the model.

The final regression has no econometric issues. The final White test shows that there is no evidence for heteroskedasticity.

White Heteroskedasticity Test (final): F-statistic 1.389822 Probability 0.225150 Obs*R-squared 11.91085 Probability 0.218382

Although there was no preliminary indication of serial correlation, the Durbin-Watson statistic was used to test for impure serial correlation. The DW statistic was 2.15; because this value is approximately equal to 2, there is no evidence of impure serial correlation within this model.

Conclusion

My model included several socioeconomic factors that attempted to explain the state murder rate in 2005. The variable with the largest effect on the dependent variable was SOP. The

SOP variable indicated that states with the Death Penalty will have a murder rate 33% higher compared to states without the Death Penalty in 2005. The socioeconomic variable with the largest impact on the 2005 state murder rate is the poverty variable. An increase of 1% in the 32 proportion of the population who lives in poverty will increase the 2005 state murder rate by 4%.

Although the Ramsey reset test concluded that there is little or no evidence of a specification error, I still believe that there are other variables that could be used to better explain the variance within the murder rate in 2005. These omissions could be the cause of a flipped sign within the

EAR variable. Some of these omitted variables could have been income inequality, gun availability, and prison sentences to name a few. Unfortunately, the unavailability of data for these variables led to their omission.

On the other hand, my regression shows that the independent variables chosen do explain approximately 66% of the variance within the state murder rate in 2005 and F-statistic and corresponding F-test indicates that my model is significant overall. Also, all of my variables are significant with a 90% confidence level. Furthermore, there are no econometric issues within my model. This indicates that my final model has not violated any of the Classical Assumptions.

As a result, I believe my model is good overall. The only changes I would make in future attempts to explain murder rates would be to find data on the omitted variables and include them in order to provide more accurate results. 33

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