Several proposals now before Congress would significantly expand this program, based largely on the belief that COPS is helping to lower crime rates.2 For example, Senator Joseph Biden (D-DE) believes that the COPS program is "the most successful crime fighting strategy this nation has ever seen."3 Empirical research, however, does not support such claims.
A previous study by The Heritage Foundation compared the historical hiring trend of police officers from 1975 to 1993 and found that COPS grants may have placed only 40,000 additional officers on the street by 1998.4 A report funded by the COPS Office and published last year by the U.S. Department of Justice estimates that the number of officers that COPS places on the streets will peak at around 57,000 by the year 2001.5 Clearly, the COPS program has not achieved its goal of placing 100,000 additional officers on America's streets to reduce crime.
The number of new officers actually deployed across the nation is one useful indicator of the program's success, but it does not specifically address the question of whether the COPS program is an effective crime-fighting strategy. This study addresses that question by measuring the program's impact on violent crime rates (see text box, "Understanding Violent Crime Rates"). It does not analyze the effect of adding officers to the street, because in many instances law enforcement agencies that received COPS grants failed to hire the additional officers required to fill the positions funded;6 it analyzes only the relationship between COPS funding and violent crime rates at the county level.
On the basis of this study, Heritage analysts found that:
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The major components of the COPS program--the hiring and redeployment grants7 --failed to show a statistically measurable effect on violent crime rates. In other words, increasing grants for hiring and redeployment of officers, per capita, is not associated with lower rates of violent crime. This finding suggests that federal support of the operational expenses of police departments is ineffective in reducing violent crime.
-
Miscellaneous grants, a minor component of the COPS program used to fund specific actions such as targeting domestic violence and gang activities, appear to be more effective than hiring and redeployment grants in reducing violent crime. A per capita increase of $1 in miscellaneous COPS grants is associated with a reduction in violent crime of almost 16.2 incidents per 100,000 residents. The effectiveness of these miscellaneous grants may be due to the fact that the agencies receiving them already were better at identifying and solving problems than other agencies.
-
Increasing the likelihood of going to prison for committing a violent crime reduces the violent crime rate. When the rate of prison sentences per violent crime arrests increases by 1 percent, for example, the expected incidence of violent crime decreases by 1.2 per 100,000 residents.
- The nationally declining violent crime rates appear to be strongly related to changes of behavior in minority communities. The model predicts that a county with a non-white population that is 1 percent higher than another county's would experience a greater reduction in its violent crime rate. The study found that a county with 1 percent more minorities experiences 57.2 fewer violent crimes per 100,000 residents, holding other factors constant. This finding is similar to the results of the National Crime Victimization Survey, which found that between 1995 and 1998, minorities experienced greater reductions in violent crime victimization rates than did whites.8
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Understanding Violent Crime Rates Heritage analysts studying the COPS program calculated a county's violent crime rate per 100,000 residents using the following formula:1
For example, the violent crime rate in a county of 200,000 residents that experienced 600 violent crimes would be 600 divided by 200,000 times 100,000, which equals 300 violent crimes per 100,000 residents. Assuming a statistically significant relationship, if police funding increases by $1 per capita and violent crime declines by 40 offenses, this county could expect a reduction of 20 incidents in its violent crime rate. The violent crime rate could be expected to fall from 300 to 280 violent crimes per 100,000 residents. 1. Violent crime is defined as the total number of murders, forcible rapes, robberies, and aggravated assaults. |
MEASURING PROGRAM EFFECTIVENESS
With few exceptions, federal crime prevention programs have been funded without sufficient attention to their effects on crime. Evaluations of these programs tend to focus on process , such as where grants were allocated and how many officers were funded, rather than results .
The Congressional Budget Office (CBO) recently noted that debates over funding federal crime prevention programs have lacked vital information about effectiveness.9 The CBO notes that "reductions in crime may have as much to do with demographic changes and the strength of the economy as with the efforts of a federal crime-prevention program."10 Measures of program effectiveness often require the use of techniques that take into account the effects of demographic and economic changes.
To enable policymakers to evaluate the effectiveness of the COPS program in fighting crime, the technique used in this CDA analysis employs statistical methods that control for the effects of socioeconomic variables. This study looks at violent crime data from 1995 to 1998, a short four-year time span that does not allow for an explanation of why the national violent crime rate has declined each year since 1991. However, the research includes over 750 counties across the country. The analysis discusses how traditional policing and community policing are expected to affect crime rates, compares the benefits of using a statistical method over anecdotal observations, explains its data collection methods and the variables in the study, and reviews the statistical analyses. For methodology and detailed statistical results, see the Appendix.
THE EFFECTS OF POLICING ON CRIME
Before the advent of community policing, researchers and practitioners explained the effects of policing on crime by pointing to the deterrent effect of police activity or to how arrests incapacitate criminals. The deterrence theory holds that increasing police activity deters crime by making criminals believe that the probability of their arrest and punishment is higher.11 The increased risk of detection decreases the benefits of illegal activities. Criminals who fear arrest and punishment will have second thoughts before committing a crime.
A related theory suggests that increased police activity not only increases deterrence, but also leads to the incapacitation of criminals.12 Increases in incapacitation are achieved by increasing the percentage of offenses that are cleared by arrest, meaning that the offenders are arrested and temporarily removed from society. Clearance rates are defined as the percentage of known offenses that result in an arrest of an offender; they are usually measured on an annual basis. Not only do increased clearance rates have a deterrence effect because specific offenders perceive criminal activity as more risky, but clearances also reduce the opportunity for offenders to commit illegal acts. After an arrest for a violent crime, offenders are frequently detained in jail while awaiting trial and subsequent incarceration. Though clearance rates do not specifically measure the incapacitation effect, they can be used to measure the effects of incapacitation on violent crime.
The theories of deterrence and incapacitation have been challenged by those who believe that police activities have little effect on crime since criminals rarely weigh the costs and benefits of illegal activities before they engage in them. For example, criminologists Michael R. Gottfredson and Travis Hirschi assert that to commit a crime, an "obvious opportunity coupled with a lack of self-control is all that is required."13 Further, the "offender sees a momentary opportunity to get something for nothing and he seizes it. These facts delineate the natural limits of law enforcement."14 These experts conclude that "no evidence exists that the augmentation of police forces or equipment, differential patrol strategies, or differential intensities of surveillance have an effect on crime rates."15
Assuming that criminals do not rationally calculate the benefits and costs of their actions, Gottfredson and Hirschi downplay the importance of policies that increase the effects of deterrence and incapacitation.16 Although advocates of community policing support the role of deterrence and incapacitation, they believe that police make a difference in fighting crime though other means.
COMMUNITY POLICING17
The concept of community policing is broad, encompassing many types of activities.18 In general, community policing is associated with officers and citizens working together to solve problems associated with crime, social and physical disorder, undesirable neighborhood conditions, and fear of crime.19
The direct consequences of violent crime are apparent, but the relationship between the fear caused by crime and social disorder is less well understood. The role of community police officers is not simply to make arrests, but also to prevent crime, work with the community to solve ongoing problems, and improve the quality of life in communities.20
Advocates of community policing believe that it effectively reduces crime by:
-
Diagnosing and managing problems in the community that produce serious crimes;
-
Fostering closer relationships with residents of the community to facilitate crime solving; and
-
Building self-defense capabilities within the community itself.21
In short, community policing officers help build community by fostering neighborhood coalitions and reducing fear of crime and social disorder.
Perhaps the best-known fact about fear is that it can destroy aspects of community that make it healthy.22 As crime increases, public areas are seen as unsafe and are less utilized during the day. Some citizens take protective action to secure their safety and belongings, barricading themselves behind deadbolts, window bars, and fences. Others change their lifestyles by staying home at night or leaving the community altogether. Officers practicing community policing still produce deterrence and incapacitation effects through arrests, but they recognize that other strategies, such as building community partnerships, help to reduce fear and decrease crime rates.
If the theory advocated by Gottfredson and Hirschi is sound, however, community policing and deterrence effects should have little impact on crime rates.
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ANALYZING PROGRAM EFFECTIVENESS The crime policy arena is filled with assertions about what is or is not effective in reducing crime. Many of these assertions are based only on anecdotal evidence, since all too often there is a lack of empirical research with which to judge the accuracy of specific claims. Senator Debbie Stabenow (D-MI) suggests, for example, that COPS funding for 53 officers in Muskegon County, Michigan, is responsible for the county's 26.6 percent reduction in crime.1 Observing that COPS grants flowed to a particular community, however, and that the crime rate has dropped is not conclusive evidence that the grants helped to decrease crime. As the CBO and others have noted, socioeconomic factors and other criminal justice policies may play a significant role in changing crime rates. Assertions about the effectiveness of COPS grants therefore are not credible if factors that influence crime are ignored in the analysis. Anecdotal examples of lower crime rates in a community that received the COPS grants could be offset by other examples of communities that received COPS grants and experienced increases in crime. For example:
Selective observation occurs when limited information is used to draw broad conclusions. The person making the conclusion may, however unknowingly, selectively observe something that he or she wants to see occur and ignore other important factors that could alter the conclusion. Anecdotal evidence is often derived through such selective observation, making it difficult to evaluate the merits of differing explanations. Testing competing theories is difficult because the anecdotal method is unable to control for other factors that could influence the observations. The statistical approach used by Heritage, by comparison, includes control variables and allows for the inclusion of many cases in order to test competing hypotheses. 1. Senator Debbie Stabenow, "Stabenow Urges President Bush to Restore COPS Funding," press release, March 23, 2001, at http://stabenow.senate.gov/press/032301cops.htm (April 23, 2001) 2. Calculations based on data from U.S. Department of Justice, Federal Bureau of Investigation, Crime in the United States 1994 (Washington, D.C., 1995), p. 69, and Crime in the United States 1998 (Washington, D.C., 1999), p. 75. |
DATA ON THE COPS GRANTS
To analyze the relationship of COPS grants to violent crime rates, Heritage researchers used data on each COPS grant; violent crime offenses and arrests at the county level; admissions to prison for violent crimes by county; county socioeconomic factors (employment, population characteristics, age distribution, and income per capita); and local government expenditures.23
Data on the amount and type of funding received by the local law enforcement agencies under the COPS program were taken from the U.S. Department of Justice (DOJ) Office of Community Oriented Policing Services Management System (CMS) database. Using a unique identification number for law enforcement agencies, known as the originating number (ORI), grants from 1994 to 1998 were matched with counties where grantees are located.24
The CMS database provides information on the total amount of money provided for each type of grant and the year in which the grant was awarded. However, the total amount awarded in a year does not always equal the amount spent that year. COPS grants intended for the hiring of new officers are to be spent by recipients at a declining rate over a three-year period, with the recipient share of employment costs increasing. The hiring grants require that after a grant is received, the recipient agency will assume total responsibility for funding the officer's fourth year of employment. In order to account accurately for the timing of funds spent, Heritage analysts allocated hiring grants by a decreasing percentage based on when the project started in the CMS database.25
Offense and arrest data for 1994 to 1998 were obtained from the Inter-university Consortium for Political and Social Research (ICPSR) at the University of Michigan.26 Crime data for each county were matched to the demographic and socioeconomic data using Federal Information Processing Standards (FIPS) codes, which are unique identifiers of counties. State prison sentencing data for 1994 to 1998 were obtained from the ICPSR as well.27
Information from the U.S. Bureau of the Census was used for the age, sex, population density, and racial/ethnic composition of the counties. Data for state and local government expenditures from 1994 to 1996 were obtained from the Census Bureau's Annual Survey of Government Finances; expenditures for 1997 were obtained from its 1997 Census of Governments.28 The Bureau of Labor Statistics supplied county unemployment and labor force information.
Due to incomplete reporting of crime data for several states and the sampling procedure used by the Census Bureau to report local government spending, securing complete data on all of the nation's 3,141 counties was not possible. However, complete data for all five years were available for 752 counties. The average total population for these 752 counties during the period in question was about 143 million people, or approximately 53.8 percent of the average total population from 1994 to 1998. From 1994 to 1998, $5.321 billion in COPS grant funding was dispersed around the nation. During the same period, total grants to the 752 counties in this study amounted to $2.267 billion, or 42.6 percent of the grants allocated to all 3,141 counties.
THE HERITAGE FINDINGS
The analysis presented in this CDA Report considers the effects of COPS grants on county-level violent crime rates. Holding socioeconomic and other crime-related variables constant can help to identify the specific effects of COPS grants on violent crime. The results can help to determine whether COPS grants are an effective federal crime-fighting strategy. If federal grants for community policing are effective, the counties that received COPS grants should have experienced a reduction in violent crime as a result of these grants.
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HOW TO INTERPRET THE HERITAGE FINDINGS This CDA Report contains the results of statistical analyses of county-level data. The statistical tests were conducted to isolate the independent effects of a number of demographic and socioeconomic factors on violent crime rates in order to measure the effect of the COPS grants alone. Because the statistical models in this study include such factors as minority population percentage, unemployment rates, and local government spending, the effect of each variable on the violent crime rate can be isolated. A finding of "statistically insignificant" indicates that the effect of a particular variable is, for statistical purposes, no different from zero. For example, if the relationship between the percentage of county residents aged 15 to 24 and violent crime rates is statistically insignificant, the percentage of 15- to 24-year-olds in the counties, when combined with other variables, cannot be used to explain changes in violent crime rates for the duration of this study. This analysis uses the 95 percent confidence level as the minimum standard for a variable to be considered statistically significant. When a variable is statistically significant at the 95 percent confidence level, there is a 5 percent chance that the variable does not have a statistically measurable impact on the dependent variable. |
What the Study Shows
Supporters of the COPS program believe that federal funding of additional police officers through hiring or redeployment of officers pays a dividend in the form of reduced crime rates. To examine this hypothesis, the Heritage statistical analysis of violent crime controlled for the effects of COPS grants, the probability of going to prison, non-white population, 15- to 24-year-old population, income per capita, unemployment rate, labor force participation, population density, the national violent crime rate trend, and the previous year's violent crime rate. Table 1 presents the findings from the Heritage model.
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Grants for Hiring and Redeployment of
Officers.
Analysis of the data shows that COPS grants for the hiring of
additional police officers and grants for redeployment, known as
Making Officer Redeployment Effective (MORE) grants, do not have a
statistically significant effect on reducing violent crime rates.29 These
major components of the COPS program appear to be ineffective in
reducing violent crime.30
There are two possible explanations for the ineffectiveness of the COPS hiring and redeployment grants: (1) the actual number of officers "added" to the street by these grants may be substantially less than the funding indicates,31 and (2) merely paying for the operational expenses of law enforcement agencies without a clear crime-fighting objective is likely to be ineffective in reducing violent crime.
According to the 1997 Department of Justice review of crime-fighting programs, community policing with no clear strategy for targeting crime risk factors, such as high-crime "hot spots" and illegal firearm possession, is ineffective in reducing crime.32 The review further states that "While the COPS Program language has stressed a community policing approach, there is no evidence that community policing per se reduces crime without a clear focus on a crime risk factor objective."33
In many instances, COPS hiring and redeployment grants may have been used for community policing in name only. Grant recipient agencies may have done the paperwork to apply for the grants without ever fully implementing community policing techniques. For example, a DOJ study found that the COPS grantees too frequently established partnerships with the community that were both merely nominal and primarily temporary.34
Miscellaneous Grants.
The results of the Heritage analysis also indicate that COPS
miscellaneous grants, including funds for addressing such specific
problems as gangs, domestic violence, and illegal use of firearms
by youth, have a statistically significant effect on reducing
violent crime rates. For each additional $1 of miscellaneous COPS
grants per capita, the expected value of violent crime declined by
almost 16.2 incidents per 100,000 people. The effectiveness of
these miscellaneous grants may be due to the fact that the agencies
receiving them were already better at identifying and solving
problems than other agencies. A different analysis that accounts
for the individual effects of the miscellaneous grants might find
that some of the grants are ineffective.
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WHAT DO "ELASTICITIES" MEAN? The elasticities for the statistically significant independent variables are presented in Chart 1. The elasticity figures represent the percentage change in the expected violent crime rate given a 1 percent change in a particular independent variable. A 1 percent increase in COPS miscellaneous grants was associated with a 0.004 percent decline in the violent crime rate. Increasing the probability of going to state prison after an arrest for a violent crime was associated with a 0.038 percent decrease in the violent crime rate. A 1 percent increase in state and local police expenditures per capita was associated with a 0.099 percent decrease in the violent crime rate, while total state and local expenditures per capita were associated with a 0.135 percent increase in violent crime rates.
Changes in the demographic and socioeconomic variables appear to have a greater effect on violent crime rates than funding does, holding other variables constant. A 1 percent increase in the non-white population is associated with a 2.79 percent decrease in violent crime rates. Increasing the labor force participation rate by 1 percent is associated with a 0.768 percent decrease in violent crime rates. A 1 percent increase in income per capita is associated with a 0.514 percent increase in violent crime rates.The remaining variables fail to have statistically significant effects on violent crime rates, so the values of their elasticities can be considered no different from zero. |
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State and Local Government Spending. This analysis finds that state and local police expenditures per capita have a negative and statistically significant effect on violent crime in the next year, while total state and local government expenditures per capita have a small positive and statistically significant relationship to violent crime rates. The model indicates that a $1 per capita increase in state and local police expenditures reduces violent crime by 1.3 incidents per 100,000 residents. A $1 increase in state and local total government expenditures per capita correlates with an increase in violent crime by 0.09 incidents per 100,000 residents. This finding may reflect the association of high-crime counties with higher social welfare spending.
Probability of Going to Prison.
The prison probability variable has a negative and
statistically significant relationship with violent crime rates.35 A 1
percent increase in the probability of going to a state prison
after an arrest for a violent crime reduces the expected amount of
violent crime by 1.2 incidents per 100,000 residents. These results
support the view that increasing the costs for committing violent
crimes has deterrent and incapacitation effects.
Non-White Population.
This analysis controls for the percentage of county population
that is non-white. Changes in behavior in minority communities are
influential in reducing violent crimes. The percentage of the
population that is non-white has a large negative and statistically
significant relationship to violent crime rates. The model predicts
that a county with a non-white population that is 1 percent higher
than another county's would have 57.2 fewer violent crimes per
100,000 residents, holding the other variables constant.36 These results
are consistent with data from the National Crime Victimization
Survey, which found that between 1995 to 1998, the violent crime
victimization rate for black and other minority groups declined by
24.7 percent and 32.5 percent, respectively.37 Over the same time period,
the violent crime victimization rate for whites declined by only
15.8 percent.
This variable captures the documented but largely unexplained phenomenon that minority communities experienced a larger than average drop in violent crime over the duration of this study. Given the short time span of the study (four years), this analysis captures more cross-sectional differences between counties than time-series differences within counties. Further research is required to account for the changes in violent crime rates for minority groups.
Income.
Increased personal income per capita has a small positive and
statistically significant relationship to violent crime rates. A $1
increase in income per capita is associated with an increase of
0.01 violent crime incidents per 100,000 residents. This result may
suggest that counties experiencing increased personal income
attract more violent predators than less prosperous counties
would.
Employment Levels.
Increases in the civilian labor force have a negative and
statistically significant relationship to violent crime rates.38 For every
1 percent increase in civilian labor force participation, violent
crime is expected to decrease by 8.8 incidents per 100,000.
Remaining Variables.
The remaining socioeconomic variables (15- to 24-year-old
population percentage, unemployment rate, and population density)
fail to have a statistically significant relationship to violent
crime rates.
Alternative Explanations
Recognizing that clearance rates are an important variable for measuring deterrence, they were included in a second statistical test.39 A third test was performed excluding both violent crime clearance rates and prison probability variables.40 Results for each of the COPS grant types in the alternative specifications are similar to the original analysis.41 The hiring and redeployment grants' effects on violent crime rates are statistically no different from zero. The miscellaneous COPS grants have a statistically significant relationship with reduced violent crime rates.42
CONCLUSION
The central argument for the COPS program is that providing additional funds to state and local law enforcement agencies above what they would typically spend on operational expenses is effective in the fight against crime. The results of this CDA analysis, however, indicate that the major components of the COPS program--its hiring and redeployment grants--have failed to show a statistically measurable effect on reducing violent crime rates at the county level.
The COPS hiring and redeployment grants were intended to enable the federal government to help fund the operational costs of local law enforcement agencies and to increase the overall number of officers on their forces--functions that traditionally are the sole responsibility of state and local governments.
The findings of the CDA analysis suggest that merely paying for the operational expenses of police departments is ineffective in reducing violent crime.43 There are two possible explanations: (1) the actual number of officers added to the street from these grants may be substantially less than the funding indicates, and (2) merely paying for the operational expenses of law enforcement agencies without a clear crime-fighting objective is likely to be ineffective in reducing violent crime.
The community policing movement preceded the COPS program, and communities throughout the nation would have continued to incorporate the concept into their work without federal involvement. The acceptance of federal COPS funding by local law enforcement agencies does not necessarily mean that community policing techniques will be implemented successfully or improved upon. A firm commitment to working with residents of a community to solve their crime problems may be more important than having the federal government pay for operational expenses.
This analysis also shows that the miscellaneous COPS grants, a minor component of the program that is targeted to specific activities like domestic violence and gangs, are more effective in reducing violent crime than are the hiring and redeployment grants. This difference in impact may be explained by the differences between the grants themselves. Miscellaneous grants are intended to help law enforcement agencies tackle specific problems; hiring and redeployment grants simply pay for operational costs and are less likely to target specific problems. Federal funds are not necessary to enable local law enforcement agencies to respond to specific problems; nevertheless, the miscellaneous grants may have flowed to agencies that already were better at identifying and solving problems that contribute to violence. Thus, the statistical findings of this study may overstate the actual effectiveness of the miscellaneous grants.
David B. Muhlhausen is a Policy Analyst in the Center for Data Analysis at The Heritage Foundation.
APPENDIX
Data Sources
County data on offenses and arrests for 1994 to 1998 were obtained from the Inter-university Consortium for Political and Social Research (ICPSR) at the University of Michigan.44 Crime data for each county were matched by Federal Information Processing Standards (FIPS) codes, which provide unique identification numbers for each county. State prison admissions data for 1994 to 1998 also were obtained from the ICPSR.45
Information about age, gender, and racial/ethnic composition of counties and population density was obtained from the U.S. Bureau of the Census.46 Data on state and local government expenditures from 1993 to 1996 were obtained from the Census Bureau's Annual Survey of Government Finances;47 state and local expenditure amounts for 1997 were obtained from its 1997 Census of Governments.48 Unemployment rates and data to calculate labor force participation were obtained from the Bureau of Labor Statistics.49
Data on the COPS grants are based on the COPS Management System (CMS) database produced by the U.S. Department of Justice Office of Community Oriented Policing Services in 2000. Heritage analysts matched individual police agencies that participate in the Federal Bureau of Investigation (FBI) Uniform Crime Reporting (UCR) Program.50
Allocation of Grants by County
The CMS database does not indicate the county or counties covered by COPS grant recipients. Heritage analysts calculated the amount of COPS funding for counties using information provided in the 1994 to 1998 Uniform Crime Reporting Program Data computer files.51 For each year, this file contains separate records for police agencies listed in the UCR system for that year. Among the variables that are part of each record are the counties served by an agency. The file lists up to three of the counties served by each police agency that serves more than one county. There is a special identifier for statewide agencies.
For purposes of this analysis, grants made to a police agency were allocated only to the first county that is listed among the potential counties listed as served. In effect, this means that in the case of an agency serving multiple (up to three) counties, all of an agency's COPS grant awards are allocated to the principal county that is served by that agency. The decision to adopt this approach was taken after an analysis of all of the grants awarded between 1994 and 1996. Allocating the COPS grant money to the counties served by multi-county agencies on the basis of the population served would have affected the distribution of less than 0.24 percent of the funds awarded during those years.
A proportion of the COPS funding is not allocated to a county under our methodology. Specifically:
Grants made to state police and other statewide crime-fighting agencies are not allocated to a specific county. In practice, it was not possible to construct an accurate formula that would reflect the actual spending across the different counties in a state.
Grants made to agencies or other organizations that could not be matched to an agency entry in the UCR were not allocated to any county. In some cases, the grant was awarded not to an existing police agency but to a consortium that consists of several agencies (i.e., grants for conferences). In other cases, the grant was awarded not to a police agency but to another entity such as a research institution or a community anti-crime organization. Many of these grants are related to crime-fighting activities on a tangential and non-localized basis. Another possibility is that clerical errors may have been made in the reporting of an agency's identification number that was used to match grants with police agencies. Finally, a number of police agencies have never participated in the Uniform Crime Reporting system and so are not included in the FBI's list of participating agencies.
Heritage analysts allocated to a county only those grant monies that could be clearly identified as awarded to a law enforcement agency operating in that county. Excluding the grants that could not be matched with the UCR databases had the effect of omitting grants that may be used for non-policing purposes. Grants to police agencies that do not participate in the UCR Program were excluded from the analysis because the dependent variable (violent crime rates) in the study is based on data from agencies that participate in the UCR. By excluding grants that are not used directly to fight crime and agencies that do not report crimes to the FBI, this methodology also avoids two potential sources of bias that would tend to reduce the statistical significance of the impact of the COPS grants on violent crime rates.
Allocation of Grants by Year
Because COPS grants for the hiring of officers are intended to be spent at a declining rate over a three-year period, the hiring grants were allocated in a declining percentage, starting in the year identified by the project start date in the COPS Management System (CMS) database.52 The CMS database includes data for 551 agencies that reported their spending patterns over the three-year life of their hiring grants. The median percentage of funds spent in each year was calculated.
To test the assumption about the spending pattern, Heritage analysts conducted a sensitivity analysis of the high and low points of the 95 percent confidence interval for the median spending pattern in each year. In the first part of Appendix Table A-1, the initial median and 95 percent confidence intervals for the spending pattern of the 551 agencies are presented. The lower half of Appendix Table A-1 includes the median and 95 percent confidence intervals that have been normalized for 100 percent. The normalized median spending pattern for the first year of the hiring grants was 38.3 percent. The normalized median spending patterns for the second and third years were 33.04 percent and 28.6 percent, respectively.
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For the sensitivity analysis, the normalized lower-bound and upper-bound confidence intervals for the median spending pattern were used for the allocation of the hiring grants by year. For instance, the analysis using the lower-bound confidence intervals assumes that money spent in the first year of the hiring grants was less than the median spending pattern.
Variables Used
A number of independent or explanatory variables thought to influence violent crime rates are included in the analysis. These variables include COPS grants, state and local expenditures, and demographic and socioeconomic variables. In each model, the dependent variable is the violent crime rate. The county violent crime rate consists of the total number of homicides, forcible rapes, robberies, and aggravated assaults per 100,000 residents. The independent variables are described below.
COPS Grants.
Per capita COPS grants were calculated by aggregating the grants
going to individual law enforcement agencies to the county level
and then dividing by county population. COPS grants were assigned
to one of three categories.
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Hiring Grants Per Capita. COPS grants for the hiring of police officers by law enforcement agencies within a county are estimated for each year of the three-year life of the grants. Then the annual estimated amounts are divided by the county's total population. This variable measures the amount of COPS hiring grant spending per county resident.
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MORE Grants Per Capita. Making Officer Redeployment Effective (MORE) grants were designed to redeploy officers from administrative tasks to community policing. These grants are intended to free current officer time available for community policing by providing funds for equipment, technology, civilian personnel, or overtime. The grants are assumed to be spent during the year of their project start date as identified by the CMS database.
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Miscellaneous Grants Per Capita. Miscellaneous grants include funding for demonstration projects related to community policing, funding to combat methamphetamine use and gang violence, and grants that encourage the hiring of military veterans.53 As with the other COPS grants, the miscellaneous grants are calculated on a per capita basis. These grants are assumed to be spent during the year of their project start date as identified by the CMS database.
Crime Variables.
Two principal violent crime variables were considered in this
analysis.
Model Specification
Statistical studies of the effects of criminal justice policies on crime are often plagued by a problem known as simultaneity.57 This problem occurs because rising crime rates result in increased demand for law enforcement, which leads to increases in police expenditures. Thus, changes in criminal justice policies, such as higher expenditures, often coincide with rising crime. In the case of police expenditures, governments are likely to increase police spending and apply for funding such as the COPS grants in reaction to increasing crime rates.
To address the problem of simultaneity, Heritage analysts lagged expenditure variables one year. Lagging COPS grants one year accounts for the fact that it can take considerable time to hire and train officers or purchase and implement the use of new technologies funded under the grants. It is reasonable to expect that this amount of time would be required before the award of a grant could be transferred into actions that could change the violent crime rate.
Lagging the dependent variable (violent crime rates) one year as an independent variable reduces problems associated with autocorrelation.58 Autocorrelation of error terms causes parameter estimates to be inefficient, so statistically significant tests will be invalid.
The use of lagged variables limits the number of years that could be included in this study. The methodology employed by the Inter-university Consortium for Political and Social Research (ICPSR) to create yearly county offense and arrest data sets changed in 1994. Therefore, county crime data prior to 1994 cannot be compared with data for 1994 and subsequent years.59 Due to this change in methodology and the lagging of the violent crime rates on the right-hand side of the models, Heritage analysts were able to examine violent crime only for the period from 1995 to 1998. The models in this report use lagged values for police expenditures so that the effects of COPS grants administered in 1994 are captured.
Each county's total population is used to weight the data. Weighting by population helps to reduce the effect of huge swings in violent crime rates in small counties. A reduction of 100 violent crimes per 100,000 residents in a county of 5,000 people is not the same as a similar rate reduction in a county populated by 2 million people.
The model also includes a trend term (the national violent crime rate) that is intended to capture the effect of unobserved factors influencing changes in violent crime across the country.
The models used in this analysis control for cross-sectional fixed effects (individual differences related to each county), which control for unobserved factors that cause violent crime rates in a particular county to differ from violent crime rates in other counties. The fixed-effects model helps control for differences in county violent crime rates that are not accounted for by the independent variables.
Including the specific differences attributable to each county in the fixed-effects model helps control for possible selection bias in the COPS program's allocation of grants. Selection bias may have occurred because agencies that are more innovative and better at fighting crime are more likely to apply for and receive COPS grants than other agencies. The fixed-effects model helps control for selection bias by giving each county an intercept, which allows individual differences of the counties to be absorbed. The fixed-effects model helps reduce selection bias, but it may fail to eliminate it entirely. The final results may be biased toward finding COPS grants to be more effective than they were in reality.
Using the White's test, heteroscedasticity was identified. Though parameter estimates remain unbiased when heteroscedasticity is present, the parameter estimates are inefficient. The standard errors for the parameter estimates will be inconsistent; thus, hypothesis tests will not be valid. To correct for this problem, the Huber/White/sandwich "robust" estimator of variance was used to produce consistent standard errors for the calculation of statistical significance tests.
Alternative Tests
The use of violent crime clearance rates may pose difficult problems because the number of violent crimes appears in the numerator of the dependent variable (violent crime rates) and in the denominator of the independent variable violent crime clearance rates.60 This occurrence may cause a relationship between clearance rates and crime to be overstated in a negative direction.61 Further, some may argue that the use of clearance rates in the model partially captures the effect of COPS funding. To avoid these possible problems, Heritage analysts did not control for the violent crime clearance rate in the original analysis.
When violent crime clearance rates are included in the model, the statistical significance of the relationship between COPS grants and violent crime rates remains unchanged. (See Appendix Table A-2 for results of the analysis that controls for violent crime clearance rates.) The hiring and MORE grants failed to have an impact on violent crime rates, while the miscellaneous grants did continue to have an effect on reducing violent crime rates. The relationship between the probability of going to prison and reducing violent crime remained statistically significant. As can be seen in Appendix Table A-2, the statistical significance of the socioeconomic variables remained constant with the absence of clearance rates, except for the labor force participation rate. When the analysts controlled for violent crime clearance rates, the relationship between labor force participation rates and violent crime rates was statistically insignificant. Violent crime clearance rates had a negative and statistically significant relationship with violent crime rates. A 1 percent increase in the violent crime clearance rate reduced violent crime by almost 4.6 incidents per 100,000 residents.
;)
Some may speculate that the probability of a prison sentence might be endogenous, since it might both be affected by violent crime rates and affect them. Communities experiencing increased crime may put more pressure on their criminal justice system's ability to arrest, prosecute, and incarcerate criminals. To eliminate this problem, the analysis presented in Table A-3 omits both the clearance and prison variables. As can be seen in Table A-3, the statistical significance of the COPS grants and other variables remains unchanged from the previous analysis. The hiring and redeployment grants were not effective as a violent crime reduction strategy.
;)
Sensitivity Analysis
To test the robustness of our findings for the effect of COPS grants on violent crime, the models were re-estimated using the low and high points of the 95 percent confidence intervals for the median spending patterns used by grantees for the COPS hiring grants.62 Regressions using the lower-bound point of the 95 percent confidence interval assume that a smaller portion of the grants was spent in the first year, causing more funds to be spent in the later years. The opposite distribution occurs when the spending pattern is based on the upper-bound point of the 95 percent confidence interval. Under this assumption, grantees spend a larger portion of funds in the first year of the grant, thus leaving less funding available for the remaining years. See Table A-4 through Table A-9 for analyses using different spending patterns for the hiring grants.
The results of testing different assumptions about the spending patterns are similar to the original analysis. The hiring and MORE grants failed to have an impact on violent crime, while the miscellaneous grants did continue to have a statistically significant relationship with reduced violent crime rates.
In response to possible concerns that a simultaneous relationship between violent crime and police expenditures does not exist, Heritage analysts re-estimated the models without lagging the expenditure variables. Due to space limitations, the results in tabular form are not presented. For all three models, none of the COPS grants, including the miscellaneous grants, had a statistically significant relationship with violent crime rates.63 To determine whether changing the spending pattern affects the findings when current-year spending variables are used, we re-estimated the models using the lower- and upper-bound points of the 95 percent confidence interval for the median spending pattern. All of the current-year COPS grants failed to have a statistically significant relationship with changes in violent crime rates.
Another set of analyses were done with the FBI's UCR Part I crime rate as the dependent variable and lagged one year as an independent variable.64 The hiring and MORE grants failed to have an impact on Part I crimes, while the miscellaneous grants had a statistically significant relationship with reduced Part I crime rates.
Tables
Regression
Results:
Estimated Effects of Independent Variables on Violent Crime Rates,
1995-1998
| Table A-4 | Model Includes Hiring Grants Calculated Using the Lower-Bound Spending Pattern |
| Table A-5 | Model Include Hiring Grants Calculated Using the Lower-Bound Spending Pattern and Includes the Violent Crime Clearance Rate |
| Table A-6 | Model Include Hiring Grants Calculated Using the Lower-Bound Spending Pattern and Excludes Violent Crime Clearance Rates and the Probability of Going to Prison |
| Table A-7 | Model Includes Hiring Grants Calculated Using the Upper-Bound Spending Pattern |
| Table A-8 | Model Includes Hiring Grants Calculated Using the Upper-Bound Spending Pattern and Includes Violent Crime Clearance Rates |
| Table A-9 | Model Includes Hiring Grants Calculated Using the Upper-Bound Spending Pattern and Excludes Violent Crime Clearance Rates and the Probability of Goin to Prison |
Endnotes
1. The author wishes to thank Center for Data Analysis Research Fellow Ralph Rector, CDA Director William W. Beach, former CDA Policy Analyst Gareth G. Davis, and CDA Research Assistant Isabel Isidro for their contributions.
2. For example, the 21st Century Law Enforcement, Crime Prevention, and Victims Assistance Act (S. 16), introduced on February 22 by Senators Thomas Daschle (D-SD), Joseph Biden, Jr. (D-DE), and Patrick Leahy (D-VT), would authorize $6.9 billion in COPS program spending over six years; alter the current funding requirements; require that up to 50 percent of the COPS money be used to continue funding grants that otherwise would expire; and eliminate the requirement that after a grant has expired, grantees must continue to employ the officer they had been paying with grant money but use their own resources to do so. In essence, it creates an obligation for the federal government to fund officer salaries, tantamount to a new federal entitlement. Moreover, the $75,000 maximum grant allocation for hiring a single officer would increase by two-thirds to $125,000. In a significant departure from its original goal, S. 16 would make funds available for reimbursement of an officer's higher education expenses.
4. Gareth Davis, David B. Muhlhausen, Dexter Ingram, and Ralph Rector, "The Facts About COPS: A Performance Overview of the Community Oriented Policing Services Program," Heritage Foundation Center for Data Analysis Report No. CDA00-10, September 25, 2000.
5. U.S. Department of Justice, Office of Justice Programs, National Evaluation of the COPS Program, 2000, p. 163.
8. Calculations based on data from U.S. Bureau of Justice Statistics, Criminal Victimization in the United States, 1995 (Washington, D.C.: U.S. Department of Justice, May 2000), at http://www.ojp.usdoj.gov/bjs/abstract/cvus95.htm (April 19, 2001), and Criminal Victimization 1998: Changes 1997-98 with Trends 1993-98 (Washington, D.C.: U.S. Department of Justice, July 1999), at http://www.ojp.usdoj.gov/bjs/abstract/cv98.htm (April 19, 2001).
9. Congressional Budget Office, Budget Options, Appendix A, February 2001, at http://www.cbo.gov/showdoc.cfm?index=2731&sequence=33 (April 16, 2001).
11. Colin Loftin and David McDowall, "The Police, Crime, and Economic Theory: An Assessment," in David H. Bayley, ed., What Works in Policing (New York: Oxford University Press, 1998), p. 10, as published in American Sociological Review, Vol. 47 (June 1982), pp. 393-401.
12. Isaac Ehrlich, "Participation in Illegitimate Activities: A Theoretical and Empirical Investigation," Journal of Political Economy, Vol. 81, No. 3 (1973), p. 535.
13. Michael R. Gottfredson and Travis Hirschi, A General Theory of Crime (Stanford, Cal.: Stanford University Press, 1990), p. 269.
16. It does not matter how "irrational" criminals are; when they are incapacitated, they cannot victimize citizens. In addition, research has demonstrated that criminals are rational. See, for example, Ehrlich, "Participation in Illegitimate Activities," pp. 521-565.
17. For more information on community policing and other law enforcement innovations, see Robert E. Moffit, and Edwin Meese III, "Twenty-One Steps Public Officials Can Take to Support Their Local Police," in Edwin Meese III and Robert E. Moffit, eds., Making America Safer: What Citizens and Their State and Local Officials Can Do to Combat Crime (Washington, D.C.: The Heritage Foundation, 1997), pp. 53-85; James Q. Wilson and George L. Kelling, "Broken Windows: The Police and Neighborhood Safety," The Atlantic Monthly, Vol. 249 (March 1982), pp. 29-38; Robert Trojanowicz, Victor E. Kappeler, Larry K. Gaines, and Bonnie Buequeroux, Community Policing: A Contemporary Perspective, 2nd ed. (Cincinnati: Anderson Publishing, 1998); and Willard M. Oliver, ed., Community Policing: Classical Readings (Upper Saddle River, N.J.: Prentice-Hall, 2000).
18. For a discussion of six cities that implemented very different styles of community policing, see Deborah Lamm Weisel and John E. Eck, "Toward a Practical Approach to Organizational Change: Community Policing Initiatives in Six Cities," in Dennis P. Rosenbaum, ed., The Challenge of Community Policing: Testing the Promises (London: Sage Publications, 1994), pp. 53-72.
20. U.S. Department of Justice, Community Oriented Policing Services, at http://www.usdoj.gov/cops/news_info/bg_info/bg_definition.htm (April 12, 2001).
21. Mark Moore, Robert C. Trojanowicz, and George L. Kelling, "Crime and Policing," in Oliver, ed., Community Policing: Classical Readings, p. 42; originally published in Perspectives on Policing, Vol. 1 (Washington, D.C.: National Institute of Justice, U.S. Department of Justice, and Program in Criminal Justice Policy and Management, John F. Kennedy School of Government, Harvard University, 1988).
24. An ORI is assigned by the FBI to law enforcement agencies to track agency information. For more information on the allocation procedure, see the Appendix. Although great care was taken to avoid inaccurate matches, it is possible that in a small number of individual cases, the COPS grant data may have been mismatched to the counties.
25. The following COPS grants were used in 1994 through 1998 to hire police officers: Police Hiring Supplement (PHS), Phase 1; Accelerated Hiring, Education, and Deployment (AHEAD); Funding Accelerated for Smaller Towns (FAST); and Universal Hiring Program (UHP). Although the COPS program became official with enactment of the Violent Crime Control and Law Enforcement Act in September 1994, Congress appropriated funding for community police officers in the fiscal year (FY) 1994 appropriation bill for the Departments of Commerce, Justice, and State (P.L. 103-121). These grants were named PHS grants and were awarded in December 1993. Congress intended them as a down payment on the goal of placing 100,000 additional officers on the street. For purposes of this analysis, PHS grants were allocated to 1994 because the award date fell in the last month of 1993.
26. U.S. Department of Justice, Federal Bureau of Investigation, Uniform Crime Reporting Program Data [United States]: County-Level Detailed Arrest and Offense Data, 1994 to 1998 (computer files), ICPSR ed., produced and distributed by the Inter-university Consortium for Political and Social Research, Ann Arbor, Michigan, at http://www.icpsr.umich.edu/index.html.
27. U.S. Department of Justice, Bureau of Justice Statistics, National Corrections Reporting Program, 1994 to 1998 [United States] (computer files), ICPSR ed., 2001, at http://www.icpsr.umich.edu/index.html.
28. 1994 to 1996 data from Annual Survey of Government Finances database, obtained from U.S. Bureau of the Census, Public Information Office, 2001. Data from 1997 Census of Governments, obtained from U.S. Bureau of the Census, Public Information Office database, 2001.
29. COPS hiring grants were intended to be used by law enforcement agencies to hire additional officers. COPS redeployment (MORE) grants provide law enforcement agencies with funds for equipment, technology, civilian personnel, or overtime so that officers can be redeployed from administrative duties to community policing. For more information on these variables, see the Appendix.
30. Some may argue that COPS grants had a displacement effect on crime within counties that this study will not observe. In theory, displacement could occur when crime in cities or towns that received COPS funding shifted to other parts of their counties; in other words, the COPS grants were effective in reducing crime in these municipalities, but the reduction was offset because criminals chose to commit crimes in other parts of the counties in which the municipalities were located. First, for this theory to be valid, displacement would have to be systematic throughout the 752 counties in the study. This scenario is highly unlikely. Second, one would have to assume that grants awarded to agencies that serve municipalities are automatically more effective than grants awarded to agencies that serve counties. This scenario also is highly unlikely.
31. For information on the failure of police departments to add officers after receiving COPS grants, see Davis et al., "The Facts About COPS"; U.S. Department of Justice, Office of Inspector General, Special Report: Police Hiring and Redeployment Grants, Summary of Audit Findings and Recommendations, Report No. 99-14, April 1999; and Michael R. Bromwich, Management and Administration of the Community Oriented Policing Services Grant Program, U.S. Department of Justice, Office of Inspector General, Audit Division, Report No. 99-21, July 1999.
32. Lawrence W. Sherman, "Policing for Crime Prevention," in Lawrence W. Sherman, Denise Gottfredson, Doris MacKenzie, John Eck, Peter Reuter, and Shawn Bushway, Preventing Crime: What Works, What Doesn't, What's Promising; A Report to the U.S. Congress (Washington, D.C.: U.S. Department of Justice, Office of Justice Programs, February 1997), p. 37.
34. Jeffery A. Roth and Joseph F. Ryan, "The COPS Program After 4 Years--National Evaluation," Research in Brief, U.S. Department of Justice, National Institute of Justice, August 2000, p. 17.
35. The probability of going to prison is defined as the percentage of arrests for violent crime that result in a state prison sentence in a given year. For more information, see the Appendix.
36. This result suggests that for the time period covered by this study, certain behaviors that influence crime may have changed for the better in minority communities. Controlling for race in statistical models is a complex matter. While some studies have linked race with crime, this does not mean that race itself influences crime. For example, in some studies that include a family variable, such as the absence of marriage, race is not a statistically significant indicator. For a detailed account of the relationship between broken families and violent crime as described in the professional social science literature, see Patrick F. Fagan, "The Real Root Causes of Violent Crime: The Breakdown of Marriage, Family, and Community," Heritage Foundation Backgrounder No. 1026, March 17, 1995.
37. Calculations based on data from U.S. Bureau of Justice Statistics, Criminal Victimization in the United States, 1995 (Washington, D.C.: U.S. Department of Justice, May 2000), at http://www.ojp.usdoj.gov/bjs/abstract/cvus95.htm (April 19, 2001), and Criminal Victimization 1998: Changes 1997-98 with Trends 1993-98 (Washington, D.C.: U.S. Department of Justice, July 1999), at http://www.ojp.usdoj.gov/bjs/abstract/cv98.htm (April 19, 2001).
38. The civilian labor force participation rate is the percentage of the county working-age population that is employed. For more information, see the Appendix.
39. The violent crime clearance rate is defined as the percentage of known violent crime offenses that result in arrest in a given year. For more information, see the Appendix.
40. The use of these two variables may present problems that influence the effect of COPS grants on violent crime rates. For more detailed information, see the Appendix.
41. The level of statistical significance for the hiring and redeployment grants failed to reach the 0.05 level. For each of the tests, the statistical significance for the miscellaneous grants was at the 0.05 level. See Appendix, Tables A-2 and A-3.
43. Elsewhere, Heritage Foundation analysts have questioned these intrusions into traditional state functions as unconstitutional or, at a minimum, destructive of fundamental principles of federalism. See, for example, Edwin Meese III and Rhett DeHart, "How Washington Subverts Your Local Sheriff," in Meese and Moffit, Making America Safer, pp. 147-154. These constitutional concerns would remain even if the COPS program were shown to be effective. In addition, other parts of the legislation authorizing the COPS program are highly problematic. Those issues, however, are beyond the scope of this paper.
44. U.S. Department of Justice, Federal Bureau of Investigation, Uniform Crime Reporting Program Data [United States]: County-Level Detailed Arrest and Offense Data, 1994 to 1998, at http://www.icpsr.umich.edu/index.html.
45. U.S. Department of Justice, Bureau of Justice Statistics, National Corrections Reporting Program, 1994 to 1998 [United States] (computer files), ICPSR ed., 2001, at http://www.icpsr.umich.edu/index.html.
46. U.S. Bureau of the Census, 1990 to 1999 Annual Time Series of County Population Estimates by Age, Sex, Race, and Hispanic Origin, data provided in 2001, at http://www.census.gov/population/www/estimates/co_casrh.html.
47. Data obtained from 1994 to 1996 Annual Survey of Government Finances database, provided by U.S. Bureau of the Census, Public Information Office, 2001.
48. Data from 1997 Census of Governments database, obtained from U.S. Bureau of the Census, Public Information Office, 2001.
49. Data on unemployment and labor force participation obtained from Bureau of Labor Statistics, Local Area Unemployment Statistics Program database, provided in 2001.
50. For further information on the matching process, see Appendix A in Davis et al., "The Facts About COPS."
51. U.S. Department of Justice, Federal Bureau of Investigation, Uniform Crime Reporting Program Data [United States]: Offenses Known and Clearances by Arrest, 1994-1998.
52. The following COPS grants were used in 1994 through 1998 to hire police officers: Police Hiring Supplement (PHS), Phase 1; Accelerated Hiring, Education, and Deployment (AHEAD); Funding Accelerated for Smaller Towns (FAST); and Universal Hiring Program (UHP). Although the COPS program became official with the enactment of the Violent Crime Control and Law Enforcement Act in September 1994, Congress appropriated funding for community police officers in the fiscal year (FY) 1994 appropriation bill for the Departments of Commerce, Justice, and State (P.L. 103-121). These grants were named PHS grants and awarded in December 1993. Congress intended these grants to be a down payment on the goal of placing 100,000 additional officers on the street. For purposes of this analysis, PHS grants were allocated to 1994 because the award date fell in the last month of 1993.
53. The miscellaneous grant variable includes the following grants: Advanced Community Policing, Anti-Gang Initiative, Community Policing to Combat Domestic Violence, Demonstration Sites Program, Distressed Neighborhood Project, Methamphetamine Initiative, School Based Partnerships, Problem Solving Partnerships, Troops to Cops, Youth Firearms Violence Initiative, and other minor grants.
55. For more information about the effectiveness of incarceration in reducing crime, see Thomas B. Marvell and Carlisle E. Moody, Jr., "Prison Population Growth and Crime Reduction," Journal of Quantitative Criminology, Vol. 10, No. 2 (1994), pp. 109-140, and Steven D. Levitt, "The Effect of Prison Population Size on Crime Rates: Evidence from Prison Overcrowding Litigation," The Quarterly Journal of Economics, May 1996, pp. 319-351.
56. Minorities are defined as people that the U.S. Bureau of the Census counts as black, American Indian, Eskimo, Aleut, Asian, Pacific Islander, and Hispanic.
57. Thomas B. Marvell and Carlisle E. Moody, "Specification Problems, Police Levels, and Crime Rates," Criminology, Vol. 34, No. 4 (1996), p. 611.
58. The use of a lagged dependent variable as an independent variable was modeled after that in Marvell and Moody, "Prison Population Growth and Crime Reduction," pp. 109-140. In addition to lagging the dependent variable on the right-hand side of the model, separate models were estimated using the first difference approach. First differencing the dependent variable resulted in no findings of statistical significance for the COPS grant variables. Because of space limitations, the results for the first differencing approach are not reported in tabular form.
59. See Inter-university Consortium for Political and Social Research, "Uniform Crime Reporting Program Data [United States]: County-Level Detailed Arrest and Offense Data," 1995 codebook.
60. William Spelman, "The Limited Importance of Prison Expansion," in Alfred Blumstein and Joel Wallman, eds., The Crime Drop in America (Cambridge: Cambridge University Press, 2000), pp. 102-103.
62. The 95 percent confidence interval means that analysts can be 95 percent confident that the true value for the median is contained within the upper and lower bounds of the interval.
