Young African-American Males: Continuing Victims of High Homicide Rates in Urban Communities

Report Crime and Justice

Young African-American Males: Continuing Victims of High Homicide Rates in Urban Communities

May 2, 2000 19 min read Download Report

Authors: David Muhlhausen and Gareth Davis

Despite a welcome decline in violent Crime rates nationwide, African-American males are still dying from criminal homicides at an alarming rate. According to statistics from the Federal Bureau of Investigation (FBI), violent Crime in the United States has fallen since 1991.1 Politicians of both parties have hailed the news of this recent decline, but violent Crime rates remain unacceptably high and continue to be well above levels experienced before the 1960s.2

To measure the extent of the progress that has been made in the fight against violent Crime over the past decade, and to get some perspective on the progress that must still be made, Heritage Foundation analysts examined the data for one of America's most vulnerable groups--young African-American males who reside in eight of the nation's largest urban communities. The jurisdictions examined were Baltimore, Maryland; Brooklyn, New York; Chicago, Illinois; Detroit, Michigan; Los Angeles, California; New Orleans, Louisiana; Philadelphia, Pennsylvania; and Washington, D.C.3

The analysis of 1991 and 1997 homicide data from these communities finds that, despite some progress, urban black males continue to face a high risk of dying from homicide, even after accounting for the recent fall in homicide rates.4 Based on 1998 data for the eight communities studied,5 a 15-year-old urban African-American male faces a probability of being murdered before reaching his 45th birthday that ranges from almost 8.5 percent in the District of Columbia to just under 2.0 percent in Brooklyn, New York. By comparison, the probability of being murdered by age 45 is 2.21 percent nationally for all U.S. black males and 0.29 percent for all white males.6

A Ray of Hope
Despite these grim findings, there are encouraging results from the analysis as well. Between 1991 and 1998, African-American males in all of the jurisdictions the Heritage staff analyzed, apart from Baltimore, experienced a drop in the risk that they would be murdered. The most spectacular decrease occurred in Brooklyn, New York, where the risk of death by homicide for black males in 1998 declined by more than two-thirds from the risk in 1991. Over the same period, African-American males in Los Angeles County experienced a 50 percent decline in the risk of homicide.

The widely uneven pace of the decline in murder rates in Brooklyn, Los Angeles County, and other cities strongly suggests that city- and county-specific factors, such as criminal justice and policing policies, may play a key role in driving down Crime rates. For example, during the mid-1990s, Mayor Rudolph Giuliani and Police Commissioner William Bratton implemented sweeping managerial reforms in the New York City Police Department.7 Based on the empirical evidence over time, it would be possible for policy analysts to examine the role that these relatively new policies may have played in the faster-than-average decline in Brooklyn's murder rate.

Measuring the Probability of Homicide

Analysts in The Heritage Foundation's Center for Data Analysis (CDA) used data on homicide deaths from the Federal Bureau of Investigation and the U.S. Centers for Disease Control (CDC) to examine the continuing impact of high murder rates on urban minority communities during the 1990s.

To begin measuring the human impact of homicide within these communities, the Heritage analysts calculated the average probability that a 15-year-old black male would be murdered before reaching his 45th birthday in the eight above-listed urban counties with large African-American populations.

Despite the recent reductions in Crime rates across the nation, African-American males in each of these eight urban areas continue to face an extremely high probability of being killed before they reach middle age. (See Chart 1.) For example:

  • Based on 1998 murder rates, approximately one in every 12 black 15-year-old males who live in Washington, D.C., can expect to be murdered before reaching age 45.

  • For Brooklyn, the major urban community with the lowest 1998 homicide rates for young black males, roughly one in every 53 black 15-year-old males will die from homicide before reaching their 45th birthday.

  • By contrast, based on the 1998 murder rates, the average 15-year-old U.S. male faces a very low one-in-185 probability of being murdered before reaching age 45. Nationally, a similarly aged black male faces an average probability of one in 45 that he will die from homicide before reaching age 45. An average white male faces a one-in-345 probability of being murdered before reaching age 45.

Methodology

The data used in this Heritage analysis are based on information from U.S. records of deaths collected for 1991 and 1997 by local and state governments. These data are compiled by the U.S. Centers for Disease Control and are available for individual counties and states.1

To measure the impact of high murder rates on African-American communities during the 1990s, the analysts collected mortality data for the 20 U.S. counties that had the largest absolute number of black residents in 1998.2 For seven of these counties, sufficient numbers of death records were available for both 1991 and 1997 to calculate age-specific homicide rates for black males aged 15 through 44 that, according to CDC criteria, are deemed to be statistically reliable. In addition, CDC state-level mortality data were used to calculate 1991 and 1997 homicide rates for the District of Columbia.3

For the purposes of CDC county mortality data, Baltimore City is treated as a county, separate from and independent of suburban Baltimore County. The murder rate for the New York borough of Brooklyn is calculated using the data for Kings County, which geographically shares the same borders. Chicago-area homicide rates are calculated on the basis of data for Cook County, Illinois. Orleans Parish data are used to calculate homicide rates for New Orleans, and Philadelphia County data are used to estimate Philadelphia City murder probabilities. Detroit homicide rates are measured by data for Wayne County, and statistics for Los Angeles are taken from CDC mortality data for Los Angeles County.

The homicide rates for 1991 and 1997 are estimated using data from records of deaths compiled by local and state governments for public health purposes.4 These CDC cause-of-death data are collected independently from the two traditional sources of Crime data. The first traditional source is the number of reported crimes recorded by police agencies (i.e., the FBI's Uniform Crime Reports statistics-gathering program). The second traditional source of data is a collection of random surveys of households that typically are not large enough to provide reliable information for individual communities (i.e., the U.S. Justice Department's National Crime Victimization Survey).5 In other words, the estimates contained in this study offer new evidence (independent of traditional data sources such as police reports) that the homicide rates for black males have fallen in many of America's large urban communities.

The data for this analysis are based on combining death rate data for four specific age groups (15-19, 20-24, 25-34, and 35-44). The method used to calculate the homicide risk takes into account changes in the share of the population in each of these age categories. As a result, the estimates of the risk of death from homicide in this analysis are controlled for changes in the age structure of the African-American male population in each community.

Probabilities of dying due to homicide are calculated using mortality data for the calendar years of 1991 and 1997 and 1998. The results of this analysis are shown in Chart 1.


1. U.S. Centers for Disease Control, Compressed Mortality Files for 1991 and 1997.

2. U.S. Bureau of the Census, Population Estimates Program, Population Division, "Counties Ranked by Black Population in 1998" (Table CO-98-16), September 15, 1999.

3. Due to its small population size, the estimated homicide rate for D.C. black males aged 35 to 44 in 1997 was judged statistically "unreliable," according to CDC criteria. However, the 1997 homicide death rates were judged to be statistically valid for black males aged 15 to 34, and the estimated rate for ages 35 to 44 was used as an input in calculating a total homicide risk for the 15-to-44 age range. Based only on the statistically "reliable" rates (i.e., data for the 15-to-34 age range in 1997), the risk of being murdered faced by a black male living in Washington, D.C., was 9.07 percent. In 1997, the total homicide risk faced by a D.C. black male during the 20 years between ages 15 and 35 is higher than the risk faced by black males over a 30-year period (between ages 15 and 45) in the seven other communities in this study. In other words, the inclusion of data for D.C. black males for the 35-to-44 age range has no bearing on the District of Columbia's ranking.

4. While the estimates of the probability of dying as a result of homicide for 1991 and 1997 are calculated directly from the CDC's Compressed Mortality Files, these data are not currently available for years after 1997. However, to take account of the change in murder rates between 1997 and 1998, CDA analysts combined data from the FBI's latest Uniform Crime Reports for 1997 and 1998 with the rates derived from the 1997 CDC mortality data to produce a preliminary estimate of the impact of 1998 murder rates on African-American life expectancies.

5. The National Criminal Victimization Survey is conducted annually by the Bureau of Justice Statistics in the U.S. Department of Justice.





A Risk Worse than Military Combat? An analysis of historical data shows that, despite different time spans, serving in the U.S. military during wartime may be preferable to living in some urban communities today.8

  • The average probability of being murdered in 1998 before reaching age 45 for a young black male ranged from 8.47 percent in Washington, D.C., to 1.89 percent in Brooklyn.

  • By comparison, the death rate for U.S. soldiers serving in the military during World War II was 2.5 percent; during World War I, it was 2.4 percent; and during the Vietnam War, 1.2 percent of those who served in the military were killed.

Strictly speaking, these military death rates are not comparable to the rate for young black males in urban communities because they were endured over much shorter periods of time; but they do illustrate the magnitude of the risk faced by African-American males in these eight communities today.

Uneven Rates
Although the overall U.S. male homicide rate declined by almost 35 percent from 1991 to 1998, not all U.S. cities benefited to the same degree from this general reduction. (See Chart 2.) During the 1991 to 1998 period, black males between the ages of 15 and 45 in the District of Columbia and the New Orleans area still faced particularly high probabilities of dying from homicide.

  • From 1991 to 1998, the homicide mortality rate fell from 10.2 percent to 8.5 percent in Washington, D.C., and from 10.4 percent to 7.1 percent in New Orleans.

  • Most dramatically, while Baltimore City had the second lowest homicide rate for black males in 1991 among the eight communities in this analysis, by 1998 its murder rate had actually risen to the second highest rank behind Washington, D.C.



The experiences of these eight communities can be divided into three broad groups:

Group 1. In two communities (Brooklyn and Los Angeles County), black males experienced large reductions in their probability of being murdered (by 67 percent and 50 percent, respectively). The black male homicide rate in Brooklyn fell at almost twice the rate achieved in total U.S. male homicide rates between 1991 and 1998.

Group 2. Black males in five communities (Chicago, Detroit, New Orleans, Philadelphia, and Washington, D.C.) experienced moderate to substantial reductions in their homicide risk. Within this group, percentage reductions in the probability of a black male's dying from homicide between the ages of 15 and 45 ranged from 11 percent in Philadelphia to over 40 percent in Detroit.

Group 3. Finally, Baltimore African-American males experienced a substantial increase in their homicide rate. Between 1991 and 1998, a 15-year-old black male living in Baltimore saw his risk of being murdered before reaching 45 soar by a factor of 38 percent (from 5.3 percent to 7.3 percent).

These stark differences in the experiences of African-American males in these eight cities suggest that factors specific to communities (such as differences in local policing and criminal justice policies) likely play a very important role in shaping the differences in their respective murder rates.9

HOMICIDE AND LIFE EXPECTANCY IN THE DISTRICT OF COLUMBIA

One of the most vital signs of an area's socioeconomic health is the life expectancy enjoyed by its inhabitants. Indeed, social scientists often cite longevity as the "gold standard" indicator to measure differences in the level of social development across countries and over time.1 In March 1998, the U.S. Centers for Disease Control estimated that life expectancy at birth during the 1989 to 1991 period for black males in the District of Columbia was 57.5 years,2 the lowest in the nation and just over six months longer than life expectancy at birth in 1990 for a male born in India.3 (See Chart 3.)

However, if the homicide rates for D.C. black males in 1989-1991 had been reduced to the level experienced by D.C. white males during the same period, life expectancy at birth for African- American males would have been raised by 3.35 years.4 This 3.35-year increase in life expectancy would be slightly greater than the entire gain in longevity experienced by all U.S. black males during the entire 20-year period between 1974 and 1994.5

In fact, if effective anti-crime policies could reduce the homicide rate faced by black males to the same levels enjoyed by white males, the result would cut the gap between black and white life expectancies in the District of Columbia by over 24 percent. In short, urban minorities are the largest stakeholders in local policies that can fight Crime successfully in the District of Columbia.


1. Robert Fogel, "Economic Growth, Population Theory, and Physiology: The Bearing of Long-Term Processes on the Making of Economic Policy," American Economic Review, Vol. 84, No. 3 (June 1994), pp. 369-395.

2. National Center for Health Statistics, U.S. Decennial Life Tables for 1989-1991, Vol. II, State Life Table No. 9, March 1998.

3. U.S. Bureau of the Census, International Data Base, Table 010, at http://www.census.gov/ipc/www/idbacc.html.

4. This calculation is based on differences in the homicide rates for black and white males at all ages.

5. G. K. Singh, K. D. Kochanek, and M. F. MacDorman, "Advance Report of Final Mortality Statistics, 1994," Monthly Vital Statistics Report, Vol. 45, No 3 (1996), Supp., p. 19. This report is published by the National Center for Health Statistics.




Case Study: New York City

Innovative policing may explain reductions in homicide rates. In New York City, for example, recent history after changes in criminal justice policies were made may suggest reasons why Crime rates dipped so dramatically from 1991 to 1998. Previously, many criminal justice experts and practitioners believed that proactive efforts by the police to prevent Crime were unwarranted, since police could "fight" Crime only by responding to reported incidents. This once-prominent "reaction only" policing strategy is fading quickly as a result of academic research detailing the effectiveness of targeting Crime where it occurs and the adoption of "broken windows" policies.

The social science research on police tactics that aggressively target Crime offers empirical evidence that police crackdowns and targeting Crime "hot spots" do reduce Crime in those areas.10 For instance in Minneapolis, Minnesota, the police conducted an experiment that targeted "hot spots" in 1988 and 1989. This effort resulted in a statistically significant reduction in Crime of 13 percent in areas that received the intervention, compared with a control group.11

At the forefront of the use of innovative policing methods that built on the Minneapolis experience has been the New York City Police Department (NYPD). Beginning with policies first put in place under Mayor David Dinkins on the transit system and later expanded citywide under Mayor Rudolph Giuliani, New York City dramatically reduced its level of crime. Its success changed the city's long-standing reputation as an urban center riddled with Crime to the distinction of being one of the safest large cities in the country. The probability of an African-American male between the ages of 15 and 45 dying of a homicide in Brooklyn declined by 67.2 percent from 1991 to 1998, compared with a national decline of 36.9 percent for all African-American males.12 This welcome decline occurred during the period that the NYPD was intentionally being transformed into an innovative and proactive crime-fighting force.

Current Police Commissioner Howard Safir and his predecessor, William Bratton, used a three-pronged approach to reduce Crime:

  • Target quality-of-life nuisances. Traditionally, big-city police departments would overlook minor quality-of-life offenses (such as aggressive panhandling, public drunkenness, or menacing behavior) in order to focus their efforts on major crimes. Bratton and Safir took a more balanced approach, which recognized that once a community tolerates quality-of-life nuisances, more serious crimes often follow--a "broken windows" approach to policing.13 When a neighborhood is besieged with social disorder, its residents often withdraw from community life, exposing the community to an influx of even more social disorder and waves of crime.14 Breaking this cycle in New York meant taking quality-of-life offenses seriously.

One notable example was the focus on subway "fare beating." The police found that in some subway-entrance neighborhoods, as many as one fare-beating arrestee in 10 carried an illegal weapon or had an outstanding warrant for a felony violation.15 By targeting small crimes, the police were able to remove more serious offenders, who would have continued perpetrating their crimes had there been no intervention, from the streets. The "broken windows" strategy sent a clear message to New York's criminal subculture that deviant behavior, and the fear and disorder it causes, would not be tolerated.

  • Use crime-mapping technology to target violent crime. Commissioner Bratton introduced crime-mapping technologies that fundamentally changed how the NYPD operated, allowing the police administration to focus resources specifically where most Crime was occurring.16 The technology's potential for helping police is extraordinary: Research shows that over half of all Crime occurs in less than 3 percent of the addresses in a city, and that Crime at these addresses is clustered around certain days of the week and times of the day.17

To target Crime more effectively, the NYPD wanted a system that enabled it to identify the "hot spots" and rapidly deploy officers to those areas. The NYPD implemented the Compstat (for computer statistics) crime-mapping system, which analyzes geographic and temporal patterns of crime. The statistics it provided allowed precinct commanders to increase their presence in those hot spots and prevent the incidences from escalating while also removing perpetrators more quickly from the street. Further, the NYPD gave precinct commanders the authority to shift resources and redeploy officers based on the data Compstat collected. Police departments across the nation are copying this approach and integrating crime-tracking systems similar to Compstat into their organizations.18

  • Bring accountability back into policing. Along with the increased discretionary power the NYPD gave its precinct commanders came a widespread demand for accountability. Each week, the NYPD reviewed precinct commanders' responses to Crime reports and judged their results. According to Bratton, "As far as the department has been concerned, [before this] statistics were not for use in combating Crime, they were only for keeping score at the end of the year."19 So he decentralized the organization from an "unfocused, inward-looking, bureaucratic organization" to one that recognized its "precincts are the primary unit of policing."20 Bratton used Compstat not only as a crime-fighting tool, but also as a way to hold his precinct commanders directly accountable for their performance.

Although fighting Crime should be the primary mission of the police, this mission cannot allow police practices to compromise constitutional protections against unreasonable search and seizure and the use of excessive force. In this context, the new aggressive style of policing adopted by the New York City Police Department has not been without controversy, especially in the wake of the February 1999 shooting of Amadou Diallo. Critics have accused New York City police officers of exercising excessive force and violating constitutional protections against unreasonable search and seizure.21 For example, a December 1999 study carried out by the Office of the Attorney General of New York State found that, "In roughly one out of every seven 'stops' conducted by the NYPD, the facts that the police officer articulates for making the 'stop'...fail to meet the legal threshold of 'reasonable suspicion.'"22

However, the degree to which the allegations of excessive force and illegal search and seizure are a product of the reforms implemented in the NYPD after 1994, or merely reflect factors already in place before the reforms were instituted, is not clear. For example, from 1993 to 1994, the rate of citizen complaints against the New York police per 100 officers increased by 29 percent, but complaints between 1994 and 1999 dropped by 22.8 percent to the 1993 level.23 An even more important indicator of the NYPD's record is the substantial decline in police shootings. Between 1993 and 1999, the total number of shootings by police officers in New York City fell by 66.5 percent, even though arrests have increased by 95.8 percent from 1993 to 1999.24 While it is probably premature to reach a final conclusion, the available evidence does not support the claim that the NYPD reforms led to an increase in excessive force and civil rights abuses.

Conclusion

Though the national death rate from homicide faced by young African-American males has fallen dramatically since 1991, it remains alarmingly high in absolute terms. In eight of the largest urban African-American communities, teenagers face probabilities of being murdered before they reach age 45 that range from one in 53 in Brooklyn to one in 12 in Washington D.C. The crushing burden of these high murder rates not only is a human tragedy for America's urban communities, but also hinders economic and social development by frightening businesses out of these areas and disrupting social and family life.

Despite this gloomy picture, the large-scale reductions in black homicide rates achieved in Brooklyn, New York, have undercut an older academic prejudice that fighting violent Crime is somehow beyond either the competence of public authorities or the capacities of the police. While this report does not draw definitive conclusions about why homicide rates have declined, the evidence does suggest that sound law enforcement policy changes may be effective in reducing the tragedy of high homicide rates. The urban communities analyzed in this study face some of the highest homicide rates in the nation and so are the biggest stakeholders in the decisions of local governments in fighting crime.

Gareth G. Davis is a former policy analyst in the Center for Data Analysis, and David B. Muhlhausen is a senior policy analyst, at the Heritage Foundation.

Appendix
Estimation of Homicide Probabilities for 1998

The estimated homicide mortality rates for 1998 were based on the percentage decline in total homicide rates between 1997 and 1998 for each jurisdiction in the study. The percentage change in homicide rates was taken from homicide and population data obtained from Federal Bureau of Investigation Uniform Crime Reports for 1997 and 1998 and U.S. Bureau of the Census 1998 population estimates for the jurisdiction involved. Specifically, this analysis used homicide rates for all demographic groups to calculate the estimated drop in homicide probabilities for black males aged 15 to 44. The 1998 estimated figures were obtained by multiplying the percentage change in homicide rates with the homicide mortality rate for 1997 from the U.S. Center for Disease Control's Compressed Mortality Files.

(1997-1998 percentage change in homicide rate
per 100,000) X (homicide mortality rate calculated
for 1997) = (1998 estimated mortality rate)

Probabilities of death by homicide were calculated for 1991 and 1997 using age-specific homicide death rates for black males taken from the CDC's Compressed Mortality Files.25 These death rates were converted to probabilities, and these probabilities were then used to calculate the period cumulative probability that a black male in each jurisdiction would suffer death from homicide between the ages of 15 and 44.26

Endnotes

1. Data compiled from U.S. Department of Justice, Federal Bureau of Investigation, Crime in the United States, Uniform Crime Reports, 1991 to 1998 editions.

2. In 1998, the violent crime and homicide rates per 100,000 were, respectively, 252 percent and 23.5 percent higher than in 1960. Data for 1960 were obtained from the U.S. Department of Justice, Bureau of Justice Statistics, at http://www.ojp.usdoj.gov/bjs/. Data for 1998 were obtained from U.S Department of Justice, Federal Bureau of Investigation, Crime in the United States 1998: Uniform Crime Reports, 1999.

3. For specific jurisdictions examined, see the Methodology, page 3.

4. Data on homicides from the FBI's 1991, 1997, and 1998 Uniform Crime Reports. Data on causes of death from the U.S. Centers for Disease Control's Compressed Mortality Files for 1991 and 1997. See CDC WONDER at http://www.cdc.gov/scientific.htm. For a description of the methodology, see page 3.

5. U.S. Bureau of the Census, Population Estimates Program, Population Division, "Counties Ranked by Black Population in 1998" (Table CO-98-16), September 15, 1999.

6. Based on data from the FBI's 1997 and 1998 Uniform Crime Reports and the CDC's 1997 Compressed Mortality Files.

7. For a firsthand account of the managerial changes in the New York City Police Department, see William J. Bratton, " Cutting Crime and Restoring Order: What America Can Learn from New York's Finest, " Heritage Lecture No. 573, October 15, 1996.

8. Figures were calculated from data provided by the U.S. Department of Veterans Affairs, Office of Public Affairs, at http://www.va.gov/pressrel/amwars97.htm.

9. Specific policy innovations that may be at least partially responsible for the large-scale reduction in Brooklyn's murder rates are examined in the next section of this paper.

10. Lawrence W. Sherman, "Police Crackdowns: Initial and Residual Deterrence," in Michael H. Tonry and Norval Morris, eds., Crime and Justice: A Review of Research (Chicago: University of Chicago Press, 1990), Vol. 12. See also Lawrence W. Sherman and David Weisburd, "Does Police Patrol Prevent Crime? The Minneapolis Hot Spots Experiment," paper presented to International Society of Criminology Conference on Urban Crime Prevention, Tokyo, April 1992.

11. Sherman and Weisburd, "Does Police Patrol Prevent Crime?"

12. Estimation for the decline in the murder probability for all black males from ages 15 to 44 was calculated by using the percentage decline in the national homicide rate from 1997 to 1998. The 7.4 percent decline was multiplied by the 1997 probability of death by homicide for all black males aged 15 to 44 to estimate the probability for 1998. The percentage change between 1991 and 1998 was then calculated.

13. George L. Kelling and Catherine M. Coles, Fixing Broken Windows: Restoring Order and Reducing Crime in Our Communities (New York: Free Press, 1996), and James Q. Wilson and George L. Kelling, "The Police and Neighborhood Safety," The Atlantic, March 1982, p. 31.

14. Kelling and Coles, Fixing Broken Windows, p. 20.

15. Ibid., p. 134.

16. William J. Bratton and William Andrews, "What We've Learned About Policing," City Journal, Spring 1999, at http://www.city-journal.org/html/cj_archives.html.

17. Lawrence W. Sherman, Patrick R. Bartin, and Michael E. Buerger, "Hot Spots of Predatory Crime: Routine Activities and the Criminology of Place," Criminology, Vol. 27 (1989), pp. 27-55.

18. Police departments in Los Angeles County, New Orleans, and Baltimore have recently adopted crime-mapping techniques. See Christopher Swope, "The Compstat Craze," Governing Magazine, September 1999, p. 40.

19. William Bratton with Peter Knobler, Turnaround: How America's Top Cop Reversed the Crime Epidemic (New York: Random House, 1998), p. 219.

20. Bratton and Andrews, "What We've Learned About Policing."

21. For example, see Timothy Lynch, "'We Own the Night': Amadou Diallo's Deadly Encounter with New York City's Street Crimes Unit," Cato Institute Briefing Paper No. 56, March 31, 2000.

22. New York City, Office of the Attorney General, "The New York City Police's 'Stop and Frisk' Practices: A Report to the People of the State of New York from the Office of the Attorney General," December 1, 1999.

23. Figures obtained from the Office of Management Analysis and Planning, New York City Police Department.

24. Police shooting figures obtained from Office of Management Analysis and Planning, New York City Police Department. Arrest data for 1993 were obtained from the Office of Analysis and Planning, New York City Police Department, and the arrest data for 1999 were obtained from the New York State Division of Criminal Justice Services.

25. For a detailed description of the data use, see p. 3 of this report.

26. The standard life table methodology was used to calculate cumulative probabilities. For a description of this technique, see Robert L Brown, Introduction to the Mathematics of Demography (Winsted, Conn.: ACTEX Publications, Inc., 1997).

Authors

David Muhlhausen
David Muhlhausen

Research Fellow in Empirical Policy Analysis

Gareth Davis

Policy Analyst