**SPRINGER BRIEFS IN POPULATION STUDIES**

## William P. O'Hare

# Differential Undercounts in the U.S. Census Who is Missed?

## SpringerBriefs in Population Studies

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William P. O'Hare

# Differential Undercounts in the U.S. Census

Who is Missed?

William P. O'Hare O'Hare Data and Demographic Services LLC Cape Charles, VA, USA

ISSN 2211-3215 ISSN 2211-3223 (electronic) SpringerBriefs in Population Studies ISBN 978-3-030-10972-1 ISBN 978-3-030-10973-8 (eBook) https://doi.org/10.1007/978-3-030-10973-8

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## Acknowledgements

I would like to thank many current and former Census Bureau employees who have given me invaluable advice and feedback. These include Scott Konicki, Eric Jensen, Deborah Griffin, Howard Hogan, Heather King, Yeris Mayol-Garcia, Greg Robinson, and Mary Mulry. I would also like to thank Hannah Denny for editorial assistance. A special thanks to my wife (Barbara O'Hare) for providing extremely helpful feedback and valuable suggestions on earlier drafts of the book. And I would like to acknowledge support from the 2020 Census Project, which is a pooled fund administered by a Census funder collaborative promoting a fair and accurate Census. None of the people above are responsible for any shortcomings or errors in the publication.

## Contents

#### Contents xi

## **Chapter 1 Who Is Missing? Undercounts and Omissions in the U.S. Census**

**Abstract** Over the past 60 years, the overall accuracy of the U.S. Decennial Census has steadily improved. But some groups still experience higher net undercounts than other groups in the Census. The issue of differential Census undercounts is introduced in this Chapter along with some of the key concepts related to measuring the accuracy of Census counts, sometimes called Census coverage. Some of the key terminology is also discussed in this Chapter along with a description of the intended audience for this publication. The contents of the publication are described Chapter by Chapter.

#### **1.1 Introduction**

The mantra of the U.S. Census Bureau is to count every person once, only once, and in the right place. This is easy to say, but difficult to achieve. The U.S. Census Bureau tries very hard to include every person in the Decennial Census, but some people are always missed. The situation is summed up neatly by the U.S. General Accounting Office (2003, p. 4),

The Bureau puts forth tremendous effort to conduct a complete and accurate count of the nation's population. However, some degree of error in the form of persons missed or counted more than once is inevitable because of limitations in Census-taking methods.

This thought is echoed by Raymondo (1992, p. 37),

As most people know, the census of population is intended to count each and every resident of the United States. As most people might suspect, any undertaking so ambitious is bound to fall short to some degree, and the fact is that the census does not count each and every person. The failure to count everyone in the census is referred to as an undercount or, more generally as a coverage error.

The extent to which people in certain groups are missed or counted more than once is reflected in Census coverage measurements. The most widely used measures of Census coverage or Census accuracy are net undercounts, net overcounts and omissions.

What is a net undercount in the Census? In every demographic group, some people are missed in the Census, and some people are counted more than once (or included inappropriately) in the Census. When the number of people missed is larger than the number of people counted more than once, it produces a net undercount. When the number of people counted more than once is larger than the number of people missed it produces a net overcount. Census Bureau whole person imputations are another component in this equation, but for the sake of simplicity they are ignored for now.

Net undercounts have been measured often and consistently in the U.S. Census over the past 60 years, and it has been the main measure used by demographers to assess Census accuracy. Robinson (2010) refers to the net undercount from the Census Bureau's Demographic Analysis method as the "gold standard." A more detailed discussion of this topic is provided in Sect. 1.4 of this Chapter and in Chap. 3.

Omissions are a key component of net undercounts. Omissions reflect people who are missed in the Census and as such they are an important focus of this book. In some ways, omissions are a better measure of Census quality than net undercounts because double counting can mask omissions. A net undercount of zero could be the result of no one being missed and no one double counted, or for example, it could reflect a situation where ten percent of the population are missed, and ten percent are double counted. Differential omissions rates reflect that same kind of inequity as differential undercount rates. Data on the characteristics of people who are missed are presented in most of the Chapters in this book.

Unfortunately, people in some groups have higher net undercount rates than people in other groups. These differences in Census coverage are referred to as a "differential undercounts" and are the focus of this book. More specifically this book focuses on the groups that have the highest net undercounts and highest omissions rates in the U.S. Census.

The main point of this publication is to present existing information on net undercounts and omissions in the U.S. Census in a simple, organized, and systematic way. I have not found a single publication that pulls together key undercount and omissions data from different Census assessment methods, for many groups, over several times periods. This publication aims to fill that niche. By putting the key information into one publication I hope this publication makes key data on Census accuracy more readily available to a wider, non-technical audience. I also hope this publication facilitates further research on Census coverage issues.

By focusing on which groups have the highest net undercounts and Census coverage differentials the primary focus of the publication is descriptive rather than analytical. Material that tries to explain why net undercounts (or net overcounts) occur is more limited in this publication.

The book draws heavily on data produced by the U.S. Census Bureau. Most of the statistics presented here are publicly available, but the key data are often buried in large statistical reports, available on some obscure portion of the Census Bureau's website, appear only in scholarly journals, in presentations made at scientific conferences, or appear in internal Census Bureau reports (see, for example, U.S. Census Bureau 1974, 2012; Fay et al. 1988; Robinson et al. 1993; Robinson and Adlaka 2002; Mayol-Garcia and Robinson 2011). In some cases, one must download and analyze data files from the Census Bureau to produce simple net undercount tabulations. For a large share of the public such information is not easily or readily available.

More specifically, this report will draw extensively on data produced by the Census Bureau's Demographic Analysis (DA) and Dual-Systems Estimates (DSE) programs. More information about these two methods is provided in Chap. 3.

Although Demographic Analysis and Dual-Systems Estimates are the best estimates available regarding Census coverage it is important to recognize these methods have some limitations. For example, the demographic groups for which these two programs produce data are limited. Census Bureau tabulations have focused on measuring Census coverage for five demographic characteristics including;

The 2010 DSE reports covers all these characteristics and the 2010 DA covers all but tenure, at least to some degree.

It should be noted that many times the most important differential undercounts are based on a combination of the characteristics noted above. For example, the net undercount for Black males age 30–49 is much higher than the net undercount rate for the total Black population or total male population. These special populations will be highlighted in the appropriate Chapters.

The characteristics noted above are important, but there are many other groups for which we would like to have data on Census undercounts. Many such groups are highlighted in public discussion of the Census. For example, in response to release of 2010 Census results, former Undersecretary of Commerce Dr. Rebecca Blank (2012, p. 1) said,

However, as has been the case for some time, today's release shows that certain populations were undercounted. More work remains to address persistent causes of undercounting, such as poverty, mobility, language isolation, low levels of education, and general awareness of the survey.

Undercounts for the groups mentioned by Dr. Blank are not measured by the Census Bureau's DA or DSE methods. Some of these groups are captured by the "hardto-count" factors (Bruce and Robinson 2003) and Mail Return Rates (Letourneau 2012) used by the Census Bureau and Census advocates. To be clear, this publication focuses on direct measures of Census coverage (net undercounts, net overcounts, and omissions) rather than metrics that reflect likelihood of being counted accurately like Mail Return Rates or hard-to-count scores.

In addition to reports and datasets from DA and DSE, I will add information from Census Bureau reports focused on some Census operations. Information on Census operations can shed light on the mechanisms by which differential Census undercounts occur. For example, see U.S. Census Bureau reports on topics such as Census Followup, Non-Response Followup, and Mail Return Rates (Govern et al. 2012; Letourneau 2012). I also draw on a series of qualitative studies that can help us understand why Census errors occur (de la Puente 1993; Schwede 2003, 2006; Schwede and Terry 2013).

The focus of this report is on Census net undercounts and omissions, but it should be noted that these are not the only types of Census errors. Census errors also include net overcounts and erroneous inclusions. Erroneous inclusions are people who are counted more than once and people who are included in the U.S. Census inappropriately. For example, an erroneous inclusion would be a foreign tourist who gets included in the Census by mistake or someone who dies before the Census date but is included inappropriately in the Census count. Another type of error is counting people in the wrong place.

From a scientific perspective net overcounts and erroneous inclusions are measurement errors just like net undercounts and omissions. But net undercounts and omissions are a much bigger public relations and public perception problem. According to Williams (2012, p. 8), "Differential undercounts are a recurrent problem in the Decennial Census and diminish the perception that the count is equitable to the entire population."

Net undercounts and omissions are much more of a problem than net overcounts. I am not aware of any lawsuit brought by a state or city because of real or perceived net overcounts, but there have been many lawsuits brought because of real or perceived net undercounts. Undercounts are also much more of a public relations problem for the Census Bureau. Note in the previous quote from Dr. Blank, she focuses on the problem of undercounts in the Census, not overcounts. Given this situation this book will focus on net undercounts and omissions with only passing note on net overcounts or erroneous inclusions.

#### **1.2 Audience**

This book is aimed largely at people outside the scholarly community such as practitioners and advocates. Because of the social equity issues raised by the differential net undercounts for many racial and Hispanic minority groups the book will be of interest to many civil rights organizations such as the Leadership Conference on Civil Rights, National Association of Latino Elected Officials, the Mexican-American Legal Defense and Education Fund, The National Urban League, The National Association for the Advancement of Colored People, Asian-American Advancing Justice League, National Congress of American Indians, and many others. One of the main purposes for writing this book is to make the high-quality data on Census errors available to a wider audience. Too many times, I have heard people assert that there is a net undercount for this group or that group when there is no good evidence to support that claim.

The book may also be useful for researchers in the demographic community because it fills an important niche regarding Census accuracy. It will provide a handy reference for the relative Census coverage rates for many key populations. In the context of scholarship, the book will help round out the literature in demography and/or population studies courses. Since the publication provides a lot of information in one place it could be a useful reference book for Census Bureau staff and related government organizations such as the U.S. General Accountability Office, The Congressional Research Service, and The U.S. Office of Management and Budget. Other possible users include professional organizations that monitor the Census such as the Population Association of America, the American Statistical Association, American Association of Public Opinion Researchers, and the non-profit organizations such as Population Reference Bureau, The Funders Census Initiative, and The Census Project.

Given this audience, some of the more detailed and esoteric aspects of the statistical methods used to assess Census coverage are ignored in favor of more straightforward language and a focus on results rather than methods. Readers who are more technically inclined can find the more detailed information through the citations offered in this publication, and the readers who are not technically inclined will get the basic information.

A significant segment of the audience for this book will be focused on one group or one Chapter. For example, the National Association for the Advancement of Colored People are likely to focus on the Chapter related to Blacks and the National Association for Latino Elected Officials are likely to focus on the Chapter related to Hispanics. Partnership for America's Children will be more interested in the Chapter on age which shows a high net undercount of young children.

#### **1.3 Terminology**

Some of the language, terminology, and nomenclature used in this publication may be unfamiliar to many readers and some terms have been used inappropriately or incorrectly in the past. In addition, some of the key terms may sound like the same thing but they have a different meaning to demographers. In general, I follow the nomenclature conventions of the U.S. Census Bureau.

The terms "net undercount" and "net overcount" have very precise meanings to demographers. But the terms "undercount" or "net undercount" are sometimes used loosely by non-demographers to mean people missed in the Census in a broad sense. In this publication the focus is on scientific measurements of net undercounts.

It is important to recognize that the net undercount does not reflect the number of people missed even though the term undercount is often used to suggest this. As stated earlier, net undercounts reflect a balance of people missed and people counted more than once or otherwise included erroneously. Demographers use the terms gross undercount or omissions to reflect the number of people missed.

Only the Dual-Systems Estimates (DSE) method produces data for omissions. I use omissions in many portions of this publication to supplement data on net undercounts. A more detailed discussion of methodology is offered in Chap. 3.

Prior to the 2010 Census, whenever the Census count was less than the DA estimate the Census Bureau typically reported the difference between a DA estimate and the Census as an undercount. But some of the information put out by the Census Bureau following the 2010 Census refers to differences between the Census count and the DA estimates rather than net undercounts or net overcounts. This is meant to reflect the fact that both the Census and the estimate to which the Census is being compared (DA or DSE) have errors. While I understand the intent of using the term "differences" rather than undercount and overcounts, I will use the traditional terms net undercount and net overcount because these terms are more widely understood, and they indicate the directionality of the differences which makes communication more efficient. In other words, saying there is a one percent difference between the Census count and the Demographic Analysis (DA) estimate does not tell a reader if the Census is larger or smaller than the DA estimate, but saying there is a one percent net undercount indicates the Census count is lower than the DA estimate.

Another issue that might cause confusion is the fact that undercounts have sometimes been reported as a negative number by the Census Bureau (Velkoff 2011) and sometimes as a positive number by the Census Bureau (U.S. Census Bureau 2012). Since I draw on Census Bureau reports that use both expressions for net undercounts, I thought it important to standardize presentation within this publication. In the remainder of this publication, the differences between the Census counts and DA or DSE estimates are shown as the Census count minus the DA or DSE estimate. So, a negative number reflects a net undercount. This is consistent with the convention used by Velkoff (2011) in reporting the first results of the 2010 DA. This presentation style was also used in a couple of recent Census Bureau papers on this topic (King et al. 2018; Jensen et al. 2018). Also, this approach is consistent with O'Hare (2015) reporting on the undercount of young children. This calculation is sometimes labeled "net Census coverage error" in other research. In this publication, a negative number consistently implies a net undercount and a positive number implies a net overcount. I chose to use the net Census coverage error construction because I feel having an undercount reflected by a negative number is more intuitive.

When figures are stated in the text as an undercount or an overcount, the positive and negative signs are not used. In converting the difference between Census counts and Demographic Analysis or Dual-Systems Estimates to percentages the difference is divided by the DA or DSE estimate not the Census figure.

Another point of potential confusion is the name applied to the Dual Systems Estimation method. The DSE has been called by different names in the past three Censuses. In the 1990 Census it was called the Post-Enumeration Survey (PES), in the 2000 Census it was called Accuracy and Coverage Evaluation (A.C.E.) and in the 2010 Census it was called Census Coverage Measurement (CCM). In the 2020 Census, this method will again be called the Post-Enumeration Survey or PES (U.S. Census Bureau 2017b). I use the term DSE for consistency.

#### *1.3.1 Net Undercounts, Omissions, and Hard-to-Count Populations*

Another term that is related to net undercounts or Census omissions is "hard-tocount" populations. Many closely related terms (hard-to-count areas, hard-to-count populations, difficult to enumerate populations, and hard-to-survey populations) have been used almost interchangeably (Tourangeau et al. 2014). Census Bureau (2017a) also uses the term "Hard-to-Reach" populations to identify groups that are difficult to enumerate accurately.

The U.S. Census Bureau (2017a, p. 2) defines hard-to-count populations as,

Hard-to-count populations face physical, economic, social, and cultural barriers to participation in the Census and require careful consideration as part of a successful communications strategy.

While this is a good conceptualization of "hard-to-count" populations, it does not specify how to measure the concept and it does not mean that hard-to-count groups necessarily are undercounted in the Census. Generally, groups that have a significant net undercount are thought of as hard-to-count groups, but not all hard-to-count groups have measurable net undercounts in the Census.

Many of the hard-to-count populations not covered by DA and DSE can be addressed to some level by identifying who lives in hard-to-count neighborhoods (O'Hare 2015). In addition, Mail Return Rates are often used as a proxy for Census coverage (Letourneau 2012; Word 1997; Erdman and Bates 2017). A set of hard-tocount factors were provided by Bruce and Robinson (2003) in the mid-1990s that are sometimes used to identify vulnerable populations. Following the 2010 Census the Census Bureau produced a new metric for identifying hard-to-count areas which is called the Low-Response Score (Erdman and Bates 2017).

But it is important to note that hard-to-count factors, Low-Response Scores, and Mail Return Rates (Bruce and Robinson 2003; Erdman and Bates 2017) are not measures of Census coverage per se. Moreover, the association between Mail Return Rates and net undercounts are not always clear. O'Hare (2016, p. 51) shows that only five of thirteen groups concentrated in neighborhoods with low Mail Return Rates had a net undercount rate that was statistically significantly different than zero.

#### **1.4 Perspectives on Differential Undercounts**

Differential undercounts suggest comparisons between the coverage rate of one group and the coverage rate of another group. But sometimes it is not clear what the appropriate comparison group should be and sometimes data for the appropriate comparison group are not available. For example, if one is looking at the net undercount rate for young children, should that undercount rate be compared to the net undercount rate for the total population, the net undercount rate for some age-group of adults, or the net undercount rate for the elderly?

Other times, there is no net undercount measurement for the group one would like to use as a comparison group. For example, for the 2010 DA undercount estimates, there are no estimates for the White population or the Non-Hispanic White population. So, demographers often compare Census coverage of the Black population to the Non-Black population. Demographers sometimes end up making comparisons that may not be the most appropriate ones from a conceptual point of view but are dictated by the data available.

Comparing all net undercount rates to the net undercount rate for the total population would provide one constant benchmark, but it would often overlook crucial differences between groups. For example, from a social justice point of view, the difference between the net undercount rate of Blacks and Non-Hispanic Whites is probably more meaningful than the difference between net undercount rates of Blacks and the total population. Keep in mind the total population includes many other hard-to-count groups besides Blacks.

If this publication were only focused on one group, the appropriate comparison group might be easy to identify. But the net undercounts and net overcounts for many groups are compared in this book. Therefore, I focus on identifying groups with high net undercount or omissions rates even if there is not a specific comparison group. One point of this book is giving readers a good sense of which groups have the highest net undercounts and omissions rates in the U.S. Census.

#### **1.5 Contents of This Book**

Following this Introductory Chapter, I provide a Chapter on the uses of Census data. It is difficult to understand the importance of Census accuracy unless one understands how Census data are used in the public and private sectors. Census undercounts are important because data accuracy is linked to many equity and social justice issues. In addition, Census undercounts are one of the biggest Census Bureau public relations issues. With respect to Census undercounts Kissam (2017, p. 797) states, "These persistent undercounts raise difficult questions about why it occurs and are troubling due to their practical implications for the conduct of public policy."

In Chap. 3, I describe the key methods used by the Census Bureau to assess accuracy in the Decennial Census. The descriptions offered here are relatively parsimonious with citations provided for readers who would like more detailed information on this topic. The strengths and limitations of each method are also noted.

In Chap. 4, I provide a summary of key undercount differentials based on age, sex, race, Hispanic Origin, and tenure. This Chapter is meant to give readers an overview of Census undercounts and provide a framework and a foundation for several later Chapters. In Chap. 4, information is also presented on some of the key groups not reflected in the Census Bureau's DA or DSE data.

The next several Chapters focus on specific demographic characteristics. I present the groups in the order in which the questions appear in the Census questionnaire.

In Chap. 5, I examine undercount differentials by age. The major points here are the very high net undercount of young children and the net overcounts of young adults and the older population (age 60 plus). In Chap. 6, I explore differences by sex, which shows, on average, males have a net undercount while females have a net overcount.

In Chaps. 7 through 11, I explore differentials in Census accuracy by major race/Hispanic Origin groups (Hispanics, Blacks, Asians, American Indians/Alaskan Native, and Native Hawaiian/Pacific Islander). Researchers differ in their views about the appropriateness of using race and Hispanic Origin as a lens for differential undercounts. Some feel differences by race should not be the focus of attention because racial differences in net undercounts are simply a product of other nonracial factors and we should be focused on these other more dominant non-racial factors. For example, Schwede et al. (2014, p. 293) state,

Though there is no reason to believe that race or ethnicity in and of itself leads to coverage error, it seems that some underlying variables associated in past studies with undercounting may also be correlated with race (e.g., mobility, complex living situations, and language isolation).

In other words, race is widely seen as a proxy for a combination of factors related to the likelihood of being missed in the Census.

Nonetheless there are least three reasons for looking at differential Census coverage through the lens of race and Hispanic Origin. First, at least from a civil rights perspective, differential undercounts among minority groups is a central problem with the Decennial Census results and many of the most pronounced differentials occur among different race groups. Second, there is a wealth of data related to Census coverage by racial categories. Examination of net undercounts by race is a very prominent facet in much of the previous work on differential undercounts. Third, several analyses show that race is still a salient factor even after many of the other factors are controlled (Erdman and Bates 2017; Fernandez et al. 2018).

Readers may also note that there is no Chapter on the White or Non-Hispanic White population. The White population is seldom discussed in the context of Census undercount because the Whites are almost always counted more accurately than their counterparts in racial and Hispanic minority groups. In this publication, data for the Non-Hispanic White population are provided in many Chapters as a comparison group for minority groups.

In Chap. 12, I examine Census coverage rates by tenure. Homeownership often conveys a status and commitment to place that impacts Census participation. Data consistently show that renters have net undercount rates while homeowners have net overcounts. Examination of differential undercounts by tenure is also a reflection of socioeconomic status since homeowners generally have higher incomes than renters.

In Chap. 13, theories and data on why people are missed in the Census are examined. The material in this Chapter includes broad frameworks for understanding why people are missed in the Census as well as several individual mechanisms that may result in someone being left out of the Census count.

Given the pervasive and long-standing differential undercount patterns, it is worth noting efforts the Census Bureau has made to reduce differential undercounts. In Chap. 14, some of the key activities the Census Bureau has utilized in the past few decades to improve Census coverage and reduce differential undercounts are reviewed.

In Chap. 15, some of the key issues surrounding the upcoming 2020 Census are examined. Some of the major developments regarding 2020 Census planning are discussed and I offer some thoughts about the implications these have for Census coverage in the 2020 Census.

Finally, in Chap. 16 I offer a brief summary of key findings and some of their implications.

Most of the focus in this book is on data from the 2010 Census with some examination of long-term trends when the data are available and appropriate. The reality is many of the groups that have high net undercounts in the 2010 Census have experienced problems with Census coverage for many decades. I feel it is important to recognize that history.

#### **1.6 Summary**

While the Census Bureau tries very hard to count every person in the country some people are always missed, and some groups are missed at a higher rate than others. The net undercount reflects the difference between people missed and people counted twice. Some groups have higher net undercount rates than others in the Census and some groups have higher omissions rates than other groups. This book focuses primarily on groups with relatively high net undercounts and high omissions rates and to a lesser extent on groups with relatively high net overcounts.

#### **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Chapter 2 The Importance of Census Accuracy: Uses of Census Data**

**Abstract** This Chapter provides readers with many reasons why the Census count is so important, including the fact that Census data are the backbone of our democratic system of government. In addition, Census-related figures are used to distribute more than \$800 billion in federal funding each year to states and localities. Countless decisions in the public and private sectors are based on Census data. Moreover, the impact of flaws in Census counts often last a decade because population estimates, projections, and survey weights, are derived from Census counts.

#### **2.1 Introduction**

To understand the importance of differential Census undercounts and omissions it is important to understand how Census data are used. In addition to our scientific and scholarly interest in obtaining correct Decennial Census counts, there are many practical and policy-related reasons why it is important to assess Census coverage. In many cases, Census coverage errors are important because they are both a data problem and a social equity issue.

According to the U.S. Census Bureau (2017), data from the Decennial Census are used for many important applications including:

A more detailed description of how Census data are used is provided in Appendix A of the Census Bureau's 2020 Census Complete Count Committee Guide (U.S. Census Bureau 2018). A number of these points are discussed in more detail below.

#### **2.2 Political Power**

Constitutional scholar Leavitt (2018, p. 2) provides a clear idea of the importance of the Census when he states,

It is impossible to overstate the constitutional significance of the Decennial Census. The requirement that has become a mandate to count each and every individual in the country- -- the 'actual Enumeration' of the population in every decade ---is embedded in the sixth sentence of the Constitution. It is the very first act that the Constitution prescribes as an express responsibility of the new federal Government.

The fact that the Decennial Census is mentioned early in the Constitution by the founding fathers, suggests the central role they envisioned for it in our system of governance. Counts from the Census are used to distribute political power both in terms of assigning seats in the U.S. House of Representatives to states based on population and in the judicially mandated one-person/one-vote rule used for constructing political districts (Grofman 1982; McKay 1965; Balinski and Young 1982; Baumle and Poston 2004). The "one person-one vote" rule requires election districts to be equal (or nearly equal) in population size. Calculation of election district population size is almost always based on data from the Decennial Census.

The fundamental relationship between Census counts and political power was summarized by Heer (1968, p. 11) 50 years ago,

Where a group defined by racial or ethnic terms and concentrated in special political jurisdictions is significantly undercounted in relation other groups. Then individual members of that group are thereby deprived of the constitutional right to equal representation in the House of Representatives and, by inference, in other legislative bodies.

Decennial Census counts for states are used for apportioning the seats in the U.S. House of Representatives and sometimes small differences can be important in determining which state gets the last seat to be assigned (Conk 1987; Baumle and Poston 2018). For example, Crocker (2011) found that if the 2010 Decennial Census count for North Carolina had been 15,753 higher it would have received an additional seat in Congress. Baumle and Poston (2004) also show that small differences in state Census counts can change which state gets the last Congressional seat assigned.

Based on projecting the 2017 Census Bureau population estimates to 2020, Brace (2017) predicts 15 to 17 states will experience changes in their congressional delegation after the post-2020 re-apportionment. However, many states are close to gaining or losing a seat depending on the demographic changes between now and 2020 and the quality of the Census count in each state. Consequently, details about how the Census is conducted could have an impact on apportionment of Congress following the 2020 Census. For example, Baumle and Poston (2018) show that failure to count non-citizens in the 2020 Census would result in several congressional seats changing states in the apportionment following the 2020 Census.

I could not find a definitive number of election districts where Census data are used to draw boundaries for political districts. In addition to the 435 seats in Congress, almost all of the 7383 state legislators are elected from single member districts (National Conference of State Legislators 2017). Also, nearly ever large city has city council members elected from single-member districts and the same is true for county commissioners. School board members and many special districts also use Census data to construct districts. Therefore, the number of election districts based on Census results must be at least 10,000.

Siegel (2002, Chap. 2) as well as Teitelbaum (2005) provide additional examples of how demographic data are used in a variety of political applications. The bottom line is that any geographic area that is undercounted is not likely to get its fair share of political power (Anderson and Fienberg 2001; Bryant and Dunn 1995).

#### **2.3 Distribution of Public Funds**

Decennial Census data are also used in many federal funding formulas that distribute federal funds to states and localities each year (Murray 1992; U.S. Senate 1992; Reamer 2010; Blumerman and Vidal 2009; Hotchkiss and Phelan 2017). Recent research indicates Census-derived data were used to distribute more than \$850 billion to states and localities through 302 programs in Fiscal Year 2016 (Reamer 2018). Table 2.1 shows data for the 16 largest federal programs that use Census-derived data to distribute funds. Places that experience a net undercount do not receive their fair share of formula-driven public resources (PriceWaterhouseCoopers 2001). The distribution of federal funds based on Census data will impact some groups more than others. The Annie E. Casey Foundation (2018) shows that these funding formulas are particularly important for programs that support needy children.

Moreover, the amount of federal money given out through funding formulas has increased in recent years. The increase is heavily driven by Medicaid and Medicare Part B where health care costs are rising faster than inflation and the large baby boomer generation is aging and expanding the number of recipients in these programs.

One question that always arises in this area is," How much money does a state lose for each uncounted person?" There is no definitive answer to this question, but an analysis by Reamer (2018) shows that for five programs that use the Federal Matching Assistance Percentage (FMAP) states, on average, would lose \$1091 each year for each uncounted person. In some states the figure was lower, and, in some states, it was higher. These figures only apply to the 37 states which are not already at the minimum FMAP value of 50 percent and only for five programs. Another study following the 2000 Census that was focused on 169 metropolitan areas concluded the loss over the 2002–2012 period was \$3392 per uncounted person in these jurisdictions but the authors note this estimate is conservative because not all programs are included (PriceWaterhouseCooper 2001, p. ES-1). In another report focused on Idaho (Miller 2018) concludes, "It's estimated each person counted brings about \$1200 per year in federal funding to state and local government."

**Table 2.1** Largest 16 federal assistance programs that distribute funds on basis of decennial censusderived data, Fiscal Year 2015

*Source* Reamer (2017)

#### *2.3.1 Federal Distribution 2015–2030 Based on Census-Derived Figures*

Reamer (2018) estimates that in Fiscal Year (FY) 2016 the federal government distributed at least \$865 billion to states and localities based on Census-derived data. The \$865 billion figure is based on the largest 35 federal programs that use Censusderived data to distribute money and there are many additional programs that are not included in this figure. In 2010 Reamer (2010) estimated that the federal government distributed about \$420 billion to states and localities based on Census-derived data in Fiscal Year (FY) 2008. The \$420 billion in FY 2008 amounts to \$465 billion in 2015 dollars. Consequently, there was an increase from \$465 billion to \$865 billion between FY2008 and FY2015. Some of the increase from FY2008 to FY2015 is based on adding programs to the calculation and some of the increase is based on increased spending by programs identified in 2008.

The increase between FY2008 and FY2015 amounts to a little more than 11 percent per year. Data shown in Table 2.2 indicate what would happen between

<sup>a</sup>*Source* Reamer (2010) <sup>b</sup>*Source* Reamer (2018)

FY2015 and FY2030 if there were an 11 percent increase per year in the amount of federal funds distributed based on Census-derived data. Perhaps most importantly in the decades following the 2020 Census more than \$26 trillion dollars could be distributed to states and localities on the basis of 2020 Census-derived data.

Of course, no one knows exactly what will happen in the future regarding the distribution of federal funds based on Census-derived data and the measurement of change between FY2008 and FY2105 is not precise, but the scenario reflected in Table 2.2 provides one plausible trajectory. Moreover, even if the projected dollars in Table 2.2 are too high by 10 or 20%, the amount of money distributed between 2020 and 2030 using Census-derived data is still enormous.

Demographic data are also used to distribute state government funds within states, but I was unable to find a good estimate of how much money is regularly distributed by state governments based on Census data.

#### **2.4 Population Estimates, Projections, and Surveys**

The undercounts in the Decennial Census also have implications for post-Census population estimates and projections. The Census Bureau's post-Census population estimates program, which produces yearly national, state, and county population estimates, uses data from the Decennial Census as the starting point to produce post-Census estimates (U.S. Census Bureau 2014a). If an age cohort is undercounted in the Census, that cohort will be under-represented in the Census Bureau's population estimates for the next decade.

Many population projections also start with the Decennial Census counts, so undercounts in the Decennial Census are likely to be reflected in projections for many years (U.S. Census Bureau 2014b). State population projections, such as those available from the University of Virginia's Weldon Cooper Center for Public Service (2013), are also affected by Census undercounts. In discussing where to get data for state and local projections Smith et al. (2001, p. 113) indicate, "The most commonly used source--and the most comprehensive in terms of demographic and geographic detail—is the Decennial Census of population and housing."

Decennial Census results and the Census Bureau's post-Census population estimates are often used to weight sample surveys both inside and outside government. If the Decennial Census counts and subsequent population estimates underestimate a population group, the weighted survey results will reflect this error (Jensen and Hogan 2017; O'Hare and Jensen 2014; O'Hare et al. 2013). Several analysts have shown how Census undercounts distort estimates of poverty rates for children (Hernandez and Denton 2001; Daponte and Wolfson 2003; O'Hare 2017).

In addition, data from the Census Bureau are often used as denominators for constructing rates such as the child mortality rate. Census undercounts may skew such rates. For example, the 2010 U.S. death rate for all children age 1–4 in 2010 was 26.5 per 100,000 and for Hispanic children age 1–4 it was 22.7 per 100,000 (Murphy et al. 2013). These rates are based on using the Census counts as denominators. If one had used the DA estimates for the population age 1–4 instead of the Census counts, the death rate for all children age 1–4 would have been 25.3 (rather than 26.5) and the rate for Hispanic children age 1–4 would have been 20.9 (rather than 22.7). This represents a 5% difference for all children and an 8 percent difference for Hispanic children. This shows how Census undercounts can lead to flawed rates.

#### **2.5 Using Census Data for Planning**

Data from the U.S. Decennial Census counts as well as estimates and projections which are based on the Census are used for many planning activities including schools (Edmonston 2001; McKibben 2007, 2012). Flaws in the Census counts can lead to inefficient use of public funds. For example, the high net undercounts of young children in many large cities and urban counties are likely to compromise school planning in those areas (O'Hare 2015).

Census data are also used in health care planning (Koebnick et al. 2012). For example, the Center for Medicare and Medicaid Services (2018) shows how Census are used in health care planning and delivery in rural America.

#### **2.6 Use of Census Data in Business**

Census data have been used in business planning as well (Headd 2003). Among other uses, Census data are used by business to determine where to start or expand a business and to determine potential customers for new products. A recent U.S. Department of Commerce publication (2015, p. 2) identifies several business and commercial uses of Census data including;

According to the National Research Council (1995, p. 292);

Retail establishments and restaurants, banks and other financial institutions, media and advertising, insurance companies, utility companies, health care providers, and many other segments of the business world use Census data.

One business group working on the 2020 Census, Council for Strong America (2018), states

A thriving economy relies on timely information about the U.S. population and how it is shifting and changing throughout the country. The Decennial census provides the broadest set of data about residents in the United States that no other body produces.

It is also important to note that many of the data products or data systems used by businesses depend on Census data as a benchmark. In the data-driven and digitaldriven work of business decision making, at least one business leader (McDonald 2017, p. 2) recognizes the important role the Census plays.

In such a digital-driven world, the Decennial counting of noses known as the U.S. Census may seem irrelevant or outdated. But in fact, the data that the Census Bureau collects –both in its Decennial count and the annual American Community Survey (ACS) – have never been more important to business constituencies.

#### **2.7 Use of Census Data in Civil Rights Protection**

For many groups, the Census is seen a civil rights issue (Leadership Conference on Civil Rights 2017). In addition to heavy use of Decennial Census data in the context of redistricting and voting rights, data from the Census are used to examine equality in jobs and education opportunities. A flawed Census can undermine the ability to examine such issues fairly. According to the Leadership Conference Education Fund (2017, p. 1), "Federal agencies rely on Census and American Community Service (ACS) data to monitor discrimination and implement civil rights laws that protect voting rights, equal employment opportunity, and more."

In addition to the use of Census data for many obvious civil rights purposes, it is also used for some lessen known civil rights programs. For example, under section 203 of the Voting Rights Act, data from the Census Bureau are used to identify jurisdictions that must provide language assistance in voting that is based on the number of people in the jurisdiction that speak a language other than English (Advancing Justice 2016).

#### **2.8 Public Perceptions of Growth or Decline**

High net undercounts can provide misleading public impressions about the size or growth of the population in a given location. And these perceptions can have a significant impact on public and private investment decisions related to a community.

This point is difficult to quantify but in many instances the size of a population translates into the importance politicians and marketers give it. In response to the 2000 Census, one public official stated, "Pride in the community is involved.  We aren't just a little burgh in south Louisiana" (cited in Prewitt 2003, p. 7). If communities are perceived as losing population because of an undercount, it can affect the willingness of investors to put money in those communities.

#### **2.9 Science and Scholarship**

West and Fein (1990) as well as Clogg and colleagues (1989) review several ways in which the Decennial Census undercounts affect social science research results. Clogg and his colleagues (1989, p. 559) conclude, "Because undercount rates (or coverage rates) vary by age, race, residence and other factors typically studied in social science research, important conceptual difficulties arise in using Decennial Census results to corroborate sampling frames or to validate survey results."

#### **2.10 Census Planning**

Finally, to improve Census-taking procedures in the future, it is important to understand which groups are undercounted at the highest rates in the past Censuses. Information on net undercounts and omissions have been used by the Census Bureau to improve the Census-taking procedure from decade to decade. For example, noting the high net undercount of young children in the 2010 Census prompted the Census Bureau to develop plans to reduce the net undercount of young children in the 2020 Census (Jarmin 2018; Walejko and Konicki 2018).

#### **2.11 Summary**

Data from the Decennial Census are used for many important applications including:

It is clear from the content of this Chapter that the Census is more than just a statistical exercise. Census data are used in some of the most important aspects of our society including our system of governance, distribution of federal dollars for many important programs, and thousands of public and private sector decisions.

#### **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Chapter 3 Methodology Used to Measure Census Coverage**

**Abstract** The two primary methods used to assess Census coverage in the U.S. are Demographic Analysis (DA) and Dual-Systems Estimates (DSE). These two methods are introduced in this Chapter along with some of their strengths and weaknesses.

#### **3.1 Introduction**

How do we know who is missed in a Census or which groups have a net undercount? Several methods have been used over time and in various countries to answer this question but in the U.S. only the Demographic Analysis (DA) method and the Dual-Systems Estimates (DSE) method provide quantitative answers to the question posed above (Mulry 2014; Hogan et al. 2013; Bryan 2004; Anderson 2004). According to the U.S. Census Bureau (2012d, p. 2),

The Census Bureau has historically relied on two principal methods to provide measures of the quality of each Census. One method is based on a post-enumeration survey, which is the topic of this report. The other method is based on demographic analysis, which uses various types of demographic data in order to build an historical account of population change.

Briefly, DA compares the Census count to an independent estimate of the expected population based on births, deaths, and net international migration. The DSE method uses a Post-Enumeration Survey to independently gather information on people that can be compared to the Census count to assess correct enumerations, omissions, and erroneous inclusions (mostly people counted more than once). Each of these methods is described in the next two sections of this Chapter along with some of their strengths and limitations.

One important difference between DA and DSE data is the level of age/sex detail available. Detailed 2010 data from the DA estimates are available so researchers can construct tables for whatever age-sex-race/Hispanic groups as they wish, within the limits of the data. For the 2010 DA data, one must download files from the Census Bureau and construct their own net undercount/overcount tables.

On the other hand, data from the DSE method are only provided for a few age/sex groups determined by the Census Bureau. The DSE data are provided in a series of reports that provide net undercounts and omissions.

#### **3.2 Demographic Analysis Methodology**

Demographic Analysis has been used since the 1950 Census to provide estimates of net undercounts in the U.S. Census. As stated above, this method creates a separate independent estimate of the expected population based on births, deaths, and net international migration and the expected population is then compared to the Census count to determine net undercounts and net overcounts. DA estimates are provided for both males and females, Black and Non-Black, by single year of age. Data on Hispanics are provided for those below age 20 in the 2010 DA estimates.

DA is an example of the cohort-component method of population estimation meaning each component of population change (births, deaths, and migration) is estimated for each birth cohort. The cohort-component method is one of the most widely used techniques in population estimation (United Nations 1970; Bryan 2004). Since there are already several detailed descriptions of the DA methodology available, I will only review the method briefly here (Robinson 2010; Himes and Clogg 1992; U.S. Census Bureau 2010).

The DA method has been used to assess the accuracy of Decennial Census figures for more than a half century (Coale 1955; Coale and Zelnick 1963; Coale and Rives 1973; Siegel and Zelnik 1966). Its origins are often traced back to an article by Price (1947), which found an unexpectedly high number of young men who turned up at the first compulsory selective service registration on October 6, 1940 and alerted demographers to the possibility of under-enumeration in the 1940 Decennial Census.

The DA method employed for the 2010 Decennial Census used one technique to estimate the population under age 75 and another method based on Medicare enrollment to estimate the population age 75 and older (West 2012). The 2010 DA estimates for the population age 0–74 are based on the compilation of historical estimates of the components of population change: Births (B), Deaths (D), and Net International Migration (NIM). The data and methodology for each of these components is described in separate background documents prepared for the development and release of the Census Bureau's 2010 DA estimates (Robinson 2010; Devine et al. 2010; Bhaskar et al. 2010).

As described by the U.S. Census Bureau (2010) the DA population estimates for age 0–74 are derived from the basic demographic accounting Eq. (3.1) applied to each birth cohort:

$$\mathbf{P}\_{0-74} = \mathbf{B} - \mathbf{D} + \text{NIM} \tag{3.1}$$

P0–74 population for each single year of age from 0 to 74 (people less than a year old are labeled age 0 by the Census Bureau)

B number of births for each age cohort

D number of deaths for each age cohort since birth

NIM -Net International Migration for each age cohort.

For example, the estimate for the population age 17 on the April 1, 2010 Decennial Census date is based on births from April 1992 through March 1993, reduced by the deaths to that cohort in each year between 1992 and 2010, and incremented by Net International Migration (NIM) of the cohort each year over the 17-year period.

The birth and death data used in the Census Bureau's DA estimates come from the U.S. National Center on Health Statistics (NCHS) and these records are widely viewed as being accurate and complete. The National Center for Health Statistics (2014, p. 2) states, "A chief advantage of birth certificate data is that information is collected for essentially every birth occurring the country each year…" After a thorough review of vital statistics prior to the 2010 Census, the U.S. Census Bureau (Devine et al. 2010, p. 3) stated:

The following assumptions are made regarding the use of vital statistics for DA:

In addition to regularly published totals, the Census Bureau receives microdata files from NCHS containing detailed monthly data on each birth and death. These files were used primarily for DA estimates by race. Construction of DA estimates by race is discussed later in this Chapter.

The Census Bureau changed the way it calculated Net International Migration (NIM) for the 2010 set of DA estimates (Bhaskar et al. 2010). The current method relies heavily on data from the Census Bureau's American Community Survey (ACS) where the location of the Residence One Year Ago (ROYA) is ascertained for everyone in the survey age 1 or older. The total number of yearly immigrants is derived from this question in each year of the ACS, and then that total number of immigrants is distributed to demographic cells (sex, age, and race) based on an accumulation of the same data over the last five years of the ACS. Five years of ACS data are used to provide more stable and reliable estimates for small demographic groups. On the other hand, it is important to note the five-year average may mask changes in trends over time. Given changing economic conditions, it would not be surprising if the immigration pattern in the 2008–2010 period differed from the pattern before 2008, however, I suspect such errors would be small.

Statistics on emigration of the foreign-born population from the U.S. are based on a residual method comparing data from the 2000 Decennial Census to later American Community Survey estimates to develop rates and then applying those rates to observed populations (Demographic Analysis Research Team 2010).

Emigration of U.S. citizens (net native migration) is derived by examining Census data from several other countries (Schachter 2008). This method of estimating out migration of the native-born population is problematic for a couple of reasons. Data are not available for every country, and the quality of some foreign censuses is suspect. See Jensen (2012) for more details on measuring net international migration. In 2018, the Census Bureau staff presented a paper with revised data for net native migration of young children based on data from the 2010 Mexican Census (Jensen et al. 2018).

In preparing for the December 2010 DA release the Census Bureau developed five estimation series with differing assumptions about births, deaths, and net international immigration to reflect the degree of uncertainty in the estimates. The estimates from the five series presented in December 2010 range from 305,684,000 to 312,713,000. The middle series of the DA estimates was nearly a perfect match to the 2010 Census count so when the DA estimates were updated in May 2012, only the middle series was updated.

#### **3.3 Dual-Systems Estimates Methodology**

The other major source of data on net undercounts and overcounts in the U.S. Decennial Census is the Census Bureau's Dual-Systems Estimates (DSE) method. This section describes the estimation method used in generating the net coverage for the household population from the DSE approach. The DSE method also provides estimates for the other components of Census coverage shown below. According to Hogan (1993) overall Census coverage can be separated in to the four components below;

The Dual-System Estimates (DSE) method compares Census results to the results of a Post-Enumeration Survey (PES) which is conducted right after Census data collection has been completed to determine the number and characteristics of people who are omitted or included erroneously (mostly those double-counted).

Nomenclature can be confusing in this arena. The terms Dual-Systems Estimates (DSE) and Post-Enumeration Survey (PES) are often used interchangeably. Moreover, the DSE/PES approach has been given a different name in each of the past three U.S. Censuses. In 2010, it was called Census Coverage Measurement (CCM), in the 2000 Census it was called Accuracy and Coverage Evaluation (A.C.E.) and in the 1990 Census it was called the Post-Enumeration Survey (PES). Sometimes the DSE or PES approach is simply called the "survey method." The DSE operation in the 2020 Census will be called PES again (U.S. Census Bureau 2017).

There is a long history of using Dual-System Estimation in measuring coverage errors in a Census (Hogan 1993; U.S. Census Bureau 2004; Wolter 1986). But it is widely believed that DSE estimates that are consistent over time began in 1990. For a detailed explanation of the CCM estimation methodology used in the 2010 Census, see Mule (2008).

Dual-System Estimation is based on what is sometimes referred to as a capturerecapture methodology. The Census is the first system or first capture point and the Post-Enumeration Survey is the second capture point. To estimate the number of people correctly included in the Census, one must take a sample from Census enumerations to match to the PES. In the 2010 Census the sample from the Census is referred to as the Enumeration or E-sample and the Post-Enumeration Survey is used to make the second capture and the population in the Post-Enumeration Survey is referred to as the Population or P-sample.

The 2010 CCM program involved a complex sample of about 170,000 housing units in a sample of Census blocks nationwide (Mule 2010). In every sampled block, Census staff did an independent listing of housing units and independent roster of every person living in those housing units as of April 1, 2010, which were then compared to Census records. Because the DSE figures are based on a sample, sampling error was calculated for each estimate to determine statistical significance. Sampling error is not a major issue for large national groups but for smaller groups and small areas, the sampling errors are often large.

The PES interview is used to determine if the person enumerated in the Post-Enumeration Survey should have been counted in a housing unit on Census day (April 1). By comparing the PES results to the Census, CCM can estimate the number of correct enumerations in the Census. Matching also produces an estimate of the erroneous enumerations. Whole-person imputations are taken from census records.

#### **3.4 Strengths and Limitations of DA and DSE Methods**

Both the DA and DSE methods for evaluating Census results have strengths and limitations which are discussed below.

There are four major limitations to DA. First, coverage estimates from DA are routinely only available for the nation as a whole. Because many people move after they are born, estimating coverage for subnational geographic units is difficult. DA only tracks in and out migration at the national level.

The population age 0–9, is an exception to this rule. Subnational analysis can be done for the population age 0–9, because the Census Bureau's population estimates for age 0–9 are not linked to the previous Decennial Census (O'Hare 2014; Mayol-Garcia and Robinson 2011; Robinson et al. 1993; Adlakha et al. 2003, U.S. Census Bureau 2014; King et al. 2018). The 2010 estimates for the population age 0–9, are based on a DA-like method that uses births, deaths, and migration to estimate state and county populations.

Second, DA estimates are only available for a few race/ethnic groups. Historically the estimates have only been available for Black and Non-Black groups. This restriction is due to the lack of race specificity and consistency for data collected on the birth and death certificates historically. The only group that has been identified relatively consistently over time is the Black population, and the residual group is labeled Non-Black. In the 2010 DA program, estimates were produced for Black Alone and for Black Alone or in Combination, but only for the population under age 30.

However, in the past few decades comparisons of Black and Non-Black groups have become more problematic because Hispanics are mostly included in the Non-Black group. The Hispanic population is growing rapidly, and Hispanics have high net undercount rates in the Census.

The 2010 DA estimates also include data for Hispanics for the first time, but only for the population under age 20. Hispanics under age 20 were included in the DA estimates in 2010 because Hispanics have been consistently identified in birth and death certificates since 1990.

The third limitation of the DA estimates is that they only supply net undercount/overcount figures. A net undercount of zero could be the result of no one being missed (omissions) or double counted (erroneous enumerations) or for example, it could be the result of ten percent of the population being missed and ten percent counted twice.

The fourth limitation of the DA methodology is the lack of any measures of uncertainty for the estimates similar to standard errors associated with estimates based on sample surveys. However, it should be noted that in the December 2010 DA release, the Census Bureau released five different estimate series based on five sets of assumptions about births, deaths, and net international migration to reflect some of the uncertainty regarding the DA estimates.

Despite these limitations, DA has been used for many decades, the underlying data and methodology are simple and robust, and it has provided useful information for those trying to understand the strengths and weaknesses of the U.S. Decennial Census. According to Robinson (2000, p. 1), "The national DA estimates have become the accepted benchmark for tracking historical trends in net Census undercounts and for assessing coverage differences by age, sex, and race (Black, all other)."

There are several important limitations of the DSE method which should also be acknowledged. First, is the issue of correlation bias. Correlation bias means the kinds of people who are undercounted in the Census are also likely to be undercounted in the PES. This violates the independence assumption of the DSE methodology. If a group of people are likely to be missed in both the Census and the PES, the undercount estimate for that group will be biased downward. According to Martin (2007, p. 436), "The same groups that are affected by coverage errors in the Census also are affected in demographic surveys conducted by the U.S. Census Bureau and other organizations."

The issue of correlation bias in the DSE approach has been discussed by other researchers (Wolter 1986; Wachter and Freedman 1999: Shores 2002; Shores and Sands 2003; The National Research Council 2009). In the 2010 DSE estimates, the Census Bureau (U.S. Census Bureau 2012c) made adjustment for correlation bias for some groups (Black men) but not for others (Hispanic men or young children).

Second, to tell if an individual was counted correctly in the Census, individuals in the Post-Enumeration Survey must be matched to those in the Census records. This raises a couple of potential problems. First, people don't always provide their names consistently. For example, a person might be listed as John Jones in the Census, and Johnathan Jones Jr. in the PES. Deciding if these two entries are a match is not always clear. Often, but not always, the Census Bureau has additional information like address and birthdates to help with matching. Nonetheless the matching procedure allows potential error.

The DSE approach is also hindered sometimes because there is little or no information for some people included in the Census. For example, as a last resort an enumerator may contact a neighbor to find out about people living in a household and the neighbor may say there are two adults and a young child, but no names or ages are provided. These people are included in the Census, but there is not enough information about them in the Census records to allow matching to the PES records.

Third, the method relies heavily on the memory of individuals. In August or September after the April 1 Census, respondents were asked to list all members of their household as of April 1. For some households and some individuals this is a challenge. As Martin (2007, p. 429) states, "Respondents interviewed months after April 1 may find it difficult to recall accurately when a move occurred."

On the other hand, the DSE method has several advantages. One advantage of the DSE method is that the Census Bureau controls all the data collection (unlike DA where they depend on vital records data). Therefore, the concepts and questions used in the PES can be made identical to those used in the Census. For example, questions about race can be asked the same way in the Census and the PES.

A major advantage of the DSE method is that it can be used to ascertain components of Census coverage such as omissions, and erroneous inclusions. This provides a much richer picture of Census coverage than simply looking at net undercounts and net overcounts.

Because the DSE is based on a carefully drawn sample, the coverage estimates include standard measures of uncertainty. DSE data can provide subnational estimates, although the extent to which this is feasible depends to some extent on sample size. In the 2010 CCM, no state had a net undercount that was statistically significantly different from zero (U.S. Census Bureau 2012b). This is likely related, at least in part, to a relatively small sample is some states.

#### **3.5 Consistencies and Inconsistencies Between DA and DSE Results**

Table 3.1 shows differences between net undercount estimates of DA and DSE in the 2010 Census for several age-sex groups. For the most part, the results of DA and DSE are relatively consistent. Generally, the groups that have a high net undercount in DA also have a high net undercount in DSE.

For all adult age groups examined, the differences are less than 1.6 percentage points. However, for the population age 0–4, the difference is 3.9 percentage points and for age 5–9 the difference is 2.5 percentage points.

O'Hare et al. (2016) provide detailed documentation of the consistencies and inconsistencies between DSE and DA estimates for young children and after close examination of the differences in the net undercount estimate for children, O'Hare

**Table 3.1** Comparison of 2010 census net coverage error from DA and DSE for demographic groups

<sup>a</sup>*Source* Calculated from U.S. Census Bureau May 2012 Demographic Analysis Release <sup>b</sup>*Source* U.S. Census Bureau (2012b, Table 13)

A negative sign implies a net undercount. The signs here are reversed from the original publication in order to keep directionality consistent within this publication

et al. (2016, p. 702) conclude, "…the DSE approach may underestimate the net undercount of young children due to correlation bias." The inconsistency of undercount estimates for young children from DA and DSE has been noted before (U.S. Census Bureau 2003, p. v; National Research Council report 2004, p. 254). Most experts agree that DA is a better method for measuring the net undercount of young children (U.S. Census Bureau 2014). Given the problems of the DSE estimates for young children they are not included in the DSE tables in the remainder of this book. To the best of my knowledge there are no plans to change the DSE methodology in the 2020 Census to eliminate this problem.

Based on a special analysis which takes advantage of the strengths of both the DA and DSE methods the U.S. Census Bureau (2016) produced reliable omissions rates for young children and used the same method to produce omissions rates for other age/sex groups. Net undercount rates and omissions rates for several groups defined by age and sex based on adjusted omissions rates are shown in Table 3.2.

Groups that have high net undercount rates typically have relatively high omissions rates, but not always. Note young children (age 0–4) had the highest net undercount rate and the highest omissions rate but males age 18–29 had a relatively low net undercount rate and a relatively high omissions rate. For people in this group, the high omissions rate is balanced by the high erroneous enumeration rate leading to a low net coverage rate. This issue is explored in Chap. 5.

**Table 3.2** Comparison of demographic analysis-based estimates of omissions and net coverage error in the 2010 census by age and sex

*Source* U.S. Census Bureau (2016, Fig. 2) aA negative sign reflects a net undercount. The signs here are reversed from the source report in order to keep directionality consistent within this publication

#### **3.6 Measuring the Net Undercount by Race**

Historically, Black is the only race group that has been coded relatively consistently in birth and death certificate data, so it is the only group for which DA estimates could be produced. The residual category is labeled Non-Black.

Different data from the Census have been used to compare Census and DA results for Blacks over time. Prior to the 1980 Census, the U.S. Decennial Census figures that were used to compare with the DA estimates for Blacks were the reported U.S. Decennial Census figures for Blacks. In 1980, the Census Bureau compared the DA estimates to a modified file which assigned people in the "some other race" category to a Black or Non-Black category (Fay et al. 1988). In 1990, the Census Bureau used the race of father from the birth certificate to assign race to newborns and then compared DA estimates for Blacks to the MARS (Modified Age, Race, and Sex) file from the Census. For 2000, the Census Bureau used race of father from the birth certificate to assign race to newborns and then DA estimates were compared to an average of Black alone and Black alone or in combination based on the Census Bureau's modified race file (U.S. Bureau of the Census 2003). While there are some inconsistencies in the way race has been measured from one Census to another, it is generally felt the DA estimates can be used to compare undercount estimates for Blacks since 1950 (National Research Council 2004; Velkoff 2011).

The revised DA estimates issued in May 2012 are used for most of the 2010 DA estimates in this book. In May 2012 the Census Bureau issued revised Demographic Analysis estimates, for the total population, the Black alone population, the Black alone or in Combination population, the Not Black Alone population and the Not Black Alone or in combination population (U.S. Census Bureau, 2012a). The estimates for the Black Alone or in Combination populations were only provided for the population below age 30.

The assessment of Black and Non-Black undercount differentials has always had some methodological issues, but those issues increased dramatically since the 2000 Census when respondents were allowed to mark more than one race. See Robinson (2010) for a good general discussion of issues associated with racial U.S. Office of Management and Budget (1997) classifications in the U.S. Decennial Census and the vital events registers.

Key to the DA method for Blacks and Non-Blacks is making the race categories in the vital events data and the Decennial Census data consistent and there are multiple problems in trying to make data collected in the U.S. Decennial Census racial categories comparable to the race data collected on birth and death certificates. In discussing the use of vital statistics for DA estimates by race the U.S. Census Bureau (Devine et al. 2010, p. 4) conclude, "…developing the estimates for DA race categories comes with a more complex, and substantial set of challenges." For a more detailed description of these problems see O'Hare (2015, Sect. 2.5).

For example, the "Some Other Race" category is a response category for the race question in the U.S. Decennial Census but not in birth or death certificates. So, to make comparisons, people who were in the "some other race" category in the Census had to be re-assigned to one or more of the five major race categories.

A second issue is the fact that U.S. Decennial Census respondents in 2000 and 2010 could mark more than one race but it wasn't until 2003 that the federal government issued new standard birth certificate forms allowing parents to mark more than one race. However, birth and death certificate data are collected by states and states did not all adopt the new forms immediately. DA analysis required that the mixed-race data from the birth (and death) certificates be put into Black and Non-Black categories, based on both single-race and multiple-race reported by mother and fathers

Another issue is that birth certificate forms only record the race of the mother and father while the race of a child is asked directly in the Decennial Census. Thus, for birth certificate data, the race of the newborn must be inferred from the race of the parent(s). This is further complicated by a significant level of missing data. While data on the race of mother is relatively complete, many birth certificates are missing data on the race of the father. In 2009, 19% of birth certificate forms did not contain the race of the father (Martin et al. 2011).

Figure 3.1 shows inconsistencies between Black Alone and Black Alone or in Combination are biggest for the youngest age groups. The youngest age groups are the ones that are dependent on matching the race data from the new birth certificates to the race data from the Census.

Given the issues described above, one should view DA estimates for Blacks (alone or alone or in combination) cautiously. Small differences or small changes over time could be due to methodological issues rather than real changes or differences.

**Fig. 3.1** 2010 census undercounts for black alone and black alone or in combination by single year of age: 0–17. *Source* U.S. Census Bureau, May 2012 DA Release

#### **3.7 Summary**

The main methods for measuring Census undercounts are Demographic Analysis (DA) and Dual-Systems Estimates (DSE). The DA method and the DSE method both have strengths and weaknesses. These two methods produce results that are fairly consistent for all age groups except young children. For the population age 0–4, the DA method estimates a net undercount of 4.6% compared to 0.7% for the DSE method (the DSE method is called Census Coverage Measurement in the 2010 Census). The DA method is widely viewed as the better method for estimates net undercount for young children because it relies heavily on vital events data which are very high quality.

Given the changing methods for identifying the race of people in the Census and in birth/death certificates, and the complications of trying to make the racial categories from the birth certificates consistent with those offered in the Census, DA net undercount estimates for Blacks should be used cautiously.

#### **References**

Adlakha, A. L, Robinson, J. G., West, K. K., & Bruce, A. (2003*). Assessment of consistency of decennial census data with demographic benchmarks at the subnational level*. Decennial Census 2000 Evaluation 0.20 Final Report.

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Chapter 4 The Big Picture; Fundamentals of Differential Undercounts**

**Abstract** The 2010 Census coverage error for the total population was very small by international and historic standards, but that masks some large coverage differences among groups. Basic differences in Census coverage by age, sex, race, Hispanic Origin, and tenure are explored in this Chapter. Key findings include, young children (age 0–4) have a higher net undercount than any other age group; males have a higher net undercount than females; Blacks, American Indians on reservations, and Hispanics have relatively high net undercounts; and renters have higher net undercount rates than homeowners. This Chapter is meant to provide an overview and foundation for much of the rest of the book.

#### **4.1 Introduction**

When the results of the 2010 Decennial Census were compared to the expected population based on Demographic Analysis (DA) and Dual-Systems Estimates (DSE), the difference was near zero (Velkoff 2011; U.S. Census Bureau 2012). The 2010 Census coverage rate is very good by historical and international standards.

However, the small difference between the expected population and the 2010 Census count for the total population has caused some people to conclude there was a high level of accuracy for the 2010 Census. For example, Rebecca Blank, then Deputy U.S. Commerce Secretary (2012, p. 1) said, "Today's Census Bureau report shows that not only was the 2010 Census delivered on time and significantly under budget- but even more important, it was extremely accurate." A similar sentiment was expressed by Census Bureau Director Groves (2012).

The high level of accuracy for the total population, however, masks crucial differences among demographic groups and that is the point of this book. It is the differential undercounts which are important for many uses of Census data discussed in Chap. 2. If all groups and all places were undercounted at the same rate, the undercount would hardly be a problem. For one thing, we could just inflate the number based on the net undercount rate.

The fundamental problem with differential Census coverage rates is that certain groups have higher net undercount rates than others. This Chapter provides an overview of key data on Census coverage differentials by age, sex, race, Hispanic Origin, and tenure, to give readers a broad picture of Census undercounts and overcounts. The information in this Chapter will provide readers with data on key measures of Census coverage and establish a foundation for most of the remaining Chapters in this book. All the topics covered in this Chapter will be pursued in more detail in subsequent Chapters.

To keep this Chapter to a manageable size, I look primarily at data from the 2010 Census. Wherever it is feasible, I look at both DA and DSE results. In some cases, however, I draw only on data from DA and in other cases I draw only on data from DSE because one source is much better than the other for a particular population (for example, DA is much better for measuring the net undercount of young children) or data for a particular group are only available from one source (for example, DSE is the only source of information for many race groups). To provide a succinct portrait, only net undercounts and net overcounts are examined in this Chapter, while subsequent Chapters will look at omissions as well as net undercounts.

Data from the 2010 DSE analysis (the method was called Census Coverage Measurement or CCM in the 2010 Census) includes five demographic categories; age, sex, race, Hispanic Origin status, and tenure. Data from the 2010 DA analysis include detailed data by age and sex, but the data on race and Hispanic Origin are limited. Historically the only race groups in DA were Black and Non-Black. In the 2010 Census, the DA data are available for Black Alone and Black Alone or in Combination for the population under age 30. In 2010, DA figures for Hispanics are only available for the population under age 20. For almost all groups the DA results and the DSE results are similar. The major exception to that is for young children (see Table 3.1).

The DSE estimates are based on a sample and therefore include sampling error. So, differences from zero need to be tested to see if the observed differences from zero might be due to chance or random error. Statistical significance is based largely on the size of the difference from zero and the size of the sample on which the estimate is based. Larger differences and estimates from larger samples are more likely to be statistically significant. The statistical significance level used throughout this book is the same one used by the Census Bureau, namely 0.10. This means an observed result that is statistically significant would only happen by random chance alone one time out of ten.

#### **4.2 Census Coverage Differentials by Age**

The Census coverage estimates from DA are the best source for examining age differentials for at least four reasons. First, DA data on age are more detailed than that from Dual-Systems Estimates (DSE). Data are available by single year of age from DA but only for large age/sex groups from DSE. Second, DA estimates have been produced since 1950, so there is more historical data. Third, in the decade prior to the 2010 Census, staff at the Census Bureau investigated several issues related to the production of DA estimates (Robinson 2010; Bhaskar et al. 2010; Devine et al.

**Fig. 4.1** Net undercount rates in 2010 census by five-year age groups. *Source* U.S. Census Bureau, May 2012 DA Release

2010). The increased input review and examination enhance the reliability of the 2010 DA estimates. Fourth, DSE estimates for the youngest ages greatly underestimate the net undercount (O'Hare et al. 2016a, b) so that data series cannot be used to examine the whole age spectrum.

Figure 4.1 shows the net coverage in the 2010 Census by five-year age groups based on DA. Figure 4.1 shows high net undercounts for the youngest population, those age 0–4, and somewhat smaller net undercounts for age 5–9. Young children had a higher net undercount than any other age group in the 2010 Census. The net undercount rate for age 0–4 is 4.6% and for age 5–9 it is 2.2%. No other age group has a net undercount rate of more than 0.7%. The high net undercount of young children has been noted in several recent publications (O'Hare 2014a, b, 2015; U.S. Census Bureau 2014b).

Figure 4.1 also shows relatively high net overcounts for two broad age-groups. The first group is those age 15–24. The second age group that has a net Census overcount is the population age 60 plus. Some of the potential explanations for undercounts and overcounts will be discussed in Chap. 5 along with a more detailed examination of differentials by age.

#### **4.3 Census Coverage Differentials by Sex**

There was a net overcount of 1.1% for females and a net undercount of 0.8% for males. As readers will see in Chap. 6, the overall coverage rates for males and females mask large differences across age and race groups. The gender differences in Census coverage are most pronounced in working-age adults.

The 2010 DSE analysis did not provide data on undercounts of males and females for the total population (all ages) but it provided information on males and females

**Table 4.1** 2010 census net undercount rates from by age and sex

*Source* U.S. Census Bureau (2012, Table 12)

Negative sign reflects a net undercount. The signs here are reversed from the source report in order to keep directionality consistent within this publication

Figures in **BOLD** are statistically significantly different from zero

for three age groups over age 18. The results are shown in Table 4.1. The coverage differentials by sex from DSE are relatively consistent with the results of DA. Data from DSE show males age 18–29 and age 30–49 had net undercount rates that were statistically significantly different than zero while females experienced a net overcount in every age group examined here (although the rates for age 18–29 was not statistically significant). The net undercount estimate for males age 30–49 is particularly high at 3.6%. Both males and females age 50 and over have a net overcount.

#### **4.4 Census Coverage Differentials by Race**

I think it is fair to say the Census net undercount differentials for race and Hispanic Origin groups are among the most widely discussed, most well-known, and most contentious. The material in this section provides a brief overview of this issue.

U.S. Decennial Census net undercounts are typically examined through a comparative lens. Historically the comparative paradigm used most often has been the comparison of Black and Non-Black populations (Fein 1989; West et al. 2014; Prewitt 2003; Schwede et al. 2015). In large part, this perspective was based on data that has been available historically. Until recently, Blacks were the only race group identified consistently across states and over time in birth and death certificates data needed for DA estimates. But in many ways, the Blacks/Non-Black comparison also reflects the prevailing Black/White perspective on racial inequality that dominated the 1950s,1960s, and 1970s. This publication expands that perspective to look at differential undercounts for other race groups as well.

For people not familiar with how the federal government collects data on race and Hispanic Origin, this arena can be confusing. Race and Hispanic Origin are measured in the U.S. Census as dictated by U.S. Office of Management and Budget (1997). Categorizing people by race has been a complicated part of the U.S. Census, ever since it was decided to count slaves as 3/5th of a person in the first Census in 1790. Prewitt (2013) provides a detailed history of how the concepts and measurement of race (and Hispanic Origin) have changed since 1790 in the context of the Census.

Race and Hispanic Origin are two separate concepts in the definitions used by the federal government. In the Census, respondents are first asked if they are Hispanic or not, then they are asked about what race group(s) they identify with.

Starting in 1997, people have been allowed to mark as many race groups as they feel apply. For people who mark only one race, this is referred to as "race alone" for example Black Alone or Asian Alone. People who mark more than one race are added to the "race alone" group for form "Race Alone or in Combination"; for example, "Black Alone or in Combination." In this construction, people can be in more than one group. Someone who marked both Black and White would be included in both Black Alone or in Combination and the White Alone or in Combination but not in the figures for Black Alone or White Alone.

Generally, the 'race alone or in combination" categories are used in this book, since that is the most inclusive way of identifying groups. It is also consistent with the recommendation the U.S. Office of Management and Budget which suggests that when data are used in a civil rights context, the race alone or in combination is the best grouping to use (U.S. Office of Management and Budget 2001). For many minority groups, the Census is largely seen in the context of civil rights enforcement (Leadership Conference Education Fund 2017).

The DSE net undercount rates for different races are shown in Table 4.2. Data for the Non-Hispanic White Alone population is provided because the rates for minority groups are typically contrasted to the rate for the Non-Hispanic White Alone population to develop differential net undercounts. The Non-Hispanic White Alone population is the numerical majority population in the nation.

In the 2010 Census, the Non-HispanicWhite Alone population had a net overcount of 0.8%, and most of the other races had net undercounts. The only exception is American Indians Alone or in Combination living in an American Indian Area off reservations where there is a net overcount of 3.9%. In part, because this is such a small population, the net overcount rate for American Indians living off reservations is not statistically significant.

For Blacks Alone or in Combination the net undercount rate is 2.1% in the 2010 Census. There is a 2.9 percentage point difference between the net undercount rate for Blacks Alone or in Combination and the net overcount of Non-Hispanic Whites Alone noted above. This differential is not new. Census coverage data for Blacks are explored in more detail in Chap. 8.

For Asians Alone or in Combination the net undercount is zero. More data for Asians are presented in Chap. 9.

The largest net undercount in Table 4.2 is for American Indians Alone or in Combination on reservations at 4.9%. Overall, American Indian and Alaskan Natives Alone or in Combination had a net undercount of 0.2% which was not statistically significantly different than zero. More information on this population is presented in Chap. 10.

**Table 4.2** 2010 census estimates of percent net undercount by race (alone or in combination) and Hispanic origin

*Source* U.S. Census Bureau (2012, Table 8)

Except for the Non-Hispanic White Alone category, the race groups include Hispanics A negative sign reflects an undercount. The signs here are reversed from the source report in order to keep directionality consistent within this publication

Figures in **BOLD** are statistically significantly different from zero

For Native Hawaiians or Pacific Islanders Alone or in Combination the net undercount rate is 1.0% which is not statistically different from zero. More information on this population are provided in Chap. 11.

The Race groups in DA are much more limited than in DSE, but the findings for Blacks and Non-Blacks are very similar to those of DSE. Based on DA analysis, Velkoff (2011) shows a Black Alone or in Combination undercount of 2.5% in the 2010 Census compared to a net overcount of 0.5% for the Non-Black population. The DA method provides data comparing Blacks and Non-Blacks for each Census from 1950 onward and these are presented in Chap. 8.

#### *4.4.1 Hispanics*

Table 4.2 shows the net undercount rate for Hispanics was 1.5% in the 2010 Census compared to a net overcount of 0.8% for Non-Hispanic White alone. More data on Census coverage for Hispanics are provided in Chap. 7.

The Hispanic population is treated as homogeneous group with respect to undercount estimates from the Census Bureau. However, it is important to recognize that subgroups within the Hispanic Populations may well have Census coverages rates that are different than the group as a whole (O'Hare 2017). The same is true for Asians. This idea is addressed in more detail in Chaps. 7 and 9.

**Table 4.3** 2010 census coverage rates by tenure

*Source* U.S. Census Bureau (2012, Table A)

A negative sign reflects an undercount. The signs here are reversed from the source report in order to keep directionality consistent within this publication

Figures in **BOLD** are statistically significantly different from zero

#### **4.5 Census Coverage Differentials by Tenure**

Table 4.3 shows the 2010 Census coverage rates for the population living in owneroccupied housing units and the population living in renter-occupied housing units. There is a net overcount for owners (0.6%) and a net undercount for renters (1.1%). Both figures are statistically significant.

This pattern of Census coverage for homeowners and renters is long standing. To some extent, homeownership may reflect socio-economic status. More information about Census coverage by tenure are presented in Chap. 12.

#### **4.6 Other Groups Missed in the Census**

Although Demographic Analysis and Dual-Systems Estimates are the best estimates available for coverage in the U.S. Census, there are some important limitations. For example, the groups for which these two programs produce data are limited. The Census Bureau research only measures Census coverage for five demographic characteristics including;

There are other groups which are widely believed to be undercounted in the Census but for which there are no direct undercount estimates from the Census Bureau. Some of these groups are identified by former Under-Secretary of Commerce following the release of data from the 2010 Census. In response to the 2010 Census results being release, then Under-Secretary of Commerce Blank (2012) stated,

More work remains to address persistent causes of undercounting, such as poverty, mobility, language isolation, low levels of education, and general awareness of the survey.

**Table 4.4** Lists of hard-to-count populations from three sources

The factors mentioned by Dr. Blank are commonly believed to be related to Census undercounts, but the Census Bureau does not produce undercount estimates for any of these characteristics (poverty, mobility, language, education, or awareness of the Census).

Groups with high net undercount rates are often referred to as hard-to-count (HTC) populations. According to the U.S. Census Bureau (2016, p. 2);

Hard-to-count populations face physical, economic, social, and cultural barriers to participation in the Census, and require careful consideration as part of a successful communications strategy.

It is important to recognize that just because the Census Bureau does not produce net undercount estimates for a group that does not mean they are not undercounted. While there are no Census undercount rates for many HTC groups other data such as Mail Return Rates (Leadership Conference Education Fund 2017) or the percent living in hard-to-count areas are sometimes available to shed light on potential Census coverage issues (U.S. Census Bureau 2014a).

Three different lists of hard-to-count populations and/or factors associated with being hard-to-count are presented in Table 4.4. These lists are meant to provide a flavor for the kinds of groups that are often thought to be missed at high rates in the Census.

**Table 4.5** Hard-to-count groups compiled by U.S. General Accountability Office based on Perusal of Census Bureau documents

Table 4.5 shows a list of hard-to-count populations compiled by the U.S. General Accountability Office based on looking over many Census Bureau documents. Clearly there are many groups that are thought be hard-to-count where the net undercount and omissions are not calculated by the Census Bureau.

#### **4.7 Summary**

Several groups have been identified as having relatively high net Census undercounts rates. Groups with the highest net undercount rates include:

Each of these differential undercounts will be explored in more detail in subsequent Chapters.

#### **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Chapter 5 Census Coverage Differentials by Age**

**Abstract** People pass through different family situations and living arrangements as they age and many of these changes over a lifetime are related to changes in the likelihood of being missed in the Census. In this Chapter, some of the biggest differences in Census coverage by age are examined and some ideas about why people are missed or overcounted are explored. Young children age 0–4 had the highest net undercount rate and highest omissions rate of any age group in the 2010 Census. The college-age population (age 18–24) and elderly people (over age 60) had net overcounts.

#### **5.1 Introduction**

In the 2010 Census, some age groups had net undercounts, some had net overcounts, and many age groups experienced little net coverage error. In this Chapter, the focus is on the age groups that had the largest net undercounts and net overcounts. In addition to looking at the net undercounts and overcounts of age groups, omissions rates are also examined.

The initial analysis in this Chapter relies heavily on Demographic Analysis (DA) estimates. I believe the strengths of DA methodology make it a particularly good technique for discussing Census coverage by age for at least four reasons. First, DA data on age is more detailed than that from Dual-Systems Estimates (DSE). Data are available by single year of age from DA but only for large age/sex groups from DSE. Second, DA estimates have been produced since 1950, so there is more historical data. Third, in the decade prior to the 2010 Census, staff at the Census Bureau investigated several issues related to the production of DA estimates (Robinson 2010; Bhaskar et al. 2010; Devine et al. 2010). The increased input, review, and examination enhance the reliability of the 2010 DA estimates. Fourth, DSE estimates for the youngest ages greatly underestimate the net undercount (O'Hare et al. 2016) so that data series cannot be used to examine the whole age spectrum.

#### **5.2 Census Net Undercounts by Age**

Figure 5.1 shows net coverage in the 2010 Census by five-year age groups based on DA. Data in Fig. 5.1 indicate a high net undercount for young children, a high net overcount for people in their late teens and early twenties and a high net overcount for people over age 60. For other age groups the net coverage is close to zero (less than 1%). Therefore, I focus on three groups, age 0–4, 18–24 and 60 and older in the remainder of this Chapter.

Perhaps the most surprising finding shown in Fig. 5.1 is the high net undercount of young children. In the words of former Census Bureau Director Groves (2010, p. 1).

It's often a surprise to many people when they learn that children tend to be undercounted in the US Censuses. Most can imagine various types of adults who fail to participate in Censuses, but don't immediately think of children being missed.

Moreover, the survey research literature shows that households with children generally respond to surveys at higher rates than those without children (Groves and Couper 1998; Brick and Williams 2012). Groves and Couper (1998, p. 138) offer this succinct summary of the relationship between children in the household and cooperation in survey research, "Without exception, every study that has examined response or cooperation finds positive effects of the presence of children in the household."

Nonetheless, Fig. 5.1 shows the population age 0–4 had the highest net undercount (4.6%) of any age group in the 2010 Census. There was a somewhat smaller net undercount (2.2%) for age 5–9. No other age group had a net undercount rate of more than 0.7%. The net undercount of young children is not only the largest net undercount of any age group, it is the largest Census coverage error in either direction (i.e. net undercounts or net overcounts). The high net undercount of young children

**Fig. 5.1** Net undercount rates in 2010 census by five-year age groups. *Source* U.S. Census Bureau, May 2012 DA Release

has been noted in several recent publications (O'Hare 2014a, b, 2015; U.S. Census Bureau 2014).

Consistent with much of the other literature on Census undercounts, among young children, racial and ethnic minorities had higher net undercounts. Based on the 2010 Census DA release, there was a net undercount of 6.3% for Black Alone or in Combination age 0–4 and 7.5% for Hispanics age 0–4 (O'Hare 2015). It should be noted that a couple of recent studies (King et al. 2018; Jensen et al. 2018) suggest that the net undercount of young children might not be quite as high as earlier estimates indicate but nonetheless is still higher than any other age group, by far. These new studies are more in the nature of experimental estimates rather than officials estimates.

The high net undercount of young children is not a new issue. Difficulty in enumerating young children accurately has been noted historically (Hacker 2013; Adams and Kasakoff 1991; U.S. Census Bureau 1944). More than 100 years ago, Young (1901, p. 21) stated, "Experience has shown that it is extremely difficult to ascertain the true number of children in any population by simple enumeration." The passage below is from a Census Bureau report following the 1940 Census, (U.S. Census Bureau 1944, p. 32) "Underenumeration of children under 5 years old, particularly infants under one year old, has been uniformly observed in the United States Census and in the Censuses of England and Wales and of various countries of continental Europe." The results of the 2010 U.S. Census suggest this situation has not changed much since then.

Why do young children have such a high net undercount rate? It is widely believed that there is not just one cause for the high net undercount of young children in the Census but there are many causes. With respect to the high net undercount of young children, the Census Bureau Task Force on the Undercount of Young Children (U.S. Census Bureau 2014) concluded, "The task force is convinced that there is no single cause for this undercount." O'Hare (2015, Chap. 7) discusses several potential ideas about why young children have a high net undercount in the Census. Over the past few years, the Census Bureau has engaged in several studies to learn more about the undercount of young children and they have produced a summary of the results (O'Hare et al. forthcoming).

Any explanation of why young children have such a high net undercount must not only explain why young children are missed, but why they are missed as a much higher rate than older children or adults. In some prior analysis, all children age 0–17 have been grouped together. For example, in the 1990 DSE results (U.S. Census Bureau 2001) all children under age 18 were treated as one group. But children (age 0–17) are not homogenous with respect to the risk of being missed in the Census.

Results from the 2010 Census shown in Fig. 5.2 indicate the net undercount is much higher for those age 0–4 than those age 14–17 (the population age 14–17 actually had a net overcount). When young children are grouped with older children it is difficult to discern why younger children are missed and older children overcounted.

Figure 5.2 shows there is almost a perfect correlation between age and Census coverage.What is responsible for this relationship between age and Census coverage? I am not aware of any theory or evidence that has been put forward to explain this strong statistical relationship.

**Fig. 5.2** 2010 census net undercount rates by single year of age: 0–17. *Source* U.S. Census Bureau, May 2012 DA Release

One factor related to the high net undercount of young children that is increasingly clear is the fact that young children are more highly concentrated than older children in the kinds of households and families that are more difficult to enumerate. Table 5.1 shows the percent of young children (age 0–4) compared to older children (age 10–17) in each of 14 situations thought to be related to being missed in the Census. In nearly every situation, young children are more highly concentrated than older children.

Recent research by Fernandez et al. (2018) shows that among children under age 5, the odds of being missed in the Census are higher for:

Fernandez and her colleagues found that, by and large, these factors hold for Non-Hispanic Whites, Hispanics, and Non-Hispanic Blacks.

Research by Fernandez et al. (2018) also shows that one of the factors that is most closely associated with young children being missed in the Census is whether they were counted in the self-response or Non-Response Followup phase of the Census. Based on logistic regression analysis, Fernandez et al. (2018) show that if young children are not included in the self-response phase of the Census, they are 74% more likely to be missed. This research suggests that the Census Bureau should enhance training among 2020 Census enumerators with respect to making sure

**Table 5.1** Hard-to-count characteristics of children by age

<sup>a</sup>*Source* 2010 Census, U.S. Census Bureau (2017a) <sup>b</sup>*Source* U. S. Census Bureau (2017b)

all young children in a household are included on returned Census questionnaires. Recently the Census Bureau (2018) issued a short publication showing some of the main reasons young children are missed in the Census.

#### **5.3 High Net Overcounts of College-Age Population**

One group with a relatively high net overcount is the population age 15–24. The net overcount for age 15–19 was 2.0% and for those age 20–24 it was 1.3%. The overcount in this age group is typically attributed to young adults being counted in the home of their parents as well as another address such as a college dormitory or military barracks (Martin 2007). Figure 5.3 shows net undercounts for the population age 15–24 by single year of age and reveals that the net overcounts peaks around age 19 or 20, which is the age many young people are in college.

**Fig. 5.3** 2010 census net coverage error by single year of age: 15–24. *Source* U.S. Census Bureau, May 2012 DA Release

**Fig. 5.4** Percent of population in colleges by age: 16–24. *Source* U.S. Census Bureau, American Community Survey

Figure 5.4 shows the percent of people attending college by single year of age from 16–24 based on data from the Census Bureau's American Community Survey. Figure 5.4 shows college attendance peaking at age 19, 20, and 21, the exact same ages as the higher net overcounts. Note that the ACS question just asked about college attendance, it does not differentiate those who leave home to go to college from those who live at home and attend college.

The 2010 Census Coverage Followup operation, showed relatively large duplication errors for people in college and people in jail (U.S. Census Bureau 2012, Table 24.) People age 18–24 are over-represented in both groups.

#### **5.4 Net Overcounts of Elderly Population**

The second age group that had a substantial Census net overcount is the population age 60 and over. The overcount for this group may be attributed to retirees with two (or more) homes and to a lesser extent older people in nursing homes or other long-term care facilities. Like young adults, some of these people are counted in more than one place. Williams (2012, p. 8) provides one example of a Census overcount, "A husband and wife, for example, might own a vacation home and fill out a questionnaire there as well as their usual residence." The 2010 Census Coverage Followup operation, showed relatively large duplication errors for people in nursing homes (U.S. Census Bureau 2012, Table 24).

In an analysis following the 2000 Census, the Census Bureau focused on people who had been included in the Census more than once (U.S. Census Bureau 2002). In a key table, they show that people over age 50 are much more likely than younger groups to be duplicated in a different state, which suggests they were being counted in more than one home such as a winter home in Florida and a summer home in Michigan. This idea is bolstered by trends from 1950 to 2010 shown in Sect. 5.6.

#### **5.5 Omissions in the 2010 Census**

Recall that the net Census undercount rate is a balance between people omitted and those included erroneously (mostly double counted) and whole-person imputations. The omissions rate captures the share of a group missed in the Census. DSE is the only method that shows omissions rates.

In many ways the omissions rate is a more meaningful statistic because in the net undercount calculation, omissions can be cancelled out by erroneous inclusions or double counting. A net undercount of 0 could be the result of no one missed and no one double counted, or for example, 10% missed, and 10% double counted.

The omissions rates for the population age 0–9 published by the Census Bureau in 2012 are suspect because the DSE methodology only reflects a small portion of the net undercount of young children in the 2010 Census (O'Hare et al. 2016). DA estimated a net undercount of 4.6% for the population age 0–4 compared to only 0.7% for DSE. The difference is generally ascribed to correlation bias in the DSE methodology (O'Hare et al. 2016). Correlation bias refers to the fact that the kinds of people missed in the Census are also missed in the Post-Enumeration Survey.

However, recent research by the Census Bureau's Task Force on the Undercount of Young Children provides updated estimates for omissions rates for several large age/sex groups by taking advantage of the strength of the DA and DSE methods (U.S. Census Bureau 2016). These improved estimates for omissions in the 2010 Census are provided in Table 5.2.

The updated omissions calculations are only available for a few age/sex groups and only for the population as a whole and not any race/Hispanic groups. The rates

**Table 5.2** 2010 Omissions by Age (Updated in 2016)

U.S. Census Bureau (2016), Table 3

are similar to the omissions rates released by the Census Bureau in 2012 except for two groups. For young children, the updated omissions rates are much higher than the earlier omissions rate estimates from the Census Bureau. For young adults the omissions rate from the updated analysis is somewhat higher than the original DSE analysis.

Young children had the highest net undercount rate of any age group and Table 5.2 shows they had the highest omissions rate of any age group in the 2010 Census. The population age 0–4 had an omissions rate of 10.3% which translate into nearly 2.2 million young children omitted from the 2010 Census.

#### **5.6 Trends Over Time**

Examination of net Census coverage rates from 1950 to 2010 indicates a significant and steady reduction in the net undercount in the total population. However, when the overall trend is decomposed by age, a more complex story emerged.

Figure 5.5 shows net undercounts by five-year age groups in every Census since 1950. While this figure is somewhat complicated here are a couple of trends that are clear. The net undercount of young children is long-standing as it has been seen in every Census since 1950. The net undercount of young children varied between 1.4 and 6% between 1950 and 2010, although the net undercount of young children has increased substantially since 1980. In fact, the net undercount of young children in the 2010 Census is almost exactly the same as the net undercount of young children in the 1950 Census.

The net overcount of people age 60 and older has emerged over the past several decades. Figure 5.5 shows the net overcount for this age group was higher in 2010 than any other Census shown and the rates for the 2000 Census are not far behind

**Fig. 5.5** Net census undercount rates by five-year age groups: 1950–2010

those of 2010. On the other hand, the net undercount rates for those age 60 and older in 1950, 1960, and 1970, are relatively low compared to the past two Censuses. This supports the idea that the overcount of the older population may be related to increases in dual home ownership for this age group which increased over this time period.

Figure 5.5 also shows that the coverage of college-aged people has changed over time. In 1950, 1960 and 1970, there was a net undercount for age 15–19 and 20–24, but in the 2000 and 2010 Census, there was a net overcount in these age groups. This is consistent with larger number of people in the young adult age group leaving the home of their parents in recent decades.

One important divergence in net census coverage trends since 1950 may not be clear from Fig. 5.5. Figure 5.6 shows net undercount rates for the adult population (age 18+) and the young child population (age 0–4) for each U.S. Decennial Census from 1950 to 2010. Figure 5.6 shows there are two very distinct periods between 1950 and 2010 related to the net undercount of young children. Between 1950 and 1980, the net undercount rates of both young children and adults improved and the differences between young children and adults were not large. Specifically, the net undercount rates for the adult population went from 3.8% undercount in 1950 to a 1.4% undercount in 1980. While the net undercount for young children fell from 4.7 to 1.4% in the same period.

Following the 1980 Census. The net undercount of young children and adults began diverging. The coverage rates for adults continued the improvement seen in the 1950–1980 period while the net undercount rates for young children increased following 1980. Specifically, the coverage rates for adults went form 1.4% net undercount in 1980 to a 0.7% overcount in 2010. The net undercount for young children increased from 1.4% in 1980 to 4.6% in 2010.

**Fig. 5.6** Net undercount rates for young children (0–4) and adults (18+): 1950–2010. *Source* O'Hare (2014a, b)

#### **5.7 Summary**

Net undercounts and overcount as well as omissions rates vary by age. Young children age 0–4 had the highest net undercount rate and highest omissions rate of any age group in the 2010 Census. Young Hispanic children and young Black Alone or in Combination children had net undercount rates that are about 50% higher than the overall net undercount rate for this age group. One reason for the high net undercount rate of young children is the fact that they are concentrated in hard-to-count families and households.

The college age population (age 18–24) had a net overcount in the 2010 Census. The high net overcount is attributed to many young adults being counted at their parent's home as well as another location such as college dormitory. This age group also had a relatively high omissions rate.

For the population age 60+, there was a relatively high net overcount in 2010. This is attributed to the fact that many people in this age group have two (or more) homes and are counted in both homes.

#### **References**

Devine, J., Sink, L., DeSalvo, B., & Cortes, R. (2010). *The use of vital statistics in the 2010 demographic analysis estimates*. Census Bureau Working Paper No. 88.

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## **Chapter 6 Census Coverage Differentials by Sex**

**Abstract** Males and females often play different roles in society at different ages and these can impact family situations and living arrangements related to the likelihood of being missed in the Census. In this Chapter, examination of differences in Census coverage by sex show that males generally have Census net undercount rates while females have net overcounts. Since 1940, the net undercount rates of both males and females have improved a lot but the differential between males and females has not narrowed.

#### **6.1 Introduction**

This Chapter focuses on Census coverage for males and females including coverage rates for subgroups defined by age, race, Hispanic Origin, and tenure. In addition to looking at the net undercounts and overcounts of males and females, omissions rates by sex are also examined.

The initial analysis shown in this Chapter relies heavily on Demographic Analysis (DA) estimates. I believe the strengths of DA methodology make it a particularly good technique for discussing Census coverage by age for at least four reasons. First, DA data on age are more detailed than that from Dual-Systems Estimates (DSE). Data are available by single year of age from DA but only for large age/sex groups from DSE. Second, DA estimates have been produced since 1940, so there is more historical data. Third, in the decade prior to the 2010 Census, staff at the Census Bureau investigated several issues related to the production of DA estimates (Robinson 2010; Bhaskar et al. 2010; Devine et al. 2010). The increased input, review, and examination enhance the reliability of the 2010 DA estimates. Fourth, DSE estimates greatly underestimate the net undercount for young children (O'Hare et al. 2016) so that data series cannot be used to examine differential undercounts for the whole age spectrum.

Both methods for measuring Census accuracy (DA and DSE) show males had lower coverage rates than females. In the 2010 Census, the DA method shows a net undercount rate of 0.8% for males compared to a 1.1% net overcount for females. In the 2010 Census, the DSE method also shows adult males typically had net undercounts while adult females typically had net overcounts. This result is not surprising. Simpson and Middleton (1997) identify adult males as being among the groups most difficult to enumerate in Censuses.

#### **6.2 Undercounts by Sex and Age**

As readers will see, in terms of Census coverage, sex matters at some ages but not very much at other ages. Figure 6.1 shows net undercount rates in the 2010 Census for males and females by five-year age groups. In general, there are no differences by sex for the youngest or the very oldest age groups, but there are very noticeable differences among adults from their mid-20s to mid-70s. Females in this age range have better coverage than males. The biggest gaps between males and females are in the 25–45-year old age range, and the gaps seen between age 45 and 65 are somewhat smaller. The biggest single year difference is age 31 where there is a 4.8% net undercount for males and a 0.2% net overcount for females.

Data from DSE are shown in Table 6.1. For age 18–49, there were statistically significant net undercount rates for males but small net overcount rates for females. For the population age 50 and over, there were net overcounts for both groups but the net overcount for males (0.3%) is much smaller than that for females (2.4%).

**Fig. 6.1** 2010 census net undecount rates for males and females by five-year age groups. *Source* U.S. Census Bureau, May 2012 DA Relesae

**Table 6.1** 2010 census net undercount rates from census coverage measurement by age and sex

*Source* U.S. Census Bureau (2012b), Table 12

A negative sign reflects a net undercount. The signs here are reversed from the source report in order to keep directionality consistent within this publication

Figures in **BOLD** are statistically significantly different from zero

**Table 6.2** Census coverage for males and females by race in the 2010 census

*Source* U.S. Census Bureau, Demographic Analysis tables released May 2012