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methodology and assumptions used to develop the recently released 
projections of the population of the United States from 1999 to 2100.  
The new series includes projections of the population by single year of 
age, sex, race, Hispanic origin, and nativity.  For the first time, 
projection results include a break on nativity, defined dichotomously 
by the presence or absence of U.S. citizenship at birth, as well as its 
cross-classification with other variables.  Also new with this series is 
the projection to quarterly reference dates, allowing users to view the 
national population seasonally, or simply to select annual reference 
dates other than July 1. In addition, international migration in the new 
series is allowed to vary over time, remaining somewhat lower than the 
constant value in the previous series for the first two decades of the 
century, but reaching considerably higher levels than in the previous one 
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<H2>Methodology and Assumptions for the Population Projections of the United 
States:  1999 to 2100</H2>
<H2>By Frederick W. Hollmann, Tammany J. Mulder, and Jeffrey E.  Kallan</H2>
<P>Population Projections Branch<BR>Population Division<BR>Bureau of the 
Census<BR>U.S. Department of Commerce<BR>Washington, DC 20233<BR>(301) 457-2428 
<P>January 2000 
<P>Population Division Working Paper No. 38 
<P>
<HR>

<P><STRONG>ABSTRACT</STRONG> 
<P>This working paper discusses the methodology and assumptions used to  develop 
the recently released projections of the population of the United  States from 
1999 to 2100.  The new series includes projections of the  population by single 
year of age, sex, race, Hispanic origin, and nativity.  While the basic 
methodology used to produce these projections is the same as in earlier Census 
Bureau national population projections, there have been changes, in both the 
time horizon and reference dates of the projections, as well as in the specific 
methods used to estimate population change.  The extension of the series to 2100 
carries the projections 20 years further into the future than any series 
previously issued by the Census Bureau.  For the first time, projection results 
include a break on nativity, defined dichotomously by the presence or absence of 
U.S. citizenship at birth, as well as its cross-classification with other 
variables.  Also new with this series is the projection to quarterly reference 
dates, allowing users to view the national population seasonally, or simply to 
select annual reference dates other than July 1. In addition, international 
migration in the new series is allowed to vary over time, remaining somewhat 
lower than the constant value in the previous series for the first two decades 
of the century, but reaching considerably higher levels than in the previous one 
after 2020.  Fertility rates in both models are allowed to change very little 
over time.  However, fertility rates by race and Hispanic origin are allowed to 
converge in the new middle series, whereas in the previous middle series they 
remained constant within race and origin category.   Finally, the new mortality 
assumptions show more improvement in life expectancy for all racial and Hispanic 
origin groups, except the non-Hispanic White population, than did the 
assumptions of the previous projection series. 
<P>* This paper reports the results of research and analysis undertaken by 
Census Bureau staff.  It has undergone a more limited review than official 
Census Bureau publications.  This report is released to inform interested 
parties of research and to encourage discussion. 
<P>
<HR>

<P>
<H3>CONTENTS</H3><A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#intro">INTRODUCTION</A><BR><A 
href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#A">THE 
METHOD OF PROJECTING THE POPULATION</A><BR>     <A 
href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#A1">Base 
Population and Base Series</A><BR>     <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#A2">The 
Cohort-Component Method</A><BR>     <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#A3">The 
Inflation-Deflation Method</A><BR>     <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#A4">Derivation 
of Births, Deaths, and  Foreign-Born Emigration from Rates</A><BR>
     <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#A5">Reflecting 
Uncertainty of Assumptions Through High and Low Variants</A><BR><A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B">ASSUMPTIONS 
FOR THE COMPONENTS OF CHANGE</A><BR>     <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B1">Fertility</A><BR>
          <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B11">Assumptions 
and Methodology</A><BR>
               <A 
href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B111">Short-term 
Fertility Assumptions</A><BR>
               <A 
href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B112">Long-term 
Fertility Assumptions</A><BR>
               <A 
href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B113">Long-term 
Assumptions for Fertility by Race and Hispanic Origin</A><BR>
               <A 
href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B114">Methodology</A><BR>
          <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B12">Low 
and High Fertility Assumptions</A><BR>     <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B2">Mortality</A><BR>
          <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B21">Assumptions 
and Methodology</A><BR>
          <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B22">Low 
and High Mortality Assumptions</A><BR>
          <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B23">Two 
Sets of Base Mortality Rates: General Issues</A><BR>
          <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B24">Base 
Mortality Rates: Detailed Construction</A><BR>
               <A 
href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B241">Mortality 
Rates by Hispanic Origin</A><BR>
               <A 
href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B242">Problems 
With Race and Hispanic Origin Mortality Rates</A><BR>
               <A 
href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B243">Old-age 
Mortality Rates</A><BR>     <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B3">International
 Migration</A><BR>          <A 
href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B31">Assumptions 
and Methodology</A><BR>
          <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B32">Projection 
of the Level of In-Migration: Middle Series, 1999 to 2020</A><BR>
          <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B33">Projection 
of the Level of In-Migration: Middle Series, 2021 to 2100</A><BR>
          <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B34">Migration 
to the U.S. by Race and Hispanic Origin</A><BR>
          <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B35">Low 
and High International Migration Assumptions</A><BR>
          <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B36">Projection 
of the Emigration of Legal U.S. Residents</A><BR>
          <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B37">Low 
and High Emigration Assumptions</A><BR>
          <A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#B38">Net 
Migration of U.S. Citizens</A><BR><A href="http://www.census.gov/population/www/documentation/twps0038/twps0038.html#sum">SUMMARY</A> 
<H3>DETAILED TABLES</H3>
<TABLE cellpadding="3">
  <TBODY>
  <TR valign="top">
    <TD nowrap=""><A href="http://www.census.gov/population/www/documentation/twps0038/tabA.txt">Table
      	A.</A></TD>
    <TD>Comparisons of Total Population, Present Series with 1994-Based 
      	Projections</TD></TR>
  <TR valign="top">
    <TD nowrap=""><A href="http://www.census.gov/population/www/documentation/twps0038/tabB.txt">Table
      	B.</A></TD>
    <TD>Projected Total Fertility Rates by Race and Hispanic Origin, 1999 	to 
      2100</TD></TR>
  <TR valign="top">
    <TD nowrap=""><A href="http://www.census.gov/population/www/documentation/twps0038/tabC.txt">Table
      	C.</A></TD>
    <TD>Projected Life Expectancy at Birth by Race and Hispanic Origin, 	1999 
      to 2100</TD></TR>
  <TR valign="top">
    <TD nowrap=""><A href="http://www.census.gov/population/www/documentation/twps0038/tabD.txt">Table
      	D.</A></TD>
    <TD>Projected Migration by Race and Hispanic Origin, 1999 to 2100</TD></TR>
  <TR valign="top">
    <TD nowrap=""><A href="http://www.census.gov/population/www/documentation/twps0038/tabE.txt">Table
      	E.</A></TD>
    <TD>Major Components of Net International Migration to the United 	States, 
      1991 to 2100</TD></TR>
  <TR valign="top">
    <TD nowrap=""><A href="http://www.census.gov/population/www/documentation/twps0038/tabF.txt">Table
      	F.</A></TD>
    <TD>Population and Dependency Ratios per 100 Persons, Four Series, 	1990 
      to 2100</TD></TR>
  <TR valign="top">
    <TD nowrap=""><A href="http://www.census.gov/population/www/documentation/twps0038/tabG.txt">Table
      	G.</A></TD>
    <TD>Standardized Rates of Foreign-Born Emigration, 1991 to 
  2100</TD></TR></TBODY></TABLE>
<P>
<HR>

<P><A name="intro"></A>
<H3><A name="intro">INTRODUCTION</A></H3>
<P>This working paper discusses the methodology and assumptions used to develop 
the recently released projections of the population of the United States from 
1999 to 2100.<SUP>1</SUP>  The new series includes projections of the population 
by single year of age, sex, race, Hispanic origin, and nativity.<SUP>2</SUP>  
While the basic methodology used to produce these projections is the same as in 
earlier Census Bureau national population projections, there have been changes, 
in both the time horizon and reference dates of the projections, as well as in 
the specific methods used to estimate population change.  The extension of the 
series to 2100 carries the projections 20 years further into the future than any 
series previously issued by the Census Bureau.  For the first time, projection 
results include a break on nativity, defined dichotomously by the presence or 
absence of U.S. citizenship at birth, as well as its cross- classification with 
other variables.  Also new with this series is the projection to quarterly
 reference dates, allowing users to view the national population seasonally, or 
simply to select annual reference dates other than July 1. In addition, 
international migration in the new series is allowed to vary over time, 
remaining somewhat lower than the constant value in the previous series for the 
first two decades of the century, but reaching considerably higher levels than 
in the previous one after 2020.  Fertility rates in both models are allowed to 
change very little over time.  However, fertility rates by race and Hispanic 
origin are allowed to converge in the new middle series, whereas in the previous
 middle series they remained constant within race and origin 
category.<SUP>3</SUP>  Finally, the new mortality assumptions show more 
improvement in life expectancy for all racial and Hispanic origin groups, except 
the non-Hispanic White population, than did the assumptions of the previous 
projection series. 
<P>Aside from these changes, the basic structure of the product closely 
resembles previous Census Bureau projections.  Race consists of four categories; 
1) White, 2) Black, 3) American Indian, Eskimo, and Aleut, 4) Asian and Pacific
 Islander (API).  Hispanic origin is dichotomous: the two categories are 
Hispanic and non-Hispanic.   All race and Hispanic origin detail incorporates 
the full distribution of eight  cross-categories.  As in previous projections, 
we have provided alternate series, defined by alternative assumptions on the 
three major determinants of population change, fertility, mortality, and
 migration.  However, the interpretation of "low" and "high" assumptions has 
changed somewhat with respect to previous projections.  In the present series, 
the extreme assumptions are presented primarily with the purpose of illustrating 
a degree of uncertainty around the central series.  They should not be 
interpreted as alternative scenarios to be adopted on their face value, as they 
are not intended to be probable developments. 
<P>The results of the new projections are not substantially different from those 
of the last series issued by the Census Bureau, when the comparison is made 
across matching dates.<SUP>4</SUP> Both middle series show the national 
population growing at a large fraction of one percent per year until 2050.  Both 
series show the rate of growth declining over time, from approximately 0.9 
percent per year in 1999 to about 0.7 percent per year around 2050.  These 
results are shown in Table A.  The lack of major difference in the population 
results for the middle series between the new and old projections can be 
explained in large part by the deterministic nature of the age distribution of 
the base population, and the predictability of its aging over time.  This 
initial age distribution represents essential information that is conveyed to 
the projected series.  The means of its conveyance is the cohort component 
method, discussed in the section that follows. 
<P><BR><A name="A"></A>
<H3><A name="A">THE METHOD OF PROJECTING THE POPULATION</A></H3>
<P>The method used to produce projections of the United States population for 
future reference dates from a current base population reflects three fundamental 
principles. 
<P>1) The projections are demographic.  Future populations are derived from a 
base population through the projection of population change by its major 
demographic components, births, deaths, and migration. 
<P>2) The projection of the demographic components of change is driven by the
 composition of the population by age, sex, race, Hispanic origin, and nativity, 
and the way these variables determine the propensity to bear children, die, and 
migrate to or from the United States. 
<P>3) The definition of the population with respect to who is included and the 
characteristics of included people remains the same throughout the projection 
period. We refer to these definitions collectively throughout the work as the 
"population universe."  This concept embraces such issues as the inclusion or
 exclusion of people uncounted by a census, the rule defining residency in the 
United States, and the way we classify people by age, race, and Hispanic origin. 
 The population universe for these projections is defined primarily by the 1990 
census, albeit with some modifications. 
<P>The first two principles mandate the use of "cohort component" methodology in 
projecting the population.  Under this methodology, knowledge of the age and sex 
composition of the population at any point in time is fundamental to the 
projection of the population.  Knowing the age-sex distribution at one date
 allows us to impute the age-sex distribution of those still alive at later 
dates, since sex does not change while age advances with the passage of time.  
This knowledge also allows the projection of demographic behaviors such as 
fertility, mortality, and the propensity to migrate, differentiated by age.  
Thus, current age-sex distribution influences future age-sex distribution 
through the components of change, as well as the aging of people over time. 
<P>To comply with the second principle described above, standard cohort 
component methodology is applied to each racial and Hispanic origin category as 
if they were separate populations.  Race and Hispanic origin are chosen because
 they are reflected in a wide range of administrative data in the United States, 
and because their categories are distinct with respect to rates of fertility and 
mortality.  Nativity, defined by citizenship at birth, is used to distinguish 
rates of emigration from the United States.  The foreign-born population is also
 projected separately, but without births, since children born within the United 
States are U.S. citizens at birth (native) by United States law. 
<P>The third principle, preservation of the population universe, imposes the 
need for a special adaptation of cohort component methodology.  The population 
universe for these projections is defined by the decennial census of April 1, 
1990, with some adaptations.  In certain critical regards, the distribution of 
this population by age, sex, race, and Hispanic origin does not submit well to 
projection by the cohort component method.  It is characterized by a pattern of 
underenumeration highly differentiated by age, as well as some misreporting of 
age, and a distribution by race and Hispanic origin substantially different from
 what appears in other administrative data sources.  In order to preserve these 
irregularities of the age detail in the projected population while maintaining 
the applicability of the cohort component method, we apply the standard method 
to a synthetic base population with characteristics "friendly" to the method.  
We then adapt the resulting projections back to the actual base population 
universe.  This process is known as "inflation-deflation."  The following
 sections discuss this modified cohort component methodology. 
<P><BR><A name="A1"><STRONG><EM><U>Base Population and Base 
Series</U></EM></STRONG> </A>
<P><A name="A1">The current series of population projections are "launched" from 
an estimated resident population by age, sex, race, Hispanic origin, and 
nativity, as of January 1, 1999.<SUP>5</SUP>  While we refer to this population 
as the base population for the series, the population universe for the series is 
defined by the <EM>estimates base population</EM> of April 1, 1990.  The 
<EM>estimates base population</EM> is the population that forms the base for 
national-level estimates produced for the Census Bureau's population estimates 
program.  This program yields the projections base population of January 1, 
1999.  We refer to the population series from April 1, 1990, to January 1, 1999, 
as the <EM>base</EM> series for the projections.  This series, and its 
associated estimates of the demographic components of change, form the data base 
from which most of the assumptions regarding  fertility, mortality, and 
migration in the projections are formulated. </A>
<P><A name="A1">The base population universe is derived primarily from the 1990 
census and consists of residents of the 50 states and the District of Columbia.  
The universe excludes the U.S. Armed Forces overseas and citizens ordinarily
 residing outside the United States.  It is subject to net underenumeration in 
the 1990 census, with the exceptions of adjustments for net underenumeration in 
certain localities resulting from the Census Test of 1995. The race distribution 
is modified to comply with the Office of Management and Budget Directive 15,
 which places all individuals within one of four major racial groups, 1) White, 
2) Black, 3) American Indian, Eskimo, and Aleut, and 4) Asian and Pacific 
Islander.<SUP>6</SUP>  The age distribution is modified to eliminate the effect 
of inconsistencies between age and year of birth in the census, arising 
primarily from delayed reporting of an age inconsistent with the decennial 
enumeration date (April 1, 1990).<SUP>7</SUP> </A>
<P><A name="A1"><BR><A name="A2"> <STRONG><EM><U>The Cohort-Component 
Method</U></EM></STRONG></A> 
<P>The <EM>cohort-component method</EM> for estimating and projecting a 
population, as previously indicated, is distinguished by its ability to preserve 
knowledge of an age distribution of a population (which may be of a single sex, 
race, and Hispanic origin) over time.  It is a special case of a <EM>component 
method</EM>, which is defined simply by the use of estimates or projections of
 births, deaths, and net migration to update a population.<SUP>8</SUP>  In its 
simplest statement, the component method is expressed by the following equation: 
<P>
<CENTER><EM>P<SUB>t</SUB> = P<SUB>t-1</SUB> + B<SUB>t-1,t</SUB> - 
D<SUB>t-1,t</SUB> + M<SUB>t-1,t</SUB></EM>     (1) 
</CENTER>
<P>where <EM>P<SUB>t</SUB></EM> = population at time 
<EM>t</EM>;<BR><EM>P<SUB>t-1</SUB></EM> = population at time 
<EM>t-1</EM>;<BR><EM>B<SUB>t-1,t</SUB></EM> = births, in the interval from time 
<EM>t-1</EM> to time <EM>t</EM>;<BR><EM>D<SUB>t-1,t</SUB></EM> = deaths, in the 
interval from time <EM>t-1</EM> to time <EM>t</EM>; 
and<BR><EM>M<SUB>t-1,t</SUB></EM> = net migration, in the interval from time  
<EM>t-1</EM> to time <EM>t</EM>. 
<P>Components of population change are estimated or projected separately, and 
applied to equation (1) recursively to produce a series of populations.  We have 
not specified the measurement unit of time, so the interval from <EM>t-1</EM> to 
<EM>t</EM> may be of any duration. 
<P>                         The cohort-component method is based on similar 
logic for individual age groups, recognizing that the source population for a
 given age group is the population at time <EM>t-1</EM> in the adjacent younger 
age group.  For the initial age group, it is births during the interval from 
<EM>t-1</EM> to  <EM>t</EM>.  For the moment, let us assume that the time unit 
is one year.  The equation is replaced by two equations, depending on whether 
the age group is zero (meaning under 1) or any other age as of the last 
birthday, denoted by <EM>a</EM>. 
<P>
<CENTER><EM>P<SUB>t</SUB>(0) = B<SUB>t-1,t</SUB> - D<SUB>t-1,t</SUB>(0) + 
 M<SUB>t-1,t</SUB>(0)</EM>     (2) 
<P><EM>P<SUB>t</SUB>(a) = P<SUB>t-1</SUB>(a-1) - D<SUB>t-1,t</SUB>(a) + 
 M<SUB>t-1,t</SUB>(a)</EM>     (3) </P></CENTER>
<P>In the case of deaths (D) and net migration (M), the interval <EM>a</EM> 
denotes age of decedents or migrants at time t--not necessarily equal to age at 
time of death or migration.  Each of the terms in equations (2) or (3), whether 
defined as a population or a number of events, relates to people born in a 
particular year (from <EM>t-a-1</EM> to <EM>t-a</EM>).   Such a group is known 
as a <EM>birth cohort</EM>, hence the term "cohort component method."  While it 
is essential that age and time in equations (2) and (3) be measured in the same
 unit, there is no requirement that the interval be one year.  For most 
applications, the time unit employed is either a single year or a five-year
 interval. 
<P>The current projections are somewhat unusual in this regard, in that the time 
interval used is a calendar quarter.  There are various reasons for the choice 
of quarter-year intervals.  The base date for the series is April 1, 1990, while 
the reference date most frequently cited tends to be mid-year, or July 1.  Data 
sources used to estimate the components of population change for the base series 
are produced for varying time intervals.  Births and deaths are produced by
 calendar year; immigration data by federal fiscal year (ending September 30).  
Although these event data are based on administrative records coded by month, 
there would be no cost advantage in standardizing them to any particular year on 
the calendar.  We therefore use the calendar quarter because it is the largest
 common subinterval of the various reporting intervals in the data.  Extending 
the series to future dates by quarter facilitates the integration of future 
assumptions with base series data, and yields an added bonus of flexibility, in 
allowing users to either utilize the quarterly series or select any quarterly 
date for an annual series. 
<P><BR><A name="A3"><STRONG><EM><U>The Inflation-Deflation 
Method</U></EM></STRONG></A> 
<P>The cohort-component method described above requires that the base population 
age distribution observe the fundamental attribute that birth cohorts are 
affected only by mortality and migration as they age.  The population universe 
specified by the estimates base population does not observe this simple
 requirement for two salient reasons.  First, the universe reflects 
underenumeration of the population at certain ages.  Second, the misstatement of 
year of birth in the census causes spurious irregularities in the age
 distribution, especially "heaping" on certain terminal digits.  If we did not 
employ the inflation-deflation method, the application of the cohort-component 
method would have the effect of advancing the age pattern of these
 irregularities over time, rendering age groups uncomparable from one year to 
the next. 
<P>The <EM>inflation-deflation method</EM> is a procedure designed to overcome 
this problem. It can be summarized in six steps, each of which is carried out 
for each sex, race, Hispanic origin, and nativity category. 
<P>1) An alternative base population universe, that is deemed to eliminate, or 
at least minimize the described irregularities in the age distribution, is
 utilized as a base population for cohort component projections.  The population 
used here, known as a <EM>Demographic Analysis Population</EM> (DA population), 
is developed from an amalgam of historical data on births, deaths, and migration 
for ages under 65, and a population of Medicare enrollees for ages 65 and over.  
The reference date for this population is April 1, 1990.<SUP>9</SUP> 
<P>2) An "inflation-deflation factor" is computed for each single-year age 
group, as the ratio of the estimates base population to the DA population in 
that group, both as of April 1, 1990.  The resulting factors may be less than or
 greater than one, although they are more likely to be less than one, because 
the net effect of census underenumeration, census duplication, age heaping, and 
discrepancies in racial classification are more likely to be negative than
 positive. 
<P>3) The DA population by age is updated from April 1, 1990 to January 1, 1999, 
then projected to future dates, by the cohort-component method, per equations 
(2) and (3), as described earlier.  Births, deaths, and foreign-born emigrants 
by age are derived by application of rates, to be discussed in the next section. 
<P>4) The population in each age group is multiplied by the inflation-deflation 
factor for the group, for each quarterly reference date.  While the factors are 
defined for full-year age groups, they are assumed to be constant across
 quarter-year ages within the full-year groups. 
<P>5) The actual base population for the projections, the estimates base 
universe, is projected using the simple component method without distribution by 
age, per equation (1) described earlier.  The total number of births, deaths, 
and foreign-born emigrants from January 1, 1999, forward are those derived in 
step 3), with results summed across age groups.  Because the number of births is 
considered to be adjusted for underregistration, births are reduced by a factor 
to reflect what would actually be registered.  The balance of the migration 
components are derived numerically via the projection assumptions, to be 
discussed later in this report. 
<P>6) A pro-rata adjustment is used to force the age distributions from step 4) 
to match the population totals from step 5). 
<P><BR><A name="A4"><STRONG><EM><U>Derivation of Births, Deaths, and 
Foreign-Born  Emigration from Rates</U></EM></STRONG></A> 
<P>The application of the cohort-component method, as stated in equations (2) 
and (3) requires numerical projections of births, deaths, and net migration.  
The formulation of assumptions (see below) yields <EM>numerical projections</EM> 
of the net migration component (without the effect of foreign-born emigration)
 for the full matrix of characteristics for each quarter.  These numerical 
projections are exogenous, in the sense that they are unaffected by population.  
However, the assumptions yield <EM>population-based rates</EM> of fertility, 
mortality and foreign-born emigration.  Therefore, the resulting numerical 
projections of these components are endogenous, meaning they are themselves 
partly a consequence of the projected population.  The derivation of numerical 
projections of endogenous components is part of step 3) in the procedure
 described in the previous section.  Because the projection procedure produces 
the population at quarterly intervals, the application of rates occurs for each 
quarterly interval and by quarter year of age.  Mortality and emigration rates 
are applied to the mid-quarter population of each age group as the population is 
generated, taking account of the fact that mortality and migration, along with 
the exogenous components,  affect the mid-quarter population in its generation. 
 Equation (3) is applied to produce all quarter-year  age groups for the 
beginning of the succeeding quarterly time interval.  Fertility rates are then 
applied to mid-quarter populations of female age groups to generate births, and
 mortality and emigration rates for first-quarter infants are applied to 
complete the youngest age group, per equation (2). 
<P>An exception to this procedure occurs in the case of the foreign-born 
population.  Foreign- born and native women of the same age, race, and Hispanic 
origin are assumed to have the same fertility and mortality rates, since the 
base data to differentiate fertility and mortality by nativity were unavailable. 
 It was therefore convenient to project the population of both nativity 
categories together, then project the foreign-born population by assuming zero
 fertility, since all newly born are native by definition.  The native 
population could then be determined by subtracting foreign-born from total 
population. 
<P>The projection assumptions produce rates for full years of age, and full-year 
rates are assumed constant across quarter-year subdivisions of age.  However, 
empirical observation of the seasonality of death and childbearing is considered 
in the derivation of deaths and births by quarter.  Data from the National 
Center for Health Statistics for calendar year 1996 provide the basis for the 
seasonal distribution of annual births and deaths.<SUP>10</SUP>  Foreign-born 
emigration rates are projected from information for an entire decade, so no 
information on seasonality was available, and none was assumed.  For
 foreign-born emigration the quarterly series was determined by the quarterly 
application of emigration rates to the foreign-born population. 
<P><BR><A name="A5"><STRONG><EM><U>Reflecting Uncertainty of Assumptions Through 
High and  Low Variants</U></EM></STRONG></A> 
<P>The new projections do not include a systematic measurement of uncertainty.  
However, in the development of each of the component assumptions, we established 
high and low variants based on a reasoned assessment of what represented 
"extreme" values.  Applying variant assumptions for each component individually
 resulted in the range of population series that would be identified with the 
maximum likely variance of that component.  To produce our lowest and highest 
series, we combined the extreme values of all three major components that 
favored, respectively, the lowest and highest population growth.  Therefore, the
 extreme projections <EM>do not represent likely scenarios in themselves</EM>, 
but purport to represent the extremes between which most likely outcomes should 
fall.  Fertility and international migration imposed a greater uncertainty on 
the projections than did mortality, because childbearing and mobility, to a 
greater extent than death, are functions of individual and collective 
decision-making that are difficult to forecast accurately. 
<P><BR><A name="B"></A>
<H3><A name="B">ASSUMPTIONS FOR THE COMPONENTS OF CHANGE</A></H3>The following 
sections describe the assumptions that determined future levels of fertility,
 mortality, and international migration, for application of the methodology 
described above. 
<P><BR><A name="B1"><STRONG><EM><U>Fertility</U></EM></STRONG></A> 
<P>The total fertility rate (TFR) for the United States has remained fairly 
constant since 1989.<SUP>11</SUP> As of 1997, the total fertility rate was 
2,032.5 births per 1,000 women.<SUP>12</SUP>  Evaluating the fertility trends of 
the recent past is useful in establishing the immediate direction of fertility. 
 However, such evaluation provides little information regarding the trend for 
the next 100 years. To formulate our fertility assumptions, we relied on 
demographic theory, analyzed past and current national and international 
fertility trends, and made use of data on birth expectations from a national 
survey. 
<P><A name="B11"><STRONG>Assumptions and Methodology</STRONG></A><BR>The 
previous projections assumed constant fertility throughout the projection period 
by race and Hispanic origin for the middle series.  The fertility assumptions 
for the current set of projections allow fertility to vary for the short- and 
long-term by race and Hispanic origin.   Fertility trends are projected 
separately for non- Hispanic Whites, non-Hispanic Blacks, non- Hispanic American 
Indians, non-Hispanic Asian and Pacific Islanders, and Hispanics.   
<P><A name="B111"><EM>Short-term Fertility Assumptions</EM></A><BR>To project 
the short-term fertility trends, the period from 1999 to 2025, we assumed 
fertility levels will reach target total fertility rates determined by birth 
expectations data and demographic theory.  Once collected and analyzed, birth 
expectations are used to represent the total number of children ever born for 
three of the five race and Hispanic origin groups in 2025.  The birth 
expectations are  further adjusted according to the method developed by van 
Hoorn and Keilman.<SUP>15</SUP> Because birth expectations data for non-Hispanic 
 American Indians and non-Hispanic Asian and Pacific Islanders are deficient, 
total fertility rates are derived for these groups by assuming they converge 
halfway to "replacement level," a total fertility rate of 2,100 per 1,000 women, 
by the year 2025.  The total fertility rate for non-Hispanic American Indians 
and non-Hispanic Asian and Pacific Islanders is assumed to decline by .006 and 
.002 births per woman per year respectively between 1998 and 2025. 
<P><A name="B112"><EM>Long-term Fertility Assumptions</EM></A><BR>Beyond the 
year 2025, we relied upon an analysis of past and current national and
 international fertility trends and demographic theory to formulate our 
assumptions.  However, a review of fertility trends and existing research by 
Westoff<SUP>16</SUP> and Day<SUP>17</SUP>, among others, provide no definitive 
long-term direction for the fertility of the United States.  Therefore, 
following 2025, long-term total fertility rates for each race and Hispanic 
origin category are assumed to move regularly toward replacement level, reaching 
2.1 in 2150.  The rate of increase or decrease to the total fertility rates 
differ among the five race and Hispanic origin groups. Table B displays the
 total fertility rates by race and Hispanic origin for the projections period of 
1999 to 2100.     
<P><A name="B113"><EM>Long-term Assumptions for Fertility by Race and Hispanic 
 Origin</EM></A><BR>Because the long-term assumptions project a slow 
stabilization of the total fertility rate, in about 150 years, the fertility 
rates of racial and Hispanic origin groups are posited to slowly converge.  
Historically, such convergence was not exhibited by non-Hispanic Blacks,
 particularly in reference to non-Hispanic Whites.  While non-Hispanic Whites 
maintained total fertility rates near 2.0 and 2.1 between 1989 and 1993, 
non-Hispanic Blacks experienced rates between 2.4 and 2.6.<SUP>18</SUP> However, 
since 1993 non-Hispanic Black fertility has declined and converged toward 
non-Hispanic  White fertility rates.  
<P>Fertility trends for particular Hispanic and Asian and Pacific Islander 
groups also diverge from national trends.  These groups, however, are comprised 
predominately of foreign-born populations which generally maintain higher
 fertility rates than native women of the same race and origin 
group.<SUP>19</SUP>  According to assimilation theory, the longer an immigrant
 female remains in the U.S., the more likely she will be to adopt fertility 
behaviors of native women of the same racial or Hispanic origin group.  
Researchers have found evidence to support the assimilation theory in regard to
 foreign-born and native fertility trends within the United States.<SUP>20</SUP> 
 Therefore, fertility rates among Hispanic and Asian and Pacific Islander women 
are assumed to converge with national levels.  In addition, exogamy and 
interracial childbearing are projected to increase in the future, further 
diminishing fertility differentials among racial and Hispanic origin groups.   
<P><A name="B114"><EM>Methodology</EM></A><BR>The middle series age-specific 
fertility rates were calculated for women 10 to 49 years old by single year of 
age and five race and Hispanic origin groups from 1999 to 2100.  To begin,
 single year age-specific fertility rates were calculated using birth 
registration data from the National Center for Health Statistics and population 
estimates for 1996 to 1998.  Age-specific  fertility rates by race and Hispanic
 origin for 1996 and birth registration data by race and Hispanic origin 
(adjusted for under-registration)  for 1997 and 1998 were available.  However, 
at the time of production, birth registration data by age of the mother were not
 available for 1997 and 1998.  Therefore, total births by mother's age and race 
were calculated for 1996, 1997 and 1998 using indirect standardization.  The 
base population used to create the age-specific fertility rates was the mid-year 
population of the Demographic Analysis (DA) universe, as defined for purposes of 
the inflation-deflation method, described above.<SUP>21</SUP> 
<P>The 1995 National Survey of Family Growth Cycle V (NSFG Cycle V) data set 
were obtained and birth expectation data were calculated for women 15 to 44 
years of age.<SUP>22</SUP>  Total fertility rates were adjusted by reducing 
birth expectations for non-Hispanic Whites and non-Hispanic  Blacks as proposed 
by the van Hoorn and Keilman method and supported by findings from the National 
Center for Health Statistics.<SUP>23</SUP> The model developed by van Hoorn and
 Keilman adjusts birth expectations to account for issues of uncertainty, period 
fertility, and "limiting factors."  Because the NSFG Cycle V adjusts for item 
non-response and total non- response, and the period adjustment is unnecessary 
as specified by the proposed method, the birth expectations were only reduced by 
10 percent to account for the "limiting factors," which generally result in
 overestimation. 
<P>Once births by single year of age of the mother were calculated, a single set 
of age-specific fertility rates were calculated and imputed to 1998 for purposes 
of the projections.  Because separate short- and long-term assumptions were
 made, rates for each of the five race and Hispanic origin groups were 
interpolated separately from 1998 to 2025 and 2025 to 2100 to reach target total 
fertility rates.  Age-specific fertility rates for Whites, Blacks, American
 Indians, and Asian and Pacific Islanders, with the Hispanic and non-Hispanic 
component of each group combined, were calculated after completing the 
projections. 
<P><A name="B12"><STRONG>Low and High Fertility Assumptions</STRONG></A><BR>The 
fertility assumptions for the highest and lowest series are based on a 
proportional increase or decrease relative to the middle series.  The range 
widens steadily as an acknowledgment of increased uncertainty, although the 
series do not represent statistical confidence intervals.  The assumptions 
required the calculation of an increase and decrease to the middle series 
age-specific fertility rates by a series of proportions.  The proportions were
 interpolated linearly from zero in 1998 to reach 15 percent in 2025, and from 
there to 25 percent in 2100.  Inflating the middle series fertility rates by 
this series of proportions yields the high variant, while deflating it by the 
same proportion yields the low variant.  The total fertility rates by race and 
Hispanic origin for the middle, low, and high series for the projections period 
of 1999 to 2100 are detailed in Table B.    
<P><BR><A name="B2"><STRONG><EM><U>Mortality</U></EM></STRONG></A> 
<P>At the present time, significant mortality differentials exist between males 
and females and between race and ethnic groups in the U.S. Life expectancy at 
birth (hereafter abbreviated as "life expectancy") has generally increased
 throughout the century for both sexes and for Whites and Blacks.  For other 
race and ethnic groups, however, data are too scarce to identify trends over 
time.  Throughout the 20th century, differentials in life expectancy between 
males and females, and between Blacks and Whites, have been quite irregular, 
increasing in some periods, and decreasing in others.  During the 1990's, the 
differentials between males and females, and between Blacks and Whites, have
 tended to narrow.  By 1997, life expectancies for males and females had reached 
73.6 and 79.4 respectively.<SUP>24</SUP> 
<P>In order to project age-specific death rates (ASDRs) and life expectancies, 
we construct current ASDRs by sex, race, and Hispanic origin groups for use as a 
projection base, using deaths provided by the National Center for Health
 Statistics (NCHS) and our own population denominators.  Readers with an 
interest in the full details of these procedures are referred to the latter part 
of this section.  As discussed later, data are not available to allow accurate
 measurement of ASDRs and life expectancies for all race and Hispanic origin 
groups.  
<P>Table C shows fairly large differences in life expectancy between males and 
females, and across race and Hispanic origin groups for the first projected year 
(which is very similar to the 1998 base period).<SUP>25</SUP>  Our projections 
assume a narrowing of the observed mortality gaps among race and Hispanic origin 
groups over time, such that by year 2100 the ASDRs of the race and Hispanic 
origin groups are much closer together than what is observed today.  We also 
assume a slight narrowing of the sex gap in mortality over the next 100 years.  
As discussed in detail in the next section on assumptions and methodology, our 
projection models are based on a mixture of projected data by other researchers, 
with our own research incorporated into the models.  For example, we use the 
research of Lee and Tuljapurkar as a source of overall life expectancy levels 
for males and females separately (without regard to race and Hispanic origin) 
for year 2065, but we use our own extrapolations for dates beyond 
that.<SUP>26</SUP>  Thus, Lee and Tuljapurkar's research influences our
 assumption about the future sex differential, but our assumptions about future 
race and Hispanic origin differentials are generated internally.  A few 
methodological considerations led to our assumption of declining race and 
Hispanic origin mortality differentials.  First, such differentials, even for 
the current period, are difficult to estimate accurately.  The definitions of 
race and origin are themselves mutable and ever-changing.  Second, and related 
to the above, increasing rates of intermarriage may serve to reduce 
differentials in the future. 
<P><A name="B21"><STRONG>Assumptions and Methodology</STRONG></A><BR>The 
previous projections report projected survival rates  primarily by extrapolating 
past annual rates of change, separately by age, sex, race and Hispanic origin 
group.<SUP>27</SUP>  In the current set of projections we create male and female
 target life tables corresponding to a far-future year (2150, which is beyond 
our projection horizon), and we force the base life tables (which are discussed 
later) for the separate race and Hispanic origin groups to converge over time to 
these target life tables.<SUP>28</SUP>  The end result of this process is a 
slight narrowing of the sex difference in mortality over time, and a more
 prominent narrowing of race and Hispanic origin differences over time, such 
that by year 2100 the race and origin groups are quite a bit more similar in 
their life expectancy than they are today.  The year 2150 was chosen as a target
 for race and ethnic convergence because it allowed our models to yield 
plausible rates of mortality decline over time for each sex, race, and Hispanic 
origin group. 
<P>A few different sources of information entered into the construction of the 
year 2150 target life tables for males and females.  First, we used projected 
life expectancies for total males and females (all race and Hispanic origin 
groups combined) for the year 2065 produced by Lee and Tuljapurkar,<SUP>29</SUP> 
which updates the original Lee-Carter stochastic time-series model.<SUP>30</SUP> 
 For our middle series, these year 2065 life expectancies are 83 for males and 
88 for females.<SUP>31</SUP>  Second, we used expert opinion regarding how much 
faster the mortality rates of some age groups will decline in the future
 relative to the others.  These were obtained by utilizing the results of a 
survey conducted at the 1997 mortality projection conference sponsored by the 
Society of Actuaries.<SUP>32</SUP>  We use the term "decline" to mean <EM>annual 
average rate of mortality decline</EM> in the rest of this section. Survey 
results are shown below. 
<P>
<TABLE cellpadding="5">
  <TBODY>
  <TR valign="top">
    <TD> </TD>
    <TD nowrap=""><U>Age 0-14 vs. 65+</U></TD>
    <TD nowrap=""><U>Age 15-64 vs. 65+</U></TD></TR>
  <TR>
    <TD nowrap="">"Next 10 years"</TD>
    <TD align="center">2.1</TD>
    <TD align="center">1.3</TD></TR>
  <TR>
    <TD nowrap="">"After 25 years"</TD>
    <TD align="center">1.6</TD>
    <TD align="center">1.2</TD></TR></TBODY></TABLE>
<P>For example,  most participants at the Society of Actuaries conference 
predict that the decline experienced by the age group under 14 years will be 2.1 
times that of the age group 65 years and older over the "next ten years."   
<P>Instead of "next 10 years" and "after 25," as reported in the Society of 
Actuaries report, we used two time periods: 1990 to 2020 and 2021 to 2150.  This 
was done because one of our projection base years is 1990 (as discussed later), 
and we wanted to adapt the Society of Actuaries report data to fit our data
 requirements. We also constrained the age group 65 years and older decline to 
be the same for the two time periods, since there is no information in the 
Society of Actuaries report about the 65 years and older decline for time 
periods before year 2020. 
<P>With the above-mentioned projected life expectancies and ratios, and with a 
base set of ASDRs by sex, race, and Hispanic origin, we obtain declines out to 
the year 2150 that satisfy the above conditions (four ratios representing age 
patterns of decline over time) as well as the conditions involving life 
expectancies for year 2065 as explained above.  Given the assumed fixed 
relationships between the declines across the broad age groups over time, there 
is only one trend that needs to be derived, which is the decline for the age 
group 65 years and older.  We then use these declines to produce ASDRs and life 
tables for males and females in 2150.  This is done by a simple extrapolation 
which assumes that the declines that led to year 2065 life tables will continue 
thereafter.  Projected ASDRs for each sex, race, and Hispanic origin group are 
then derived by interpolating between the 1990 base ASDRs (by each sex, race, 
and Hispanic origin) and the year 2150 ASDRs, a procedure which reflects our 
race and Hispanic origin convergence assumption.  This yields life tables for 
the ten groups which are consistent with the year 2065 male and female life
 expectancies (all race and origin groups combined) projected by Lee and 
Tuljapurkar.   
<P>However, we do not present life expectancies and ASDRs for years beyond 
2100--those data points are beyond our projection horizon, and were developed 
solely to achieve a narrowing of differentials over time within the projection
 period (to 2100).  Year 2150 was chosen because it yields the most acceptable 
rates of mortality decline for the sex, race, and ethnic groups.  For example, 
using year 2100 as a target life table would yield too rapid rates of mortality 
decline for some subgroups, in our opinion. 
<P>Table C shows projected life expectancies for each of the ten specific sex, 
race, and Hispanic origin groups.  Life expectancies for aggregations of these 
groups (White, Black, American Indian, and API) are based on life tables we 
constructed at a later stage using weighted averages of ASDRs.  To weight the
 averages, we used the separate sex and race populations (in the case of race 
aggregation) or the separate sex populations (in the case of sex aggregation) 
(not shown).  
<P><A name="B22"><STRONG>Low and High Mortality Assumptions</STRONG></A><BR>As 
discussed earlier, the year 2150 target life tables for males and females are 
based partly on Lee and Tuljapurkar's projected life expectancies for year 2065 
(83 for males, 88 for females). The low and high life expectancy series are 
constructed using the same methodology and data as the middle series, except 
that different values  are used for year 2065 life expectancies.  For the low 
life expectancy series, we use 81 and 86 for males and females respectively.  
For the high life expectancy series, we use 86 and 90 for males and females 
respectively.  These low and high values are the lower limit and upper limit
 respectively of the 95 percent confidence interval reported by Lee and 
Tuljapurkar.<SUP>33</SUP> Thus, we end up with a set of male and female target 
life tables (year 2150) for each of the three series.  The procedures for 
producing the ASDRs for all intervening years between the base and target (year 
2150) years, and for the sex, race, and ethnic groups, are identical across the 
three series.  As expected, there is an increasing divergence of life 
expectancies over the course of the projection period between the low and high 
series, for any given sex, race, and ethnic group.  
<P><A name="B23"><STRONG>Two Sets of Base Mortality Rates: General 
Issues</STRONG></A><BR>While the general procedure to obtain projected ASDRs for 
all sex, race, and Hispanic groups involves interpolation between a base set of
 ASDRs (one set for each sex, race, and Hispanic origin subgroup) and year 2150 
target ASDRs (one set for each sex, as described earlier), the procedures are, 
in fact, more complicated because we use two sets of base ASDRs at different 
stages of the projection process. 
<P>We first create the long-term series of ASDRs out to year 2150 using 1990 
ASDRs as a starting point.  We call these 1990 ASDRs the "primary base."  We 
construct these base ASDRs using 1990 deaths from NCHS and 1990 census
 population denominators, by sex, race, and Hispanic origin. We consider these 
to be more appropriate for projecting a long-term series, as compared with rates 
which use our postcensal population estimates as denominators.  Yet, we prefer 
to have a smooth transition from our national estimates in 1998 to our national
 projections for subsequent years.  In order to avoid sharp breaks between the 
ASDRs for 1998 (and earlier) assumed in our national estimates, and those 
assumed for the projections for 1999 and beyond, we subsequently create a new 
set of ASDRs for 1999 through 2020 for use in the projections. These new ASDRs 
are produced by interpolating from the 1996 to 1998 combined ASDRs of the 
national estimates series (which we refer to here as the "secondary base") to 
the year 2021 ASDRs of the projection series that was based on the primary base, 
for each sex, race, and Hispanic origin group.  We call these new and more 
consistent ASDRs the "bridge series," and we replace the original 1999 to 2020 
projected ASDRs with this bridge series, in order to smooth out the transition 
from national estimates to national projections.     
<P><A name="B24"><STRONG>Base Mortality Rates: Detailed 
Construction</STRONG></A><BR>Procedures for constructing the primary base ASDRs 
are discussed below.  Because the procedures for constructing the secondary base
 ASDRs are similar, we do not repeat those here. 
<P>Base ASDRs are constructed with 1990 deaths obtained from NCHS (by age, race, 
and Hispanic origin) divided by a July 1, 1990, population in the demographic 
analysis (DA) universe (as discussed under "inflation-deflation")  for the 
appropriate subgroup.  All ASDRs in this study are central death rates, and
 based on single years of age.  Although we obtain NCHS deaths for Whites, 
Blacks, American Indian, API, and Hispanics, we do not obtain deaths for the 
non-Hispanic portions of the four racial groups.  The latter are constructed 
using a series of steps described below.   
<P><A name="B241"><EM>Mortality Rates by Hispanic Origin</EM></A><BR>We first 
calculate Hispanic ASDRs using a 45-state  1990 numerator of Hispanic deaths and 
a corresponding 45-state Hispanic population denominator (1990 uncorrected, 
census-level).  We excluded five states either because they did not collect 
Hispanic origin on the death certificate (Louisiana, New Hampshire, and 
 Oklahoma) or because they had relatively high  proportions of unknown Hispanic 
origin  (Connecticut and New York).  Excluding these five  states eliminates 
most of the approximately 106,000 unknown Hispanic origin deaths (5 percent  of
 all deaths) that appear in the 1990 NCHS mortality files.  Among the 45 states, 
only 0.67 percent of the deaths are of unknown Hispanic origin and are excluded 
from the calculation of ASDRs  (probably contributing to an underestimation of 
Hispanic death rates).   
<P>The following steps are used to derive ASDRs for the non-Hispanic portions of 
racial groups: 
<P>1) We obtain estimated numbers of deaths to Hispanic White, Hispanic Black, 
Hispanic American Indian, and Hispanic API by multiplying  the Hispanic ASDRs by 
the Hispanic portion of each race population (DA-level), by age and sex. 
<P>2) We obtain estimated numbers of deaths to four race (any Hispanic) groups 
by multiplying race (any Hispanic) ASDRs by the respective race populations. 
<P>3) Subtracting 1) from 2) yields  deaths to Non-Hispanic  White, Non-Hispanic 
Black, Non-Hispanic American Indian, and Non-Hispanic API, by age and sex.   
<P>4) ASDRs for each sex, race, and Hispanic origin group are then obtained by 
dividing these deaths by their respective sex, race, and Hispanic origin 
population denominator.    
<P><A name="B242"><EM>Problems With Race and Hispanic Origin Mortality 
Rates</EM></A><BR>There are well-known difficulties in calculating accurate 
mortality rates for some race and Hispanic origin groups in current or past 
years, including both the 1990 primary base years and the 1996 to 1998 secondary 
base years.  The numerators and denominators of the ASDRs come from different 
sources, and they differ in important ways. Some of these differences include 1) 
how race and ethnicity is reported and classified (being self-reported in the 
census, but not self-reported on death certificates) 2) how missing data are 
handled, and 3) how responses such as "other race" are handled. Thus, there is 
inconsistent reporting of race and ethnicity between the two data sources--death
 records and census records.  There is convincing evidence that the ASDRs for 
some race and ethnic groups, as currently measured, are underestimated.  One 
study that compared race and ethnic identification on CPS surveys with those of 
death certificates suggests that API death rates could be underestimated by 12
 percent, and by 25 percent for American Indians.<SUP>34 35</SUP>  However, we 
do not yet know of an adequate way to adjust our race and ethnic mortality 
rates, and correction factors are not available at this time.  We currently use 
the existing data until we have a stronger basis for making adjustments.  
<P><A name="B243"><EM>Old-age Mortality Rates</EM></A><BR>We do not calculate 
ASDRs for the age group 85 years and older in the same manner as we do for the 
under 85 years population (i.e, NCHS deaths divided by population denominators),
 due to the inaccuracies that can result from such a procedure.  There are 
problems of age mis-reporting  in both the numerators (death records) and 
denominators (census-based population data).  Instead, we use a mathematical 
model developed by Coale and Kisker to obtain ASDRs for each 
subgroup.<SUP>36</SUP>  We inserted different parameters into the original Coale 
and Kisker formulas in order to force them to produce death rates of 1.0 for 
both males and females at age 115 for all race and Hispanic origin groups.  
<P><BR><A name="B3"><STRONG><EM><U>International Migration</U></EM></STRONG><A> 
</A>
<P><A>Among the three major components of national population change--births, 
deaths, and international migration--international migration is the component 
for which demographic science offers the least to future projections.  Births 
and deaths can be projected as rates, with demographic detail, so the emerging 
size and structure (age, sex, race, and Hispanic origin) of the populations at 
risk of death and childbearing are a key determinant of  these components of
 population change.  Moreover, the epidemiological basis for the propensity to 
die,  as well as the social and economic basis for the propensity to bear 
children are both the subjects of substantial academic inquiry.  This body of
 research has yielded a basis for projecting their future course, as reflected 
in previous sections of this report.  International migration to the United 
States, by contrast, has public policy as a major determinant.  While it may be 
acceptable in the near term to view migration as a consequence of existing 
immigration law and policy, this assumption loses merit for the longer term.  
Emigration of the foreign-born population can be projected relative to a
 population at risk (e.g., the foreign-born population) through the use of 
emigration rates, but there is little or nothing in the way of theory to 
indicate how these rates might change over time. </A>
<P><A><A name="B31"> <STRONG>Assumptions and Methodology</STRONG></A><BR>
International migration, in previous United States population projections 
produced by the Census Bureau, has been projected as a constant value with a 
constant matrix of demographic characteristics.  The constant-level assumption
 has been based on the experience of the last few years prior to the launch date 
of the projections, incorporating separate assumptions for legal immigration, 
refugee movements, emigration (of natives and foreign-born combined), net
 migration from Puerto Rico, and net undocumented migration.  High and low
 variants have been determined by establishing reasonable maximum and minimum 
values of each of these components, and holding them constant over time, with a 
linear transition over a few years from current to ultimate values.   
<P>The current projection series incorporate three major changes from past 
practice in the projection of international migration.  First, we decided that 
the constant migration assumption was inappropriate for a projection series (the
 middle series) that would be widely interpreted as the Census Bureau's forecast 
of population.  This determination was primarily on account of an increased 
level of public debate regarding immigration policy, as well as the highly
 transitory nature of some recent developments in international migration.  The 
former mandated a more critical view of how migration might change in the 
future, while the latter tended to discredit the interpretation of the base
 series in a simplistic manner.  However, we have not been able to develop a 
dynamic model for future international migration that reflects adequately the 
current base series information, yet conforms to any unifying theory of future
 change.  We have, therefore, projected migration with consideration of a large 
amount of underlying current detail, coupled with some consideration of factors 
that could influence its change in the future.  The resulting projections seek 
to reflect current trends in specific aspects of  migration, and to gauge their 
likely future direction and magnitude. 
<P>The second change from past practice is that we allow characteristics of the 
projected population to influence the migration assumption.  In the past, we 
have expressly avoided incorporating population "feedback" mechanisms when
 formulating assumptions on any components of population change, assuming a 
unidirectional causative sequence from determinants of components to components 
and from components to the population.  In the case of fertility and mortality, 
we continue this practice, simply because there is little evidence that such
 feedbacks are important.  In order to develop a dynamic assumption regarding 
future migration, it is necessary to consider the plausible links that tie 
demographic characteristics of the future population to immigration policy.  
Thus, we consider the future direction in the age composition of the population, 
as it might affect policy regarding the immigration of working-age people. 
<P>A third major innovation in the current projections of international 
migration relates to the projection of the emigration of foreign-born residents. 
 Because we have projected the foreign-born population in the current
 projections, we were able to model foreign-born emigration as a function of the 
population at risk, in much the same way as we projected mortality.  Thus, 
foreign-born emigration is projected, in all series, as rates by age, and sex,
 rather than as number of emigrants.  The comparatively low level of native-born
 emigration is projected numerically, as in the past. 
<P>We are unable to project total in-migration and total out-migration, as we 
have no such estimates in the base series.  For some of the components of 
international migration, information sources for the base series offer no
 disaggregation of gross in-migration from gross out-migration.  Specifically, 
the net flow of migrants from Puerto Rico (treated as international in this 
context), the net flow of undocumented migrants from foreign countries, and the 
net flow of other legal non-immigrant residents (mostly foreign students) are 
imputed only as net flows--not as a balance of measured in- and out-migration.  
Consequently, the concept of "in-migration" to the U.S. in these projections is 
a somewhat artificial construct consisting of in-migration of refugees, 
in-migration  of newly arriving legal immigrants, in-migration of non-immigrants 
who will later become legal immigrants, net undocumented migration, net Puerto 
Rican migration, and the net movement of other legal but temporary 
non-immigrants  to the United States.  This flow is in large part a one-way flow 
to the U.S., but embodies some reverse elements in the components only 
measurable as net flows in the base series.  By the same token, the separately
 projected "out-migration" component is confined to the emigration of legal 
permanent U.S. residents to permanent residence abroad, excluding resettlement 
in Puerto Rico. 
<P>Table D provides a summary of "in-migration" (as previously described) and 
the emigration of legal residents for four single years in the projection 
series. 
<P><A name="B32"><STRONG>Projection of the Level of In-Migration: Middle Series, 
1999 to  2020</STRONG></A><BR>The determination of the trend in migration to the 
United States from 1999 to 2020 in the middle series is based on consideration 
of current trends in the arrival of people born in different areas of the world. 
 The trend is based on the following guiding assumptions. 
<P>1) A rapid increase in the level of migration during the 1990's occurred 
largely because millions of people legalized in 1987 and 1988 under the 
Immigration Reform and Control Act (IRCA) of 1986, were becoming U.S. citizens 
in increasing numbers.  As they became citizens, they could sponsor the legal 
immigration of immediate relatives without being subject to numerical limits.  
We deemed this flow, composed largely of people from Mexico and Central America, 
to be somewhat transitory.  Hence, migration from this source is projected to 
reach a peak early in the decade of 2000 to 2010, then gradually decline to zero 
as the supply of potential reunifications is exhausted.  In particular, legal 
migration from Mexico is assumed to return to the levels of the early 1990's by 
2010. 
<P>2) We assume that there will be no change in immigration policy which would 
result in any change in the quantity of immigrant visas available in numerically 
limited legal categories between 1998 and 2020.  Numerically limited categories 
embrace all legal immigration except for the adjustment of refugees and asylees 
to immigrant status, the admission of immediate relatives of U.S. citizens, and 
a few other categories of little demographic consequence. 
<P>3) The flow of refugees to permanent residence in the U.S. would tend to 
decline between 1998 and 2020, except for a near-term increase to 2000 in the 
number of refugees from the republics of the former Yugoslavia.  The decline in 
the flow from the principal sources of the last 30 years, Southeast Asia and 
Cuba, is apparent in the current refugee data series from 1995 forward.  The 
trend from the former Yugoslavia has been sharply upward since 1991, although
 the timing and the height of the peak in this trend will depend on the course 
of world events, as well as the direction of United States refugee resettlement 
policy. 
<P>4) Undocumented migration of people born in Mexico and Central America is 
viewed primarily as a function of the degree of success in controlling the 
southwest border, and is not projected to change from levels assumed for the
 1990's base series. 
<P>5) Legal migration from places other than Mexico, Central America, and 
refugee sources will vary in trend, depending on recent observations, and, to a 
lesser extent, the perceived demographic capacity of the source countries to 
supply migrants.  The emerging sources of migration that continue to increase in
 importance under this assumption are South Asia, Sub-Saharan Africa, and the 
Middle East.   We project a modest decline for the Philippines, and little 
change in the influx from other areas. 
<P>A summary of the numerical assumption for migration to the United States used 
for the middle series is excerpted in Table E, together with the current trend 
from 1991 to 1998.  The first block of this table, showing the middle series 
assumption, indicates a modest rise in in- migration from 1,234,000 in 1998 to 
1,272,000 in 2002, a decline to 1,036,000 by 2010, followed by a gradual rise to 
1,090,000 by 2020.  The rise and decline are propelled mainly by the previously 
postulated trends from Mexico (IRCA-related family reunifications) and the
 former Yugoslavia (refugee movements), while the subsequent rise is dominated 
by the relatively more gradual trends from the emerging sources identified in 
point 4 above. 
<P><A name="B33"><STRONG>Projection of the Level of In-Migration: Middle Series, 
2021 to  2100</STRONG></A><BR>For the period from 2021 to 2100, the focus of the 
projection of migration into the U.S. shifts from the individual consideration 
of various sources of migration from abroad to the trend in the aggregate level. 
 The projection of migration by source region follows, but only with the aim of 
establishing a distribution that can be used to impute demographic 
characteristics.  The principal assumptions are as follows, and are reflected, 
once again, in the first block of Table E. 
<P>1) Driven by a rapid increase in the dependency ratio (number of people in 
the traditionally dependent age groups, under 15 years and 65 years  and over, 
relative to the balance of the population), migration to the U.S. would increase 
from 2020 to 2030, from a level of 1,090,000 in 2020 to 1,450,000 in 2030. 
<P>2) From 2030 to 2100, migration into the United States would remain 
numerically constant at 1,450,000, even in the presence of an increasing
 population, hence, its direct proportional impact on the population would 
decline. 
<P>The phenomenon underlying the projected increase through the 2020's is a 
pervasive one in all considerations of the future demographic characteristics of 
the United States.  The historic rise in births that occurred in the United 
States from 1946 through the 1950's, followed by the decline through the early 
1970's, left a bulge in the age distribution that has ensured an unnaturally low 
dependency burden through the 1980's and 1990's on into the early 2010's.  Table 
F shows the trend in population, the dependency ratio, and the elderly 
dependency ratio (defined as the ratio of people aged 65 and over to people in 
ages 15 to 64), under various migration assumptions.  In the complete absence of 
migration in or out of the United States from 1999 onward ("zero migration," in
 Table F), the dependency ratio rises from 53.0 percent in 2015 (close to the 
current level) to 69.4 percent by 2030, while the elderly dependency ratio 
endures a near parallel rise from 23.5 to 37.1.  Our projections anticipate an
 increase in the influx of migrants to the United States as a response to this 
dramatic downward shift in the availability of potential workers relative to 
people outside the normal working ages.  The anticipated increase, from 
1,090,000 to 1,450,000 annually, while large in percentage terms (33 percent) is 
modest relative to shifts that have occurred in migration in the United States 
and elsewhere in the industrialized world in response to economic and 
demographic shifts of this importance.  The migration response to the economic 
boom of the 1920's in the United States, and the labor migration from
 southeastern to northern Europe in the period following World War II are 
examples of migratory shifts far more dramatic than the one projected here.  On 
the other hand, to project a much larger shift (for example, a shift comparable 
to what the U.S. experienced in the early 20th century) would tend to overlook 
the possibility of restrictive policies intended to limit such a shift. 
<P>The impact of this projected migration trend on the dependency ratio, while 
not impressive, should be of some significance in the long-term.  In the zero 
migration model (first block, Table F), the dependency ratio increases from 58.1
 percentage points, to 69.4, an increase of 11.3 percentage points, from 2020 to 
2030.  Under the middle-series migration assumption, it increases from 57.2 
percentage points to 65.9, up 8.7 percentage points during the same period.  
<P><A name="B34"><STRONG>Migration to the U.S. by Race and Hispanic 
Origin</STRONG></A><BR>As previously indicated, the projection methodology makes 
use of the distribution of international migration by country of birth in the
 base year, distinguishing among major regions of the world in establishing the 
trend.  This fact is most reflected in the resulting distribution of
 international migration by age, sex, race, and Hispanic origin.  In the 
projection of in-migration  from 1999 to 2020, projections are determined 
primarily by current trends by country of birth, with consideration of the legal
 bases of migration.  In the projections from 2021 to 2100, the international 
population projections of the International Program Center (IPC) of the Census 
Bureau are tapped for information on the relative projected growth of the 
working-age component of the population of various world regions to the year 
2050.<SUP>37</SUP>  These projections show considerably more rapid population 
growth through the early part of the next century for countries of South Asia, 
sub-Saharan  Africa and the Middle East, than for countries of the Western 
Hemisphere including Mexico, which have seen considerable declines in fertility 
in recent years. 
<P>The strategy in these projections was to allow the composition of 
international migrants by race and Hispanic origin to reflect the probable
 contribution of the various world regions to the level of in-migration to the 
United States dynamically.  The resulting percentage distribution by race and 
Hispanic origin for the middle series is shown in Table D, middle block, for 
selected years in the series.  The declining contribution of the Western
 Hemisphere and Europe, and the industrialized countries of East Asia are 
reflected in decreasing levels of in-migration for the Hispanic and White 
populations.  The increasing contribution of the Middle East, South Asia, 
Southeast Asia, China, and sub-Saharan  Africa are reflected in increased
 migration for the Black and API populations. 
<P><A name="B35"><STRONG>Low and High International Migration 
Assumptions</STRONG></A><BR>The objective in projecting low and high variants 
for the international migration assumption is to establish a candid view of the
 uncertainty surrounding the middle series projection.  Three qualitative 
considerations governed the choice of the upper and lower limits for 
in-migration. 
<P>1) The margin of uncertainty around the middle-level  assumption is, of 
necessity, relatively wider for international migration than for births and 
deaths.  The exogenous character of this component, and its reliance on 
unpredictable external factors such as the internal policy environment and world 
events, as well as the lack of demographic determinism in its projection, ensure 
a comparatively high level of uncertainty for this component. 
<P>2) The displacement between high, middle, and low variants should increase 
over time, as it did for both fertility and mortality.  Uncertainty in any 
component increases along with the elapsed time from the relatively certain 
present to any projected reference date. 
<P>3) The pace of the increase in the spread between high and low should 
decrease over time.  While somewhat less obvious, this follows from the goal to 
reflect uncertainty in the population series. The population series is most 
affected by <EM>cumulative</EM>, rather than current levels of international 
migration.  Because some of the error in the middle series migration assumption 
should be caused by fluctuations in the level of migration, rather than 
long-term trends, a portion of it can be expected to wash out with the passage 
of time.  Similar reasoning was applied to the projection of the low and high 
variants of fertility, where fluctuations over time are also expected.  This 
effect was not considered important in the projection of mortality. 
<P>4) We assume that the difference between high and middle assumptions will 
exceed the difference between low and middle assumptions.  Specifically, we 
assume that the differences in the logarithms of the three series (high minus 
middle, middle minus low) are equal.  This is equivalent to saying that the
 series are equidistant in a multiplicative sense, or that the ratios of high to 
medium equal the ratios of medium to low.  This follows from the nature of the 
theoretical upper and lower bounds.  We can presume that the theoretical
 high-end constraints on gross in-migration are defined only by the population 
of the rest of the world, and can thus be ignored (treated as infinity), while 
the low-end constraint is zero.  We discount the fact that some out-migration of
 illegal residents, temporary residents, and people moving to Puerto Rico are 
included in our definition of in-migration, previously described, on the 
assumption that these elements are small relative to in-migration as a whole.  A
 similar reasoning would not apply to fertility and mortality, because the 
determinants of their variability above and below the middle assumption are 
presumed comparable. 
<P>To establish the high variant, we assumed a deviation from the middle series 
of zero in 1998 (since this was the base year), 75 percent in 2010, and 150 
percent in 2100.  Multipliers applied to the middle series were thus 1.00 for
 1998, 1.75 for 2010, and 2.50 for 2100.  A logarithmic function was fitted to 
these three multipliers to produce an annual series.  We established the low 
variant by computing the reciprocal of these multipliers: 1.00 for 1998, 0.57 
for 2010, and 0.40 for 2100, which amounted to reducing the middle series by 43
 percent (actually 3/7) in 2010, and 60 percent in 2100. 
<P>At its most extreme, the implied range for international migration to the 
U.S. in 2100 was from 580,000 migrants to the U.S. to 3,625,000, with the 
middle-level assumption at 1,450,000.  In 2010 (the low point in the middle 
series), the low, high, and middle values were, respectively, 592,000, 
1,812,000, and 1,036,000.  Data for these and other selected dates in the series 
are shown in Table E. 
<P>In reviewing the extreme variants for their plausibility (albeit as extreme 
assumptions), we also considered their impact on population size and dependency 
ratios over the period of the projections.  We projected the population using
 each of the three migration assumptions and equal values for fertility and 
mortality rates.  These results are shown in Table F.  The results for 
dependency ratios show a spread between the low and high migration series of 1.3
 percentage points in 2020, increasing to 4.3 points by 2030, after the 
projected increase (reflected in all three series) of the 2020's.  The spread 
increases to 6.2 percentage points by 2100.  For total resident population, the 
three models produce levels of 437 million, 571 million, and 854 million, 
respectively, in 2100.  The long-term spread in the dependency ratio between 
high and low appears comparatively modest, and changed very little over the last 
70 years of the projection period.  This is explained by the fact that many of 
the larger numbers of annual migrants entering under the high assumption have 
dependent children and age out of the working life span during the period of the
 projections, thereby reducing the difference in the dependency ratio.  The 
differences in population are indeed stark, with the high-migration  assumption 
yielding near double the population produced by the low-migration assumption in 
2100. International migration may address a high dependency ratio decisively in
 the short-term, yet is highly inefficient in reducing it over the longer 
term--especially if considerations of population scale, as well as age 
composition, are taken into account. 
<P><A name="B36"><STRONG>Projection of Emigration of Legal U.S. 
Residents</STRONG></A><BR>As previously indicated, emigration of legal
 foreign-born residents is projected on the basis of age-sex-specific rates, 
applied to a population at risk, rather than a postulated numerical trend. 
 Current values of these rates were developed on the basis of research conducted 
by the Census Bureau.<SUP>38</SUP>  The underlying method involves computing a 
matrix of differences between the number of foreign-born people enumerated in
 the 1980 census, and the number of foreign-born people arrived before 1980 
enumerated in the 1990 census.  This calculation is carried out for large 
groupings of country of birth, age, and sex, an adjustment is made for residents 
who died during the decade, and the balance is assumed to be the number of 
emigrants.  Considerable modification of the numbers had to be carried out 
because of problems such as negative differences for some countries of birth
 (theoretically impossible, but for misreporting on the census) and allowances 
for differential reporting of undocumented residents in the two censuses.  When 
these distributions are divided by an interpolated mid-decade population, they
 produce a schedule of rates, which, when applied to the foreign-born 
population, produce a projection of emigration.  Unlike the case of
 in-migration, this projection method also produced the results in the base 
series from 1990 to 1998, since no current data on foreign-born  emigration are 
available. 
<P>For the middle series, we assumed that foreign-born  emigration rates 
remained constant throughout the duration of the projections.  This means that 
trends in emigration are driven mainly by the size of the foreign-born
 population, and secondarily by its composition by age, sex, and country of 
birth.  As shown in Table G, the age-sex-country-standardized rate (standardized 
on the 1990 base population) is set at 12.1 per thousand population. 
<P>Native emigration was estimated as a constant for the base series and the 
middle series, at 48,000 per year.  This assumption is based on research 
employing reports of U.S.-born respondents in foreign censuses, as well as some
 imputation for countries of destination for which no such data were 
available.<SUP>39</SUP> 
<P>As shown in Table E, these two assumptions yield an annual emigration trend 
from 252,000 in 1991, to 278,000 in 1998, the base year for the projections.  
This increases steadily with the increase in the foreign-born population, to a
 level of 524,000 in the year 2100.  The juxtaposition of constant in-migration 
with increasing emigration throughout the last 70 years of the next century, 
presumes a decline in the numerical level of annual net migration to the United 
States, and an even greater decline in the impact of this component relative to 
overall population size. 
<P><A name="B37"><STRONG>Low and High Emigration Assumptions</STRONG></A><BR>The 
extreme variants of foreign-born emigration rates are based on the same logic 
underlying the derivation of the extreme variants of in-migration,  except that 
the application was to rates, rather than numbers.  Because higher emigration 
implies lower net migration, the high-level multipliers were used to determine
 the emigration rates used for the low migration series, and the reverse was 
true for the high migration series.  Because emigration in a given year in the 
middle series was on the order of 1.2 percent of the foreign-born population, 
the upper-level constraint of 100 percent was assumed to be infinity, while the 
lower-level constraint was zero.  Thus, the multiplicative approach to producing 
the extreme variants was deemed appropriate.  Low-migration foreign-born 
 emigration rates for 2010 were obtained by multiplying the middle-series by 
1.75, while the multiplier for 2100 was 2.50.  The multipliers for the 
high-migration series were the reciprocals of the multipliers for the 
low-migration  series.  The results are shown in Table G. 
<P>The fact that foreign-born emigration is driven by projected rates, rather 
than projected numbers, allows a crossover in numerical emigration among the 
three series, around 2055.  In the early years of the projections, from 1999 to 
2054, the numerical level of emigration is higher for the low-migration series 
than for the high-migration series.  From 2055 to 2100 the reverse is true, 
since the larger size of the foreign-born population in the high-migration
 series relative to the low-migration series overcomes the effect of the lower 
emigration rates for the foreign-born in the high migration series. 
<P>The derivation of native-born emigration for the high and low assumptions 
follows essentially the same logic as that used to derive high and low variants 
for gross in-migration.  Multipliers that increase (for the high assumption) or
 decrease (for the low assumption) logarithmically are applied to the middle 
series assumption of 48,000 per year. 
<P><A name="B38"><STRONG>Net Migration of U.S. Citizens</STRONG></A><BR>The net 
migration of U.S. citizens (aside from emigrants who depart the U.S. 
permanently) is a small component of population change that tends to be driven 
primarily by the movement of U.S. military personnel between the U.S. and
 abroad.  Because it is dominated by military movement, this migration is highly 
dependent on the future course of world events. Because of the impossibility of 
projecting such developments, we adopt a conservative strategy in projecting 
this component.  The overseas population of military and dependents is held at a 
constant level, with a constant distribution by age, sex, race, and Hispanic 
origin.  Migration is therefore equal to the number of overseas births, minus 
the number of overseas deaths, plus the balance of net inductions and discharges 
to the military from the overseas population.  The age distribution of this flow 
is based on the characteristics of net migration required to counteract the 
natural aging of each category of sex, race, and Hispanic origin in the overseas
 population.  No high and low variants were determined for the net migration of 
U.S. citizens. 
<P><BR><A name="sum"></A>
<H3><A name="sum">SUMMARY</A></H3>In developing population projections for the
 United States, we have made a number of decisions regarding the scope of the 
projections and the assumptions that were somewhat "bolder" than those adopted 
in most previous series.  The boldest decision was undoubtedly the one to extend 
the series to the year 2100.  In making this decision, we were fully aware of 
the precarious nature of any population projection that is three human 
generations past the existing population base.  While the trend over the first
 20 years of a projection series is generally dominated by the characteristics 
of the base population in demographic projections, populations for dates 50 to 
100 years in the future are highly subject to behavioral decisions by 
individuals, policy decisions by governments at home and abroad, and possible 
unexpected developments in health and morbidity.  In formulating assumptions for 
the highest and lowest series that are progressively extreme, we have attempted 
to convey a sense of the caution with which any such long-term projections
 should be interpreted. 
<P>Another area of innovation in these projections is in the projection of 
international migration.  Once again, we recognize the uncertainty about the 
future course of migration that has tended to motivate simpler, more 
parsimonious assumptions in the past.  Yet, we decided that this component of 
change had received enough public attention in recent years that we could not
 credibly assume it to be unaffected by demographic changes in the population, 
as the constant-level projection tacitly assumes. 
<P>Projecting the human population continues to be an evolving science, and we 
fully expect that future developments, including the upcoming 2000 census, will 
provide us with the basis to revise these assumptions in future years. 
<P>
<HR width="33%" align="left">
<SUP>1</SUP> At the time of release for this report, the results of these 
projections are located on the  Census Bureau site of the Worldwide Web.  U.S. 
Census Bureau; “National Population Projections;”  <http: natproj.html="" 
projections="" www="" population="" www.census.gov="">
<P><SUP>2</SUP> The information on the Hispanic population shown in this report 
was collected in the  50 States and the District of Columbia and, therefore, 
does not include residents of Puerto Rico. 
<P><SUP>3</SUP> People of Hispanic origin may be of any race. 
<P><SUP>4</SUP> Jennifer Cheeseman Day, U.S. Census Bureau, <EM>Population 
Projections of the  United States by Age, Sex, Race, and Hispanic Origin: 1995 
to 2050</EM>, Current Population Reports,  P25-1130, U.S. Government Printing 
Office, Washington, District of Columbia, 1996. 
<P><SUP>5</SUP> U.S. Census Bureau, “Population Growth Rate Remains Stable, 
Census Bureau  Reports,” National Population Estimates, Released as Press 
Release No. CB99-101, June 4, 1999.   At the time of release for this report, 
the results of the national estimates  are located on the Census  Bureau site of 
the Worldwide Web.  U.S. Census Bureau; “National Population Estimates;” 
published  June 1999, <http: www="" population="" www.census.gov="" uspop.html="" 
estimates=""></http:>
<P><SUP>6</SUP> Throughout the remainder of this report, “American Indian” is 
used to describe the  American Indian, Eskimo, and Aleut population. 
<P><SUP>7</SUP> U.S. Census Bureau, <EM>Age, Sex, Race, and Hispanic Origin 
Information  from the 1990 Census: A Comparison of Census Results with Results 
Where Age and Race Have  Been Modified</EM>, CPH-L-74, U.S. Government Printing 
Office, Washington, District of Columbia, 1991. 
<P><SUP>8</SUP> These methods are discussed in various demographic texts, e.g., 
Henry Shryock  and Jacob Siegel, <EM>Methods and Materials of Demography</EM>, 
Academic Press, Orlando, Florida, 1976. 
<P><SUP>9</SUP> For a description of the 1990 Demographic Analysis population 
and its derivation,  see J. G. Robinson, B. Ahmed, P. Das Gupta, and K.A. 
Woodrow, “Estimation of Population Coverage  in the 1990 United States Census 
Based on Demographic Analysis,” <EM>Journal of the American  Statistical 
Association</EM>, Vol. 88-423 (1993): pp. 1061-1071. 
<P><SUP>10</SUP> For seasonality of births see Stephanie J. Ventura, J. Martin, 
S. Curtin, T. Mathews,  National Center for Health Statistics, <EM>Report of 
Final Natality Statistics</EM>, 1996, Monthly  Vital Statistics Report, Vol. 
46-11 Supplement, 1998.; for seasonality of deaths see unpublished tabulations 
 from National Center for Health Statistics, 1996 detailed mortality file. 
<P><SUP>11</SUP> The total fertility rate is a standardized measure of the 
average number of live births  per 1,000 women experiencing specific 
age-specific fertility rates throughout their childbearing years  without 
accounting for mortality. 
<P><SUP>12</SUP> Stephanie J. Ventura, J. Martin, S. Curtin, T. Mathews, 
National Center for Health  Statistics, <EM>Births: Final Data for 1997</EM>, 
National Vital Statistics Report, Vol. 47-18, 1999. 
<P><SUP>13</SUP> Jennifer Cheeseman Day, U.S. Census Bureau, <EM>Population 
Projections of the  United States by Age, Sex, Race, and Hispanic Origin: 1995 
to 2050</EM>, Current Population Reports,  P25-1130, U.S. Government Printing 
Office, Washington, District of Columbia, 1996. 
<P><SUP>14</SUP> Each sub-group of Hispanics is assumed to maintain identical 
fertility trends. 
<P><SUP>15</SUP> W. van Hoorn and N. Keilman,  “Birth Expectations and Their Use 
in Fertility  Forecasting,” <EM>Eurostat Working Papers</EM>,  E4/1997-4 (1997). 
<P><SUP>16</SUP> Charles Westoff,  “The Return to Replacement Level Fertility: A 
Magnet Force?”  <EM>Future of Demographic Trends in Europe and North 
America</EM>, Academic Press, London, England, 1991. 
<P><SUP>17</SUP> Lincoln H. Day,  “Recent Fertility Trends in Industrialized 
Countries: Toward a Fluctuating  or Stable Pattern?” <EM>European Journal of 
Population</EM>, Vol. 11 (1995): pp. 275-288. 
<P><SUP>18</SUP> Stephanie J. Ventura, J. Martin, S. Curtin, T. Mathews, 
National Center for  Health Statistics,  <EM>Report of Final Natality 
Statistics, 1996</EM>, Monthly Vital Statistics  Report, Vol. 46-11 Supplement, 
1998. 
<P><SUP>19</SUP> Martin O’Connell, U.S. Census Bureau, <EM>Studies In American 
Fertility</EM>,  Current Population Reports, P23-176, U.S. Government Printing 
Office, Washington, District of Columbia, 1991. 
<P><SUP>20</SUP> Joan R. Kahn, “Immigrant and Native Fertility During the 1980s: 
Adaptation and  Expectations for the Future,” <EM>International Migration 
Review</EM>, Vol. 28-3, (1994): pp.  501-519.;  and  Deanna Pagnini,  
“Immigration and Fertility in New Jersey: A Comparison of Native  and 
Foreign-Born Women,” pp. 259-290 in <EM>Keys to Successful Immigration</EM>, 
Urban  Institute Press, Washington, District of Columbia, 1997. 
<P><SUP>21</SUP> Age-specific fertility rates calculated for the projections 
differ from those calculated  by the National Center for Health Statistics as a 
result of applying different base populations. 
<P><SUP>22</SUP> National Center for Health Statistics, <EM>National Survey of 
Family Growth, Cycle V</EM>, 1995. 
<P><SUP>23</SUP> According to the National Center for Health Statistics, “The 
expectations  of young women 25-29 years of age in 1988 exceed the estimated 
completed fertility of women  in their earliest 40’s at the time by about 9 
percent (the difference between 2.33 and the average of  2.07, 2.12, and 2.17, 
above).”  In Linda S. Peterson, National Center for Health Statistics,  
<EM>Birth  Expectations of Women in the United States, 1973-88</EM>, Vital and 
Health Statistics, Vol. 23-17, 1995: p. 8. 
<P><SUP>24</SUP> For detailed information on mortality trends between 1900 and 
1990, see  Robert N. Anderson, National Center for Health Statistics, <EM>U.S. 
Decennial Life Tables for  1989-91</EM>, Vol. 1-3, Hyattsville, Maryland, 1999.  
<BR>     For mortality patterns trough 1997 and 
mortality rates  for the five race and Hispanic origin groups see Donna L. 
Hoyert, K. D. Kochanek, and S. L.  Murphy, National Center for Health 
Statistics, <EM>Deaths: Final data for 1997</EM>,  National Vital Statistics 
Reports, Vol. 47-19, Hyattsville, Maryland, 1999. 
<P><SUP>25</SUP> In this mortality section, the term "race and Hispanic origin 
groups" refers  specifically to five groups:  Hispanic, Non-Hispanic White, 
Non-Hispanic Black, Non-Hispanic  American Indian, and Non-Hispanic API.  We use 
“race and ethnicity” in a more general sense  to include all race and ethnic 
groups. 
<P><SUP>26</SUP> Ron Lee  and S. Tuljapurkar, <EM>Population Forecasting for 
Fiscal Planning:  Issues and Innovations</EM>, unpublished manuscript, 
September, 1998. 
<P><SUP>27</SUP> Jennifer Cheeseman Day, U.S. Census Bureau, <EM>Population 
Projections of the  United States by Age, Sex, Race, and Hispanic Origin: 1995 
to 2050</EM>, Current Population  Reports, P25-1130, U.S. Government Printing 
Office, Washington, District of Columbia, 1996. 
<P><SUP>28</SUP> We use the term “life table” throughout this text for 
convenience.   Most of our  work is actually based on schedules of age-specific 
central death rates, which can be converted to life  tables and  used to 
calculate life expectancies at birth and at age 65. 
<P><SUP>29</SUP> Ron Lee  and S. Tuljapurkar, <EM>Population Forecasting for 
Fiscal Planning:  Issues and Innovations</EM>, unpublished manuscript, 
September, 1998. 
<P><SUP>30</SUP> Ron Lee and L. Carter, “Modeling and Forecasting US Mortality," 
<EM>Journal  of the American Statistical Association</EM>, Vol. 87-419 (1992): 
pp. 659-675. 
<P><SUP>31</SUP> Personal  correspondence, Carl Boe for Lee and Tuljapurkar 
10/19/98. 
<P><SUP>32</SUP> Margorie Rosenberg and Warren Luckner, “Summary of Results of 
Survey of  Seminar Attendees,”  <EM>North American Actuarial Journal</EM>, Vol. 
2-4 (1998): pp. 64-82. 
<P><SUP>33</SUP> Personal correspondence, Carl Boe for Lee and Tuljapurkar 
10/19/98. 
<P><SUP>34</SUP> P. Sorlie, E. Rogot, and N. Johnson, “Validity of Demographic 
Characteristics  on the Death Certificate,” <EM>Epidemiology</EM>, Vol. 3-2 
(1992): pp. 181-184.<BR>     Additional discussion and 
evidence related to the  underestimation of American Indian mortality can be 
found in U.S. Department of Health and  Human Services, Indian Health Service, 
<EM>1997 Trends in Indian Health</EM>,  Rockville, Maryland, 1997.; and in 
Support Services International, Inc., <EM>Adjusting for  Miscoding of Indian 
Race on State Death Certificates</EM>, Final Report Submitted to the  Division 
of Program Statistics, Indian Health Service, 1996. 
<P><SUP>35</SUP> The use of the DA universe for population denominators tends to 
obviate biases of  differential reporting between Blacks and all other races 
combined, since the DA procedure uses death  registration data to define these 
categories. However, the break of “other race” into American Indian,  API, and 
White required the use of census data, with all it’s biases relative to death 
registration. 
<P><SUP>36</SUP> Ansley Coale and E. Kisker, “Defects in Data on Old-Age 
Mortality in the U.S.:  New Procedures for Calculating Schedules and Life Tables 
at the Highest Ages,” <EM>Asian and  Pacific Population Forum</EM>,Vol. 4-1 
(1990): p. 32. 
<P><SUP>37</SUP> U.S. Census Bureau, International Program Center; 
<EM>International Data Base (IDB)</EM>;  <http: www="" www.census.gov="" 
idbnew.html="" ipc="">; (11 January 1999) </http:>
<P><SUP>38</SUP> Bashir Ahmed and J. Gregory Robinson, Population Division, U.S. 
Census Bureau,  “Estimates of Emigration of the Foreign-born Population: 
1980-1990,” <EM>Working Paper No. 9</EM>, 1994. 
<P><SUP>39</SUP> Edward Fernandez, Population Division, U.S. Census Bureau, 
“Estimation of the  Annual Emigration of U.S. Born Persons by Using Foreign 
Censuses and Selected Administrative  Data: Circa 1980,” <EM>Working Paper No. 
10</EM>, 1995. 
<P>
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