**Methodology Summary**

**Interim Population Projections for States by Age and Sex: 2004 to
2030**

Population Projections Branch

Population Division

U.S. Census Bureau

The interim state population projections were prepared to be consistent
with the interim United States (U.S.) national population projections
released in March 2004
([[http://www.census.gov/ipc/www/usinterimproj]{.underline}](../(http://www.census.gov/ipc/www/usinterimproj/).)
). The cohort-component method was used to produce interim state
population projections by single year of age and sex. Each birth cohort
(the people born in a specified year) was projected forward (e.g., from
age 27 in one year to age 28 a year later). Each component of population
change -- births, deaths, internal migration, and international
migration -- was projected separately from 2000 to 2030 based on recent
fertility, mortality, and migration trends. Rates of fertility,
mortality, and migration were held constant throughout the projection
period with small adjustments to fit the estimated components of change
from 2001 to 2003. The sum of the projected total state populations by
single year of age (0 to 85 and older) and sex were controlled to the
interim U.S. population projections from 2004 to 2030 by single year of
age and sex.

The interim state projections in this release are based on the general
assumption that recent demographic trends will continue in the future.
The projections represent the results of incorporating these assumptions
in a mathematical projection model and are not forecasts of what future
population trends will be.

Projected fertility and mortality rates were based on birth and death
statistics by state from the National Center for Health Statistics
(NCHS). Projected internal migration was based on data on state
migration patterns derived from the Internal Revenue Service (IRS) and
Census 2000 data. Projected international migration was based on the
estimates of net international migration by state derived from the
Population Estimates Program and data on the foreign-born population
enumerated in Census 2000.

**I. Methodology Overview**

The cohort-component method was used to produce the state projections,
which were made as of July 1 in projection years. The base population by
single year of age and sex was carried forward from April 1, 2000 (the
reference date for Census 2000) to July 1, 2000 by interpolating the
population between Census 2000 and the projected 2001 population. The
July 1, 2000 population was then used as a base to project the
population in future years. The projections for 2001, 2002, and 2003
were compared with the population estimates already published for those
years. Differences between these projections and estimates were used to
derive small adjustments in the projected components of population
change for the 2004-to-2030 period. For more information about the
population estimates, see the website:
[http://www.census.gov/popest/datasets.html]{.underline}

Fertility rates, mortality rates (converted to survival rates to project
population), internal migration rates, and international migration rates
by age and sex were developed for 2000. For each age, the survival rate
was applied to the population to obtain the population that would be one
year older in the following year. The survived population and initial
population were averaged to derive the population base to which rates of
migration and childbearing were applied. Age-specific fertility rates
were applied to women of childbearing age to derive projected births.
Then the projected in-migration and out-migration rates were applied to
the population base in each state to derive internal migration. The
projected age and sex composition derived from Census 2000 data on
migration between 1995 and 2000 was used to distribute internal
migration by age and sex to states. The net international migration by
state was based on the most recent estimates of net international
migration rates. The distribution of projected net international
migration by age and sex was based on the projected composition derived
from the foreign-born population entering the United States between 1995
and 2000.

II**. Fertility and projection of births**

Data on 1999 and 2000 births by single year of age of mother, obtained
from NCHS, were used to derive age-specific fertility rates based on the
Census 2000 population. Fertility rates by state from this calculation
were held constant throughout the projection years. Total fertility
rates, which are the sum of the age-specific fertility rates, represent
the implied completed fertility rate of women based on 1999 and 2000
age-specific fertility rates (Table 1).

The total number of projected births by state was calculated as the
product of the age-specific fertility rates and the female population of
childbearing ages. The projected births for each year starting in 2004
were adjusted based on the average ratio of estimated births to
projected births for 2001 to 2003 (Table 1).

**III. Mortality and projection of deaths**

Data on 1999 and 2000 deaths by state of residence were obtained from
NCHS and used to calculate age-sex- specific death rates based on the
Census 2000 population. A logistic smoothing technique was used to
smooth and extrapolate the death rates by age to age 110 and over, which
were then used to construct life tables and to derive survival rates.
The state mortality rates for 2000 were held constant throughout the
projection years. Average life expectancy at birth by state is shown in
Table 2.

For each year in each age-sex group, the total of the starting
population plus net migration multiplied by the projected survival rate
was used to derive the projected population at the end of each year. The
projected deaths were the difference between the survived population and
the population at the beginning of each year. The projected deaths for
each year, starting in 2004, were adjusted based on the difference
between projected deaths and estimated deaths for 2001-2003 (Table 2).

**IV. Internal migration**

Rates of state-to-region and region-to-state migration flows based on
aggregate data from the IRS were used to project internal migration into
the future.[^1] The 1995-2000 census migration characteristics were used
to project the composition of migrants, which, in turn, was controlled
to the projected migration flows to derive total projected migration by
age and sex.

Aggregate IRS data were used to derive annual region-to-state
(in-migration) and state-to-region (out-migration) migration flows for
states from 1975-1976 to 1999-2000. The four regions used in these
calculations are the Northeast, Midwest, South, and West.[^2] The
migration rates for a total of 408 migration flows in each of 25 years
were calculated. Univariate, non-seasonal, time series autoregressive
integrated moving average (ARIMA) models were used to project the
migration rates from each state to each of the four regions and the
rates from each region to each state. As these models are best suited to
short-term forecasting, they were used for the years from 2000 to 2005.
For the 2006-2025 period, migration rates were obtained by interpolating
between the projected 2005 rate and the series mean calculated from the
1975 to 2000 migration series. From 2026 to 2030, the series was held
constant at the mean. This approach provided a smooth trend line
gradually moving toward the series mean. The means of the time series
from 1975-1976 to 1999-2000 for the 408 migration flows are shown in
Table 3.

The 1995-to-2000 census-based rates of migration by age and sex for the
each of 408 region-to-state and state-to-region migration flows were
used to project the composition of migrants by age and sex. The
projected region-to-state migration flows by age and sex were summed to
derive in-migration, and the state-to-region migrations were summed to
derive out-migration by age and sex.

**V. International migration**

The interim state population projections used the Census Bureau's
estimates of net international migration rates for states between 2001
and 2003. The rates for the years between 2004 and 2010 resulted from
the exponential interpolation of the 2003 rates and the mean of the
2000-2003 rates. For the years 2010 and beyond, the international
migration rates were assumed to return to the mean of the 2000-2003
rates. The average annual estimate of international migration for the
United States between 2000 and 2003 was about 1.3 million. The estimates
of net international migration rates for states are shown in Table 4.

The proportions of the foreign-born population that entered each state
in the five years prior to Census 2000 were used to project the
composition of net international migration by age and sex. The projected
composition of net international migration by age and sex for each state
was applied to the projected net international migration to derive the
projected net international migration by age and sex.

**VI. Final population projections**

As a last step in the projection process, the resulting state population
projections by age and sex were adjusted proportionally to be consistent
by single year of age and sex with the interim population projections
for the United States released in March 2004.

**VII. Future Population Projections**

This set of state population projections represents only an interim
update to incorporate the Census 2000 population results. In the future,
we plan to develop a revised set of population projections to include
projections by race and Hispanic origin as well as by age and sex.

[^1]: The migration flows between small states were too small to derive
    reliable state-to-state migration rates.

[^2]: Northeast region includes Maine, Vermont, New Hampshire,
    Massachusetts, Rhode Island, Connecticut, New York, New Jersey, and
    Pennsylvania. Midwest region includes Wisconsin, Michigan, Illinois,
    Indiana, Ohio, Minnesota, Nebraska, Iowa, Kansas, Missouri, North
    Dakota, and South Dakota. South region includes Delaware, District
    of Columbia, Florida, Georgia, Maryland, North Carolina, South
    Carolina, Virginia, West Virginia, Alabama, Kentucky, Mississippi,
    Tennessee, Arkansas, Louisiana, Oklahoma, and Texas. West region
    includes Arizona, Colorado, Idaho, Montana, Nevada, New Mexico,
    Utah, Wyoming, Alaska, California, Hawaii, Oregon, and Washington.