Projections of the Number of Households and Families
in the United States: 1995 to 2010
Source: U.S. Bureau of the Census
Release date: May 1996
INTRODUCTION AND GENERAL ASSUMPTIONS
The projections of the number of households and families in the United
States for the years 1995 to 2010 are based on the 1990 census, as enumerated,
with modifications for age and race1/, and household estimates from 1991 to
19942/, and are projected forward using alternative marital status and
household-type proportions. These household projections are not intended as
a forecast, but represent the results of assumptions about future trends in
population change and household formation. The increase in the number of
households (occupied housing units) is not necessarily identical to the volume
of housing construction which may take place during the projection period. The
number of housing units is likely to differ from the increase in the number of
households because of changes in the number of vacant units (vacant housing
units are not counted as households), the demolition of existing units, and
conversions or mergers in existing structures.
Three Alternative Series
Three alternative series were selected to illuminate alternative patterns of
future household change. Series 1, based on a time series model, is the
preferred projection in light of past and possible future trends in household
change. Series 2 reflects the consequences of projected change in the age/sex
structure of the population only, that is, assuming no change from the
composition in 1990 of the proportion maintaining households for specific
types by age and sex. This series provides a basis for evaluating the
implications of alternative assumptions in other series. Series 3 reflects the
consequences of projected change in both the age/sex structure and race/origin
composition of the population; again this assumes no change in the composition
in 1990 proportions maintaining specific types of households by age and sex,
also projected separately by race and Hispanic origin.
Household Types
Household types are arranged into two groups: family households and
nonfamily households. A family household contains at least two persons -- the
householder and at least one other person related to the householder by birth,
marriage, or adoption -- and is categorized into three types: married couple;
female householder with no spouse present; and male householder with no spouse
present. A nonfamily household may contain only one person -- the householder
-- or additional persons who are not relatives of the householder. Nonfamily
households may be classified as either female nonfamily or male nonfamily
households. For each year, the total number of households is the sum of the
five mutually exclusive household types. By census definition, householders
must be at least 15 years of age.
DETAILED METHODOLOGY AND ASSUMPTIONS
Estimates of Households
These household projections are consistent with the 1990 census, as
enumerated, and the household estimates based on administrative records which
advance the 1990 census household count through the decade.3/ It is important
to note that these projections differ from previous CPS-based household
projections created by the U.S. Census Bureau4/ since independently derived
household estimates began only recently and were not available for previous
household projections.
The U.S. Census Bureau produces several other products which provide
differing estimates of the number of households; these include the American
Housing Survey (AHS), the Housing Vacancy Survey (HVS), and the Current
Population Survey (CPS).5/ The March CPS is the only one which presents annual
detailed characteristics on household composition. All three products indicate
a greater number of households than that found in the 1990 census count. Among
the reasons for these differences are survey weighting differences, sampling
frame variations, and reference month differences. After 1993, the CPS and
HVS were adjusted for the 1990 census net population undercount,6/ thus
showing an even larger number of households.
Starting Point Issues
The 1994 household estimates, used as the starting point for the household
projections, presented two challenges: lack of household type detail, and
"jump off" point differences. In the first challenge, the household estimates
consistent with the 1990 census as enumerated included data only for the total
number of U.S. households by 5-year age groups; specific details, such as type
of household and marital status of householder, required to project the future
household composition, were not available. Therefore, these items were
obtained from the 1990 census and carried forward based on proportional annual
changes in the CPS. For each year, 1990 through 1994, sums of these detailed
household types were calculated; these sums differed from the official
estimates. To obtain estimates by type consistent with the official total, the
detailed household-type projections were multiplied by the ratio of their sums
to the official total estimates for each year.
The second challenge emerged in the first projection year, 1995. The
difference between the total number of households, controlled to the previous
estimates (1990 through 1994) and the projected number of households with no
control produced dramatic shifts in the rate of household change from 1994 to
1995, an artifact of different methodologies to arrive at the total number.
Therefore, an overall check (by broad age group) was created by averaging the
annual modifications for the 5 overlapping years (1990 through 1994) and then
applying these averaged adjustments to the total projected number of
households by broad age group for every year from 1995 to 2010.
Demographic Assumptions
Various demographic factors influence trends in household change. Age at
first marriage influences the proportion of persons never married. Increased
age at first marriage can lead to an increase in the proportion of younger
persons in nonfamily living arrangements, either living alone or with
roommates and can reduce the proportion of persons maintaining family
households. Divorces can influence household composition by leading to
increases in adults forming their own households; that is, family households
with no spouse and nonfamily households, thereby reducing the proportion
maintaining married-couple households. The effect of nonmarital childbearing
augments the proportion of family households with no spouse present,
especially female family householders with children. Postponed or foregone
childbearing may also decrease the proportion of younger married couples with
children and delayed childbearing may increase the proportion of older married
couples with children. Longer life expectancy (assumed in the base population
projections P25-1130) increases the proportion of married couples in older
ages by deferring widowhood; however, differential increases in life
expectancy by sex can lead to more people living alone at older ages. All of
these demographic effects may be accentuated by the changes in the age
composition of the population.
Although many of these demographic trends changed dramatically during the
1970's and 1980's, recent evidence suggests some of these demographic
components may be slowing and, in some cases, reversing themselves7/. Hence,
the following assumptions and rationale underlie the household projections.
First, age at first marriage will continue to increase, but at a slower pace
than previously. Since the late 1970's and early 1980's, the quinquennial
increases in percent never married have become gradually smaller for younger
age groups (under 30). This suggests that we have passed the peak in the rate
of increase and may expect more modest future gains in age at first marriage.
Second, the divorce rate leveled off and declined slightly after 1979. This
had an especially striking effect in reducing the rate of change in the
married-couple household proportions ages 20-44. As these cohorts become older
during the next 15 years, a similar leveling can be expected at the older
ages. The leveling of divorce also moderates change in the proportion of
persons with children but no spouse in the home, especially for women.
Although the proportion of men maintaining other families has been increasing
through age 34, an acceleration of this trend seems unlikely.
Methodology
The methodology used to create the projections in this report employed five
household-type matrices: married-couple household; female family household, no
spouse present; male family household, no spouse present; nonfamily, female
householder; and nonfamily, male householder; and one marital status matrix
(never married, ever married). Each matrix contained proportions by the
demographic characteristics of the householder: age group (15-17, 18-19,
20-24, 25-29, 30-34, 35-44, 45-54, 55-64, 65-74, 75+), sex (male, female),
race (Total; White; Black; American Indian, Eskimo, and Aleut; Asian and
Pacific Islander), and Hispanic origin (Hispanic origin or not of Hispanic
origin). The projected number of households by type is the product of the
proportions by type of household and the household population at risk.
Compared to earlier household projection reports, data used in this report
are blended from a large number of sources: the 1990 census, the 1959-1993
Current Population Surveys (CPS), estimates of the number of households
(1990-1994), population estimates (1990-1994), and population projections
(1995-2010).
Creation of the household population.
By definition, the household population consists of the resident population
excluding people living in group quarters (i.e., 9 or more people living
together who are unrelated to the householder). Projections of the group
quarters population (GQ) are calculated using constant rates (by single years
of age, sex, race, and Hispanic origin) based on the 1990 census.8/ For each
year, the GQ rates were applied to future populations by age, sex, race, and
Hispanic origin to create the projected group quarters population. The
difference between the projected resident population and the projected group
quarters population is the projected household population. The projected
population in households was then summed for each year to form the ten broad
age groups specified earlier and the under 15 population.
Creation of future proportions maintaining households. The proportions used in
Series 1 were initially founded on a time series model. This model was based
on estimates of the annual changes in householder proportions for the past
three decades to project changes to the year 2010. One hundred annual
proportion series from 1959 to 1993 of marital status9/ and type of
householder10/ data by age and sex were prepared based on Current Population
Survey data. Slight changes in the CPS and its universe during the time period
required several modifications to the data in order to preserve a consistent
series of household proportions (see P25-986).
The 100 sets of proportions were first transformed using the logistic
transformation, which is often used to transform a data set of proportions to
better approximate a normal distribution. If xt is the proportion in a given
category for the year t, the transformed value, yt, is
yt = log(xt/(1-xt))
Since values of exactly 0 and exactly 1 cannot be used with this
transformation, values of 0 were defined to be outliers, effectively removing
them from the model fitting. There were no values of exactly 1. A time series
model (discussed below) was fitted to each yt series. Empirical outlier
detection techniques were applied as part of the model fitting. The model was
then used (with a restriction discussed below) to forecast yt, and forecasts
of xt were obtained from the inverse transformation,
xt = exp(yt)/(1 + exp(yt)).
The time series model used was the ARIMA(0,2,1) model, which involves twice
differencing the yt series and modeling autocorrelation in the resulting
differenced series with a moving average (MA) model of order 1. This model was
used in developing a previous set of household projections, as discussed in
more detail by Bell, et al. (1986).11/ Forecasts from this model (of the
transformed data) follow a straight line emanating from the last data point.
The slope of the forecast line is estimated by a weighted average of the year-
to-year changes (first differences), with more weight given to the changes in
recent years as long as the MA parameter is less than 1. The model implicitly
allows for changing trends in that as new data become available the slope of
the forecast line changes.
When the ARIMA(0,2,1) model was fitted to the 100 time series of transformed
proportions, estimates of the MA parameter were equal to 1 for about 75
percent of the series, and for many of the remaining series the parameter
estimates were near 1. When the MA parameter is 1, the ARIMA(0,2,1) model
reduces to a constant slope model with all the historical data given equal
weight in determining the slope. Rather than accept this result from the
fitted models, forecasting was instead performed with the MA parameter set
equal to .85 for every series. This was done for two reasons. First, since the
time series available are relatively short (35 observations), there is
actually considerable uncertainty about the correct or best values of the MA
parameters. Second, it was believed appropriate for the most recent data to
exert heavier influence in the determination of the slope of the forecast
line.
The preliminary projected results based on this model were judged to be on
the high side of the range of reasonable demographic assumptions. (See
Demographic Assumptions section.) Thus, Series 1 projections were developed by
using projected slopes that were less extreme than those obtained from the
model described above. Specifically, the change in the proportions never
married were reduced by two-thirds for ages under 35 and three-quarters for
ages 35 and over; the change in the proportions for married-family households
were reduced by one-third for all age groups. Since there was little projected
change in the remaining household types, those proportions were simply left at
their 1990 level.
In order to provide projections more refined than in the past with regard to
living alone and children in households, special tabulations from the 1990
census were generated for this report; these proportions are assumed to remain
constant at their 1990 levels throughout the projected time period. This
included the proportion of nonfamily households with people living alone, the
proportion of families by type of family with children, and the proportion of
married couples by sex of the reference person
Creation of marital status projections.
Since householders and spouses in married-couple families are limited to the
population who are ever married, projections of married-couple families
require projections of the marital status (never married and ever married) of
the future household population. First, initial proportions of the household
population ever married by age, sex, race, and Hispanic origin were created.
Then, future proportions were derived by multiplying the ever-married
proportion's projected rate of change (based on time series data for Series 1;
for Series 2 and 3 the projected change is 1.0; that is, no change) by the
previous year's proportion by age, sex, race, and Hispanic origin. These
proportions are multiplied by the projected household population for each
corresponding year to produce the projected ever-married population for each
year.
Creation of married-couple household projections.
Current proportions of married-couple families are based on the ever-married
universe. The change in the projected proportion of married-couple families
(based on time series data for Series 1; for Series 2 and 3, the projected
change is 1.0; that is, no change) is multiplied by the current rate for each
subsequent year, creating projected annual proportions of married-couple
households. Then, the projected proportions of married-couple households by
age, sex, race, and Hispanic origin for each year are applied to the future
ever-married population to produce the annual number of married-couple
households.12/
Creation of other family and nonfamily household projections.
The universe for female family households, male family households, and
nonfamily households is the total population in households minus the
population in married-couple households (husbands and wives). Starting
proportions from the 1990 census are created for each household type for the
base year by age, sex, race, and Hispanic origin. Then, projected proportions
are created by applying the annual change in the household formation by type
(based on time series data for Series 1; for Series 2 and 3, the projected
change is 1.0; that is, no change) to the proportion in the previous year. The
number of households by type are derived by multiplying the annual proportions
by the population for each year.
SYMBOLS
- Represents zero or rounds to zero.
NA Not available.
X Not applicable.
\1 See Byerly, Edwin R. and Kevin Deardorff, National and State Population
Estimates: 1990 to 1994, U.S. Bureau of the Census, Current Population
Reports, P25-1127, U.S. Government Printing Office, Washington, DC, 1995.
\2 See Census Bureau Press Release CB95-108, Estimates of Housing Units,
Households, and Persons per Household for States: April 1, 1990 and July 1,
1994, June 12, 1995.
\3 See Prevost, Ron, State Housing Unit and Household Estimates: April 1,
1980, to July 1, 1993, U.S. Bureau of the Census, Current Population Reports,
P25-1123, U.S. Government Printing Office, Washington, DC, 1994.
\4 Current Population Reports P25-986; P25-805; P25-607; P25-394; P25-360;
P20-123; P20-90; P20-69; and P20-42.
\5 The American Housing Survey and the Housing Vacancy Survey focus on
housing units. By definition, the number of households is equivalent to the
number of occupied housing units.
\6 Beginning in 1994, the Current Population Survey began using in its base
population controls the 1990 census adjusted for undercount by the Post
Enumeration Survey. For more specific details on the Current Population Survey
population base, see Bureau of Labor Statistics, "Introduction of 1990
Census-Based Population Controls" in Employment and Earnings, Vol. 41, No. 2,
February 1994, pp.32-37.
\7 For further information see Current Population Reports, P20-483 and
P20-484.
\8 These numbers cannot be directly compared to published results by age and
race because modifications were made to the data to adjust for age
misreporting and the reporting of an unspecified race in the 1990 census. This
file also includes corrections to the census made through March 1994.
\9 Only one marital status group needed to be calculated since the remainder
is ever married.
\10 These householder types included married-couple householders, family
householders with no spouse present, and nonfamily householders; this series
also included proportions of persons in households not related to the
householder.
\11 Bell, William R., James E. Bozik, Sandra K. McKenzie, and Holly B.
Shulman (1986) Time Series Analysis of Household Headship Proportions:
1959-1985, Research Report Number 86/01, Statistical Research Division, U.S.
Bureau of the Census.
\12 As a technical refinement to take into account current data collection
procedures which distinguish whether the husband or wife is listed as the
reference person in a married-couple household, the following adjustment was
made. The number of married-couple men and women was obtained as the average
number of males and females maintaining married-couple households. Using
proportions of reported male and female householders in married-couple
households from the 1990 census, the sex of the householder was determined for
each age/race/origin group; the remainder were classified as spouses.