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.