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.