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Household and Living Arrangement Projections at the Subnational Level: An Extended Cohort-Component Approach

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Demography

Abstract

This article presents the core methodological ideas and empirical assessments of an extended cohort-component approach (known as the “ProFamy model”), and applications to simultaneously project household composition, living arrangements, and population sizes–gender structures at the subnational level in the United States. Comparisons of projections from 1990 to 2000 using this approach with census counts in 2000 for each of the 50 states and Washington, DC show that 68.0 %, 17.0 %, 11.2 %, and 3.8 % of the absolute percentage errors are <3.0 %, 3.0 % to 4.99 %, 5.0 % to 9.99 %, and ≥10.0 %, respectively. Another analysis compares average forecast errors between the extended cohort-component approach and the still widely used classic headship-rate method, by projecting number-of-bedrooms–specific housing demands from 1990 to 2000 and then comparing those projections with census counts in 2000 for each of the 50 states and Washington, DC. The results demonstrate that, compared with the extended cohort-component approach, the headship-rate method produces substantially more serious forecast errors because it cannot project households by size while the extended cohort-component approach projects detailed household sizes. We also present illustrative household and living arrangement projections for the five decades from 2000 to 2050, with medium-, small-, and large-family scenarios for each of the 50 states; Washington, DC; six counties of southern California; and the Minneapolis–St. Paul metropolitan area. Among many interesting numerical outcomes of household and living arrangement projections with medium, low, and high bounds, the aging of American households over the next few decades across all states/areas is particularly striking. Finally, the limitations of the present study and potential future lines of research are discussed.

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Notes

  1. For example, changes in headship rates may depend on whether the census or survey was carried out in the daytime or evening and whether more women or men were available to complete the questionnaire.

  2. The ProFamy model was built on methodological advances in multidimensional demography (Land and Rogers 1982; Rogers 1975, 1995; Schoen 1988; Willekens et al. 1982) and based on Bongaarts’s and Zeng’s one-sex family status life table models (Bongaarts 1987; Zeng 1986, 1988, 1991).

  3. The “subnational level” referred in this article does not include small counties/cities/towns and other kinds of small areas (possibly even tracts or block groups) that do not have reasonably reliable data from which to estimate the demographic summary parameters.

  4. A married or cohabiting man cannot be a reference person because we already chose the married or cohabiting woman as the reference person, and one household cannot have two reference persons.

  5. The seven marital/union statuses are (1) never-married and not cohabiting, (2) married, (3) widowed and not cohabiting, (4) divorced and not cohabiting, (5) never-married and cohabiting, (6) widowed and cohabiting, and (7) divorced and cohabiting.

  6. Because number of coresiding children is equal to or less than parity, the number of composite statuses of parity and coresiding children is rather than (6 × 6).

  7. Ideally, one may wish to differentiate the marital-/union-status transition probabilities by parity and coresidence status with children. Such differentiation is, however, not practically feasible because it would require a data set with a very large sample size (not available to us currently but not theoretically impossible at some future time point for some specific populations) for estimating the parity-/coresidence-/marital-status-/union-status–specific transition probabilities at each single age for men and women of each race group, with a reasonable accuracy.

  8. With the model standard schedules in hand, analysts can concentrate on projecting future demographic summary parameters. This can be done by using conventional time series analysis by statistical software (e.g., SAS, SPSS, or STATA) or expert opinion approach. Time series data on other related socioeconomic covariates (e.g., average income, education, urbanization) also can be used in projecting the demographic summary parameters.

  9. The numerical projections reported in this article were calculated with the ProFamy computer software program, which contains a demographic database of the U.S. age-specific schedules of demographic rates to assist users in making projections. The ProFamy software for household and living arrangements projections can be downloaded (http://www.profamy.com/).

  10. National Survey of Family Households (NSFH) conducted in 1987–1988, 1992–1994, and 2002; National Survey of Family Growth (NSFG) conducted in 1983, 1988, 1995, and 2002; Current Population Surveys (CPS) conducted in 1980, 1985, 1990, and 1995; Survey of Income and Program Participation (SIPP) conducted in 1996. (See Zeng et al. (2012) for discussions on justifications of pooling data from the four surveys.)

  11. We compare six main indices of household projections and six main indices of population projections for each of the 50 states and Washington, DC, and thus both of the number of household indices and the total number of population indices under comparisons are 306.

  12. We performed another set of the tests of projections from 2000 onward using ProFamy approach and data prior to 2001 and comparing the projections and the American Community Survey (ACS) observations in 2006 for each of the 50 states and Washington, DC. It turns out that 34.2 %, 35.0 %, 21.9 %, and 9.0 % of the percentage errors of the 306 indices of the household projections are <1.0 %, 1.0 % to 2.99 %, 3.0 % to 4.99 %, and 5.0 % to 9.99 %, respectively, and none is more than 10 %. A similar scale and pattern of forecast errors were also found in tests of projections from 2000 onward using ProFamy approach and data prior to 2001 and comparing the projected and ACS observations in 2006 and 2009 for the six SC counties and the M-S area (Wang 2009a,b, 2011a,b). We did not present detailed results from these additional tests here (they are available upon request), mainly because the 2006 and 2009 ACS data may not be accurate enough to serve as a benchmark standard for the validation tests (Alexander et al. 2010; Swanson 2010).

  13. The zero-bedroom housing unit term means that the bedroom is mixed with the living room.

  14. Our research indicates that the increase in proportion of American households with six or more persons in 2000 compared with 1990 is due to the changing racial composition of the population, given that Hispanic, Asian, and other nonwhite and nonblack minority groups have higher proportions of large households with six or more persons and are growing substantially faster.

  15. One common approach in population projection is to hold some of the current demographic rates constant throughout the projection horizon (e.g., Day 1996; Treadway 1997). Smith et al. (2001:83–84) argued that neither the direction nor the magnitude of future changes can be predicted accurately, and thus if upward or downward movements are more or less equally likely, the constant demographic rates provide a reasonable forecast of future rates.

  16. Low mortality may (1) reduce the U.S. average household size through increasing number of elderly households that are mostly small (one or two persons) and (2) increase the size of some households by increasing the survivorship of adults and children in these larger households. The effects of the latter may be smaller than those of the former because a further decrease in adult and child mortality in the United States is limited, but the prolongation of elderly life span may have larger effects.

  17. The race-/sex-specific demographic parameters (TFR is parity-specific) (see parameters (a–h in Table 1, panel 3) in the medium-, small-, and large-family scenarios in selected years from 2000 to 2050 for each of the 50 states; Washington, DC; each SC county; and the M-S area can be listed in one large table. Including them in this article would require an unfeasibly large number of pages.

  18. Zeng et al. (2010) preliminarily assessed the projection accuracy of the combined approach using the ratio method and the ProFamy approach by calculating projections from 1990 to 2000 and comparing projections with census-observed counts in 2000 for sets of randomly selected 25 counties and 25 cities that are more or less evenly distributed across the United States. The comparisons show that most forecast errors are reasonably small, at less than 5 %.

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Acknowledgments

The research reported in this article was mainly supported by NIA/NIH SBIR Phase I and Phase II project grants. We also thank the Population Division of U.S. Census Bureau, NICHD (grant 5 R01 HD41042-03), NIA (grant 1R03AG18647-1A1) and NSFC international collaboration project (grant 71110107025), Duke University, Peking University, and the Max Planck Institute for Demographic Research for supporting related basic and applied research. We thank Huashuai Chen for preparing the graphics.

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Authors and Affiliations

  1. Center for the Study of Aging and Human Development and Geriatric Division of Medical School, Population Research Institute, Duke University, Box 3003, Durham, NC, 27710, USA

    Yi Zeng

  2. Center for Healthy Aging and Development Studies, National School of Development, Peking University, Beijing, 100871, China

    Yi Zeng

  3. Population Research Institute and Department of Sociology, Center for Population Health and Aging, Duke University, Durham, NC, USA

    Kenneth C. Land

  4. Center for Population Health and Aging of Population Research Institute, Duke University, Household and Consumption Forecasting, Inc., Durham, NC, USA

    Zhenglian Wang

  5. Center for Study of Aging and Human Development, Duke University, Durham, NC, USA

    Danan Gu

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  1. Yi Zeng
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Zeng, Y., Land, K.C., Wang, Z. et al. Household and Living Arrangement Projections at the Subnational Level: An Extended Cohort-Component Approach. Demography 50, 827–852 (2013). https://doi.org/10.1007/s13524-012-0171-3

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