Abstract
A fundamental limitation of current multistate life table methodology-evident in recent estimates of active life expectancy for the elderly-is the inability to estimate tables from data on small longitudinal panels in the presence of multiple covariates (such as sex, race, and socioeconomic status). This paper presents an approach to such an estimation based on an isomorphism between the structure of the stochastic model underlying a conventional specification of the increment-decrement life table and that of Markov panel regression models for simple state spaces. We argue that Markov panel regression procedures can be used to provide smoothed or graduated group-specific estimates of transition probabilities that are more stable across short age intervals than those computed directly from sample data. We then join these estimates with increment-decrement life table methods to compute group-specific total, active, and dependent life expectancy estimates. To illustrate the methods, we describe an empirical application to the estimation of such life expectancies specific to sex, race, and education (years of school completed) for a longitudinal panel of elderly persons. We find that education extends both total life expectancy and active life expectancy. Education thus may serve as a powerful social protective mechanism delaying the onset of health problems at older ages.
The text of this article is only available as a PDF.
References
Andreev, E., W. Lutz, and S. Scherbov. 1989. “Averaging Life Expectancy.” Working Paper 89-35, Population Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
Branch, L.G., Guralnik, J.M., Foley, D.J., Kohout, F.J., Wetle, T.T., Ostfeld, A., & Katz, S. (
1991
). “Active Life Expectancy for 10,000 Caucasian Men and Women in Three Communities.”
. Journal of Gerontology: Medical Sciences
, 46
, 145
–50
.Branch, L.G., & Ku, L. (
1989
). “Transition Probabilities to Dependency, Institutionalization and Death among the Elderly over a Decade.”
. Journal of Aging and Health
, 1
, 370
–408
. 10.1177/089826438900100306Chiang, C.L. (
1984
). The Life Table and Its Applications
. Malabar, FL
: Krieger Publishing Co.
.Coale, A., & Kisker, E.E. (
1986
). “Mortality Crossover: Reality or Bad Data?”
. Population Studies
, 40
, 389
–401
. 10.1080/0032472031000142316Coleman, J.S. (
1968
). “The Mathematical Study of Social Change.”
. In Blalock, H.M., & Blalock, A.B. (Eds.), Methodology in Social Research
(pp. 428
–478
). New York
: McGraw-Hill
.Efron, B. (
1982
). The Jackknife, the Bootstrap and Other Resampling Plans
. Philadelphia
: Society for Industrial and Applied Mathematics
.Gill, R.D. (
1992
). “Multistate Life-Tables and Regression Models.”
. Mathematical Population Studies
, 3
, 259
–76
. 10.1080/08898489209525345Guilkey, D.K., & Rindfuss, R.R. (
1987
). “Logistic Regression Multivariate Life Tables: A Communicable Approach.”
. Sociological Methods and Research
, 16
, 276
–300
. 10.1177/0049124187016002004Guralnik, J.M., Land, K.C., Blazer, D., Fillenbaum, G.G., & Branch, L.G. (
1993
). “Educational Status and Active Life Expectancy among Older Blacks and Whites.”
. New England Journal of Medicine
, 329
(8
), 110
–16
. 10.1056/NEJM199307083290208Hannan, M.T. (
1984
). “Multistate Demography and Event History Analysis.”
. In Diekmann, A., & Mitter, P. (Eds.), Stochastic Modeling of Social Processes
(pp. 39
–88
). New York
: Academic Press
.Hayward, M.D., & Grady, W.R. (
1990
). “Work and Retirement among a Cohort of Older Men in the United States, 1966–1983.”
. Demography
, 27
, 337
–56
. 10.2307/2061372Hoem, J.M. (
1977
). “A Markov Chain Model of Working Life Tables.”
. Scandinavian Actuarial Journal
, 1977
, 1
–20
.Hoem, J.M., & Jensen, U.F. (
1982
). “Multistate Life Table Methodology: A Probabilist Critique.”
. In Land, K.C., & Rogers, A. (Eds.), Multidimensional Mathematical Demography
(pp. 155
–264
). New York
: Academic Press
.Katz, S., Branch, L.G., Branson, M.H., Papsidero, J.A., Beck, J.C., & Greer, D.S. (
1983
). “Active Life Expectancy.”
. New England Journal of Medicine
, 309
, 1218
–24
. 10.1056/NEJM198311173092005Katz, S., Ford, A.B., Moskowitz, R.W., Jackson, B.A., & Jaffe, M.W. (
1963
). “Studies of Illness in the Aged.”
. Journal of the American Medical Association
, 185
, 94
–99
.Keyfitz, N. (
1989
). Applied Mathematical Demography
. 2nd ed.New York
: Springer-Verlag
.Kitagawa, E.M., & Hauser, P.M. (
1973
). Differential Mortality in the United States: A Study in Socioeconomic Epidemiology
. Cambridge, MA
: Harvard University Press
.Korn, E.L., & Graubard, B.I. (
1991
). “Epidemiologic Studies Utilizing Surveys: Accounting for the Sampling Design.”
. American Journal of Public Health
, 81
, 1166
–73
. 10.2105/AJPH.81.9.1166Land, K.C., & Hough, G.C. (
1986
). “Improving the Accuracy of Intercensal Estimates and Postcensal Projections of the Civilian Noninstitutional Population: A Parameterization of Institutional Prevalence Rates.”
. Journal of the American Statistical Association
, 81
, 62
–74
. 10.2307/2287968Land, K.C. (
1989
). “New Methods for Tables of School Life, with Applications to U.S. Data from Recent School Years.”
. Journal of the American Statistical Association
, 84
, 63
–75
. 10.2307/2289847Land, K.C., & Schoen, R. (
1982
). “Statistical Methods for Markov-Generated Increment-Decrement Life Tables with Polynomial Gross Flow Functions.”
. In Land, K.C., & Rogers, A. (Eds.), Multidimensional Mathematical Demography
(pp. 265
–346
). New York
: Academic Press
.Ledent, J. (
1980
). “Multistate Life Tables: Movement versus Transition Perspectives.”
. Environment and Planning A
, 12
, 533
–62
. 10.1068/a120533U.S. Decennial Life Tables for 1979–81. Vol. 2, State Life Tables, Number 34, North Carolina
. (1986
). Washington, DC
: U.S. Government Printing Office
.Vital Statistics of the United States, 1987: Life Tables
. (1990
). Washington, DC
: U.S. Government Printing Office
.Norberg, R. (
1991
). “Reserves in Life and Pension Insurance.”
. Scandinavian Actuarial Journal
, 74
, 3
–24
.Preston, S.H., Keyfitz, N., & Schoen, R. (
1972
). Causes of Death: Life Tables for National Populations
. New York
: Seminar Press
.Rendall, M.S. (
1991
). “Estimation of Variance About Working Life Expectancies for Older Americans.”
. Providence
: Brown University
.Rogers, A. (
1975
). Introduction to Multiregional Mathematical Demography
. New York
: Wiley
.Rogers, A. (
1992
). “Heterogeneity and Selection in Multistate Population Analysis.”
. Demography
, 29
, 31
–38
. 10.2307/2061361Rogers, A., Rogers, R.G., & Belanger, A. (
1990
). “Longer Life but Worse Health? Measurement and Dynamics.”
. The Gerontologist
, 30
, 640
–49
.Rogers, A., Rogers, R.G., & Branch, L.G. (
1989
). “A Multistate Analysis of Active Life Expectancy.”
. Public Health Reports
, 104
, 222
–26
.Sanders, B.S. (
1964
). “Measuring Community Health Levels.”
. American Journal of Public Health
, 54
, 1063
–70
. 10.2105/AJPH.54.7.1063Saveland, W., & Glick, P.C. (
1969
). “First-Marriage Decrement Tables by Color and Sex for the United States in 1958–60.”
. Demography
, 6
, 243
–60
. 10.2307/2060394Schoen, R. (
1975
). “Constructing Increment-Decrement Life Tables.”
. Demography
, 12
, 313
–24
. 10.2307/2060768Schoen, R., & Land, K.C. (
1979
). “A General Algorithm for Estimating a Markov-Generated Increment-Decrement Life Table, with Applications to Marital Status Patterns.”
. Journal of the American Statistical Association
, 74
, 761
–76
. 10.2307/2286398Schoen, R., & Woodrow, K. (
1980
). “Labor Force Status Life Tables for the United States, 1972.”
. Demography
, 17
, 297
–322
. 10.2307/2061105Singer, B., & Spilerman, S. (
1974
). “Social Mobility Models for Heterogeneous Populations.”
. Sociological Methodology
, 1974
, 356
–401
.Singer, B. (
1976
). “The Representation of Social Processes by Markov Models.”
. American Journal of Sociology
, 82
, 1
–54
. 10.1086/226269Smith, S.J. (
1982
). Tables of Working Life: The Increment-Decrement Model
. Washington, DC
: Bureau of Labor Statistics
.Smith, S.J. and F.W. Horvath. 1984. “New Developments in Multistate Working Life Tables.” Paper presented at the annual meetings of the Population Association of America, Minneapolis.
Stockwell, E.G., & Nam, C.B. (
1963
). “Illustrative Tables of School Life.”
. Journal of the American Statistical Association
, 58
, 1113
–24
. 10.2307/2283337Sullivan, D.F. (
1971
). “A Single Index of Mortality and Morbidity.”
. HSMHA Health Reports
, 86
, 347
–54
. 10.2307/4594169Trussell, J., & Hammerslough, C. (
1983
). “A Hazards-ModelAnalysis of the Covariates of Infant and Child Mortality in Sri Lanka.”
. Demography
, 20
, 1
–26
. 10.2307/2060898Tuma, N.B., Hannan, M.T., & Groeneveld, L.P. (
1979
). “Dynamic Analysis of Event Histories.”
. American Journal of Sociology
, 84
, 820
–54
. 10.1086/226863Vaupel, J.W., & Yashin, A.I. (
1985
). “Heterogeneity’s Ruses: Some Surprising Effects of Selection on Population Dynamics.”
. The American Statistician
, 39
, 176
–85
. 10.2307/2683925Wiener, J.M., Hanley, R.J., Clark, R., & Van Nostrand, I.F. (
1990
). “Measuring the Activities of Daily Living: Comparisons across National Surveys.”
. Journal of Gerontology: Social Sciences
, 45
, 229
–37
.Wilmoth, J. 1993. “Indirect Estimation of Oldest-Old Mortality Trends: A Critical Application of the Coale-Kisker Procedure.” Paper presented at the annual meetings of the Population Association of America, Cincinnati, Ohio.
© Population Association of America 1994
1994
Issue Section:
Deah and Active Life Expectancy
