Identification of Parameters in Cohort Models

Abstract

Linear-additive age-period cohort models that permit the maximum number of aging effects, period effects, and cohort effects (full cohort models) are underidentified. In this article, some general rules will be given for detecting identified and underidentified parameters in any full cohort model under zero-sum restrictions. It will be demonstrated that only one parameter in a dimension is identified whenever the number of parameters in this dimension is uneven. Otherwise, no parameter is identified. Full cohort models for larger tables contain more overidentifying restrictions, but the number of identified parameters never exceeds four. Furthermore, it will be shown which additional parameter restrictions are sufficient and which are inappropriate for the identification of all parameters in a model.

Get full access to this article

View all access options for this article.

References

BALTES, P. B. (1968) “Longitudinal and cross-sectional sequences in the study of age and generation effects.” Human Development 11: 145-171.

BALTES, P. B. and J. R. NESSELROADE (1970) “Multivariate longitudinal and cross-sectional sequences for analyzing ontogenetic and generational change: a methodological note.” Developmental Psychology 1: 169-171.

FIENBERG, S. E. and W. M. MASON (1978) “Identification and estimation of age-period-cohort models in the analysis of discrete archival data,” in K. F. Schuessler (ed.) Sociological Methodology 1979. San Francisco: Jossey-Bass.

FIENBERG, S. E. and W. M. MASON (1976) “Identification and estimation of age, period, and cohort effects in the analysis of discrete archival data.” American Statistical Association: Proceedings of the Social Statistics Section, Part 1, 133-137.

GLENN, N. D. (1976) “Cohort analysts' futile quest. Statistical attempts to separate age, period and cohort effects.” Amer. Soc. Rev. 41: 900-904.

HAYS, W. L. (1973) Statistics for the Social Sciences (2nd ed). London: Holt, Rinehart & Winston.

INGLEHART, R. (1981) “Post-materialism in an environment of insecurity.” Amer. Pol. Sci. Rev. 75: 880-900.

JÖRESKOG, K. G. (1973) “A general method for estimating a linear structural equation system,” in A. S. Goldberger and O. D. Duncan (eds.) Structural Equation Models in the Social Sciences. New York: Seminar Press.

JÖRESKOG, K. G. and D. SÖRBOM (1978), LISRELIV. Analysis of Linear Structural Relationships by the Method of Maximum Likelihood. Chicago: International Education Service.

10.

JÖRESKOG, K. G. and D. SÖRBOM (1977) “Statistical models and methods for analysis of longitudinal data,” in D. J. Aigner and A. S. Goldberger (eds.) Latent Variables in Socioeconomic Models. Amsterdam: North-Holland.

11.

JÖRESKOG, K. G. and M. van THILLO (1972) “LISREL—a general computer program for estimating a linear structural equation system involving unmeasured variables.” Research Report 73-75. University of Uppsala.

12.

KNOKE, D. AND M. HOUT (1976) “Reply to Glenn.” Amer. Soc. Rev. 41: 905-908.

13.

KNOKE, D. AND M. HOUT (1974) “Social and demographical factors in American party affiliations, 1952-72.” Amer. Soc. Rev. 39: 700-713.

14.

MASON, K. O. , W. MASON , and H. H. WINSBOROUGH , (1976) “Reply to Glenn.” Amer. Soc. Rev. 41: 904-905.

15.

MASON, K. O. , W. MASON , H. H. WINSBOROUGH and W. K. POOLE (1973) “Some methodological issues in cohort analysis of archival data.” Amer. Soc. Rev. 38: 242-258.

16.

PULLUM, T. W. (1980) “Separating age, period, and cohort effects in white U.S. fertility, 1920-1970.” Social Sci. Research 9: 225-244.

17.

PULLUM, T. W. (1977) “Parametrizing age, period, and cohort effects: an application to U.S. delinquency rates, 1964-1973,” in K. F. Schuessler (ed.) Sociological Methodology 1978. San Francisco: Jossey-Bass.

18.

WERTS, C. E. , K. G. JÖRESKOG , and R. L. LINN (1973) “Identification and estimation in path analysis with unmeasured variables.” Amer. J. of Sociology 78: 1469-1484.

19.

WHEATON, B. , B. MUTHEN , D. F. ALWIN , and G. F. SUMMERS (1977) “Assessing reliability and stability in panel models,” in D. R. Heise (ed.) Sociological Methodology 1977. San Francisco: Jossey-Bass.