Generalized linear models with equality constraints on age-period-cohort effect > s
Syntax
apc_cglim depvar [indepvars] [if exp] [in range] [weight] , constraint(constraintspec) agepfx(string) periodpfx(string) cohortpfx(string) [age(varname) period(varname) cohort(varname) generate(newvarname) glm_options ]
Replay syntax
apc_cglim [, glm_options ]
apc_cglim allows all varlists and weights that are allowed by glm.
Description
apc_cglim estimates age-period-cohort models in which a single equality constraint on the coefficients is used to solve the age-period-cohort identification problem. apc_cglim adds an indicator variable for each unique value of age, period and cohort to the list of independent variables, applies a constraint to these indicator variables, then executes glm.
Note that although CGLIM models can, in general, involve multiple constraints, apc_cglim implements only one constraint. See Yang, Fu and Land (2004) and Mason and Smith (1985) for discussion of CGLIM models.
Normalizations and constraints
The first category in each of age, period and cohort is omitted from the set of indicator variables. The coefficient on one additional indicator variable must be constrained to achieve identification.
apc_cglim allows constraints that set the coefficient on one indicator variable equal to the coefficient on another indicator variable. constraintspec is a string of the form "r#=s#" where r and s can each be either a, p or c and where # can be any value of age, period or cohort that appears in the dataset. For example, constraint("a2=c6") sets the coefficient on the indicator variable for age=2 equal to the coefficient on the indicator variable for cohort=6.
The value for the first coefficient cannot be the lowest value of the category since the lowest indicator variable is already omitted. To constrain a coefficient to be zero, make the second coefficient in the constraint be the lowest value in a category, for example a2=a1 if the lowest value of age is 1 and you want to constrain the coefficient on the age=2 indicator to be zero.
Options
agepfx(string), periodpfx(string) and cohortpfx(string) specify stub names for the generated indicator variables. The names appear in the output, and the indicator variables will in the dataset after use. Variables with these names must not already exist.
age(varname), period(varname) and cohort(varname) specify the age, period and cohort variables. At least two of these three must be specified. If all three are specified, they must satisfy age+cohort=period. If only two are specified, the missing variable is generated according to age+cohort=period.
generate(newvarname) stores the generated value of age, period or cohort in a new variable.
glm_options can be any valid options for glm.
References
Yang, Y., Fu, W., and Land, K. 2004. A Methodological Comparison of Age-Period-Cohort Models: The Intrinsic Estimator and Conventional Generalized Linear Models. Sociological Methodology 34(1), 75-110.
Mason, W.M., and Smith, H.L. 1985. Age-Period-Cohort Analysis and the Study of Deaths from Pulmonary Tuberculosis. Pp. 151-228 in Cohort Analysis in Social Research, edited by W.M. Mason and S.E. Fienberg. New York: Springer-Verlag.
Authors
Sam Schulhofer-Wohl Department of Economics The University of Chicago 1126 E. 59th St. Chicago, IL 60637 sschulh1@uchicago.edu
Yang Yang, Ph.D. Department of Sociology Population Research Center and Center on Aging at NORC The University of Chicago 1126 E. 59th St. Chicago, IL 60637 (O) 773-834-1113 yangy@uchicago.edu
Also see
Online: help for glm; apc_ie (if installed).