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Generalized linear models with equality constraints on age-period-cohort effect> sSyntax

apc_cglimdepvar[indepvars] [ifexp] [inrange] [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_cglimallows allvarlistsandweightsthat are allowed byglm.

Description

apc_cglimestimates age-period-cohort models in which a single equality constraint on the coefficients is used to solve the age-period-cohort identification problem.apc_cglimadds an indicator variable for each unique value ofage,periodandcohortto the list of independent variables, applies a constraint to these indicator variables, then executesglm.Note that although CGLIM models can, in general, involve multiple constraints,

apc_cglimimplements only one constraint. See Yang, Fu and Land (2004) and Mason and Smith (1985) for discussion of CGLIM models.

Normalizations and constraintsThe first category in each of

age,periodandcohortis omitted from the set of indicator variables. The coefficient on one additional indicator variable must be constrained to achieve identification.

apc_cglimallows constraints that set the coefficient on one indicator variable equal to the coefficient on another indicator variable.constraintspecis a string of the form "r#=s#" whererandscan each be eithera,porcand where#can be any value ofage,periodorcohortthat appears in the dataset. For example,constraint("a2=c6")sets the coefficient on the indicator variable forage=2equal to the coefficient on the indicator variable forcohort=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=a1if the lowest value ofageis 1 and you want to constrain the coefficient on theage=2indicator to be zero.

Options

agepfx(string),periodpfx(string)andcohortpfx(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)andcohort(varname)specify theage,periodandcohortvariables. At least two of these three must be specified. If all three are specified, they must satisfyage+cohort=period. If only two are specified, the missing variable is generated according toage+cohort=period.

generate(newvarname)stores the generated value ofage,periodorcohortin a new variable.

glm_optionscan be any valid options forglm.

ReferencesYang, Y., Fu, W., and Land, K. 2004. A Methodological Comparison of Age-Period-Cohort Models: The Intrinsic Estimator and Conventional Generalized Linear Models.

Sociological Methodology34(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 inSocial Research, edited by W.M. Mason and S.E. Fienberg. New York: Springer-Verlag.

AuthorsSam 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 seeOnline: help for glm; apc_ie (if installed).