{smcl}
{* 24Jun2006}{...}
{hline}
help for {hi:apc_cglim}
{hline}

{title:Generalized linear models with equality constraints on age-period-cohort effects}

{p 4}Syntax

{p 8 14}{cmd:apc_cglim} {it:depvar} [{it:indepvars}]
[{cmd:if} {it:exp}] [{cmd:in} {it:range}] [{it:weight}]
{cmd:,}
{cmd:constraint(}{it:constraintspec}{cmd:)}
{cmd:agepfx(}{it:string}{cmd:)}
{cmd:periodpfx(}{it:string}{cmd:)}
{cmd:cohortpfx(}{it:string}{cmd:)}
{bind:[{cmd:age(}{it:varname}{cmd:)}}
{cmd:period(}{it:varname}{cmd:)}
{cmd:cohort(}{it:varname}{cmd:)}
{cmdab:gen:erate(}{it:newvarname}{cmd:)}
{bind:{it:glm_options} ]}

{p 4}Replay syntax

{p 8 14}{cmd:apc_cglim} {bind:[{cmd:,}} {bind:{it:glm_options} ]}

{p 4} {cmd:apc_cglim} allows all {it:varlists} and {it:weights} that are 
allowed by {cmd:glm}.


{title:Description}

{p} {cmd: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. {cmd:apc_cglim} adds an 
indicator variable for each unique value of {it:age}, {it:period} and 
{it:cohort} to the list of independent variables, applies a constraint to 
these indicator variables, then executes {cmd:glm}.

{p} Note that although CGLIM models can, in general, involve multiple 
constraints, {cmd:apc_cglim} implements only one constraint. See Yang, Fu 
and Land (2004) and Mason and Smith (1985) for discussion of CGLIM models.


{title:Normalizations and constraints}

{p} The first category in each of {it:age}, {it:period} and {it:cohort} is 
omitted from the set of indicator variables. The coefficient on one 
additional indicator variable must be constrained to achieve 
identification.

{p} {cmd:apc_cglim} allows constraints that set the coefficient on one 
indicator variable equal to the coefficient on another indicator variable. 
{it:constraintspec} is a string of the form "{it:r#=s#}" where {it:r} and 
{it:s} can each be either {it:a}, {it:p} or {it:c} and where {it:#} can be 
any value of {it:age}, {it:period} or {it:cohort} that appears in the 
dataset. For example, 
{cmd:constraint(}{it:"a2=c6"}{cmd:)} sets the coefficient on the indicator 
variable for {it:age=2} equal to the coefficient on the indicator variable 
for {it:cohort=6}. 

{p} 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 {it:a2=a1} if 
the lowest value of {it:age} is 1 and you want to constrain the 
coefficient on the {it:age=2} indicator to be zero.


{title:Options}

{p 0 4} {cmd:agepfx(}{it:string}{cmd:)}, 
{cmd:periodpfx(}{it:string}{cmd:)} and {cmd:cohortpfx(}{it:string}{cmd:)} 
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.

{p 0 4} {cmd:age(}{it:varname}{cmd:)}, {cmd:period(}{it:varname}{cmd:)} 
and {cmd:cohort(}{it:varname}{cmd:)} specify the {it:age}, {it:period} and 
{it:cohort} variables. At least two of these three must be specified. If 
all three are specified, they must satisfy {it:age}+{it:cohort}={it:period}.
If only two are specified, the missing variable is generated according to 
{it:age}+{it:cohort}={it:period}.

{p 0 4} {cmd:generate(}{it:newvarname}{cmd:)} stores the generated value 
of {it:age}, {it:period} or {it:cohort} in a new variable.

{p} {it:glm_options} can be any valid options for {cmd:glm}.


{title:References}

{p 0 4}Yang, Y., Fu, W., and Land, K. 2004. A Methodological Comparison of
Age-Period-Cohort Models: The Intrinsic Estimator and Conventional
Generalized Linear Models. {it:Sociological Methodology} 34(1), 75-110.

{p 0 4}Mason, W.M., and Smith, H.L. 1985. Age-Period-Cohort Analysis and 
the Study of Deaths from Pulmonary Tuberculosis. Pp. 151-228 in
{it:Cohort Analysis in Social Research}, edited by W.M. Mason and
S.E. Fienberg. New York: Springer-Verlag.


{title: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


{title:Also see}

{p 0 19} Online: help for {help glm}; {help apc_ie} (if installed).{p_end}