help ie_reg

Title

ie_reg -- intrinsic estimator for age, period, cohort (APC) applications

Syntax

ie_reg depvar [indepvars] [if] [in] [weight] [, options]

options

irr eform results

Description

ie_reg computes coefficients from an APC analysis characterized by a design matrix that is not full rank
due to perfect linear dependence between age, period, and cohort. However, ie_reg does not require strict linear dependence
to estimate APC parameters.

The dependent variable is assumed to be in the form of a log rate or rate.
In order to obtain APC estimates that are normalized according to conventional applications (i.e., apc_ie),
it is necessary that an ANOVA design matrix be constructed using the last factor level of each
APC factor as the reference as shown below. Optionally, the user may request the full set of ANOVA normalized estimates
that include the reference category which are obtained using ie_norm, a modified version of Ben Jann's devcon utility with
exactly the same syntax.

Example code for ANOVA design coding

qui tab age, gen(a)
scal arow = r(r)
qui tab period, gen(p)
scal prow = r(r)
qui gen cohort = period - age
qui tab cohort, gen(c)
scal crow = r(r)

* construct ANOVA normalization using last category as reference

forval i = 1/`=arow' {
gen aC`i' = a`i' - a`=arow'
}

forval i = 1/`=prow' {
gen pC`i' = p`i' - p`=prow'
}

forval i = 1/`=crow' {
gen cC`i' = c`i' - c`=crow'
}

Examples

APC regression model

ie_reg logr aC1-aC6 pC1-pC3 cC1-cC9

fully normalized solution

ie_norm, groups(aC1-aC7, pC1-pC4, cC1-cC10)

Estimation Details

ie_reg employes a generalized inverse.

Saved Results

ie_reg saves the following in e():

Scalars

e(N) number of cells

e(ll) MSE

e(k) number of estimated parameters

Macros

e(depvar) name of dependent variable

Matrices

e(Coef) 1 X K vector of estimates

e(Var) K X K variance-covariance matrix

Functions

e(sample) marks estimation sample

References

Daniel A. Powers (2012). "Black-White Differences in Maternal Age, Maternal Birth Cohort, and
Period Effects on Infant Mortality in the U.S. (1983-2002)." Presented at the annual meetings of the Population
Research Association of America, San Francisco, CA, May 4 2012.

Author

Daniel A. Powers, University of Texas at Austin, dpowers@austin.utexas.edu

Also see

Online: help for devcon and help for ie_rate