help ie_reg-------------------------------------------------------------------------------

Title

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

Syntaxie_regdepvar[indepvars] [if] [in] [weight] [,options]

optionsDescription -------------------------------------------------------------------------irreform resultsDescription

ie_regcomputes 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_regdoes 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 thelastfactor 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 usingie_norm, a modified version of Ben Jann'sdevconutility with exactly the same syntax.

Example code for ANOVA design codingqui 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 modelie_reg logr aC1-aC6 pC1-pC3 cC1-cC9

fully normalized solutionie_norm, groups(aC1-aC7, pC1-pC4, cC1-cC10)

Estimation Details

ie_regemployes a generalized inverse.

Saved Results

ie_regsaves the following ine():Scalars

e(N)number of cellse(ll)MSEe(k)number of estimated parametersMacros

e(depvar)name of dependent variableMatrices

e(Coef)1 XKvector of estimatese(Var)KXKvariance-covariance matrixFunctions

e(sample)marks estimation sample

ReferencesDaniel 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.

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

Also see