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Re: st: RE: [questions on -heckman- and income decomposition]
1. The comments on the VCE underestimation are in place for two-step
procedure where you generate lambda first, and then plug it in into
the first equation. Then indeed the standard errors do not account for
sampling variability in lambda. This was the only method feasible 25
years back, and I don't think the issue arises in the FIML procedure,
which is Stata's default for -heckman-, anyway.
2. As long as all those decompositions are linear functions of the
coefficients (as far as I can recall), you can get the standard errors
from -lincom- command, although you would have to do all of the
algebra from scratch. If there are any non-linearities involved, the
goal can be achieved with -nlcom- instead.
[Wishes and Grumbles section: I know of only one case of a worse
general-sounding name that can be given to a very specific purpose
program: I used to have -svybs- on my web page before I figured out
that (i) what it does is statistically wrong, and (ii) what it does
can be accomplished by the standard -bootstrap-, anyway.
Decompositions are quite common in both statistics and applied areas;
ANOVA decomposition of variance may be in place, and I know that
people in quantitative psychology are fond of variance decompositions
trying to attribute something like R^2 to every variable in the model.
Shorrocks suggested Shapley decomposition as a general analytical tool
for inequality and poverty analysis, and it is certainly applicable in
this case, too. I am pretty sure there are many other decompositions
of which I am not aware... so the title like -decompose- for a program
that does only one specific decomposition does not sound right to me.
Oh well... I must be in a bad mood these days, as my latest Statalist
postings are mostly criticizing :). And of course Nick was right about
the informative subject lines, as well as reporting one's own attempts
to find relevant info in Stata's help, FAQ and Statalist archives
> > 1. I am using Heckman model for selectivity. Heckman
> > (1979, page 158)
> > states that when the coefficient of the selection bias (that is the
> > coefficient of inverse Mills' Ratio) is not statistically
> > equal to zero,
> > then the "standard" variance-covariance matrix leads to an
> > understatement
> > of true errors and overstatement of significance levels. In
> > this case a
> > correction is suggested by Heckman (pages 158-160). Wooldridge,
> > Econometric Analysis of Cross Section and Panel Data, 2002,
> > pages 139-141
> > discusses the same issue and provides formulas.
> > Is there a built in commend (program) that one can
> > use for the
> > correction? Has any one done this? How do I get this done?
> > 2. Ian Watson and Ben Jann have written two commands for
> > decomposition
> > of wage differentials. The STATA syntaxes are decomp and
> > decompose. Both
> > produce various components of the decomposition, but do not perform
> > statistical testing of the components. Ronald L. Oaxaca and Michael
> > Ransom, Journal of Economic and Social Measurement, 1998,
> > pages 55-61, show
> > how to use delta method for obtaining standard errors of the
> > components of
> > wage differentials. Does STATA do this procedure? Has it been
> > implemented yet? Has any user written a commend file for these tests?
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