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st: RE: bootstrapping and sample selection

From   "David E Moore" <>
Subject   st: RE: bootstrapping and sample selection
Date   Wed, 20 Aug 2003 13:41:15 -0700

Excellent question.  While there may be a simpler practical solution to your
particular problem, the general question remains.  My suggestion would be to
impose a constraint on the resampling such that the proportion of participants
remains the same.  In other words, draw a sample that gets you nearly the exact
same proportion of participants every time.  What I don't know is how this
restriction affects the variance estimates.  I suspect it biases them downward,
so you might need to take this into account if you follow such an approach.

As an aside, I assume the problem arises because of a small sample, otherwise it
seems unlikely that you would ever end up with all participants or
non-participants.  Of course, any configuration's possible in a truly random
draw.  It just seems highly unlikely.

> -----Original Message-----
> From:
> []On Behalf Of Axel
> Heitmueller
> Sent: Wednesday, August 20, 2003 4:19 AM
> To:
> Subject: st: bootstrapping and sample selection
> hi there,
> suppose one would like to bootstrap a standard heckman two step
> regression in order to recover the adjusted standard errors (I know
> the program provides the corrected s.e. but I need it for a double
> sample selection case). One approach (the obvious) is to draw
> from the entire sample N (including both participants and non-
> participants let say). yet, some of the draws will contain very
> unequal proportions of the two groups, e.g. only participants or non-
> participants. in these cases the results for mills ratio, correlation
> coefficient (rho) and sigma will be problematic as values become
> very large or very low depending on the draw.
> an alternative is to keep the numbers of the subsamples N1 and N2
> (participants and non-participants) constant and draw from these
> fixed subsamples. then, the above problems disappear. yet, this is
> very close to a two sample bootstrap which requires the two
> samples to be random and independent. this is problematic as one
> applies heckman because they may not be independent.
> I had a look for literature on bootstrapping and two step regression
> but couldn't find much. would be great if someone could give me a
> hint how to proceed in these circumstances.
> cheers
> axel
> Axel Heitmueller,
> Centre for Economic Reform and Transformation, CERT
> School of Management
> Heriot-Watt University
> Edinburgh
> EH14 4AS
> UK
> phone +44(0)131 451 3969
> fax +44 (0)131 451 3296
> *
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