st: Subsample Bootstrap

["Tim R. Sass" <tsass@coss.fsu.edu>]

Dear Statalisters,

I am iteratively estimating a model and then using the bootstrap procedure 
to derive the standard errors and t-stats.  The procedure works fine on a 
moderately sized sample, but each replication of the bootstrap takes over 
three hours on my full sample (over 1 million obs.).  In order to speed up 
the process I would like to perform each repetition of the bootstrap on a 
subsample of the data, say 100,000 observations.  This can of course be 
done by setting the size() option in bootstrap.  The FAQs warn against 
this, however, saying "the standard error estimates are dependent upon the 
number of observations in each replication.  Here, on average, we would 
expect the variance estimate of b[foreign] to be twice as large for a 
sample of 37 observations than that for 74 observations.  This is due 
mainly to the form of the variance of the sample mean."

Is there some straightforward correction I can make to get the correct 
standard errors when using the size() option in bootstrap?

Alternatively, I thought about just taking the estimated coefficients from 
each repetition of the bootstrap and then forming an empirical distribution 
from these estimates to get the standard errors.  But I am not quite sure 
how to accomplish this in Stata.

Any help on these ideas or alternative solutions would be greatly appreciated.

Tim

Tim R. Sass
Professor                               Voice:   (850)644-7087
Department of Economics         Fax:      (850)644-4535
Florida State University                E-mail:   tsass@coss.fsu.edu
Tallahassee, FL  32306-2180     Internet: http://garnet.acns.fsu.edu/~tsass 

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