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st: Subsample Bootstrap

From   "Tim R. Sass" <>
Subject   st: Subsample Bootstrap
Date   Fri, 20 Jan 2006 11:05:04 -0500

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 R. Sass
Professor Voice: (850)644-7087
Department of Economics Fax: (850)644-4535
Florida State University E-mail:
Tallahassee, FL 32306-2180 Internet:

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