st: Bootstrapped p-values for regressions with clustered data with few clusters

[Jacob Felson <felsonj@gmail.com>]

This inquiry was prompted by responses to a previous question about
the effect of clustering on the size of the standard error of a
coefficient.  It is my understanding now that th standard errors
estimated using the cluster command are not reliable when the number
of clusters is small (say, m < 30).  This is the situation with the
data I am using, which contain information from 4 nations (n = 6175).
Bootstrapping is offered as an alternative in a paper by Cameron,
Gelbach and Miller (2006).   I looked into implementing the pairs
cluster bootstrap-t procedure on my data from Cameron et al. (2006).

I would like to include nation fixed effects and an interaction
between nation indicator variables and a key independent variable.
I'm interested to know whether the effect of variable differs across
nations.   It is problematic (or maybe not possible) to estimate fixed
effects and interactions with the nation indicator variable on many of
the bootstrapped cluster samples.  Many of these samples of course do
not include all of the clusters.  Does one simply estimate the fixed
effects and interactions which one can in each model, and then use the
different bootstrapped samples to estimate p-values for each
coefficient?

For example, for the indicator variable and interaction with nation 2,
could one simply gather and use all of the bootstrapped samples that
include nation 2?  And so on with the other nations?


Thank you for all of your help.


Jacob Felson
Assistant Professor
Department of Sociology
William Paterson University


Reference

Cameron, Colin, Jonah Gelbach and Douglas Miller. 2006.
"Bootstrap-Based Improvements for Inference with Clustered Errors"
NBER Working Paper No. 344.
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