Folks,

I’ve just noticed some very strange behavior when I
try to generate studentized bootstrap confidence intervals in a model with only
a constant (this is problem 5.6 in Davidson/MacKinnon’s ETM). The model
is earnings data regressed on a dummy variable for a particular income group,
so it’s just estimating the mean.

Here are the results from running a studentized bootstrap:

For the coefficient on G3 (point estimate 27973.6):

Studentized 95% confidence interval = 16009.7 to
17410.2

Based on 999 replications, using resampled residuals

The graph of the sampling distribution, on the other hand,
is centered roughly on the point estimate (see ‘studentized.pdf’,
attached).

When I do a regular bootstrap confidence interval, I get

For the coefficient on G3 (point estimate 27973.6):

95% confidence interval = 42857 to 44843

Based on 999 replications, using resampled residuals

With the distribution in ‘bootstrap.pdf’.

Things seem to work ok in a model with all three group
dummies and no constant.

PS

===============================

Dr. Peter Summers

Assistant Professor

Department of Economics

===============================