Thanks very much!!! Just in time before I need to do some
bootstrapping as a part of testing my results in my dissertation. It
works with the heteroscedasticity corrected OLS also right?
On 3/28/07, Allin Cottrell <cottrell(a)wfu.edu> wrote:
Andreas K suggested a short while ago that gretl should offer
various bootstrap options via the graphical interface (GUI). I
agreed at the time that this was a good idea. Here's a note on
progress so far (in CVS, and the current gretl snapshot for
First, the limitation: all of the following new stuff applies only
to single-equation models estimated via OLS. (Though please note
that we already offer bootstrapped confidence intervals for
impulse response functions in relation to VARs.)
When you estimate a model via OLS in the GUI, the model viewer
window has a menu bar, including items labeled "Analysis" and
New under "Analysis": there's a "Bootstrap..." item. This opens
dialog box where you get to make five choices:
(1) The variable/coefficient to examine.
(2) "Confidence interval" vs "Studentized confidence interval" vs
(3) "Resampled residuals" vs "Simulate normal errors".
(4) Number of replications (default 1000).
(5) Show graph of bootstrap sampling distribution (no/yes).
In relation to (1): you only get to examine one coefficient at a
time by this particular means.
On (2): the default (95%) confidence interval is based directly on
the quantiles of the bootstrap coefficient estimates. The
"studentized" version is as per Davidson and MacKinnon's
"Econometric Theory and Methods" (ETM), chapter 5: at each
bootstrap replication a t-ratio is formed as (a) the difference
between the current and the baseline coefficient estimate, divided
by (b) the baseline estimated standard error. Then the confidence
interval is formed based on the quantiles of this t-ratio, as
explained in ETM. The "P-value" variant is, again, as explained
On (3): you get to choose between resampling with replacement of
the original residuals (rescaled as suggested in ETM), and
simulated normal errors with the empirically given variance.
Andreas suggested including the option of "case resampling" (that
is, resampling the (y, X) pairs rather than the residuals. I have
not implemented this to date for two reasons: first, it seems
statistically dodgy, and second it is considerably more burdensome
from the computational viewpoint. (You can economize substantially
if the X matrix is treated as constant across the bootstrap
Point (4) should be mostly self-explanatory. However, when you're
doing a (1 - alpha) confidence interval, then, as explained in
ETM, it is desirable that alpha(B + 1)/2 is an integer (where B is
the number of replications). So gretl adjusts the user-chosen B
value to ensure this is the case.
Point (5) again should be self-explanatory: you can get gretl to
make a graph of the density of the bootstrapped coefficient or
t-ratio. This option employs gretl's kernel density estimation
The above all pertains to the "Analysis/Bootstrap" menu item. In
addition you have options under "Tests/Linear restrictions". The
restrictions dialog now has a "Use bootstrap" check box. If you
check this, you get a bootstrapped F-test for whatever set of
linear restictions you have entered. The methodology is as
described in ETM for bootstrapped P-values.
Autoregressive models: If the set of regressors includes the first
lag of the dependent variable this should be handled correctly:
the bootstrap data sets are calculated recursively, taking into
account the autoregression. Please note that higher-order
autoregressions are _not_ currently recognized and handled
In script mode: For single-equation models estimated via OLS, you
can append the --boot flag to the "restrict" command to get
bootstrapped tests. You can also set the default number of
bootstrap replications using the "set" command with "bootrep"
parameter. For example:
set bootrep 10000
Testing and comments welcome!
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