12:41 p.m.
Dear all,
I am running gretl under Windows XP and am repeatedly
experiencing difficulties when letting gretl perform a panel diagnostics
(following a pooled OLS). In fact, gretl freezes with most data sets,
a.o. some from Wooldridge's "Introductory Econometrics".
The script I use to perform the panel diagnostic is as follows
(example is the data set wagepan.gdt from Wooldridge):
open wagepan.gdt
setobs 8 1:1 --stacked-cross-section
model1 <- pooled 19 0 17 3 5 4 27 7 18
model2 <- hausman
I would like to know whether any other gretl user has already
experienced the same problem, or whether it is just my fault - which I
would be happy to admit.
Best wishes,
Martin
2:48 p.m.
On Wed, 9 Feb 2005, Martin Obermaier wrote:
I am running gretl under Windows XP and am repeatedly
experiencing difficulties when letting gretl perform a panel diagnostics
(following a pooled OLS). In fact, gretl freezes with most data sets,
a.o. some from Wooldridge's "Introductory Econometrics".
The script I use to perform the panel diagnostic is as follows
(example is the data set wagepan.gdt from Wooldridge):
open wagepan.gdt
setobs 8 1:1 --stacked-cross-section
model1 <- pooled 19 0 17 3 5 4 27 7 18
model2 <- hausman
I can confirm that this script causes gretl to crash :-(
I will work on this and post again when the problem is fixed.
Allin Cottrell
12:56 a.m.
On Wed, 9 Feb 2005, Martin Obermaier wrote that
open wagepan.gdt
setobs 8 1:1 --stacked-cross-section
model1 <- pooled 19 0 17 3 5 4 27 7 18
model2 <- hausman
crashes gretl. I've now looked into this. One easy-to-fix thing is
that I was not dealing properly with the case where there are
insufficient degrees of freedom to calculate the group means
regression. That was the immediate cause of the crash, and it's now
fixed in CVS.
Actually, though, with the "wagepan" data there are plenty of
degrees of freedom (545 people observed in each of 8 years). But
your setobs line, with --stacked-cross-section, has confused gretl.
This is a case of --stacked-time-series (the observations go from
1980 to 1987 for the first person, then from 1980 to 1987 for the
second and so on, making a little time series for each person).
Nonetheless, gretl shouldn't crash!
I'm afraid, though, that this example has exposed some more
difficult issues, which I'm working on but have not fully resolved.
There are 545 cross-sectional units in this example, and gretl, up
to now, has calculated the within-goups regression by including a
dummy variable for each unit. With this number of units, that's
just silly. It's much more efficient to subtract the group means.
So I've coded that, but then another issue appeared: what if, when
you subtract the group means, some of the variables become all zero?
For instance there's a "black" dummy variable in your model. Since
nobody changed their color over the 8 years, the deviation from the
"group mean" is always zero for this variable. I need to devise a
way of handling such issues of perfect collinearity.
Of course, the same problem arises if you have a variable like
"black" and try to include a dummy variable specific to each person
-- it's just that the problem may not be so apparent.
If anyone on the list has thoughts on the Right Way to handle this
issue, I'd be very glad to hear them!
Allin Cottrell
3:45 a.m.
On Thu, 10 Feb 2005, Allin Cottrell wrote:
For instance there's a "black" dummy variable in your
model. Since
nobody changed their color over the 8 years, the deviation from the
"group mean" is always zero for this variable. I need to devise a
way of handling such issues of perfect collinearity.
Of course, the same problem arises if you have a variable like
"black" and try to include a dummy variable specific to each person
-- it's just that the problem may not be so apparent.
If anyone on the list has thoughts on the Right Way to handle this
issue, I'd be very glad to hear them!
Well, this is a known problem in panel data estimation. Collinearity here
is a by-product of under-identification. Allow me a brief
recap of the econometric issues involved (I'm going to use LaTeX
notation, sorry for those unfamiliar):
in general, a static panel data model can be written as:
y_{it} = X_{it} \beta + Z_i \gamma + \alpha_i + \epsilon_{it}
where the X's are time-varying regressors and the Z's are time-invariant
(like "black") in the example; note that Z also includes the constant
term. The fundamental difference between the within estimator and the GLS
estimator is in the treatment of the individual effects \alpha_i.
- the within estimator treats the \alpha's as given. No assumptions are
made on the distribution of the individual effects, and the \alpha's are
treated, for all purposes, as nuisance parameters. Therefore, \gamma
is obviously unidentified. In this context, the only parameter it makes
sense to estimate is \beta.
- in GLS estimation, we introduce an additional hypothesis on the
distribution of the \alpha's, that is:
E(\alpha_i | X_{it} , Z_i) = 0 ;
under this hypothesis, it becomes possible to estimate not only \beta, but
\gamma as well and GLS just happens to be the best linear unbiased
estimator in this case; some estimators have been devised for dealing
with the case where the \alpha_i's are correlated with the explanatory
variables, but I consider it a niche market for gretl, at least for now.
This is the reason why the Hausman test commonly used just contrasts the
within and GLS estimates of \beta (as opposed to \beta AND \gamma):
simply, no estimator of \gamma exists unless we make some assumptions on
\alpha_i.
I feel that we ought to have a panel estimation command that, given a list
of regressors:
1) spits out the OLS (pooled) estimate;
2) performs within estimation with time-varying regressors only, and
prints the results out;
3) does GLS for all regressors;
4) computes and prints the Breusch-Pagan poolability test (aka OLS vs
rest of the world) and the Hausman test (aka GLS vs within).
The ideal way to deal I would like it would be having a command like (ok,
I know the command "panel" is already taken):
panel y const x1 x2 z1 x3
having gretl figure out which regressors belong to the X's and which
don't. An acceptable alternative could be
panel y x1 x2 x3 ; const z1
where it's the user's responsibility to separate the two sets.
Thoughts, anybody?
Riccardo `Jack' Lucchetti
Dipartimento di Economia
Università di Ancona
jack(a)dea.unian.it
http://www.econ.unian.it/lucchetti
3:17 p.m.
On Thu, 10 Feb 2005, jack wrote [many helpful things].
Thanks for the clear exposition, Jack.
I feel that we ought to have a panel estimation command that, given a
list
of regressors:
1) spits out the OLS (pooled) estimate;
2) performs within estimation with time-varying regressors only, and
prints the results out;
3) does GLS for all regressors;
4) computes and prints the Breusch-Pagan poolability test (aka OLS vs
rest of the world) and the Hausman test (aka GLS vs within).
This is now on the way. It's not a single command (you start with
"pooled" then do "hausman"), but
* The "hausman" command now only uses time-varying regressors in the
fixed effects model (gretl detects which ones are time-varying).
* The Hausman test is restricted to the slope coefficients for the
time-varying regressors.
* The random effects model (which is printed as part of the
"hausman" output, provided the group means regression can be
calculated) includes all regressors.
This is in CVS; it's also in the current win32 snapshot
ftp://ricardo.ecn.wfu.edu/oub/gretl/gretl_install.exe
I'd be glad if people can test the new code and see if it works!
Allin Cottrell
10:43 a.m.
New subject: more on panel diagnostics
Here are some further thoughts on panel data estimation. In the
first part I'm "thinking out loud", trying to test my understanding
of what's wanted. But the discussion leads up to a specific
question on what gretl should do, and I'd appreciate hearing
people's thoughts on that.
A common first step with panel data is pooled OLS. This is much
the simplest model. Its simplicity is purchased with the
assumption of homogeneity, across both time periods and
cross-sectional units. This assumption is testable and one
generally expects to see it tested.
A common step in relaxing the homogeneity assumption is the "fixed
effects" model, which allows the intercept (hence, the average
value of the dependent variable) to differ across... Ah, to differ
across what? In the context of gretl's "hausman" command, I've
been assuming that the answer is always, "to differ across
cross-sectional units", but I'm not sure that's right.
With fixed effects, one can allow the intercept to differ by
cross-sectional unit, by time period, or by both. What is the
econometrician likely to want?
Well, panel datasets can be "long and thin" or "short and fat".
For a "long and thin" case consider Panel A, which consists of
observations on 4 firms over 25 years. For a "short and fat"
case, consider Panel B, which comprises observations on 1000
individuals in each of 4 years.
I'm now thinking: the most "natural" version of the fixed effect
model, considered as a first step in relaxing the homogeneity
assumption of pooled OLS, allows the intercept to differ across
the smaller dimension of the panel. Thus with Panel A we'd allow
the intercept to differ by firm, but with Panel B we'd allow it to
differ by year.
As Jack just pointed out, if you're doing fixed effects with
intercepts differing by cross-sectional units, it's necessary to
screen out variables that are not time-varying. Similarly, if one
were doing fixed effects with period-specific intercepts, it would
be necessary to screen out variables that do not vary across
cross-sectional units.
Specific question: for gretl's testing of pooled OLS models,
should there be a command option to determine which dimension is
used for the fixed effects, e.g.
--group-effects versus --time-effects (versus --both-effects ?)
Allin Cottrell
--
Allin Cottrell
Department of Economics
Wake Forest University, NC
7178
days inactive
7180
days old
5 comments
3 participants
participants (3)
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Allin Cottrell -
jack -
Martin Obermaier