[Gretl-users] Re: on near-zero std errors values
On Fri, 29 Jan 2021, Artur Bala wrote:
Hi,
Probably the topic of "How small is really small?" has been already
discussed but I'm still a bit confused.
Now, for the following estimation, Stata considers that std errors are 0
and provides no output. Instead, gretl reports quite small values resulting
in very "optimistic" p-values.
Obviously, the missing F statistic and a R2=1 should provoke doubt and
question the validity of the model...though those *** seem confusing :).
In such circumstances, is there a way to make gretl "judge" that std.errors
are actually 0 and omit t tests?
In my opinion, we need to take no such action. Let me explain my point.
The standard errors one see printed by the side of estimated coefficients
are, per se, just descriptive statistics that give you an idea of how
sensitive the objective function (the sum of squares) is to changes in
that parameter. If that number is small, it means that small changes in
that parameter make the model much worse in fitting the dependent
variable. That's what the standard errors are.
That said, you _may_ give them an inferential interpretation and use them
to construct hypothesis tests and confidence intervals, but then, the
burden of correctly interpreting their meaning is on the user. The fact
that many, in the economic profession, have come to the unfortunate habit
of automatically thinking "no stars -> bad, two stars -> good, three stars
-> wow" should not deter us, as authors of a statistical package, from
reporting the statistic in the most precise way possible and refrain from
patronising the user.
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Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
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