| Lack of correlation between the instruments and the endogenous regressors is just one of the many forms in which an IV model could be misspecified. Another forms of misspecification is correlation between the instruments and the error terms in the "structural equation†of interest despite the fact that instruments are “strong" (in the sense that they strongly predict the outcome in the "first stage†regression). Yet another form is incorrect specification of the “structural equation†itself. This is why I don’t agree that incorrect specification is an extreme form of weak identification.
I also don't agree with what we should conclude from White (1982). In some cases the assumed model may still do fine (i.e., it’s a good approximation given our purposes), but it may also not do fine (i.e., it’s not a good approximation given our purposes). It all depends on the model you assume and your goals. This is why I said that the assumed model `better be “not too simplistic" given the problem at hand’.
But I agree with you that the results by McDonald and Shalizi have little to do with DSGE in general and a lot to do instead with the use of the “canonical model†from Smets and Wouters (2007).
I hope this helps.
Franco On Jan 5, 2023, at 15:51, Alessandro Casini <
> wrote:
Franco think about IV. Weak IV
means the first-stage coefficient approaches zero. Incorrect
specification means that there is no first-stage coefficient
(the instrument is not an instrument) (or the first-stage
coefficient is zero). So you can seen incorrect instrument as an
extreme case of weak IV.
Yes, your point on Kullback-Leibler (KL) follows White (1982).
That paper told economists that even if we misspecified the
model we may still do fine. In Theory. Unfortunately, if you
misspecified a highly nonlinear, complex model like DSGE models,
then you get weird results with ML. So ML theoretically useful
even when models are misspecified but not so practically useful
in certain circumstances. The types of weird results in Mc
Donald and Shalizi are just due to losing identification. Things
can go very wrong not matter what White (1982)'s results say.
Alessandro
On 1/5/2023 3:38 PM, Franco Peracchi
wrote:
">
I don’t agree that incorrect specification is an extreme form of
weak identification and that ML is useless when the assumed model
(a family of probability distributions indexed by a parameter that
may well be infinite dimensional) is incorrectly specified, which
is the typical case. If the assumed model is incorrectly
specified, ML estimates the best approximation, in the
Kullback-Leibler (KL) sense to the DGP. In my view, this is the
best we can do given a model. Of course, the assumed model better
be “not too simplistic" given the problem at hand. Further, it
better be identifiable, that is, there must be a unique element in
the assumed parametric family that is at shortest KL “distanceâ€
from the DGP.
Buon anno!
Franco
On Jan 5, 2023, at 15:16, Alessandro Casini
"><
> wrote:
Thank
you Gianluca. Yes, Johansen's point is formally very
clear. If one chooses a statistical model that
contains the economic model as a submodel, but not the
DGP, then yes ML is useless. That would mean no
identification, which is an extreme case of weak
identification (I am a nice guy, I did not want to be
too negativeðŸ˜).
I
think a problem with identification can give rise to
the results in Mc Donald and Shalizi. However,
identification is a big deal in Macroeconomics or in
Economics more generally. DSGE may be suffer more from
it, but also other approaches have to deal with
identification.
I
have been thinking often about what could be the
sources of weak identification/no identification. My
conclusion about identification problems in
Macroeconomics is that any model cannot get (strong)
identification when fitted to 20+ years of data. The
parameters of the DGP has changed many times. Economic
theory yields time-invariant restrictions between
economic variables (i.e., parameters are implied to be
constant). So any model cannot fit this data well. At
best, we can only hope to get strong identification in
sub-samples.
Alessandro
On 1/5/2023 2:34 PM, Gianluca
Cubadda wrote:
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Hi Alessandro,
please have
a look at the paper by Soren Johansen that I
mentioned in my reply to Pasquale.
Shortly,
Soren argues that it is fundamentally wrong to use
ML methods when the statistical model is not a
credible (and testable) representation of the
(statistical) data generating process. If one
takes this point, then the problem with DSGEs is
even more serious than weak identification…
Ciao,
Gianluca
Hi, I only had a glance at
the Introduction. I think their results might be
credible. But isn't this known in Econometrics as
weak identification? Because weak identification
is a long-study problem in Macroeconometrics and
also in DSGE model. It might be that their results
are just consequences of weak identification. The paper does not mention
weak identification. I was expecting a discussion
of this. For example, Fernéndez-Villaverde
(2010) in his survey of DSGE estimation writes:
"likelihoods of DSGE models are full of local maxima
and minima and of nearly at surfaces... the standard
errors of the estimates are notoriously di‑difficult
to compute and their asymptotic distribution a poor
approximation to the small sample one." So it is possible to get weird results if one does
not have strong identification. Best, Alessandro
On 1/5/2023
1:14 PM, Pasquale Scaramozzino wrote:
First of all,
happy new year to you all!
Here it is another paper that is raising lots of
discussions:
https://arxiv.org/abs/2210.16224
I don't know if those results have already been
formally checked.
Ciao,
Gianluca
Pasquale Scaramozzino
Professore di Economia Politica
Dipartimento di Economia e Finanza
Facoltà di Economia
Università di Roma "Tor Vergata"
via Columbia, 2
00133 Roma
Italy
pho. 0039 06 7259 5727
fax 0039 06 2020 500
http://economia.uniroma2.it/def/faculty/229/scaramozzino-pasquale
http://ideas.repec.org/e/psc186.html
--
Alessandro Casini (
" moz-do-not-send="true" class="moz-txt-link-freetext" style="color: blue; text-decoration: underline;">
)
Department of Economics and Finance
University of Rome Tor Vergata
Via Columbia 2
00133 Rome, Italy
http://alessandro-casini.com
--
Alessandro Casini (
" style="color: blue; text-decoration: underline;" moz-do-not-send="true">
)
Department of Economics and Finance
University of Rome Tor Vergata
Via Columbia 2
00133 Rome, Italy
http://alessandro-casini.com
--
Alessandro Casini (
">
)
Department of Economics and Finance
University of Rome Tor Vergata
Via Columbia 2
00133 Rome, Italy
http://alessandro-casini.com
|