Fabio Canova 85gradient or the Hessian display problematic features. Furthermore, it can be shown
that population responses fall within a 68% band centered around the estimates
of the responses to monetary shocks computed with the parameter estimates, even
when the sample size isT=120. Therefore, the practice of showing that the
model’s responses computed using the estimated parameters lie within the confi-
dence bands of the responses estimated from the data is not particular informative
as far as identification problems are concerned. Large standard errors do emerge
when identification failures exist, but also when other problems are present (for
example, very noisy data or regime switches). Hence, associating large standard
errors with identification issues is, in general, incorrect.
It is also important to stress that the addition of measurement errors for estima-
tion purposes can distort the identification properties of structural parameters. It is
not particularly difficult to conceive situations where a parameter that was identi-
fied by certain features of the model becomes free to move and fit other properties
of the data it was not designed for, once measurement error is added. Therefore,
while there is some logic in adding measurement errors to link the model variables
to the observables, one should be careful and investigate the consequences that
such a process has on the identification properties of the parameters.
2.3 Structural VARs
Structural VAR inference is typically perceived to be at the extreme opposite to
structural model-based inference. SVAR models take a minimalist approach to the
estimation problem and consider only a very limited sub-set of the large number
of restrictions that DSGE models impose on the data. For example, the fact that
the matricesH 1 andH 2 in (2.4) depend onθis typically neglected and only a part
of the information present inA 0 (θ)is used. Furthermore, the singularity that the
model imposes on the data is completely disregarded.
This minimalist approach has one obvious disadvantage: if less structure is
imposed on the data, fewer interesting economic questions can be asked. However,
such a limited information approach is advantageous when some of the model’s
restrictions are dubious, which would be the case if the model is misspecified in
some dimensions, or fragile, which would be the case if the restrictions depend on
the functional forms or the parameter values one specifies. In this case, neglecting
these restrictions can robustify estimation and inference.
As we have mentioned in the introduction, and despite recent attempts to make
them more realistic, the current generation of DSGE models is still far from repro-
ducing the DGP of the actual data in many respects: models fail to capture, for
example, the heterogeneities present in the actual world; important relationships
are modeled with black-box frictions; timing restrictions are used to make them
compatible with the dynamics observed in the data; andad hocshocks are often
employed to dynamically span the probabilistic space of the data. Since mis-
specification is likely to be pervasive, system-wide and even limited-information
classical structural methods are problematic, even when identification problems
are absent.