Palgrave Handbook of Econometrics: Applied Econometrics

Carlo Favero 833

in a paper by Christiano, Eichenbaum and Evans (1998). There are three relevant
steps:

1. monetary policy shocks are identified in actual economies, that is, in a VAR
   without theoretical restrictions;


2. the response of relevant economic variables to monetary shocks is then
   described;


3. finally, the same experiment is performed in the model economies to compare
   actual and model-based responses as an evaluation tool and a selection criterion
   for theoretical models.

The identification of the shocks of interest is the first and most relevant step
in VAR-based model evaluation. VAR modeling recognizes that identification and
estimation of structural parameters is impossible without explicitly modeling
expectations. Therefore, a structure like(16.7)can only be used to run special
experiments that do not involve simulating different scenarios for the parame-
ters of interest. A natural way to achieve these results is to experiment with the
shocksνMt.Factsare then provided by looking at impulse response analysis, vari-
ance decompositions and historical decompositions. Impulse response analysis
describes the effect over time of a policy shock on the variables of interest, variance
decomposition illustrates how much of the variance of the forecasting errors for
macroeconomic variables at different horizons can be attributed to policy shocks,
and historical decomposition allows the researcher to evaluate the effect of zeroing
policy shocks on the variables of interest. All these experiments are run by keeping
estimated parameters unaltered. Importantly, running these experiments is easier if
shocks to the different variables included in the VAR are orthogonal to each other,
otherwise it would not be possible to simulate a policy shock by maintaining all
the other shocks at zero. As a consequence, VAR models need a structure because
orthogonal shocks are normally not a feature of the statistical model. This fact
generates an identification problem. In the reduced form we have:

(

Yt

Mt

)

=A−^1 C(L)

(

Yt− 1

Mt− 1

)

+

(

uYt

uMt

)

,

whereudenotes the VAR residual vector, normally and independently distributed
with full variance-covariance matrix. The relation between the residuals inuand
the structural disturbances inνis therefore:

A

(

utY

uMt

)

=B

(

νYt

νMt

)

. (16.8)

Undoing the partitioning, we have:

ut=A−^1 Bυt,