Palgrave Handbook of Econometrics: Applied Econometrics

Fabio Canova 79

1.2 1.4

1 1.6 1.8

1.5

–0.04

–0.02

0

λπ λ

π

Monetary shocks

λy

λy 1.2

1.4 1.6

1.8

1

1.5

–20

–10

0

All shocks

0.96 0.6 0.8

0.98

0

ω

Phillips curve shocks

β 0.6

0.98 0.96 0.8

0

ω

All shocks

β

0.20.4 0.6

0.8

1.81.6

2.2 2

–2

–1

–2

–1

–2

–1

0

h

IS shocks

φ

0.2 0.4 0.6

0.8

1.81.6

2.2 2

–4

–2

0

h

All shocks

φ

Figure 2.2 Distance function and contour plots

as the other parameters are allowed to be adjusted. Figure 2.3, which is repro-
duced from Canova and Gambetti (2007), shows that the shape and, in many
cases, the size of the responses at almost all horizons to the three shocks are
similar in the two regimes. Hence, if this were the only information available
to the investigator, it would be difficult to detect which regime has generated
the data.
This latter problem is a special case of a general pathology that applied investiga-
tors often face when dealing with DSGE models: the objective functions that one
constructs from the aggregate decision rules may display multiple peaks, which
may be clearly separated (as is the case in the above example; see also Lubik and
Schorfheide, 2004) or not (see the example discussed in section 5 of Canova and
Sala, 2005). Observational equivalence, probably more than any other identifica-
tion problem, prevents attaching any meaningful economic interpretation to the
outcomes of the estimation process and, obviously, conducting any meaningful
policy analysis with the estimated model.
What generates the identification problems we have detected? All the non-
linear transformations, which are necessary to go from the structural parameters
to the distance function, contribute. For example, consider the case of the price
indexation parameterω, which enters nonlinearly in the model and in several of