Economic Models - Convex Optimization

186 Fabrizio Iacone and Renzo Orsi
Of course, given the small dimension of the samples and the potential
instability of the models due to the transition, a certain caution should still
be exerted in the interpretation of the results. But, we think that even in
this case our analysis is at least able to get a general, broad picture of the
situation: the lack of precision that may be attributed to the small dimension
of the sample, for example, is already taken into account in the standard
error. If, under normality, a test statistic rejects the null hypothesis despite
the large variability due to the small sample, then we would still regard the
estimate as informative, although may be only on the sign.
3. The Empirical Evidence
3.1. Germany
As a benchmark case, we first estimated the model for Germany over the
period 1991Q1–2004Q1. The choice of the sample is two-fold: first, only
data after the German re-unification were considered, leaving many of the
problems related to that particular transition out of the discussion; second,
this time span is roughly the same one covered by the data of the CEECs in
most of the applied analyzes, making the results comparable in this sense.
We called this a “benchmark” model because it is widely assumed that this
transmission mechanism for monetary policy was at work in Germany in
the years we are interested in. Furthermore, Germany is geographically
and economically close to the CEECs, accounting for a large share of their
international trade. Finally, it is an interesting reference because Germany
is the biggest country in the euro-area: if the monetary transmission in the
CEECs works in a very different way, their integration in the euro may
adversely affect the dynamics of inflation.
The estimated model for Germany was
⎧
ŷ ⎪⎨ t = 0.011 + 0.769y t−1
(0.005) (0.084)
⎪⎩ ̂π t =−1.02π t−1
(0.10)
− 0.0038y t−1
(0.00163)
− 0.86π t−2
(0.12)
− 0.71π t−3 + 17.62y t−2
(0.10) (12.18)
over the period 1991Q2–2004Q1 for the AD, and 1993Q1–2004Q1 for
the PC.
According to the diagnostic tests, the AD equation was correctly specified
and stable over the whole sample; the CUSUMsq hit the boundary in
the period 1993–1996, but we found no evidence of break with the Chow