Economic Models - Convex Optimization

188 Fabrizio Iacone and Renzo Orsi
The variables referred to the trade partners were then not significant in
the AD equation: we found a certain effect at least for the real exchange rate
depreciation, and with a sign consistent with the macroeconomic theory,
but the realization of the t statistic was still rather below the critical value.
The absence of the two variables referring to the international trade could
be interpreted as a sign that Poland is still large enough to be more sensible
to the internal rather than to the international developments, but notice that
the situation was reversed for the PC equation, where only the external
conditions had a significant effect on the inflationary dynamics (again we
found that the effect of the omitted explanatory variable, y t−1 in this case,
had the sign predicted by the macroeconomic theory, but it failed to be
significantly different than 0).
We concluded performing a Forecast test for a break in 2000Q2 in
the PC equation, rejecting it (P-value 0.65). Since at that point, the Polish
national bank abandoned the exchange rate commitment and left the direct
inflation targeting to stand alone, it is fair to conclude that the change of
monetary target did not result in a destabilization of the inflation dynamics.
Since the target for monetary policy is defined mainly because it is assumed
that in that way the expected inflation can be favorably influenced, we prefer
not to give a structural interpretation of a backward looking formulation
of the inflation equation, but in this case we can at least conclude that the
change of target did not result in a worsening of the expectation of inflation.
Thus, it is likely that by 2000, the Polish central bank acquired sufficient
credibility to move away from a commitment that would have exposed it
to pressure from market speculation.
Although we summarized the diagnostic tests, concluding that the instability
that may be associated to the transition to a market economy can be
largely confined to the period before 1994, we also estimated a more restrictive
specification, in which the sample for the AD equation is from 1995
onwards, and for the PC from 1998 onwards. We considered this second
specification, because the residuals were not normally distributed, and an
asymptotic interpretation of the outcome of the autocorrelation test for the
AD equation was particularly dubious because the test statistic reached
approximately, the limit critical value, the P-value being slightly lower
than 0.05 (it was 0.046). As far as the PC equation, the Chow test did not
identify any break in 1998Q1 but the CUSUMsq statistic did indeed signal
a potential break in this year, albeit only mildly. The estimates in the more