Economic Models - Convex Optimization

180 Fabrizio Iacone and Renzo Orsi
Following Svensson (2000), we then augmented the model by introducing
the level of the economic activity in the international partners wt and the
percent real exchange rate depreciation (q t −q t−1 ), where q t = p ∗ t +e t −p t
is the logarithm of the real exchange rate and p t ,p ∗ t and e t are the logarithm
of the local and foreign level of prices and of the nominal exchange
rate, respectively. Both the variables are added to the AD equation, and
the real exchange rate is added to the PC equation as well. For the AD,
the assumption is that phases of high economic activity abroad result in
higher demand of locally produced goods, while a too high level of prices
(in real terms) causes a shift of the domestic and foreign demand towards
the external producers. The real exchange rate entered the PC equation,
because the international competition imposes some price discipline to the
local producers: for given foreign prices, a nominal exchange rate appreciation
makes foreign goods cheaper in local currency, thus, forcing the
domestic producers to lower their prices to keep up with the external competitors,
while for given nominal exchange rate higher foreign prices give
the domestic producers to set higher prices and stay in the market; we also
refer to Svensson (2000), where he explains how an increase in foreign
prices in local currency, either due to the move of the foreign price itself or
to the exchange rate, results in higher cost of inputs and then feeds back in
higher prices of output.
Maintaining the autoregressive structure of Rudebush and Svensson,
we describe the economy with the two equations model
π t = α 0 + α π1 π t−1 + α π2 π t−2 + α π3 π t−3
+ α π4 π t−4 + α y y t−1 − α q (q t−1 − q t−5 ) + ε π,t PC
y t = β 0 + β y y t−1 − β w w t−1 − β q (q t−1 − q t−5 ) + ε y,t AD
where we actually considered relevant for the exchange rate the depreciation
over the whole year.
In the original model, Svensson considered the real exchange rate rather
than the percent depreciation: in our model specification, we preferred the
latter because as we saw the real exchange rates of most of the CEECs
appreciated since the beginning of the transition without resulting in a
dramatic decline of the economic activity.
Moreover, we kept the AD/PC structure as a general reference, but
given that the specification is somewhat arbitrary, we tried to adapt it to
the economies considered. Our sample starts from 1990, and to avoid the
risk of model instability in the very first part of the sample, the data were
used only to compute the output gap or as lags. In some cases, we did