THE ECONOMETRICS OF MACROECONOMIC MODELLING
The nominal exchange rate vt
The nominal exchange rate affects wages and prices via import prices pit. Let pft be an index of import prices in foreign currencies. Then, as a first step in the completion of the model, we make use of the identity
pit = Vt + pft
and attempt to model the (log) of the trade weighted exchange rate index vt. In doing so, we follow Akram (2004), who models the exchange rate as equilibrium-correcting to the real exchange rate, which means that it is determined by PPP in steady state,
ecmv, t = vt + pwt - pt,
where pwt is the log of a trade-weighted index of foreign consumer prices. Figure 9.4 shows the time-series properties of ecmv, t, together with the corresponding term ecmy, t from the aggregate demand equation developed later.
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Figure 9.4. The equilibrium-correction terms of the exchange rate and the aggregate demand equations |
The graphs of the ecms indicate stationary behaviour, corresponding to short - run deviations from steady state.
The resulting model is given as
Avt = — 0.35ARSt — 0.41 sRISKt + 0.15 (s ■ A(euro/dollar))t (0.08) (0.19) (0.04)
— 0.13 AoilSTt —0.06 (v + pw — p)t-2 + 0.04 Vdumt + 0.02 (0.03) (0.03) (0.004) (0.01)
(9.7)
T = 1972(4)-2001(1) = 114
<r = 1.24%
Far(i-S)(5, 102) = 1.76[0.13]
xLmaiity(2) = 5.64[0.06]
FHETx2(12, 94) = 0.55[0.88].
(Reference: see Table 9.2. The numbers in [..] are p-values.)
Akram (2004) documents significant non-linear effects of the USD price of North Sea oil on the Norwegian exchange rate. Our model is built along the same lines and therefore features non-linear effects from oil prices (oilt) in the form of a smooth transition function (see Terasvirta 1998),
AoilSTt = Aoilt/{1 + exp[4(oilt — 14.47)]}.
The implication is that an oil price below 14 USD triggers depreciation of the krone.
As for the other right-hand side variables, the first term implies that there is a negative (appreciation) effect of an increase in the money market interest rate ARSt. The variable sRISKt captures deviations from uncovered interest rate parity (see Rpdseth 2000, p.15) after 1998(4):
sRISKt = RSt-1 — RWt — (Avt-1 — 0.8vt-1) for t > 1998(4)
sRISKt = 0.0394 for t A 1998(4),
where RWt is the three months Euro money market rate and (Avt-1 — 0.8vt-1) is the expected change in the nominal exhange rate, E(Avt). The term (s • A(euro/dollar))t reflects the fact that we are modelling the trade-weighted exchange rate, which is influenced by the changes in the relative value of United States dollar to Euro (Ecu). This effect is relevant for the period after the abolition of currency controls in Norway in 1990(2), which is why we multiply with a step dummy, st, that is 0 before 1990(3) and 1 after.
Finally, there is a composite dummy
Vdumt = [—2 x i73q1 + i78q1 + i82q3 + i86q3 + 0.7i86q4 — 0.1s86q4_01q4 — i97q1 + i97q2]t
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to take account of devaluation events. Figure 9.5 shows the sequence of 1-step residuals for the estimated Avt equation, together with similar graphs for the following three marginal models reported.
Figure 9.5. Marginal equations: recursive residuals and ±2 standard errors (a)
