the effects that fluctuations in the copper price have on the real exchange rate and, consequently, on competitiveness. The adjustment coefficients show that the Chilean interest rate is equilibrium error correcting in the long and medium run. The domestic price is equilibrium error increasing in the long run but equilibrium error correcting in the medium run. Thus, if the domestic price is above its long-run benchmark value, in the medium run both the domestic inflation rate and changes in the domestic interest rate will tend to increase, generating an increase in the equilibrium error term ˆ v 1, t . In the long run, however, the domestic price will tend to increase, which generates a decrease in ˆ v 1, t . To restore the long-run equilibrium, the domestic interest rate starts increasing. The second polynomially cointegrating relationship, ˜ β 0 2 ˜ x t + ˜ d 0 2 4 ˜ x t , can be interpreted as a long-run relationship between the interest rate spread, trend-adjusted prices, and changes in the nominal exchange rate and is expressed as: 22 When α ij = 0, the corresponding d ij is not shown in Equations ( 27 ) and ( 28 ). Furthermore, only d ij coefficients with a | t-value | ≥ 2.5 are shown.
Econometrics 2017 , 5 , 29 16 of 21 i d , t - i f , t = 0.03 ˜ p d , t - 0.28 ˜ p f , t + 1.21 4 p d . t + 0.17 4 p f , t + 1.01 4 s t - 0.001 4 i d , t + 1.13 + ˆ v 2, t (28) where ˜ p f , t and ˜ p d , t are, respectively, the trend-adjusted prices in US and Chile and ˆ v 2, t ∼ I ( 0 ) is the equilibrium error. The equation shows that the interest rate spread is positively co-moving with the relative trend-adjusted level of prices, domestic and foreign inflation rates, and changes in both nominal exchange rate and domestic interest rate. This relationship might describe a central bank’s reaction rule. The Chilean trend-adjusted price, ˜ p d , t , might tentatively be interpreted as a proxy for a long-run indicator of the inflation target. That is, given the US interest rate and US trend-adjusted price, if the domestic price is above (below) its long-run trend, the central bank may use contractionary (expansionary) monetary policy that increases (decreases) the domestic interest rate. The above argument may be used to explain the relationship between the interest rate spread and the changes in the nominal exchange rate. For example, the central bank may use contractionary monetary policy to counteract inflationary pressures due to exchange rate depreciation. The adjustment coefficients show that when the interest rate spread has been under its long-run value, the domestic inflation rate and the domestic interest rate will tend to decrease in the medium run. Furthermore, the domestic price is equilibrium error correcting to the central bank’s reaction rule in the long run, whereas the domestic interest rate is equilibrium error increasing in the long run. Then, if the interest rate spread is under its long-run equilibrium value, the domestic interest rate will tend to decrease. This generates further decreases in the equilibrium error ˆ v 2, t . However, at the same time, the domestic price will tend to decrease, so it starts to restore the equilibrium.
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