Investment and Interest Rate Policy in the Open Economy

4.2 Backward-looking rules

We now turn our attention to backward-looking interest-rate rules. The determinacy
analysis proceeds as before except now the aggregate system is five-dimensional and de-
terminacy requires two eigenvalues to lie inside the unit circle and the remaining three
eigenvalues be outside the unit circle. The difference system is six-dimensional under con-
sumer price inflation targeting and determinacy therefore requires that there are exactly
three eigenvalues inside the unit circle and three eigenvalues outside the unit circle. As
before the capital dynamics eigenvalue can lie inside or outside the unit circle depending
on the size of a. Since responding to backward inflation makes the analytical conditions
for determinacy more complex to derive, we will simply report some numerical results.
Suppose α = 0.36, β = 0.99 and δ = 0.025. Then determinacy of the aggregate system
requires that 1 < μ < 3.171 otherwise no equilibrium exists. Figures 3 and 4 depict the
regions in the parameter space (a, μ) that are associated with determinacy (D), (first-
order) indeterminacy (I) and an explosive solution (N) around the neighborhood of the
steady state, for both possible indexes of inflation. First consider the case when the
capital dynamics root is unstable (a ≥ 0.4716). Inspection of figure 3 suggests that if
domestic price inflation is targeted the open-economy places no additional restrictions for
equilibrium determinacy. However if consumer price inflation is targeted, figure 4 sug-
gests that the upper bound on the inflation coefficient is more severe in the open-economy.
Furthermore the range of determinacy decreases as the degree of trade openness increases
therefore implying that this upper bound is increasing with respect to a. Next consider
the case where the eigenvalue associated with the capital dynamics lies inside the unit cir-
cle (a < 0.4716). If domestic price inflation is targeted then determinacy is not possible,
whereas if consumer price inflation is targeted determinacy prevails.

24

<<   22   23   24   25   26   27   28   >>

More intriguing information