Macroeconomic Interdependence in a Two-Country DSGE Model under Diverging Interest-Rate Rules



7. Impulse-Response Analysis

curves (56) and (57) with respect to expected movements in the TOT:26

!/


(0.5 - 1)[(-1)x0.8 - (-1)]


[(-1) - 0.8]0.8

0.5[(- 1)x0.8 - (-1)]
[(
-1) - 0.8]0.8


0.07,


-0.07.


Set the degree of price stickiness to δ = δ* = 0.75 across countries, which corresponds to an average
duration of a price of 4 quarters. This implies the following for the slope coefficients
μ, μ* of the NKPCs
(49) and (50) with respect to the domestic (foreign) output gap:

(1 - 0.75)(1 - 0.75x0.97)[0.8 - (-1)]

--------------------------------------------≈ 0.16.

0.75

Calculating the characteristic determinant det(M - kI7) while using the above parameter configuration
then yields the subsequent numerical eigenvalues:

k1 = 0,

k2 = 0.5441,

k3 = 0.8176 + 0.2411i,

k4 = 0.8176 - 0.2411i,

k5 = 0.9775,

k6 = 13.3372,

k7 = 18.2548.

Since M contains five stable (k1 to k5 ) and two unstable eigenvalues (k6 and k7), there is a unique
stationary solution to the system of equations (63) such that the rational expectations equilibrium indeed
is determinate.

Notice that the above results have been derived for a calibrated version of the two-country DSGE model
only so that they may not necessarily be universally applicable.

7. Impulse-Response Analysis

After having assured for determinacy of the rational expectations equilibrium, it would be interesting to
investigate how the endogenous variables of the model react to simulated transitory shocks at home and
abroad. This impulse-response analysis can also be viewed as additional robustness test for the goodness
of the present model specification.

For this purpose, let us assume the following autocorrelation coefficients of the domestic and foreign
productivity, cost-push, and monetary policy shocks:
ζa = ζa* = ζu = ζu* = ζv = ζv* = 0.8.27 Moreover,
Ψa = Ψa = 0.3 shall be proposed for the correlation coefficients of the interdependent productivity
shocks.

Using the above specification and starting from the non-stochastic zero-inflation steady state, we entail

26Note that if we examined the special case of ρ = 1, which corresponds to logarithmic utility of consumption, we would
get three implications for the dynamic IS curves (56) and (57): [1] the intertemporal elasticity of substitution of real
consumption 1
is equal to 1 across countries, [2] the impact of the TOT vanishes since ÿ = ÿ* = 0, and [3] the
coefficients on the aggregate productivity shocks
Et [∆at],Et [∆α*] simplify to 1. Hence, the dynamic IS curves
would be isomorphic to their closed-economy counterparts. Let us remind the reader at this point that even though the
TOT effects would disappear for this case, the two economies would remain interdependent because of the positively
correlated aggregate productivity shocks
Et [∆at] ,Et [∆α*].

27We propose this relatively high serial correlation of the transitory shock variables mainly for illustrative reasons. Quali-
tatively, we would obtain the same results if we used smaller autocorrelation coefficients.

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