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

A. Appendix

be written as nPt,H Yt , which yields the subsequent equilibrium condition on the world market for domestic
goods (26):

Pt,HYt = PtCt^w .

Note that the equilibrium condition on the world market for foreign goods (27) can be derived analo-
gously.

Both equations immediately collapse to the definition of the TOT given by equation (28):

T .₌ Pt,F ₌ StP*,F ₌ Yt
^t : p         p         v* '

Pt,H    Pt,H    Yt

Furthermore, substituting equation (22) for the household’s instantaneous profits into the intertemporal
budget constraint (17) we get:

(1 + it_-1)Bt_-1 + Mt_-1 + Pt(h)Yt(h) = PtCt + Mt + Bt + Ptτt.

Integrating from 0 to n and using ₀ⁿ Pt (h)Yt (h)dh = nPt,H Yt one obtains:

(1 + i_t-1)B_t-1 + M_t-1 + P_t,H Y_t = P_tC_t + M_t + B_t + P_tτ_t.

Due to the government’s budget constraint (36) the preceding equation rearranges to the domestic balance
of payments identity (29):

Pt,H Yt ^- PtCt + it-1Bt-1 ^≡ Bt ^- Bt-1^.

Note that the foreign balance of payments identity (30) can be derived analogously.

A.4. Dynamic IS Curves

First rewrite the domestic Euler equation for real consumption (18) as follows:

After having done so, use the condition for domestic goods market clearing (34) into the preceding
equation:

(Tt^n-1Yt)^-ρ = β(1 + it)PtEt

The non-stochastic zero-inflation steady-state version of this equations reads as follows:

Y )^—p

The ratio of the last two equations then reads:

By taking the natural logarithm of this ratio, one obtains:

-p[(n - 1)tt + yt - (n - 1)t - y] = ln(1 + it ) - ln(1 + i) + pt - Et [Pt+1] - ρ{(n - 1)Et [tt+1] + Et [yt+1]} + P[(n - 1)?+ y].

Note that ln(1 + it) ≈ it and ln(1 +^yi) ≈^yi. Moreover, the approximation ln Et[Ψt+1] ≈ Et [Ψt+1] - 1 =
Et [Ψt+1 - 1] ≈ Et[ln Ψt+1] = Etψt+1 assures for the exchangeability of the ln and expectations operators
for a generic random variable Ψ.

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