A. Appendix
be written as nPt,H Yt , which yields the subsequent equilibrium condition on the world market for domestic
goods (26):
Pt,HYt = PtCtw .
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 + it-1)Bt-1 + Mt-1 + Pt,H Yt = PtCt + Mt + Bt + Ptτt.
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:
Ct-ρ = β(1 + it)PtEt
-ρ
Ct +1
Pt+1
After having done so, use the condition for domestic goods market clearing (34) into the preceding
equation:
( Tt— Yt++1) -
Pt+1
(Ttn-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:
Tnr1 Yt ʌ
/'n— 1YΛ J
1 + it
1 + i
Et
Pt
( ∣ ' Yt +1)-ρ
Pt+1
( T n — 1 Y) —p
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.
32
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