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

4. Market Clearing under Flexible Prices

Using the definition of the TOT (28) the preceding equations can be rewritten as:

Ct  =  Tt^n-1Yt,

C *  _ T nγ *

(34)

(35)

These are the conditions for domestic and foreign goods market clearing, which imply that households
across countries always consume exactly their real incomes (see Obstfeld/Rogoff 2001, p. 8).

Moreover, B0 _ B₀^* _ 0 together with (14), (29), (30), and (31) also implies that Ct _ C_t^* _ C_t^w at all
times such that

* w                      *       n-1                n * n * 1-n

Ct _ C_t _ C_t _ nCt + (1 - n)C_t _ nT_t  Yt + (1 - n)T_t Y_t _ Y_t (Y_t )   ,

while making use of (34) and (35).

In consequence, consumption shares across countries are not only time-constant but even equal (see
Obstfeld/Rogoff 2001, p. 8). Since current and capital accounts between the two countries are in
balance at all times and in all possible states of the world, the mechanism of adjustment to shocks in the
world economy will only be represented by movements in the TOT, but not by changes in the countries’
net asset positions. Hence, international financial markets are redundant anyway such that explicitly
modeling financial market completeness by introducing Arrow-Debreu securities can be waived.

4.2. National Money Markets and World Currency Market

The government is assumed to set its expenditures equal to its revenues at all times such that the
government budget is always in balance and no seignorage can occur (see Obstfeld/Rogoff 1996, p.
523):¹⁶

Mt - Mt-1 + Ptτt _ 0.

(36)

Note that an analogous equation to (36) also holds abroad.

Equation (36) describes domestic money supply. Combining (36) with (19) and using the condition
for domestic goods market clearing (34), one obtains two equations in M, which can be set equal and
eventually solved for P :

Pt _

_________Mt-1_________

X ¹ ( ¹+^t ´ ¹ ( TnYt* )^ε + τt

Making use of (9), an analogous equation in P can be computed abroad such that both equations can
again be set equal and finally solved for S :

St _

■                      1

Mt-1 (X* )¹ (+f) ^ε (TtⁿYt* )^ε + τ_t*

^Mt^*-1

■                       1                                    ■

X¹ (⅛^t)^ε (Tt¹ Yt)^ρ + τt

As one can see from the above formula, the current equilibrium nominal exchange rate St positively
depends on past domestic nominal money balances M_t-1, current domestic opportunity costs of holding
money i_t /(1 + i_t), current foreign output Y_t^* , and current foreign real lump-sum taxes τ_t^* . The depen-
dence on the remaining variables is of opposite sign, except for the current TOT Tt , whose influence
is ambiguous. An increase of S illustrates a depreciation of the domestic currency, whereas a decrease
characterizes an appreciation.

¹⁶One could extend the model by introducing government spending (shocks) (see Obstfeld/Rogoff 2001, pp. 37-38),
which shall be waived for this analysis however.

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