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

A. Appendix

etary policy into the framework. Another possibility would be to alter the specification and correlation
patterns of the various macroeconomic shocks. As already stated in Section 2, Gall (2008) gives various
suggestions on how to extend a basic closed-economy New Keynesian model. Out of these suggestions we
find that introducing labor market frictions, migration, and unemployment, imperfect information and
learning, or the use of real capital as additional production factor would be particularly appealing (see
Gall 2008, pp. 188-190).

An immediate application of the present framework, however, would be an empirical one. Similar to
Rubaszek/Skrzypczynski (2008) who treat the US as a closed economy, one could test the forecasting
performance of this model against an unconstrained vector autoregressive (VAR) model while using the
same data.

A. Appendix

A.1. Consumption-based Consumer and Producer Price Indexes, Demand Curves
for Individual and Composite Goods

The derivation of all price indexes and demand curves follows the ideas in Obstfeld/Rogoff (1996,
pp. 662, 664) for the basic Obstfeld/Rogoff (1995) model.

Consumption-based Consumer Price Index, Demand Curves for Composite Goods The representative
domestic household maximizes

n 1-n

C =  CHCF

nn (1 - n)^{1 -n}

with respect to CH sub ject to the budget constraint

PC = PHCH +PFCF.

Hence,

_Cn _C1-n

Λ = —HF--λ ( Ph Ch + Pf Cf - PC ) → max

nⁿ(1 - n)^{1-n      H H F F}          CH

Solving this expression for CH , one obtains the subsequent preliminary demand function for the composite
domestic good:

CH = λ   PH    n C_f.

^H 1-n

Multiplying the preceding equation with PH , one obtains:

1 ⁿ n

Ph Ch = λ ^n-1 PHn^-1  ---Cf

^H 1-n

with PHCH = nPC. Now combine the preceding equation with the preliminary demand function from
above. Then one gets for CH equation (12):

Ch=n μ PH )¹ C.

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