Relation of two countries
Now we look at the possibility of comparing domestic and foreign growth
rates, i.e. answering questions such as: What happens when the domestic economy
grows, but the foreign economy grows faster?
For this purpose we look at the domestic and foreign economy symmetrically.
The following applies
In money market equilibrium, the respective supply of money
determines the quantity of money. We replace this in the money demand
equations and by dividing, we obtain
Here, we insert the purchasing power parity equation and obtain:
Solved for the exchange rate ,
where the variables marked with
the ratio of the respective domestic to the foreign variables. This equation
can be interpreted quite clearly, since a change of x% in a tilde variable
that the domestic variable has changed by x% more than the foreign variable. We
show this with the example of money supply using the approximations
valid for small
Now we replace
on both sides, we obtain
The interpretation of the above equation can also be formally derived by
"loglinearizing", i.e. logarithmizing both sides of the equation and then
calculating the difference to the previous period. The result is the same as
Therefore, the following applies:
- 1. An increase of x% in the relative supply of money
1. causes the currency to devalue by x%.
- If the domestic supply of money
increases by x% more than the foreign supply
the currency devalues by x%.
- An increase of the relative real GDP
by x% causes the currency to appreciate by x%.
- If the domestic GDP
by x% more than the foreign GDP ,
the currency appreciates by x%.
- Ein Anstieg des relativen Kassenhaltungskoeffizienten (Stabilität der
Transmissionsmechanismen am Finanzmarkt)
Preisniveaus um x% lässt die Währung um x% aufwerten.
Herein, the individual changes are additive.
(c) by Christian Bauer
Prof. Dr. Christian Bauer
Chair of monetary economics
Tel.: +49 (0)651/201-2743