Chapter 16
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

Md = kPy&Md = kPy Ms = Md&Ms = Md

In money market equilibrium, the respective supply of money (Ms and Ms) determines the quantity of money. We replace this in the money demand equations and by dividing, we obtain

M0s M0s = kPy kPy

Here, we insert the purchasing power parity equation and obtain:

P = SP M0s M0s = S ky ky

Solved for the exchange rate S, we get

S = M M ky ky = M̃ k̃,

where the variables marked with ̃ indicate 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 ̃ means 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 1+x 1+y 1 + x y and 1 + x 1 + y 1 + x + y which are valid for small x and y, respectively.

M̃ = 1 + x 100 M̃0 M = 1 + ϕM 100 M0 M = 1 + ϕM 100 M0

Now we replace M̃ = M M

1 + x 100 M̃0 = M̃ = M M = 1 + ϕM 100 M0 1 + ϕM 100 M0 = 1 + ϕM 100 1 + ϕM 100 M̃0

By reducing M̃0 on both sides, we obtain

1 + x 100 = 1 + ϕM 100 1 + ϕM 100 1 + ϕM 100 ϕM 100  oder  ϕM ϕM = x.

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 above.

S = M̃ k̃ log S = log M̃ k̃ = log M̃ log k̃ log = log M log Mlog k log klog y log y log S0 = log M0 log M0log k 0 log k0log y 0 log y0 Δ log S0 = Δ log M0 Δ log M0Δ log k 0 Δ log k0Δ log y 0 Δ log y0 ϕS = ϕM ϕMϕk ϕkϕy ϕy

Therefore, the following applies:

  1. 1. An increase of x% in the relative supply of money M̃ 1. causes the currency to devalue by x%.
  2. If the domestic supply of money M increases by x% more than the foreign supply M, the currency devalues by x%.
  3. An increase of the relative real GDP by x% causes the currency to appreciate by x%.
  4. If the domestic GDP y by x% more than the foreign GDP y,, the currency appreciates by x%.
  5. Ein Anstieg des relativen Kassenhaltungskoeffizienten (Stabilität der Transmissionsmechanismen am Finanzmarkt) k̃ 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
Trier University
D-54296 Trier
Tel.: +49 (0)651/201-2743