# Mundell-Fleming model

One of the main assumptions in the MF model is the assumption of interest rate parity. We begin by explaining this assumption.

## Interest rates within in the same currency area

A currency area is a geographic area where the same currency is used. United Kingdom is one example of a currency area and all the countries using the euro is another (France, for example, is not a currency area, as they use the euro).

Within a currency area, at a certain point in time, there can be no significant differences in the interest rate geographically. With large differences, there would be arbitrage possibilities (the argument is similar to that of the law of one price). If it was possible to borrow/lend at interest rates 6%/5% in Paris and at the interest rates 4%/3% in Athens, you could become very wealthy.

## Interest rates between currency areas

Between currency areas, it is not as simple. Even if you can borrow at 4% in one area and lend at 5% in another, you cannot be sure that you will make a profit. The reason, of course, is that the exchange rate may change and what you gain from the interest rate differential, you lose from changes in the exchange rate.

However, if you somehow knew that the exchange rate would be the same in the future, then the interest rates would have to be the same. But even with fixed exchange rates, you cannot know this for sure as exchange rates may be devalued or revalued.

## Expected depreciation

To figure out the relationship between the domestic interest rate R and the foreign interest rate RU we introduce the concept expected depreciation: nEe. The expected depreciation indicates how much investors expect the domestic currency to lose against the foreign currency within a given period.

For example, if E = 0.8 €/\$ today and it is expected that E = 1 €/\$ in one year, the expected depreciation is equal to 25%, nEe = 0.25. If you expect an appreciation of say 10%, we write nEe = -0.1.

## Interest rate parity

An important assumption in the Mundell-Fleming model is the assumption of interest rate parity:

R " RU + nEe E

The domestic interest rate should be approximately equal to the foreign rate plus the expected depreciation. If the foreign one-year interest rate is 3% and you expect our currency to lose 2% to the foreign currency, then, according to the interest rate parity, the domestic one-year interest rate should be approximately 5%. The exact result is 1 + R = (1 + RU)(1 + nEe) or R = 5.06%.

Interest rate parity can be justified using arbitrage arguments. If interest rate parity holds, the expected return abroad will be the same as the domestic return and there will be no major flows of capital in either direction.

Say again that R = 5%, RU = 3%, nEe = 2% and E = 0.8 €/\$ initially. If you invest 1000 in the euro area, you have 1050 after 1 year. If you invest them abroad, you invest \$1250. At 3%, you have \$1287.5 a year later. If the actual depreciation is equal to the expected, E = 0.816 one year later. \$1287.5 at the rate 0.816 €/\$ is approximately equal to 1050.

Note that the actual rate of return may differ between countries if the actual depreciation differs from the expected depreciation. However, as long as expected returns are the same, there will be no major movements affecting the current exchange rate.

## Modeling expected depreciation

Fully extending the neoclassical synthesis to an open economy is not simple. The main reason for this is that we need a model for how expectations on the exchange rate are formed. A simple solution to this problem is to assume that expectations are exogenous. In more advanced models, expectations are endogenous. Fortunately, a simple model with exogenous expectations leads to results that are similar to more complex models with endogenous expectations.

We assume that nEe = 0 if the exchange rate is fixed. In practice, this means that we do not expect any devaluations or revaluations. With i Ee = 0, R = RF.

We assume that nEe = n - if in the long run if the exchange rate is flexible. If the domestic inflation is 4% above the rest of the world, we expect a 4% depreciation of the exchange rate. In the short run, i Ee is assumed to be fixed (and equal to the inflation differentials in the last period).

If our country is small in relation to the rest of the world (the foreign country), it is reasonable to assume that RF is determined as if the foreign "country" was a closed economy while our interest rate R is affected by RF. With fixed exchange rates, our interest rate is simply equal to the world interest rate. With a flexible exchange rate, our interest rate is equal to the world interest rate plus or minus a given constant (nEe).