The Fisher Effect and Real Interest Rate Parity

Suppose you like imports. (It's nice to get exotic goods.)

You probably do this with your domestic currency, but you're essentially paying a foreign price, with a spot rate, $$S_{f/d}$$, with your domestic currency as the base currency. Considering the transactions involved, what do you think would make your imports cheaper for you?

No, that wouldn't do the trick. Remember that your currency is the base currency. So a lower nominal exchange rate means that your currency is weaker. That won't help you buy cheaper foreign goods.

That's right! Sure, a lower foreign price level means lower foreign prices. That's good for you. Since your currency is the base currency of the exchange rate, a higher exchange rate will mean a stronger domestic currency and more buying power, not a lower one. Also, you earn money in your domestic currency, so a lower domestic price level means lower wages for you when measured in foreign currency. So you would like that to be higher as well.

Well, no. It might not seem too obvious, but this will actually hurt your buying power. Consider that any wages you earn at home are part of that price level, so a lower price level means lower wages when measured against foreign goods.

Speaking of real things, what do you think is more likely to be the same between two countries: their real interest rates or nominal interest rates?

No. Actually, the real interest rates are much more likely to be similar, given any two countries.

Yes!

This goes back to the idea of interest rate parity conditions. A risk-free rate should be a risk-free rate just about anywhere. Now the focus is on nominal interest rates versus real interest rates, and this relationship can be summarized according to the __Fisher effect__ as $$\displaystyle i = r + \pi^e $$, which just means that a nominal interest rate, _i_, is the sum of the real rate and expected inflation.

If you think about this effect holding for two countries, both of which have the same real interest rate, what does that imply for the inflation rates in both countries?

No, that's not necessary. Notice that there are three components here, so holding one constant allows for the other two to adjust.

That's not right. The level of real interest rates doesn't relate to this difference at all.

Precisely. You just start with the pair of nominal rates in each country: $$\displaystyle i_f = r_f + \pi_f^e $$ and $$ i_d = r_d + \pi_d^e $$. Subtracting one from the other and rearranging leads to $$\displaystyle r_f - r_d = (i_f - i_d) - (\pi_f^e - \pi_d^e) $$. So the real interest rate differential is the nominal interest rate differential minus the inflation rate differential. And it follows that if the real interest rates are the same, the nominal rate differential should be the inflation rate differential.

If uncovered interest rate parity holds, then any difference in the nominal interest rate should cause that same change in the exchange rates. And if _ex ante_ PPP holds, then the inflation rate differential should also cause that same change in the exchange rates. So if these conditions both hold, then what can you conclude?

Exactly! This is called the __real interest rate parity__ condition, and it follows directly from those other two parity conditions. Together, they suggest that the nominal interest rate differential will equal the expected inflation rate differential. If that's true, the Fisher effect shows the real rates to be the same. So any difference in nominal rates is blamed solely on differences in expected inflation. $$\displaystyle i_f - i_d = \pi_f^e - \pi_d^e $$ That's the __international Fisher effect__. Again, this stuff doesn't really hold up in the short run, but it's a decent tool to use if you have a longer-term focus.

Actually, it will. It just depends on these two forces. They're not assumed to be zero here; just equal.

No. That's a good general assumption, and it implies positive real rates. But it doesn't follow from these parity conditions.

To summarize: [[summary]]

A lower exchange rate

A lower foreign price level

A lower domestic price level

Real interest rates

Nominal interest rates

They must be the same as well

Any difference would be the same as the real interest rate

Any difference would be the same as the difference in nominal interest rates

The real rates are the same

The exchange rate will not change

Nominal rates will be higher than inflation rates

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