Inflation and Real Exchange Rates

Inflation and Exchange Rate formula

What is the formula for calculating the real exchange rate, and what does inflation have to do with it?

Let's take it one step at a time. First, here is the formula:

\(\hbox {Real exchange rate} = \hbox {Nominal exchange rate} \times \frac {\hbox {Domestic price}} {\hbox {Foreign price}}\)

Note how the nominal exchange rate is defined here:

\(\hbox {Nominal exchange rate} = \hbox{Foreign currency per domestic currency}\)

Let's do a small example to make sure that we get what this formula is saying.

But as economists, we are usually not just concerned with the relative price of one item but the comparison of the general price levels in different economies. To do this, we substitute the domestic price and foreign price in the earlier formula with the domestic and foreign price indexes.

\(\hbox{Real exchange rate} = \frac {\hbox{e} \times \hbox{P}} {\hbox{P*}} \)

Where:

\(\hbox{e}\) - the nominal exchange rate;

\(\hbox{P}\) - the domestic price index;

\(\hbox{P*}\) - the foreign price index.

Relationship between Inflation and Exchange Rate

What is the relationship between inflation and the exchange rate? What does inflation have to do with the nominal and real exchange rates? Well, the answer is: it depends.

The effects of inflation on the exchange rate

Inflation does not have direct effects on the nominal exchange rate, but the underlying cause of inflation might. Why is that? One cause of high inflation is an increase in the money supply. The nominal exchange rate is determined by the supply and demand of currencies in the foreign exchange market.

Inflation certainly affects the real exchange rate, but the real exchange rate also depends on whether and how the nominal exchange rate changes. All else equal, if the general price level is higher, goods and services become more expensive for foreigners. But if the increase in the general price level is coupled with a depreciation of the domestic currency in the same proportion, the real exchange stays the same as before. Let's do some calculations with an example to see this more clearly.

How to Calculate the Real Exchange Rate with Inflation?

How do we calculate the real exchange rate with information on inflation? We can simply plug in numbers in the real exchange rate formula:

\(\hbox {Real exchange rate} = \hbox {Nominal exchange rate} \times \frac {\hbox {Domestic price index}} {\hbox {Foreign price index}}\)

Where the nominal exchange rate is defined as:

\(\hbox {Nominal exchange rate} = \hbox{Foreign currency per domestic currency}\)

Calculating real exchange rate with inflation. Currency depreciation and inflation cancel each other out

Let's say that the Canadian dollar depreciates by 20% against the US dollar. The exchange rate goes from 1.1 Canadian dollars per US dollar to 1.32 Canadian dollars per US dollar. It's a depreciation of the Canadian dollar because you get more of it for the same amount of the US dollar.

Does this mean that things in Canada are cheaper than before for tourists from the US? The 20% depreciation is about the nominal exchange rate. We need to know about the real exchange rate because that is what actually matters. It turns out that during this time, Canada experiences some inflation, but the US does not. The general price level in Canada rises by 20%, with the price index rising from 100 to 120, while the US price index remains at 100. Where does this leave the real exchange rate?

\(\hbox {Real exchange rate} = \hbox {Nominal exchange rate} \times \frac {\hbox {Domestic price index}} {\hbox {Foreign price index}}\)

Real exchange rate before:

\(\hbox {Canadian dollars per US dollar} \times \frac {P_{US}} {P_{Can}} = 1.1 \times \frac {100} {100} = 1.1 \)

Real exchange rate after:

\(\hbox {Canadian dollars per US dollar} \times \frac {P_{US}} {P_{Can}} = 1.32 \times \frac {100} {120} = 1.1 \)

We see that the real exchange rate is the same. Things in Canada do not become cheaper for US tourists even if the Canadian dollar depreciates because the increase in inflation cancels it out.

Calculating real exchange rate with inflation. What about sticky prices?

The price of everything doesn't always adjust immediately in the face of inflation. Businesses may find it costly to increase their prices and decide to absorb some of the cost increases. This phenomenon is known as sticky prices. When a currency depreciates against other currencies, but the prices in that country don't increase as much, then things in that country have become cheaper for foreigners.