Purchasing Power Parity & the International Fisher Effect

1. Purchasing Power Parity (PPP)

We briefly introduced Relative PPP in our last lesson as the theory that changes in exchange rates are driven by inflation differentials. Let's now explore this concept more formally, distinguishing between its two main versions.

The foundation of PPP is the law of one price, which states that in the absence of trade frictions (like transport costs and tariffs), an identical good should sell for the same price everywhere once you convert currencies. PPP extends this idea from a single good to a broad basket of goods.

To see how this works in practice, let's explore the two forms of PPP: Absolute and Relative.

Let's summarize the key points and formulas from the video.

Absolute PPP

Absolute PPP states that the spot exchange rate between two currencies should be equal to the ratio of the two countries' price levels.

The formula is:
$S_{d/f}=\frac{P_d}{P_f}$
Where:

• $S_{d/f}$ is the spot exchange rate (domestic currency per unit of foreign currency).
• $P_d$ is the price level in the domestic country (e.g., a CPI basket).
• $P_f$ is the price level in the foreign country.

As the video explained, Absolute PPP rarely holds true in the real world due to:

• Transaction costs: Shipping goods isn't free.
• Trade barriers: Tariffs and quotas artificially raise prices.
• Non-traded goods: Services like haircuts and housing are included in price indexes but can't be traded internationally.
• Different consumption baskets: The "typical" basket of goods differs between countries.

Relative PPP

Relative PPP is a more dynamic and less strict version. It states that the rate of change in an exchange rate is determined by the difference in the inflation rates between the two countries.

The approximate formula is:
$\%\Delta S_{d/f}\approx I_d-I_f$
Where:

• $\%\Delta S_{d/f}$ is the expected percentage change in the spot exchange rate.
• $I_d$ is the inflation rate in the domestic country.
• $I_f$ is the inflation rate in the foreign country.

This theory implies that the currency of the country with the higher inflation rate should depreciate over time to maintain the balance of purchasing power. While it doesn't hold perfectly in the short run, empirical evidence suggests it is a reasonable indicator of long-term exchange rate trends.

For a more detailed look at the formulas and the introduction of a forward-looking version, Ex Ante PPP, please review the following text.

2. The International Fisher Effect (IFE)

The International Fisher Effect (IFE) provides another link between economic variables and exchange rates. It connects nominal interest rate differentials to expected changes in the spot exchange rate. To understand it, we must first start with the domestic Fisher Effect.

The Foundation: The Domestic Fisher Effect

The Fisher Effect, named after economist Irving Fisher, deconstructs a nominal interest rate into two components: the real rate of return and compensation for expected inflation.

As the video illustrates, the relationship is:
$i\approx r+{\pi }^e$
Where:

• $i$ is the nominal interest rate.
• $r$ is the real interest rate.
• ${\pi }^e$ is the expected rate of inflation.

Lenders demand a nominal interest rate that not only provides a real return ($r$) but also compensates them for the loss of purchasing power due to expected inflation (${\pi }^e$).

Extending to the International Fisher Effect

The International Fisher Effect extends this logic to a global context. We start by writing the Fisher equation for two countries, domestic (d) and foreign (f):

1. $i_d\approx r_d+{\pi }_d^e$
2. $i_f\approx r_f+{\pi }_f^e$

Now, we make a crucial assumption: in a world with perfect capital mobility, real interest rates are expected to be equal across countries ($r_d=r_f$). If one country offered a higher real return, capital would flood in, bidding down that return until it equalized with the rest of the world.

Given this assumption, if we subtract the second equation from the first, the real rates cancel out, and we get:
$i_d-i_f\approx {\pi }_d^e-{\pi }_f^e$

This equation tells us that the difference in nominal interest rates between two countries should approximate the expected difference in their inflation rates.

The final step is to link this to exchange rates. From Relative PPP, we know that $\%\Delta S_{d/f}^e\approx {\pi }_d^e-{\pi }_f^e$. By substituting this into our equation above, we arrive at the International Fisher Effect:
$\%\Delta S_{d/f}^e\approx i_d-i_f$

The IFE states that the expected percentage change in the spot exchange rate should be approximately equal to the difference in the nominal interest rates between the two countries. The currency of the country with the higher nominal interest rate is expected to depreciate by roughly the amount of the interest rate differential. This depreciation would ensure that an investor earns the same return whether they invest in the domestic or the foreign country, eliminating any arbitrage opportunity.

For a formal derivation, refer back to our AnalystPrep reading.

3. Synthesis: A Unified Framework

PPP and IFE are not isolated theories. They are part of a unified framework of international parity conditions that link interest rates, inflation rates, and exchange rates. The following diagram is an excellent tool for visualizing these connections.

Let's trace the relationships, assuming the domestic currency is the USD and the foreign is the EUR:

1. (Top) Interest Rate Differential (i_USD - i_EUR): The difference between nominal interest rates in the U.S. and the Eurozone.
2. (Right) Expected Inflation Differential (π_USD^e - π_EUR^e): The link between the interest rate differential (Top) and the inflation differential (Right) is the International Fisher Effect.
3. (Bottom) Expected Change in Spot Rate (%ΔS^e): The link between the inflation differential (Right) and the expected spot rate change (Bottom) is Purchasing Power Parity.
4. The direct link between the interest rate differential (Top) and the expected spot rate change (Bottom) is Uncovered Interest Rate Parity, which is essentially another name for the IFE.

This framework shows that, in an efficient market without frictions, these economic forces should align. A higher nominal interest rate in one country must be associated with higher expected inflation, which in turn implies an expected depreciation of that country's currency.

Conclusion

In this lesson, we have taken a deep dive into two fundamental theories of exchange rate determination: Purchasing Power Parity and the International Fisher Effect.

Key Takeaways:

• Purchasing Power Parity (PPP) links exchange rates to price levels.
  • Absolute PPP states that the exchange rate equals the ratio of price levels, but it rarely holds.
  • Relative PPP states that the percentage change in the exchange rate is approximately equal to the inflation differential. This is considered a better long-run predictor.
• The International Fisher Effect (IFE) links exchange rates to nominal interest rates. It builds on the domestic Fisher Effect ($i=r+{\pi }^e$) and the assumption that real rates are equal globally.
• The IFE concludes that the expected change in the spot exchange rate is approximately equal to the nominal interest rate differential ($\%\Delta S^e\approx i_d-i_f$). The country with the higher interest rate is expected to see its currency depreciate.
• Together, these parity conditions provide a unified, long-run theoretical framework for understanding the relationships between inflation, interest rates, and exchange rates.

Preview of the Next Lesson:

We have now explored how exchange rates are quoted, the regimes they operate under, and the theories that explain their movements. In the final lesson of this module, we will examine the real-world consequences of these currency fluctuations. We will answer the question: What is the impact of exchange rate movements on international trade and capital flows?