📖 购买力平价（PPP）

Economics

I. Lesson Focus

This lesson examines the theory of Purchasing Power Parity (PPP), one of the fundamental frameworks for understanding long-run exchange rate determination. Candidates must master both absolute and relative PPP, be able to calculate implied equilibrium exchange rates, judge whether a currency is overvalued or undervalued, forecast future exchange rate movements based on inflation differentials, and recognize the limitations of the theory in real-world applications.

II. The Problem

Suppose one U.S. dollar buys a certain basket of goods in the United States, while the identical basket costs 6.5 Chinese yuan in China. According to purchasing power parity, what should the equilibrium exchange rate be? If the current market rate is 7.2 CNY per USD, is the renminbi overvalued or undervalued, and how should the exchange rate be expected to adjust over time? These questions lie at the heart of exchange-rate determination in the CFA Level I curriculum. Candidates frequently confuse absolute and relative PPP, misapply base periods, or ignore the direction of currency appreciation/depreciation implied by inflation differentials. This lesson systematically resolves these valuation and forecasting issues with clear formulas and numerical applications.

III. Core Logic of Purchasing Power Parity Theory

Purchasing Power Parity (PPP) asserts that, in the long run, exchange rates between two currencies should adjust so that a identical basket of goods costs the same in both countries when expressed in a common currency. The theory rests on the Law of One Price: in the absence of transportation costs and trade barriers, identical goods must sell for the same price worldwide after exchange-rate conversion.

For a basket priced at P_US (in USD) in the United States and P_CN (in CNY) in China, the equilibrium exchange rate S (CNY per USD) under absolute PPP is:

$$ S = \frac{P_{CN}}{P_{US}} $$

Absolute PPP uses actual price levels to determine the fair exchange rate. In practice, transportation costs, tariffs, and non-tradable goods (services, real estate, haircuts) cause absolute PPP to rarely hold exactly. Economists therefore rely more heavily on Relative PPP, which focuses on changes in price levels (i.e., inflation rates) rather than absolute levels.

The approximate relative PPP formula is:

$$ \% \Delta S_{f/d} \approx \pi_f - \pi_d $$

where: - $\% \Delta S_{f/d}$ = percentage change in the foreign/domestic exchange rate (positive value means foreign currency appreciates against domestic currency) - $\pi_f$ = foreign inflation rate - $\pi_d$ = domestic inflation rate

The formula implies that the currency of the higher-inflation country is expected to depreciate by approximately the inflation differential.

IV. Applying Absolute PPP: Identifying Overvaluation and Undervaluation

When the market exchange rate deviates from the PPP-implied rate, the currency is said to be misaligned.

• If market rate (domestic currency per foreign currency) > PPP rate → domestic currency is undervalued
• If market rate < PPP rate → domestic currency is overvalued

The Big Mac Index, published by The Economist, is the most famous practical application of absolute PPP. It uses the local-currency price of a McDonald’s Big Mac as a proxy for a broader basket of goods.

V. Using Relative PPP for Exchange-Rate Forecasting

Relative PPP is particularly useful for forecasting the direction and magnitude of exchange-rate changes. Assume: - U.S. expected inflation = 2% per year - Chinese expected inflation = 5% per year - Current spot rate S₀ = 7.0 CNY/USD

According to relative PPP, the renminbi is expected to depreciate by approximately 5% – 2% = 3% per year.
Expected rate in one year ≈ 7.0 × (1.03) = 7.21 CNY/USD.

VI. Assumptions, Limitations, and the Balassa-Samuelson Effect

PPP requires strong assumptions: 1. Goods are identical and perfectly tradable 2. No transaction costs, tariffs, or quotas 3. Prices are fully flexible 4. Only tradable goods are considered

In reality, the Balassa-Samuelson Effect explains why richer countries’ currencies tend to appear overvalued under absolute PPP: higher productivity in tradable sectors raises wages and prices in non-tradable sectors, pushing the overall price level higher.

Worked Cases

Case 1: Absolute PPP Valuation

A representative basket costs $100 in the United States and ¥680 in China. The current market rate is 7.5 CNY/USD.

Calculation:
PPP-implied rate = 680 / 100 = 6.8 CNY/USD
Market rate (7.5) > PPP rate (6.8) → renminbi is undervalued by (7.5 – 6.8)/6.8 ≈ 10.29%.

Conclusion: The renminbi’s real purchasing power is stronger than the market rate suggests; it should appreciate over the long term.

Case 2: Multi-period Relative PPP Forecast

Current rate S₀ = 1.25 USD/EUR.
U.S. expected inflation = 3% per year.
Eurozone expected inflation = 1.5% per year.
Forecast horizon = 3 years.

Calculation:
Annual expected appreciation of the euro vs. USD = 3% – 1.5% = 1.5%.
Expected rate in 3 years = 1.25 × (1.015)^3 ≈ 1.25 × 1.0456 ≈ 1.307 USD/EUR.

Conclusion: The USD is expected to depreciate against the euro.

Case 3: Combined Judgment with Proper Base Period

In 2010 the exchange rate was 6.5 CNY/USD and inflation rates were equal. Over the subsequent 5 years China averaged 6% inflation and the United States 2%. Current market rate is 7.1 CNY/USD.

Calculation:
Cumulative inflation factor = (1.06 / 1.02)^5 ≈ 1.2098.
PPP-implied current rate = 6.5 × 1.2098 ≈ 7.864 CNY/USD.
Market rate (7.1) < PPP rate (7.864) → renminbi is overvalued by approximately 9.7%.

Common Mistake: Candidates often add 5 × (6% – 2%) = 20% instead of compounding, producing inaccurate forecasts.

Traps

Key Formulas

• Absolute PPP: $ S_{PPP} = \frac{P_{foreign}}{P_{home}} $
• Approximate Relative PPP: $\% \Delta S_{f/d} \approx \pi_f - \pi_d $
• Exact Relative PPP: $ S_t = S_0 \times \frac{(1+\pi_f)^t}{(1+\pi_d)^t} $
• Undervaluation test (domestic/foreign quote): Market rate > PPP rate implies domestic currency undervalued
• Expected depreciation rate ≈ inflation differential

Practice Questions

Q1. According to absolute purchasing power parity, if a basket costs $50 in the United States and £32 in the United Kingdom, the equilibrium exchange rate is closest to:
A. 0.64 USD/GBP
B. 1.5625 USD/GBP
C. 0.64 GBP/USD
D. 1.5625 GBP/USD

Q2. U.S. inflation is 2.5% and Japanese inflation is 0.8%. According to relative PPP, the yen is expected to:
A. appreciate by 1.7% against the USD
B. depreciate by 1.7% against the USD
C. appreciate by 3.3% against the USD
D. depreciate by 3.3% against the USD

Q3. The current exchange rate is 9.0 MXN per USD. Mexican inflation is expected to be 8% and U.S. inflation 3%. The expected exchange rate in one year according to relative PPP is closest to:
A. 8.55 MXN/USD
B. 9.45 MXN/USD
C. 9.36 MXN/USD
D. 8.64 MXN/USD

Q4. If the renminbi is significantly undervalued according to absolute PPP, the most likely long-term outcome is:
A. continued depreciation of the renminbi
B. appreciation of the renminbi
C. persistently higher Chinese inflation
D. widening trade surplus

Q5. Which of the following is least likely to cause PPP to fail?
A. Existence of non-tradable goods
B. Transportation costs and tariffs
C. Completely independent monetary policies
D. Price stickiness

Q6. A country with persistently higher inflation than its trading partners will most likely experience:
A. real effective appreciation
B. nominal appreciation
C. nominal depreciation
D. unchanged real exchange rate

Q7. The Big Mac Index indicates a currency is overvalued by 20%. This most likely means the local price of a Big Mac is:
A. 20% lower than the PPP-implied price
B. 20% higher than the PPP-implied price
C. consistent with 20% higher local inflation
D. consistent with 20% higher local interest rates

Q8. The current rate is 1.35 CAD per USD. Canadian inflation is expected to be 2% and U.S. inflation 4%. The two-year-ahead expected exchange rate according to relative PPP is closest to:
A. 1.29 CAD/USD
B. 1.41 CAD/USD
C. 1.32 CAD/USD
D. 1.22 CAD/USD

Answers

Takeaways

• Absolute PPP determines exchange-rate levels; relative PPP forecasts percentage changes.
• Currencies of high-inflation countries are expected to depreciate by roughly the inflation differential.
• Market rate > PPP rate (domestic per foreign) indicates undervaluation; the reverse indicates overvaluation.
• PPP works better in the long run; short-run rates are heavily influenced by capital flows and interest rates.
• Always compound inflation differentials rather than simply adding them.
• The Balassa-Samuelson effect explains why developed-country currencies often appear overvalued under absolute PPP.