L17-18: Purchasing power parity

Purchasing Power Parity (PPP)

Definition

• Basic Principle: Assuming no tariffs (taxes on imports - duties imposed by a government on imported goods) and transportation costs, for every product i in the economy, Pi = SPi^*, where:

  • P_i is the price of product i in the domestic economy. The domestic economy refers to the country whose perspective is being taken.

  • P_i^* is the price of product i in the foreign economy. The foreign economy is the other country being compared against the domestic economy.

  • S is the nominal exchange rate (domestic currency per unit of foreign currency). The nominal exchange rate is the rate at which one currency can be exchanged for another.

• This is derived from the 'law of one price' or the arbitrage principle applied internationally. The 'law of one price' suggests that identical goods should have the same price in all locations. Arbitrage is the simultaneous purchase and sale of an asset to profit from an imbalance in the price.

Absolute Purchasing Power Parity (APPP)

• Equation: P = SP^*

  • P is the general price level in the domestic country. The general price level refers to an average of all prices of goods and services in an economy.

  • P^* is the general price level in the foreign country.

• Concept: APPP states that the general level of prices, when converted to a common currency, should be the same in every country. It is a strict interpretation of PPP and is rarely observed in practice due to various market imperfections.

Consumer Price Index (CPI) and PPP

• CPI is defined as the weighted average of individual product prices, with weights determined by expenditure shares. The CPI is commonly used to measure the general price level in an economy.

• If the weights used in constructing the CPI are identical across home and foreign countries, then the condition P = SP^* can hold. However, different consumption patterns and variations in the basket of goods can cause deviations from APPP.

PPP as a Benchmark

• PPP provides an important benchmark for analyzing exchange rate movements. It assumes that exchange rates adjust to equalize the purchasing power of currencies.

• If PPP holds continuously, competitiveness is equalized across countries, meaning no country has a general price advantage. This is an idealized scenario.

• In reality, international competitiveness is rarely constant, making deviations from PPP important to measure. These deviations are often due to factors like trade barriers, transportation costs, and non-traded goods.

PPP and Exchange Rate Determination

• PPP serves as a theory for determining exchange rates. It posits that exchange rates will adjust to reflect changes in the price levels of countries.

• Example: If the exchange rate that equates the purchasing power of money between the UK and USA is 0.75 (1 USD = 0.75 GBP), the actual exchange rate should tend towards 0.75 in the long run. This is based on the idea that arbitrageurs will exploit any differences in purchasing power.

• Currency Valuation:

  • If the actual exchange rate is 0.9 GBP (for example), the pound is undervalued and needs to appreciate. This means the pound is cheaper than its PPP value.

  • If the actual exchange rate is 1 USD = 0.5 GBP, the pound is overvalued and needs to depreciate. This means the pound is more expensive than its PPP value.

Implications of Currency Valuation

• Undervalued Pound:

  • Exports become cheaper in foreign markets, boosting demand for UK goods and services. Exports are goods and services produced in the domestic country and sold to foreign countries.

  • Imports become more expensive for domestic households, potentially leading to higher inflation. Imports are goods and services purchased from foreign countries by domestic residents.

• Overvalued Pound: The opposite occurs; exports become more expensive, reducing demand, and imports become cheaper, which can lower inflation but harm domestic industries.

Currency Manipulation

• Western policymakers have often suspected that China manipulates its currency to maintain an artificially undervalued exchange rate, boosting exports. This gives Chinese exporters a competitive advantage. Currency manipulation refers to actions taken by a government to influence the exchange rate of its currency.

• If true, this also means Chinese households pay more for imported products, indicating it doesn't benefit all groups within China. Currency manipulation can distort trade balances and lead to international tensions.

Real Exchange Rate

• Definition: Q = \frac{SP^*}{P}

  • Q is the real exchange rate.

• The real exchange rate represents the price of foreign goods and services relative to domestic ones, or the nominal exchange rate adjusted for relative prices. It is a measure of international competitiveness.

• If APPP holds, Q should equal one. A value different from one indicates deviation from PPP.

• It measures the purchasing power of a unit of foreign currency in the foreign economy relative to the purchasing power of an equivalent unit of domestic currency in the domestic economy. This helps in assessing whether a currency is under- or overvalued.

Relative Purchasing Power Parity

• Mathematical Derivation:

  • Start with P = SP^*.

  • Take natural logs: p = s + p^*, where lowercase letters denote logs of the uppercase variables. Log transformation simplifies the equations and facilitates analysis of percentage changes.

  • Differentiate with respect to time: \frac{d(\log P)}{dt} = \frac{dP}{P} = dp and so forth. This step converts the equation into rates of change.

  • Therefore, dp = ds + dp^*

  • Rearranging, dp - dp^* = ds

• Relative PPP: The equation dp - dp^* = ds represents Relative Purchasing Power Parity. It links changes in exchange rates to differences in inflation rates.

• Interpretation: If a domestic country has a higher inflation rate than a foreign country, its exchange rate should depreciate. This ensures that the relative purchasing power is maintained. Depreciation refers to a decrease in the value of a currency relative to another currency.

• The more rapidly prices rise in the home economy relative to the foreign economy, the more rapidly the domestic currency loses value relative to the foreign currency. This is a dynamic version of the PPP theory.

Evidence for PPP

• The analysis often omits tariffs and transportation costs, which can significantly affect prices and exchange rates. These costs create deviations from PPP.

• If transaction costs are proportional to the price of traded products, the absolute PPP equation can be modified to P = K(SP^*), where K represents transaction costs. This modified equation accounts for the impact of transaction costs on PPP. Transaction costs are expenses incurred when buying or selling a good or service.

• The term K will not appear in the Relative PPP equation because relative changes are considered rather than absolute levels.

• Empirical evidence doesn't strongly support PPP initially. Exchange rates are much more volatile than prices, and PPP tends to hold better in the long run. Short-term deviations are common due to market frictions and speculation. Market frictions include factors that impede the smooth functioning of markets, such as information asymmetry and regulatory barriers.

Balassa-Samuelson Hypothesis

• Assumption: Productivity increases are more rapid in the traded goods sector (manufacturing) compared to the non-traded goods sector (services). This is particularly relevant for developing countries. The traded goods sector includes goods and services that are exported or imported, while the non-traded goods sector consists of goods and services that are primarily consumed domestically.

• Wage Dynamics: Wages in the traded goods sector rise faster than in the non-traded goods sector. With an integrated labor market, wages in the non-traded goods sector also increase to match wages in the traded sector, even without a corresponding productivity increase. This wage equalization puts upward pressure on prices in the non-traded sector.

• Price Level Impact: Consequently, non-traded goods prices rise, increasing the overall price level. This leads to deviations from PPP.

• If Home country is growing faster than the Foreign country, the Home country’s non-traded to traded goods price ratio is growing faster than the Foreign country’s non-traded to traded goods price ratio. Therefore, the Home country’s price level is growing faster than the Foreign country’s price level which implies its real exchange rate is appreciating (Q is falling). This appreciation reflects the increased relative price of domestic goods. Appreciation refers to an increase in the value of a currency relative to another currency.

Implications of Balassa-Samuelson Hypothesis

• The hypothesis suggests that the general price level will be higher in richer countries because of the higher price of non-tradeable services. This is because services are more labor-intensive and benefit less from technological improvements.

• Fast-growing developing countries should experience an appreciation of their currency. This is due to increasing productivity in the traded goods sector.

• Empirical evidence on the Balassa-Samuelson hypothesis is mixed. While it explains some deviations from PPP, it does not fully account for all exchange rate movements.

• When evaluating the equilibrium level of a real exchange rate, productivity differences must be considered. These differences can lead to sustained deviations from PPP.

• The existence of non-tradeable goods is possibly the most important exception to PPP. These goods do not face international competition, and their prices can vary significantly across countries.

PPP Exchange Rates and Developing Countries

• BigMac Index Example: Suppose a BigMac costs 5 USD in the USA. PPP suggests that identical goods and services should cost the same when converted to a common currency. The BigMac Index is a popular, albeit simplistic, way to assess PPP.

• The PPP exchange rate equates the purchasing power of an identical basket of goods and services. It provides a theoretical rate that eliminates price differences.

• Example with China: If a BigMac costs 25 yuan RMB in China and the current exchange rate is 7 (1 USD = 7 yuan RMB), the price of a BigMac when converted to USD is \frac{25}{7} \approx 3.6 USD (lower than 5 USD). This indicates that the yuan is undervalued relative to the dollar. The yuan (RMB) is the currency of China.

• China’s currency appears significantly undervalued; China’s PPP exchange rate, in this case, would be