Explain the purchasing power parity theorem and apply it to work out a foreign currency's appreciation or depreciation.
The idea
Purchasing power parity says exchange rates adjust so that identical goods cost the same across countries. Absolute PPP gives the rate as a ratio of price levels. S = domestic price level ÷ foreign price level. Here S is the rate in domestic currency per unit of foreign currency. Relative PPP applies the idea to changes: the percentage change in the exchange rate is roughly the domestic inflation rate minus the foreign inflation rate. The exact form of relative PPP is S1 = S0 × (1 + domestic inflation) ÷ (1 + foreign inflation). S0 and S1 are the rates at the start and end of the period. The currency of the higher-inflation country is therefore expected to depreciate. For example, if domestic inflation is 8% and foreign inflation is 2%, the foreign currency is expected to appreciate by 1.08 ÷ 1.02 − 1 = 5.88% against the domestic one. PPP is a long-run tendency and often fails in the short run. Do not invert the ratio, and use the exact form when inflation is high.
Formulas
Exchange rate under absolute purchasing power parity
S = domestic price level ÷ foreign price level
- domestic price level
- the cost of the basket in domestic currency
- foreign price level
- the cost of the same basket in foreign currency
S comes out in domestic currency per unit of foreign currency; inverting the ratio is the usual error. PPP is a long-run tendency and often fails in the short run.
Expected exchange rate under exact relative PPP
S1 = S0 × (1 + domestic inflation) ÷ (1 + foreign inflation)
- S0
- the rate at the start, domestic currency per unit of foreign currency
- domestic inflation
- the inflation rate in the domestic country over the period
- foreign inflation
- the inflation rate in the foreign country over the period
The higher-inflation currency is expected to depreciate. The simple inflation difference is close only when inflation is low, so use this form when it is high.
A practice question
According to absolute purchasing power parity, a basket of goods costs USD 120 in the United States and EUR 100 in the euro area. What is the PPP-implied exchange rate in USD per EUR?
- 1.2000 - correct
- 0.8333Why not: Inverts the ratio, giving EUR per USD.
- 0.2000Why not: Takes the price difference (120 - 100) over 100 instead of the ratio of the price levels.
- 1.0000Why not: Treats PPP as fixing the nominal rate at parity; it equates the cost of the basket, so the rate equals the price ratio.
Absolute PPP says the same basket should cost the same in common currency: USD 120 = EUR 100 x S, so S = 120/100 = 1.2000 USD per EUR.
A harder one
EUR/USD (USD per EUR) is 1.0850. Expected one-year inflation is 8% in the United States and 2% in the euro area. Using exact relative PPP, the expected EUR/USD rate in one year is closest to:
- 1.0247Why not: Inverts the inflation ratio; the USD (higher inflation) should lose value, raising USD per EUR.
- 1.1718Why not: Uses only US inflation and ignores the euro-area inflation.
- 1.1488 - correct
- 1.1952Why not: Multiplies by both inflation factors instead of dividing by the foreign one.
Relative PPP: S1 = S0 x (1 + inflation USD) / (1 + inflation EUR) = 1.0850 x 1.08/1.02 = 1.1488. The USD is expected to depreciate because US inflation is higher.
The hardest tier
A basket costs USD 250 in the United States and EUR 220 in the euro area. EUR/USD spot is 1.0850. What change in the EUR/USD rate would be required for absolute PPP to hold?
- The EUR must appreciate by about 4.73% - correct
- The EUR must depreciate by about 4.73%Why not: Wrong direction: the PPP rate of 1.1364 is above the spot rate of 1.0850, so the EUR must rise.
- The EUR must appreciate by about 4.52%Why not: Divides the gap by the PPP rate; the percentage change needed is measured from the current spot rate.
- The EUR must appreciate by about 13.64%Why not: Uses the basket price ratio minus one, ignoring the existing spot rate.
PPP rate = 250/220 = 1.1364 USD per EUR. Required change = 1.1364/1.0850 - 1 = +4.73%. The EUR is undervalued relative to PPP.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
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