Absolute PPP: The Law of One Price Applied to Exchange Rates
Originator
Gustav Cassel (1918), from a much older idea
Field
International finance
What it answers
What should an exchange rate be, if prices alone determined it?
Where it is used
International finance modules, exchange-rate forecasting, macroeconomics
Absolute purchasing power parity states that the exchange rate between two currencies equals the ratio of their price levels. If a basket of goods costs £100 in the United Kingdom and $130 in the United States, the absolute PPP exchange rate is $1.30 per pound.
The claim is an application of the law of one price to whole economies. The law of one price says an identical good must sell for the same amount everywhere once prices are expressed in a common currency, because otherwise it would pay to buy in the cheap market and sell in the dear one until the gap closed. Absolute PPP asserts that what holds for one good holds for the basket.
The formula
S = P<sub>domestic</sub> ÷ P<sub>foreign</sub>
where S is the spot rate expressed as units of domestic currency per unit of foreign currency, and P is the price of a common basket in each economy.
Two things are being assumed rather than derived, and naming them explicitly at the outset is half of any critical answer to a question on this topic: that the basket is genuinely identical in both countries, and that arbitrage across it is possible at negligible cost.
A worked calculation
A standard basket costs €2,400 in the eurozone and £2,000 in the United Kingdom.
Implied rate. £2,000 ÷ €2,400 = £0.8333 per euro, equivalently €1.20 per pound.
Suppose the actual market rate is £0.78 per euro.
Cost of the basket in the eurozone, in sterling. €2,400 × £0.78 = £1,872.
Cost at home. £2,000.
The same basket is £128 cheaper bought in euros, so on this measure sterling is overvalued against the euro — a pound buys more abroad than at home.
Degree of misalignment. (0.8333 − 0.78) ÷ 0.8333 = 6.4 per cent. Absolute PPP predicts the euro should appreciate against sterling by roughly that much, or that eurozone prices should rise relative to British ones, until the gap closes.
The direction is the part worth getting right, and the reliable way to check it is the one used above: price the same basket both ways and see which is cheaper. A currency whose goods are expensive when converted is overvalued.
Absolute against relative PPP
The two are regularly confused, and the distinction is the most commonly examined point in this area.
Absolute PPP is a statement about levels: the rate equals the ratio of price levels. It requires the baskets to be identical and comparable, which is a demanding condition.
Relative PPP is a statement about changes: the percentage change in the exchange rate equals the difference in inflation rates between the two countries.
%ΔS ≈ π<sub>domestic</sub> − π<sub>foreign</sub>
Relative PPP survives several of the objections that sink the absolute version. Transport costs and tariffs create a persistent wedge between price levels, so absolute PPP fails — but if the wedge is roughly constant, it cancels out of the change, and the relative version can still hold.
This is why the empirical literature treats them so differently. Absolute PPP is rejected almost universally; relative PPP has meaningful support over long horizons and high-inflation episodes, and almost none over one or two years.
Why it fails
Non-traded goods. A haircut, a rent, a restaurant meal and most services cannot be arbitraged across borders at all. They form a large share of any consumption basket, and no mechanism pushes their prices towards equality.
Transport costs and trade barriers. Arbitrage only operates where the price gap exceeds the cost of moving the goods and clearing the border. Below that threshold, prices can differ indefinitely without any profitable trade existing.
Basket composition. Consumption patterns differ, so national price indices weight different goods. Comparing two indices computed on different baskets is not comparing like with like, and the resulting ratio is not the quantity the theory describes.
Pricing to market. Firms with market power set different prices in different countries deliberately, according to what each market will bear. Identical cars and identical pharmaceuticals sell at substantially different prices across borders, sustained by contract and distribution control rather than by transport cost.
Balassa–Samuelson. The most substantial theoretical objection. Productivity differences concentrate in traded goods, but wages equalise across sectors within a country, so a rich and productive economy has expensive non-traded services relative to a poorer one. Price levels are therefore systematically higher in richer countries, and absolute PPP does not merely fail at random: it fails in a predictable direction.
What the evidence shows
Studies of the law of one price for individual traded goods find persistent deviations even for commodities that ought to arbitrage easily, and deviations widen with distance and with border crossings.
For the aggregate, deviations from absolute PPP are large and long-lived. Estimates of how quickly they decay put the half-life at roughly three to five years, which is far too slow for the relation to be useful as a forecast at any horizon a business plans over. The finding was sufficiently awkward to earn a name — the PPP puzzle — because the persistence is difficult to reconcile with the observed volatility of real exchange rates.
The practical summary is that PPP is a long-run anchor instead of a short-run predictor, and that anyone using it to forecast next year's rate is applying it outside the range in which it has any support.
The real exchange rate, which is the same idea rearranged
Absolute PPP is easier to test when written as a statement about the real exchange rate.
Q = (S × P<sub>foreign</sub>) ÷ P<sub>domestic</sub>
The real exchange rate Q is the foreign price level converted into domestic currency, divided by the domestic price level. If absolute PPP holds, Q equals one and stays there. Every deviation from PPP is a movement of Q away from one, so testing PPP and testing whether the real exchange rate is stationary are the same exercise.
On the worked figures above, Q = (0.78 × 2,400) ÷ 2,000 = 0.936. The deviation from parity is 1 − Q = 6.4 per cent, the same misalignment computed earlier, now expressed as a single index number and not as a gap between two rates. Sterling goods are the dearer of the two.
Framing it this way makes the empirical question precise. If Q wanders without returning, PPP is false in any useful sense. If Q returns slowly to a constant, PPP holds in the long run and the speed of return is the number that matters. The evidence supports the second, with a return so slow that it is nearly indistinguishable from the first over the horizons most decisions cover.
A worked relative PPP comparison
The relative version is worth computing alongside, because the contrast is the point.
Suppose the current rate is £0.78 per euro, United Kingdom inflation runs at 4 per cent over the year and eurozone inflation at 2 per cent.
Expected change in the rate ≈ 4% − 2% = 2 per cent depreciation of sterling.
Expected rate = £0.78 × (1.04 ÷ 1.02) = £0.7953 per euro.
Notice what this does and does not claim. It says nothing about whether £0.78 was the right starting point — it takes the market rate as given and predicts the movement. Absolute PPP, by contrast, says the starting point itself was wrong by 6.4 per cent. A question asking which currency is overvalued needs the absolute version; a question asking where the rate will be next year needs the relative one.
Where it is genuinely useful
Income comparison. Comparing gross domestic product across countries at market exchange rates overstates rich economies and understates poor ones, precisely because non-traded services are cheap where wages are low. International institutions therefore publish PPP-adjusted figures, which are the correct series for comparing living standards.
Long-run misalignment. Large, persistent deviations do carry information about whether a currency is far from any sustainable level, even though they say nothing about timing.
Setting a long-horizon planning assumption. A treasury team deciding what rate to assume for a ten-year investment appraisal has no better anchor than parity, precisely because no short-run forecast has any skill at that distance. The assumption is weak; every alternative is weaker, and stating which one was used and why is more defensible than adopting the forward curve and calling it a forecast.
Informal indices. The best known, based on the price of a single standardised burger across countries, is a deliberately simplified application. Its value is pedagogical: a single identical good, sold everywhere, still shows deviations of thirty per cent or more, and it demonstrates the failure of the theory more efficiently than a formal test.
For an assignment, the strongest structure is to state the theory, compute the implied rate, compare it with the market, and then explain the gap using the specific reasons that fit the pair of countries in question — non-traded share for a developed and a developing economy, pricing to market for two rich economies with a branded product. Listing all five objections generically does less than selecting the one the data supports, and a sentence naming which objection would have to be false for the theory to hold in this particular case is worth more than a paragraph naming all of them.