# Purchasing Power Parity (PPP) and the Exchange Rate

by Philip Pilkington

Article of the Week from Fixing the Economists

There is a theory that floats around out there called the ‘Purchasing Power Parity theory of the Exchange Rate’ — or something to that effect, the name seems to change depending on what source you go to.

The theory, stripped right down, amounts to something like this: the ‘correct’ value of the exchange rate will be the old exchange rate times the change in the price level in one of the two countries involved divided by the change in the price level of the other of the two countries involved.

Let’s take a concrete example to be a bit clearer: the exchange rate between the yen and the US dollar (USD). So,

On the left hand side of the equation, denoted by a *, is the ‘equilibrium’ exchange rate between the USD and the yen in the future — i.e. time t+1. As we can see it is determined by the actually existing exchange rate in the here and now — i.e. time t — together with the inflation differential between the two countries.

Intuitively that means that if the we are trying to figure out what the USD/yen exchange rate should be a year from now and we know that the inflation rate is going to be 10% more in the US than in Japan we will expect the USD to depreciate by 10% relative to the yen. Again, if the inflation differential between the US and Japan is positive then the USD should fall relative to the yen.

Let’s do an example to illustrate this. Let’s say that the USD/yen exchange rate starts at parity — i.e. 1USD = 1yen. Now, let’s say that the inflation rate in the US is 10% more than the inflation rate in Japan. We denote this through two price indices, the US index being 10% higher than the Japanese index. So,

We do the calculations and we get,

As we can see, the USD has devalued by 10% against the yen. Whereas before 1USD could buy 1yen, now it takes 1.10USDs to buy 1yen. The yen has become 10% more expensive.

The problems with this theory, which is often used as a rule-of-thumb, are varied. A handy list of them can be found here. Obviously I cannot run through all of them here but the one that stands out most to me is the following:

The theory assumes that changes in price levels could bring about changes in exchange rates not vice versa, that is, changes in exchange rates cannot affect domestic price levels of the countries concerned. This is not correct. Empirical evidence has shown that exchange rate governs price rather than the latter governing the former. Prof. Halm opines that the national price levels follow rather than precede the movements of exchange rates. He states: “A process of equalisation through arbitrage takes place so automatically that the national prices of commodities seem to follow rather than to determine the movements of the exchange rates.”

This strikes me as a particularly poignant criticism as it gets to root of the causality involved in the hypothesis behind the theory.

In an interesting paper by Rudi Dornbusch entitled simple Purchasing Power Parity the author points out that the status of the theory may be compared to the old Quantity Theory of Money. He writes,

The PPP theory has somewhat the same status as the Quantity Theory of Money (QT): by different authors and at different points in time it has been considered an identity, a truism, an empirical regularity or a grossly misleading simplification. The theory remains controversial, as does the QT, because strict versions are demonstrably wrong while soft versions deprive it of any useful content. (p1)

This strikes me as a very astute analogy. The PPP theory of exchange rates seems to try to make the same reductive assumptions about causality as the stronger forms of the QTM.

But let’s turn to some empirical evidence to see how it holds up. Given our above examples let’s take the yen/USD exchange rate during a period of turbulence between 1974 and 1990. The below chart lays out two variables: the yen/USD exchange rate and the inflation differential. The latter is calculated by subtracting the US inflation rate from the Japanese inflation rate. So, a positive differential indicates a higher rate of inflation in the US and a negative differential indicates a higher inflation rate in Japan.

As we can see, between 1974 and the beginning of 1978 inflation in Japan was substantially higher than inflation in the US. According to the PPP theory of the exchange rate this should mean that the USD should have appreciated against the yen by a similar amount to the differential. Alas, such was not the case. Rather, between 1976 and 1978 the USD fell in value against the yen.

Conversely, between 1978 and 1983 inflation in the US was higher than inflation in Japan. According to the PPP theory this should have resulted in a depreciation of the USD relative to the yen. What we actually saw was, again, precisely the opposite. The USD appreciated. So much so that in 1985 the Reagan administration had to request that they be allowed forcibly depreciate their currency against the yen in what has since come to be known as the Plaza Accord.

After the Plaza Accord the rate of inflation stayed higher in the US than in Japan. But this begs the question: since the depreciation was forced would it not be more logical that it was the depreciation itself that was causing the higher inflation, due to higher import costs in the US, rather than vice versa?

Let’s lay this out in plain English: if the PPP theory were correct we would expect to see the blue line on the graph pushed downward whenever the red bars climbed upwards and vice versa. In actual fact, we do not see this; indeed, as just highlighted, we often see exactly the opposite. And when we do see the blue line fall (i.e. the dollar devalue) and the red line climb (i.e. US inflation) it appears that the causality is precisely the reverse: the devaluation takes place first and the uptick in inflation results from this.

Naturally, some will say that the PPP theory must be handled in a more nuanced way to make accurate predictions about exchange rate moves. But if it performs this poorly — I would say: counter-factually — when used in a simplistic way it is altogether dubious whether any more nuanced application is not likely an instance of hocus-pocus; much like the old Monetarist attempts to explain output and inflation with reference to expansions and contractions in the money supply.

On that note, I leave the reader with the opinion of Paul Samuelson as quoted in Dornbusch’s excellent paper,

Unless very sophisticated indeed, the PPP is a misleading, pretentious doctrine, promising what is rare in economics, detailed numerical prediction.

Indeed. Although, given the state of the expanded models, we might add: as the model is expanded and becomes ever more cumbersome it becomes ever more dubious.

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