## Purchasing Power Parity (PPP) and the Exchange Rate

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.

Philip Pilkington is a macroeconomist and investment professional. Writing about all things macro and investment. Views my own.You can follow him on Twitter at @philippilk.
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### 6 Responses to Purchasing Power Parity (PPP) and the Exchange Rate

1. Nick Edmonds says:

Nice post.

The causal direction from exchange rate to prices is often overlooked but for economies like the UK, for example, it is a crucial part of the inflation process. Interestingly though, I never saw this as contradictory to the theory of PPP. I always thought the theory was that both prices and the exchange rate would move to restore parity – not just the exchange rate. But maybe I misremember.

The comparison with the quantity theory is a good one, and I often think that PPP must appeal to monetarists for the same reasons. And there is something intuitively appealing about it. If the price level goes up 100-fold, the exchange rate must fall 100-fold, mustn’t it? Otherwise, all the prices will be hugely out of line. But it suffers from the same flaws the QTM does. Relative price movements can and do happen and they are not independent of changes in general price level.

The interesting empirical question is whether persistent significant deviations from parity can be observed and the overwhelming evidence is that they can.

• I think that this is what Dornbusch is getting at in the quote I lay out. You can find similar quotes from Keynes. Like the QTM if we understand it as an identity, as you’re implying, then it is largely a meaningless tautology. So far as I can tell, those who employ it assume a unidirectional causation from prices to moves in the exchange rate.

Yes, I agree on the monetarism point. John Harvey, in his excellent book ‘Currencies, Capital Flows and Crises’ shows how you can couple the PPP model with a vertical aggregate supply curve and a downward sloping aggregate demand curve to get a monetarist model. (Pp15-19).

As to the empirics, the PPP theory is rubbish. Even if it held to some extent in a world without central banks and capital markets, the existence of CBs that control interest rates and habitually manipulate FX prices together with the enormous amount of capital flows worldwide render the theory meaningless.

• Cesar says:

Totally agree.
Even a simple real world example such as the EUR/CHF cap reveals the PPP as theoretical *at best*.

2. Josh S says:

You might be interested in the exchange rate work by Frydman and Goldberg which they call Imperfect Knowledge Economics. It contends that deviations from PPP are explained by deviations from UIP and vice versa. Put differently, real exchange rates can be pretty well explained by real interest rate differentials.

• Yes, I was considering doing a post on UIRP and CIRP next. It is an awfully messy theory. It makes very little sense in a world with capital flows and CBs setting the interest rate. But it is also desperately hard to untangle. Watch this space though. Maybe in the future.

• Jan says:

Excellent piece of work Phil!Impressive! But i don´t see any of the regular complaining commenters of either the neoclassical- austrian or kaldorian or whatsoever nittpicking types! So something must be wrong! Ha!

I figured it out! You forgot to mention that the Purchasing Power Parity was named and coined by Swedish economist Gustav Cassel in December 1918 in. Abnormal Deviations in International Exchanges. 28, No. 112 The Economic Journal. pp. 413–415. http://www.jstor.org/discover/10.2307/2223329?uid=3738984&uid=2&uid=4&sid=21103038432773

So it´s all okey Phil,in absence of the regular nittpickers i have to fill the role!
Have a good one Phil!