After the familiar introduction on PPP (*Big Mac Index*), we can start by introducing Rudiger Dornbusch’s NBER Paper on PPP published in March 1985. In his working paper, Professor Dornbusch states that the PPP theory of exchange rate has ‘the same status in the history of economic thought and in economic policy as the Quantity Theory of Money (QT)’. The QT version most commonly used is the Fisher Identity (Economist Irving Fisher in his book The Purchasing Power of Money) defined by:

M.V = P.T, where

M = Money supply, or stock of money in coins, notes and bank deposits

V = Velocity of circulation

P = Some measure of the Price level (i.e. CPI)

T = Volume of Transactions in the economy

**1. Historical context**

The notion of purchasing power parity PPP can be traced to the 16-century Spanish Salamanca school, but the protagonist of the theory is the Swedish Economist Gustav Cassel. During and after WWI, he observed that countries like Germany or Hungary a sharp depreciation of the purchasing power of their currencies in addition to hyperinflation. Therefore, he proposed a model of PPP that became a benchmark for long run nominal exchange rate determination.

**2. Statement of the PPP theory:**

Let Pi and Pi* be the price of the *ith* commodity at home and abroad respectively (both in local currencies) and e the exchange rate. Let P and P* represent the price level at home and abroad.

In an integrated, competitive market (no cost for transport and no barriers to international trade for the good), the concept is based on the *Law of one Price* where identical goods will have the same price in different markers when quoted in the same currency.

For unless Pi = e.Pi* (1)

There will be an opportunity for profitable arbitrage.

Arbitrage: Recall that arbitrage is the possibility to make a profit in financial market without risk and without net investment of capital. A portfolio π has an arbitrage opportunity if there exists T > 0 such that Xo = 0, Xt >= 0 (P – a.s.), P(Xt > 0) > 0.

For instance, if Pi < e.Pi*, then an arbitrageur will buy the good domestically for Pi, sell it abroad for Pi* and realize a risk-free profit as Pi*.e – Pi > 0. Such arbitrage, purchasing the cheap good and selling it where it is dear, would continue until the equality (1) held.

As we said, equation (1) states that the price of the ith commodity must be the same in both markets (i.e. two different countries, for instance US and UK). The Equation is known as Commodity Price Parity (CPP).

Example: Let’s say that the price of one ounce of gold sold in London is 846 GBP, whereas it is sold of for USD 1,290 in New York. If we apply equation (2), we can conclude that the implied rate for Cable (GBP/USD) is 1.5248 (as a result of 1,290 / 846).

**Limits: ** As we all know, in the real world, CPP may not hold for different reasons:

– Transactions costs (transportations costs, insurance fees)

– Non-traded Goods: items such as electricity, water supply, or goods with very high transportation costs such as gravel.

– Restraints of Trade

– Imperfect Competition

**3. Purchasing Power**

In an economy with a collection of commodities, ‘purchasing power’ is defined in terms of a representative bundle of goods. We evaluate purchasing power by constructing a price index based on a basket of (consumption) goods.

**3.1. Absolute purchasing power parity**

Let P = f(p1,…, pi,…,pn) and P* = g(p1*,…,pi*,…pn*) be domestic and foreign price indices.

Then, if the prices of each good (in dollars) are equalized across countries, and if the same goods enter each country’s market basket with the same weights, then *Absolute* PPP prevails.

e = P/P* = ($ price of a standard market basket of foods) / £ (price of the same standard basket) (2)

If pi / pi* = k for i = 1,…,n , then

e = P/P* = k (3)

There can be no objection to equation (2) as a theoretical statement. However, as we mentioned it earlier (limits), objections arise when equation (2) is interpreted as an empirical proposition (Tariffs, transportation costs make it difficult for the spot prices of a commodity i to be equal in different location at a given time).

Strong (Absolute) PPP implies that whatever monetary or real disturbances in the economy, the price of a common market of basket of goods will be the same, i.e. P/e.P*=1.

**3.2. Relative Purchasing Power Parity**

The relative version of PPP restates the theory in terms of changes in relative price levels and exchange rate: e = C. P/P*,

where C is a constant that reflect the trade obstacles. The difference in the rate of change in prices at home and abroad – difference in the inflation rate – is equal to the percentage depreciation or appreciation of the exchange rate:

ê = π – π* (4)

where ^ denotes a percentage change, π – π* the inflation differences between two markets (i.e. countries) reflected in percentage changes in the exchange rate. For instance, if the inflation rate is π = 2% in the US and π* = 1% in the UK, then the British Pound (GBP) should appreciate by ê = π – π* = 1% against the USD.

Prices in the US are rising faster than in the UK, therefore UK exports are becoming more competitive (compare to US ones), raising importers’ interest. This should generate a higher demand for GBP (relative to USD), hence sending Cable (GBP/USD) higher.

Equation (4) was applied by Gustav Cassel to an analysis of exchange rate changes during World War, as according to PPP, the fair value of an exchange rate between two countries is determined by the two countries’ relative price levels.

**4. Opening**

Since the early 1980s (after the collapse of Bretton Woods), advances in econometrics and longer time series covering the period of floating exchange rates were two important developments in the new generation of fair value models. The next article will focus on the two dominating families of currency fair values widely used today: the Behavioural Equilibrium Exchange Rate (BEER) models and Underlying Balance (UB) models adopted for flexible exchange rates.

**References:**

Dornbusch, Rudiger (1985), “Purchasing Power Parity”. NBER Working Paper No. 1591.

Isaac, Alan G. Lecture in Purchasing Power Parity.

Jerry Coakley and Stuart Snaith (2004), “Testing for Long Run Purchasing Power Parity”.