What is the Relative Version of Purchasing Power Parity Theory of Rate of Exchange?

The relative version of the Purchasing Power Parity theory is propounded by Cassel as a means for measuring departures from “equilibrium.” As compared to the absolute doctrine, it is stated in a more modest form and concerns itself with the relationship between changes in internal purchasing power and the changes in exchange rates.

Thus, the theory in its relative version states that the changes in the equilibrium rate of exchange will be governed by the changes in the ratio of their respective purchasing power. Here some past exchange rate is assumed to be an equilibrium rate, and is adopted as the base rate.

And as changes in purchasing power can be measured by changes in the indices of domestic prices of the countries concerned, the changes in equilibrium rate can be measured by the ratio of the price-indices of the respective countries. Thus, the new equilibrium rate (in the given or later period) can be known by relating the indices of domestic prices in the given period related to price indices in the two countries in the base period to the base rate (old equilibrium rate).

In symbolic terms, thus, the formulation of purchasing power parity (PPP formula) may I) expressed as:

To illustrate the point, let us assume that, in the base year India-U.S. rate is Re. 1 = 20 cents and price indices are 100 in both countries. Now suppose that, in the later period the price index in India goes up to 300, and in U.S. it goes upto 150, then the new rate will be:

That is to say, when prices in country A doubled relative to prices in B, from period 0 to period 1, the exchange rate R should fall by half (or the price of foreign exchange expressed in local currency should double).

It appears, however, and even Gustav Cassel himself admitted it, that the purchasing power parity (PPP) theory cannot be used to calculate the equilibrium rate as such, but only the new equilibrium rate on the basis of a known equilibrium rate. Gustav Cassel states, “It is only when we know the exchange rate which represents a certain equilibrium that we can calculate the rate which represents the same equilibrium at an altered value of the monetary units of the two countries.”

The PPP theory also suggests that inflation has its impact on the exchange rate A country’s currency tends to appreciate/depreciate in proportion to the difference between domestic inflation (DIR.) and foreign inflation (FIR), if it is to maintain its purchasing power parity (PPP). Thus:

PPP = DIR – FIR

If, DIR > FIR, there is exchange depreciation of currency.

If, DIR < FIR, there is appreciation of currency’s exchange rate. In short, inflation and exchange depreciation are interdependent and jointly determined.

For empirical study the purchasing power parity (PPP) hypothesis may be stated to form an equilibrium relationship between the changes in exchange rates and price levels of the countries in question, as follows:

Where,

ER= Exchange rate, i.e., the domestic currency price of foreign exchange.

PR= the price ratio of the domestic price index to the foreign price index.

U=error terms representing deviations from PPP.

T= time element

PPP holds a long-run constraints to the ER charges when ER and PR{ show non-stationarity in the same order of integration and the deviations from PPP, i.e., (Ut) is stationary or mean-reverting. As per the PPP theory, ER PRt could respond to correct the short-run U(. The exchange rate, as an asset price, however, tends to react faster. As such, it bears largely the burden of snort-run adjustment to eliminate deviations from purchasing power parity (see Frankel: 1982, and Baghestani: 1997

Empirically 