RDP 9309: Alternative Concepts of the Real Exchange Rate: A Reconciliation 2. The Theory of Real Exchange Rates

The ‘conventional’ real exchange rate is based on deviations from PPP and draws on an established body of empirical literature.^[2] Proponents of PPP claim that, in the long run, nominal exchange rates should move in line with inflation differentials so that their real values remain constant (Cassel 1918; Officer 1976). Deviations from PPP represent a change in the real value of the currency. A real exchange rate that measures such deviation can be expressed as:

where: E is the nominal exchange rate index expressed in units of foreign currency per unit of domestic currency; P is the domestic price index; and P^* is the foreign price index. A fall in R_p represents a real depreciation.

In contrast, the relative domestic price form of the real exchange rate does not include a rate of exchange between currencies. Instead, it is the ratio of the domestic price indices for non-traded (P_n) and traded goods (P_t):

where P_t is the composite price of exports and imports.^[3]

Again, a fall in R_r represents a real depreciation. This relative domestic price concept has evolved from the ‘Australian model’ in which a unique relative price of traded and non-traded goods is required for the simultaneous attainment of internal and external balance (Salter 1959; Swan 1960, 1963).^[4] While explicit reference to this domestic price ratio as a real exchange rate stems from Gregory (1976), the notion was popularised by Dornbusch (1980). Dornbusch demonstrated that if the domestic price of non-traded goods is given, attainment of the equilibrium relative price requires adjustment of the domestic price of traded goods. Given the law of one price, this requires an adjustment of the exchange rate. Thus, changes in R_r can be associated with a rate of exchange between currencies.^[5] The equilibrating role afforded to domestic relative prices in the Australian model has become central to the theory of open economy macroeconomics.

Clearly, the relative domestic price form of the real exchange rate and that based on deviations from PPP are fundamentally different in expression and have evolved from different streams of literature. However, they are related. In fact, under a special set of restrictive conditions, deviations from PPP will be proportional to changes in domestic relative prices.

In order to demonstrate this relationship, the general price levels used in R_p must be decomposed into their traded and non-traded goods components:

where: a star (*) denotes the foreign variable; α is the share of non-traded goods in domestic consumption; and β is the share of non-traded goods in foreign consumption.

Following Lowe (1992),^[6] substituting these price terms into equation (1) and rearranging gives:

Thus R_r (the relative price form of the real exchange rate) can be recognised as a term in the numerator of this expression for R_p (that real exchange rate which measures deviations from PPP).

From equation (5) it is apparent that movements in R_p will only be proportional to those in R_r if the following two conditions hold:

1. the law of one price; and
2. relative internal prices abroad remain unchanged.

First, if the law of one price holds, the price index for traded goods, expressed in a common currency, will be the same in both the domestic and foreign countries (so that P_t E = ). In this case, equation (5) can be rewritten as:

Second, movements in R_p and R_r will only be proportional if is constant.^[7] In this case:

where ^· denotes proportional change. The important point to note is that even if both conditions are satisfied, movements in the two forms of the real exchange rate will not be the same; they will instead be proportional, governed by the factor of proportionality α.

In the limit, if α were unity so that all goods are non-traded, changes in R_p would be identical to changes in R_r. Thus the difference between the changes in the two forms of real exchange rate will be greater, the larger is the share of tradeables in domestic consumption.^[8] There is, however, a direct relationship between the two measures of the real exchange rate.

Footnotes

The concept of PPP has evolved over several centuries; for a review see Officer (1976) and Dornbusch (1987). [2]

For the composite commodity theorem to be invoked, the relative price of exports and imports must remain stable (Green 1976). This implies a constant terms of trade assumption. [3]

In this model, the economy comprises a traded and non-traded goods sector in which the relative prices of these goods influence the allocation of resources and expenditure. The price of traded goods is determined on world markets in accordance with the law of one price, while the price of non-traded goods is determined by domestic demand. The economy has attained internal balance if there is equality of demand for and supply of non-traded goods. Similarly, external balance is represented by the equality of demand for and supply of traded goods. Equilibrium is defined by the simultaneous attainment of internal and external balance. [4]

In turn, given prices of non-traded goods abroad, all movements in R_r can be associated with a change in the real value of the currency. [5]

See also expositions by Clements and Frenkel (1980), McKenzie (1986), Nguyen and Martin (1987) and Dwyer (1991). [6]

It should be noted that if is not constant, differences between α and β will be a further source of divergence. Thus conceptually, differences in the degree of openness between nations will influence divergent movement between the two forms of real exchange rate. The extent to which this emerges as an important practical issue is, however, difficult to measure. [7]

If α were zero so that all goods are traded, changes in R_p would also be zero so that no deviations from purchasing power parity would occur as long as the law of one price held. [8]