Handbook of Exchange Rates

6.2 Categorization of Purchasing-Power-Parity Theories

This essay interprets PPP theory broadly.¹ Consider the variables P (domestic price index), P^* (foreign price index), E (nominal exchange rate), R (PPP), and Q (real exchange rate), where R = P^*/P and Q = ER. E is defined as the number of units of domestic currency per unit of foreign currency, but may alternatively be expressed as an index number; R may be reexpressed as an index number; and Q is always dimensionless.

Any PPP theory can be represented by the implicit function G( E, P, P^*, X), where X is a vector of variables that can include (i) E, P, P^* in earliest periods and (ii) additional variables in the current period and in earlier periods. For a specific G function to be considered a PPP theory, it is necessary that certain minimum requirements be satisfied. First, the G equation must be solvable in terms of E: E = g(P, P^*, X). The E that results from solving the G function may be the actual exchange rate in the current period, the equilibrium exchange rate in the current period, or the long-run equilibrium exchange rate. Second, partial derivatives must have sign consistent with PPP theory: ∂E/∂P > 0, ∂E/∂P^* < 0.

Inclusion of (ii) variables other than E, P, and P^* in G results in an “augmented PPP theory” (the term suggested in Officer, 1948, p. 188). Is an augmented PPP theory legitimately classified within the domain of PPP? Reasonable scholars may differ on this point, but a sensible statement is as follows: The ...