Long-Run Exchange Rate Modeling: A Comment on MacDonald

Abstract

IN HIS excellent survey of long-run modeling of exchange rates, MacDonald (1995) raises some controversial issues that are frequently encountered in the literature on the extensively researched purchasing power parity (PPP) hypothesis. These issues are: (1) the distinction between absolute and relative PPP; (2) Cassel's PPP and commodity arbitrage; and (3) testing the properties of proportionality and symmetry. This note provides some brief comments on these issues. Let us start with the first issue. Following Frenkel (1978), economists distinguish between the two versions of PPP by specifying the former in levels (MacDonald's equation (17)) and the latter in first differences (the stochastic version of MacDonald's equation (4)). However, if the variables underlying MacDonald's equation (17) (exchange rate and prices) are integrated of order one, and if they are cointegrated, then the equation that supposedly represents relative PPP will be misspecified because it does not contain an error correction term. If an error correction term is included, the distinction will not be between absolute and relative PPP, but rather between long-run and short-run PPP. Moreover, a first-difference specification is problematic because it represents efficient markets PPP under rational expectations. The problem here is that efficient markets PPP predicts that the real exchange rate follows a random walk, implying that conventional PPP does not hold. Hence, an econometrically valid first-difference model should be interpreted to indicate the failure of conventional PPP since the model is based on the assumption that it does not hold.