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.

The distinction between absolute and relative PPP on the basis of model specification is empirically redundant because price indices are typically measured relative to a base period. This means that absolute PPP is not testable empirically and that MacDonald’s equation (17) represents relative, not absolute, PPP. Furthermore, the distinction is also theoretically useless. This is because any linear functional relationship can be used to obtain the value of the dependent variable at any point in time corresponding to the value of the independent variable at the same point in time, or the rate of change in the dependent variable between two points in time corresponding to the rate of change of the independent variable during the same time interval. It is obvious that MacDonald’s equation (17) can be rewritten to encompass terms in levels and first differences, in which case one cannot tell whether it represents absolute or relative PPP.

It also seems that the distinction between absolute and relative PPP has a dubious origin in the history of economic thought: it emerged out of the misinterpretation of Cassel by his contemporaries and subsequent economists. In fact. Cassel (1922), p. 138) referred to what is called absolute PPP as “pure dogma.” And while the criticism of PPP is mostly directed at its absolute version. PPP meant only one thing for Cassel: the operational theory that—in the absence of other factors that impinge upon the exchange rate—can be represented by a functional relationship between exchange rates and prices (see, for example, Holmes (1967)). This brings us to the second issue. While MacDonald derives PPP from the law of one price, which means that it is an arbitrage relationship, Cassel’s view of PPP (to which MacDonald recurrently refers) is simply an extension of the quantity theory of money to the case of an open economy.

The third issue is that of testing the proportionality and symmetry restrictions. First, it seems to me that MacDonald’s assertion that the Engle-Granger two-step method precludes the possibility of testing the restrictions does not do the method any justice. It is possible to carry out these tests within the framework of the two–step method by correcting the t-statistics of the coefficients of the static cointegrating regression along the lines suggested by West (1988). The Johansen procedure is certainly not the only method whereby the restrictions can be tested. This task can also be accomplished by using the Engle-Yoo (1991) three-step method, or the dynamic specifications suggested by Wickens and Breusch (1988) and by Stock and Watson (1993). The fact that these procedures have not been used in the PPP literature is a manifestation of the gap between econometric theory and applied econometrics.

MacDonald also raises the point as to why the symmetry and proportionality restrictions do not seem to hold. The point that I want to make in this respect is that there is usually more evidence for symmetry than for proportionality because the latter requires more stringent conditions to hold (e.g., Moosa (1994)). It can be demonstrated, for example, that the introduction of nontraded goods and transportation costs does not affect the property of symmetry, but it does cause proportionality to cease to hold.