Question

Explain carefully why the empirical finding that the real exchange rate is mean reverting and the PPP condition holds in the long-run constitutes evidence in favour of the view that nominal shocks are the predominant source of business cycle fluctuations.

Answer 1

The purchasing power parity (PPP) exchange rate is the exchange rate between two currencies which would equate the two relevant national price levels if expressed in a common currency at that rate so that the purchasing power of a unit of one currency would be the same in both economies. If the nominal exchange rate is defined simply as the price of one currency in terms of another, then the real exchange rate is the nominal exchange rate adjusted for relative national price level di¤erences. When PPP holds, the real exchange rate is a constant, so that movements in the real exchange rate represent deviations from PPP. While very few contemporary economists would hold that PPP holds continuously in the real world, many or most seem to have an inclination towards PPP ‘as an anchor for long-run real exchange rates’ (Rogo, 1996). Moreover, estimates of PPP exchange rates are important for important policy purposes such as determining the degree of misalignment of the nominal exchange rate and the appropriate policy response, the setting of exchange rate parities in fixed exchange rate arrangments or in determining the appropriate level at which to enter a monetary, and the international comparison of national income levels. It is not surprising, therefore, that a large literature on PPP, both academic and policy-related, has evolved. One way the empirical literature has sought to examine the validity of PPP has been to see whether the real exchange rate tends to settle down at a long-run equilibrium level - i.e. to see whether time series on real exchange rates appear to have been generated by ‘mean-reverting’ processes. As noted by Lothian and Taylor (1996), however, professional academic opinion on the validity of PPP itself seems to display mean reversion. Prior to the 1970s, post-war academic opinion seemed to assume some form of long-run PPP, as evidenced, for example, by the classic study of Friedman and Schwartz (1963). Then, with the rise in dominance of the monetary approach to the exchange rate comcomitant with the switch to ‡oating exchange rates among the major industrialized countries in the early 1970s, there seemed to be a move towards belief in continuous PPP (see, for example, the studies in Frenkel and Johnson, 1978). However, the poor empirical performance of monetary models of the exchange rate, as experience with ‡oating rates unfolded, together with less formal but nevertheless compelling evidence of the excess volatility of nominal exchange rates compared to movements in relative national price levels, led to an acknowledgment of the ‘collapse of PPP’ by even its foremost advocates by the end of the 1980s (Frenkel, 1981). While Dornbusch’s ‘overshooting’ refinement of the Mundell-Fleming model, by providing a rationale for short-run deviations from PPP (Dornbusch, 1976), did somewhat reinstate the professional standing of the concept, empirical evidence published mostly in the 1980s, appeared to drive the final nails in the coffin of PPP, even considered as a condition that should hold only on average and over long periods of time. In particular, neither Roll (1979) nor Adler and Lehmann (1983) could reject the null hypothesis of random-walk behavior in deviations from PPP (the real exchange rate) and subsequent cointegration studies similarly found no evidence of long-run PPP (Taylor, 1988; Mark, 1990). Thus, the professional consensus shifted yet again to a position opposite to the strongly held belief in continuous PPP which had held sway barely a decade before - i.e. towards a view that PPP was of virtually no use empirically over any time horizon (e.g. Stockman, 1987). Following an early warning from Frankel (1986), however, a number of authors noted that the tests typically employed during the 1980s to test for long-run stability of the real exchange may have very low power to reject a null hypothesis of real exchange rate instability when applied to data for the recent floating rate period alone (e.g. Froot and Rogo¤, 1995; Lothian and Taylor, 1996, 1997). The argument is that if the real exchange rate is, in fact, stable in the sense that it tends to revert towards its mean over long periods of time, then the examination of just one real exchange rate over a period of twenty-five years or so may not yield enough information to be able to detect slow mean reversion towards purchasing power parity. This led to two developments in research, both aimed at circumventing the problem of low power displayed by conventional unit root tests applied to the real exchange rate. In the first of these developments, researchers sought to increase the power of unit root tests by increasing the length of the sample period under consideration (e.g. Frankel, 1986; Diebold, Husted and Rush, 1991; Cheung and Lai, 1993a; Lothian and Taylor, 1996). These studies have in fact been able to find significant evidence of real exchange rate mean-reversion. In the second line of development of this research, researchers sought to increase test power by using panel unit root tests applied jointly to a number of real exchange rate series over the recent float and, in many of these studies, the unit-root hypothesis is also rejected for groups of real exchange rates (e.g. Frankel and Rose, 1996; Wu, 1996; Flood and Taylor, 1996; Papell, 1998; Taylor and Sarno, 1998; Sarno and Taylor, 1998) 2 . A serious problem with panel unit root tests as they appear to have been interpreted in this context, however, as first noted by Taylor and Sarno (1998), is that the null hypothesis in such tests is, in fact, a joint null hypothesis that all of the series are generated by unit-root processes, and the probability of rejection of the joint null hypothesis may be quite high when as few as just one of the series under consideration is a realization of a stationary process. Unfortunately, researchers applying panel unit root tests to real exchange rates appear to have interpreted rejection of the joint null hypothesis as implying that all of the series are generated by stationary processes, instead of the correct interpretation that at least one of the series must have been so generated. 3 Nevertheless, Rogo¤ (1996), notes that, even if we were to take the results of the long-span or panel-data studies as having provided evidence of significant mean-reversion in the real exchange rate, there appears to be a consensus among these studies that the size of the half-life of deviations from PPP is about three to five years. If we take as given that real shocks cannot account for the major part of the short-run volatility of real exchange rates (since it seems incredible that shocks to real factors such as tastes and technology could be so volatile) and that nominal shocks can only have strong effects over a time frame in which nominal wages and prices are sticky, then the apparently high degree of persistence in the real exchange rate becomes something of a puzzle. Rogo (1996) sums this issue up as follows: ‘The purchasing power parity puzzle then is this: How can one reconcile the enormous short-term volatility of real exchange rates with the extremely slow rate at which shocks appear to damp out?’. Taylor, Peel and Sarno (2001) argue that the key both to detecting significant mean reversion in the real exchange rate and to solving Rogo¤’s PPP puzzle lies in allowing for nonlinearities in real exchange rate adjustment. The rationale for nonlinear real exchange rate adjustment is discussed more fully in Section 2, although the intuition seems reasonably clear: the further the real exchange rate is from its long-run equilibrium, the stronger will be the forces driving it back towards equilibrium. This may be due, for example, to greater goods arbitrage as the misalignment grows (Obstfeld and A.M. Taylor, 1997), or to a greater likelihood of government intervention (Taylor, 2003), or to a growing degree of consensus concerning the appropriate or likely direction of nominal exchange rate movements (Kilian and Taylor, 1993). In an examination of major dollar real exchange rates over the recent ‡oat, Taylor, Peel, and Sarno (2001) …nd that the speed of real exchange rate adjustment appears to be much faster than hitherto recorded, especially for larger real exchange rate shocks. Parallel to the recent literature on nonlinearities in real exchange rate adjustment, researchers have also stressed the importance of real shocks to the underlying equilibrium real exchange rate (e.g. Engel, 2000). As discussed in Section 3, the idea that productivity shocks may a¤ect the equilibrium real exchange rate - the so-called Harrod-Balassa-Samuelson e¤ect - has a fairly long history in economics (Harrod, 1933; Balassa, 1964; Samuelson, 1964), although empirical evidence in its support appears to be relatively weak (Froot and Rogo, 1995). Recently, however, Lothian and Taylor (2000) suggest that Harrod-Balass-Samuelson may also be important in shedding light on the PPP puzzle: by allowing for underlying shifts in the equilibrium dollar-sterling real exchange rate over the past two hundred years through the use of nonlinear time trends, they find the estimated half-life of real exchange rate shocks may be substantially reduced even without explicit allowance for nonlinear real exchange rate adjustment. In the present paper, using long-span data on the dollar-sterling and dollar franc real exchange rates over the past two centuries, we apply the …ndings of the various strands of the recent real exchange rate literature in order to develop a way of examining the statistical and economic signi…cance of the Harrod-Balassa-Samuelson e¤ect in a nonlinear context, and the implications for the PPP puzzle of so doing. In addition, we allow for shifts in real exchange rate volatility across nominal exchange rate regimes which has been recorded by a number of authors (see Frankel and Rose, 1995), using a data-instigated approach to determining the de facto rather than de jure shift in regime, consistent with the recent work of Reinhart and Rogo (2002).