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We propose an empirical model for deviations from long-run purchasing power parity (PPP) that simultaneously accounts for three key features: (i) adjustment toward PPP may occur via nominal exchange rates and relative prices at different speeds; (ii) different exchange rate regimes may generate regime shifts in the structural dynamics of PPP deviations; (iii) nonlinear reversion toward PPP in response to shocks. This empirical framework encompasses and synthesizes much previous empirical research. Using over a century of data for the G5 countries, we provide evidence that long-run PPP holds, the relative importance of nominal exchange rates and prices in restoring PPP varies over time and across different exchange rate regimes, and reversion to PPP occurs nonlinearly, at a speed that is fairly consistent with the nominal rigidities suggested by conventional open economy models.

The purchasing power parity (PPP) hypothesis states that national price levels should be equal when expressed in a common currency. A large literature in international finance has examined empirically the validity of PPP over the long run either by testing whether nominal exchange rates and relative prices move together in the long run or by testing whether the real exchange rate has a tendency to revert to a stable equilibrium level over time. The latter approach is motivated by the fact that the real exchange rate may be defined as the nominal exchange rate adjusted for relative national price levels, and therefore variations in the real exchange rate represent deviations from PPP, which must be stationary if long-run PPP holds (see the surveys of Froot and Rogoff, 1995, Rogoff, 1996, Sarno and Taylor, 2002, Taylor and Taylor, 2004 and Sarno, 2005). Although long-run PPP is such a simple proposition about exchange rate behavior, it has attracted the attention of researchers for decades because it has important economic implications on several fronts. In particular, the degree of persistence in the real exchange rate can be used to infer what the principal impulses driving exchange rate movements are. For example, if the real exchange rate is highly persistent or close to a random walk, then the shocks are likely to be real-side, principally technology shocks, whereas if it is not very persistent, then the shocks must be principally to aggregate demand, such as, for example, innovations to monetary policy (Rogoff, 1996). Further, from a theoretical perspective, if PPP is not a valid long-run international parity condition, this casts doubts on the predictions of much open economy macroeconomics that is based on the assumption of long-run PPP. Indeed, the implications of open economy dynamic models are very sensitive to the presence or absence of a unit root in the real exchange rate (e.g. Lane, 2001 and Sarno, 2001). Finally, estimates of PPP exchange rates are often used for practical purposes such as determining the degree of misalignment of the nominal exchange rate and the appropriate policy response, the setting of exchange rate parities, and the international comparison of national income levels. These practical uses of the PPP concept would obviously be of limited use if PPP deviations contain a unit root. Regardless of the great interest in this area of research, manifested by the large number of papers on PPP published over the last few decades, and despite the increasing quality of data sets utilized and the econometric techniques employed, the validity of long-run PPP and the properties of PPP deviations remain the subject of ongoing controversies. Specifically, earlier cointegration studies generally reported the absence of significant mean reversion of the real exchange rate for the recent floating experience (e.g. Mark, 1990), but were supportive of reversion toward PPP for the gold standard period (Diebold et al., 1991), for the interwar float (Taylor and McMahon, 1988), for the 1950s US–Canadian float (McNown and Wallace, 1989), and for the exchange rates of high-inflation countries (Choudhry et al., 1991). Some applied work on long-run PPP among the major industrialized economies has, however, been more favorable to the long-run PPP hypothesis for the recent float (e.g. Corbae and Ouliaris, 1988, Cheung and Lai, 1993, Cheung and Lai, 1994, Cheung and Lai, 1998, Frankel and Rose, 1996, Coe and Serletis, 2002 and Serletis and Gogas, 2004). One well-documented explanation for the inability to find evidence of long-run PPP is the low power of conventional unit root and cointegration tests with a sample span corresponding to the length of the recent float (Froot and Rogoff, 1995 and Lothian and Taylor, 1997). Researchers have sought to overcome the power problem either through long-span studies (e.g. Kim, 1990, Lothian and Taylor, 1996 and Taylor, 2002) or through panel unit root studies (e.g. Abuaf and Jorion, 1990, Frankel and Rose, 1996, O’Connell, 1998, Papell, 1998, Sarno and Taylor, 1998 and Taylor and Sarno, 1998) or through time-series models that account for the possibility of nonlinear mean reversion toward PPP (e.g. Michael et al., 1997, Obstfeld and Taylor, 1997, Baum et al., 2001, Coakley and Fuertes, 2001, Taylor, 2001, Taylor et al., 2001, Nakagawa, 2002 and Imbs et al., 2003). However, whether or not the long-span or panel-data studies do in fact answer the question whether PPP holds in the long run remains contentious (e.g. Engel, 1999 and Engel, 2000).1 With respect to studies using nonlinear models of the real exchange rate, they unanimously support the validity of long-run PPP (see Michael et al., 1997, Obstfeld and Taylor, 1997, Baum et al., 2001, Coakley and Fuertes, 2001, O’Connell and Wei, 2001, Taylor et al., 2001 and Imbs et al., 2003). However, since they are based on univariate regressions for the real exchange rate and do not allow for the possibility that the dynamics of PPP deviations be affected by monetary and exchange rate regimes, to date these studies have not shed light on whether nominal exchange rates or prices drive the adjustment toward the PPP equilibrium and do not investigate the role of different nominal regimes on the behavior of PPP deviations.

In this paper we have re-examined the behavior of deviations from PPP using a century of data for the four dollar exchange rates obtaining among the G5 countries. We begun by noting the empirical success in establishing the validity of long-run PPP recorded by both long-span studies and studies based on nonlinear real exchange rate models, which contrasts with the unfavorable evidence provided by studies based on standard unit root tests and most cointegration tests as well as with the mixed evidence provided by studies employing panel unit root tests. However, long-span studies have often been accused of ignoring the possible regime shifts that may characterize PPP deviations across different monetary and exchange rate regimes. We also illustrated how linear and nonlinear real exchange rate autoregressions impose potentially invalid restrictions on the unknown data generating process driving the relationship between nominal exchange rates and prices, and how these restrictions may prevent us from detecting reversion toward PPP. This process of interpretation of the time series evidence of the relevant literature led us to employ a nonlinear empirical framework for PPP deviations which facilitates a study of long-span data while taking into account possible regime shifts and at the same time investigating whether, if PPP is validated by the data, adjustment toward the long-run equilibrium level defined by PPP is driven primarily by the exchange rate, by relative prices, or by both. Within this framework, we are able to shed light on three hotly debated questions: whether PPP holds; whether nominal exchange rates or relative prices or both of them are responsible for responding to PPP disequilibria; and whether the half-lives of PPP deviations during floating regimes are consistent with standard dynamic general equilibrium open economy models with nominal rigidities. Our results are encouraging on a number of fronts. First, the nonlinear MSIAH-VECMs clearly indicate that long-run PPP holds for each of the four exchange rates examined over the last century and under each of the monetary regimes that characterize it. Second, we find that during fixed exchange rate regimes, relative prices adjust to restore deviations from long-run equilibrium, while exchange rates bear most of the burden of adjustment during flexible exchange rate regimes. The estimated transition probabilities are consistent with the view that the relative importance of exchange rates and relative prices in restoring the long-run equilibrium level of the exchange rate varies over time and is affected by the nominal exchange rate arrangement in operation. Third, the estimated half-lives implied by the models are rather different for fixed and floating rate regimes. During fixed exchange rate regimes the effects of system-wide shocks on the PPP equilibrium relationship may be very persistent indeed, with half lives ranging from two to almost ten years, depending on the shock size. However, the corresponding half-lives during flexible exchange rate regimes are drastically shorter, presumably because the nominal exchange rate is allowed to contribute to restoring PPP. In fact, large shocks to PPP will last for less than one year on average across countries. Overall, we leave this study with some degree of optimism, which may be summarized in the following three points: long-run PPP may hold after all; PPP deviations are reversed more quickly under floating rate regimes, when nominal exchange rates are allowed to respond to shocks; the speed at which PPP deviations dissipate is fairly consistent with the predictions of standard open economy macro theory.