تقدیر بزرگ، استهلاک بزرگ، و فرضیه برابری قدرت خرید

Although there has been much recent work on purchasing power parity (PPP), neither univariate nor panel methods have produced strong rejections of unit roots in US dollar real exchange rates for industrialized countries during the post-1973 period. We investigate the hypothesis that these non-rejections can be explained by one episode, the large appreciation and depreciation of the dollar in the 1980s, by developing unit root tests which account for this event and maintain long-run PPP. Using panel methods, we can strongly reject the unit root null for those countries that adhere to the typical pattern of the dollar’s rise and fall.

Purchasing power parity (PPP) is one of the most enduring topics in international economics, and the question of whether PPP holds during the post-Bretton-Woods system of flexible nominal exchange rates has been extensively analyzed. While the failure of PPP to hold in the short run was obvious after the first few years of generalized floating, long-run PPP has been subject to a “mean reversion in economic thought” (Lothian and Taylor, 1997). In the mid-1970s, models such as Dornbusch (1976) routinely used PPP as a long-run equilibrium condition. By the mid-1980s, the widespread failure to reject unit roots in real exchange rates led authors such as Stockman (1990) to construct models where long-run PPP did not hold. By the mid-1990s, however, research on both long-horizon data and on panels of post-1973 real exchange rates has led to a renewed belief in the validity of long-run PPP. All variants of PPP postulate that the real exchange rate reverts to a constant mean. Evidence of long run PPP can be provided by tests of a unit root in the real exchange rate. If the unit root null hypothesis can be rejected in favor of a level stationary alternative, then there is long-run mean reversion and, therefore, long-run PPP.1 The starting point for research on PPP during the current float is the observation that, using conventional Augmented-Dickey–Fuller (ADF) tests on univariate real exchange rates for industrial countries, the unit root null is rarely rejected. While these findings were initially taken as evidence against PPP, it has become clear that they say more about the low power of unit root tests with short time spans of data than about PPP.2 In response to these problems, research on long-run PPP has progressed in two directions. First, univariate techniques have been applied to long-horizon real exchange rates spanning one to two centuries. This data, however, combines periods of fixed and floating nominal exchange regimes, and cannot answer the question of whether evidence of PPP would be found with the same time span of flexible rates.3 Second, tests for unit roots in panel data, notably those of Levin and Lin (1992) and Im et al. (1997) have been used to test for PPP among industrialized countries in the post-1973 period.4 Panel unit root tests have not produced strong evidence of PPP for quarterly post-1973 US dollar based real exchange rates. Papell (1997), using data for 21 industrialized countries from 1973 to 1994, cannot reject the unit root null at the 10% level when serial correlation is taken into account in calculating lag lengths and computing critical values. This result is unchanged when the sample is extended through 1996 in Papell and Theodoridis (1998). O’Connell (1998a), emphasizing contemporaneous correlation, also reports non-rejections of the unit root null for post-1973 real exchange rates.5 The non-rejections are not caused by the low power of panel unit root tests. Levin and Lin (1992) and Bowman (1999) both report very high size adjusted power for panels of the size, time span, and half-lives of the post-1973 real exchange rates. These power results, however, depend crucially on the assumption of independence across individuals, and are not applicable if cross-sectional correlation is present. Dollar-based real exchange rates are highly contemporaneously correlated. Engel et al. (1997) and O’Connell (1998a) stress the importance of adequately controlling for contemporaneous correlation in panel unit root tests involving real exchange rates. O’Connell proposes a maximum likelihood procedure to account for contemporaneous correlation, but at the cost of severely restricting the degree of serial correlation. The behavior of most, but not all, dollar-based real exchange rates has been dominated by one episode: the large nominal appreciation and depreciation of the dollar in the 1980s. While there is widespread agreement that the initial appreciation of the dollar was caused by the monetary/fiscal policy mix of the United States in the late 1970s and early 1980s, there has been no successful explanation of the magnitude of the dollar’s appreciation based on economic fundamentals. Frankel and Froot (1990), for example, suggest that the dollar “overshot the overshooting equilibrium.” In the absence of fundamentals-based explanations, the appreciation is often described as a bubble, with a very rapid depreciation after the bubble burst. The rise and fall of the dollar is illustrated, in Fig. 1, by depicting nominal and real German mark and Norwegian krone exchange rates. The real exchange rate follows the pattern of appreciation and depreciation of the nominal exchange rate at high frequencies. Over longer horizons, the possibility of PPP emerges. It appears that the real exchange rate fluctuates around approximately the same mean in 1988–1996 as in 1973–1980. These short- and long-horizon patterns, which are consistent with sticky-price models, characterize most dollar-based exchange rates of European countries. The patterns, however, are not universal. Fig. 1 also depicts nominal and real Japanese yen and Australian dollar exchange rates. While the real and nominal exchange rates move together at high frequencies, the 1980–1987 episode is not so dominant and it does not appear that the pre-1980 and post-1987 real exchange rates fluctuate around the same (or necessarily any) mean.

The proliferation of recent work on purchasing power parity underscores its importance as a central topic in international economics. The development of panel unit root tests presents both a challenge and an opportunity for researchers attempting to find strong evidence of long-run purchasing power parity using data from the current float. The opportunity occurs because, in contrast with univariate methods, panel unit root tests with 20 individuals and 100 quarterly observations have sufficient power to reject the unit root null in favor of a level stationary alternative, even with half-lives of over 4 years. The challenge arises because, again in contrast with univariate methods, failure to reject the unit root null in real exchange rates can no longer be ascribed to low power of the tests. We investigate the hypothesis that the failure to reject unit roots in real exchange rates with panel methods can be explained by the great appreciation and depreciation of the dollar. We extend Perron’s (1989) changing growth model to develop univariate and panel unit root tests that allow for three breaks in the slope of the trend function, with the dates of the breaks determined endogenously. The coefficients on the break dummy variables are restricted so as to produce a constant mean prior to the first and following the third breaks. Furthermore, the coefficients are constrained so that the pre- and post-break means are equal. These restrictions ensures that rejection of the unit root null in favor of the PPP restricted broken trend alternative is evidence of long-run purchasing power parity. Even among the class of models which satisfy the PPP restrictions, the range of possibilities for multiple structural changes are enormous. In general, there can be multiple breaks in the intercept, slope, or both, of the trend function. Post-1973 dollar-based real exchange rates, drawn from a nominal flexible exchange rate regime, appear to be better characterized by long swings (slope changes) than by discrete jumps (intercept changes). Although our choice of three breaks is motivated by the rise and fall of the dollar, it also receives statistical support. We use tests developed by Bai (1999) to show that, out of the class of models with up to five slope changes, the strongest evidence of structural change for 13 out of 20 countries is for three breaks. While the univariate tests do not produce evidence against unit roots in real exchange rates, they provide a classification of the 20 countries into two groups. The real exchange rates of the 15 countries with the smallest root median squared error (RMSE) of the break dates follow the typical pattern associated with the sharp rise and even sharper fall of the dollar in the 1980s, and have breaks that are, on average, less than 1 year away from the median. The exceptions to the typical pattern, in descending order of their RMSE’s, are Japan, Australia, Portugal, Canada, and Greece. The central result of the paper is that panel unit root tests that account for PPP restricted structural change provide very strong evidence against the unit root hypothesis, and thus evidence of purchasing power parity, for panels of between 11 and 15 typical countries, as well as for the panel of 16 which includes one atypical country. Unit root tests that do not account for structural change provide no evidence of PPP for these panels. For larger panels of 17 to 20 countries, which include more atypical countries, the opposite occurs. Incorporating structural change decreases the evidence of PPP. Does this constitute evidence of PPP? We conduct simulations to investigate the size and power of the tests, and find that the results are most consistent with the hypothesis that the 15 typical countries are stationary while the others contain a unit root. Furthermore, the results are clearly inconsistent with either more than 16 or fewer than 14 stationary countries. Our conclusions are twofold first, we find very strong evidence that PPP holds for most of the countries; second, we find that PPP does not hold for all countries. The delineation among countries is very sharp. PPP holds for those countries, almost all European, that follow the typical pattern of the rise and fall of the dollar in the 1980s. PPP does not hold for the other, almost all non-European, countries that do not follow the typical pattern.