Purchasing power parity under the gold standard.

• Author: Hegwood, Natalie D.

1. Introduction

   Long-run purchasing power parity (LRPPP), a mainstay of international economic theory, has proved difficult to back up empirically. Many attempts have been made using various time series of data, yet results continue to be mixed. (1) A standout exception to these mixed results is presented by Diebold, Husted, and Rush (1991), whose work has been interpreted as very strong evidence of LRPPP because of their across-the-board rejection of the unit root for a large sample of real exchange rates. Baillie (1996, p. 51) cites Diebold, Husted, and Rush as reestablishing "Purchasing Power Parity as a meaningful long run concept" despite the substantial mixed results of other studies. These mixed results are usually attributed to the power problems associated with standard unit root tests, especially for small samples. Diebold, Husted, and Rush (1991) overcome these shortcomings by loosening the structure of the model to allow a long-memory process.

   Diebold, Husted, and Rush (1991) model real exchange rate behavior using autoregressive, fractionally integrated moving-average (ARFIMA) models. In doing so, they reject the unit root for 16 real exchange rates from the gold standard era in favor of a fractionally integrated alternative hypothesis. A long-memory process is essentially a stationary one, "but where the autocorrelations take far longer to decay than the exponential rate associated with the autoregressive moving average (ARMA) class" (Baillie 1996, p. 6). This observation implies that purchasing power parity (PPP) holds, but in some cases only in the extreme long run. We agree with Diebold, Husted, and Rush (1991) that the structure of standard unit root tests is overly restrictive. However, we offer a different solution to this problem.

   From standard unit root tests, one must conclude that either all deviations from PPP are permanent or all deviations dissipate over time. However, there is a third possibility that has both theoretical and empirical support. Unit root tests do not allow the possibility that while most deviations dissipate, a few remain as permanent shocks. Real exchange rates may show substantial mean reversion, but to a changing mean rather than to the constant PPP value. This idea, which we call quasi purchasing power parity (QPPP), draws support from the Balassa-Samuelson theory, which asserts that productivity shocks can have permanent effects on real exchange rates. Samuelson (1994, p. 202) criticizes "economists who tried to use PPP as a guide even when substantive microeconomic changes had taken place between the previous putative equilibrium period and the new status quo." He cites an example from the 1980s when the actual yen/dollar exchange rate was 150 yen per dollar. According to PPP, the equilibrium exchange rate was 200 yen per dollar, yet the rate proceeded to drop to 110 yen per dollar and below. In QPPP terms, this situation would represent not a lack of mean reversion, but evidence of an equilibrium that had shifted away from PPP. This is a form of the Penn effect, whereby "a rich country, in comparison with a poor one, will be estimated to be richer than it really is if you pretend that the simplified Cassel version of purchasing-power parity ... is correct" (Samuelson 1994, p. 201). We assert that this Penn effect can occur not just between rich and poor countries, but between any two countries if one of these countries is affected by a permanent external shock.

   QPPP also supports Engel's (1996, p. 1) proposition that the real exchange rate "evolves as the sum of two processes--a stationary but persistent component and a non-stationary component." It is generally held that while the exchange rate deviates from its long-run equilibrium value in the short run, it eventually converges to that equilibrium value in the long run. The question, then, is, What is that long-run equilibrium value? "Some argue it is the PPP level, while others argue that there is a complex set of factors determining the long-run value, including such things as the relative labor productivities at home and abroad" (Engel 1996, p. 1). If this is true, then there is no reason to base exchange rate predictions on the PPP value, and there is therefore no reason to assume that PPP holds even in the long run.

   QPPP differs from LRPPP in that the mean of the real exchange rate time series need not be constant. While LRPPP requires mean reversion to a constant (the PPP value), QPPP allows mean reversion to an occasionally shifting mean. If this is the true behavior of real exchange rates, then it explains the mixed results of unit root tests that do not allow this option.

   We therefore find two problems with the analysis of Diebold, Husted, and Rush (1991). First, a rejection of the unit root for any model (ARMA, ARFIMA, or otherwise) does not rule out the possibility of a shifting mean. Engel (1996) has shown that in very large samples, the nonstationary element of a combined process is likely to be overshadowed, allowing a rejection of the unit root. Conversely, Perron (1988) shows that a series that is stationary around a changing mean will mimic the behavior of a random walk and therefore not allow a rejection of the unit root. This finding demonstrates that whether or not the unit root is rejected, there remains the possibility that the series is actually stationary around a changing mean. If the mean is not constant, then the real exchange rate is not returning to its PPP value following a shock.

   Second, allowing PPP deviations to dissipate so slowly departs from the basic PPP premise that equilibrium is achieved through arbitrage. If arbitrage is the equilibrium mechanism, a long-memory process does not seem reasonable. Rogoff (1996, p. 647) asks, "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?" He calls this question "the purchasing power parity puzzle" (p. 647). He then describes how models with sticky nominal prices, such as Dornbusch's (1976) overshooting model, can explain only part of the failure of short-run PPP. "If this were the entire story, however, one would expect substantial convergence to PPP over one to two years, as wages and prices adjust to a shock" (Rogoff 1996, p. 654).

   In this paper, we reevaluate the data of Diebold, Husted, and Rush (1991) to determine if QPPP is a more reasonable model than fractional integration to explain the behavior of real exchange rates. We use a procedure developed by Bai and Perron (1998) to test for structural changes (mean shifts) in the data. If mean shifts are found, LRPPP cannot be said to hold, despite rejection of the unit root by Diebold, Husted, and Rush (1991).

   Our results from the Bai-Perron tests indicate numerous mean shifts in each of the 16 real exchange rate series. It could be argued that if the direction of the mean shifts alternates, this behavior could still be interpreted as very slowly dissipating temporary shocks whose mean reversion can be picked up only by a fractionally integrated model. However, we find that in general, these deviations do not oscillate and are therefore not exhibiting long-memory mean reversion.

   To further investigate the soundness of QPPP as a more reasonable model than fractional integration, it is interesting to examine the speed of mean reversion as measured by the half-lives of PPP deviations. Because QPPP allows the mean of the real exchange rate to shift, we would expect quicker mean reversion than under LRPPP. This is an appealing aspect of the QPPP idea because it repositions arbitrage as a viable equilibrium mechanism.

   We calculate half-lives with and without the mean being allowed to shift at the break dates indicated by the Bai-Perron test. Our results show a substantial increase in the speed of mean...