Long-run purchasing power parity with short-run data: evidence with a null hypothesis of stationarity

https://doi.org/10.1016/S0261-5606(99)00028-5Get rights and content

Abstract

We investigate long-run Purchasing Power Parity with data from the current floating exchange rate period by using tests where stationarity and cointegration are the null, rather than the alternative, hypotheses. In most cases, we cannot reject either the null hypothesis of stationarity of the real exchange rate or the null of cointegration between the nominal exchange rate and the domestic and foreign price levels. This constitutes evidence of long-run Purchasing Power Parity because, using the same tests, we can reject the null of stationarity for the nominal exchange rate. Confirmation of the results is provided by a Monte Carlo study.

Introduction

Purchasing Power Parity (PPP) is the intuitively appealing idea that exchange rates should tend to equalize national price levels and, as such, serves as the basis for many open economy macroeconomic models. While it is clear that PPP does not hold as a short-run proposition, empirical support for it even as a long-run equilibrium condition is mixed.

Testing for long run PPP has been facilitated by advances in testing for unit roots and cointegration. These tests compare the null hypothesis that the real exchange rate follows a random walk against the alternative hypothesis that PPP holds in the long run. Alternatively, the null is no cointegration between the nominal exchange rate and the domestic and foreign price levels. In that case, the cointegration alternative only provides strong evidence of long run PPP if the proportionality and symmetry restrictions are satisfied.1 The most commonly used tests are Augmented-Dickey–Fuller (ADF) tests for unit roots and Engle–Granger (EG) tests for cointegration.2

There has been a plethora of work using these tests, which is described in the recent surveys by Froot and Rogoff (1995) and Rogoff (1996). The most striking finding is that, using data from the current flexible exchange rate period, the unit root null is only infrequently rejected for real exchange rates when the United States dollar is the numeraire currency. While the no cointegration null, a weaker hypothesis, is rejected somewhat more often, the proportionality restrictions required for long run PPP are typically violated.3

The most common explanation for the failure to reject the unit root and no cointegration nulls is the low power of these tests over short time spans of data. Frankel (1986), Froot and Rogoff (1995) and Lothian and Taylor (1996) show that, using standard Dickey–Fuller tests, the post-Bretton Woods period is far too short to reliably reject the unit root null against a stationarity alternative. In response to these problems, researchers have turned to longer data sets, panel testing procedures, more powerful tests, and nonlinear methods.

Using longer data sets, Frankel (1986) and Lothian and Taylor (1996) report strong rejections of unit roots in real exchange rates. These studies, however, which use data from both fixed and flexible exchange rate periods, cannot answer the question of whether the unit root null would be rejected with a century of flexible exchange rate data.

In order to isolate the current flexible exchange rate period, researchers have turned to panel data procedures that gain power by exploiting both cross-sectional and time series variation. While Abuaf and Jorion (1990), Frankel and Rose (1996), Jorion and Sweeney (1996), Papell (1997), Papell and Theodoridis, 1998a, Papell and Theodoridis, 1998b and O'Connell (1998) provide additional evidence of PPP beyond what can be found by univariate methods, and Pedroni (1997) provides evidence of panel cointegration, the rejections of the unit root null are not uniformly strong. While unit roots in real exchange rates can be rejected if German mark (or other European currencies) are used as the numeraire, and can be rejected using monthly data with the US dollar as the numeraire, the unit root null cannot be rejected for the canonical case of quarterly post-1973 US dollar based real exchange rates.

The mixed results from panel methods have inspired research on alternative ways to increase power. One approach is to use more powerful univariate tests. Cheung and Lai (1998) use tests developed by Elliot et al. (1996) for the 10 bilateral exchange rates between France, Germany, Japan, the UK, and the US. While they provide more support for PPP than ADF tests, most of their rejections of the unit root null in favor of a level stationary alternative are only at the 10% significance level.4 Edison et al. (1997) employ tests for cointegration based on Horvath and Watson (1995). Although they show that these tests are superior to others when using small data sets, they provide, at best, a modest increase in rejections of the no cointegration null in the post-Bretton Woods period.

The most recent approach is to investigate the effects of nonlinear mean reversion on testing for PPP. Taylor and Sarno (1998) provide evidence that real exchange rates over the post Bretton Woods period exhibit nonlinear mean reversion. Furthermore, they show that, if a process is in fact nonlinearly mean reverting, univariate ADF tests will have very low power to reject the unit root null.

This paper proposes a complementary approach. We investigate long run purchasing power parity using KPSS tests developed by Kwiatkowski et al. (1992) and Shin (1994) where stationarity and cointegration are the null, rather than the alternative, hypotheses. We find that, in most cases, we cannot reject either the null hypothesis of stationarity of the real exchange rate or the null of cointegration between the nominal exchange rate and the domestic and foreign price levels.5

Why is this not a trivial result? If the post-Bretton Woods period is too short to reliably reject the unit root and no cointegration nulls, how can it possibly be long enough to reject stationarity and cointegration? How can failure to reject both sides of a hypothesis be evidence of anything?

The answer comes from investigating nominal exchange rates. It is well known that ADF tests fail to reject the unit root null for nominal exchange rates. Using KPSS tests, we reject the null of stationarity in almost all cases, providing strong evidence that the nominal exchange rate has a unit root. But if, over the same time span, the stationarity null can be rejected for nominal, but not for real, exchange rates, the failure to reject the null of stationarity cannot simply be an artifact of the short time period of the data. The same argument applies to the cointegration tests. In this case, the rejection of the stationarity null for nominal exchange rates, combined with the failure to reject the cointegration null, constitutes weak evidence of long run PPP.

An important stylized fact of flexible exchange rates, documented by Lothian (1998), is that the correlation between nominal and real exchange rates, which is positive and substantial with year-to-year changes, weakens considerably with 3-year averages and is virtually non-existent with 7-year and full-period averages. Our result that the stationary null can be rejected for nominal, but not real, exchange rates provides additional econometric evidence that the correlation between nominal and real exchange rates dissipates completely in the long run.

We provide confirmation of these assertions by conducting a Monte Carlo study using artificial data which replicates the time series properties of nominal and real exchange rates. We find that, if both nominal and real exchange rates contain unit roots, the stationary null will be rejected for nominal, but not for real, exchange rates in 22% of the cases. Since this is only about one-third as often as in the actual data, it seems unlikely that our results would occur if PPP did not hold. On the other hand, if the nominal exchange rate contains a unit root and the real exchange rate is stationary, the same result occurs much more often. Similar evidence is found for the cointegration tests.

This paper is organized as follows: In Section 2, we describe the data and give the results of the ADF and KPSS tests for both nominal and real exchange rates. The cointegration tests are presented in Section 3, and conclusions are provided in Section 4.

Section snippets

Unit root tests for nominal and real exchange rates

We use quarterly, nominal, end-of-period exchange rates and Consumer Price Indexes for twenty-one industrialized countries obtained from the International Monetary Fund (1997) International Financial Statistics. The IMF classifies twenty-three countries as industrialized, but we omit Iceland because its CPI series has data gaps and Luxembourg because it has a currency union with Belgium. With the United States as the domestic or numeraire country, we are able to analyze twenty nominal and real

Cointegration tests

Univariate tests ask whether the real exchange rate qt is stationarity. Cointegration tests have the possibility of testing weaker versions of PPP, since they require only thatet−δ1pt−δ2ptbe stationary for some constant δ1 and δ2.

We test for cointegration between the nominal exchange rate and the domestic and foreign prices by conducting two types of tests: The Engle–Granger (EG) test, which has a null hypothesis of no cointegration, and the Shin (1994) version of the KPSS test, where the null

Conclusions

The purpose of this paper was to construct tests of long-run Purchasing Power Parity that can be implemented with short-run data from the current floating exchange rate period. The most commonly used tests, Augmented-Dickey–Fuller tests for unit roots and Engle–Granger tests for cointegration, do not have sufficient power over the span of data. The ADF tests generally cannot reject the unit root null for either real or nominal exchange rates while the EG tests similarly cannot reject the no

Acknowledgements

We are grateful to Menzie Chinn, Eric Fisher, Lutz Kilian, James Lothian, Peter Pedroni, and an anonymous referee for very helpful comments.

References (32)

  • D Papell et al.

    Increasing evidence of purchasing power parity over the current float

    Journal of International Money and Finance

    (1998)
  • D Steigerwald

    Purchasing power parity, unit roots, and dynamic structure

    Journal of Empirical Finance

    (1996)
  • N Abuaf et al.

    Purchasing power parity in the long run

    The Journal of Finance

    (1990)
  • J.Y Campbell et al.

    Pitfalls and opportunities: What macroeconomists should know about unit roots

  • Caner, M., Kilian, L., 1999. Size distortions of tests of the null hypothesis of stationarity: Evidence and...
  • Y Cheung et al.

    Deterministic, stochastic, and segmented trends in aggregate output: A cross country analysis

    Oxford Economic Papers

    (1996)
  • Cited by (0)

    View full text