DISCUSSION PAPER SERIES
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No. 2658
NON-LINEAR MEAN REVERSION IN REAL
EXCHANGE RATES: TOWARDS A
SOLUTION TO THE PURCHASING
POWER PARITY PUZZLES
Mark P Taylor, David A Peel
and Lucio Sarno
ISSN 0265-8003
NON-LINEAR MEAN REVERSION IN
REAL EXCHANGE RATES: TOWARDS
A SOLUTION TO THE PURCHASING
POWER PARITY PUZZLES
Mark P Taylor, Warwick Business School and CEPR
David A Peel, Cardiff Business School
Lucio Sarno, University of Oxford
Discussion Paper No. 2658
January 2001
Centre for Economic Policy Research
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CEPR Discussion Paper No. 2658
January 2001
ABSTRACT
Non-linear Mean Reversion in Real Exchange Rates:
Towards a Solution to the Purchasing Power Parity Puzzles*
We fit non-linearly mean-reverting models to real dollar exchange rates over
the post-Bretton Woods period, consistent with a theoretical literature on
transaction costs in international arbitrage. The half lives of real exchange rate
shocks, calculated through Monte Carlo integration, imply faster adjustment
speeds than hitherto recorded. Monte Carlo simulations reconcile our results
with the large empirical literature on unit roots in real exchange rates by
showing that when the real exchange rate is non-linearly mean-reverting,
standard univariate unit root tests have low power, while multivariate tests
have much higher power to reject a false null hypothesis
JEL Classification: C10, F31, F41
Keywords: non-linear dynamics, purchasing power parity, real exchange rate,
test power, unit root test
Mark P Taylor
Warwick Business School
University of Warwick
Coventry CV4 7AL
UK
Tel: (44 24) 76573 008
Fax: (44 24) 76523 032
Email:
[email protected]
For further Discussion Paperss by this author see: www.cepr.org/pubs/new-dps/dplist.asp?authorid=100357
David A Peel
Cardiff Business School
Aberconway Building
Cardiff University
Cardiff CF10 3EU
WALES
Tel: (44 29) 20875514
Fax: (44 29) 20874419
Email:
[email protected]
Lucio Sarno
Warwick Business School
University of Warwick
Coventry CV4 7AL
UK
Tel: (44 24) 528219
Fax: (44 24) 572871
Email:
[email protected]
For further Discussion Papers by this author see: www.cepr.org/pubs/new-dps/dplist.asp?authorid=138519
*The research reported in this paper was conducted with the aid of a research
grant from the Leverhulme Trust, which Taylor gratefully acknowledges. It
consolidates research reported in preliminary form in Taylor and Peel (1998)
and Taylor and Sarno (1999a, 1999b). The authors are grateful to participants
in seminars at which previous versions of the paper were presented, including
presentations at Columbia University; the Stern School of Business, New York
University; the University of Houston; Rice University; the London School of
Economics; the London Business School; the University of Oxford; the
University of Salerno; the University of Nottingham; the University of
Southampton; the University of Warwick; Brunel University; the Bank of
England; the 1999 ASSA Annual Meetings, New York; and the 1999 Annual
Conference of the Society for Non-linear Dynamics and Econometrics, New
York. The authors alone are responsible for any errors that may remain.
NON-TECHNICAL SUMMARY
Purchasing power parity (PPP) is the proposition that national price levels
should be equal when expressed in a common currency. Since the real
exchange rate is the nominal exchange rate adjusted for relative national price
levels, variations in the real exchange rate represent deviations from PPP.
While very few contemporary economists would hold that PPP holds
continuously in the real world, ‘most instinctively believe in some variant of
purchasing power parity as an anchor for long-run real exchange rates’
(Rogoff, 1996), and indeed the implication or assumption of much reasoning in
international macroeconomics is that some form of PPP holds at least as a
long-term relationship. Moreover, estimates of PPP exchange rates are
important 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. It is not surprising, therefore, that a
large empirical literature on PPP has evolved. This literature, at least as it has
developed since the late 1980s, has thrown up at least two important puzzles.
A large number of studies of real exchange rates among industrialized
countries in the post-Bretton Woods period have found that time-series
deviations from PPP appear to be characterized by non-stationary (or more
particularly unit root) behaviour for exchange rates, implying the absence of
any long-run tendency towards PPP (Rogoff, 1996). This might be thought of
as the first PPP puzzle. One potential solution to the first PPP puzzle is by
reference to the low power of the statistical tests employed. In particular, since
conventional tests for unit roots may have very low power to reject a false null
hypothesis with a sample span corresponding to the length of the recent float,
i.e. since about 1973 (Frankel, 1986, 1990; Lothian and Taylor, 1997), a
number of researchers have sought to increase the power of their tests by
increasing the length of the sample period under consideration or by using
panel unit root tests applied jointly to a number of real exchange rate series
over the recent float. In many of these studies, evidence in favour of PPP is
detected.
that the null hypothesis in such tests is generally that all of the series are
generated by unit root processes, so that the probability of rejection of the null
hypothesis may be quite high when as few as just one of the series under
consideration is a realization of a stationary process.
Moreover, even if we take the results of the long span or panel data studies as
having solved the first PPP puzzle, a second PPP puzzle then arises. Among
the long span and panel data studies which do report significant mean
reversion of the real exchange rate, there appears to be a consensus that the
size of the half-life of deviations from PPP is about three to five years (Rogoff,
1996). 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 a second PPP puzzle is the
apparently high degree of persistence in the real exchange rate (Rogoff,
1996).
We seek to resolve the first and second purchasing power parity puzzles
through an investigation of non-linearities in real exchange rate adjustment
toward long-run equilibrium during the post-Bretton Woods period. Our
empirical results provide strong confirmation that four major real bilateral
dollar exchange rates are well characterized by non-linearly mean-reverting
processes over the floating rate period since 1973. The estimated models
imply an equilibrium level of the real exchange rate in the neighbourhood of
which the behaviour of the log-level of the real exchange rate is close to a
random walk, becoming increasingly mean-reverting with the absolute size of
the deviation from equilibrium. This is consistent with a number of recent
theoretical contributions on the nature of real exchange rate dynamics in the
presence of international arbitrage costs.
We estimated the impulse response functions corresponding to our estimated
non-linear real exchange rate models by Monte Carlo methods. Because of
the non-linearity, the half-lives of shocks to the real exchange rates vary both
with the size of the shock and with the initial conditions. By taking account of
statistically significant non-linearities, we find the speed of real exchange rate
adjustment to be typically much faster than the apparently ‘glacial’ speeds of
real exchange rate adjustment recorded hitherto (Rogoff 1996).
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