
 Start

2098
 Prefix

like transaction costs, taxation, subsidies, actual or
threatened trade restrictions, the existence o fnontraded goods, imper fect competition,
foreign exchange market interventions, and the differential composition of market baskets
and price indices across countries, one may expect PPP to be valid only in the longrun.
Empirical studies over long periods have supported longrun PPP
 Exact

(Diebold et al. (1991), Taylor (1996), Michael et al. (1997)).
 Suffix

However, results are mixed when the
recent Boatingrate period is examined. Using standard unitroot tests, Corbae and
Ouliaris (1988), Meese and Rogoff (1988), Edison and Fisher (1991), and Grilli and
Kaminsky (1991) cannot reject the unitroot null hypothesis for real exchange rates in
the managedBoat regime.
 (check this in PDF content)

 Start

2317
 Prefix

Empirical studies over long periods have supported longrun PPP (Diebold et al. (1991), Taylor (1996), Michael et al. (1997)). However, results are mixed when the
recent Boatingrate period is examined. Using standard unitroot tests, Corbae and
Ouliaris (1988),
 Exact

Meese and Rogoff (1988), Edison and Fisher (1991), and Grilli and Kaminsky (1991)
 Suffix

cannot reject the unitroot null hypothesis for real exchange rates in
the managedBoat regime. In contrast, Pedroni (1995), Frankel and Rose (1996), Lothian
(1997), Oh (1996), Wu (1996), and Papell and Theodoridis (1998) 1nd strong evidence of
mean reversion in real exchange rates by implementing panel data variants o fstandard
unitroot tests.
 (check this in PDF content)

 Start

2516
 Prefix

Using standard unitroot tests, Corbae and
Ouliaris (1988), Meese and Rogoff (1988), Edison and Fisher (1991), and Grilli and Kaminsky (1991) cannot reject the unitroot null hypothesis for real exchange rates in
the managedBoat regime. In contrast,
 Exact

Pedroni (1995), Frankel and Rose (1996), Lothian (1997), Oh (1996), Wu (1996), and Papell and Theodoridis (1998)
 Suffix

1nd strong evidence of
mean reversion in real exchange rates by implementing panel data variants o fstandard
unitroot tests.However, OFConnell (1998a) strongly disputes these meanreversion
1ndings in real exchange rates as they fail to control for crosssectional dependence in
the data.
 (check this in PDF content)

 Start

2761
 Prefix

In contrast, Pedroni (1995), Frankel and Rose (1996), Lothian (1997), Oh (1996), Wu (1996), and Papell and Theodoridis (1998) 1nd strong evidence of
mean reversion in real exchange rates by implementing panel data variants o fstandard
unitroot tests.However,
 Exact

OFConnell (1998a)
 Suffix

strongly disputes these meanreversion
1ndings in real exchange rates as they fail to control for crosssectional dependence in
the data. Additional evidence against reversion to PPP based on a panel o freal exchange
3
4
1
Relative PPP, which is implied by absolute PPP, states that the growth rate in the nominal exchange rate equals
the differential between the growth rates in home and foreig
 (check this in PDF content)

 Start

3197
 Prefix

Additional evidence against reversion to PPP based on a panel o freal exchange
3
4
1
Relative PPP, which is implied by absolute PPP, states that the growth rate in the nominal exchange rate equals
the differential between the growth rates in home and foreign price indices.
See
 Exact

Rogoff (1996) and Froot and Rogoff (1995)
 Suffix

for a review of the literature on PPP.
Employing an alternative multivariate unitroot test where the null hypothesis is nonstationarity o fat least one o f
the series under consideration, Taylor and Sarno (1998) 1nd strong support for mean reversion in a panel of CPIbased
U.
 (check this in PDF content)

 Start

3426
 Prefix

See Rogoff (1996) and Froot and Rogoff (1995) for a review of the literature on PPP.
Employing an alternative multivariate unitroot test where the null hypothesis is nonstationarity o fat least one o f
the series under consideration,
 Exact

Taylor and Sarno (1998)
 Suffix

1nd strong support for mean reversion in a panel of CPIbased
U.S. dollar exchange rates o fthe G5 countries. However, their evidence is not supportive o fmean reversion for GNP
deBator and PPICbased real exchange rates for the same panel of countries.
 (check this in PDF content)

 Start

3886
 Prefix

However, their evidence is not supportive o fmean reversion for GNP
deBator and PPICbased real exchange rates for the same panel of countries. Taylor and Sarno also point to a number
o fpit falls when using panel unitroot tests.
See Higgins and Zakra jsek (1999) for evidence contrary to that of OFConnellFs.
2
3
4
2
rates is reported in
 Exact

Engel et al. (1997). Papell (1997) and Liu and Maddala (1996)
 Suffix

also
1nd that evidence o fmean reversion in panels o freal exchange rates is very sensitive to
the groups o fcountries considered.
Recently, an alternative explanation bases the persistence o fmanagedBoat deviations
from parity on the presence of market frictions that impede commodity trade.
 (check this in PDF content)

 Start

4239
 Prefix

Papell (1997) and Liu and Maddala (1996) also
1nd that evidence o fmean reversion in panels o freal exchange rates is very sensitive to
the groups o fcountries considered.
Recently, an alternative explanation bases the persistence o fmanagedBoat deviations
from parity on the presence of market frictions that impede commodity trade.
 Exact

Dumas (1992),
 Suffix

Uppal (1993), Sercu et al. (1995), and Coleman (1995) develop equilibrium
models o freal exchange rate determination which take into account transactions costs
and show that adjustment o freal exchange rates toward PPP is necessarily a nonlinear
process.
 (check this in PDF content)

 Start

4269
 Prefix

Papell (1997) and Liu and Maddala (1996) also
1nd that evidence o fmean reversion in panels o freal exchange rates is very sensitive to
the groups o fcountries considered.
Recently, an alternative explanation bases the persistence o fmanagedBoat deviations
from parity on the presence of market frictions that impede commodity trade. Dumas (1992), Uppal (1993),
 Exact

Sercu et al. (1995), and Coleman (1995)
 Suffix

develop equilibrium
models o freal exchange rate determination which take into account transactions costs
and show that adjustment o freal exchange rates toward PPP is necessarily a nonlinear
process.
 (check this in PDF content)

 Start

5045
 Prefix

In this dynamic equilibrium framework, deviations
from PPP follow a nonlinear stochastic process that is meanreverting.
In an initial test o fthe hypothesis o fthe analytic work o fPPP adjustment process
based on market frictions,
 Exact

Michael et al. (1997)
 Suffix

apply an exponential smooth transition
autoregression (ESTAR) model to two data setsCa twocentury span o fannual data and
a monthly sample o finterwar observationsCand 1nd strong support for the nonlinear
representation.
 (check this in PDF content)

 Start

5345
 Prefix

o fthe hypothesis o fthe analytic work o fPPP adjustment process
based on market frictions, Michael et al. (1997) apply an exponential smooth transition
autoregression (ESTAR) model to two data setsCa twocentury span o fannual data and
a monthly sample o finterwar observationsCand 1nd strong support for the nonlinear
representation. Subsequently, using threshold autoregression modelling,
 Exact

Obstfeld and Taylor (1997) and OFConnell and Wei (1997)
 Suffix

report additional evidence o fnonlinear
price adjustment induced by the presence o ftransaction costs. However, OFConnell
(1998b), utilizing an equilibrium threshold autoregression (TAR) model to postBretton
Woods real exchange rates in a panel framework, 1nds little support to a marketfrictions
5
6
7
8
5
6
7
8
A summary o fstylized facts regarding real exchange rate behavior in th
 (check this in PDF content)

 Start

5527
 Prefix

Subsequently, using threshold autoregression modelling, Obstfeld and Taylor (1997) and OFConnell and Wei (1997) report additional evidence o fnonlinear
price adjustment induced by the presence o ftransaction costs. However,
 Exact

OFConnell (1998b),
 Suffix

utilizing an equilibrium threshold autoregression (TAR) model to postBretton
Woods real exchange rates in a panel framework, 1nds little support to a marketfrictions
5
6
7
8
5
6
7
8
A summary o fstylized facts regarding real exchange rate behavior in the postBretton Woods era is presented in
Lothian (1998).
 (check this in PDF content)

 Start

5840
 Prefix

However, OFConnell (1998b), utilizing an equilibrium threshold autoregression (TAR) model to postBretton
Woods real exchange rates in a panel framework, 1nds little support to a marketfrictions
5
6
7
8
5
6
7
8
A summary o fstylized facts regarding real exchange rate behavior in the postBretton Woods era is presented in
 Exact

Lothian (1998).
 Suffix

Instead o fassuming instantaneous trade, Coleman considers the case in which time elapses when goods are shipped
between markets.
Goldberg et al. (1997) derive a nonlinear Gmean reverting elastic random walk toward a stochastic PPP rateH and
1nd that the meanreversion process is not linear for some countries.
 (check this in PDF content)

 Start

5984
 Prefix

(TAR) model to postBretton
Woods real exchange rates in a panel framework, 1nds little support to a marketfrictions
5
6
7
8
5
6
7
8
A summary o fstylized facts regarding real exchange rate behavior in the postBretton Woods era is presented in
Lothian (1998). Instead o fassuming instantaneous trade, Coleman considers the case in which time elapses when goods are shipped
between markets.
 Exact

Goldberg et al. (1997)
 Suffix

derive a nonlinear Gmean reverting elastic random walk toward a stochastic PPP rateH and
1nd that the meanreversion process is not linear for some countries.
Obstfeld and Taylor detect Iband reversionF for price differentials of disaggregated as well as aggregated CPIs for
thirtytwo city and country locations during the 19801985 period.
 (check this in PDF content)

 Start

7010
 Prefix

First, we estimate
the deviations series from PPP using cointegration analysis, rather than imposing the
strict PPPcointegrating vector in calculating real exchange rates. Strong PPP
might not hold due to differential composition o fprice indices across countries
 Exact

(Patel (1990)),
 Suffix

differential productivity shocks (Fisher and Park (1991)), and measurement errors in prices as a result o faggregation and index construction (Taylor (1988), Cheung
and Lai (1993)). This latter rationale is very compelling, since available price indices are
likely to be Bawed approximations to the theoretical constructs underlying PPP.
 (check this in PDF content)

 Start

7058
 Prefix

First, we estimate
the deviations series from PPP using cointegration analysis, rather than imposing the
strict PPPcointegrating vector in calculating real exchange rates. Strong PPP
might not hold due to differential composition o fprice indices across countries (Patel (1990)), differential productivity shocks
 Exact

(Fisher and Park (1991)), and
 Suffix

measurement errors in prices as a result o faggregation and index construction (Taylor (1988), Cheung
and Lai (1993)). This latter rationale is very compelling, since available price indices are
likely to be Bawed approximations to the theoretical constructs underlying PPP.
 (check this in PDF content)

 Start

7168
 Prefix

Strong PPP
might not hold due to differential composition o fprice indices across countries (Patel (1990)), differential productivity shocks (Fisher and Park (1991)), and measurement errors in prices as a result o faggregation and index construction
 Exact

(Taylor (1988),
 Suffix

Cheung
and Lai (1993)). This latter rationale is very compelling, since available price indices are
likely to be Bawed approximations to the theoretical constructs underlying PPP. These
analytical justi1cations which explain why the cointegrating vector between nominal exchange rates and prices may vary greatly across countries have received strong empirical
support.
 (check this in PDF content)

 Start

7589
 Prefix

These
analytical justi1cations which explain why the cointegrating vector between nominal exchange rates and prices may vary greatly across countries have received strong empirical
support. The data in several studies (e.g.
 Exact

Pedroni (1997) and Li (1999))
 Suffix

strongly reject the symmetry and proportionality restrictions required for strict PPP. As a second
contribution, we employ the ESTAR framework to analyze the dynamic behavior of deviations from PPP, which may be advantageous relative to the standard TAR framework
in which regime changes occur abruptly.
 (check this in PDF content)

 Start

8262
 Prefix

Consistent with Teräsvirta (1994), i fan aggregated process is observed, which is the case with our data set here, regime changes
may be smooth rather than discrete as long as heterogeneous economic agents do not act
simultaneously (which is unlikely) even i fthey individually make dichotomous decisions.
Additionally, in the analytics by
 Exact

Dumas (1992) and
 Suffix

others, the adjustment process to
parity is smooth rather than discrete.
We apply the ESTAR methodology to a sample o fpostBretton Woods monthly data
for a broad set of U.S. trading partners: seventeen countriesF CPIbased measures and
eleven countriesF WPIbased measures.
 (check this in PDF content)

 Start

10726
 Prefix

Section 4 concludes with a summary o fthe evidence.
2.1
2 Nonlinear Adjustment toward PPP
The ESTAR model of deviations from PPP
In a framework of dynamic equilibrium in spatially separated markets,
 Exact

Dumas (1992),
 Suffix

Uppal (1993), Sercu et al. (1995), and Coleman (1995) show that the presence o ftransaction costs in international trade implies that deviations from PPP converge to parity in a
5
nonlinear fashion. Transaction costs create a band of inaction within which international
price differentials are not arbitraged away; only price differentials exceeding transaction
costs (outside the band) are pro1table
 (check this in PDF content)

 Start

10753
 Prefix

Section 4 concludes with a summary o fthe evidence.
2.1
2 Nonlinear Adjustment toward PPP
The ESTAR model of deviations from PPP
In a framework of dynamic equilibrium in spatially separated markets, Dumas (1992), Uppal (1993),
 Exact

Sercu et al. (1995), and Coleman (1995)
 Suffix

show that the presence o ftransaction costs in international trade implies that deviations from PPP converge to parity in a
5
nonlinear fashion. Transaction costs create a band of inaction within which international
price differentials are not arbitraged away; only price differentials exceeding transaction
costs (outside the band) are pro1table to arbitrage.
 (check this in PDF content)

 Start

12629
 Prefix

Therefore, in equilibrium under rational expectations the real exchange rate can deviate from its parity value
of unity. In this framework, the real exchange rate exhibits mean reversion for large
deviations from PPP, but Gspends most of the time away from parity...H
 Exact

(Dumas (1992),
 Suffix

p.154).
To model the behavior o fthe real exchange rate in this nonlinear context, we must
specify a structure which may be considered a generalization of the standard linear model
and which may be estimated from the available data.
 (check this in PDF content)

 Start

14052
 Prefix

Also, as long as heterogeneous economic
agents (who individually make dichotomous decisions) do not act simultaneously, regime
changes at an aggregated level may be smooth rather than discrete.
These considerations led
 Exact

Michael et al. (1997) to
 Suffix

apply a particular form of the
Ismooth transitionF threshold autoregressive (STAR) model. In the STAR framework,
the 1xed thresholds o fa standard threshold autoregressive (TAR) model are replaced with
a smooth function, which need only be continuous and nondecreasing (Tong (1993), p.
108).
 (check this in PDF content)

 Start

14355
 Prefix

These considerations led Michael et al. (1997) to apply a particular form of the
Ismooth transitionF threshold autoregressive (STAR) model. In the STAR framework,
the 1xed thresholds o fa standard threshold autoregressive (TAR) model are replaced with
a smooth function, which need only be continuous and nondecreasing
 Exact

(Tong (1993),
 Suffix

p.
108). The need for symmetry in the response to positive and negative deviations from
PPP leads to the exponential STAR, or ESTAR model described by Teräsvirta (1994).
The ESTAR model can be viewed as a generalization o fthe doublethreshold TAR model.
 (check this in PDF content)

 Start

14951
 Prefix

It is particularly attractive in the present context, as the strength o fthe equilibrating
force is increasing in the (absolute) magnitude of the degree of disequilibrium, in line with
predictions from the analytics of Dumas and others. Their framework, in which G...longrun behavior is very different from shortrun behavior...H
 Exact

(Dumas (1992),
 Suffix

p. 171), is
poorly approximated by the constant speed o fadjustment o fthe linear cointegration
framework, compared to the Bexible nature of the ESTAR approach. In this context, the
ESTAR model will be more suitable than the TAR framework in analyzing the dynamic
behavior o fthe deviations from PPP.
 (check this in PDF content)

 Start

17241
 Prefix

modelFs estimate o fthe impact o fthe lagged
levelwill be inconsistent due to misspeci1cation (essentially, the omitted variables in
the bracketed portion o fIn the ESTAR model, the coefficientwill govern the
adjustment process for small deviations from PPP, whereas when deviations are sizable,
and Fapproaches unity, thecoefficient becomes more and more important. The
8
t
y
.\r
\r
()
o f
 Exact

Granger and Teräsvirta (1993,
 Suffix

p.124). The scaling speeds the convergence and improves the stability o fthe nonlinear
least squares estimation algorithm and makes it possible to compare estimates o facross equations.
(+)
\r\r
\r
\r
quantitymust be negative to ensure global stability and mean reversion in
the IouterF regime.
 (check this in PDF content)

 Start

22256
 Prefix

InternationalFinancialStatistics
3.2
Tests for cointegration
t
()ttt
(111)
ε
S,P,P
,,
The validity o fthe PPP hypothesis as a longrun equilibrium concept requires that
in (5) be a stationary process, that is, the system variablesshould form a
cointegrated system
 Exact

(Engle and Granger (1987)).
 Suffix

The strict (absolute) version o fPPP
requires that the cointegrating vector be, imposing the joint restrictions of
symmetryand proportionality. However, as discussed above,
these restrictions may not be consistent with the empirical evidence due to measurement
errors in prices, differential composition o fprice indices across countries, and differential
productivity shocks.
 (check this in PDF content)

 Start

22735
 Prefix

However, as discussed above,
these restrictions may not be consistent with the empirical evidence due to measurement
errors in prices, differential composition o fprice indices across countries, and differential
productivity shocks.
The PPP relationship in (5) is estimated using the Johansen method
 Exact

(Johansen (1988), Johansen and Juselius (1990)),
 Suffix

a reduced rank regression technique.The Johansen
11
1212
(=)(==1)
13
13
All system variables have been tested for the presence of a unit root using the Augmented DickeyFuller and
method employs a VAR framework which incorporates both the short and longrun
dynamics o fthe system.
 (check this in PDF content)

 Start

27115
 Prefix

This
is especially true for CPIbased real exchange rates for Germany, Denmark, Norway, and
Finland and WPIbased real exchange rates for Japan and Greece, for which no evidence
o flinear cointegration was found.
p,
,
16 17
15
Some authors (e.g.
 Exact

Papell and Theodoridis (1998))
 Suffix

argue that the strengthening o fthe evidence in support
of longrun PPP for extended samples is only found when using panel methods but not univariate methods. These
studies however impose the symmetry and proportionality restrictions in constructing the deviations series from parity:
restrictions clearly rejected by the data.
 (check this in PDF content)

 Start

32791
 Prefix

Additionally, a
comparison o fthe values o fthe transition parameter obtained here with those reported
F
F,
()=0)
()=1)
ˆ
180
HF,.
,,
:+=0(1263)=9168
ˆˆ
The hypothesisresults in anwith a marginal signi1cance level o f0.002.
However, the evidence for Norway should be interpreted with caution, as none of the crucial coefficients (and
are individually statistically signi1cant.
ˆ)
15
in
 Exact

Michael et al. (1997)
 Suffix

suggests that the persistence o fdeviations from parity is much
stronger in the postBretton Woods era than in the interwar period (the 1920s) or in the
twocentury span 18021992 included in their study.
19
3.5
Generalized impulse response functions
To obtain further insights into the dynamic structure of real exchange rates, we perform
impulse response function analysis to evaluate the propagat
 (check this in PDF content)

 Start

33472
 Prefix

Unlike a linear model, impulse response functions for a
nonlinear model are characterized by dependence on initial conditions (history or path
dependence) and the size and sign o fthe innovation (shock dependence. or asymmetry).
Following
 Exact

Koop et al. (1996),
 Suffix

the impulse response function can be expressed as the
difference between two conditional 1rstmoment pro1les:
(6)

1+1+1
1
Xttthtttht
X
tt
()=[][]
GI h, ,ω EX  ,ω EX ω
GIX h
tω
t
whereis the generalized impulse response function of a variable,is the forecasting horizon,is the perturbation to the process at time ,is the conditioning
information set at time(reBecting the history o
 (check this in PDF content)

 Start

34393
 Prefix

We produce impulse response functions by estimatingcorresponding to a representative (average) history or initial conditions vector. Setting the conditioning vector to
ensures that the vector o finitial conditions G...lies near the center o fthe
data where the conditional density is most precisely estimatedH
 Exact

(Gallant et al., (1993),
 Suffix

p. 887). The conditional forecasts are simulated realizations obtained by iterating the
1
[]
[]
E
E
0
=[]
ωEω
11
tt
20
19
This section was included at the suggestion o fan anonymous re feree.
20
11
An alternative strategy of estimating generalized impulse response functions for a nonlinear model involves esti[]ttEωω.
matingfor each historyand then average the obtained sequences over all possi
 (check this in PDF content)

 Start

35106
 Prefix

involves esti[]ttEωω.
matingfor each historyand then average the obtained sequences over all possible drawings fromGiven
nonlinearities, the impulse response functions derived by these alternative strategies are not expected to be the same.
16
time series model, randomly drawing with replacement from the estimated residuals of
the model, and then averaging over the number o frandom draws (see
 Exact

Koop et al.(1996)
 Suffix

for a detailed description of this methodology). For our real exchange rate series, we
derive impulse response functions by settingmonths and averaging the
conditional forecast for each forecasting horizon over 5,000 draws.
 (check this in PDF content)

 Start

40466
 Prefix

Evidence from generalized impulse response functions also supports the presence o fnonlinearities. This evidence o fnonlinear adjustment
to parity is in contrast to the negative evidence obtained by
 Exact

OFConnell (1998b)
 Suffix

for panels
o freal exchange rates in a TAR framework.
Although the unitroot hypothesis may be rejected for a number of the PPP deviations series, a shock to these series dies out very slowly. Future research may focus
on the factors that distinguish those countries whose deviations from longrun PPP are
characterized by nonlinear behavior, as well as those related to this unusually slow speed
o
 (check this in PDF content)