ï»¿ WPS6411
Policy Research Working Paper 6411
Estimating the Half-life of Theoretically
Founded Real Exchange Rate Misalignments
Megumi Kubota
The World Bank
Europe and Central Asia Region
Poverty Reduction and Economic Management, Macroeconomics 1 Unit
April 2013
Policy Research Working Paper 6411
Abstract
This paper models empirically the short and long-term reversion of real exchange rate misalignments with
behavior of the real exchange rate misalignmentâ€”a key respect to a fundamentals-based equilibrium level. The
variable in academic and policy circles. The equilibrium paper reconciles two strands of the empirical literature
real exchange rate is derived from a theoretical model that estimate the half-life of purchasing power parity
with intertemporal external equilibrium and internal deviations: one, the linear adjustment model that renders
equilibrium (in traded and non-traded markets) based the consensus half-life estimates of purchasing power
on the current account dynamics and Harrod-Balassa- parity deviations, and another, the non-linear adjustment
Samuelson productivity, respectively. This provides a model of purchasing power parity deviations. The model
bridge between theory and empirics that links the real estimates the half-life of real exchange rate deviations
exchange rate and its fundamentals (terms of trade, the from their fundamental equilibrium at approximately
ratio of net foreign assets to gross domestic product, 2.8 years. Consequently, about 25 percent of the real
and productivity differentials). The paper contributes to exchange rate deviation from its equilibrium level is
the literature by: (a) estimating an unrestricted vector corrected in the next year. Approximately 43 percent
error correction model that examines the short-term of the countries in the sample have a half-life of real
dynamics of real exchange rate misalignments and exchange rate deviations from equilibrium less than 2.5
links these deviations with shocks to fundamentals yearsâ€”which is consistent with predictions from non-
from 1970 to 2010, and (b) computing the speed of linear mean reversion models.
This paper is a product of the Poverty Reduction and Economic Management, Macroeconomics 1 Unit, Europe and Central
Asia Region. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution
to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://
econ.worldbank.org. The author may be contacted at mkubota@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Estimating the Half-life of Theoretically Founded
Real Exchange Rate Misalignments
Megumi Kubota*
JEL Classification: F31, F41
Key Words: Misalignment, Fundamentals, the HBS Effect, an Unrestricted VECM,
A Half-life
Sector Board: EPOL
*
Kubota: The World Bank, Poverty and Economic Management, Macroeconomics 1 Unit, Europe and
Central Asia (ECA). 1818 H Street, NW, Washington, DC, 20433 USA; mkubota@worldbank.org; tel:
+(1)202-473-4844. The author is grateful to Michael Wickens as well as CÃ©sar CalderÃ³n, Ronald
MacDonald, Neil Rankin and Peter N. Smith. The data is updated although this paper is based on the
University of York Discussion Paper No. 2009/24 and of her PhD thesis â€œReal Exchange Rate
Misalignmentsâ€? at the University of York in 2009. This paper was presented at the 2013 Annual
Conference of Royal Economic Society at Royal Holloway, University of London. The views
expressed in this paper are those of the author and do not necessarily reflect those of the World Bank or
its Board of Directors. The usual disclaimer applies and all errors are hers.
1. Introduction
The goal of this paper is to model empirically real exchange rate (RER)
misalignments using a general equilibrium model of exchange rate determination and
provide a bridge between theory and empirics for RER misalignments that conforms a
suitable analytical framework for macroeconomic policy evaluation. The paper also
reconciles two strands of the empirical literature that estimate the half-life of
deviations from purchasing power parity (PPP): one, the linear adjustment model that
renders the consensus half-life estimates of PPP deviations as documented by Rogoff
(1996), and another, the non-linear adjustment model of PPP deviations as estimated
by Lothian and Taylor (2000) and Taylor, Peel and Sarno (2001).
The first strand of the literature assumes that the adjustment of the real exchange
rate to its PPP level follows a linear model. This model predicts a constant speed of
mean reversion and the estimate of the half-life of PPP deviations lies within a
consensus interval of 3-5 years (Rogoff, 1996). The second strand of the literature
assumes that the presence of transaction costs in international trade may lead to a non-
linear adjustment of the real exchange rate to its PPP equilibrium. This model predicts
that the speed of reversion (and, hence, the half-life of these deviations) depends on
the extent of the deviation from PPP. Lothian and Taylor (2000) examine the behavior
of the US$-Sterling Pound real exchange rate over 200 years and find that the half-life
of deviations from PPP may be as low as 2.5 years. Analogous evidence is presented
by Taylor, Peel and Sarno (2001) for major exchange rates for the post-Bretton
Woods period.
Our strategy consists of estimating an unrestricted vector error correction model
(VECM) in the spirit of the research by Bewley (1979) and Wickens and Breusch
(1987). Using this econometric technique, this paper departs from previous research
by calculating the speed of mean reversion of RER deviations from its fundamental-
based equilibrium level â€”as opposed to calculating deviations from a PPP based
measure equilibrium level. This paper reconciles the evidence from the two strands of
the literature summarized above by accounting simultaneously for the adjustment of
RER fundamentals to the equilibrium.
The main message of this paper is that our model estimates the (mode of the
distribution of the) half-life of (country estimates of) RER deviations from their
2
fundamental equilibrium at approximately 2.8 years. Consequently, approximately 25
percent of the RER deviation from its equilibrium level is corrected in the next year.
To estimate the half-life of RER deviations from the equilibrium, we use a
heterogeneous sample of 80 countries â€“ of which 22 are industrial economies and 58
are developing countries â€“ over the period 1970-2010. Each country has at most 41
observations. Accordingly, for 34 countries among our sample of 80 countries, our
estimates show that the half-life is less than 2.5 years (average of the distribution,
therefore, we are able to capture smaller half-lives for some countries (42.5 percent of
the total countries) â€”as predicted by the non-linear mean reversion models.
Our theory-based measure of the equilibrium RER (ERER) model is consistent
with simultaneous external and internal equilibrium (Obstfeld and Rogoff, 1985;
Obstfeld and Stockman, 1985; Edwards, 1989; Alberola and Lopez, 2001). 1 The
ERER yields external equilibrium that guarantees a sustainable current account
position â€”as in Mussa (1984) and Frenkel and Mussa (1985). This is compatible with
long-run sustainable capital flows. The ERER also guarantees internal equilibrium if
this relative price helps achieve equilibrium in the non-traded goods markets not only
in the current but also in future periods â€”as in Balassa (1964) and Samuelson (1964).
The dynamic behavior is driven by RER fundamentals such as net foreign assets
(NFA), terms of trade (TOT) and the Harrod-Balassa-Samuelson (HBS) productivity
differentials.
Movements in the RER are typically driven by shifts in the relative price of traded
to non-traded goods. 2 This relative price signals the allocation of resources across
different sectors. The RER provides a measure of the relative incentives to different
types of activity in an economy and a way to examine a broader set of
macroeconomic, structural and sectoral policies as well as their effectiveness in
influencing export and import performance.
RER misalignments may result from two types of shocks: (a) time-inconsistent
macroeconomic (domestic) policy shocks (e.g. unsound monetary or fiscal policies),
1
The model presented in this paper uses a simple theoretical framework to determine the RER
equilibrium path (Kubota, 2009a, b). As specified, this model focuses on three key determinants of the
real exchange rate: net foreign assets, terms of trade and productivity differentials. An extension to this
framework would introduce a government in the model. For instance, some models of exchange rate
determination have introduced government spending as another RER determinant (e.g. Froot and
Rogoff, 1991; De Gregorio, Giovannini and Wolf, 1994; Chinn, 1999; Galstyan and Lane, 2009).
2
If productivity grows faster in tradable vis-Ã -vis non-tradable goods, the corresponding increase of
wages in tradables will push wages in nontradables upward. As a result, a real appreciation of the
currency will occur. This is known as the HBS effect.
3
and (b) adverse external shocks (e.g. sharp increases in foreign interest rates and
deterioration of terms of trade). As claimed by Rogoff (1996), RER misalignments are
very persistent and may be linked to the evolution of fundamentals â€”e.g. these can be
driven by real shocks that cause shifts in relative prices and consistent with some
external and internal equilibrium (Lucas, 1982; Stockman, 1987; Edwards, 1989). It is
preferable to measure RER misalignments in terms of deviations from its long-run
equilibrium value, and to use this indicator for a better assessment of the link between
(the persistence of) RER misalignments and economic policies and, hence, examine
their consequences on economic performance.
This paper provides a better assessment of the speed of convergence of real
exchange rate deviations to their equilibrium level. This is relevant for policymakers
that use the exchange rate to foster export-led growth. Examining the properties of
mean reversion would allow us to identify the duration of these RER deviations (e.g.
undervaluations in the case of excess depreciation of the currency). In turn, the real
undervaluation of the currency can arguably trigger growth (Hausmann, Pritchett and
Rodrik, 2005; Rodrik, 2007). In this context, activist exchange rate policies to keep
the RER undervalued may generate competitive gains that help exports grow and,
hence, promote economic growth (Aizenman and Lee, 2007). On the other hand, a
loss of competitiveness due to real overvaluation of the currency may have an adverse
impact on economic performance if it comes from weak macroeconomic
fundamentals and inconsistent exchange rate policies. 3 This paper consists of the
following sections: Section 2 discusses the empirical methodology and modeling
while it estimates and analyzes the unrestricted VECM on RER misalignments.
Section 3 concludes.
2. Empirical Methodology
In this section we first present an overview of the empirical methodology, and
then explain our strategy to model RER misalignments. We finally analyze the
regression estimates of an unrestricted vector error correction model for 80 countries
(22 industrial countries and 58 developing countries) from 1970 to 2010.
3
For instance, the experience of Latin American countries in the 1980s in defending their nominal peg
in the context of substantial fiscal and external imbalances lead to a significant RER overvaluation
which distorted relative prices.
4
2.1 Overview of the Empirical Methodology
We use an unrestricted VECM to estimate RER misalignments. The error
correction model (ECM) applied to a vector of the RER and its fundamentals provide
us a consistent integration of short-run dynamic adjustment with long-run equilibrium
specification. We follow the Wickens-Breusch methodology (1987) to estimate the
ECM on a country-by-country basis. This implies estimating a linear transformation
of the autoregressive distributed lag (ARDL) model. One of the advantages of this
method is that the ECM regression can instantaneously provide parameters to explain
the extent of short-run adjustment to disequilibrium (Banerjee, Galbraith and Dolado,
1990). The Wickens-Breusch estimator belongs to the instrumental variable (IV)
estimator family and is an alternative to the Engle-Granger (1987) estimator. The
Granger representation theorem links cointegration to error correction models.
Johansen merges cointegration and error correction modeling in a vector
autoregression (VAR) framework. This section outlines Johansenâ€™s approach to
cointegration modeling. The VAR undertaking in this paper (which includes lagged
levels and differences of the RER and its fundamentals) is equivalent to an
unrestricted VECM. If the dependent variable is cointegrated, then the VAR
representation is not the most suitable representation for analysis because the
cointegrating relations are not explicitly apparent. The cointegrating relations become
apparent if the VAR in levels is transformed to a vector error correction
representation.
In Kubota (2009a, b), I examine the theoretical and empirical linkages between
the real exchange rate and its fundamentals. I also conduct time series and panel data
unit root tests as well as cointegration test. 4 The estimates of the long-run
cointegration relationship between the real effective exchange rate (REER) and its
fundamentals (terms of trade, the net foreign assets to GDP ratio and HBS
productivity differentials) are consistent with the predictions of the theoretical model:
4
Kubota (2009a, b) estimates the long-run RER equation for 79 countries from 1970 to 2005 and tests
the stationary of RER and its fundamentals by conducting time series, homogeneous panel unit root
tests (Maddala and Wu, 1999; Levin, Lin and Chu, 2002) and heterogeneous tests (Im, Pesaran and
Shin, 2003; Pesaran, 2007). She also tests the cointegration of these series using time series techniques
(Johansen, 1988, 1991), homogeneous panel cointegration tests (McCoskey and Kao, 1998; Kao, 1999)
and heterogeneous tests (Pedroni, 1999). The panel data estimation of the fundamental RER equation is
addressed by using non-stationary time series techniques for heterogeneous panels such as the mean
group estimator (MGE) by Pesaran, Smith and Im (1996) and the pooled mean group estimator
(PMGE) by Pesaran, Shin and Smith (1999).
5
all positive relationship about 80 percent between REER and TOT, of almost half
between REER and the net foreign assets to GDP ratio and about 40 percent between
REER and HBS productivity differentials.
The empirical implementation of the model on a large cross-country time-series
sample poses two main challenges. First, although the model defines a long-run
relationship among the RER and its fundamentals, the RER may not always be in
equilibrium at every point in time due to imperfections, rigidities or regulations. The
equilibrium may be achieved gradually in the long run. Consequently, in the empirical
analysis, the process of a short-run adjustment must complement the long run
equilibrium model. As a result, we implement the unrestricted VECM techniques to
model the RER misalignments and to analyze their behavior.
2.2 Modeling the RER Misalignment and its Short-Run Behavior
The long-run equilibrium solution for the RER ( qt ) consists of both the
BOP
intertemporal BOP equilibrium ( qt ) and the equilibrium in tradable and non-
PRO
tradable goods ( qt ) (Kubota, 2009a, b). RER misalignment, expressed as the
deviation in the actual (log of) RER ( qt ) from its equilibrium value, is such that:
mist = qt âˆ’ qt = ( qtBOP + qtPRO ) âˆ’ ( qtBOP + qtPRO ) (1)
The dynamic adjustment of the RER to equilibrium is modeled through an ECM:
m n
âˆ†mist = âˆ‘ Î² i âˆ†mist âˆ’ i + âˆ‘ Î³ j âˆ†qt âˆ’ j âˆ’ (1 âˆ’ Î± )mist âˆ’1 + ut (2)
i =1 j =0
where i=1,â€¦,m and j=0,â€¦,n
The coefficient Î± in equation (2) captures the speed of mean reversion in RER. For
instance, if RER misalignment is one percent, (1 âˆ’ Î± ) percent would be corrected by
next period. If we reformulate equation (2) in terms of qt and qt , then,
6
m n
q t = âˆ‘ Î± i q t âˆ’i + âˆ‘ Î² j xt âˆ’ j + u t
i =1 j =0
qt =
âˆ‘Î² j
â‹… xt
1 âˆ’ âˆ‘Î± i
ï£® ï£¹
where and x t = ï£¯TOTt NFAy t HBS t ï£º is the matrix of the RER fundamentals where
ï£° ï£»
all variables in xt are expressed in logs except for the ratio of net foreign assets to
GDP (NFAy) where TOT stands for terms of trade in logs and HBS stands for HBS
productivity differentials in logs.
Wickens and Breusch (1987) show the equivalence of the estimates of different
transformation of the ECM family of models, including: (i) the IV estimation of
ARDL regressors by Bewley (1979); (ii) the Barsden (1989) transformation, and (iii)
the OLS estimation of the general ECM by Banerjee, Galbraith and Dolado (1990).
To estimate our model we first introduce the following empirical representation of the
unrestricted VECM:
âˆ†qt = Âµ âˆ’ (1 âˆ’ Î± )( qt âˆ’1 âˆ’ Î¸xt âˆ’1 ) + ( Î² âˆ’ Î¸ ) âˆ†xt + et (3)
In the VECM, âˆ†qt and its lags are I(0). After running the regression (3), we plot
{Î± i }in=1 coefficients in Figure 1.1 where n is the number of countries (i.e. n = 80). Then
we run the second regression with 3 lags:
âˆ†qt = Î½ + Lâˆ†qt âˆ’1 + Lqt + Îµ t
2.3 The Unrestricted VECM Analysis
This section focuses on the results from applying our unrestricted VECM analysis
on 80 countries (22 industrial countries and 58 developing countries) from 1970 to
2010. Figure 1.1 plots the histogram of the estimated Î± in equation (3) for our sample
of countries (n=80). The distribution of these estimated coefficients shows that the 5th
percentile is 0.46 and the 95th percentile is 0.95. Figure 1.2 complements this
7
information by plotting the estimated values of the Î± coefficients for the 80 countries
in our sample. We observe that these coefficients fluctuate from 0.466 to 0.991, and
then the mode of the distribution is around 0.75. The mode of the distribution implies
that it is commonplace to our sample countries that: (a) 25 percent of the RER
disequilibrium in the previous period would be corrected by the current period, and
(b) the half-life of their deviation from the equilibrium is equal to 2.8 years.
Consequently, our half-life lies close to the lower bound of consensus interval of
Rogoff (1996). The median of the distribution of the Î± coefficients is also calculated,
and it is equal to the mode of the distribution. The average of Î± across countries is
equal to 0.72 â€”still quite close to the values of the median and the mode of the cross-
country distribution of Î± coefficients. 5 As a result, these coefficients appear to be
normally distributed and most of estimated Î± coefficients are statistically significant.
Our estimates of the half-lives of RER deviations from equilibrium are a
fundamental-based equilibrium RER as opposed to deviations from PPP levels. Our
adjustment to equilibrium implies an adjustment of RER fundamentals such as net
foreign assets, terms of trade and traded to non-traded productivity differentials.
Therefore, we argue that calculating the half-life which is the speed of adjustment in a
multivariate model for RER and fundamentals may account for the non-linear
adjustment.
Table 1 presents our econometric analysis for a selected group of eight countries.
The coefficient for the lagged REER conveys information about the speed of
convergence to the real exchange rate equilibrium. When compared to the half-life
consensus estimates of three to five years by Rogoff (1996), our estimate of the half-
life of RER deviation is about 2.8 years â€”which is slightly shorter than the consensus
one. However, there is heterogeneity across countries. 6 For example, among most
selected countries in Table 1 negative coefficients for lagged REER are statistically
significant between 0.2 and 0.8 except Germany and Chile. This implies that, if RER
5
The mode of the distribution of half-live of deviations from the equilibrium RER level is equal to:
ï£« ln 0.5 ï£¶ where the mode of Î± coefficient is around 0.752... The average of the
2.796 â‰ˆ ï£¬ ï£·
ï£¬ âˆ’ (1 âˆ’ 0.752...) ï£·
ï£ ï£¸
distribution of the Î± coefficient is 0.724; therefore, this half-life of RER deviations from equilibrium is
2.51 years.
6
It is reasonable to assume that countries can differ regarding, for instance, the extent of market
imperfections (say, labor or product market rigidities), monetary arrangements or different access to the
international markets for goods and assets â€”and perhaps even in the parameters characterizing the
long-run equilibrium. Thus, it is important to take into account the very likely possibility of parameter
heterogeneity across countries.
8
misalignment is 1 percent, it will be subsequently corrected between 20 and 80
percent by the next year for most countries. Mean reversion of REER is, for instance,
faster in China, at about 1.58 years, than in Argentina, at about 2.25 years.
The country estimates of half-lives of deviations from ERER show that these
estimates are less than 2.5 years for 34 countries â€”as predicted by non-linear models
of mean reversion. This implies that 42.5 percent of the half-life estimations falls into
nonlinear half-life estimations (Lothian and Taylor, 2000; Taylor, Peel and Sarno,
2001) although 2.5 years half-lives are larger in their estimated deviations from PPP
while our half-lives are within a shorter range of our results.
Figure 1.3 plots the half-life of deviations from ERER against the level of income
per capita. The latter variable is proxied using GDP per capita from World Bankâ€™s
World Development Indicators. It suggests that the half-life of deviations from ERER
is longer, the higher the level of GDP per capita is. The findings of this paper also
support those of the model with non-linear adjustment: deviations from equilibrium
may be larger in countries with lower income per capita levels.
Figures 1.4 and 1.5 depict a positive relationship between the half-life of
deviations from ERER and the flexibility of the exchange rate arrangement. The data
on these arrangements is taken from the database developed by Reinhart and Rogoff
(2004) and updated by Ilzetzky, Reinhart and Rogoff (2009). Figure 1.4 shows the
scatterplot with the average coarse index while Figure 1.5 presents the plot for the
average fine index. In all these cases, the higher the index, the more flexible is the
exchange rate regime. Consequently, the figures show that the half-life to ERER is
longer the more flexible the exchange rate regime. 7
2.4 RER Misalignments: An Error Correction Model Representation
From our VECM estimation, we plot the response of the real effective exchange
rate to its own impulse and to shocks in fundamentals. As described in equation (3),
we regress the difference of real effective exchange rate on lagged fundamentals and
differences of fundamentals. Figures 2.1 through 2.4 depict the response of change in
REER (logs) to impulses/shocks to lagged REER (logs), lagged fundamentals and
7
The mode of half-life is 2.76 excluding three outliers Chile, India and Senegal while the average half-
life is 3.6 years that within Rogoffâ€™s consensus interval.
9
change in fundamentals for the full sample in equation (3). As an illustration of our
VAR estimates, we characterize the response of REER to its own shock and shocks in
fundamentals for all sample countries while we discuss Argentina and China as
examples in this paper. Figures 2.1 and 2.3 illustrate the impulse-response function
(IRF) of changes in REER on the different determinants for Argentina whereas
Figures 2.2 and 2.4 present analogous results for China to characterize the response of
REER to its own shock and to shocks in fundamentals.
The short-run behavior
Figures 2.1 and 2.2 illustrate the IRF to show the response of the changes in
REER to transitory shocks to its fundamentals for Argentina and China, respectively.
The inclusion of exogenous variables (fundamentals) in first differences in the
specification captures the short-term behavior. Therefore, those coefficients explain
the short-term response of the exchange rate to each of these fundamentals.
Table 1 also presents the estimates of the unrestricted VECM of the exchange rate
for eight selected countries: most countries (seven out of eight) in this table have a
statistically significant coefficient for the log differences of terms of trade. Six of
these countries exhibit a positive coefficient (Argentina has a positive insignificant
coefficient) whereas China displays a negative coefficient for the log differences of
TOT. Consequently, this coefficient implies that, for most countries, surges in TOT
(or temporary positive TOT shocks) lead to a real appreciation of the domestic
currency â€”except in China because temporary positive TOT shocks may depreciate
Chinaâ€™s real exchange rate in the short run. We illustrate the dynamic effects of
transitory TOT changes on the real exchange rate for Argentina and China. Our
findings mentioned above are consistent with Figure 2.2 for China â€”as temporary
TOT shocks have a small negative initial impact on the REER and then fluctuate with
a small degree of appreciation. In contrast, Figure 2.1 for Argentina shows that
temporary TOT shocks have a large initial impact on REER and then appreciate in
real terms although in the case of Argentina it is statistically insignificant.
In response to the transitory shocks to the ratio of net foreign assets to GDP, the
British pound appreciates significantly in real terms while a positive short-run impact
on net foreign assets to GDP ratio in Australia indicates a significant appreciation of
the exchange rate; therefore, the results are mixed. In response to a transitory shock to
productivity differentials, a negative significant coefficient in Argentina and Chile
10
signals a real depreciation of the domestic currency. This finding is consistent with
the slow depreciation toward the final period for Argentina in Figure 2.1
IRF analysis on Argentina and China
We provide a closer look into the dynamics of exchange rate misalignments in
Argentina and China because these two countries have experienced periods of
significant undervaluation of their currency in real terms. We analyze a case of
undervaluation in their currencies and the RER misalignment dynamics with IRF
produced by the unrestricted VECM modeling.
Argentina
In the case of Argentina, the country underwent a massive depreciation of the peso
in the wake of the 2001-2 currency crisis. Kubota (2009a, b) shows that the existing
misalignment before the crisis (an overvaluation of the currency) was reduced by 32%
in 2002. The Argentinean government abandoned the convertibility system (1-to-1
hard peg to the US dollar) and in the aftermath of the crisis they followed a more
aggressive activist exchange rate policy by keeping the currency undervalued in real
terms.
When examining the dynamic behavior of RER misalignments in Argentina,
shocks to productivity differentials depreciate the real effective exchange rate and the
dynamic response is statistically significant. Figure 2.3 shows the response of the
subsequent changes in REER to shocks to lagged REER and lagged fundamentals in
period t. In response to the shock to the net foreign asset to GDP ratio, the real
effective exchange rate appreciates after a maximum decline occurring after period 5.
Temporary surges in lagged productivity differentials lead to a small statistically
significant appreciation of the currency in the short run between periods 2 and 4 and
create a curve around period 5, and then, it starts to depreciate slightly afterwards
(which is consistent with the result in Table 1). The response of the real effective
exchange rate to period 8 is above 0.1 and statistically insignificant. Surges in
productivity slightly depreciate toward the final period although they lead to a small
real appreciation of the currency in the short run after period 2. Shocks that lead to a
deviation from the equilibrium of the lagged real effective exchange rate have a large
initial impact up to the first period, and then the real effective exchange rate
depreciates. This dynamic response is consistent with the results in Table 1.
11
Temporary shocks to terms of trade have an insignificant effect as the results show in
Table 1.
China
China has arguably conducted an industrial policy anchored to, among other
things, the real undervaluation of the Chinese Renminbi (Chinn and Ito, 2007; Cheung
and Qian, 2007). Kubota (2009a, b) observes that the real value of the Remninbi was
undervalued by more than one-third (72 %) in 2005.
At the dynamic path of RER misalignments in China, shocks to the net foreign
asset to GDP ratio lead to a statistically significant depreciation of the REER. Figure
2.4 shows the response of the subsequent changes in the REER to shocks to lagged
REER and lagged fundamentals in period t. In response to the shock to the net foreign
asset to GDP ratio, the REER depreciates significantly with a maximum decline
occurring after period 2. Temporary surges in productivity differentials lead to a small
statistically significant appreciation of the currency in the short run after period 2
(which is consistent with the result in Table 1). Temporary lagged real effective
exchange rate shock has a large initial impact up to the first period. Then it
depreciates up to period 3, appreciates up to the 5th period and then fluctuates with a
2-period cycle. It seems to be statistically significant. Temporary shocks of terms of
trade have a small significant depreciation in a period 2, and then they lead to a
gradual RER appreciation.
3. Conclusion
The main goal of this paper is to build a bridge between theoretical and empirical
modeling of RER misalignments. The VECM modeling strategy in the spirit of the
research by Bewley (1979) and Wickens and Breusch (1987) provides the framework
for empirical modeling while the theoretical model links the equilibriums in the BOP
and in the traded and non-traded goods markets. Our estimates aim at reconciling the
univariate estimates of the half-life of PPP deviations estimated using the linear model
(Rogoff, 1996) and the non-linear adjustment model (Lothian and Taylor, 2000;
Taylor, Peel and Sarno, 2001).
12
This paper, in contrast to previous research, estimates the half-life of RER
deviations from a theoretically-based equilibrium level while modeling RER
misalignments. The average estimate of the half-life is approximately equal to 2.8
years â€”which is close to the lower bound of the consensus interval estimated by
Rogoff (1996). In addition, 42.5 percent of our half-life estimations are less than 2.5
years that falls into nonlinear half-life estimation as suggested by Taylor et al. (2001)
for large deviations from the equilibrium. In this sense, our unrestricted VECM
estimations â€”which account for adjustment in fundamentalsâ€” are able to capture
estimates of half-life that reconciles both strands from the empirical literature. Our
estimates show a normally distributed histogram of Î± coefficients for the full sample
of countries. Consequently, Î± coefficients are statistically significant and support the
evidence of our empirical modeling of RER misalignments.
The IRFs obtained from the dynamic system estimation supports the predictions
of the theoretical model of RER determination; therefore, an equilibrium real
appreciation follows a positive and permanent shock in TOT, the ratio of NFA to
GDP and HBS productivity differentials.
Further avenues of research in this area â€”and beyond the scope of this paperâ€”
include the characterization of the persistence of RER deviations (as proxied by the Î±
coefficient) and its linkages to the macroeconomic policy framework in place. For
instance, one would test whether countries with higher Î± (i.e. lower speed of mean
reversion) display more flexible exchange rate arrangements, have more rigid labor or
output market regulations, or have substantial dollarized liabilities, among other
factors.
13
References
Aizenman, Joshua, and Jaewoo Lee. 2007. â€œInternational Reserves: Precautionary
Versus Mercantilist Views, Theory and Evidence.â€? Open Economies Review,
18(2): 191-214.
Alberola, Enrique, and Humberto Lopez. 2001. â€œInternal and External Exchange Rate
Equilibrium in a Cointegration Framework: An Application to the Spanish
Peseta.â€? Spanish Economic Review, 3: 23-40.
Balassa, BÃ©la. 1964. â€œThe Purchasing Power Parity Doctrine: A Reappraisal.â€? Journal
of Political Economy, 72: 584-596.
Banerjee, Anindya, John Galbraith, and Juan Dolado. 1990. â€œDynamic Specification
and Linear Transformation of the Autoregressive-Distributed Lag Model.â€?
Oxford Bulletin if Economics and Statistics, 52(1): 95-104.
Bardsen, Gunnar. 1989. â€œThe Estimation of Long-run Coefficients from Error-
Correction Models.â€? Oxford Bulletin of Economics and Statistics, 51: 345-350.
Bewley, Ronald. 1979. â€œThe Direct Estimation of the Equilibrium Response in a
Linear Model.â€? Economic Letters, 3: 357-361.
Chinn, Menzie. 1999. â€œOn the Won and Other East Asian Currencies.â€? International
Journal of Finance and Economics, 113-127.
Chinn, Menzie, and Hiro Ito. 2007. â€œA New Measure of Financial Openness.â€? University
of Wisconsin, Madison, miemo.
Cheung, Yin-Wong, and Xingwang Qian. 2007. â€œHoarding of International Reserves: Mrs
Machlupâ€™s Wardrobe and the Joneses.â€? CESIFO Working Paper No.2065.
De Gregorio, Jose, Alberto Giovanni, and Holger Wolf. 1994. â€œInternational Evidence
on Tradables and Nontradables Inflation.â€? European Economics Review,
38(6): 1225-1244.
Edwards, Sebastian. 1989. Real Exchange Rates, Devaluation, and Adjustment.
Cambridge, Mass.: The MIT Press.
Engel, Robert F., and Clive W.J. Granger. (1987) â€œCo-integration and Error
Correction: Representation, Estimation, and Testing.â€? Econometrica, 55(2),
251-76.
Frenkel, Jacob A., and Michael Mussa. 1985. â€œAsset Markets, Exchange Rates, and
the Balance of Payment.â€? in Ronald W. Jones, and Peter B. Kenen (eds.),
Handbook of International Economics. Amsterdam: North-Holland.
Froot, Kenneth, and Kenneth Rogoff. 1991. â€œThe EMS, the EMU, and the Trasition to
a Common Currency.â€? NBER Chapters, in: NBER Macroeconomics Annual
1991, volume 6, 269-328.
Galstyan, Vahagn, and Phillip Lane. 2009. â€œThe Composigion of Government
Spending and the Real Exchange Rate.â€? Journal of Money, Credit and
Banking, 41 (6): 1233-1249.
Hausmann, Ricardo, Lant Pritchett, and Dani Rodrik. 2005. â€œGrowth Accelerations.â€?
Joyrnal of Economic Growth, 10(4): 303-329.
Im, Kyung So, M. Hashem Pesaran, and Yongcheol Shin. 2003. â€œTesting for Unit
Roots in Heterogeneous Panels.â€? Journal of Econometrics, 115(1): 53-74.
Johansen, Soren J. 1988. â€œStatistical Analysis of Cointegration Vectors.â€? Journal of
Economic Dynamic and Control, 12: 231-254.
Johansen, Soren J. 1991. â€œEstimation and Hypothesis Testing of Cointegration
Vectors in Gaussian Vector Autoregressive Models.â€? Econometrica, 59(6):
1551-1580.
Kao, Chihwa. 1999. â€œSpurious regression and residual-based tests for cointegration in
panel data.â€? Journal of Econometrics, 90(1): 1-44.
14
Kubota, Megumi. 2009a. â€œReal Exchange Rate Misalignments: Theoretical Modeling
and Empirical Evidence.â€? Discussion Papers in Economics 2009/24 the
University of York.
Kubota, Megumi. 2009b. â€œReal Exchange Rate Misalignments.â€? Doctoral Thesis
(Ph.D.), the University of York.
Levin, Andrew, Chien-Fu Lin, and Chia-Shang James Chu. 2002. â€œUnit Root Tests in
Panel Data: Asymptotic and Finite-Sample Properties.â€? Journal of
Econometrics, 108(1): 1-24.
Lothinan, James R., and Mark P.Taylor. 2000. â€œPurchasing power parity over two
centuries: strengthening the case for real exchange rate stability A reply to
Cuddington and Liang.â€? Journal of International Money and Finance, 19:
759-764.
Lucas, Robert. E., Jr. 1982. â€œInterest Rates and Currency Prices in a Two-country
World.â€? Journal of Monetary Economics, 10: 335-359.
Maddala, Gangadharrao S., and Shaowen Wu. 1999. â€œA Comparative Study of Unit
Root Tests with Panel Data and a New Simple Test.â€? Oxford Bulletin of
Economics and Statistics, Special Issue, 61: 631-652.
McCoskey, Suzanne, and Chihwa Kao. 1998. â€œA Residual-Based Test of the Null of
Cointegration in Panel Data.â€? Econometric Reviews, 17(1): 57-84.
Mussa, Michael. 1984. â€œTheory of Exchange Rate Determination, in Exchange Rate
Theory and Practice.â€? in Bilson, John, and Marston, Richard (eds.), Exchange
Rate Theory and Practice. Chicago: University of Chicago Press, 13-78.
Obstfeld, Maurice, and Kenneth S. Rogoff. 1985. â€œThe Intertemporal Approach to the
Current Account.â€? in Grossman, Gene M. and Rogoff, Kenneth S. (eds.),
Handbook of International Economics, vol.3. Amsterdam: North Holland.
Obstfeld, Maurice, and Alan C. Stockman. 1985. â€œExchange-rate Dynamics.â€? in
Grossman, Gene M. and Rogoff, Kenneth S. (eds.), Handbook of International
Economics, vol.3. Amsterdam: North Holland.
Rodrik, Dani. 2007. â€œThe Real Exchange Rate and Economic Growth: Theory and
Evidence.â€? Working Paper 2008-0141, Weatherhead Center for International
Affairs, Harvard University.
Pedroni, Peter, 1999. Critical Values for Cointegration Tests in Heterogeneous Panels
with Multiple Regressors. Oxford Bulletin of Economics and Statistics,
61(Special Issue): 653-690.
Pesaran, M. Hashem, Ron P. Smith, and Kyung So Im. 1996. â€œDynamic Linear
Models for Heterogenous Panels.â€? in Laszlo MÃ¡tyÃ¡s, and Patrick Sevestre.
(eds.), Econometrics of Panel Data. Boston; Dordrecht and London: Kluwer
Academic.
Pesaran, M. Hashem, Yongcheol Shin, and Ron P. Smith. 1999. â€œPooled Mean Group
Estimation of Dynamic Heterogeneous Panel.â€? Journal of the American
Statistical Association, 94: 621-634.
Pesaran, M. Hashem. 2007. â€œA Simple Panel Unit Root Test in the Presence of Cross-
Section Dependence.â€? Journal of Applied Econometrics, 22(2): 265-312.
Rogoff, Kenneth. 1996. â€œThe Purchasing Power Parity Puzzle.â€? Journal of Economic
Literature, 34: 647-668.
Samuelson, Paul A., 1964. â€œTheoretical Notes on the Trade Problems.â€? Review of
Economics and Statistics, 23, 1-6.
Stockman, Alan C. 1987. â€œThe Equilibrium Approach to the Exchange Rates.â€?
Federal Reserve Bank of Richmond, Economic Review, 73: 12-30.
15
Taylor, Mark P., David A. Peel, and Lucio Sarno. 2001. â€œNonlinear Mean-Reversion
in Real Exchange Rates: Toward a Solution the Purchasing Power Parity
Puzzles.â€? International Economic Review. 42(4): 1015-1042.
Wickens, Michael, and Trevor S. Breusch. 1987. "Dynamic Specification, the Long-
run and the Estimation of Transformed." Economic Journal. 98(390): 189-
205.
16
Figure 1.1: Î± Coefficients
Figure 1.2
Figure 1.3: Half-life of RER deviations from equilibrium vs. 1970 Real GDP per
capita
18
16
14
12
10
a half-life
8
6
4
2
0
0 20 40 60 80 100
GDP per capita (1970)
Figure 1.4: Half-life of RER deviations from equilibrium vs. Exchange rate
flexibility
18
16
14
12
a half-life
10
8
6
4
2
0
0 1 2 3 4 5
average coarse
Note: This figure uses the coarse definition of exchange rate regime from Ilzetzki, Reinhart and Rogoff
(2009).
19
Figure 1.5: Half-life of RER deviations from equilibrium vs. Exchange rate
flexibility
18
16
14
12
10
a half-life
8
6
4
2
0
0 2 4 6 8 10 12 14
average fine
Note: This figure uses the fine definition of exchange rate regime from Ilzetzki, Reinhart and Rogoff
(2009).
Figure 2.1: Short-term response of the real exchange rate to shocks in
fundamentals, Argentina
Notes: del = difference, q = REER, tot = terms of trade and prd = productivity differentials
20
Figure 2.2: Short-term response of the real exchange rate to shocks in
fundamentals, China
Notes: del = difference, q = REER, tot = terms of trade and prd = productivity differentials
Figure 2.3: Response of the exchange rate to deviations in fundamentals from the
equilibrium, Argentina
Notes: del = difference, q = REER, tot = terms of trade and prd = productivity differentials
21
Figure 2.4: Response of the exchange rate to deviations in fundamentals from the
equilibrium, China
Notes: del = difference, q = REER, tot = terms of trade and prd = productivity differentials
22