Download Taylor Rules and Exchange Rate Predictability in Emerging

Taylor Rules and Exchange
Rate Predictability in
Emerging Economies
Jaqueson K. Galimberti
Marcelo L. Moura
Insper Working Paper
WPE: 217/2010
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T AYLOR R ULES
AND
IN
E XCHANGE R ATE P REDICTABILITY
E MERGING E CONOMIES
J A Q U E S O N K. G A L I M B E R T I
UNIVERSIDADE FEDERAL DE SANTA CATARINA
M A R C E L O L. M O U R A †
INSPER – INSITUTE OF EDUCATION AND RESEARCH
FEBRUARY, 2010
Abstract
This study links exchange rate determination and endogenous monetary policy represented by Taylor
rules. We fill a gap in the literature by focusing on a group of fifteen emerging economies that adopted
free-floating exchange rate and inflation targeting beginning in the mid-1990s. Due to the limited
time-series span, a common obstacle to studying emerging economies, we employ panel data regressions
to produce more efficient estimates. Following the recent literature, we use a robust set of out-of-sample
statistics using bootstrapped and asymptotic distributions for the Diebold-Mariano, Clark and West and
Theil’s U ratio. By evaluating different specifications for the Taylor rule exchange rate model based on
their out-of-sample performance, we find that the forward-looking specification shows strong evidence of
exchange rate predictability.
Key words: Taylor rule exchange rate model; forecasting; emerging economies; panel data; bootstrap.
JEL:
†
F31, F37, F41, F47.
Corresponding author: Rua Quatá 300, São Paulo-SP – Brazil – CEP:04546-042,Tel.: 4504-2435, [email protected]
1
1 - INTRODUCTION
This study aims to investigate exchange rate predictability for a selected group of fifteen emerging
economies (Brazil, Chile, Czech Republic, Colombia, Hungary, Israel, Mexico, Peru, Philippines, Poland,
Romania, South Africa, South Korea, Thailand and Turkey) that share similar monetary policy regimes
and have adopted free-floating exchange rate regimes. We contribute to the literature by joining two
promising approaches. First, we use panel data regression to deal with limited time series and increase
forecasting efficiency. Second, we investigate more realistic endogenous monetary models by testing a
robust set exchange rate Taylor rule model. We also respond to Rogoff and Stavrakeva’s (2008) criticism
of exchange rate models’ predictability regarding the misinterpretation and biased use of out-of-sample
statistics. In particular, we construct appropriate bootstrapped confidence intervals for out-of-sample
statistics from Diebold and Mariano (1995), Clark and West (2006, 2007) and Theil’s U ratio.
Where does this study stand regarding the exchange rate predictability literature? First, let us say a few
words about the literature itself. Testing exchange rate models became popular after the major
industrialized economies adopted floating exchange rates with the abandonment of the Bretton Woods
system in the early 1970s.1 The gathering of data on independently floating exchange rates allowed the
proliferation of several empirical studies, as in Bilson (1978), Hodrick, (1978), and Putnan and
Woodburry (1980). These found favorable evidence for the exchange rate models of the 1970s:
significant coefficients with the expected signs, fine model in-sample fit and satisfactory performance in
the diagnosis tests.
However, the empirical results changed drastically beginning in the 1980s with Meese and Rogoff’s
(1983) seminal paper. Using the United States-related exchange rate data for the United Kingdom, Japan,
and Germany, they concluded that, in a one- to twelve-month forecasting horizon, the random walk
model performs at least as well as the exchange rate models of that time, namely, the flexible price and
sticky price monetary models and a hybrid model by Hooper and Morton (1982).
A plethora of studies followed Meese and Rogoff’s (1983) work. Some claimed to reverse the
no-predictability results, such as Mark (1995). Using innovative bootstrapping techniques and exchange
rate data from 1973 to 1991 for Canada, Germany, Japan and Switzerland relative to the US dollar, the
author found support for forecasting monetary models at horizons between 12 and 16 quarters for some
countries. However, predictability evidence was short lived. Subsequently, criticism came from Kilian
(1999), who demonstrated that Mark’s results were not robust for sample modifications and that they
crucially depended on the assumed data generating process. Furthermore, Mark’s (1995) implicit
assumption of cointegration of the exchange rate and monetary fundamentals has also been subject to
criticism. Berkowitz and Giorgianni (2001) showed that if the assumption of cointegration is not valid,
then tests are biased toward rejection of the null of no predictability.
Inconclusive results were common until the early to mid-2000s. Sarno and Taylor (2002), who surveyed
the literature of the 1980s and 1990s, claimed: ‘the empirical results tended to be fragile in the sense that
they were hard to replicate in different samples or countries.’ Cheung, Chinn, and Pascual (2005) tested
predictability for the US dollar-based exchange rates of the Canadian dollar, British pound, Deutsche
mark and Japanese yen by assessing a wider set of models than those used in the 1980s and 1990s. Their
results were inconclusive: ‘model/specification/currency combinations that work well in one period do
not necessarily work well in another period’.
1
This system, established in 1944, determined that each country should fix its exchange rate in relation to the U.S. dollar,
which was convertible to a fixed amount of gold.
2
Surprisingly, in the last half of the 2000s a large number of studies claimed evidence of exchange rate
out-of-sample performance. According to Engel, Mark and West (2007), emphasizing the importance of
the monetary policy rule, using exchange rate models determined by expected present values of
fundamentals, longer data spans and panel data provided more hope for the existence of exchange rate
predictability.
Basically, these studies focus on two alternative approaches. Some use larger panel data sets in a set of
similar countries, such as Groen (2005), Rapach and Wohar (2004) and Mark and Sul (2001). These
studies use unit root and panel cointegration techniques and find evidence of predictability for the
monetary model, especially over longer horizons. However, the models used in most of these studies are
the old monetary models of the 1970s and 1980s.
Investing in more innovative and realistic models, another line of research still focuses on
country-by-country estimation but assumes endogenous monetary policy in exchange rate Taylor models.
Some recent studies on this include the following: Molodtsova and Papell (2009), Engel and West (2005)
and Engel, Mark and West (2007) for industrialized countries and Moura (2008), Moura, Mendonça and
Lima (2008) and Ketenci and Uz (2008) for developing economies. The basic approach of the Taylor
exchange rate model is to conciliate uncovered interest parity with interest rates determined
endogenously, as they are in practice, by a Taylor rule reaction function. In summary, all of these studies
found significant evidence of exchange predictability for the Taylor model.
However, despite the large number of studies with evidence of exchange rate predictability, the
controversy was not over. Rogoff and Stavrakeva (2008) claimed that most of the predictability found in
recent results is due to the misinterpretation of new out-of-sample tests, as in Clark and West (2006,
2007), and failure to test for robustness using different alternative time windows.
Finally, we can answer the question we posed in the beginning of this section. Our study adds to the
recent developments in research of exchange rate determination on emerging economies. More
specifically, this study groups the recent promising approaches and responds to criticism of them. In fact,
we can specify three main contributions. First, instead of looking at just one or two models, the panel data
are estimated for an extensive set of models to provide a better comparison group. Second, we contribute
to the study of emerging economies with similar characteristics: countries that, despite their increasing
importance in the world economy, are not as well studied as the industrialized economies. Third, we
improve forecasting accuracy evaluation by using a larger, robust set of out-of-sample statistics.
The remainder of this work is divided into five sections. Section 2 explains the Taylor rule exchange rate
model. Section 3 describes the data and the panel unit root and cointegration tests run in our selected
series and models. Section 4 details the forecasting approach and the bootstrapping methodology. Section
5 discusses the results, and the last section presents the conclusions, limitations, and likely extensions of
this work.
2. TAYLOR MODELS OF EXCHANGE RATE DETERMINATION
Since the mid-1980s, most central banks have started to use interest rate as their policy instrument instead
of the control of some aggregate measure of the money supply. This characteristic has an important
implication for exchange rate models: instead of using an exogenous interest rate as an explanatory
variable for the exchange rate, it is important to use an endogenous monetary policy rule, a point already
made by Engel, Mark and West (2007).
3
Engel, Mark and West’s (2007) approach
Their approach builds an exchange rate model that incorporates such characteristics. Interest rates are set
by the central bank through a reaction function determined by:
it =    q qt    Et t 1   y yt   it 1  ut
(2.1),
where it is the logarithm of one plus the nominal interest rate at time t, qt is the logarithm of the real
exchange rate at time t, t 1 is the logarithm of one plus the inflation rate at time t 1, yt is the
logarithm of one plus the output gap at time t, and  q ,   ,  y and  are parameters for which we assume
 q > 0,   > 0,  y > 0, 0   < 1 .
For our benchmark country, which will be the United States, a similar Taylor reaction function is defined
as:
it =  *    Et t1   y yt   it1  ut
(2.2),
where the same notation applies, with an asterisk denoting that the variable refers to the benchmark
country. One important assumption we made is that the interest rate reacts to the real exchange rate for
our emerging economies (see equation (2.1)) but does not for the United States (equation (2.2)). This
assumption is quite reasonable for emerging economies: Moura and Carvalho (2009) estimated Taylor
rules for seven Latin American emerging economies and found that Taylor rules including exchange rates
as explanatory variables yield superior predictability results.
The last part of the Taylor model assumes uncovered interest parity, that is:
it  it = Et st 1  st
(2.3),
where st is the logarithm of the nominal exchange rate, and Et denotes the conditional expectation
operator.
Using equations (2.1) through (2.3) and assuming that the home and benchmark countries have similar
parameters, we have:


st = Et st 1   q qt     *    Et  t 1   t1    y  yt  yt     it 1  it1   ut  ut (2.4).
Solving this finite difference equation forward implies:
st  pt  pt *  b nj =0b j X t  j  t
(2.5),
where pt and pt * are the respective logarithms of consumer price indices for the reference and benchmark
countries and:
b

1
,
1  q
4
X t  j      *      1 Et  t 1 j   t1 j    y  yt  j  yt j     it 1 j  it1 j   and
= b nj =0b j  ut  j  ut j 
t
To estimate (2.5), we assume the same approach used by Moura (2008), where expectations for the near
future are a proxy for future expected values. Formally, we will assume that we can approximate
expectations for all future dates j= 1, 2, 3, … by expectations at a fixed date K  12.

E y
E i



Et  t 1 j   t1 j  Et  t  K   t K ,
t



 and
 yt j  Et yt  K  yt K ,
t
t j
t
t 1 j
 it1 j  Et it  K  it K

vt   vt 1 .


This assumption leads us to the final empirical specification, which we define as the EMW symmetric
model:



st    pt  p*t  1 Et  t 12   t12   2 Et yt 12  yt12
  3 Et (it 12  i

t 12

(2.6).
)   4 qt 1  vt
An alternative specification would assume no asymmetry in the reaction function parameters, leading to
the forward-looking EMW asymmetric model:



st    pt  p*t  1 Et  t 12   1* Et  t12   2 Et  yt 12    2* Et yt12
  3 Et (it 12 )   3* Et (it12 )   4 qt 1  vt

(2.7).
Molodtsova and Papell’s (2009) approach
An alternative formulation of the Taylor model is based on Molodtsova and Papell (2009), hereinafter
denoted the MP model. We now assume contemporaneous Taylor rules for both the home and foreign
countries:
it =      t   y yt   it 1  ut
(2.8)
it =  *    t   y yt   it1  ut
(2.9).
and
In addition, the uncovered interest parity holds without expected values,
st 1 = st   it  it 
(2.10).
The model is then solved by substituting equations (2.8) and (2.9) into (2.10). If we additionally assume
symmetrical parameters in the reaction functions, this leads to the following empirical specification:
5




st  st 1     1  t 1   t1   2 y t 1  y t1   3 ( it  2  it 2 )  vt
(2.11).
If we instead assume asymmetrical parameters in the Taylor rules, we have:
st  st 1    1 t 1  1* t1   2 yt 1   2* yt1   3it  2   3*it 2  vt
(2.12).
We will call equation (2.11) the MP symmetric model and (2.12) the MP asymmetric model. One possible
criticism of the approach followed by Molodtsova and Papell (2009) is that the Taylor rules are
misspecified because it is likely that Central Banks react not to contemporaneous inflation and output gap
but instead to expected values. In these forward-looking specification, we replace inflation and output gap
in (2.8) and (2.9) with their respective expected values. With this modification, the empirical
specifications for the symmetrical and asymmetrical cases are:



st  st 1    1 Et  t 12   t12   2 Et yt 12  yt12

  3 Et (it 12  it12 )  vt
(2.13)
and


   E i    E i   v
st  st 1    1 Et  t 12   1* Et  t12   2 Et  yt 12 

  2* Et yt12
3
t
t 12
*
3
t

t 12
(2.14).
t
Exchange rates derived from (2.13) and (2.14) will be denoted as, respectively, the MP-expected
symmetric and the MP-expected asymmetric models.
3. PANEL UNIT ROOT AND COINTEGRATION TESTS
Our data set constitutes an unbalanced panel of monthly data from January 1995 to December 2008 for
fifteen inflation targeters in developing countries: Brazil, Chile, Colombia, Mexico, Peru, Czech
Republic, Hungary, Poland, Romania, Turkey, Israel, Thailand, Philippines, South Korea and South
Africa. The data were collected from Thomson DataStream and International Monetary Fund Statistics. A
detailed description of each series is shown in the Appendix.
The criterion for choosing the countries and the size of the sample was that all of the countries, during
most of the sample period, adopted the independently floating exchange regime and the monetary
framework given by the inflation target system according to the International Monetary Fund (IMF)
definition. Table 1 provides a detailed explanation of the exchange rate regime classification and the
monetary policy framework adopted for each country. We can see that the majority of the countries
adopted the current regime (at the time of this writing) during the late 1990s and the remainder in the
early 2000s. There is also significant homogeneity across countries in terms of exchange rate regime,
entity that defines the inflation targets, situations where the target can be disregarded, target indicator and
inflation target level. Therefore, at least in terms of monetary policy and exchange rate regimes, it makes
sense to group those countries in a panel data model.
Our process of estimation for a posteriori evaluation of the forecasting potential extends the methodology
of Cheung, Chinn and Pascual (2005) of country-by-country models to an unbalanced one-way error
component model, as described in Baltagi (2008). More specifically, we can nest all of the models
6
discussed above, as well as equations (2.6), (2.7), (2.11), (2.12), (2.13) and (2.14) presented in Section
2, into the model:
sit  X it   uit
uit  i  vit
i  1, 2,..., Nt
t  1, 2,..., T
(3.1),
where Nt  N  15 is the number of countries observed at time t , X t is the vector of economic
fundamentals, and  is a vector of coefficients. Notice that the error has two components: An
unobservable country effect i and a stochastic disturbance term vit . We assume i to be a fixed
parameter to be estimated and the remainder of the disturbance to be stochastic, vit ~ IID(0,  v2 ) .
Before we proceed with the estimation of the exchange rate models based on equation (3.1), we run some
diagnostic panel tests. The importance of these tests will become clear in section 4, when we will
introduce our error correction model to forecast exchange rates. As mentioned in Westerlund and Basher
(2007), cointegration implies and is implied by an error correction model.
Therefore, first, we test for the stationarity of our variables by running panel unit root tests. These tests
have a higher power than unit root tests of individual time series. Then, we test for cointegration among
the variables in each of the exchange rate models of section 2. Similarly to panel unit root tests, panel
cointegration tests are motivated by having more power than individual time-series cointegration tests. By
pooling countries with similar characteristics, we increase the span of the data by adding cross-sectional
variation, which will increase the power of the unit root and cointegration panel tests; see Baltagi (2008).
Phillips and Moon (1999) studied a range of regressions within panel vectors with and without
cointegrating relations. Differently from pure time-series spurious regression, where OLS estimates of the
coefficient  are not consistent, the use of panel data gives consistent estimates of the coefficients.
According to Baltagi (2008), the result found by Phillips and Moon (1999) is due to the fact that the panel
estimator averages out across individuals because it samples from independent cross-sections. This leads
to a stronger overall signal than is obtained in the pure time series case.
In Table 2 we show the results for three alternative unit root tests developed by Levin, Lin & Chu (2002),
hereinafter referred to as LLC; Im, Pesaran and Shin (2003), hereinafter referred to as IPS; and Hadri
(2002), hereinafter referred to as HAD. These three alternative tests were chosen because they allow for
different null assumptions. LLC assumes a null of a common unit root process, whereas the IPS test has
the null of an individual unit root process. Finally, the HAD test reverses the null, assuming stationarity.
In general, the results in Table 2 point to the rejection of the null of non-stationarity, implying that most
of the series are stationary processes. The only exceptions are the inflation rate, the relative interest rate
and the relative output gap, which have inconclusive results.
In Table 3, we perform panel cointegration tests developed by Kao (1999). The goal is to test for a unit
root in the residuals of each estimated Taylor rule exchange rate model, equations (2.6), (2.7), (2.11),
(2.12), (2.13) and (2.14). We chose to use Kao’s (1999) panel cointegration tests, which use ADF-type
unit root tests of the panel data residuals to check for the null of no cointegration. Like the two-step Engle
and Granger (1987) cointegration test for single time-series, if the variables are cointegrated, the residuals
should be stationary. Table 4 displays the results of Kao’s tests, which reveal strong evidence of
cointegration for all of the assumed Taylor models.
7
4. FORECASTING METHODOLOGY
The forecasting exercise extends the error correction methodology adopted by Cheung, Chinn, and
Pascual (2005) for country-by-country equations to a one-error component panel data model. More
specifically, we first estimate specification (3.1) for each model, obtaining, for each country, the
fundamental value for the exchange rate:
sˆit  X it ˆ  ˆ i
i  1, 2,..., N t  1, 2,..., T
(4.1).
Then, we estimate a country-specific error correction model, stripped from the short-run dynamics. This
error correction model is created on a country-by-country basis by the following equation:
si ,t  k  sit   ik  ik ( sˆit  sit )  vit
(4.2).
For each country, the estimated parameters of equation (4.2) are used to forecast the future values of the
exchange rate at one, six and twelve months ahead. The parameter ik is essential in the sense that it will
dictate convergence of the exchange rate to its fundamental value.
An alternative formulation to the error correction model defined in equation (4.2) is to pool the
constant,  ik , and the slope parameters, ik . This procedure will imply a pooled error correction model:
si ,t  k  sit   k  k ( sˆit  sit )  vit
(4.3).
The pooled error correction model is adopted in Mark and Sul (2001) and is tested by Westerlund and
Basher (2007). Basically, it assumes that the predictability of the exchange rate is homogeneously
distributed across the emerging economies in our panel. Given the similarities across our sample data in
terms of exchange rates, regimes and monetary policies, as previously discussed, we believe this
assumption is not so strong. For robustness purposes, however, we will test the predictability of both
approaches: the country specific error correction model, equation (4.2), and the pooled error correction
model, equation (4.3).
Therefore, to build an out-of-sample forecast for the exchange rate, we perform this two-step procedure
recursively using rolling regressions. Equations (3.1) and (4.2) or (4.3) are estimated for an initial sample
of fixed size — in our case, 48 periods — and result in forecasts for one, six and twelve months ahead.
Using the rolling regressions method, we displace the estimation of the models one period ahead, keeping
the size of the initial sample constant. We repeat the procedure up to sample exhaustion. The results from
this procedure were then compared with those obtained iswith the forecasting of a model that assumes the
exchange rate following a driftless random walk given by:
sirw,t k  sit
i  1, 2,..., N t  1, 2,..., T
(4.4).
In order to compare the out-of-sample predictive accuracy of these forecasts we use asymptotic and
bootstrapped versions of three testing statistics: the Theil’s U ratio (TU), the Diebold and Mariano (1995)
statistic (DM), and the Clark and West (2006, 2007) statistic (CW). The bootstrapped distributions of
these statistics are generated following a similar procedure as that proposed by Westerlund and Basher
(2007). Specifically, for each country in our sample we estimate, by least squares, the data generating
8
process (DGP) of the exchange rate and its deviation from the fundamentals as an error correction model
under the null hypothesis of no predictability, as shown in equation (4.5).
Δsi,t  μˆ i  vˆi,t
p
q
k 1
k 1
Δzi,t  αˆi  γˆi zi,t   δˆi,k Δsi,t  k   φˆi,k Δz i,t  k  uˆi,t
(4.5)
Where zit  sit  sˆit is the deviation of the exchange rate from its fundamental value predicted by the
Taylor rule models, equations (2.6), (2.7), (2.11), (2.12), (2.13) and (2.14) presented in Section 2, and
the lag orders p and q are selected using the Akaike information criteria.
The residuals obtained from the estimation of equation (4.5) are subsequently resampled with
replacement, and the resulting bootstrapped residuals are then used to recursively 2 construct the
bootstrapped sample of zi,t and si,t. These simulated series are then used to estimate equations (4.2), (4.3)
and (4.4). Finally, the out-of-sample test statistics are obtained and this bootstrapping procedure is
repeated 1,000 times in order to draw the empirical distribution of these statistics.
5. RESULTS
Tables 4.a and 4.b present the results of the forecasting exercise for the country-specific and pooled error
correction models, respectively, by reporting the statistics proposed by Diebold and Mariano (1995) with
bootstrapped confidence intervals, hereinafter referred to as DMB. The DMB statistic is computed as the
mean of the difference in the squared forecasting errors between the random walk benchmark and the
specified exchange rate model. Under the null hypothesis, this difference is zero. Positive values of this
statistic, associated with the rejection of the null at 10% or lower, are considered in cases where the
exchange rate model outperforms the random walk.
We find the best predictability performance for the EMW Taylor model using the country-specific
models. This model, using the methodology proposed by Engel, Mark and West (2007), presents evidence
of better forecasting than the random walk for 13 of our 15 countries included in the sample and in 27 out
of 45 country/horizon combinations, or 60% of the cases. To give a better visual idea of how accurate
these forecasts are, Figure 1 presents the EMW symmetric Taylor model using the country-specific
models, with values forecasted six months ahead and the realized values for the logarithm of the exchange
rates for all countries. To avoid distortion caused by scale, the realized logarithms of nominal exchange
rate values were normalized to zero in January 1993.
The EMW symmetric model in the pooled error correction specification shows performance similar to
that of its country-specific counterpart; see Table 4.b. The model beats the random walk in 56% of the
overall country/horizon combinations and for 12 out of 15 countries in our sample. The EMW
asymmetric model has slightly lower performance than its symmetric counterpart. This result is coherent
with the known fact that imposing restrictions, such as the symmetry in parameters, can sometimes
improve predictability because it involves estimating a considerably smaller number of coefficients.
Regarding the MP specifications, the performance is very modest. In fact, predictability is found in less
than 10% of all country/horizon combinations for the variants of Molodtsova and Papell’s (2009) Taylor
rule model, less than our significance level for the test. This poor performance of the MP model was
2
We use the actual data for starting values of the recursion, and discard the first 100 simulated observations in order to
attenuate potential bias.
9
already reported by Rogoff and Stavrakeva (2008) for industrialized economies when measuring
out-of-sample performance with a bootstrapped Diebold and Mariano (1995) statistic. Thus, there was not
much surprise when we found the same result for emerging economies in this study.
In general, we also find that predictability worsens as we increase the forecasting horizon from one to six
and twelve months. This is a different result from most of the literature for industrialized economies, but
it makes much more economic sense if the convergence of the exchange rate to equilibrium values is fast
enough.
To evaluate results in a more systematic way, in panel A of Tables 5.a and 5.b we present the hit rate
(number and percentage of times the model outperformed the random walk) for the DMB statistic. To
verify the robustness of our results, we present in the same tables the hit rates of the bootstrap versions for
the Clark and West (2006, 2007) and Theil’s U statistic, hereinafter denominated, respectively, CWB and
TUB. Qualitatively, the relative performances of the models are the same for the DMB, CMW and TUB
statistics. Quantitatively, TUB has the highest hit rates in both country-specific and pooled error
correction models, while the CMW is about the same as the DMB in the country-specific version and
slightly higher in the pooled version.
Finally, in Tables 6.a and 6.b we present the DM and CW statistics using asymptotic distributions for
constructing confidence intervals. The reported results confirm the criticism reported by Rogoff and
Stavrakeva (2008). In general, the use of the asymptotic distribution instead of the bootstrapped version
decreases predictability for the DM statistic and increases it for the CW.
In summary, our results indicate three important facts. First, compared to the literature on exchange rate
predictability for industrialized countries, the predictability of Taylor rule exchange rate models applied
to this group of emerging countries performed much better. Second, compared to other emerging
economies studies using country-by-country analysis, the use of pooling information significantly
improved predictability. Our interpretation is that this last result comes from the fact that we grouped
countries with similar characteristics and that we increased efficiency in estimation by using panel data
regressions. Third, we also verified that some heterogeneity existed by using country fixed effects in our
panel, and permitting different adjustment coefficients on the country-specific error correction
specification, equation (4.2), improves results.
6. CONCLUSIONS, LIMITATIONS AND FUTURE EXTENSIONS
This study contributes to the literature by linking the study of inflation targeting to exchange rate
determination and by linking Taylor models to panel data forecasting. From this, we find that inflation
targeting in emerging economies appears to have exchange rates driven by forward-looking macro
variables. Our endogenous monetary policy Taylor model for the EMW specification indeed outperforms
the random walk for 60% of the analyzed country/horizon combinations.
Another important conclusion is that significant predictability results can be obtained by pooling
information for countries with similar monetary policies and exchange rate frameworks. Because we do
not possess longer time series for developing economies, the use of panel data regressions more than
compensates for the homogeneity constraints that are imposed. One possible reason for the apparent
success of pooling information may also come from the fact that global market investors analyze these
countries in a similar manner, leading to common responses to macroeconomic fundamentals.
The study has many limitations that may lead to promising future studies. To name one important
limitation, we dealt with partial equilibrium analysis. Modern macroeconomic models simultaneously
10
determine many other variables besides the exchange rate in the form of dynamic stochastic general
equilibrium (DSGE) models; see Galí and Gertler (2007). Using more complete DSGE models to predict
exchange rates would be a promising next step.
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Clark, Todd E. and West, Kenneth D., “Approximately normal tests for equal predictive accuracy in
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Diebold, Francis X., Mariano, Roberto S., “Comparing predictive accuracy”, Journal of Business and
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Think”, NBER Macroeconomics Annual, Cambridge, Massachusetts, 2007.
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Hodrick, Robert J., “An Empirical Analysis of the Monetary Approach to the Determination of the
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Panels”, Journal of Econometrics, Vol. 115 (1), 2003, 53–74.
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Econometrics, Vol. 90, 1999, 1-44.
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ten new EU members and Turkey”, Emerging Markets Review, Vol. 9 (1), 2008, 57-69.
Kilian, Lutz, “Exchange Rates and Monetary Fundamentals: What do we Learn from Long-Horizon
Regressions?”, Journal of Applied Econometrics, Vol. 14 (5), 1999, 491–510.
Levin, Andrew, Lin, Chien-Fu and Chu, James, “Unit Root Tests in Panel Data: Asymptotic and
Finite-Sample Properties”, Journal of Econometrics, Vol. 108 (1), 2002, 1–24.
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the Sample?”, Journal of International Economics, Vol. 43 (1), 1983, 933–48.
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Fundamentals”, Journal of International Economics, Vol. 77 (2), 2009,167-180.
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The Case of Brazil”, Revista de Economia Aplicada, Vol.12 (3), 2008, 395 - 416.
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Latin America?”, Journal of Macroeconomics, doi:10.1016/j.jmacro.2009.03.002, 2009.
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Rates?” Working paper series: The Federal Reserve Bank of St. Louis, WP 2002–007, 2002.
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A closer Look at Panels”, Journal of International Money and Finance, Vol. 23 (6), 2004, 867–95.
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Cambridge, 2002.
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Monetary Exchange Rate Model?, Journal of Forecasting, Vol. 26, 2007, 365–-383.
APPENDIX: DATA DESCRIPTION
Data for all fifteen emerging economies plus the United States exist in an unbalanced way from January
1995 to December 2008. The data sources for all variables are DataStream and the IMF’s International
Financial Statistics.
All of the expected values for macroeconomic variables were obtained from the Consensus Economic
Forecast Survey available from DataStream. Because expected values are available on a monthly basis for
current-year and next-year values, 12-month-ahead values were computed as an average of the current
year’s and next year’s values, where weights are proportional to the respective number of months in the
current year and the next year for a 12-month period.
‘Exchange rate’ is the logarithm of the end of the month values of the nominal exchange rates, defined as
home currency per US dollar. ‘Expected inflation’ is the logarithm of the ratio of one plus the country’s
expected inflation over one plus US expected inflation. We add one because the expected inflation less
target can be negative.
‘Expected industrial production gap’ is the logarithm of one plus the country’s expected industrial
production gap divided by one plus the US expected industrial production gap. Again, we add one to
avoid a logarithm of negative values. First, the expected 12-months-ahead industrial production series
was computed using Consensus Economic Forecast values; then, a Hodrick-Prescott filter was applied to
this series to capture the expected industrial production gap.
‘Expected interest rates’ is the logarithm of the country’s nominal interest rate divided by the nominal
interest rate of the US. ‘Real exchange rate’ is defined as the logarithm of the nominal exchange rate
multiplied by the country’s price level ratio to the US price level. ‘Price level’ is the consumer price index
normalized to the value of one at the initial date, January 1999. ‘Industrial production’ is the logarithm of
the seasonally-adjusted industrial production index of each country divided by its US counterpart.
‘Interest rate’ is the logarithm of the short-term monetary policy nominal interest rate divided by the US
federal fund rates.
13
Table 1 - Exchange rate regime classification and monetary policy framework for the selected emerging economie
Start date of the
Inflation
Targeting
IMF exchange rate
Country
Regime
classification
Entity who defines the target Situation where the target can be disregarded
Brazil
Jun-99
Independently
Government in consultation
None
floating
with central bank
Chile
Jan-91
Independently
Central bank in consultation None
floating
with government
Colombia Sep-99
If managed floating Jointly by government and
None
with no precentral bank
Czech
Jan-98
Independently
Central bank
Natual disasters, price and exchange rate
Republic
floating
schocks that are not consequence of the
domestic monetary policy
Hungary
Jan-01
Independently
Jointly by government and
None
floating
central bank
Israel
Jan-92
Independently
Government in consultation
None
floating
with central bank
Korea
Jan-98
Independently
Central bank in consultation None
floating
with government
Central bank
None
Mexico
Jan-99
Independently
floating
Peru
Jan-94
If managed floating Central bank in consultation None
with no prewith government
Philipines Jan-02
Independently
Jointly by government and
None
floating
central bank
Poland
Oct-98
Independently
Central bank
None
floating
Romania
Aug-05
If managed floating Jointly by government and
Events that cannot be foreseen or that are out
with no precentral bank
of Central Bank control
South
Feb-02
Independently
Central bank
Events that cannot be foreseen or that are out
Africa
floating
of Central Bank control
Thailand
Apr-00
If managed floating Government in consultation
None
with central bank
with no preTurkey
Jan-02
Independently
Jointly by government and
None
floating
central bank
Indicator for the
target
Headline CPI
Headline CPI
Headline CPI
Core CPI (excl.
regulated prices and
inderect taxes)
Headline CPI
Headline CPI
Headline CPI(before
2000)/Core inflation
Headline CPI
Headline CPI
Headline CPI
Headline CPI
Headline CPI
Core CPI (excl.
interest costs)
Core CPI ( excl. raw
food and energy
Headline CPI
Note: Information on inflation targets was obtained from the respective Central Banks’ websites. Information on the exchange rate classifications was obtained from the IMF website:
http://www.imf.org/external/np/mfd/er/2008/eng/0408.htm.
14
Table 2 - Unit Root Panel Tests
Series
Nominal Exchange Rate
Inflation Rate
Output Gap (S.A.)
Monetary Policy Interest Rate
Expected Interest Rate (t+12)
Expected Inflation Rate (t+12)
Expected Outuput Gap (t+12)
Relative Inflation Rate to the U.S.
Relative Output Gap (S.A.) to the U.S.
Relative Interest Rate to the U.S.
Relative Expected Interest Rate (t+12) to the U.S.
Relative Expected Inflation Rate (t+12) to the U.S.
Relative Expected Outuput Gap (t+12) to the U.S.
Rlative Price Level to the U.S.
Real Exchange Rate
Levin, Lin &
Chu (t-value)
-7.72187 ***
42.7841
-6.06282 ***
-2.95529 ***
-6.01859 ***
3.99509
-11.9397 ***
-2.87019 ***
42.6943
-4.2458 ***
-3.07767 ***
-4.41728 ***
-1.761 **
-3.29341 ***
-11.9397 ***
Im, Pesaran
and Shin
(W-stat)
-3.4495 ***
0.85231
-11.8641 ***
-2.33125 ***
-4.71155 ***
-5.78669 ***
-7.52095 ***
-2.32548 **
0.8479
-11.5362 ***
-3.70912 ***
-2.57669 ***
-9.01665 ***
-3.79184 ***
-7.52095 ***
PP - Fisher
(Chi-square)
59.9117 ***
287.387 ***
663.302 ***
63.5501 ***
57.6064 ***
295.598 ***
336.089 ***
47.5094 **
288.191 ***
690.898 ***
88.6203 ***
39.3604
454.195 ***
65.0789 ***
336.089 ***
Note: All series are monthly values and are defined as the natural logarithms of their respective nominal values. All tests
assume the unit root as the null. The first test, Levin, Lin & Chu, assumes a common unit root process, whereas all other
tests assume individual unit root processes for each country. The asterisks to the right of the numbers, ***, ** and *, denote
statistical significance at 1%, 5% and 10%, respectively.
15
Table 3 - Cointegration Panel Tests - Kao (1999)
Model
Statistic
EMW - Symmetric
-28.008 ***
EMW - Asymmetric
-29.990 ***
MP - Symmetric
-4.936 ***
MP - Asymmetric
-4.756 ***
MP Expected - Symmetric
-3.325 ***
MP Expected - Asymmetric
-3.799 ***
Note: All series are monthly values and are defined as the natural
logarithm of the ratios of their respective nominal values for the
reference country and the United States. All tests assume no
cointegration as the null. The asterisks to the right of the numbers,
***, ** and *, denote statistical significance at 1%, 5% and 10%,
respectively.
16
Table 4.a - Forecasting evaluation - Diebold and Mariano (1995) statistic with bootstrapped confidence intervals –
Country-specific error correction model
EMW
EMW
MP
MP Expected
MP Expected
Symmetric
Asymmetric MP Symmetric
Asymmetric
Symmetric
Asymmetric
Country
BRA
CHI
MEX
PER
COL
KOR
1 m.
0.000964***
3.37
0.000677***
2.59
-0.00022
-1.62
-0.000222
-1.62
-0.000345
-2.37
-0.000324
-2.38
6 m.
-0.000603
-0.33
-0.003787
-1.38
-0.003288
-1.03
-0.003163
-1.00
-0.004751
-2.32
-0.004754
-2.32
12 m.
-0.017681
-2.87
-0.026014
-2.91
-0.026578
-1.97
-0.026115
-1.97
-0.025276
-2.98
-0.024929
-3.04
1 m.
0.000829***
2.56
0.000767***
2.56
-0.000358
-0.71
-0.000328
-0.72
-0.00071
-0.93
-0.000411
-0.80
6 m.
0.005763***
1.61
0.004873**
1.31
-0.002409
-0.53
-0.002669
-0.59
-0.00292
-0.64
-0.002595
-0.58
12 m.
-0.008957
-0.87
-0.008555
-0.87
-0.013161
-1.02
-0.017074
-1.20
-0.013771
-1.05
-0.010857
-0.86
1 m.
0.000221***
1.67
0.0000762**
0.95
-0.0000215
-1.36
-0.00000588
-0.35
-0.0000152
-1.12
-0.000026
-1.30
6 m.
-0.000154
-0.36
-0.000629
-1.01
-0.00043
-1.66
-0.000443
-1.63
-0.000435
-1.63
-0.000431
-1.64
12 m.
0.000304
0.30
-0.000186
-0.13
-0.001067
-1.15
-0.001125
-1.21
-0.001016
-1.09
-0.000979
-1.07
1 m.
0.0000278***
1.18
-0.0000106*
-0.51
-0.0000197
-1.29
-0.0000259
-1.83
-0.0000368
-1.48
-0.000048
-1.87
6 m.
0.000426***
1.91
0.000109**
0.34
-0.000473
-1.79
-0.000442
-1.69
-0.000548
-2.07
-0.000566
-2.09
12 m.
-0.00075
-1.47
-0.001877
-2.09
-0.00213
-2.56
-0.002
-2.40
-0.002265
-2.74
-0.002228
-2.58
1 m.
0.00000635
2.43
0.00000357
1.17
0.0000061
2.71
0.00000291
1.03
0.00000548
2.20
0.000000563
0.12
6 m.
0.00016
2.92
0.000149
2.13
0.000122
1.81
0.000142
2.21
0.000124
1.75
0.000149
2.41
12 m.
0.000472
3.12
0.000411
2.25
0.000328
1.66
0.00038
1.95
0.000291
1.37
0.000381
2.01
1 m.
0.000238***
3.17
0.000177***
3.11
-0.0000286
-1.13
-0.0000183
-0.89
-0.0000341
-1.14
-0.0000212
-0.87
6 m.
0.002095***
2.20
0.001796***
1.73
-0.000468
-0.88
-0.000457
-0.86
-0.000467
-0.66
-0.000458
-0.70
12 m.
0.000987*
0.85
0.001629*
1.05
0.0000469
0.04
0.000182
0.15
-0.000142
-0.14
-0.0000714
-0.07
17
Table 4.a - Forecasting evaluation - Diebold and Mariano (1995) statistic with bootstrapped confidence intervals –
Country-specific error correction model
Country
PHI
1 m.
THA
ISR
SAF
POL
CZE
EMW
Symmetric
EMW
Asymmetric MP Symmetric
MP
Asymmetric
MP Expected
Symmetric
MP Expected
Asymmetric
0.0000455***
1.01
0.00013**
1.52
0.0000479**
0.71
0.000659***
2.31
0.000536***
2.19
0.000106***
1.61
6 m.
0.001913***
1.88
0.001618**
1.73
-0.000641
-0.47
-0.000586
-0.43
0.0000659
0.04
0.000189
0.12
12 m.
0.004944**
2.17
0.003963*
1.56
-0.002737
-0.87
-0.002398
-0.78
0.003998
1.57
0.004214*
1.63
1 m.
0.00104***
2.64
0.000965***
2.84
0.000037
0.12
0.000031
0.10
-0.000221
-1.04
-0.000206
-0.97
6 m.
-0.004467
-1.63
-0.004333
-1.45
0.000476
0.04
0.000358
0.03
-0.016103
-2.54
-0.016372
-2.55
12 m.
-0.062881
-2.82
-0.063851
-2.75
-0.02679
-0.60
-0.027129
-0.61
-0.093392
-3.02
-0.09341
-3.05
1 m.
0.0000986***
2.57
0.000124***
2.98
0.0000161*
0.57
0.0000139*
0.48
0.0000225**
0.80
0.0000214**
0.79
6 m.
0.000502**
0.70
0.000443**
0.48
-0.000263
-0.29
-0.000286
-0.30
-0.000257
-0.28
-0.000265
-0.29
12 m.
-0.000645
-0.38
-0.000364
-0.17
-0.001899
-0.81
-0.002097
-0.90
-0.002148
-0.91
-0.001911
-0.81
1 m.
0.0000266***
0.59
0.0000202**
0.45
-0.0000284
-1.04
-0.0000296
-1.10
-0.0000272
-0.99
-0.0000305
-1.10
6 m.
0.000656***
2.37
0.000384**
0.81
-0.00041
-0.65
-0.000381
-0.60
-0.000387
-0.61
-0.000329
-0.52
12 m.
0.000164*
0.12
-0.001426
-0.78
-0.001573
-0.73
-0.001473
-0.68
-0.001541
-0.70
-0.001459
-0.66
1 m.
0.000373***
2.48
0.000153***
1.10
0.000047**
0.88
0.0000138*
0.24
0.0000537*
0.75
0.00000513
0.07
6 m.
0.00225***
2.30
0.001777***
1.69
0.0000537
0.04
0.00013
0.10
0.000757
0.49
0.000893
0.57
12 m.
0.005192***
1.66
0.004167***
1.24
-0.000653
-0.18
-0.000448
-0.12
0.006237
1.87
0.006411
1.93
1 m.
0.000482***
2.88
0.000419***
3.14
-0.00000383
-0.04
-0.00000266
-0.03
-0.0000104
-0.11
-0.0000114
-0.12
6 m.
0.002302***
2.03
0.002033***
1.66
-0.001473
-0.87
-0.001615
-0.95
-0.001609
-0.93
-0.001642
-0.97
12 m.
-0.001973***
-0.47
-0.002525
-0.59
-0.008574
-1.57
-0.00825
-1.55
-0.008513
-1.57
-0.00825
-1.55
18
Table 4.a - Forecasting evaluation - Diebold and Mariano (1995) statistic with bootstrapped confidence intervals –
Country-specific error correction model
Country
HUN 1 m.
ROM
TUR
EMW
Symmetric
EMW
Asymmetric MP Symmetric
MP
Asymmetric
MP Expected
Symmetric
MP Expected
Asymmetric
0.000165***
1.30
-0.000041*
-0.27
-0.000199
-1.00
-0.000108
-1.19
-0.000155
-0.95
-0.0000766
-1.07
6 m.
0.001083***
1.70
0.000159**
0.18
-0.001422
-1.55
-0.001224
-1.47
-0.001433
-1.55
-0.001303
-1.48
12 m.
-0.002418
-1.30
-0.004772
-1.72
-0.003358
-1.20
-0.003426
-1.21
-0.00355
-1.24
-0.003455
-1.20
1 m.
0.0000781
0.54
0.0000913
0.77
0.000186
1.32
0.000143
1.00
-0.000102
-1.53
-0.000126
-2.05
6 m.
-0.007194
-3.15
-0.006203
-2.88
-0.002898
-0.95
-0.003439
-1.09
-0.006518
-3.51
-0.00677
-3.51
12 m.
-0.054306
-2.86
-0.045205
-2.97
-0.035269
-3.29
-0.036354
-3.33
-0.041001
-3.74
-0.038856
-3.71
1 m.
0.000363***
1.63
0.000132**
0.71
-0.000102
-1.54
-0.0000945
-1.49
-0.000122
-1.45
-0.000123
-1.54
6 m.
-0.000529
-0.59
-0.001113
-1.20
-0.001876
-1.32
-0.001768
-1.25
-0.001592
-1.21
-0.001401
-1.08
12 m.
-0.005248
-1.41
-0.008753
-1.94
-0.013481
-2.86
-0.013392
-2.88
-0.004729
-1.31
-0.00454
-1.30
Note: The Diebold and Mariano (1995) S-statistics were computed using a driftless random walk as the benchmark against the forecasted values
provided by the specified exchange rate model and the country-specific error correction model as specified in equations (4.1) and (4.2). For a onesided test where the null assumes that the statistic is not positive, the number of stars following the statistic, ***, ** or *, means rejection of the
null at the 99%, 95% or 90% level, respectively. Below the S-statistic value, we present the t-distribution statistic. Rejection of the null implies
that we fail to reject that the exchange rate model has better forecasting power than the random walk benchmark. The p-values are the
bootstrapped versions of the respective test statistics and are based on 1000 iterations.
19
Table 4.b - Forecasting evaluation - Diebold and Mariano (1995) statistic with bootstrapped confidence intervals Pooled error correction model
EMW
EMW
MP
MP Expected
MP Expected
Symmetric
Asymmetric MP Symmetric
Asymmetric
Symmetric
Asymmetric
Country
BRA
CHI
MEX
PER
COL
KOR
1 m.
0.000979***
4.42
0.000762***
3.91
-0.000101
-0.89
-0.000085
-0.78
-0.000098
-0.86
-0.0000974
-0.88
6 m.
0.003321**
1.70
0.001715**
0.69
-0.003207
-1.06
-0.00324
-1.06
-0.003462
-1.14
-0.003448
-1.13
12 m.
-0.005449
-0.75
-0.008965
-1.08
-0.017679
-1.49
-0.0179
-1.51
-0.020434
-1.58
-0.020023
-1.56
1 m.
0.001252***
2.12
0.001126***
2.20
0.000217**
1.16
0.000175*
0.90
0.000209**
1.10
0.000169*
0.85
6 m.
0.006898**
1.91
0.005455**
1.45
-0.001938
-0.45
-0.002183
-0.50
-0.001931
-0.45
-0.00213
-0.49
12 m.
0.002029
0.27
-0.000367
-0.04
-0.007895
-0.68
-0.008382
-0.72
-0.008045
-0.69
-0.008205
-0.70
1 m.
0.000246**
1.60
0.0000616
0.53
0.000013
0.53
-0.000000151
-0.01
0.0000132
0.57
-0.00000282
-0.21
6 m.
-0.000548
-1.06
-0.001306
-1.64
-0.000906
-1.86
-0.00091
-1.85
-0.000892
-1.84
-0.000885
-1.82
12 m.
-0.001254
-0.91
-0.002483
-1.23
-0.00325
-2.08
-0.003271
-2.10
-0.003235
-2.05
-0.003324
-2.15
1 m.
0.00000378
0.08
-0.0000299
-0.79
0.000004
0.32
-0.00000133
-0.10
0.00000843*
0.68
0.00000659*
0.50
6 m.
0.000447***
2.54
-0.000046
-0.14
-0.000514
-1.89
-0.000498
-1.83
-0.000518
-1.89
-0.000529
-1.90
12 m.
-0.0000349
-0.07
-0.00109
-1.36
-0.002253
-2.56
-0.002087
-2.40
-0.002326
-2.60
-0.002335
-2.51
1 m.
-0.0000116
-1.94
-0.0000857
-4.02
0.00000619
2.68
0.00000424
1.55
0.00000612
2.65
0.00000413
1.54
6 m.
0.000106
1.75
-0.000324
-1.90
0.000163
2.35
0.000163
2.38
0.000163
2.35
0.000164
2.36
12 m.
0.000643
3.10
-0.000000641
0.00
0.000582
2.28
0.000607
2.46
0.000582
2.27
0.000622
2.50
1 m.
0.000214***
3.89
0.000163***
3.61
-0.00000599
-0.30
-0.0000106
-0.49
-0.00000774*
-0.39
-0.0000103
-0.49
6 m.
0.001299***
2.72
0.001158***
1.75
-0.000326
-0.80
-0.000308
-0.76
-0.000348
-1.05
-0.000352
-1.05
12 m.
0.00074**
0.92
0.000607**
0.46
-0.001
-0.72
-0.000859
-0.62
-0.000653
-0.59
-0.000571
-0.52
20
Table 4.b - Forecasting evaluation - Diebold and Mariano (1995) statistic with bootstrapped confidence intervals Pooled error correction model
EMW
EMW
MP
MP Expected
MP Expected
Symmetric
Asymmetric
MP
Symmetric
Asymmetric
Symmetric
Asymmetric
Country
PHI
1 m.
0.000597***
0.000466*** 0.0000828*** 0.0000436*** 0.0000764***
0.0000396**
3.10
2.87
1.97
0.87
1.83
0.74
THA
ISR
SAF
6 m.
0.001765***
2.04
0.000753**
0.81
-0.000339
-0.26
-0.000332
-0.25
-0.000624
-0.46
-0.000629
-0.46
12 m.
0.001587*
0.66
-0.000941
-0.33
-0.000921
-0.30
-0.000599
-0.20
-0.002045
-0.59
-0.002048
-0.58
1 m.
0.001706***
2.95
0.001479***
3.20
0.000323
0.86
0.000313
0.82
0.000299
0.84
0.000306
0.85
6 m.
0.017561
1.49
0.015931
1.42
0.004267
0.35
0.004068
0.33
0.003756
0.31
0.003544
0.30
12 m.
0.025417
0.68
0.023813
0.63
0.001342
0.03
0.000725
0.02
-0.00144
-0.03
-0.002052
-0.05
1 m.
0.0000965***
2.52
0.000122***
2.88
-0.00000428
-0.15
-0.00000571
-0.19
-0.000000241
-0.01
-0.0000038
-0.14
6 m.
0.001247**
2.04
0.001267**
1.63
-0.000275
-0.31
-0.000284
-0.32
-0.000292
-0.33
-0.000286
-0.32
12 m.
0.001796
0.89
0.001369
0.58
-0.000825
-0.31
-0.00078
-0.29
-0.000908
-0.34
-0.000761
-0.28
1 m.
0.0000403***
1.04
0.0000275**
0.60
-0.00000135
-0.06
-0.00000616
-0.28
-0.00000257
-0.11
-0.00000743
-0.32
6 m.
0.000789***
2.93
0.000382*
0.79
-0.000259
-0.43
-0.000252
-0.42
-0.00026
-0.43
-0.00025
-0.41
-0.000828
-0.48
-0.00162
-0.72
-0.001556
-0.69
-0.001647
-0.72
-0.001504
-0.66
12 m.
POL
CZE
0.000271
0.21
1 m.
0.000388***
3.29
0.000128***
1.03
0.0000532**
1.15
0.0000278*
0.52
0.0000226
0.49
-0.000001
-0.02
6 m.
0.001433**
1.61
-0.000772**
-0.59
0.000196
0.17
0.000233
0.20
-0.000956
-0.69
-0.000914
-0.66
12 m.
0.001062
0.37
-0.003009***
-0.78
0.000666
0.19
0.000893
0.25
-0.002209
-0.50
-0.002028
-0.46
1 m.
0.000438***
2.55
0.000384***
2.65
0.0000464
0.65
0.0000417
0.56
0.000047
0.67
0.0000474
0.65
6 m.
0.004014***
2.55
0.003813**
2.24
0.0000931
0.05
-0.0000215
-0.01
0.0000258
0.01
-0.0000526
-0.03
12 m.
0.003788***
0.87
0.002393
0.50
-0.003006
-0.52
-0.00311
-0.54
-0.003174
-0.54
-0.00324
-0.55
21
Table 4.b - Forecasting evaluation - Diebold and Mariano (1995) statistic with bootstrapped confidence intervals Pooled error correction model
EMW
EMW
MP
MP Expected
MP Expected
Symmetric
Asymmetric
MP
Symmetric
Asymmetric
Symmetric
Asymmetric
Country
HUN 1 m.
0.000272***
0.000114**
-0.0000637
-0.0000565
-0.0000613
-0.0000456
2.07
0.92
-1.04
-1.31
-1.06
-1.28
ROM
TUR
6 m.
0.000795**
1.39
-0.0000265
-0.03
-0.001742
-1.82
-0.001786
-1.85
-0.001754
-1.82
-0.001777
-1.82
12 m.
-0.003262
-1.64
-0.005175
-1.98
-0.007569
-2.01
-0.007684
-2.02
-0.007476
-2.02
-0.00741
-1.99
1 m.
0.000278
1.19
0.000248
1.60
0.000236
1.28
0.000207
1.12
0.000217
1.29
0.000204
1.21
6 m.
0.001864
0.48
0.002397
0.68
0.0000232
0.01
-0.0000591
-0.01
-0.002028
-0.53
-0.002046
-0.54
12 m.
-0.014121
-1.03
-0.013173
-0.98
-0.01731
-1.17
-0.017212
-1.17
-0.023769
-1.59
-0.023977
-1.61
1 m.
0.000354***
2.09
0.000118**
0.73
-0.000063
-1.17
-0.0000478
-0.99
-0.0000619
-1.20
-0.0000533
-1.14
6 m.
-0.00045
-0.39
-0.002466
-1.68
-0.001375
-1.09
-0.001348
-1.06
-0.001464
-1.17
-0.00141
-1.12
12 m.
-0.004549
-1.15
-0.008592
-1.74
-0.008591
-1.62
-0.008405
-1.60
-0.009676
-1.77
-0.009605
-1.76
Note: The Diebold and Mariano (1995) S-statistics were computed using a driftless random walk as the benchmark against the forecasted values
provided by the specified exchange rate model and the pooled error correction model as specified in equations (4.1) and (4.3). For a one-sided test
where the null assumes that the statistic is not positive, the number of stars following the statistic, ***, ** or *, means rejection of the null at the
99%, 95% or 90% level, respectively. Below the S-statistic value, we present the t-distribution statistic. Rejection of the null implies that we fail
to reject that the exchange rate model has better forecasting power than the random walk benchmark. The p-values are the bootstrapped versions
of the respective test statistics and are based on 1000 iterations.
22
Table 5.a - Number of times the model outperformed the random walk at the 10% significance level or less
- Bootstrapped out-of-sample statistics – Country-specific error correction model
EMW
Symmet.
EMW
Asymmet.
MP
Symmet.
MP
Asymmet.
MP
Expected
Symmet.
MP
Expected
Asymmet.
Average
of all
models
3
7%
3
7%
3
7%
11
24%
Horizon
Panel A - Diebold and Mariano statistic (Bootstraped Version)
All
Number
27
25
3
Hit rate
60%
56%
7%
1m
Number
Hit rate
13
87%
13
87%
3
20%
3
20%
3
20%
2
13%
6
41%
6m
Number
Hit rate
9
60%
9
60%
0
0%
0
0%
0
0%
0
0%
3
20%
12m
Number
Hit rate
5
33%
3
20%
0
0%
0
0%
0
0%
1
7%
2
10%
Panel B - Clark and West statistic (Bootstraped version)
Number
26
23
5
Hit rate
58%
51%
11%
4
9%
3
7%
4
9%
11
24%
1m
Number
Hit rate
13
87%
13
87%
4
27%
3
20%
3
20%
2
13%
6
42%
6m
Number
Hit rate
10
67%
9
60%
0
0%
1
7%
0
0%
0
0%
3
22%
12m
Number
Hit rate
3
20%
1
7%
1
7%
0
0%
0
0%
2
13%
1
8%
Panel B - Theil's U (Bootstraped version)
All
Number
34
32
Hit rate
76%
71%
15
33%
15
33%
14
31%
17
38%
21
47%
1m
Number
Hit rate
13
87%
13
87%
7
47%
7
47%
7
47%
7
47%
9
60%
6m
Number
Hit rate
12
80%
11
73%
5
33%
5
33%
4
27%
6
40%
7
48%
12m
Number
Hit rate
9
60%
8
53%
3
20%
3
20%
3
20%
4
27%
5
33%
Note: All statistics were computed using a driftless random walk as the benchmark against the forecasted values provided by the
specified exchange rate model and the country-specific error correction model as specified in equations (4.1) and (4.2). The hit
rate number corresponds to the number of times, considering the model and horizon combination, when the p-values were
significant at the 10% level or less. The p-values are the bootstrapped versions of the respective test statistics and are based on
1000 iterations. In this table, they are presented in basis points, which can therefore be multiplied by 1,000 iterations.
23
Table 5.b - Number of times the model outperformed the random walk at the 10% significance level or less Bootstrapped out-of-sample statistics – Pooled error correction model
EMW
Symmet.
EMW
Asymmet.
MP
Symmet.
MP
Asymmet.
MP
Expected
Symmet.
3
7%
4
9%
3
7%
10
22%
Horizon
Panel A - Diebold and Mariano statistic (Bootstraped Version)
All
Number
25
21
3
Hit rate
56%
47%
7%
MP
Expected Average of
Asymmet. all models
1m
Number
Hit rate
12
80%
11
73%
3
20%
3
20%
4
27%
3
20%
6
40%
6m
Number
Hit rate
10
67%
8
53%
0
0%
0
0%
0
0%
0
0%
3
20%
12m
Number
Hit rate
3
20%
2
13%
0
0%
0
0%
0
0%
0
0%
1
6%
Panel B - Clark and West statistic (Bootstraped version)
Number
34
30
8
Hit rate
76%
67%
18%
7
16%
8
18%
6
13%
16
34%
1m
Number
Hit rate
13
87%
14
93%
4
27%
3
20%
4
27%
2
13%
7
44%
6m
Number
Hit rate
13
87%
11
73%
1
7%
1
7%
1
7%
1
7%
5
31%
12m
Number
Hit rate
8
53%
5
33%
3
20%
3
20%
3
20%
3
20%
4
28%
Panel B - Theil's U (Bootstraped version)
All
Number
36
29
Hit rate
80%
64%
15
33%
15
33%
18
40%
18
40%
22
49%
1m
Number
Hit rate
15
100%
13
87%
7
47%
7
47%
9
60%
9
60%
10
67%
6m
Number
Hit rate
13
87%
9
60%
5
33%
5
33%
6
40%
6
40%
7
49%
12m
Number
Hit rate
8
53%
7
47%
3
20%
3
20%
3
20%
3
20%
5
30%
Note: All statistics were computed using a driftless random walk as the benchmark against the forecasted values provided by the
specified exchange rate model and the pooled error correction model as specified in equations (4.1) and (4.3). The hit rate number
corresponds to the number of times, considering the model and horizon combination, when the p-values were significant at the
10% level or less. The p-values are the bootstrapped versions of the respective test statistics and are based on 1000 iterations. In
this table, they are presented in basis points, which can therefore be multiplied by 1,000 iterations.
24
Table 6.a - Number of times the model outperformed the random walk at the 10% significance level or
less - Asymptotic out-of-sample statistics - Country-specific error correction model
EMW
Symmet.
EMW
Asymmet.
MP
Symmet.
MP
Asymmet.
Horizon
Panel A - Diebold and Mariano statistic (Asymptotic distribution)
All Number
24
19
8
8
Hit rate
53%
42%
18%
18%
MP
Expected
Symmet.
MP
Expected
Asymmet.
Average
of all
models
12
27%
14
31%
14
31%
1m
Number
Hit rate
10
67%
7
47%
1
7%
1
7%
2
13%
3
20%
4
27%
6m
Number
Hit rate
9
60%
5
33%
3
20%
2
13%
5
33%
5
33%
5
32%
12m Number
Hit rate
5
33%
7
47%
4
27%
5
33%
5
33%
6
40%
5
36%
18
40%
12
27%
12
27%
21
47%
Panel B - Clark and West statistic (Asymptotic distribution)
Number
34
31
19
Hit rate
76%
69%
42%
1m
Number
Hit rate
15
100%
15
100%
9
60%
8
53%
5
33%
5
33%
10
63%
6m
Number
Hit rate
12
80%
11
73%
5
33%
5
33%
3
20%
3
20%
7
43%
12m Number
Hit rate
3
20%
1
7%
1
7%
0
0%
0
0%
2
13%
1
8%
Note: All statistics were computed using a driftless random walk as the benchmark against the forecasted values provided by the
specified exchange rate model and the country-specific error correction model as specified in equations (4.1) and (4.2). The hit
rate number corresponds to the number of times, considering the model and horizon combination, the p-values were significant
at the 10% level or less. The p-values assume asymptotic distributions of the respective test statistics.
25
Table 6.b - Number of times the model outperformed the random walk at the 10% significance level or
less - Asymptotic out-of-sample statistics – Pooled error correction model
MP
MP Average
EMW
EMW
MP
MP Expected
Expected
of all
Symmet.
Asymmet.
Symmet.
Asymmet.
Symmet.
Asymmet.
models
Horizon
Panel A - Diebold and Mariano statistic (Asymptotic distribution)
All Number
21
14
10
8
11
9
12
Hit rate
47%
31%
22%
18%
24%
20%
27%
1m
Number
Hit rate
11
73%
8
53%
2
13%
0
0%
2
13%
0
0%
4
26%
6m
Number
Hit rate
9
60%
4
27%
4
27%
4
27%
4
27%
4
27%
5
32%
12m Number
Hit rate
1
7%
2
13%
4
27%
4
27%
5
33%
5
33%
4
23%
21
47%
21
47%
20
44%
27
59%
Panel B - Clark and West statistic (Asymptotic distribution)
Number
40
37
21
Hit rate
89%
82%
47%
1m
Number
Hit rate
15
100%
15
100%
9
60%
9
60%
10
67%
9
60%
11
74%
6m
Number
Hit rate
14
93%
13
87%
6
40%
6
40%
5
33%
5
33%
8
54%
12m Number
Hit rate
8
53%
5
33%
3
20%
3
20%
3
20%
3
20%
4
28%
Note: All statistics were computed using a driftless random walk as the benchmark against the forecasted values provided by the
specified exchange rate model and the pooled error correction model as specified in equations (4.1) and (4.3). The hit rate
number corresponds to the number of times, considering the model and horizon combination, the p-values were significant at
the 10% level or less. The p-values assume asymptotic distributions of the respective test statistics.
26
Figure 1 – Realized and predicted exchange rates – EMW/country specific error correction
South Africa
.8
Brazil
1.4
.7
Chile
6.8
1.2
6.4
.6
1.0
.5
.4
0.8
6.0
.3
0.6
5.6
.2
0.4
.1
5.2
0.2
.0
-.1
0.0
95 96 97 98 99 00 01 02 03 04 05 06 07 08
4.8
95 96 97 98 99 00 01 02 03 04 05 06 07 08
Mexico
95 96 97 98 99 00 01 02 03 04 05 06 07 08
Peru
1.6
.8
1.4
.7
1.2
.6
1.0
.5
0.8
.4
0.6
.3
Colombia
.4
.3
.2
.1
0.4
.0
.2
95 96 97 98 99 00 01 02 03 04 05 06 07 08
South Korea
.6
-.1
95 96 97 98 99 00 01 02 03 04 05 06 07 08
95 96 97 98 99 00 01 02 03 04 05 06 07 08
Philippines
1.1
Thailand
6
1.0
.5
5
0.9
.4
0.8
4
0.7
.3
0.6
3
.2
0.5
0.4
2
.1
0.3
.0
0.2
95 96 97 98 99 00 01 02 03 04 05 06 07 08
1
95 96 97 98 99 00 01 02 03 04 05 06 07 08
Israel
95 96 97 98 99 00 01 02 03 04 05 06 07 08
Polandl
Czech Republic
1.0
.4
1.4
0.8
.2
1.2
0.6
.0
0.4
-.2
0.2
-.4
0.0
-.6
-0.2
-.8
1.0
0.8
0.6
0.4
95 96 97 98 99 00 01 02 03 04 05 06 07 08
.7
0.0
95 96 97 98 99 00 01 02 03 04 05 06 07 08
Hungary
.8
0.2
95 96 97 98 99 00 01 02 03 04 05 06 07 08
Romania
Turkey
4.5
1.4
4.0
1.2
.6
3.5
.5
1.0
.4
3.0
.3
2.5
0.8
.2
0.6
2.0
.1
.0
1.5
-.1
1.0
95 96 97 98 99 00 01 02 03 04 05 06 07 08
0.4
0.2
95 96 97 98 99 00 01 02 03 04 05 06 07 08
95 96 97 98 99 00 01 02 03 04 05 06 07 08
Exchange Rate (solid)
Predicted Exchange Rate (dash)
27