Are there swift transitions in the smooth transition regressions of the exchange rate volatility of dollarized versus non-dollarized economies?
Mengesha, Lula G.
INTRODUCTION
Most exchange rates tend to exhibit non-linearity and to vary from
one regime to another. For this reason, it is vital to study how
exchange rate movements differ across countries and what this implies.
This study examines the nonlinearity of the exchange rate volatility of
dollarized and non-dollarized economies. It seeks to discover whether
there is an abrupt or smooth transition in the two sets of economies as
a result of global financial stress. To this end, we employ smooth
transition regressions using the exchange rate volatility and six
indicators of global financial stress, following the study by Coudert et
al. (2011).
Our study differs from that of Coudert et al (2011) in two key
aspects. First, while their study specifically examines the impact of
global financial stress on the exchange rate volatility of emerging
markets, we extend their study by examining the cases of dollarized and
non-dollarized economies. Second, while their study focuses on showing
an increase in volatility and spillovers as a result of the global
financial crisis, this study examines the nature of the transitions in
the exchange rate volatility of dollarized and nondollarized economies.
Daily data from 16 countries over the period 1994-2013 are
selected, for which GARCH (1,1) is used to capture the exchange rate
volatility and the volatility of global financial stress indicators.
Before employing smooth transition regression analysis, a linearity test
is carried out to identify whether or not the exchange rate volatility
exhibit non-linearity. The results show the existence of non-linearity
in each series with higher exchange rate volatility in the non-linear
regime of the non-dollarized economies as a result of an increase in the
global financial stress. Furthermore, the results suggest that, on
average, there are abrupt transitions in the exchange rate volatility of
dollarized economies relative to non-dollarized economies. This implies
that anchoring a currency to the US dollars results in the need for
rapid policy reactions, particularly at times of US financial crisis.
The remainder of the paper is organized as follows: the next
section discusses the literature review followed by the methodology used
in the study; the following section explains the data type and sources;
the penultimate section reports the results, and the final section gives
the conclusion.
LITERATURE REVIEW
The 'first generation models' of exchange rate movements
provided testable propositions regarding the linear relationship between
exchange rate changes and fundamentals such as money stocks, prices,
output, current account and so on. (see De Grauwe and Vansteenkiste,
2007). Subsequent models were based on utility maximization by
representative agents. Furthermore, nonlinearity was introduced into the
'first generation models' by Frankel and Froot (1990), De
Grauwe and Dewachter (1993), Kurz and Motolese (1999) and Kilian and
Taylor (2003). The models allow for changes in exchange rates that are
different from the fundamentals. The introduction of non-linear models
shed significant light on exchange rate dynamics including exchange rate
volatility, which is the main concern of this paper.
Exchange rate volatility tends to increase during financial crises.
Some evidence of this can be seen in the increase in the exchange rate
volatility in the Latin American, Asian and global markets because of
the financial crises of the Argentine, Asian and US economies (Coudert
et al., 2011; Chang et al., 2010; Kohler, 2010; Baharumshah and Wooi,
2007; and Cai et al., 2008). Exchange rate volatility during global
financial crises normally displays nonlinearity, which requires using
special modeling techniques to determine the influence of one on the
other. It should be noted here that, even in the absence of global or
regional finical crises, non-linearity seems to prevail in most exchange
rates that are drawn from long periods (Brooks, 1996; Hsieh, 1989; Lin
et al., 2011; and Kiran, 2012). The non-linearity of the exchange rates
indicates regime switching dynamics and varies from one economy to
another.
Our study differs from previous studies in that it addresses the
impact of global financial stress indicators on the exchange rate
volatility of dollarized and non-dollarized economies. Moreover, it
examines the nature of transitions in the exchange rate volatility of
dollarized and non-dollarized economies as well as its implication in
each set of the economies. By doing so, the paper contributes to the
knowledge of exchange rate volatility transitions as well as the role of
global financial stress indicators in exchange rate volatility.
METHODOLOGY
To capture the exchange rate volatility of each country,
Generalized Autoregressive Conditional Heteroskedasticity (GARCH) is
used. In the procedure, whether there is an Autoregressive Conditional
Heteroskedasticity (ARCH) effect in each series is determined before the
estimation of GARCH (1,1). The GARCH model is specified as follows:
[[epsilon].sub.i,t] = [[alpha].sub.i] + [u.sub.i,t] (1)
[[sigma].sup.2.sub.i,t] = [[mu].sub.i] +
[[alpha].sub.i][u.sup.2.sub.i,t-1] + [[beta].sub.i]
[[sigma].sup.2.sub.i,t-1] (2)
where [[epsilon].sub.i,t] stands for the exchange rate of country i
at time t. The term [u.sub.i,t] is the random error term for country i
at time f and is normally distributed, N (0, [[sigma].sup.2.sub.t]).
[[sigma].sup.2.sub.i,t] is the conditional variance term for country i
at time t-1. [[alpha].sub.i] and [[beta].sub.i] are ARCH and GARCH
parameters for country i respectively. The volatility of each global
financial stress indicator is also measured using GARCH (1,1).
The non-linear relationship between exchange rate volatility and
the global financial stress indicators can be examined using non-linear
models. In general, non-linearity can be captured by Threshold
Autoregressive (TAR), Hamilton's Markov switching (1989) and the
smooth transition autoregressive (STAR) models. The threshold
autoregressive model, proposed by Tong (1978) and explained in detail in
Tong (1990) allows the model parameters to change based on the value of
the threshold variable. Although the TAR model captures non-linearity,
the idea is that regime switching is discontinuous.
The Markov switching model assumes that changes in the regime are
managed by the result of an unobserved Markov chain. This means that it
is uncertain whether or not a particular regime has occurred at a
particular point in time. However, one can assign probabilities to the
incidence of the different regimes. Different from Markov switching, the
STAR model, which is proposed by Terasvirta (1994), allows the regime
switch to be the result of the past value of a dependent variable. The
series, therefore, are allowed to switch endogenously from one regime to
another regime according to the value of the dependent variable. It
should be noted here that, if the regime switching is based on the value
of an exogenous variable instead of the value of the dependent variable,
then the STAR model takes the form of STR (smooth transition
regression).
This paper selects the STR model over the other non-linear models
discussed previously for several key reasons. First, the study by
Sarantis (1999) shows that the STAR models outperform the Markov
switching model in out-of-sample forecasting. In addition to this, the
study by Liew et al. (2002) indicates that the nominal rate adjustment
more accurately fits the STAR. Second, besides its suitability for
modeling time series with asymmetric variation (see Terasvirta and
Anderson, 1992, and Terasvirta, 1995), it is easy to interpret the
estimated, locally linear, model. Third, since the main concern of this
paper is to determine the smoothness or abruptness of the transition,
STR is more appropriate than the remaining models.
Following Coudert et al. (2011), this study employs a bivariate
framework to determine the relationship between the exchange rate
volatility and the stress on the global financial markets and thereby
examines the features of the transition functions. Therefore, the STR
model of order p can be specified as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
Equation 3 incorporates linear and non-linear parts. [v.sub.t]
stands for exchange rate volatility at time t. [[mu].sub.10] and
[[mu].sub.20] are the constant terms of the linear and nonlinear parts
respectively. g([[tau].sub.t][gamma], c) is the transition function,
which is bounded between 0 and 1. [[tau].sub.t] represents the
transition variable, [gamma] stands for the slope parameter and c is the
threshold parameter. [[tau].sub.t] = [S.sub.t-d.], d > 0 is a
transition lag or delay and is one of the global financial stress
indicators. [gamma] > 0 determines the speed and smoothness of the
transition from one regime to another. The transition function can take
the following forms:
g([[tau].sub.t], [gamma], c) = (1 + exp (-[gamma][([[tau].sub.t] -
c))).sup.-1] (4)
g([[tau].sub.t], [gamma], c) = (1 - exp (-[gamma][([[tau].sub.t] -
c))).sup.2]) (5)
Putting Equations 4 and 5 into Equation 3 yields a logistic smooth
transition regression (LSTR) and exponential smooth transition
regression (ESTR) respectively (see Terasvirta and Anderson, 1992).
There are certain features that are worth noting here. First, both
transition functions switch between 0 and 1 very slowly and smoothly if
the value of [gamma] is small. If the value of [gamma] is large,
however, both transition functions become steeper and switch between 0
and 1 quickly. Second, there is asymmetric realization in the logistic
function, which means that the LSTR model switches smoothly between the
regimes depending on how much the transition variable is smaller or
larger than the value of c. On the other hand, there is symmetric
realization in the exponential function, which indicates that the ESTR
model switches smoothly between the regimes depending on how far the
transition variable is from c (see University of Washington, 2005).
Third, when [gamma] goes to infinity and if [[tau].sub.t] [much
less than] c then g([[tau].sub.t][gamma], c) = 0. However if
[[tau].sub.t] > c, then g(([[tau].sub.t][gamma], c)) = 1. In this
case, the LSTR model becomes a TAR model (Tong, 1990), but ESTR is
different. If [gamma] goes to 0, g([[tau].sub.t][gamma], c) becomes a
linear AR (p) model. Both LSTR and ESTR, therefore, become linear
models. To recover the TAR model in the case of ESTR, the modified
exponential function of Equation 5, following Coudert et al. (2011) and
Jansen and Terasvirta (1996), can be specified as:
g(([[tau].sub.t], [gamma], c) = [(1 + exp(-[gamma]([[tau].sub.t] -
[c.sub.1])([[tau].sub.t] - [c.sub.2]))).sup.-1] (6)
From Equation 6, if [c.sub.1] [not equal to] [c.sub.2] and [gamma]
goes to infinity, g(([[tau].sub.t][gamma], c) = 1 for [[tau].sub.t] <
[c.sub.l] and [[tau].sub.t] > [c.sub.2]. However,
g([[tau].sub.t][gamma], c) = 0 for [c.sub.1] [less than or equal to]
[[tau].sub.t], [less than or equal to] [c.sub.2]. For this reason,
Equation 3 with the transition function of Equation 6 recovers three
regime threshold models. Further to the specification of STR discussed
so far, Terasvirta (1994) discussed the following steps in the
estimation process.
(a) Specifying a linear autoregressive model; that is determining p
in the linear autoregressive part of the model.
(b) Testing linearity for different values of d, the transition lag
or delay, and determining the value of d.
In carrying out the linearity test, Luukkonen et al. (1988) suggest
testing the null hypothesis of linearity from the following auxiliary
regression that is found by transforming the transition function in
Equation 3 into its third-order Taylor approximation. The null
hypothesis that needs to be tested from the following auxiliary
regression, therefore, is [H.sub.0]: [[beta].sub.ij] = [[beta].sub.2j] =
[[beta].sub.3j] = 0 (j = 1, ... , p).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
where [v.sub.t] stands for exchange rate volatility. [x.sub.i,t]
(i-1, ... , 6) is the volatility of one of the six indicators of global
financial stress that can be included in the model one at a time and
then the p-value can be examined to decide whether to keep it as a
transition variable or not. In case when more than one transition
variable is found, then the transition variable with the lowest p-value
is selected. [y.sub.t] = (1, [x.sub.i,t], [v.sub.t-j] ... ,
[v.sub.t-p]).
(c) Choosing between LSTR and ESTR models. This can be done based
on the following tests (Terasvirta, 1994).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
If [H.sub.04] is rejected, then the model will be LSTR. However, if
[H.sub.04] is accepted and [H.sub.03] is rejected, then ESTR will be
chosen. In case when [H.sub.04] and [H.sub.03] are not rejected but
[H.sub.02] is rejected, the LSTR model will be selected.
DATA
Daily time series data ranging from 19 March 1994 to 30 August 2013
are used. Altogether 16 countries are selected, eight of them are
dollarized and eight are non-dollarized economies. The selection of
dollarized countries is based on the study by Reinhart et al (2003),
which discusses different groups of dollarized economies ranging from
low to very high rates of dollarization. This paper selects only
moderate to very highly dollarized economies. (1) The exchange of each
country's local currency to US dollar is collected from DataStream.
Some of the dollarized economies included in the sample are Argentina,
Brazil, Indonesia, Mexico, Mozambique, South Korea, Uruguay and
Venezuela. The non-dollarized economies are Australia, Canada, Japan,
Norway, New Zealand, Sweden, Switzerland and United Kingdom.
Following Coudert et al. (2011), six indicators of global financial
stress are used: the world stock index (W), the emerging countries'
stock index (EM), the implied volatility of the S&P500 index (IV),
the advanced countries' stock index (A), and commodity indices such
as Commodity Research Bureau (CRB) and the Standard & Poor's
Goldman Sachs Commodity Index (S&P GSCI) are selected. It should be
noted here, in contrast to the study by Coudert et al. (2011), our study
incorporates non-dollarized economies, which are mainly advanced
countries. For this reason, A is added to the global stress indicators
instead of EMBI, the emerging markets' bond index. The data for
each of the global financial stress indicators is drawn from DataStream.
Table 1 indicates that the exchange rate return has the lowest
standard deviation in the UK market followed by the Canadian. By
contrast, there is a high standard deviation of the exchange rate return
in the Australian market followed by the New Zealand market. The
exchange rate returns in all the economies apart from Japan and Sweden
have positive skewness. However, all the returns have positive Kurtosis
that means that the distributions are leptokurtic.
As can be seen from Table 2, the South Korean market shows the
lowest standard deviation of the exchange rate returns next to the
Uruguayan market. There is relatively high standard deviation of the
exchange rate returns in the Venezuelan market. On average, in
comparison to the results in Table 2, the standard deviation of the
exchange rate returns is slightly higher in the dollarized markets than
in non-dollarized markets. The results also show that, with the
exception of the returns in the South Korean market, the returns in the
remaining markets have positive skewness. However, all the markets have
excessive positive kurtosis.
Before using non-linear estimation method, the data are tested for
variability and non-linearity to make sure the exchange rate data of the
selected dollarized economies are non-rigid and non-linear. To verify
this, first, an ARCH effect test is carried out for each series and, as
discussed in the next section, the results suggest that there is
evidence of the ARCH effect in each market series implying the use of
GARCH to capture volatility is appropriate. Second, a linearity test is
applied, and the results indicate that the series are non-linear. After
verifying the fact that the data are variable and non-linear, smooth
transition regression is used
Empirical results
To verify whether GARCH (1,1) is appropriate for capturing the
volatility of exchange rate returns, the ARCH effect test is performed
as mentioned in the methodology section. The results of the test are
reported in Table 3. The test statistics in the second and fourth
columns of the table suggest that the null hypothesis; that is, there is
no ARCH effect in the exchange rates quoted across the selected markets
can be rejected. Thus, there is evidence of the ARCH effect in each
market series, which indicates that the use of GARCH is appropriate.
After detecting the ARCH effect in the series, the lag length of the
GARCH is determined based on the ARCH-LM test. To carry out this
procedure, first GARCH (1,1) is estimated for each series and then
whether there is a remaining ARCH effect in the series is examined. The
results are reported in the third and fifth columns of Table 3.
It is evident from the table that the null hypothesis of no ARCH
effect in the series can be accepted as the test statistic results are
very low for all the rates quoted across the markets. Since the ARCH
effect disappears from the series, there is no need to add extra lags in
the GARCH to measure the exchange rate volatility of each market. The
disappearance of the ARCH effect from each series after the estimation
of GARCH (1,1) indicates that the volatility of each series can be
captured well enough by GARCH (1,1).
Table 4 reports the ARCH effect test results before and after GARCH
(1,1) estimation of the global financial stress indicators. The same
explanation that is discussed earlier applies to these results.
After measuring the exchange rate volatility using GARCH (1,1), the
next step is to determine the order p in the linear autoregressive part
of the model. This has been carried out using AIC information criterion.
Given the definite value of the p order, the null hypothesis of
linearity in Equation 7 is tested. To find the value of the transition
lag or delay, an F-test is carried out on the coefficients of the null
hypothesis using different values of the transition lag or delay one at
a time. The one with the highest rejection value is then selected as a
transition lag or delay. The results are shown in Table 5.
For both dollarized and non-dollarized economies, linearity test
results indicate that there are high F-test results. This means that
there is non-linearity in the exchange rate volatility of each economy
given the selected indicator of global financial stress. It can be seen
from Table 5 that there is weak linearity test rejection with a
relatively lower F-test result in the Mexican economy. Furthermore,
while EM is the main transition variable in most dollarized economies,
S&P GSCI and EM are equally dominant transition variables in most of
the non-dollarized economies. This might be partly explained by the fact
that the dollarized economies are from emerging countries for which EM
can most likely play a major role as a transition variable. EM also
plays a significant role as a transition variable in the non-dollarized
economies of Japan, New Zealand and Canada. This could be because of the
close trade links of these economies with the emerging markets.
It should be noted here that linearity has also been rejected when
other transition variables of global financial stress indicators are
used for most of the economies except for the Mexican, Argentinian,
Venezuelan and Uruguayan markets. However, the transition variables with
the results of highest linearity test rejection are chosen as the
transition variables, which are listed in Table 5. In the exchange rate
volatility of the Mexican market, the rejection of linearity is tight.
The linearity rejection is obtained only when EM at lags 1 and 3, W at
lag 2 and A at lag 3 are used. Similarly, the linearity of the exchange
rate volatility of the Uruguayan market has been accepted for all the
global financial stress indicators except A, W and IV at time t and at t
- 1. The lag order ranges from 1 to 10, with the highest lag order
coming from the Argentine and Norwegian markets and the lowest from the
Australian and Uruguayan markets. The transition variables and the lag
orders found in Table 5 determine whether the STR takes the form of the
LSTR or ESTR. Moreover, an estimation of the STR is made based on the
outcome of the LSTR and ESTR determination. The results are shown in
Table 6. It should be noted here that the estimated starting values for
the slope and the threshold coefficients are determined using grid
search of JMulTi.
Several economic conclusions can be drawn from Table 6. First, the
STR specification tends to be dominated by LSTR relative to ESTR. This
is evident from the results in the table that, apart from the
specification of the Venezuelan and Australian markets, all the
remaining markets are estimated by the LSTR model. As mentioned in the
methodology section, this indicates that there is an asymmetric
realization in the markets. In other words, there is regime switching of
the exchange rate volatility depending on the degree to which the
transition variable is smaller or greater than the threshold value. More
precisely, it indicates that the exchange rate volatility in these
markets pursues two regimes depending on the level of global financial
stress is low or high. On the other hand, estimation based on the ESTR
specification of Equation 3 with the transition function of Equation 6
indicates that the exchange rate volatility in the markets follows three
regimes. It shows that there are two extreme regimes with an
intermediate regime. While the exchange rate in the intermediate regime
shows no inclination to revert to its equilibrium value, there are mean
reverting and symmetric dynamics in the two extreme regimes.
Second, the estimated results of the coefficients in the linear
part of the model suggest a positive and statistically significant
impact of the selected global financial stress indicator on the
economies of Brazil, Canada, Japan and United Kingdom. In contrast to
these results, there are negative and statistically significant
influences of the indicators of global financial stresses on the
exchange rate volatility of the Australian, New Zealand and Venezuelan
markets. This indicates that these economies might have adopted a
tighter exchange rate policy during the first regime. This could result
from intermittent intervention of the central banks to keep their
exchange rates within a certain range. The actions of the central banks
might have reduced the exchange rate volatility during the first
episodes of global financial stress volatility.
In the non-linear part of the model, the estimated results show
that there are positive and statistically significant effects of the
indicators of global financial stress on the exchange rate volatility of
the Australian, Brazilian, United Kingdom, Canadian, Japanese,
Norwegian, New Zealand, Swedish and Venezuelan markets. This means that
there is an increase in the exchange rate volatility of these markets
with the increase in the global financial volatility. Compared with the
results in the linear regime, the number of positively and statistically
affected economies is greater in the non-linear regime. This result is
marked by the dominance of the non-dollarized markets. With the
exception of the Brazilian and Venezuelan markets, the dollarized
economies tend to be unaffected by the indicators of global financial
stress volatility in the non-linear regime. The significant and dominant
impact of the global financial volatility in non-dollarized economies
shows the exposure of the economies to the global financial markets,
their openness and the magnitude of the financial market operations
within the economies. Furthermore, it shows that these economies might
have eased their exchange rate policies when the global financial stress
crossed the threshold. Of all the dollarized and non-dollarized
economies, the Canadian, Japanese and United Kingdom markets demonstrate
positive and statistically significant impact of the indicators of
global financial stress volatility on their exchange rate volatility in
both the linear and non-linear regimes.
[FIGURE 1 OMITTED]
Third, the slope coefficient which determines the speed and
smoothness of the transition from one regime to another is statistically
significant in all the economies. While Mozambique has the highest slope
coefficient, Sweden has the lowest followed by Brazil and Japan. This
shows that the slope of the transition function is steep in the case of
Mozambique whereas the transition function for Sweden is smooth. This
implies that, while the exchange rate volatility in the Mozambican
market has abrupt transitions between the regimes, the Swedish market
has relatively smooth transitions. Among nondollarized economies,
Australia has relatively the highest slope coefficient at 55.72. This
suggests that there is rapid transition of the exchange rate volatility
between the regimes in the Australian market relative to the remaining
nondollarized economies. Figure 1 shows the transition function against
the transition variable for Australia, Sweden and Mozambique
respectively. The figure clearly shows that there is smoother transition
in the Swedish economy than in the economies of Australia and
Mozambique. This is further evidence of the fact that the smaller the
value of the slope coefficient, the smoother the transition is in the
economy.
In comparison with non-dollarized economies, the slope coefficient
results of the dollarized economies are high. The fastest transition of
the latter economies relative to the former economies might be explained
to some degree by their partial dollarization. Their economies are
likely to be highly affected by global financial stress, particularly
after the US financial crisis, which required them to embrace a quick
fix and involuntarily adopt rapid reaction in their exchange rate
policies. Since some of the dollarized economies not only have trade
links but also a currency link with the United States, whatever affects
the US economy is likely to greatly influence their policies. The
outcome of this will then be reflected in the transition of the exchange
rate volatility between the regimes.
CONCLUSION
Non-linearity tends to be a common feature in most exchange rates
and their volatility. By taking a sample of sixteen countries using
smooth transition regressions, this paper examines whether the exchange
rate volatility of some dollarized and non-dollarized economies exhibits
a non-linear pattern as a result of global financial stress. The results
suggest that linearity is significantly rejected in all the economies,
implying that there is regime switching in the exchange rate volatility
of each of the economies. While for the non-dollarized economies the
rejection of linearity occurs when each of the indicators of the global
financial stress is used as a transition variable, for dollarized
economies such as the Mexican, Argentinian, Venezuelan and Uruguayan
rejection of linearity was achieved for only very few transition
variables.
In the non-linear regimes of almost all the non-dollarized
economies apart from Switzerland, the results show that exchange rate
volatility increases with the increase in global financial stress
volatility. This indirectly indicates that the financial markets are
more active and play a more influential role in the foreign exchange
markets of non-dollarized economies than that of dollarized economies.
The negative and statistically significant impact of global financial
stress volatility on the exchange rate volatility in the linear regimes
of Australia, New Zealand and Venezuela and also in the non-linear
regimes of Uruguay and Switzerland suggests that there might be a
'leaning against the wind' action taken by the central banks
to keep the exchange rates within a narrower ranges.
The analysis of the slope coefficients in the transition function
of smooth transition regressions indicates that, in general, the slope
is higher in the estimated results of the dollarized economies than
non-dollarized economies. Therefore, there is a more abrupt transition
of the exchange rate volatility between the regimes in the dollarized
economies than in the non-dollarized economies. The smoothness of the
transition in non-dollarized economies might be because of currency
detachment from the US economy from which the rise in the global
financial stress volatility originated. Moreover, the changes in their
exchange rate policies through their monetary policies might assist
their economies to peruse smooth rather than abrupt transition in the
exchange rate volatility. On the other hand, the currency attachment of
the dollarized economies because of their partial dollarization might
expose these economies to sudden and rapid transitions.
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(1) The word dollarization has been defined as the use of
convertible foreign currency in the domestic economy by some scholars.
It has also been interpreted as the use of US dollars within a country
by some other scholars. Dollarization has also been defined as official
or full (de jure), unofficial or partial (de facto), financial, real and
liability dollarization.
In this study, the word dollarization stands for partial [de facto)
dollarization with particular emphasis on the use of US dollars. Some of
the reasons for this is that the US dollar has the greatest market share
and most countries rely on the US dollar more than other convertible
currencies. An attempt was made to include the less dollarized economies
but there was an issue of passing the test of non-linearity, which is
crucial in the estimation of smooth transition regression
LULA G. MENGESHA
University of Waikato, Private Bag 3015, Hamilton 3240, New
Zealand.
E-mail: luliyey@gmail.com
Table 1: Descriptive statistics of the exchange rate returns of
non-dollarized economies
RAU RCA RJP RNR
Mean -4.76E-05 -4.32E-05 -2.36E-05 -4.00E-05
Maximum 0.087 0.034 0.0517 0.048
Minimum -0.080 -0.039 -0.077 -0.055
Standard Deviation 0.008 0.005 0.007 0.007
Skewness 0.44 0.18 -0.60 0.04
Kurtosis 15.61 7.54 10.26 6.93
Observations 5118 5118 5118 5118
RNZ RSWN RSWS RUK
Mean -6.15E-05 -3.90E-05 -8.83E-05 -6.97E-06
Maximum 0.069 0.042 0.091 0.036
Minimum -0.060 -0.056 -0.044 -0.042
Standard Deviation 0.008 0.008 0.007 0.006
Skewness 0.34 -0.03 0.25 0.26
Kurtosis 7.25 5.93 10.73 6.42
Observations 5118 5118 5118 5118
Note: RAU = exchange rate return of Australia, RCA = exchange rate
return of Canada, RJP = exchange rate return of Japan, RNR = exchange
rate return of Norway, RNZ = exchange rate return of New Zealand,
RSWN = exchange rate return of Sweden, RSWN = exchange rate return of
Switzerland, RUK = exchange rate return on United Kingdom.
Table 2: Descriptive statistics of the exchange rate returns of
dollarized economies
RAR RBR RIN RME
Mean 0 0.001 0 0
Maximum 0.342 0.106 0.316 0.297
Minimum -0.171 -0.120 -0.236 -0.168
Standard Deviation 0.009 0.010 0.016 0.010
Skewness 13.84 0.38 3.07 6.29
Kurtosis 498.16 17.82 114.14 225.00
Observations 5118 5118 5118 5118
RMQ RSK RUR RVN
Mean 0 6.10E-05 0 0.001
Maximum 0.289 0.136 0.135 0.534
Minimum -0.184 -0.202 -0.096 -0.276
Standard Deviation 0.012 0.009 0.007 0.017
Skewness 3.48 -1.45 2.85 18.69
Kurtosis 116.65 95.39 64.72 559.93
Observations 5118 5118 5118 5118
Note: RAR= exchange rate return of Argentina, RBR = exchange rate
return of Brazil, RIN= exchange rate return of Indonesia, RME =
exchange rate return of Mexico, RMQ = exchange rate return of
Mozambique, RSK = exchange rate return of South Korea, RUR = exchange
rate return of Uruguay, RVN = exchange rate return of Venezuela.
Table 3: ARCH effect test results of dollarized and non-dollarized
economies
Dollarized Non-dollarized
Before After Before After
GARCH (1,1) GARCH (1,1) GARCH (1,1) GARCH (1,1)
Country F-statistic F-statistic F-statistic F-statistic
Argentina 72.65 0
(0.000) (0.987)
Australia 285.93 0.362
(0.000) (0.548)
Brazil 474.59 0.008
(0.000) (0.927)
Canada 489.80 0.522
(0.000) (0.470)
Indonesia 326.32 0.176
(0.000) (0.675)
Japan 70.00 0.833
(0.000) (0.362)
Mexico 10.89 0
(0.001) (0.979)
Mozambique 167.35 0.001
(0.000) (0.974)
Norway 377.90 1.403
(0.000) (0.236)
New Zealand 222.94 0.172
(0.000) (0.679)
South Korea 314.50 0.205
(0.000) (0.651)
Sweden 105.98 0.203
(0.000) (0.653)
Switzerland 15.61 0.875
(0.000) (0.345)
Uruguay 165.48 0.069
(0.000) (0.793)
Venezuela 2.972 0.056
(0.031) (0.940)
United Kingdom 320.94 0.653
(0.000) (0.419)
Note: the results in parentheses are the p-values.
Table 4: ARCH effect test results of the indices
Before GARCH (1,1) After GARCH (1,1)
Index F-statistic F-statistic
W 269.64 0
(0.000) (0.983)
EM 233.62 0.053
(0.000) (0.818)
A 265.52 2.116
(0.000) (0.146)
CRB 250.91 1.119
(0.000) (0.290)
S&P GSCI 121.85 2.282
(0.000) (0.131)
Note: the results in parentheses are the p-values.
Table 5: Linearity test results, transition variables and lag orders
Country Dollarized
Lag order Transition Variable F-test
Argentina 10 IV 5.44
(0.001)
Australia
Brazil 4 A 12.84
(0.000)
Canada
Indonesia 6 EM 27.17
(0.000)
Japan
Mexico 9 EM 2.57
(0.052)
Mozambique 3 CBR 12.11
(0.000)
Norway
New Zealand
South Korea 5 CBR 55.98
(0.000)
Sweden
Switzerland
Uruguay 1 8.80
(0.000)
Venezuela 3 EM 5.99
(0.000)
United Kingdom
Country Non-dollarized
Lag order Transition Variable F-test
Argentina
Australia 1 S&P GSCI 116.84
(0.000)
Brazil
Canada 8 EM 25.23
(0.000)
Indonesia
Japan 5 EM 9.38
(0.000)
Mexico
Mozambique
Norway 10 S&P GSCI 22.93
(0.000)
New Zealand 6 EM 31.99
(0.000)
South Korea
Sweden 4 S&P GSCI 16.62
(0.000)
Switzerland 4 W 7.24
(0.000)
Uruguay
Venezuela
United Kingdom 5 A 11.97
(0.000)
Note: the results in parentheses are the p-values.
Table 6: The estimation results
Country Dollarized
STR Slope Linear Non-linear
Type coefficient coefficient coefficient
Argentine LSTR 98.23 0 -0
(3.12) (0.22) (-0.39)
Australia
Brazil LSTR 1.22 0.08 1.05
(3.75) (5.46) (5.53)
Canada
Indonesia LSTR 154.67 0.498 -0.50
(3.19) (1.62) (-1.57)
Japan
Mexico LSTR 138.81 -0.018 0.017
(14.85) (-0.44) (0.40)
Mozambique LSTR 536.43 0.32 -0.46
(2.51) (0.06) (-0.09)
Norway
New Zealand
South Korea LSTR 346.60 -0.88 1.70
(1.68) (-0.28) (0.54)
Sweden
Switzerland
Uruguay LSTR 211.66 0.015 -0.03
(1.90) (0.92) (-1.81)
Venezuela ESTR 60.54 -12.85 12.85
(5.43) (-2.21) (2.22)
United
Kingdom
Country Non-dollarized
STR Slope Linear Non-linear
Type coefficient coefficient coefficient
Argentine
Australia ESTR 55.72 -0.016 0.017
(2.83) (-2.56) (2.76)
Brazil
Canada LSTR 9.50 0.001 0.003
(2.56) (3.02) (3.09)
Indonesia
Japan LSTR 2.32 0.002 0.005
(2.01) (2.38) (2.70)
Mexico
Mozambique
Norway LSTR 4.10 0.003 0.03
(4.31) (1.50) (2.93)
New Zealand LSTR 0.51 -0.03 0.03
(4.79) (-1.97) (2.44)
South Korea
Sweden LSTR 1.09 -0 0.029
(3.76) (-0.16) (3.56)
Switzerland LSTR 2.73 0.002 -0.009
(3.42) (1.02) (-3.04)
Uruguay
Venezuela
United LSTR 6.60 0.009 0.022
Kingdom (2.23) (3.35) (5.57)
Note: the results in parentheses are the t-ratios.
