Download Parallel market

Regime dependence between the official and parallel foreign
currency markets for Dollars in Greece
Angelos Kanas
Department of Economics
University of Crete
University Campus
GR-74100
Rethymno, Greece
and
Georgios P. Kouretas*
Department of Economics
University of Crete
University Campus
GR-74100
Rethymno, Greece
May 2003
Abstract
*Corresponding author: email: [email protected]
1
1. Introduction
A `parallel` or `black` market for US dollars has operated continuously in
Greece since World War II, as a result of the huge government budget deficit and the
loans that had to be made to finance the German occupation troops, which eventually
led to a 3 year period of sustained hyperinflation (1945-1948) in Greece. Coupled
with unstable political and social conditions, this monetary situation led the people to
lose confidence in the national currency and most of the transactions were made in US
dollars or in gold sovereigns. This situation continued even after the implementation
of the major reconstruction plan in the 1950s which had as a distinct feature the
devaluation of the drachma by 100 percent against the dollar until very recently when,
as a result of Greece’s joining of the European Economic Community, this market
ceased to exist in the early 1990s. Although Greece has allowed the Greek drachma to
float against major currencies since April 1975, following the collapse of the BrettonWoods agreement and the establishment of a system of flexible exchange rates in
international transactions, the movement to the managed float was accompanied by
the imposition of trade and foreign exchange restrictions so that the official exchange
rate was not purely market-determined but was still rather administratively
determined. Thus, the size of the parallel market was quite considerable with the
premium being on average 15%.
2. The emergence of the Greek black market for foreign currency
A `parallel` or `black` market for US dollars has operated continuously in
Greece since World War II, as a result of the huge government budget deficit and the
loans that had to be made to finance the German occupation troops, which eventually
led to a 3 year period of sustained hyperinflation (1945-1948) in Greece. Coupled
2
with unstable political and social conditions, this monetary situation led the people to
lose confidence in the national currency and most of the transactions were made in US
dollars or in gold sovereigns. This situation continued even after the implementation
of the major reconstruction plan in the 1950s which had as a distinct feature the
devaluation of the drachma by 100 percent against the dollar.
Following the collapse of the Bretton-Woods agreement and the establishment
of a system of flexible exchange rates in international transactions, Greece has
allowed the Greek drachma to float against major currencies since April 1975. The
link to the US dollar was abandoned and a variable trade-weighted system was
adopted, where the US dollar had the greatest weight. Greece`s joining of the
European Economic Community in 1981 led the Bank of Greece to adjust the tradeweighted system and place a greater weight on the Deutschemark and other European
currencies and smaller weight on the dollar. However, the movement to the managed
float was accompanied by the imposition of trade and foreign exchange restrictions
(Manalis, 1993) so that the official exchange rate was not purely market-determined
but was still rather administratively determined. Thus, the parallel market for dollars
which developed after World War II was still very much in effect, undermining these
restrictions while smuggling of goods was taking place. The two oil price shocks, the
chronic high inflation and corresponding current account deficits gave a new
momentum to the activities in the parallel market for US dollars during the second
half of the 1970s and the first half of the 1980s. By 1984 the size of the market was
substantial and, according to the estimates by Pavlopoulos (1987), the annual volume
of transactions was approaching 400 million US dollars. Figure 1 shows the evolution
of the parallel and official drachma-dollar exchange rates from 1975 to 1993, while
Figure 2 shows the evolution of the parallel market premium for the same period. The
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premium is positive apart from short periods in the second half of the 1980s when it
turned to a discount. During that period there were two discrete devaluations of the
drachma which were implemented in January 1983 and October 1995 and each one
was equal to 15%. The negative premium is explained by the fact that for some
periods after 1985 the Bank of Greece forced the commercial banks not to accept
foreign currency without proper identification of the source of the foreign currency. In
that case the seller was willing to undersell his foreign currency in the black market.
In addition, the case of a negative premium after the second devaluation may also be
explained by the likelihood that the parallel market agents were expecting a higher
percentage of devaluation of the drachma than the realized one, which led to selling
dollars at a discount. In January 1986 a liberalization process for capital flows began
which was completed in May 1994 when all capital controls on short-term capital
were lifted, which led to the virtual elimination of the market by the end of 1993
(Papaioannou and Gatzonas, 1997).
3. Econometric methodology
3.1 The Markov Switching Vector Error Correction model
The Markov Switching Vector Error Correction model (MS-VECM),
introduced in Artis et al. (2000) is a multivariate generalisation of the univariate
Markov Switching autoregressive (MS-AR) model introduced by Hamilton (1989).
The general formulation of the mean-adjusted l-th order MS-AR model, with regimedependent mean and variance, is
yt   (st )  a1 (yt 1   (st 1 ))  ...  al (yt l   (st l ))  ut ,
ut | st ~ NID(0, (st ))
(1)
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where  yt is a Tx1 vector containing the observations for the single stationary time
series {  yt}, T is the sample size, μ(st) is the regime-dependent conditional mean, st
 {1, 2, …, M } is an unobserved regime variable, where M denotes the number of
feasible regimes, and ut is the innovation process with a regime-dependent variancecovariance matrix  ( st ) . The unobservable realisation of the regime st  {1, 2, …,
M} is assumed to be governed by a discrete state Markov process defined by the
constant transition probabilities pij:
pij  Pr( st 1  j | st  i ) ,
M
 pij  1 ,
i, j  1,..., M 
(2)
j 1
An l-th order MS-Vector Error Correction model [MS-VECM(l)] model can
be considered as a multivariate generalization of (1). Consider the K-dimensional time
series vector  Yt = (  y1t , …,  yKt)’, t = 1, …, T. The MS-VECM(l) model for ΔYt
is given by
Yt   (st )  A1 (Yt 1   (st 1 ))  ...  Al (Yt l   (st l ))  d ( Yt 1 )  ut
(3)
ut ~ NID( 0, ( st ))
where
A1, …, Al are autoregressive parameter matrices, ( Yt ) is the error
correction term, and μ(st), Σ(st) are parameter shift functions describing the
dependence of the parameters μ and Σ on the regime st, e.g. μ(st) = μ1 if st = 1, …,
μ(st) = μM if st = M. The MS-VECM(l) is completed by considering the regimegenerating Markov process in (2) which allows us to infer the evolution of regimes
from the data. It is assumed that st follows an irreducible ergodic M state Markov
process with the transition matrix given by matrix P1
1
A comprehensive discussion of the theory of Markov chains is given by Hamilton (1994).
5
P=
p11
p 21
...
pM 1
p12
p 22
...
pM 2
... p1M
... p 2 M
... ...
... p MM
(4)
As the objective of this paper is to model volatility regimes, we focus on a
particular version of (3) which allows only for regime-dependent variance (i.e.
heteroscedastic error term), while the mean is assumed to be regime-invariant. This
model is given in equation (5), and is denoted as the MSH(M)-VECM(l) model:
Yt    A1 (Yt 1   )  ...  Al (Yt l   )  d (  Yt 1 )  1 / 2 ( st )u t ,
ut ~NID(0, IK)
(5)
In this study, we consider the 2-dimensional vector ΔΥt=(Δot, Δpt)′, where Δot
denotes the series of percentage changes of the official exchange rate, and Δpt denotes
the series of percentage change of the parallel currency market. We consider a model
with 2 regimes, namely a ‘low’ volatility regime (regime 1) and a ‘high’ volatility
regime (regime 2).2 Thus, for the 2-dimensional 2-regime model [MSH(2)-VECM(l)],
equation (5) is written as:
l
l
k 1
k 1
ot  a o   a o ,o ,k ot  k   a o , p ,k pt  k  d1 (ot 1  bpt 1 )  1 / 2 ( st )u o ,t ,
uo,t ~NID(0, 1).
2
Allowing for a higher number of regimes, and since we are interested in multivariate estimation,
would considerably complicate the estimation. Standard likelihood ratio tests of the null hypothesis of
two regimes against the alternative of three regimes cannot be used because the parameters pij are
unidentified under the third regime. Precise Hansen (1992) tests are computationally expensive in this
case, because of the large number of parameters needed for the grid.
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l
l
k 1
k 1
pt  a p   a p ,o ,k ot  k   a p , p ,k pt  k  d 2 (ot 1  bpt 1 )  1 / 2 ( st )u p ,t ,
(6)
up,t ~NID(0,1)
pij  Pr( st  j | st 1  i ) ,
2
 pij  1 ,
i , j  1,2
j 1
where pij are the constant transition probabilities. Maximum likelihood estimation of
the model given in (6) is based on the Expectation Maximisation (EM) algorithm
discussed in Hamilton (1989), and Krolzig (1997a, 1997b).3 As a byproduct of the
maximum likelihood estimation, Hamilton (1989), shows that several inferences can
be drawn. Firstly, one can calculate the unconditional probability that the system will
be in regime 1 at any given date. This unconditional probability is given by
Pr( st  1) 
1  p 22
2  p11  p 22
(7)
Secondly, a set of conditional probabilities can be obtained, namely the ‘smoothed’
probabilities, representing the ex-post inference about the system being in regime st at
date t, based on the entire sample T. For the 2-regime model, the smoothed
probabilities at time t are represented by a 1x2 vector, and for the entire sample T,
they are represented by a Tx2 matrix. The smoothed probabilities that the system of
the two markets is (i.e. the equity market and the Mexican currency market are
jointly) in regime 1 and 2 are denoted by p1c,,te , p 2c,,te respectively. Thirdly, one could
date the regime switches based on the Tx2 matrix of the smoothed probabilities.
3
The EM algorithm has been introduced by Dempster et al. (1977) for models where the observed time
series depend on an unobservable stochastic variable, i.e. st. Each iteration of the EM algorithm
involves two steps. The first step, known as the expectation step, involves the estimation of the
unobserved states st by determining their smoothed probabilities. The second step, known as the
maximisation step, involves estimating the parameter vector from maximising the likelihood function
where the unknown conditional probabilities are replaced with the smoothed probabilities obtained
7
Assigning dates to regime switches and thus, the classification of regimes, amounts to
assigning every observation ΔYt to a given regime. On the basis of the smoothed
probability for each date t, we assign that date to a given regime according to the
highest smoothed probability. For 2 regimes, the rule is to assign the observation to
the first regime if Pr(st = 1 | ΔYT ) > 0.5, and to assign it to the second regime if Pr(st
= 1 | ΔYT ) < 0.5. Lastly, the average duration of each regime can be calculated, on the
basis of the formula di = (1-pii)-1, i = 1,2, where di is the average duration of regime i.
3.2.Testing for volatility regime independence
An important advantage of MSH(2)-VECM(l) is that it allows for testing of
whether the high volatility regime of the official currency market is independent of
the high volatility regime of the parallel market. To formally test the null hypothesis
of independence, we estimate a univariate model for the official market of the form:
l
l
k 1
k 1
ot  a o   a o ,k ot k   a p ,k pt k  1 / 2 ( st )u t , ut ~NID(0, 1)
(8)
In this model, lagged parallel market returns enter as an exogenous
explanatory variable in order for the right hand side of this model to be the same as
the right hand side of the official market equation in MSH(2)-VECM(l) in (6) and to
have the same conditioning set. The model in (8) is called the MSH(2)-ARX(l) model
for official currency market. Similarly, for the parallel currency market, we estimate
an MSH(2)-ARX(l) model in which lagged official market percentage changes enter
as an exogenous variable:
from the first step. Having obtained the parameter vector, the filtered and the smoothed probabilities
are updated and so on, guaranteeing an increase in the value of the likelihood function at each step.
8
l
l
k 1
k 1
pt  a p   a p ,k pt  k   a ' o ,k ot  k 1 / 2 ( s t )u ' t , u t' ~NID(0, 1).
(9)
From the estimation of (8), we obtain the Tx1 vector of the smoothed
probabilities that the official market is in the high volatility regime at time t, p 2o,t .
Similarly, from estimating (9), we obtain the Tx1 vector of probabilities that the
parallel market is in the high volatility regime at time t, p 2p,t . If the volatility regimes
of the two markets are independent, then the probability that the system of the two
markets is (i.e. the probability that both markets are jointly) in the high volatility
regime ( p 2o,,tp ) should be equal to the product of the probability that the official market
is in the high volatility regime ( p 2o,t ) and the probability that the parallel currency
market is in the high volatility regime ( p 2p,t ) at time t. Therefore, the null hypothesis
of independence is:
p2o,,tp  p2o,t p2p,t , t  { 1,...,T }
(10)
with the alternative of dependence being p2o,,tp  p2o,t p2p,t , where p 2o,,tp denotes the
smoothed probabilities that the official market and the parallel market are jointly (i.e.
the probabilities that the system of the two markets is) in the high volatility regime.
To test this hypothesis, we obtain the Tx1 vector containing the products of the
probability that the official market is in the high volatility regime at time t and the
corresponding probability that the parallel market is in the high volatility regime at
time t ( p2o,t p2p,t ) , t  { 1,...,T } . Then, we compare this Tx1 vector with the Tx1
vector of the smoothed probabilities p 2o,,tp . This is a paired data comparison (namely,
p2o,1 p2p,1 vsv p 2o,,1p , p2o, 2 p2p, 2 vsv p2c,,e2 , p2o,3 p2p,3 vsv p 2o,,3p , …, p2o,T p2p,T vsv p 2p,T,o ), and is
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carried out using the Wilcoxon test.4 The null hypothesis of this test is that the two
series come from the same distribution with the same location, which is equivalent to
the independence hypothesis. The alternative hypothesis is that the two series come
from two distributions of identical shape but different location, which is equivalent to
volatility regime dependence. Our tests are based on both asymptotic and
bootstrapped critical values for the Wilcoxon test.5
3.2. Regime-dependent impulse responses using the Markov Switching VAR model
An additional means of measuring how the official currency market reacts to
disturbances from the parallel market and vice versa is to employ impulse response
analysis. We use the estimated Markov Switching VAR models to calculate the
response of the official market to a shock in the parallel market, and the response of
the parallel to a shock in the official. We seek to explore which market exercises the
more persistent impact on the other. Our impulse response functions are regimedependent; they measure the expected changes in one market at time t+h to a one
standard deviation shock to the other market at time t within each regime.6 The
regime-dependent impulse response function for regime i is defined as follows:
Et qt  h
st  ...  st  h  i   ri,h
u r ,t
for
h≥0
(1)
4
Unlike the two-sampled t-test, the Wilcoxon test does not assume that the observations come from
normal (Gaussian) distributions. For an analytical exposition, see Hollander and Wolfe (1973).
5
The bootstrapped critical values were calculated as follows: From the empirical distribution of
p2c,,te , p2e,t p2c,t , we draw with replacement a bootstrap sample of T observations and calculate the
Wilcoxon statistic. We repeat this 1000 times and thus obtain 1000 test statistics. Next, we establish the
5% fractiles of the distribution of these 1000 statistics. The bootstrapped marginal significance level is
based on those critical values. The bootstrapped experiments were conducted using S-PLUS.
10
where h is the time horizon (in months). Estimates of the response vectors can be
derived by combining the parameter estimates of the unrestricted Markov switching
VAR model in (XX) with the estimate of the matrix Ẑ (st) obtained through
identification restrictions.7 For exposition purposes, let us assume that we seek to
estimate the impulse response of the official exchange rate changes from a shock in
the parallel market. A one standard deviation shock to the parallel market implies that
the initial disturbance vector is u0(0, 1), i.e. a vector of zeros apart from the 2nd
element which is 1. Pre-multiplying this vector by the estimate of the regimedependent matrix Zˆ (st ) gives the impact responses. The remaining response vectors
can be estimated by solving forward for the official exchange rate changes. The
following expression shows the solutions linking the estimated response vectors with
estimated parameters:
ˆ
ri, h

min( h , p )

l 1
Aˆ lihl 1 Zˆ ( st )u 0 ,
for
h
(2)
4. Empirical results
5. Conclusions
6
Ehrmann et al. (2003) argue that regime-dependent impulse response functions can be a useful
analytical tool.
7
See Ehrmann et al. (2003).
>0
11
References
Table 1. Descriptive statistics
12
Official
Parallel
Market
market
Mean
Standard
Deviation
Skewness
Kurtosis
JB
LBS(4)
COINT
Notes:
1. LBS(4) denotes the Ljung-Box statistic with 4 lags for the squared returns. This is
distributed as  42 .
2. JB denotes the Jarque-Bera normality test. This is distributed as  22 .
3. COINT denotes the Johansen and Juselius (1990) test for bivariate cointegration between
the logarithm of the Mexican exchange rate and the logarithm of each country's equity
index. This test was computed on the assumption of a linear deterministic trend in the
data. The 5% critical value is 25.32.
4. * denotes statistical significance at the 5% level.
Table 2. Official and Parallel currency market: MSH(2)-VECM.
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Parameters
 (s  1)  (s  2) (No volatility regime switch, homoscedastic VECM(4))
HA:  (s  1)  (s  2) (Volatility regime switch, heteroscedastic MSH(2)-VECM(4))
H0:
Likelihood
LR
AIC
HQIC
ae
ae,e,1
ae,e,2
ae,e,3
ae,e,4
ae,c,1
ae,c,2
ae,c,3
ae,c,4
ac
ac,e,1
ac,e,2
ac,e,3
ac,e,4
ac,c,1
ac,c,2
ac,c,3
ac,c,4
p11
p 22
(continued overleaf)
(Table 2 continued)
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Parameters
SD
of
equity
market: Regime 1
SD
of
equity
market: Regime 2
S.D. of
currency
Regime 1
parallel
market:
S.D of
currency
Regime 2
official
market:
Correlation coef:
Regime 1
Correlation Coef:
Regime 2.
Unconditional
probability:
Regime 1
Unconditional
probability:
Regime 2
Average Duration:
d1
d2
Regime
classification:
High-volatility
regime
Notes:
1. LR denotes the value of the likelihood ratio test for testing the null hypothesis:
H0:  ( s1 )   ( s2 ) , namely no volatility regime switch (linear VECM). The values in
curly brackets next to the LR statistic are the marginal significance level of this test,
based on Davies (1987).
2. S.D. stands for the standard deviation.
3. The values in brackets report the respective values from the corresponding linear
VECM(4) model.
4. t-statistics are reported in parentheses.
5. * denotes statistical significance at the 5% level.
15
Table 3. Tests for independence between the volatility regime of the official and
parallel currency markets
Wilcoxon statistic
Marginal significance level
Bootstrap
Asymptotic
Notes:
1. The null hypothesis is that of independence in volatility regimes between the official and
parallel currency markets. The alternative is that of dependence.
2. The bootstrapped marginal significance is based on 1000 repetitions. (These experiments
were conducted in S-PLUS).
3. * denotes rejection of the null hypothesis of independence in favour of the alternative of
dependence at the 5% level.
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