black and official exchange rate volatility and foreign exchange controls: evidence from greece

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INTERNATIONAL JOURNAL OF FINANCE AND ECONOMICS Int. J. Fin. Econ. 6: 13–25 (2001) BLACK AND OFFICIAL EXCHANGE RATE VOLATILITY AND FOREIGN EXCHANGE CONTROLS: EVIDENCE FROM GREECE ANGELOS KANAS and GEORGIOS P. KOURETAS* Department of Economics, Uni6ersity of Crete, Uni6ersity Campus, GR-74100, Rethymno, Greece ABSTRACT This paper examines the issue of volatility and capital controls to the official and black market exchange rates of the Greek Drachma using the monthly exchange rate against the US dollar for the period 1975 – 1993. Specifically, we apply a GARCH(1, 1) model to study the behaviour of the official and black market drachma/dollar exhange rate. The main findings of the analysis are: (i) in contrast to the findings of previous studies using monthly rates, GARCH processes characterize the drachma/dollar exchange rate series in both markets; (ii) the relaxation of foreign exchange controls increased the volatility of the exchange rate in the official market as implied by theory; (iii) the persistence of volatility is reduced when account is taken of the liberalization process of capital movements; and (iv) The forecasts of volatility are improved when the GARCH forecasts are used against traditional measures. Copyright © 2001 John Wiley & Sons, Ltd. KEY WORDS: black market; capital controls; exchange rate volatility; GARCH JEL CODE: F31; F32; C22; C52 1. INTRODUCTION Since the collapse of the fixed exchange rate system, a growing interest has emerged in empirical finance in modelling and forecasting exchange rates and their volatility. Emphasis on volatility grew out of the need to obtain reliable inputs in the pricing of financial products, such as options and futures, in developing optimal hedging techniques and all sorts of risk exposure from transactions with foreign economies. Early research on the stochastic behaviour of price changes (returns) of financial assets is based on the assumptions of normality and constant variance (homoskedasticity). The seminal works of Mandelbrot (1963) and Fama (1965) found that the empirical distribution of price changes of financial assets is leptokurtic when compared with the normal distribution, thus rejecting the assumption of normality. Furthermore, Mandelbrot (1967) and Fielitz (1971) provide evidence rejecting the assumptions of homoskedasticity and independence over time. In order to account for these ‘peculiarities’, Engle (1982) developed the autoregressive conditional heteroskedastic (ARCH) methodology, which allows for the modelling of the time-varying volatility of the financial assets. This methodology was later generalized by Bollerslev (1986) who proposed the generalized ARCH (GARCH) methodology. Several variations of these models have appeared along with numerous empirical applications in the financial markets in the last decade (see Bollerslev et al., 1992 and Bera and Higgins, 1993 for an extensive literature review). Exchange rates behave like other financial assets. Mussa (1979) and Friedman and Vandersteel (1982) have shown that exchange rate movements are characterized by time-varying volatility which means that exchange rates tend not to be independent but to exhibit ‘volatility clustering’. This is the case where periods of large absolute changes tend to cluster together followed by periods of relatively small absolute changes. Several studies have extensively investigated the pattern of volatility of all major exchange rates by applying Engle’s (1982) ARCH model and Bollerslev’s (1986) GARCH model. Thus, Baillie and * Corrrespondence to: Department of Economics, University of Crete, University Campus, GR-74100, Rethymno, Greece. Tel.: +30 831 77412; fax: +30 831 77406; e-mail: [email protected] Copyright © 2001 John Wiley & Sons, Ltd.

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Page 1: Black and official exchange rate volatility and foreign exchange controls: evidence from Greece

INTERNATIONAL JOURNAL OF FINANCE AND ECONOMICS

Int. J. Fin. Econ. 6: 13–25 (2001)

BLACK AND OFFICIAL EXCHANGE RATE VOLATILITY ANDFOREIGN EXCHANGE CONTROLS: EVIDENCE FROM GREECE

ANGELOS KANAS and GEORGIOS P. KOURETAS*Department of Economics, Uni6ersity of Crete, Uni6ersity Campus, GR-74100, Rethymno, Greece

ABSTRACT

This paper examines the issue of volatility and capital controls to the official and black market exchange rates of theGreek Drachma using the monthly exchange rate against the US dollar for the period 1975–1993. Specifically, weapply a GARCH(1, 1) model to study the behaviour of the official and black market drachma/dollar exhange rate.The main findings of the analysis are: (i) in contrast to the findings of previous studies using monthly rates, GARCHprocesses characterize the drachma/dollar exchange rate series in both markets; (ii) the relaxation of foreign exchangecontrols increased the volatility of the exchange rate in the official market as implied by theory; (iii) the persistenceof volatility is reduced when account is taken of the liberalization process of capital movements; and (iv) Theforecasts of volatility are improved when the GARCH forecasts are used against traditional measures. Copyright© 2001 John Wiley & Sons, Ltd.

KEY WORDS: black market; capital controls; exchange rate volatility; GARCH

JEL CODE: F31; F32; C22; C52

1. INTRODUCTION

Since the collapse of the fixed exchange rate system, a growing interest has emerged in empirical financein modelling and forecasting exchange rates and their volatility. Emphasis on volatility grew out of theneed to obtain reliable inputs in the pricing of financial products, such as options and futures, indeveloping optimal hedging techniques and all sorts of risk exposure from transactions with foreigneconomies. Early research on the stochastic behaviour of price changes (returns) of financial assets isbased on the assumptions of normality and constant variance (homoskedasticity). The seminal works ofMandelbrot (1963) and Fama (1965) found that the empirical distribution of price changes of financialassets is leptokurtic when compared with the normal distribution, thus rejecting the assumption ofnormality. Furthermore, Mandelbrot (1967) and Fielitz (1971) provide evidence rejecting the assumptionsof homoskedasticity and independence over time.

In order to account for these ‘peculiarities’, Engle (1982) developed the autoregressive conditionalheteroskedastic (ARCH) methodology, which allows for the modelling of the time-varying volatility of thefinancial assets. This methodology was later generalized by Bollerslev (1986) who proposed thegeneralized ARCH (GARCH) methodology. Several variations of these models have appeared along withnumerous empirical applications in the financial markets in the last decade (see Bollerslev et al., 1992 andBera and Higgins, 1993 for an extensive literature review).

Exchange rates behave like other financial assets. Mussa (1979) and Friedman and Vandersteel (1982)have shown that exchange rate movements are characterized by time-varying volatility which means thatexchange rates tend not to be independent but to exhibit ‘volatility clustering’. This is the case whereperiods of large absolute changes tend to cluster together followed by periods of relatively small absolutechanges. Several studies have extensively investigated the pattern of volatility of all major exchange ratesby applying Engle’s (1982) ARCH model and Bollerslev’s (1986) GARCH model. Thus, Baillie and

* Corrrespondence to: Department of Economics, University of Crete, University Campus, GR-74100, Rethymno, Greece. Tel.:+30 831 77412; fax: +30 831 77406; e-mail: [email protected]

Copyright © 2001 John Wiley & Sons, Ltd.

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A. KANAS AND G.P. KOURETAS14

Bollerslev (1989, 1990a,b) have shown that short-run exchange rate changes for major Europeancurrencies behave as martingale processes with leptokurtic distributions and conditionally heteroskedastic(GARCH) errors. Similarly, Bollerslev (1987), Diebold (1988), Hsieh (1988, 1989a,b), Akgiray (1989),Akgiray and Booth (1990) have shown that these models fit well to daily and weekly data for all majorcurrencies during the floating exchange rate period. Furthermore, Baillie and Bollerslev (1989) haveshown that ARCH effects tend to weaken as the frequency of the sampled data decreases, while Diebold(1988) and Drost and Nijman (1993) have shown that ARCH processes converge to normality undertemporal aggregation.

This paper examines whether ARCH processes characterize a set of exchange rates that have receivedvery little attention in the finance literature. There are a number of interesting issues which we considerin the present analysis. First, we are interested in examining whether this class of models characterize lowfrequency montlhy data, not only of official exchange rates but also of black market exchange rates.Second, with the application of the GARCH modelling of exchange rates, we also look into the effects offoreign exchange controls on the behaviour of the exchange rates. As Phylaktis and Wood (1984) argue,foreign exchange controls reduce the volatility of exchange rates. Contrary to the conventional empiricalwork on the effectiveness of foreign exchange controls which has focused on the effects of foreignexchange controls on the international interest rate arbitrage,1 we examine the effects of the foreignexchange restrictions on the official and black market exchange rates.

The existence of parallel or ‘black’ markets, particularly for US dollars, is a well known feature of manydeveloping countries and countries where trade and capital controls exist (Agenor, 1992; Montiel et al.,1993; Edwards, 1999). Foreign exchange and trade controls are a major factor in the parallel or ‘black’market for foreign currency. When access to the official foreign exchange market is restricted, then thoseagents who need foreign exchange in order to make international transactions of goods, services andassets will have an incentive to find an alternative source. Thus, the development of excess demand forforeign currency at the official rate gives an incentive to those who have an excess supply of foreigncurrency to sell it illegally at a price higher than the official rate. Thus, the existence of foreign exchangecontrols causes a divergence between the equilibrium rate and the official rate and this leads to theemergence of a parallel or ‘black’ market for foreign exchange in the country. The size of this marketvaries from country to country and depends on the type of the exchange and trade restrictions imposedand the degree to which these restrictions are enforced by the authorities.

Furthermore, our empirical investigation examines the possible effects that a shift in the exchange ratepolicy through a removal of the foreign exchange restrictions will have on the persistence of shocks tovolatility, i.e. whether past volatility explains current volatility. This is an important issue, especially formodelling the pricing of such financial assets as derivatives, where we must take into account whether ashock to volatility is permanent or transitory (Phylaktis and Wood, 1984; Edwards, 1999).

The final feature of this work deals with the evaluation of the ability of the GARCH models to provideimproved forecasts to volatility over traditional measures. This is done with the applications of fourstandard statistics, namely, the mean error (ME), the root mean square error (RMSE), the mean absolutepercentage error (MAE) and the mean absolute percentage error (MAPE).

For this analysis we choose to model the distributional properties of the official and black marketexchange rates of the Greek drachma against the US dollar. The parallel market for US dollars has beenoperating in Greece since the end of World War II. Its size has been considerable with the premium beingon average 15%. However, Greece’s joining of the European Economic Community (EEC) eventually ledto the abandoning of all trade and foreign exchange controls, i.e. a distinct shift in the policy concerningthese policies, so that the black market for dollars ceased to exist by the end of 1993.

The main findings of the paper are summarized as follows. First, in contrast to the observation ofprevious studies using monthly rates, it is shown that a GARCH(1, 1) model with t-distributions areshown to characterize the drachma/dollar exchange rate series in the official and black market for foreigncurrency. Second, the relaxation of foreign exchange controls increased the volatility of the exchange rateas implied by theory. Third, the persistence of volatility is reduced when account is taken of theliberalization process of capital movements. Finally, it is shown that the GARCH(1, 1) forecasts ofvolatility are superior to the ones provided by two other traditional measures.

Copyright © 2001 John Wiley & Sons, Ltd. Int. J. Fin. Econ. 6: 13–25 (2001)

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BLACK AND OFFICIAL EXCHANGE RATE VOLATILITY AND FOREIGN EXCHANGE CONTROLS 15

The organization of the paper is as follows. The second section discusses recent developments in theGreek foreign exchange market. The third section describes the data and presents some preliminaryresults. The fourth section presents the GARCH model. The fifth section reports and discusses theestimation of the model for the drachma/dollar official and black market exchange rates, the issue ofcapital controls along with the forecasting performance of the estimated model while the last sectionprovides our concluding remarks.

2. THE GREEK FOREIGN EXCHANGE MARKET

A parallel or ‘black’ market for US dollars has operated continuously in Greece since World War II, asa result of the huge government budget deficit and the loans that had to be made to finance the Germanoccupation troops. This ultimately led to a 3-year period of sustained hyperinflation (1945–1948) inGreece. Coupled with unstable political and social conditions, this monetary situation led the people tolose confidence in the national currency and most of the transactions were made in US dollars or in goldsovereigns. This situation continued even after the implementation of a major reconstruction plan in the1950s which had as a distinct feature the devaluation of the drachma by 100% against the dollar.

Following the collapse of the Bretton-Woods agreement and the establishment of a system of flexibleexchange rates in international transactions, Greece has allowed the Greek drachma to float against majorcurrencies since April 1975. The link to the US dollar was abandoned and a variable trade-weightedsystem was adopted, in which the US dollar had the greatest weight. Greece’s joining of the EEC in 1981led the Bank of Greece to adjust the trade-weighted system and place a greater weight on theDeutschemark and other European currencies and smaller weight on the dollar. However, the movementto 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. It was still ratheradministratively determined and thus, the parallel market for dollars which developed after World WarII was still very much in operation, undermining these restrictions. The two oil price shocks, the chronichigh inflation and corresponding current account deficits gave a new momentum to the activities in theparallel market for US dollars during the second half of the 1970s and the first half of the 1980s. By 1984the size of the market was substantial and, according to the estimates by Pavlopoulos (1987), the volumeof transactions was approaching 400 million US dollars. Figure 1 shows the evolution of the parallel andofficial drachma–dollar exchange rate from 1975 to 1993, while Figure 2 shows the evolution of the

Figure 1. The official and black market exchange rates. LGRUS= the official market exchange rate; LPAR= the black marketexchange rate.

Copyright © 2001 John Wiley & Sons, Ltd. Int. J. Fin. Econ. 6: 13–25 (2001)

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A. KANAS AND G.P. KOURETAS16

Figure 2. The black market premium. BLPR= the black market premium.

parallel market premium for the same period. The premium is positive apart from short periods in thesecond half of the 1980s when it turned to a discount. During that period there were two discretedevaluations of the drachma which were implemented in January 1983 and October 1985 and each onewas equal to 15%. The negative premium is explained by the fact that for some periods after 1985 theBank of Greece forced the commercial banks not to accept foreign currency without proper identificationof the seller. In that case the seller was willing to undersell his foreign currency in the black market. Inaddition, the case of a negative premium after the second devaluation may also be explained by thelikelihood that the parallel market agents were expecting a higher percentage of devaluation of thedrachma than the realized one, which led to selling dollars at a discount. In January 1986 a liberalizationprocess for capital flows began which was completed in May 1994 when all capital controls on short-termcapital were lifted, which led to the virtual elimination of the market by the end of 1993.

3. DATA AND PRELIMINARY RESULTS

The data consist of end-of-month observations of the official and parallel drachma/US dollar exchangerates and the sample period spans from April 1975, when Greece adopted a managed floating exchangerate, to December 1993. The data for the official exchange rate were taken from the InternationalFinancial Statistics of the International Monetary Fund and the black market exchange rate data weretaken from the World Currency Yearbook. Both series are taken in natural logarithms.

In order to avoid the problem of non-stationarity which is a well known feature of the exchange rateseries, it is necessary to make use of first- (or higher) differentiated data. To examine, whether theexchange rate series are stationary, we apply the Phillips and Perron (1988) test for the null hypothesis ofa unit root against the alternative of stationarity of the exchange rate series and the Kwiatkowski et al.(1992) Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test for the null hypothesis of level or trendstationarity against the alternative of non-stationarity. The results of the unit root and stationarity testsare presented in Table 1. The results show that we are unable to reject the null hypothesis ofnon-stationarity with the Phillips–Perron test and we reject the null hypothesis of stationarity with theKPSS test for the levels of both series. The results are reversed when we take the first difference of eachexchange rate series which leads us to the conclusion that the official and black drachma/dollar exchangerates are realizations of I(1) processes.

Copyright © 2001 John Wiley & Sons, Ltd. Int. J. Fin. Econ. 6: 13–25 (2001)

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BLACK AND OFFICIAL EXCHANGE RATE VOLATILITY AND FOREIGN EXCHANGE CONTROLS 17

Table 1. Unit root and stationarity tests

Variable Level First difference

Z(ta*) hm Z(ta*) hm

eo −0.22 1.923* −15.32* 0.098ep −0.47 2.455* −15.66* 0.100

eo and ep are, respectively, the official and parallel exchange rate. Z(ta*) is the Phillips–Perron testfor the null of non-stationarity, when only a constant appears. To construct the Z(ta*) statistic wehave allowed for up to fourth autocorrelation and used a Bartlett window to ensure positivedefiniteness. The critical value at the 5% level is −2.87 (MacKinnon, 1987). hm, denotes the KPSS(1992) test for the null of stationarity, when only a constant appears. The critical value at the 5%level is 0.463. An asterisk denotes statistical significance at the 5% level.

Given the results of this preliminary analysis we will subsequently only consider the first differences foreach exchange rate:

Det=100�(et−et−1) (1)

which corresponds to the approximate percentage nominal return on each currency obtained from time tto t−1.

Table 2 reports several preliminary statistics for monthly percentage changes in the official and parallelexchange rates. The skewness and kyrtosis measures indicate that both series are positively skewed andhighly leptokurtic relative to the normal distribution (this is more evident for the parallel rate).Furthermore, the Kolmogorov D-statistic as well the Bera–Jarque normality test reject the assumption ofnormality. Rejection of normality can be partially attributed to intertemporal dependencies in themoments of the series. Table 2 also presents the Ljung and Box (1978) portmanteau test statistics Q andQ2 (for the squared data) to test for first- and second-moment dependencies in the distribution of theexchange rate series. The Q statistic indicates that percentage monthly returns of both rates are serialcorrelated. The Q2 statistic for the official and parallel exchange rate is significant, providing evidence ofstrong second-moment dependencies (conditional heteroskedasticity) in the distribution of the exchangerate series.2 Finally, the standard deviation (S.D.) indicates that there is greater variance of exchange ratereturns in the black market than in the official market.

Table 2. Summary statistics on monthly exchange rate changes

Statistic DepDeo

Mean 0.009 −0.009Standard deviation 0.032 0.056Skewness 1.38* −0.40Kyrtosis 7.90* 17.63*D-statistic 0.258*0.296*B-J 295.26 2781.47*

59.32*Q(24) 50.87*Q2(24) 93.27*33.74*

Det=100 � [log et−log et−1]; D-statistic is the Kolmogorov–Smyrnov statistic for the null ofnormality; B-J is the Bera–Jarque test for the null hypothesis of normality; Q(24) and Q2(24) arethe Ljung–Box test statistics for up to 24th-order serial correlation in the Det and Det

2 series,respectively. An asterisk denotes statistical significance at the 5% critical level.

Copyright © 2001 John Wiley & Sons, Ltd. Int. J. Fin. Econ. 6: 13–25 (2001)

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A. KANAS AND G.P. KOURETAS18

4. ECONOMETRIC METHODOLOGY

This paper employs the GARCH model, developed by Bollerslev (1986), to study the time-seriesbehaviour of the Greek official and black market exchange rates. GARCH modelling of exchange rateshas been used extensively by several researchers, who found that the GARCH(1, 1) model describes dailyor weekly data of official exchange rates satisfactorily (Taylor, 1986; Akgiray, 1989; Baillie and Bollerslev,1989, 1990a,b; Hsieh, 1989a,b; McCurdy and Morgan, 1988). Although this model are widely used wepresent here a brief discussion.

A GARCH process of orders p and q, denoted as GARCH(p, q), can be described as follows:

et �Vt−1�F(mt, nt) (2)

mt=f0+f1et− j+ot (3)

nt=a0+ %p

i=1

aio t− i2 + %

q

j=1

bjnt− j (4)

and

ot=et−f0−f1et− i (5)

where p\0 and q]0 are the orders of the process, and the parameters satisfy the conditionsa0\0, ai, bj]0, i=1, . . . , p, j=1, . . . , q. F(mt, nt) is the conditional distribution of the variable, withconditional mean mt and variance nt. Vt−1 is the set of all information available at time t(et−1, et−2, . . . ).ot represents a market innovation or shock. The statistical properties of this class of processes have beenstudied by Weiss (1984), Bollerslev (1986) and Milhoj (1987). The empirical distribution of variablesgenerated by these processes are heavy tailed, compared to the normal distribution.

The unconditional mean and variance of a GARCH process are constant, but the conditional mean andvariance are time dependent. The conditional mean mt is linearly related to past innovations(moving-average process) which captures the presence of serial correlation in the et series and theconditional standard deviation intended to test for possible linkages between the first and secondmoments of the distribution of et. The conditional variance nt, is specified as a function of paststandardized innovations and past conditional variances and this is consistent with the actual volatilitypattern of the foreign exchange market where there are both stable and unstable periods. Normally, largervalues for innovations o t−1

2 , . . . , and/or past conditional variances nt−1, . . . , will result in larger valuesof nt, and vice versa.

To estimate the parameters u= (f0, f1, a0, . . . , ap, b0, . . . , bq) of a GARCH(p, q) model, it isnecessary to specify the conditional distribution function F(mt, nt). In this paper we follow Bollerslev(1987), Akgiray and Booth (1990) and Baillie and Bollerslev (1990a,b) and we use the student’st-distribution as the most appropriate. Given a sample of monthly returns, for our case, e1, . . . , et andinitial values e0, os, ns for s=0, . . . , r=max(p, q), the log-likelihood function is then given by:

%T

t=1

log f(yt/xt, yt−1; u)

=T log!G[(6+1/2]

[p1/2G(n/2)(n−2)−1/2

"− (1/2) %

T

t=1

log(ht)− [(n+1)/2] %T

t=1

log�

1+(yt−x %tb)2

ht(n−2)n

(6)

where f(yt/xt, yt−1; u) is the t-student density function, and mt and nt are calculated recursively byEquations (3)–(5). The maximum likelihood estimates of the parameters for the GARCH(p, q) areobtained from the numerical maximization of L(u �p, q). Furthermore, we are required to prespecify thevalues of p and q and then the likelihood function can be maximized for several combinations of p andq and the maximum values can be compared with the use of appropriate statistical tests in order to decideon the optimal order of the process. The BFGS algorithm is used to maximize L(U).3

Copyright © 2001 John Wiley & Sons, Ltd. Int. J. Fin. Econ. 6: 13–25 (2001)

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BLACK AND OFFICIAL EXCHANGE RATE VOLATILITY AND FOREIGN EXCHANGE CONTROLS 19

5. EMPIRICAL FINDINGS

5.1. Estimation of the GARCH Model

Table 3 presents the results of the GARCH(1, 1) model estimation for both exchange rates. TheGARCH coefficients a and b are statistically significant greater than zero according to the asymptotict-statistics for both cases. The strength of the significance for both exchange rates is one indication of theappropriateness of the GARCH models for the exchange rate data. Furthermore, we have applied therobust to non-normality Lagrange multiplier (LM) test statistic in order to evaluate the descriptivevalidity of the estimated models (Bollerslev and Wooldridge, 1992). Thus, the LM(2) statistic tests the nullhypothesis of normality against a data generation process that follows a GARCH(1, 1) specification andis statistically significant at the 5% critical level.4,5

Table 3 also reports the skewness and kyrtosis of the standardized residuals.6 In both cases a fall in thedegree of leptokyrtosis is shown compared to the one reported in Table 2 for the changes in the exchangerates. This finding indicates an improvement in the goodness of fit of the models. According to Jensen’sinequality, if the models are correctly specified then the coefficients of kyrtosis of the standardizedresiduals should be less than the kyrtosis of the original data (Hsieh, 1989a). However, kyrtosis of thestandardized residuals remains different from the normal value, a result which is in line with earlier

Table 3. Maximum-likelihood estimates of GARCH(1, 1) model

Statistic DepDeo

220Number of observations 220Likelihood function 587.50 534.05

−0.004*f0 0.0036*(2.562) (−2.055)

−0.0044f1 0.0778(−0.077) (1.183)

f2 0.155* 0.0122(2.793) (0.196)

f3 −0.0384 0.044(0.617)(−0.906)

0.00020.0009a0

(1.123) (1.209)

0.271a1 0.331(5.201)(5.662)

0.715b 0.559(8.333)(5.344)

13.77*14.26*LM(2) H0: a1=b=0m3 −3.11*1.11*m4 5.33* 14.41*

35.99Q(24) 34.9836.25Q2(24) 15.04

2.06*df 2.44*(57.34) (5.54)

Det=100 � [log et−log et−1]; for both exchange rates the mean equation is an AR(3); m3 and m4

are the coefficients of skewness and kyrtosis of the standardized residuals respectively;Q(24) and Q2(24) are the Ljung–Box statistics of 24th order of the standardized residuals andsquared standardized residuals, respectively. The number in parentheses are robust t-statistics,(Bollerslev and Wooldridge, 1992). df are the degrees of freedom of the t-distribution and theirstatistical significance implies departure from normality. An asterisk denotes statistical significanceat the 5% critical level.

Copyright © 2001 John Wiley & Sons, Ltd. Int. J. Fin. Econ. 6: 13–25 (2001)

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A. KANAS AND G.P. KOURETAS20

findings for daily data in McCurdy and Morgan (1987, 1988). Hsieh (1988, 1989a) and Baillie andBollerslev (1989, 1990a), for weekly data in Lastrapes (1989) and for the intraday rates in Baillie andBollerslev (1990b) and Engle et al. (1990).

An important element of the estimation results presented in Table 3 concerns the magnitude of theGARCH coefficients. The sum of the GARCH parameters (a1+b) is less than unity, and the b estimatesare substantially larger than those of a1. These results indicate that the fitted models are second-orderstationary and that at least the second moment exists (Bollerslev, 1986). Additionally, the sum (a1+b) isapproximately equal to 0.98 for the GARCH(1, 1) process in the official market and 0.93 for theGARCH(1, 1) process in the black market, evidence that the persistence in shocks to volatility is relativelylarge and that the response function of volatility of shocks decays at a relatively slow rate.7

5.2. Measuring the Effects of Capital Mo6ement Liberalization

Lamourex and Lastrapes (1990) argue that the presence of large persistence could implymisspecification of the variance due to a structural change in the unconditional variance of the process,as represented by changes in a0 in Equation (4). A one-time change in the unconditional variance of aprocess leads to the appearance of a sequence of large and small deviations which may considered aspersistence in a fitted GARCH model.

In January 1986 Greece began the process of relaxing the foreign exchange controls (Papaioannou andGatzonas, 1997). This process ended in May 1994 when all restrictions on short-run capital were lifted.In order to capture the possible effects on the volatility of the official and black exchange rates we includea dummy variable, which takes the value of 1 during the period of the capital movement liberalization and0 otherwise. Therefore, the GARCH(1, 1) model is modified to:

mt=f0+f1et−1+gDt+ot et �Vt−1�F(mt, nt) (7)

nt=a0+a1o t−12 +bnt−1+dDt (8)

where Dt is the foreign exchange control dummy variable.Table 4 presents the estimations for the modified GARCH models for the official and black market

exchange rates. The first important issue is concerned with the effectiveness of the capital controlsimposed by the Greek government and the Bank of Greece. This is tested through an LM(2) test with thenull hypothesis being g=d=0. The x2 statistic has a value 36.12 which is significant at the 5% level, andthus, we reject the null hypothesis that the foreign exchange controls are not statistically different thanzero, in the official market. Furthermore, the value of the kyrtosis statistic of the standardized residualsdecreased, which is an indication of an improvement in the specification of the model. The coefficient d

of the dummy variable Dt for the capital controls included in the conditional variance has a positive sign,which implies that the increased capital mobility since January 1986 resulted in an increase in the volatilityof the official drachma/dollar exchange rate.

Contrary to our findings for the official market the foreign exchange controls do not seem to have anyeffect on the volatility of exchange rates in the parallel market for dollars in Greece. The correspondingvalue of the LM(2) test is 3.77 which is not significant at the 5% level. Given that capital controls wereeffective in the official market, this finding is reasonable implying that economic agents could not evadethe controls by resorting to the black market.

An additional interesting point concerns the estimated constant coefficient f0 of the conditional meanequation. The estimated constant is statistically significant at the 5% level, for the official exchange rate,an indication of the degree of intervention by the Greek authorities in the foreign exchange market inorder to keep the official exchange rate on some trend (Table 4). Thus, the positive sign of the estimatedconstant highlights the official intervention to depreciate the drachma, a policy which was stronglyimplemented via the two devaluations of the drachma by 15% in January 1983 and October 1985. Thepreceding analysis is consistent with the finding that the estimated coefficient f0 in the black marketexchange rate equation does not show a significant drift, which might be an expected outcome given thatthis exchange rate is market determined.

Copyright © 2001 John Wiley & Sons, Ltd. Int. J. Fin. Econ. 6: 13–25 (2001)

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BLACK AND OFFICIAL EXCHANGE RATE VOLATILITY AND FOREIGN EXCHANGE CONTROLS 21

Table 4. GARCH estimation and allowing for a shift in policy concerning foreignexchange controls

Statistic Deo Dep

Number of observations 220 220Likelihood function 494.248 434.676

f0 0.0057* −0.004(3.137) (−2.22)

f1 0.028 0.071(0.355) (0.935)

f2 0.130 0.008(1.832) (1.124)

f3 −0.013 0.070(−0.202) (0.1.139)

g 0.090 0.041(1.854) (0.840)

a0 0.003* 0.0002*(5.801) (5.024)

a1 0.195* 0.289*(9.221) (4.366)

b 0.497* 0.401*(11.82) (5.887)

d 0.277* 0.006(2.687) (1.247)

LM(4) H0: g=a1=b=d=0 36.12* 3.55LM(2) H0: g=d=0 29.32* 1.68m3 0.96* −3.99*m4 4.19* 13.58*Q(24) 33.20 35.71Q2(24) 12.89 26.62

df 3.90* 2.20*(6.60) (25.23)

Det=100 � [log et−log et−1]; for both exchange rates the mean equation is an AR(3); m3 and m4

are the coefficients of skewness and kyrtosis of the standardized residuals respectively;Q(24) and Q2(24) are the Ljung–Box statistics of 24th order of the standardized residuals andsquared standardized residuals, respectively. The number in parentheses are robust t-statistics(Bollerslev and Wooldridge, 1992). df are the degrees of freedom of the t-distribution and theirstatistical significance implies departure from normality. An asterisk denotes statistical significanceat the 5% critical level.

The final issue, which needs further investigation, is the decline of the GARCH coefficients in theofficial market when the dummy variable is included. This seems to imply that the persistence of volatilityis reduced in the official market exchange rate when we take account of the policy change associated withthe abolition of capital controls. Thus, we observe that the sum (a1+b) has declined from 0.98 to 0.69.Lamourex and Lastrapes (1990) suggest a testing methodology that allows us to assess the statisticalsignificance of the decline in these coefficients. The test is to consider the null hypothesis that (a1+b) inthe restricted model equals (a1+b) in the unrestricted model, when the dummy variable is included,against the alternative hypothesis that (a1+b) in the unrestricted model is less than (a1+b) in therestricted model. High persistence in variance (measured by (a1+b) in the restricted model), and nodiscrete structural shifts are assumed under the null hypothesis. Furthermore, in order to control for TypeI, we adopt the bootstrap technique outlined in Lamourex and Lastrapes (1990) in order to characterize

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A. KANAS AND G.P. KOURETAS22

the sampling distribution of the estimator of (a1+b) in the unrestricted model under the nullhypothesis.8,9

The 5% critical values were found to be 0.723, which means that the probability is 5% that theunrestricted (a1+b) lies below 0.723, given that the null a1+b=0.98 is true. Therefore, we reject thenull hypothesis in favour of the alternative that the (a1+b) in the restricted model is greater than the(a1+b) in the unrestricted model. This finding provides support for the argument that shifts in policyregimes may result in the appearance of ARCH processes that are integrated in variance (Diebold, 1986;Lamourex and Lastrapes, 1990).

5.3. Forecasts of Volatility

The coefficient estimates in the previous section show that any realistic process for foreign exchangereturns must allow for high degrees of dependence in the series of conditional variances and, to a lesserextent, in the series of conditional means. Among other things, any intertemporal dependence is valuableinformation for forecasting purposes. In this section, we calculate several forecasts of foreign exchangereturns and we compare their accuracies. Given the set V0 of all information about past and presentreturns (e0, et−1, . . . ), forecasts of the variance of future returns (either var(e1�V0), or var(e1+ ···+eN)�V0

for some N) may be obtained.Forecasts of future variance are useful for a number of reasons. First, the forecasting performance of

the GARCH model provides additional evidence of its overall usefulness as practical model of exchangereturns. Second, given that risk is a major element of volatility, expected future volatility is an importantfactor in the pricing of financial assets. Thus, good predictions of volatility can be used to analyse anyrelation between current prices and expected risk.

Table 5 reports four statistics, namely the ME, the RMSE, the MAE, and the MAPE, which are usedto evaluate and compare the following forecasts; the benchmark forecast which is the simple historicalaverage; the exponential weighted moving average and the GARCH forecast. It clearly seen that theGARCH models can simulate the actual pattern of foreign exchange volatility very closely. The GARCHforecasts are generally less biased, as smaller ME values imply, and more accurate, as smaller values ofthe other three parameters imply. Therefore, we can conclude that ex ante measures of variance can besatisfactorily estimated by GARCH models of exchange returns. Although none of the forecasts are asaccurate as desirable (the smallest MAPE is greater than 30%), GARCH forecasts show substantialimprovement over the traditional forecasts such as the historical sample averages.

Table 5. Forecasts of monthly variances

GARCH forecastEWMA forecastHistorical estimateStatistic

0.001830.00245ME 0.000320.002590.0003260.00356RMSE

0.000325 0.000398MAE 0.00237MAPE 0.519 0.460 0.260

EWMA=exponential weighted moving average.Letting Ei=Vs,z−Vs,z

(a) denotes the forecast error in the sth month, the statistics are calculated asfollowing:

ME= (1/24) %24

s=1

Es

RMSE=�

(1/24) % Es2n1/2

MAE= (1/24) %24

s=1

�Es �

MAPE= (1/24) %24

s=1

)Es

Vs

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BLACK AND OFFICIAL EXCHANGE RATE VOLATILITY AND FOREIGN EXCHANGE CONTROLS 23

As a final point in our discussion on the forecasting accuracy of the alternative models we may arguethat persistence in volatility may be a good reason for the GARCH results to be more accurate than thoseof the other models. The finding that a1+b is very close to unity and that this sum is dominated by b

indicates, as we have already explained, that changes in market volatility tend to be persistent, and thisis probably why GARCH forecasts are better than the others (Akgiray, 1989).

6. SUMMARY AND CONCLUSIONS

The empirical evidence presented in this paper indicates that time series of monthly Greek official andblack market exchange rates exhibit significant levels of dependence. The probability distribution of et isnot independent of et+s for several values of s. There are several important findings which stem from ourstudy. First, conditional heteroskedastic GARCH processes which allow for autocorrelation between thefirst and second moments of return distributions over time have been satisfactorily fitted to the monthlyofficial and parallel drachma/dollar exchange rate data. This result contradicts the argument of Domowitzand Hakkio (1985), Diebold (1988) and Baillie and Bollerslev (1989) that ARCH effects are particularlyhighly significant with daily and weekly data while these effects tend to weaken with less frequent data.An explanation for the presence of ARCH effects in monthly data has been put forward by Bollerslev etal. (1992) who argue that the reasons for the existence of ARCH effects in daily and weekly data such asthe amount and quality of information, may well persist with monthly data as well, and this may be moreevident in the parallel market for foreign exchange. Second, there is evidence that the removal of foreignexchange controls by the Greek authorities since January 1986, led to an increase in the volatility of thedrachma/dollar official exchange rate. Third, for both the official and black market drachma/dollarexchange rates we provide evidence of persistence of shocks to volatility. Furthermore, such volatilitypersistence is decreased in the case of the official exchange rate when we take into consideration therelaxation of foreign exchange controls in January 1986. Finally, the ability to forecast the volatility offoreign exchange returns of the GARCH class of models has been examined and it was shown that theGARCH(1, 1) model provides better fit and forecast accuracy for both markets than two traditionalmeasures, a result that may be explained by the presence of persistence in market volatility.

ACKNOWLEDGEMENTS

Part of this paper was written while the second author was Visiting Fellow at the Department ofEconomics, European University Institute, San Domenico di Fiesole, Italy. The hospitality of EUI andthe Robert Schuman Centre is gratefully acknowledged. The second author also acknowledges generousfinancial support from EUI. An earlier version of the paper was presented at the 2000 European FinancialManagement Association Meetings, Athens, 28 June–1 July 2000 and thanks are due to conferenceparticipants for many helpful comments and discussions. This paper has also benefited from commentsduring workshops at Athens University of Economics and Business, European University Institute,Michigan State University, University of Crete, University of Cyprus, University of Birmingham andUniversity of Essex. We would also like to thank without implicating Michael Artis, Richard Baillie,Anindya Banerjee, Dimitris Georgoutsos, Soren Johansen, Katarina Juselius, Aris Spanos, Peter Schmidtand Jeffrey Wooldridge for many helpful comments and discussions.

NOTES

1. See, for example, Dooley and Isard (1980), Otani and Tiwari (1981), Claasen and Wyplosz (1982), Giavazzi (1986) and Phylaktis(1988, 1990), Artis and Taylor (1989), whereas Otani (1983) examined the effects of foreign exchange controls on the officialexchange market for Japan.

2. The standard errors for skewness and kyrtosis are (6/T)1/2 and (24/T)1/2, respectively.3. This is the Broyden, Fletcher, Golfarb and Shanno algorithm. See Press et al. (1988).4. Higher-order GARCH processes were modelled but did not prove superior to the GARCH(1, 1) specification. Given that

different GARCH(p, q) are nested within some higher order GARCH model, this task can be accomplished through a likelihood

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A. KANAS AND G.P. KOURETAS24

ratio (LR) test that has been developed by Engle (1982) and Bollerslev (1986) for the respective cases of the ARCH and GARCHmodels. The LR test statistic is specified as LR(number of constraints)=2[max L(unconstrainted)−max L(constrained)] and isasymptotically distributed as a x2 with degrees of freedom equal to the difference in the number of parameters under the null andthe alternative hypothesis.

5. Koutmos and Theodossiou (1994) have found similar results for several weekly drachma exchange rates. However, they arguedthat an EGARCH-M(1, 1) model is the most appropriate to model the distribution of these weekly rates.

6. The standardized residuals are defined as w= ot/n t1/2.

7. Engle and Bollerslev (1986), Bollerslev (1987), McCurdy and Morgan (1987, 1988), Hsieh (1988, 1989a), Akgiray (1989), Baillieand Bollerslev (1989), and Lastrapes (1989) are among the many studies which have found similar results about the persistenceof volatility shocks in the foreign exchange markets.

8. To test the null hypothesis, we draw 500 bootstrap samples from the standardized residuals of the restricted GARCH(1, 1) model.The bootstrap residuals, which contain the characteristics of the actual distribution, are transformed into a true GARCH(1, 1)with b=0.99. For each of the 500 realizations of the true process, the GARCH model is estimated under the null. The fifthpercentile value (0.9558) is subtracted from the value of 0.99. This deviation (0.0342) is in turn subtracted from bunder therestricted estimation.

9. Phylaktis and Kassimatis (1997) received similar results for the case of four Pasific Basin countries.

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