Volailiy in Inernaional Tourism Demand for Small Island Tourism Economies Riaz Shareef and Michael McAleer School of Economics and Commerce, Universiy of Wesern Ausralia. (Riaz.Shareef@uwa.edu.au, Michael.McAleer@uwa.edu.au,) Absrac: Volailiy in monhly inernaional ouris arrivals is defined as he squared deviaion from mean monhly inernaional ouris arrivals. Consequenly, volailiy is direcly relaed o he sandard deviaion, which is a common measure of financial risk. Flucuaing variaions, or condiional volailiy, in inernaional monhly ouris arrivals are ypically associaed wih unanicipaed evens. There are imevarying effecs relaed o SITEs, such as naural disasers, ehnic conflics, crime, he hrea of errorism, and business cycles in ouris source counries, among ohers, which cause variaions in monhly inernaional ouris arrivals. In his paper, we show how he generalised auoregressive condiional heeroscedasiciy (GARCH) model can be used o measure he condiional volailiy in monhly inernaional ouris arrivals o six SITEs, namely Barbados, Cyprus, Dominica, Fiji, Maldives and Seychelles, and o appraise he implicaions of condiional volailiy of SITEs for modelling ouris arrivals. Keywords: Island economies, ouris arrivals, condiional volailiy, GARCH, GJR, regulariy condiions. 1. INTRODUCTION Volailiy in monhly inernaional ouris arrivals is defined as he squared deviaion from mean monhly inernaional ouris arrivals. Consequenly, volailiy is direcly relaed o he sandard deviaion, which is a common measure of financial risk. Monhly inernaional ouris arrivals o each of he six Small Island Tourism Economies (SITEs) analysed in his paper, namely Barbados, Cyprus, Dominica, Fiji, Maldives and Seychelles, exhibi disinc paerns and posiive rends. However, monhly inernaional ouris arrivals for some SITEs have increased rapidly for exended periods, and sabilised hereafer. Mos imporanly, here have been increasing variaions in monhly inernaional ouris arrivals in SITEs for exended periods, wih subsequenly dampened variaions. Such flucuaing variaions in monhly inernaional ouris arrivals, which vary over ime, are regarded as he condiional volailiy in ouris arrivals, and can be modelled using economeric ime series echniques. Flucuaing variaions, or condiional volailiy, in inernaional monhly ouris arrivals are ypically associaed wih unanicipaed evens. There are ime-varying effecs relaed o SITEs, such as naural disasers, ehnic conflics, crime, he hrea of errorism, and business cycles in ouris source counries, among many ohers, which cause variaions in monhly inernaional ouris arrivals. Owing o he naure of hese evens, recovery from variaions in ouris arrivals from unanicipaed evens may ake longer for some counries han for ohers. In his paper, we show how he generalised auoregressive condiional heeroscedasiciy (GARCH) model of Engle (198) can be used o measure he condiional volailiy in monhly inernaional ouris arrivals o six SITEs. An awareness of he condiional volailiy inheren in monhly inernaional ouris arrivals and echniques for modelling such volailiy are vial for a criical analysis of SITEs, which depend heavily on ourism for heir macroeconomic sabiliy. The informaion ha can be ascerained from hese models abou he volailiy in monhly inernaional ouris arrivals is crucial for policymakers, as such informaion would enable hem o insigae policies regarding income, bilaeral exchange raes, employmen, governmen revenue, and so forh. Such informaion is also crucial for decision makers in he privae secor, as i would enable hem o aler heir operaions according o flucuaions in volailiy. The GARCH model is well esablished in he financial economics and economerics lieraure. Exensive heoreical developmens regarding he srucural and saisical properies of he model 1
have evolved (for derivaions of he regulariy condiions and asympoic properies of a wide variey of GARCH models, see Ling and McAleer (00a, 00b, 003)). In his paper we model monhly inernaional ouris arrivals daa. GARCH is applied o model monhly inernaional ouris arrivals in SITEs, which rely overwhelmingly on ourism as a primary source of expor revenue. Such research would be expeced o make a significan conribuion o he exising ourism research lieraure. The GARCH model is appealing because boh he condiional mean, which is used o capure he rends and growh raes in inernaional ourism arrivals, and he condiional variance, which is used o capure deviaions from he mean monhly inernaional ouris arrivals, are esimaed simulaneously. Consequenly, he parameer esimaes of boh he condiional mean and he condiional variance can be obained joinly for purposes of saisical inference.this paper models he condiional volailiy of he logarihm of inernaional ouris arrivals and he growh rae of monhly inernaional ouris arrivals for six SITEs. As he effecs of posiive and negaive shocks in inernaional ourism arrivals may have differen effecs on ourism volailiy, i is useful o examine an asymmeric model of condiional volailiy. For his reason, wo popular univariae models of condiional volailiy, namely GARCH and he asymmeric GJR model of Glosen, Jagannahan and Runkle (199), are esimaed and discussed.. SMALL ISLAND TOURISM ECONOMIES In he lieraure on small economies, several aemps have been made o concepualise he size of an economy, ye here has been lile agreemen o dae. The issue of size firs emerged in economics of inernaional rade, where he small counry is he price aker; he large counry is he price maker wih respec o impors, and expor prices in world markes. SITE Mean (1980-000) Pop. (mills) GDP per capia ( 000 US$) Pop. (mills) Mean 000 GDP per capia ( 000 US$) Surface Area (km ) Barbados 0.6 7.1 0.7 8.3 430 Cyprus 0.69 10.0 0.76 14.1 9,40 Dominica 0.07 3.4 0.07 3.4 750 Fiji 0.73.3 0.81.4 18,70 Maldives 0.1 1.3 0.8 1.9 300 Seychelles 0.07 5.9 0.08 7.0 450 Mean 0.34 5.0 0.38 6. 4,907 Source: WDIs 00, The World Bank Table 1. Common Size Measures of SITEs Size is a relaive raher han absolue concep. In he lieraure, size deals wih quanifiable variables, where populaion, GDP and land area are mos widely used. Some noable examples in emphasising size are Kuznes (1960), where a counry wih a populaion of 10 million or less is regarded as small. By his measure, he World Bank s (00) World Developmen Indicaors (WDI) daa show here are 130 small economies. In Robinson (1960), a populaion hreshold of 10 o 15 million is used. Armsrong and Read (00) argue ha populaion is ofen used because i is convenien and provides informaion abou he size of he domesic marke and labour force. Clearly, here is debae as o he definiion of wha consiues a small counry. There are six SITEs examined in his paper, hese being he only SITEs for which monhly inernaional ouris arrivals daa are available. Viewing he populaions of hese 6 SITEs in Table 1, hey are home o over wo million people. Their populaions range in size from micro-economies like Dominica and Seychelles, wih populaions beween 50,000 and 100,000, o mini-economies like Barbados and Maldives, which have populaions beween 100,000 and 500,000, and Cyprus and Fiji, which have populaions beween 500,000 and 1 million. All of he economies repored in his paper are former Briish colonies, which gained independence during he laer half of he las cenury. All of hese SITEs have relaively large per capia GDP figures. SITEs in his paper are in four geographic regions of he world, wih of hem in he Caribbean, 1 in he Pacific Ocean, in he Indian Ocean, and 1 in he Medierranean. Tourism plays a dominan role in he economic well being of SITEs, and ourism earnings accoun for a significan proporion of he value added in heir naional produc. The fundamenal aim of ourism developmen in SITEs is o increase foreign exchange earnings o finance impors. These SITEs have an overwhelming reliance on service indusries, of which ourism accouns for he highes proporion in expor earnings. In economic planning, ourism has a predominan emphasis in SITEs where he climae is well suied for ourism developmen and he islands are sraegically locaed. The square of he deviaion from he mean of a GDP growh rae is known as he volailiy of GDP growh. In SITEs, he volailiy of GDP growh rae ends o be very high. Shareef (003) calculaed he real GDP growh rae and is volailiy for 0 SITEs. Mala in he Medierranean recorded he lowes mean volailiy for he period 1980-00, while S. Lucia in he Caribbean Sea recorded he highes mean volailiy of 56.9 for he same period.
SITEs need a consisen inflow of foreign capial o smooh ou consumpion over he long run, while compensaing for any adverse shocks o domesic producion. A common feaure of SITEs is ha hey depend heavily on foreign aid o finance developmen (see Commonwealh Secrearia/World Bank Join Task Force on Small Saes (000). Aid flows have dropped sharply during he las decade of he 0 h Cenury, due o he collapse of communism in Europe. Aid from donor counries has been divered owards former Sovie allies. SITEs have experienced a dramaic decline in per capia aid of around US$145 in 1990 o less han US$ 100 per capia in 000. They have very limied access o commercial borrowings because hese are perceived o suffer from frequen naural disasers or for oher reasons considered o be high risk. Alhough SITEs have achieved high average per capia GDP relaive o he larger developing counries, povery coninues o be an unabaed challenge. Generally, wih he increase in per capia GDP, here has been a decline in povery (Commonwealh Secrearia/World Bank Join Task Force on Small Saes (000)). However, here are a number of small economies ha have higher povery raes han refleced in heir per capia incomes, primarily because SITEs are island archipelagos. In such archipelagos, a large proporion of economic aciviy is confined o he capial, while he dispersed communiies remain poor. Povery prevalence becomes high wih he uneven disribuion of income. The high volailiy of GDP, ogeher wih he populaion s inabiliy o absorb negaive shocks o heir incomes, means ha inequaliy is furher aggravaed and hardship is inensified. 3. COMPOSTION OF TOURIST ARRIVALS IN SITES Tourism arrivals from eleven major markes represen a significan proporion of he oal inernaional ouris arrivals o SITEs. Among hese eleven markes are he world s riches seven counries, he Group of 7. The oher 4 counries, namely Swizerland, Sweden, Ausralia and New Zealand, are among he highes per capia income counries of he world. The eleven counries are geographically locaed wih varying measures of disance relaive o he six SITEs. These counries are diverse in heir social and economic culures, bu explain more han wo-hirds of he composiion of inernaional ouris arrivals in all he SITEs, excep for Dominica. The capaciy of he Dominican ourism indusry is relaively small compared wih he res of he six SITEs. Moreover, he relaively small magniudes of mean percenages of ouriss from a wide variey of naionaliies o Dominica is he dominan feaure, besides US ouriss dominaing he visior profile, accouning for jus below one-fifh. During he same period, in Barbados, Cyprus and Dominica, inernaional ouris arrivals accoun for six of he eleven source markes. While Fiji welcomed ouriss from seven of hese eleven sources, Maldives and Seychelles received ouriss from he mos number of source markes. The USA, UK and Germany are he dominan markes for ouriss o hese SITEs. Moreover, hese hree markes also correspond o quie subsanial mean percenages across mos of he SITEs. Alhough he USA is he world s larges and riches economy, heir prominence in inernaional ouris arrivals is noable only in he wo Caribbean SITEs, namely Barbados and Dominica, followed by Fiji. In he Indian Ocean SITEs, US ouriss feaure wih very low mean percenages. However, UK ouriss are spread more evenly among he six economies compared wih US ouriss. UK ouriss are he mos widely ravelled among he eleven ourism markes, arguably because of he Briish colonial heriage aached o hese SITEs. Generally, European ouriss seem o ravel o island desinaions compared wih US and Canadian ouriss. German ouriss have smaller magniudes han heir UK counerpars. The Germans are followed by French and Ialian ouriss who ravel more o he Indian Ocean SITEs as compared wih heir Medierranean and Caribbean counerpars. Canadian, Swiss, Swedish and Japanese ouris arrivals appear among hree SITEs, wih varying visior profiles. Canadians end o ravel o he Caribbean and he Pacific, Swiss and Swedish ouriss are presen among all he regions excep he Pacific, while Japanese ouriss appear in he Indian Ocean and Pacific Ocean SITEs. Ausralian and New Zealand ouriss ravel subsanially o SITEs in he Pacific region, bu heir arrivals are relaively small among he oher SITEs. 4. DATA This paper models he condiional volailiy of he logarihm and he growh rae of inernaional ouris arrivals in six SITEs. For hese SITEs, he frequency of he daa is monhly, and he samples are as follows: The sample periods for hese six SITEs are as follows: Barbados, January 1973 o December 00 (Barbados Tourism Auhoriy); Cyprus, January 1976 o December 00 (Cyprus Tourism Organizaion and Saisics Service of Cyprus); Dominica, January 1990 o December 001 (Cenral Saisical Office); Fiji, January 1968 o December 00 (Fiji Islands Bureau of Saisics); Maldives, January 1986 o June 003 (Minisry of Tourism); and Seychelles, January 1971 o May 003 (Minisry of Informaion Technology and Communicaion). In he case of Cyprus, monhly ouris arrivals daa were no 3
available for 1995, so he mean monhly ouris arrivals for 1993, 1994, 1996 and 1997 were used o consruc he daa for 1995 in esimaing he rends and volailiies in inernaional ouris arrivals. The logarihm of inernaional ouris arrivals o each of hese SITEs exhibis disinc seasonal paerns and posiive rends. For Barbados, here are some cyclical effecs, which coincide wih he business cycles in he US economy. These business cycles are he boom period in he laer half of he 1970s, he slump due o he second oil price shock of 1979, and he recession in he early 1990s. In Cyprus, he only visible change in monhly inernaional ouris arrivals is he oulier of he 1991 Gulf War. In Dominica and he Maldives, here are no apparen changes during he respecive sample periods. However, in Fiji, he coups of 1987 and 000 are quie noiceable. Unil he second oil shock of 1979, ourism was rapidly increasing in Seychelles, afer which he growh rae of inernaional ouris arrivals has sabilised. The volailiy of he logarihm of he deseasonalised and derended monhly ouris arrivals were calculaed from he square of he esimaed residuals using non-linear leas squares. The mos visible cases of volailiy cluserings of monhly inernaional ourism demand are Barbados, Cyprus and Seychelles. In Barbados, in he firs hird of he sample, monhly inernaional ourism arrivals have been highly volaile owing o he economic cycles in he US economy. For Cyprus and Seychelles, here is volailiy clusering in he lae-1970s o mid-1980s due o he second oil price shock. For Fiji, volailiy cluserings are virually non-exisen, whereas for Dominica and Maldives, volailiy seems o be accompanied by seasonaliy in ouris arrivals. The growh rae of monhly inernaional ouris arrivals is defined as he log-difference of monhly inernaional ouris arrivals. Viewing he growh raes for he six SITEs, excep for Fiji, here are dramaic changes in he magniudes of he growh raes of monhly inernaional ouris arrivals. Cyprus, Maldives and Dominica show a very high degree of variaion in he growh raes, in heir respecive samples. Barbados and Seychelles share similar growh raes, while Fiji shows he lowes variaions. The volailiy of he growh rae of deseasonalised monhly inernaional ouris arrivals is calculaed from he square of he esimaed residuals using non-linear leas squares. In his case, he dependen variable is he log-difference of TA. The volailiy among he six SITEs show slighly differen paerns over he respecive sample periods, wih he simple correlaion coefficiens for he volailiies being 0.86, 0.93, 0.91, 0.98, 0.9 and 0.60 for Barbados, Cyprus, Dominica, Fiji, Maldives and Seychelles, respecively. For Barbados, here is clear evidence of volailiy clusering during he early 1970s and in he mid- 1980s, afer which here is lile evidence of volailiy clusering. Volailiy clusering is visible for Cyprus in he mid-1970s. In Dominica, in lae 1999 and early 000, here is volailiy clusering. The volailiy srucure of Fiji resembles ha of a financial ime series, wih volailiy clusering no so profound, excep for ouliers, which signify he coups d'éa of 1987 and 000. In Seychelles, volailiy clusering is noiceable in he early 1970s, whereas in he Maldives, here are few exreme observaions and lile volailiy clusering. 5. UNIVARIATE MODELS OF TOURISM DEMAND This secion discusses alernaive models of he volailiy of he logarihm of inernaional ouris arrivals using he Auoregressive Condiional Heeroscedasiciy (ARCH) model proposed by Engle (198), as well as subsequen developmens in Bollersllev (1986). The mos widely used variaion for symmeric shocks is he GARCH model. In he presence of asymmeric behaviour beween posiive and negaive shocks, he GJR model of Glosen e al. (199) is also widely used. Ling and McAleer (00a, 00b, 003) have made furher heoreical advances in boh he univariae and mulivariae frameworks. 5.1. Symmeric GARCH(1,1) The uncerainy ( h ) in he ARMA(1,1)- GARCH(1,1) model for he logarihm of monhly inernaional ouris arrivals, log TA is given in Table, and he uncondiional shocks for monhly inernaional ouris arrivals are given by ε, where ω > 0, α 0 and β 0 are sufficien condiions o ensure ha he condiional variance h > 0. The ARCH (or α ) effec capures he shor-run persisence of shocks, while he GARCH (or β ) effec measures he conribuion of shocks o long-run persisence, α + β. The parameers are ypically esimaed by maximum likelihood o obain Quasi-Maximum Likelihood Esimaors (QMLE) in he absence of normaliy of η. I has been shown by Ling and McAleer (003) ha QMLE of GARCH (p,q) is consisen if he second momen is finie. The well known necessary and sufficien condiion for he exisence of he second momen of ε for GARCH(1,1) is α + β <1, which is also sufficien for consisency of he QMLE. Jeanheau (1998) showed ha he weaker log-momen condiion is sufficien for consisency of he QMLE for he 4
univariae GARCH (p,q) model. Hence, a sufficien condiion for he QMLE of GARCH(1,1) o be consisen and asympoically normal is given by he log-momen condiion (see Table ). 5.. Asymmeric GJR(1,1) The effecs of posiive shocks on he condiional variance h are assumed o be he same as negaive shocks in he symmeric GARCH model. Asymmeric behaviour is capured in he GJR model, as defined in Table, where ω > 0, α + γ 0 and β 0 are sufficien condiions for h > 0, and I( η ) is an indicaor variable (see Table ). The indicaor variable disinguishes beween posiive and negaive shocks such ha asymmeric effecs are capured by γ, wih γ > 0. In he GJR model, he asymmeric effec, γ, measures he conribuion of shocks o boh shor run persisence, α + γ /, and long run persisence, α + β + γ /. The necessary and sufficien condiion for he exisence of he second momen of GJR(1,1) under symmery of η is given in Table (see Ling and McAleer (00b)). The weaker sufficien log-momen condiion for GJR(1,1) is also given in Table. McAleer e al. (00) demonsraed ha he QMLE of he parameers are consisen and asympoically normal if he log-normal condiion is saisfied. Model Specificaion ARMA-GARCH (1,1): ε = η h, η iid (0,1) h = ω + αε + βh 1 1 Sufficien Condiions for h > 0 ω > 0. α 0 β 0 Regulariy Condiions Log-momen: E [log( αη + β )] < 0 Second Momen: α + β <1 ARMA-GJR(1,1): ε = η h, η iid (0,1) h = ω + ( α + γi ( η 1)) ε + βh 1 1 1, η < 0 I( η ) = 0, η 0 ω > 0 α +γ / 0 β 0 Log-momen: E [(log(( α + γi ( η )) η + β )] < 0 Second Momen: α + β + γ / < 1 Table. Symmeric GARCH (1,1) and Asymmeric GJR(1,1) Models of Condiional Volailiies 6. EMPIRICAL RESULTS The GARCH(1,1) and GJR(1,1) models are used for six SITEs o esimae he volailiy of he logarihm and he growh rae of monhly inernaional ouris arrivals. The empirical models used ake accoun of seasonal effecs and deerminisic ime rends. Uncerainy in ouris arrivals is esimaed from he uncondiional shocks in he condiional mean. In his paper, an ARMA(1,1) specificaion is esimaed wih monhly seasonal dummies and deerminisic ime rends. Esimaes of he parameers of he condiional mean and condiional variance for he GARCH(1,1) and GJR(1,1) models for 6 SITEs are available on reques. The Brend-Hall-Hall- Hausman (Bernd e al. (1974)) algorihm in EViews 4.1 is used o obain he esimaes of he parameers, wih boh asympoic -raios and he Bollerslev-Wooldridge (199) robus -raios. The esimaes for he logarihm of ouris arrivals are somewha differen in he 6 SITEs. The AR(1) esimaes are highly significan for all SITEs, showing a high degree of persisence of ouris arrivals o hese desinaions. A large majoriy of he 1 seasonal dummies for he logarihm of ouris arrivals are significan, indicaing srong monhly seasonaliy (he resuls are available on reques). As hese SITEs are in ropical and subropical regions, while he ouris source markes are in he emperae zones, seasonaliy is generally observed during November and December. This feaure of seasonaliy can be generalised across all SITEs. 5
For Fiji, he same principle applies, bu since heir main ouris sources are in he souhern hemisphere, he monhs change o July and Augus. Cyprus has he longes ouris season, which is from February o Augus. For he logarihm of monhly inernaional ouris arrivals, he esimaes of he condiional volailiy using GARCH(1,1) and GJR(1,1) are highly saisfacory. The sufficien condiions o ensure posiiviy of he condiional variance are me for all six SITEs, excep for Maldives. I is worh noing ha he empirical log-momen and second momen condiions are saisfied for boh models and all six SITEs, which indicaes model adequacy for policy analysis and formulaion. The asymmeric effecs are generally saisfacory, wih he excepion of Dominica. This implies ha he effec of posiive shocks on condiional volailiy is greaer han negaive shocks in he shor and long run. Thus, he resuls for Dominica sugges ha an unexpeced fall in monhly inernaional ouris arrivals decreases he uncerainy abou fuure monhly inernaional ouris arrivals, which is conrary o he resuls for he oher five SITEs. The esimaes for he growh rae of monhly inernaional ouris arrivals vary among he six desinaion counries, bu no subsanially. Virually all of he esimaed seasonal effecs in boh models are saisically significan. The esimaes of condiional volailiy for boh models using he growh in monhly inernaional ouris arrivals are reasonable, excep for he Maldives, so ha inferences regarding he esimaes are valid for 5 of he 6 SITEs. An ineresing feaure of he esimaes is ha he asymmeric effec is negaive for Dominica, Maldives and Seychelles. This oucome implies ha he shor and long run effecs of a negaive shock in he growh rae of monhly inernaional ouris arrivals will resul in less uncerainy in subsequen periods. However, for Barbados, Cyprus, and Fiji, if here is a negaive shock o he expeced growh rae of monhly inernaional ouris arrivals, here will subsequenly be greaer uncerainy. This is perfecly plausible, as Fiji experienced miliary coups in 1987 and 000, which undermined he percepions of inernaional ravellers, and as Cyprus has had a volaile poliical climae for an exended period, which creaed uncerainy in ouris arrivals. ACKNOWLEDGEMENTS The auhors wish o hank Felix Chan and Suhejla Hoi for helpful commens and suggesions. The firs auhor is mos graeful for an Ausralian Research Council Research Assisanship and a C.A. Vargovic Memorial Fund Award, School of Economics and Commerce, UWA, for financial suppor. The second auhor wishes o acknowledge he financial suppor of he Ausralian Research Council. REFERENCES Armsrong, H.W. and Read, R. (00), The Phanom of Libery?: Economic Growh and he Vulnerabiliy of Small Saes, Journal of Inernaional Developmen, 14 (3), 435-458. Bernd, E.K., Hall, B.H., Hall, R.E. and Hausman, J. (1974), Esimaion and Inference in Nonlinear Srucural Models, Annals of Economic and Social Measuremen, 3, 653-665. Bollerslev, T. (1986), Generalised Auoregressive Condiional Heeroscedasiciy, Journal of Economerics, 31, 307-37. Bollerslev, T. and Woodridge, J.M. (199), Quasi-maximum Likelihood Esimaion and Inference in Dynamic Models wih Time-Varying Covariances, Economeric Reviews, 11, 143-173. Commonwealh Secrearia/World Bank Join Task Force on Small Saes (000), Small Saes: Meeing Challenges in he Global Economy, London: Commonwealh Secrearia/Washingon, D.C., The World Bank. Engle, R.F. (198), Auoregressive Condiional Heeroscedasiciy wih Esimaes of he Variance of Unied Kingdom Inflaion, Economerica, 50, 987-1007. Glosen, L., Jagannahan, R. and Runkle, D. (199), On he Relaion Beween he Expeced Value and Volailiy of Nominal Excess Reurn on Socks, Journal of Finance, 46, 1779-1801. Kuznes, S. (1960), Economic Growh of Small Naions, in E.A.G. Robinson (ed.), The Economic Consequences of he Size of Naions, London, Macmillan, 14-3. Ling, S. and McAleer, M. (00a), Necessary and Sufficien Momen Condiions for GARCH (r,s) and Asymmeric Power of GARCH(r,s) Models, Economeric Theory, 18, 7-79. Ling, S. and McAleer, M. (00b), Saionary and he Exisence of Momens of a Family of GARCH Processes, Journal of Economerics, 106, 109-117. Ling, S. and McAleer, M. (003), Asympoic Theory for a Vecor ARMA-GARCH Model, Economeric Theory, 19, 78-308. McAleer, M., Chan, F. and Marinova, D. (003), An Economeric Analysis of Asymmeric Volailiy: Theory and Applicaions o Paens, o appear in Journal of Economerics. 6
Robinson, E.A.G. (ed.) (1960), Economic Consequences of he Size of Naions, London, Macmillan, 14-3. Shareef, R. (003), Small Island Tourism Economies: A Bird's Eye View, in D. Pos (ed.), Proceedings of he Inernaional Conference on Modelling and Simulaion: Socio-economic Sysems, Townsville, Ausralia, 3, 114-119. World Bank (00), World Developmen Indicaors, CD-ROM 7