Modelling International Tourism Demand and Volatility in Small Island Tourism Economies. Riaz Shareef* and Michael McAleer*

Transcription

1 Modelling Inernaional Tourism Demand and Volailiy in Small Island Tourism Economies By Riaz Shareef* and Michael McAleer* *School of Accouning, Finance and Economics Edih Cowan Universiy **School of Economics and Commerce, Universiy of Wesern Ausralia School of Accouning, Finance and Economics & FIMARC Working Paper Series Edih Cowan Universiy December 2005 Working Paper 0517 Correspondence auhor: Riaz Shareef School of Accouning, Finance and Economics Faculy of Business and Law Edih Cowan Universiy 100 Joondalup Drive Joondalup WA 6027 Ausralia Phone: Fax: r.shareef@ecu.edu.au

2 Absrac Small Island Tourism Economies (SITEs) vary in heir size, land area, locaion, narrow resource bases, economic developmen, an overwhelming reliance on ourism, and a consisen inflow of foreign direc invesmen for economic growh. SITEs differ in heir ehnic diversiy, poliical sysems, economic and environmenal vulnerabiliy, ecological fragiliy, and he risks facing invesors. Owing o naural disasers, ehnic conflics, crime, and he hrea of global errorism, here have been dramaic changes in he arrivals of inernaional ouriss o SITEs. These variaions in inernaional ourism demand o SITEs, paricularly he condiional variance (or volailiy) in inernaional ouris arrivals, have no previously been analysed in he ourism research lieraure. An examinaion of he condiional volailiy of inernaional ouris arrivals is essenial for policy analysis and markeing purposes. This paper models he condiional mean and condiional variance of he logarihm of monhly inernaional ouris arrivals and he growh rae (or log-difference) in he monhly inernaional ouris arrivals for six SITEs, namely Barbados, Cyprus, Dominica, Fiji, Maldives, and Seychelles. Diagnosic checks of he regulariy condiions of he logarihm of monhly inernaional ouris arrivals and heir growh raes sugges ha he esimaed univariae models of rends and volailiy are saisically adequae. Therefore, he esimaed models are appropriae for purposes of public and privae secor managemen of ourism. Keywords: Island economies; small size; vulnerabiliy; inernaional ourism demand; arrival rae; rends; volailiy; ime-varying condiional variance; GARCH; GJR; asymmery; shocks; regulariy condiions Acknowledgemens: The auhors wish o hank Felix Chan, Suhejla Hoi, Chrisine Lim and wo anonymous referees for helpful commens and suggesions. The firs auhor is mos graeful for a UWA Research Gran, and he second auhor wishes o acknowledge financial suppor of Ausralian Research Council.

3 1. Inroducion Among academics and mulilaeral organisaions, he ineres in research surrounding all aspecs of he world s small island economies has been growing rapidly. Islands wih small populaions are also very small erriorially, and hese wo aspecs of heir smallness end o be conneced. These counries differ in he exen o which hey are home o differen ehnic minoriies, poliical culures, hisorical experiences and vulnerabiliy o exernal inervenions and naural disasers, ecological fragiliy, and percepions of insulariy and heir underlying consequences. They share common characerisics such as relaively small populaions, low producive capaciy, ecological surroundings, and pleasan climaes, all of which foser ourism. Decolonisaion led o poliical expecaions by he world s smalles islands, which achieved independence and consolidaed heir posiions in he Unied Naions. The increasing imporance and paricular problems of small islands have been capured in he Briish Commonwealh s research publicaions and developmen projecs. These developmens have produced a variey of island-relaed research programmes a mulilaeral agencies and academic insiuions, which have addressed he special problems and opporuniies associaed wih hese small island economies in a period of globalisaion. Regarding he economies analysed in his paper, he mos frequenly examined aspec has been heir delicae ecosysems o global warming and rises in sea levels. These counries have voiced heir concerns abou global warming and rises in sea levels in various inernaional fora, and are signaories o inernaional environmenal agreemens peraining o he reducion of greenhouse gases, mos recenly he Kyoo Proocol. There is only a scan lieraure on he significance of ourism in Small Island Tourism Economies (SITEs) and heir economic implicaions. Alhough inernaional ourism is presenly he fases growing and mos imporan radeable secor in he world economy, his imporan secor has ofen been negleced and he exan lieraure is limied. Consequenly, lile is known abou he relaionship beween ourism developmen and economic performance, paricularly wih respec o SITEs. The fundamenal aim of his paper is o assess he flucuaions and volailiy in ouris arrivals o SITEs. Since SITEs depend primarily on ourism earnings as a source of foreign exchange and employmen, a careful

4 2 examinaion of he volailiy of ouris arrivals is imporan o formulae macroeconomic policy, as well as decision making in he public and privae secors. Demand heory suggess ha subsiuabiliy or complemenariy beween wo producs is associaed wih he sign of he cross-price elasiciy, which should be derived from an appropriae demand models (see, for example, De Mello e al. (2002), who used an AIDS model). However, due o daa consrains, especially a he monhly level, i is no possible o formulae such economic models for some of he SITEs examined in his paper. Owing o ime-varying effecs such as naural disasers, ehnic conflics, crime, and he hrea of global errorism, among ohers, here have been dramaic changes in he arrivals of inernaional ouriss o SITEs. Variaions in inernaional ourism demand, paricularly he condiional variance (or volailiy) in inernaional ouris arrivals, have recenly been invesigaed in he ourism research lieraure (see Chan e al. (2004), Chan e al. (2005), Shareef and McAleer (2005), and Hoi, León and McAleer (2005)). The plan of he paper is as follows. Secion 2 discusses he salien feaures of SITES and heir implicaions for inernaional ourism. Secion 3 provides qualiaive descripions regarding he paerns of ourism in 6 SITEs. Secion 4 describes he daa used, namely he logarihm of inernaional ouris arrivals and he growh rae (or log-difference) of inernaional ouris arrivals in hese 6 SITEs. Specificaions of wo univariae volailiy models, namely he Generalised Auoregressive Condiional Heeroscedasiciy (GARCH) model of Engle (1982) and Bollerslev (1986), and he asymmeric GJR model of Glosen, Jagannahan and Runkle (1992), are esimaed and discussed in Secion 5. This is followed by a discussion of he empirical resuls in Secion 6. Some concluding remarks are given in Secion Salien Feaures of SITEs and Their Implicaions for Volailiy in Inernaional Tourism The debae regarding he size of an economy in he lieraure has coninued for a considerable period, bu agreemen has no ye been reached. Armsrong and Read (2002) have argued ha in he exising concepualisaions of size, here is a endency o include larger economies and o exclude smaller economies. Researchers have used commonly

5 3 available macroeconomic variables, such a populaion, GDP and land area o deermine he size of he economy. For example, Kuznes (1960) considered small economies as hose wih a populaion of less han 10 million, whereas Robinson (1960) argued ha economies wih a populaion of beween 10 o 15 million were small. Furhermore, he Briish Commonwealh considers a small economy when he populaion is less han one million. Armsrong and Read (1995) applied microeconomic heory in a macroeconomic framework o address he issue of size, paricularly wih respec o small economies. They argued ha he mos appropriae mehodology o deermine he size of an economy would be o apply he concep of subopimaliy by incorporaing producion and rade. In his formulaion, he minimum efficien scale (MES) is he opimal level of oupu ha would deermine he size of an economy. In order o deermine he choice of economies for an empirical analysis, an upper limi of populaion or GDP has no been used because economies can exceed an arbirary limi bu reain he characerisics of a small economy. There are six SITEs examined in his paper, hese being he only SITEs for which monhly inernaional ouris arrivals daa are available. As given in Table 1, hese SITEs are home o slighly more han wo million people. All of he economies included in his paper are former Briish colonies, and have gained independence during he las fory years. Two of he six SITEs are in he Caribbean; one is in he Pacific Ocean, wo in he Indian Ocean, and one in he Medierranean. Dommen (1980) argues ha an island is land surrounded by waer, bu no all freesanding land masses are necessarily islands. However, all of he six SITEs examined in his paper are sovereign saes surrounded by waer. In he six SITEs, here are exensive coasal areas, including wha are widely regarded as some of he world s mos popular beaches. Furhermore, hey have one of he world s mos delicae ecosysems and are hreaened by frequen naural disasers, which can have serious economic and social implicaions. These six SITEs rely considerably on ourism, which accouns for a significan proporion of he levels of heir respecive GDP. In hese SITEs, ourism has been encouraged o earn foreign exchange o finance developmen expendiures, as well as for employmen. As illusraed in Figures 1a and 1b, hese SITEs rely subsanially on service indusries 1, of which ourism accouns for he highes proporion in expor earnings. In hese SITEs, he economic benefis are no fully absorbed ino he respecive economies due o he enclave naure of he

6 4 developmen in ourism faciliies. Tourism requires careful planning in order o achieve economic benefis ha will be susainable and also minimise any environmenal damage. According o he Commonwealh Secrearia/World Bank Join Task Force on Small Saes (2000), SITEs have displayed relaively profound volailiy in GDP. Owing o heir low relaive endowmens of naural resources, SITEs are more sensiive o changes in he inernaional marke condiions. Moreover, mos SITEs are considered environmenally vulnerable. Armsrong and Read (1998) have saed ha he mos sriking feaure of SITEs is heir narrow producive base and he small domesic marke. Therefore, SITEs end o specialise in one or wo economic aciviies, where ourism is he main economic secor. There is very lile agriculure and manufacuring in SITEs because expors from SITEs are uncompeiive and do no receive preferenial reamen in inernaional markes. SITEs have frequenly experienced naural disasers and are highly vulnerable, he mos recen example being he 2004 Boxing Day Tsunami. Briguglio (1995) saed ha vulnerabiliy consiues economic, sraegic and environmenal facors. In he afermah of his disaser, he world has winessed he scale of environmenal vulnerabiliy in he economy and social fabric of SITEs. In inernaional financial markes, SITEs are caegorised as highrisk eniies because of he frequen incidence of naural disasers. Therefore, i is difficul for SITEs o raise capial for developmen. The imporance of ourism in SITEs can be idenified by examining he policy areas where shocks o monhly inernaional ouris arrivals can have he mos profound impacs. Tourism earnings have a direc impac in he balance of paymens of SITEs. A posiive shock o inernaional ouris arrivals will improve he curren accoun balance and financial reserves. Hence, such an effec would srenghen exchange rae, would make impors cheaper, and would evenually improve he welfare of ciizens. In mos SITEs, several levies on ourism-relaed aciviies conribue direcly o governmen finances. Any posiive shocks will increase governmen revenues and provide greaer financial resources for developmen expendiure. Tourism requires low-skilled labour. I is probably no coincidence ha he economically acive populaion in SITEs has relaively low skills. An improvemen in he occupancy of ouris faciliies has a posiive impac on employmen. Finally, ourism has exensive muliplier effecs on he economy, whereby he relaively under-developed agriculural secor could be susained hrough servicing he ourism indusry. Similarly, he

7 5 consrucion, ranspor and communicaions indusries, and many oher ancillary services o he ourism secor, are indirecly affeced. For an exensive analysis of SITEs and he implicaions of being a SITE, see Chan e al. (2005), Hoi, McAleer and Shareef (2005), and Shareef and Hoi (2005). 3. Paerns of Inernaional Touris Arrivals in SITEs This secion examines he srucure of inernaional ouris arrivals in SITEs, which is imperaive in he assessmen of ouris demand. This will primarily enail esablishing wheher hese SITEs represen feaures of compeiive or complemenary ourism markes hrough comparing he cross-correlaion coefficiens. The cross-correlaions for he inernaional ouris arrivals are calculaed using he annual numbers of inernaional ouris arrivals from he eleven principal markes o he six desinaion SITEs during he period 1980 o Table 2 shows he mean percenages of he composiion of he principal eleven naionaliies of ouris arrivals o he six SITEs. Touriss from hese eleven differen markes accoun for a significan proporion in monhly inernaional ouris arrivals in SITEs. These eleven markes are USA, UK, Canada, France, Germany, Ialy, Japan, Swizerland, Sweden, Ausralia and New Zealand. These eleven ouris source counries are siuaion in varying disances from he six SITEs analysed in his paper. These eleven source markes have diverse social and economic culures bu hey accoun for more han sixy per cen of he monhly inernaional ouris arrivals in SITEs excep Dominica. Dominica is hos o a large proporion of US ouriss. In Barbados, Cyprus and Dominica, monhly inernaional ouris arrivals accoun for six of he eleven source counries. Fiji welcomed ouriss from seven of he eleven, while Maldives and Seychelles received ouriss from he mos number of source markes. As illusraed in Table 2, he USA, UK and German ouriss dominae ourism in hese SITEs. The highes mean percenages of US ouris arrivals feaure significanly in Barbados and Dominica in he Caribbean and followed by Fiji. The mean percenages of ouriss from UK are more evenly disribued among he six SITEs. Clearly, i is eviden ha Briish ouriss are he mos widely ravelled among he eleven differen source markes, owing o heir colonial heriage aached o hese SITEs. In general, European ouriss feaure more in

8 6 island desinaions relaive o heir US and Canadian counerpars. The visior profiles of Canadian, Swiss, Swedish and Japanese ouriss are mixed. 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. A preliminary analysis of he cross-correlaions of inernaional ourism provides background informaion on policies on long-erm ourism planning and markeing. In he lieraure on ourism demand, desinaions are considered as subsiues when hey are in he same geographic region or share similar characerisics. If he cross-correlaion coefficiens are negaive, hey are considered o be subsiues. Conversely, complemenariy among desinaions is recognised when he esimaed cross-correlaion coefficiens are posiive. In he ourism lieraure, he findings on subsiuabiliy or complemenariy of a desinaion are mixed. Anasasopoulos (1991) saes ha desinaions which are close o each oher have posiive and large relaive correlaion coefficiens. Addiionally, such correlaions are very low or negaive among desinaions which are far apar. Syriopoulos and Sinclair (1993) indicae ha desinaions show a wide range of subsiuabiliy and complemenariy, depending on he ouris originaing counries. Yannopoulos (1987) concluded ha, while economeric evidence suggess a complemenary relaionship beween wo desinaions, he relaionship may no necessarily be symmeric. Thus, an increase in inernaional ouris arrivals o Sri Lanka may increase inernaional ouris arrivals o he Maldives. Neverheless, an increase in inernaional ouris arrivals o he Maldives may no increase inernaional ouris arrivals o Sri Lanka, even hough he duraion of air ravel beween he wo counries is one hour. Whie (1985) found boh subsiuabiliy and complemenariy among desinaions for ravellers originaing from several differen counries. Rosensweig (1988) found a degree of boh compeiive and complemenary elasiciies for ourism in he Caribbean. In a sudy based on limied daa, Leiper (1989) deermined he main desinaion raios for several desinaions for ouriss from Japan, New Zealand and Ausralia. In his paper, inernaional ouris arrivals o six SITEs for he period approximae he oal demand for inernaional ourism. In spie of he limied daa availabiliy o assess he compeiive and complemenary relaionships of inernaional ourism demand

9 7 among SITEs, he broades possible marke srucure (ourism originaing counries) is considered. The cross-correlaions of inernaional ouris arrivals are given in Tables 3a-3l, which show ha he growh in inernaional ourism arrivals grew simulaneously in all six SITEs (Table 3a). The cross-correlaion coefficiens for oal inernaional ouris arrivals o all six SITEs have a range of 0.75 o 0.96, and are relaively large. For oal monhly inernaional ouris arrivals o hese SITEs, he esimaed cross-correlaion coefficiens sugges ha he six SITEs feaured are complemens. The main reason for he high esimaed cross-correlaion coefficiens is ha hese six desinaions (SITEs) have very similar economic, social and geophysical characerisics. These resuls are consisen wih previous findings in he lieraure. The correlaions were calculaed such ha he relaionship beween wo series x and y are given by 2 : and cxy ( l) r xy ( l) = (1) c (0) c (0) xx yy (l) c xy = T 1 = 1 T + 1 = 1 (( x (( y x)( y y)( x y)) / T x)) / T (2) where l = 0, ± 1, ± 2, For he eleven markes, he cross-correlaion coefficiens of inernaional ouris arrivals show considerable variabiliy. Thus, ouriss from some markes consider some desinaions as subsiues, while ouriss from oher markes consider hem as complemens. According o he esimaed cross-correlaion coefficiens, he Briish, French and Ialian ouriss consider all six SITEs as complemens, while he oher nine markes consider some as subsiues and some as complemens. The magniudes of he cross-correlaion coefficiens reveal ha Briish, French and Ialian ouriss judge hese six SITEs wih subsanial variaion in percepions. From he esimaed coefficiens, Briish and French ouriss judge hese six desinaions in a similar manner, while Ialians seem o show some discreion in heir judgmen. The US, Canadian, German and Swedish ouriss show a grea deal of cauious percepion abou he six SITEs,

10 8 wih a higher degree of variabiliy in he magniudes of he esimaed coefficiens. Swiss ouriss consider mos of he six SITEs as complemens, while revealing ha here is a grea deal of subsiuabiliy beween Seychelles, Barbados and Dominica. Japanese ouriss consider Seychelles o be subsiuable wih he oher five SITEs. 4. Characerisics of he Daa The empirical secion in his paper models he condiional volailiy of he logarihm of inernaional ouris arrivals and he growh rae of inernaional ouris arrivals in six SITEs. I is well known ha volailiy is a measure of he variaion in an asse price or asse reurn over a given period. Volailiy clusering is a phenomenon in he ime series of an asse price or asse reurn, where periods of high volailiy are observed as being followed by periods of low volailiy, and vice-versa For insance, sock reurns prior o an earnings announcemen are frequenly observed o have higher variance han hose observed during he weeks afer he release dae. For hese SITEs, he frequency of he daa observaions is monhly, and he sample periods are as follows: Barbados, January 1973 o December 2002 (Barbados Tourism Auhoriy); Cyprus, January 1976 o December 2002 (Cyprus Tourism Organizaion and Saisics Service of Cyprus); Dominica, January 1990 o December 2001 (Cenral Saisical Office); Fiji, January 1968 o December 2002 (Fiji Islands Bureau of Saisics); Maldives, January 1986 o June 2003 (Minisry of Tourism); and Seychelles, January 1971 o May 2003 (Minisry of Informaion Technology and Communicaion). In he case of Cyprus, monhly ouris arrivals daa were no available for 1995, so he mean monhly ouris arrivals for 1993, 1994, 1996 and 1997 were used in calculaing he rends and volailiies. As given in Figure 2, he logarihm of inernaional ouris arrivals o each of hese SITEs displays differen disinc seasonal paerns and increasing rends. Touris arrivals in Barbados exhibi cyclical movemens which maps wih he business cycles in he US economy. These business cycles are clear manifesaions of he boom period in he laer half of he 1970s, he recession resuling from he second oil price shock of 1979, and he recession in he early 1990s. In Cyprus, he 1991 Gulf War creaes a visible change in monhly inernaional ouris arrivals. There are disinc changes in monhly inernaional ouris arrivals in he respecive sample periods of Dominica and he Maldives. However, in Fiji, he coups d éa of 1987 and 2000 are quie noiceable. In Seychelles, ourism was

11 9 rapidly rising unil he second oil shock of 1979 and here afer he growh rae of inernaional ouris arrivals has sabilised. The volailiies of he logarihm of he deseasonalised and derended monhly ouris arrivals are illusraed in Figure 3. These volailiies were calculaed from he square of he 2 esimaed residuals ε from he following regression using non-linear leas squares: logta = ARMA(1,1) + 12 i= 1 2 * φ D + θ + θ + θ + ε (3) i i Vol ε = ε (4) 2 ( ) where TA is he oal monhly inernaional ouris arrivals a ime ; D i (= 1 in monh i = 1, 2,, 12, and = 0 elsewhere) denoes 12 seasonal dummies; = 1,... T, where T = 360, 324, 144, and 210 for Barbados, Cyprus, Dominica and Maldives, respecively; T = 88 and * = 89,..., 420 for Fiji; and T = 150 and * = 151,..., 389 for Seychelles. Several cases of volailiy clusering are observed for Barbados, Cyprus and Seychelles. In Barbados, in he firs half of he sample, monhly inernaional ouris arrivals have been highly volaile due o he business cycle effecs of he US economy. For Seychelles and Cyprus volailiy clusering is around he firs and second oil price shock of 1973 and 1979, respecively are quie eviden. While volailiy clusering for Maldives and Dominica is associaed wih seasonaliy of ouris arrivals, volailiy clusering in Fiji is associaed wih he coups d éa of 1987 and The log-difference of monhly inernaional ouris arrivals is defined as he growh rae of monhly inernaional ouris arrivals, and is illusraed in Figure 4. Excep for Fiji, we observe ha 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 volailiies of he growh rae of deseasonalised monhly inernaional ouris arrivals are given in Figure 5. These volailiies were calculaed from he square of he esimaed residuals, ν, from he following regression using non-linear leas squares: 2

12 10 Δ logta = ARMA(1,1) + 12 i= 1 φ D + ν (5) i i Vol 2 ( ) ν ν =. (6) In equaion (5), he dependen variable is he log-difference of TA. The volailiies among he six SITEs show slighly differen paerns over he respecive sample periods, wih he simple correlaion coefficiens for he volailiies in Figures 3 and 5 being 0.86, 0.93, 0.91, 0.98, 0.92 and 0.60 for Barbados, Cyprus, Dominica, Fiji, Maldives and Seychelles, respecively. There is clear evidence of volailiy clusering in he case of Barbados 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 2000, here is volailiy clusering. The srucure of volailiy in Fiji bears a resemblance o ha of a financial ime series wih less profound volailiy clusering, excep for ouliers, which signify he coups d éa of 1987 and In Seychelles, volailiy clusering is noiceable in he early 1970s, whereas in he Maldives, here are few exreme observaions and lile volailiy clusering. I is imporan o noe ha he volailiies of he logarihm of monhly inernaional ouris arrivals and he growh rae of monhly inernaional ouris arrivals o he six SITEs show somewha similar dynamic behavioural paerns. However, here are visible differences in he magniudes of he calculaed volailiies, paricularly in he cases of Barbados, Dominica, Fiji and Seychelles. This is plausible for monhly inernaional ouris arrivals, so here would seem o be a srong case for esimaing boh symmeric and asymmeric ARCHype condiional volailiy models for boh he logarihm of monhly inernaional ourism arrivals and heir log-differences o hese six SITEs. 5. Univariae Models of Volailiy in 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 (1982), as well as subsequen developmens in Bollersllev (1986), Bollerslev e al. (1992), Bollerslev e al. (1994), and Li e al. (2002), among ohers. The mos widely used variaion for symmeric shocks is he generalised ARCH (GARCH) model of

13 11 Bollerslev (1986). In he presence of asymmeric behaviour beween posiive and negaive shocks, he GJR model of Glosen e al. (1992) is also widely used. Ling and McAleer (2002a, 2002b, 2003) have made furher heoreical advances in boh he univariae and mulivariae frameworks. A comprehensive comparison of univariae and mulivariae, condiional and sochasic, volailiy models is given in McAleer (2005). Consider he ARMA(1,1)-GARCH(1,1) model for he logarihm of monhly inernaional ouris arrivals, log TA given in equaion (3), where D i are 12 seasonal dummies, is a linear ime rend, * is a linear ime rend afer he breakpoin, quadraic ime rend, and he uncondiional shocks are given by: 2 is a h ε = η, η iid (0,1) (7) h 2 = ω + αε 1 + βh 1 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 (namely, an indicaion of he srengh of he shocks in he shor run), while he GARCH (or β ) effec measures he conribuion of shocks o long-run persisence, α + β (namely, an indicaion of he srengh of he shocks in he long run). In equaions (3), (4), (5) and (6), he parameers are ypically esimaed by maximum likelihood o obain Quasi-Maximum Likelihood Esimaors (QMLE) in he absence of normaliy of η. The condiional log-likelihood funcion is given as follows: 2 l = 1 log h + ε. (8) 2 h I has been shown by Ling and McAleer (2003) 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 univariae GARCH (p,q) model.

14 12 Hence, a sufficien condiion for he QMLE of GARCH(1,1) o be consisen and asympoically normal is given by: 2 E [log( αη + β )] < 0. (9) McAleer e al. (2003) argue ha he log-momen condiion is no sraighforward o check in pracice as i involves he expecaion of an unknown random variable and unknown parameers. Thus, he sronger second momen condiion is far more sraighforward o check in pracice. 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, for which GJR(1,1) is defined as follows: h 2 = + ( α + γi ( η ε 1 + βh 1 ω 1)) (10) where ω > 0, α + γ 0 and β 0 are sufficien condiions for h > 0, and I η ) is an indicaor variable defined by: ( 1, η < 0 I( η ) = (11) 0, η 0. 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 γ effec,γ, measures he conribuion of shocks o boh shor run persisence, α +, and long 2 γ run persisence, α + β +. The necessary and sufficien condiion for he exisence of he 2 second momen of GJR(1,1) under symmery of η is given in Ling and McAleer (2002b) as: 1 α + β + γ < 1. (12) 2 The weaker sufficien log-momen condiion for he GJR(1,1) model is given by McAleer e al. (2003) as follows:

15 13 E 2 [(log(( α γi( η)) η β)] <. (13) McAleer e al. (2003) also demonsrae ha he QMLE of he parameers are consisen and asympoically normal if he log-normal condiion is saisfied, so ha he inferences drawn from he esimaed parameers are valid. 6. Empirical Resuls This secion models he volailiy of he logarihm of monhly inernaional ouris arrivals and he growh rae of monhly inernaional ouris arrivals using he GARCH(1,1) and GJR(1,1) models, as defined in equaions (7) and (10) for differen periods for six SITEs. In order o accommodae he presence of seasonal effecs and various deerminisic ime rends, he logarihm of ouris arrivals is given by equaion (3), and he condiional mean for he growh rae of monhly inernaional ouris arrivals is given by equaion (5). Modelling he mean equaion is imporan o esimae accuraely he uncondiional shocks, ε, from which o esimae he condiional variance, h. Time series daa on monhly inernaional ouris arrivals show a considerable degree of persisence. The lieraure on univariae ime series analysis of ourism demand has shown ha ARMA models fi he daa reasonably well. Moreover, for he six SITEs examined, here is evidence of non-lineariy in he series. In he cases of Fiji and Seychelles, here appear o be srucural breaks in early 1975 and mid-1983, respecively, and in hese have been accommodaed in esimaing he condiional means. Hence, an ARMA(p,q) specificaion is esimaed wih monhly seasonal dummies and various deerminisic ime rends, possibly wih breakpoins. In his paper, we have examined various orders of ARMA, and ARMA (1,1) seems o be he opimal specificaion based on he Akaike Informaion Crierion and Schwarz Bayesian Informaion Crierion. Esimaes of he parameers of he condiional mean and he condiional variance for he wo models using he six samples are given in Tables 4 o 7. The Bernd-Hall-Hall-Hausman (Bernd e al. (1974)) algorihm incorporaed in EViews 4.1 is used o obain he esimaes of he parameers. Where ieraions fail o converge, he Marquand algorihm is used. The hree enries correspond o he esimae (in bold), asympoic -raio and he Bollerslev-Wooldridge

16 14 (1992) robus -raio. A linear rend is used for Fiji before he breakpoin a April 1975, and a separae linear rend is used hereafer. Boh a linear and quadraic rend are used for Seychelles before he breakpoin a June 1983, and a separae linear rend is used hereafer. 6.1 Esimaes of he Logarihm of Monhly Inernaional Touris Arrivals The primary reason for modelling he logarihms and log-differences of monhly inernaional ouris arrivals raher han heir levels is he presence of uni roos in some of he series. The Phillips-Perron (PP) es for saionariy, wih runcaed lags of order 5, was conduced using he EViews 4.1 economeric sofware package for he six SITEs. In Table 4, he PP es resuls are presened for he respecive sample periods for he six SITEs. For Barbados, Cyprus, Fiji and Seychelles, he criical values a 5 and 10 percen are he same, and Dominica and Maldives share he same criical values a 5 and 10 percen. Excep for Maldives, he es reveals ha he logarihms of monhly ouris arrivals are saionary, while he log-difference series are saionary for all six SITEs. In conducing hese ess, differen opions of lags were used, bu he resuls were found o be robus. The PP es is considered superior o he more widely used Augmened-Dickey Fuller (ADF) es because he ADF akes ino accoun only serial correlaion, while he PP es accommodaes boh serial correlaion and heeroscedasiciy. Esimaes of GARCH(1,1) and GJR(1,1) for he logarihm of monhly inernaional ouris arrivals are given in Tables 5 and 6, respecively. The condiional mean esimaes for GARCH(1,1) and GJR(1,1) are somewha differen in he 6 SITEs. The AR(1) esimaes for GARCH(1,1) and GJR(1,1) are highly significan for all SITEs, showing a high degree of persisence of ouris visiaions o hese desinaions. All of he esimaed parameers for AR(1) in GARCH(1,1) and GJR(1,1) are very close o one. Moreover, i is imporan o noe he negaive coefficien of he AR(1) erm for Dominica and Maldives in he case of GARCH(1,1) and GJR(1,1), while he MA(1) esimaes are highly significan for only Barbados, Dominica, Fiji and Seychelles. The significance of he MA(1) erm indicaes ha he uncondiional shock in he previous period accouns for he deerminaion of ouris arrivals in he curren period. The large majoriy of he coefficiens of he 12 seasonal dummies incorporaed in he condiional mean are significan, indicaing ha here is srong seasonaliy in monhly

17 15 inernaional ouris arrivals in hese SITEs. Since he SITEs are locaed in ropical and subropical regions, while he ouris source markes are in he emperae zones, seasonaliy is generally observed during he colder monhs of he ouris source counries, paricularly November and December. This feaure of seasonaliy can be generalised across all SITEs. For Fiji, he same principle applies, bu since heir main ouris sources are in he souhern hemisphere, he monhs change o July and Augus, which are he coldes monhs of he year for Ausralian and New Zealand ouriss. Cyprus has he longes ouris season, which is from February o Augus. The esimaes of he seasonal dummy variables are no repored, bu are available on reques. 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 ω > 0, α 0, β 0 ensure posiiviy of he condiional variance are me for all six SITEs, excep for Maldives, where he ARCH effec is negaive for boh GARCH(1,1) and GJR(1,1). I is worh noing ha he log-momen and second momen condiions are saisfied for boh GARCH(1,1) and GJR(1,1) for all six SITEs, which is a srong empirical resul. Therefore, he momens exis, and he QMLE of he coefficiens of he condiional variance for boh hese models are consisen and asympoically normal. Hence, inference on hese esimaes can be implemened for policy analysis and formulaion. The asymmeric effecs, γ, given in Table 6 are generally saisfacory, wih he excepion of Dominica, where a negaive coefficien is recorded. This implies ha he effec of posiive shocks on condiional volailiy is greaer han negaive shocks in boh he shor run 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. Therefore, if here is an unexpeced fall in he number of monhly inernaional ouris arrivals in all six SITEs excep for Dominica, here will be greaer uncerainy surrounding ourism earnings. As a resul, earmarked developmen expendiures will have o be posponed, expecaions abou an exchange rae devaluaion or depreciaion will become greaer, and ourism service providers will be considering cos-cuing measures such as redundancy packages for employees. Furhermore, upgrading of some ouris faciliies and some conracion in he consrucion indusry may occur.

18 Esimaes of he Growh Rae of Monhly Inernaional Touris Arrivals The esimaes for GARCH(1,1) and GJR(1,1) for he growh rae of monhly inernaional ouris arrivals are given in Tables 7 and 8, respecively. The condiional means for boh GARCH(1,1) and GJR(1,1) vary among he six desinaion counries, bu no subsanially. The AR(1) esimaes for GARCH(1,1) are significan only for Barbados, Cyprus and Fiji, while he AR(1) esimaes for GJR(1,1) are significan for all SITEs, bu Seychelles. The MA(1) esimaes for GARCH(1,1) are significan for all SITEs, bu Maldives, while he MA(1) esimaes of GJR(1,1) are significan for all SITEs. Virually all of he esimaes of he seasonal dummy variables in boh GARCH(1,1) and GJR(1,1) are significan a he 5 percen level. The esimaes of he condiional volailiy using GARCH(1,1) and GJR(1,1) for he growh rae of monhly inernaional ouris arrivals are reasonable, excep for he Maldives. The log-momen condiion could no be calculaed for Dominica and Maldives because of he negaive esimae of he asymmery coefficien for Dominica, and he negaive esimaes of boh he asymmery coefficien and he GARCH effec for Maldives, while he second momen condiion is no saisfied for Maldives. However, he second momen condiion is saisfied for Dominica. Thus, inference regarding he esimaes may be suspec only for Maldives. For he oher five SITEs, eiher he log-momen condiion or he second momen condiion, or boh, is saisfied for GARCH(1,1) and GJR(1,1), so he QMLE are consisen and asympoically normal. An ineresing feaure of he resuls in Table 8 is ha he esimae of he asymmeric effec in GJR(1,1) 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 for hese hree SITEs. However, for Barbados, Cyprus, and Fiji, if here is a negaive shock o he expeced growh rae of monhly inernaional ouris arrivals, here will be greaer uncerainy in subsequen periods. This is perfecly plausible, paricularly as Fiji experienced miliary coups d éa in 1987 and 2000, which undermined he percepions of inernaional ravellers, and as Cyprus has had a volaile poliical climae for an exended period, which has creaed greaer uncerainy for ouriss.

19 17 7. Conclusion This paper examined he composiion, rends and volailiies of monhly inernaional ouris arrivals, and he growh rae of monhly ouris arrivals, for six SITEs, namely Barbados, Cyprus, Dominica, Fiji, Maldives and Seychelles. The relaive cross-correlaion coefficiens of monhly inernaional ouris arrivals showed ha all six SITEs are complemenary desinaions as far as oal monhly inernaional ouris arrivals are concerned. However, when he monhly arrivals from differen ouris source markes o hese six economies were examined separaely, some markes considered hese SITEs as subsiues as well as complemens. For purposes of esimaion, he condiional means of he logarihm of monhly inernaional ouris arrivals and he growh rae of monhly inernaional ouris arrivals were specified for each SITE as ARMA(1,1) models. In addiion, 12 monhly seasonal dummy variables were included in each case, as well as a combinaion of linear and quadraic ime rends for he monhly ourism arrivals. Two models, namely GARCH(1,1) and GJR(1,1), were used o esimae he condiional volailiy of he shocks o ourism arrivals o each of hese SITEs. Esimaes based on he respecive sample periods for each of he SITEs for boh he logarihm of monhly inernaional ouris arrivals and he growh rae of monhly inernaional ouris arrivals were found o be saisfacory, in general. The log-momen and second momen condiions were ypically saisfied empirically, so ha he momens exised and he QMLE were boh consisen and asympoically normal. This gave subsanial suppor o he saisical adequacy of he empirical esimaes of he condiional volailiies. Therefore, he esimaed models are appropriae for purposes of public and privae secor managemen of ourism. The logarihm of monhly inernaional ouris arrivals was saionary for all six SITEs, excep for Maldives, and he growh rae of monhly inernaional ouris arrivals was saionary for all six SITEs. Therefore, inference on he esimaes was valid. The esimaes of he GJR (1,1) model for he growh rae of monhly inernaional ouris arrivals for Barbados, Cyprus and Fiji provided he mos accurae informaion for policy formulaion. If here were an unanicipaed fall in monhly ouris arrivals due o unexpeced shocks, such as he US

20 18 business cycles for he case of Barbados, he unfavourable poliical developmens in Cyprus and he coups d éa in Fiji, his would creae greaer uncerainy for monhly inernaional ouris arrivals. In such cases, governmens would have o revise heir expeced revenues and migh have o forego cerain projecs. Touris service providers would also have o adjus heir operaions, wih a view o greaer uncerainy in capaciy uilisaion.

21 19 Noes 1. These include value added in wholesale and reail rade (including hoels and resaurans), ranspor, governmen, financial, professional, and personal services such as educaion, healh care and real esae services. 2. These specificaions are given in EViews 4.1 Users Guide, p. 214.

22 20 References Anasasopoulos, P. (1991), Demand for Travel, Annals of Tourism Research, 18, Armsrong, H.W. and R. Read (1995), Wesern European Micro-Saes and Auonomous Regions: The Advanages of Size and Sovereigny, World Developmen, 23(7), Armsrong, H.W. and R. Read (1998), Trade and Growh in Small Saes: The Impac of Global Trade Liberalisaion, World Economy, 21(4), Armsrong, H.W. and R. Read (2002), The Phanom of Libery?: Economic Growh and he Vulnerabiliy of Small Saes, Journal of Inernaional Developmen, 14(3), Bernd, E.K., B.H. Hall, R.E. Hall and J. Hausman (1974), Esimaion and Inference in Nonlinear Srucural Models, Annals of Economic and Social Measuremen, 3, Bollerslev, T. (1986), Generalised Auoregressive Condiional Heeroscedasiciy, Journal of Economerics, 31, Bollerslev, T., R.Y. Chou and K.F. Kroner (1992), ARCH Modelling in Finance: A Review of he Theory and Empirical Evidence, Journal of Economerics, 52, Bollerslev, T., R.F. Engle and D.B. Nelson (1994), ARCH Models in R.F Engle and D.L McFadden (eds.), Handbook of Economerics, 4, (Norh Holland-Amserdam), pp Bollerslev, T. and J.M. Woodridge (1992), Quasi-maximum Likelihood Esimaion and Inference in Dynamic Models wih Time-Varying Covariances, Economeric Reviews, 11, Briguglio, L. (1995), Small Island Developing Saes and Their Economic Vulnerabiliies, World Developmen, 23(9), Chan, F., S. Hoi, R. Shareef and M. McAleer (2005), Forecasing Inernaional Tourism Demand and Uncerainy for Barbados, Cyprus and Fiji, in A. Lanza, A. Markandya and F. Pigliaru (eds.), The Economics of Tourism and Susainable Developmen, Edward Elgar, UK, pp Chan, F., C. Lim and M. McAleer (2004), Modelling Mulivariae Inernaional Tourism Demand and Volailiy, Tourism Managemen, 26, Commonwealh Secrearia/World Bank Join Task Force on Small Saes (2000), Small Saes: Meeing Challenges in he Global Economy, London: Commonwealh Secrearia/Washingon, D.C., The World Bank. De Mello, M., A. Pack and M.T. Sinclair (2002), A Sysem of Equaions Model of UK Tourism Demand in Neighbouring Counries, Applied Economics, 34,

23 21 Dommen, E. (1980), Some Disinguishing Characerisics of Island Saes, World Developmen, 8, Engle, R.F. (1982), Auoregressive Condiional Heeroscedasiciy wih Esimaes of he Variance of Unied Kingdom Inflaion, Economerica, 50, Glosen, L., R. Jagannahan and D. Runkle (1992), On he Relaion Beween he Expeced Value and Volailiy of Nominal Excess Reurn on Socks, Journal of Finance, 46, Hoi, S., C.J. León and M. McAleer (2005), Modelling he Uncerainy in Inernaional Touris Arrivals o he Canary Islands, unpublished paper, School of Economics and Commerce, Universiy of Wesern Ausralia. Hoi, S., M. McAleer and R. Shareef (2005), Modelling Inernaional Tourism and Counry Risk Spillovers for Cyprus and Mala, unpublished paper, School of Economics and Commerce, Universiy of Wesern Ausralia. Jeanheau, T. (1998), Srong Consisency of Esimaors for Mulivariae ARCH Models, Economeric Theory, 14, Kuznes, S. (1960), Economic Growh of Small Naions, in E.A.G. Robinson (ed.), The Economic Consequences of he Size of Naions, London, Macmillan, pp Leiper, N. (1989), Main Desinaion Raios: Analyses of Touris Flows, Annals of Tourism Research, 16, Li, W.K., S. Ling and M. McAleer (2002), Recen Theoreical Resuls for Time Series Models wih GARCH Errors, Journal of Economic Surveys, 16, Reprined in M. McAleer and L. Oxley (eds.), Conribuions o Financial Economerics: Theoreical and Pracical Issues, Blackwell, Oxford, 2002, pp Ling, S. and M. McAleer (2002a), Necessary and Sufficien Momen Condiions for GARCH (r,s) and Asymmeric Power of GARCH(r,s) Models, Economeric Theory, 18, Ling, S. and M. McAleer (2002b), Saionary and he Exisence of Momens of a Family of GARCH Processes, Journal of Economerics, 106, Ling, S. and M. McAleer (2003), Asympoic Theory for a Vecor ARMA-GARCH Model, Economeric Theory, 19, McAleer, M. (2005), Auomaed Inference and Learning in Modeling Financial Volailiy, Economeric Theory, 21, McAleer, M., F. Chan and D. Marinova (2003), An Economeric Analysis of Asymmeric Volailiy: Theory and Applicaions o Paens, o appear in Journal of Economerics. Robinson, E.A.G. (ed.) (1960), Economic Consequences of he Size of Naions, London, Macmillan, pp

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25 Agriculure Manufacuring Indusry Services Barbados Cyprus Dominica Fiji Maldives Seychelles Figure 1(a): Economic Srucure of he Six SITEs Expors (% of GDP) ITRs (% of Expors) Barbados Cyprus Dominica Fiji M aldives Seychelles Figure 1(b). Inernaional Tourism Receips (ITRs) and Toal Expors

26 BARBADOS 13 CYPRUS DOMINICA F I J I MALDIVES 10 9 SEYCHELLES Figure 2: Logarihm of Monhly Inernaional Tourism Arrivals

27 BARBADOS.7.6 CYPRUS DOMINICA 1.6 F I J I MALDIVES SEYCHELLES Figure 3: Volailiy of he Logarihm of Monhly Deseasonalised and Derended Inernaional Tourism Arrivals

28 CYPRUS BARBADOS DOMINICA 1.2 F I J I MALDIVES.8.6 SEYCHELLES Figure 4: Growh Rae of Monhly Inernaional Touris Arrivals

29 BARBADOS CYPRUS DOMINICA FIJI MALDIVES.5 SEYCHELLES Figure 5: Volailiy of he Growh Rae of Deseasonalised Monhly Inernaional Touris Arrivals

30 28 Table 1: Common Size Measures of SITEs SITEs Mean GDP GDP per per Pop. (m) Pop. (m) capia capia (USD) (USD) Surface Area (km2) Barbados , , Cyprus , ,100 9,240 Dominica , , Fiji , ,400 18,270 Maldives , , Seychelles , , Mean , ,167 4,907 Source: World Developmen Indicaors (WDI) 2002, The World Bank, Table 2: Percenage Sources of Inernaional Touris Arrivals o SITEs SITEs USA CAN UK GER FRA ITA SWI SWE JAP AUS NZ Toal Barbados Cyprus Dominica Fiji Maldives Seychelles Source: World Tourism Organisaion and respecive Governmen Saisics Offices and Bureaux. The figures in Table 2 are he mean percenage sources of inernaional ouris arrivals in SITEs from 1980 o 2000 from USA, Canada (CAN), UK, Germany (GER), France (FRA), Ialy (ITA), Swizerland (SWI), Sweden (SWE), Japan (JAP), Ausralia (AUS) and New Zealand (NZ). - means he percenages are well below 1%.

31 29 Table 3: Cross-correlaions of Inernaional Touris Arrivals for Individual Markes (a) All Touriss (b) American Touriss BRB CYP DMA FJI MDV SYC BRB CYP DMA FJI MDV SYC BRB 1 BRB 1 CYP CYP DMA DMA FJI FJI MDV MDV SYC SYC (c) Canadian Touriss (d) Briish Touriss BRB CYP DMA FJI MDV SYC BRB CYP DMA FJI MDV SYC BRB 1 BRB 1 CYP CYP DMA DMA FJI FJI MDV MDV SYC SYC (e) German Touriss (f) French Touriss BRB CYP DMA FJI MDV SYC BRB CYP DMA FJI MDV SYC BRB 1 BRB 1 CYP CYP DMA DMA FJI FJI MDV MDV SYC SYC (g) Ialian Touriss (h) Swiss Touriss BRB CYP DMA FJI MDV SYC BRB CYP DMA FJI MDV SYC BRB 1 BRB 1 CYP CYP DMA DMA FJI FJI MDV MDV SYC SYC (i) Swedish Touriss (j) Japanese Touriss BRB CYP DMA FJI MDV SYC BRB CYP DMA FJI MDV SYC BRB 1 BRB 1 CYP CYP DMA DMA FJI FJI MDV MDV SYC SYC (k) Ausralian Touriss (l) New Zealand Touriss BRB CYP DMA FJI MDV SYC BRB CYP DMA FJI MDV SYC BRB 1 BRB 1 CYP na 1 CYP na 1 DMA na na 1 DMA na na 1 FJI 0.30 na na 1 FJI 0.70 na na 1 MDV 0.52 na na MDV 0.62 na na SYC 0.07 na na SYC na na Source: World Tourism Organisaion (WTO) and he respecive Governmen Saisics Offices and Bureaux.