DOCUMENT DE TREBALL XREAP

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1 DOCUMENT DE TREBALL XREAP EXPLAINING HIGH ECONOMIC GROWTH IN SMALL TOURISM COUNTRIES WITH A DYNAMIC GENERAL EQUILIBRIUM MODEL Carmen Álvarez-Albelo; Raúl Hernández-Marín

2 XREAP EXPLAINING HIGH ECONOMIC GROWTH IN SMALL TOURISM COUNTRIES WITH A DYNAMIC GENERAL EQUILIBRIUM MODEL Carmen Álvarez-Albelo a, Raúl Hernández-Marín b Absrac This paper shows ha ourism specialisaion can help o explain he observed high growh raes of small counries. For his purpose, wo models of growh and rade are consruced o represen he rade relaions beween wo counries. One of he counries is large, rich, has an own source of susained growh and produces a radable capial good. The oher is a small poor economy, which does no have an own engine of growh and produces radable ourism services. The poor counry expors ourism services o and impors capial goods from he rich economy. In one model ourism is a luxury good, while in he oher he expendiure elasiciy of ourism impors is uniary. Two main resuls are obained. In he long run, he ourism counry overcomes decreasing reurns and permanenly grows because is erms of rade coninuously improve. Since he ourism secor is relaively less producive han he capial good secor, ourism services become relaively scarcer and hence more expensive han he capial good. Moreover, along he ransiion he growh rae of he ourism economy holds well above he one of he rich counry for a long ime. The growh rae differenial beween counries is paricularly high when ourism is a luxury good. In his case, here is a faser increase in he ourism demand. As a resul, invesmen of he small economy is boosed and is erms of rade highly improve. Keywords: High growh, small ourism counries, erms of rade, luxury good, dynamic general equilibrium. JEL Codes: F43, O33, O4. a Deparmen of Economic Analysis, Universiy of La Laguna and CREB. b Deparmen of Applied Economics, Universiy of La Laguna.

3 XREAP Inroducion The specialisaion in ourism has deeply conribued o alleviae povery of counries, and especially of hose facing serious obsacles o developmen. As repored by he World Tourism Organisaion, ourism is one of he major expor secors of developing economies and is he primary source of foreign exchange earnings of he 46 of he 49 leas developed counries. A rigorous empirical analysis by Brau, Lanza and Pigliaru (007) has far confirmed his exen. More specifically, i has showed ha ourism economies have being growing a higher raes han oher counry groups, including he OECD. This resul is even more sriking if one akes ino accoun ha mos of hem are islands or archipelagos and, hence, face wo imporan difficulies for developmen: smallness and remoeness. This evidence poses wo quesions: Could growh of small ourism counries be susainable in he long run? How does ourism specialisaion operae in fuelling growh of hose economies? In his paper, we offer heoreical answers o hese quesions ha lie in wo facors: erms of rade improvemens, and he fac ha ourism is a luxury good (e.g. Lanza, Temple and Urga, 003; Smeral, 004). To do ha, we consruc a heoreical srucure ha represens he rade relaions beween a large rich counry (counry ) and a small poor economy (counry ). The heoreical srucure ness wo differen models ha only differ in preferences. In he firs one (model ) ourism services are a luxury good, while he expendiure elasiciy of ourism impors is uniary in he alernaive framework (model ). The models allow us o evaluae he impac of he specialisaion in he producion of a luxury good, namely ourism services, on economic growh. Our analysis is based on he following assumpions. Counry has exogenous improvemens of produciviy, while counry does no possesses an own source of susained growh. Counries and have comparaive advanage in he producion of capial goods and ourism services, respecively. The capial good producion is used wihin counry and also expored. The whole producion of ourism services of counry is bough abroad. In addiion, boh economies produce a non-radable good of consumpion. The represenaive household in counry derives uiliy from

4 XREAP consumpion and ourism services. Homes in counry only obain uiliy from consumpion. In boh models susained growh is ransmied from counry o counry. Therefore, we affirmaively answer he firs quesion. Counry overcomes decreasing reurns and permanenly grows in he long run because is erms of rade coninuously improve. This finding hinges on secoral relaive produciviy. Since he ourism secor is relaively less producive han he capial good secor, ourism services become relaively scarcer and hence more expensive han he capial good. The effecs of erms of rade improvemens on he growh rae of counry s income per capia operae hrough wo channels. Firs, hey imply an increase in he purchasing pariy power of counry and, second, hey allow a permanen increase in gross invesmen per capia and hus in capial per capia. A his poin, i is worhwhile o noice ha he engine of growh of counry canno be idenified using sandard echniques based on he compuaion of he Solow residual. In his sense, a sandard analysis of produciviy gains would lead o he wrong conclusion ha growh of counry will be exhaused in he long run. The answer o he second quesion is relaed o he ransiional behaviour of he economies. Therefore, we calibrae he models, numerically solve hem and compare heir resuls regarding he ime evoluion of counries growh raes. In he calibraion we impose a uniary price elasiciy of ourism demand because i allows us o isolae he effec of an increase in counry s income on is ourism impors and he economic growh of counry. Moreover, his choice is in he line of he empirical esimaes of his elasiciy. Our calibraion sraegy yields he same long run equilibrium in boh models, and hen heir predicions only differ due o he naure of ourism good. We have obained he resul ha ourism specialisaion has a posiive impac on counry s growh as long as ourism is a luxury good. More concreely, in boh models counry grows faser han counry, bu he growh rae differenial is significanly higher in model. The reason is wofold: he erms of rade improvemens and he accumulaion For insance, Smeral (004) obains a price elasiciy of ourism impors of.4. 3

5 XREAP of capial of counry are larger in model han in model. Indeed, along he ransiion he raio of ourism impors o income of counry grows much faser in model han in model. As a consequence, he increase in he relaive price of ourism services (counry s erms of rade) is higher in he firs model han in he laer one. Since invesmen of counry is deermined by is ourism expors, a higher capial accumulaion akes place in model han in model. The res of he paper is organised as follows. Secion exposes he empirical facs regarding counry size, ourism specialisaion and growh. Secion 3 oulines he models. Secion 4 solves for he compeiive equilibrium of he wo-counry economy and characerises he long run equilibrium. The calibraion of he models is described in Secion 5. Secion 6 exposes he oucomes from he compuaion of he models. Secion 7 summarises and concludes. Lasly, he hree appendices conain some echnical deails.. Sylised Facs Regarding Counry Size, Tourism Specialisaion and Economic Growh The analysis of he relaionship beween counry size, ourism specialisaion and economic growh allows wo relevan sylised facs o be observed. Firs, smaller counries end o be more specialised in ourism han bigger ones. Second, small counries specialised in ourism end o grow faser han oher groups of economies. Given ha ourism is considered a low produciviy secor, here seems o be a conradicion beween specialisaion in ourism and obaining high economic growh raes. There is no inernaionally agreed-upon indicaor for defining when a counry is said o be specialised in ourism. Here, we use as an indicaor he number of ouris arrivals in relaion o he local populaion. In his respec, Figure clearly shows ha, in he year 000, smaller counries received more ouriss per inhabian han larger ones. Taken from a sample of 79 counries for which daa was available. The year was chosen in order o avoid he insabiliy in inernaional ourism following 00. 4

6 XREAP Figure : Relaionship beween Touris Arrivals per Inhabian and Populaion, LN ouriss per hab Ln populaion y = -0,5069x + 5,653 R = 0,58 Source: World Developmen Indicaors, 00, World Bank. Though he explanaion of he posiive relaionship beween small size and ouris arrivals per inhabian is beyond he scope of his paper, i needs o be jusified. Hernández-Marín (006) menions four possible causes for his. Firs, small counries are ofen islands and islands have an aracion bonus; each island or small desinaion is viewed by ouriss as a differeniaed produc, and ouriss show a preference for variey. Second, small counries have ofen srong comparaive advanages in ourism because of he lack of indusrial alernaives due o high ranspor coss, lack of compeiion, scarciy of naural resources, diseconomies of scale, ec. Third, small counries ofen enjoy social and poliical cohesion and hus are viewed as safe places. Forh, small counries have been a preferred choice of our operaors due o heir dependence on air ravel. The indicaor used in Figure has he disadvanage of using arrivals for idenifying when a counry is specialised in ourism. I would be more accurae o use an indicaor capuring he economic imporance of inbound ourism. Given he non-exisence of 5

7 XREAP inernaional daa series regarding he ourism GDP, in Table we use ourism income in relaion o GDP as an indicaor 3. Table shows he characerisics of counries in he world wih he highes ourism specialisaion. Mos of hem are very small and mos of he small are islands. In he able, here are weny five counries wih a raio of ourism income o GDP higher han 0 percen. Among hose counries, weny one are small (less han one million inhabians), weny wo are islands, and he four larges ones have beween one and eigh million inhabians 4. Table : Counries wih he Highes Tourism Specialisaion, 998 Counry Tourism Receips/ GDP (%) Populaion Small Island Anigua and Barbuda 4, Yes Yes Araba 47, Yes Yes The Bahamas 3, Yes Yes Bahrain 0, Yes Yes Barbados 30, Yes Yes Belice 4, Yes No Cyprus, Yes Yes Dominica 4, Yes Yes Dominican Republic 3, No Yes Esonia, No No Fiji 6, Yes Yes Grenada 7, Yes Yes Jamaica 7, No Yes Jordan 3, No No Macao, China 40, Yes Yes Maldives 56, Yes Yes Mala 3, Yes Yes Mauriius 6, Yes Yes Palau 49,44 8,0 Yes Yes Samoa 7, Yes Yes Seychelles 3, Yes Yes S. Kis and Nevis 6, Yes Yes S. Lucia 45, Yes Yes S. Vincen and he Grenadines,6.80 Yes Yes Vanuau 30, Yes Yes Source: World Developmen Indicaors 00 and 005, World Bank. 3 The year 998 has been chosen because i is he period wih more available informaion and, in addiion, i is prior o 00 (see foonoe ). We have followed a sandard hreshold of one million inhabians o consider a counry as small (e.g. Easerly and Kraay, 000). 4 There were available daa for 64 counries. Of hose, 39 are large, 35 small and 4 islands. 6

8 XREAP The second sylised, namely he high economic growh of small counries specialised in he ourism indusry, has an even greaer scope. To his respec, Brau, Lanza and Pigliaru (007) reached he conclusion ha i is necessary o inroduce ourism specialisaion as an independen variable when analysing small counries, since hose specialised in his secor are no disadvanaged. On he conrary, as shown in Table, hey grew more han oher groups of counries during he period In his sense, we should add ha alhough smallness may consiue a disadvanage for economic developmen, when accompanied by ourism specialisaion i acually becomes an advanage. Furhermore, hese auhors found ha he higher growh experienced by small ourism counries is no due o he radiional deerminans of growh (i.e. he convergence effec, a greaer propensiy o savings-invesmen or greaer openness o rade), wha seems o reinforce he hypohesis ha he deermining facor of heir greaer rae of growh is he combinaion of ourism specialisaion and heir small size 5. Table : Economic Growh of Counry Groups, Counry group Growh of Number of GDP per capia (%) counries OECD.9 Oil exporer Small.70 9 Small ourism > Small ourism > Small < Less Developed Counries All counries Source: Brau, Lanza and Pigliaru (007). The high economic growh of small ourism counries conrass wih a large body of lieraure which highlighs he difficulies facing small economies (e.g. Sreeen, 993; Srinivasan, 986; Armsrong e al., 998). Some of hese sudies sress he difficulies experienced in achieving economies of scale, high ranspor coss, he lack of compeiion in domesic markes, ec. However, several empirical works have shown ha hose difficulies do no necessarily lead o lower growh. In fac, in heir exensive empirical review, Easerly and Kraay (000) failed o find worse economic resuls in he smaller counries han in he larger ones. 5 By ouris counries hese auhors mean counries for which ouris income exceeds 0% of he GDP. 7

9 XREAP The explanaions of he high growh raes of small ourism counries focus on four facors. Hernández-Marín (006) shows ha he secoral change from aciviies of low produciviy (e.g. agriculure) owards ourism can help explaining emporary high growh raes in small ourism counries. However, here is a relevan percenage of economic growh ha coninues unexplained. Lanza, Temple and Urga (003) have looked a wheher or no economic growh resuling from ourism specialisaion is susainable in he long run. The auhors emphasise he apparen conradicory fac of growh being fuelled by a secor wih low growh of produciviy. They offer wo coheren explanaions o his fac. The firs one is opimisic and saes ha he reduced produciviy growh in he ourism secor may be compensaed, on he one hand, by an improvemen in he erms of rade 6 in favour of he secor, on he oher hand, by he fac ha ourism can be considered a luxury good, which may promoe rapid growh in boh he secor iself and he res of he economy. The pessimisic explanaion says ha rapid growh is merely emporary if i is based on he increasing use of naural resources linked o ourism. As he economy approaches full employmen of hese resources, he evoluion of labour produciviy becomes a deermining facor of growh and, as a resul, ourism counries will grow more slowly han ohers. The auhors empirically esed he wo hypoheses and found suppor for he opimisic one. Neverheless, hey poined ou ha he resuls should be inerpreed wih cauion for wo reasons. Firsly, in he shor run he exisence of unemploymen may reduce he improvemen of erms of rade for ourism desinaions and, secondly, he emergence of new desinaions may lead o he same resul in he long run. The consequences of high ourism growh and specializaion have been sudied by Capó, Riera and Roselló (005), who consider high growh raes in island regions of Spain as a manifesaion of duch desease. This means ha explosive ourism growh in small open economies provokes boh ren and allocaion effecs ha resul in deindusrializaion. Neverheless, he paper is no clear enough abou why rapid ourism growh can be problemaic, and herefore he long run effecs of such a process are no clear. This is because, on he one hand, ourism specialisaion means an improvemen in 6 The relevance of erms of rade improvemens was also poined ou by Copeland (99). 8

10 XREAP welfare following comparaive advanages. Bu, on he oher hand, excessive specializaion in small ourism counries could lead o an increase in heir vulnerabiliy o exernal shocks. 3. The Models Time is discree and endless ( = 0,,,... ). There are wo counries denoed by i =,, ha are involved in rade of capial goods and ourism services. Counry is large and rich, has an own source of susained growh and is specialized in he producion of a capial or invesmen good. Counry represens a small and poor economy, which does no possess an own engine of growh and is specialized in he producion of ourism services. The capial good producion is used wihin counry and also expored. The whole producion of ourism services of counry is bough abroad. In addiion, boh counries produce a non-radable good of consumpion. The capial good is aken as numeraire. The ime evoluion of populaion is crucial in our analysis because he growh possibiliies of counry depend, in a grea exen, on how he relaive size of he economies evolves hrough ime. Thus, we have o inroduce realisic assumpions regarding populaion. In mos growh models he growh rae of populaion is consan. This is obviously a simplificaion given ha he populaion grows faser in less developed counries han in developed economies 7. In our model he ime evoluion of populaion is consisen wih his observed fac. More specifically, a each period he economies are inhabied by a coninuum of measure i L > 0, i =, of idenical homes. From now on, he super-index in he variables will denoe he counry. The populaion of each economy evolves as follows: 7 This fac is described, for insance, in he repor World Populaion Profile: 998 (p. 0) delivered by he US Agency for Inernaional Developmen and he American Bureau of he Census. 9

11 XREAP Counry Counry ( ) L + = ( + n + ) L, + ( ) L = + n L, + L > 0 given, n = n + n n ϕ, 0 0 ( ) n 0, L > 0, n > n given, ϕ 0,, () L > L. 0 0 The equaions in () imply ha he populaion of counry grows a he consan rae n a each period. The populaion growh rae of counry, n +, is iniially higher han counry s, sricly decreases hough ime and evenually converges o n. The parameer ϕ deermines he speed of convergence. Lasly, he value of L 0 has o be higher enough han L 0 o guaranee ha L L never becomes smaller han he uni. In wha follows, we will refer o L L as he relaive size of counry. A each period households supply inelasically one uni of ime in he labour marke, and hence he populaion consiues he labour force of he economy. To his respec, variables in he models will be expressed in per capia (or per worker) erms. Of course, his does no apply for prices. I is also assumed ha all markes are perfecly compeiive, inernaional facor flows are no allowed and agens have perfec foresigh. Nex, we describe he environmen wih deail. 3.. Firms The goods are produced wih he following Cobb-Douglas echnologies: Counry Counry α α α α ( γ ) ( ) ( ) ( ) ( ) ( γ ) ( ) ( ) ( ) ( ) z = + k l, x = k l, z, x, α α α α = + c, = c, c k l, c k l, ( ) γ > 0, α 0, () where z denoes he producion of capial good in counry, x is he producion of ourism services in counry and i c denoes he producion of consumpion good in 0

12 XREAP counry i. Technologies use capial and labour as facor inpus. In each economy resources mus be allocaed beween secors. Thus, k z, and k c, represen he amouns of capial inpu allocaed o he producion of capial and consumpion goods, respecively, in counry, while k x, and k c, are hose amouns assigned o produce ourism services and consumpion good, respecively, in counry. From now on, he firs sub-index will indicae he secor. As he model is expressed in per capia erms, he variables l and l are he proporions of labour used in capial and consumpion good secors, respecively, in counry. Similarly, he variables l and l are hose proporions used in ourism and consumpion good secors, respecively, in counry. Since γ > 0, he oal facor produciviy (TFP) grows a he same rae in boh secors of counry. Counry, however, does no have an own engine of susained growh. The firm problems can be formulaed as saic ones. The objecive funcions of firms a are curren profis, π : Counry Counry ( ) ( ) ( ) ( ) ( ) ( ) π = z r + δ k w l, π = p x r + δ k w l, z, z, x, x, x, π = p c r + δ k w l, π = p c r + δ k w l, c, c, c, c, c, c, (3) where p c, and p c, are he relaive prices of consumpion in counry and, respecively, and p x, is he relaive price of ourism services. The omission of he super-index in p x, indicaes inernaional price. Therefore, p x, and p x, are he erms of rade of counry and, respecively. The variable i r is he ineres rae and denoes he wage. The depreciaion rae of capial, δ > 0, is assumed o be he same in boh counries and across secors. i w

13 XREAP Households The represenaive household in counry and maximizes is oal uiliy discouned a he rae ρ. Counries differ in preferences as follows: Counry Counry ( ρ ) (% % ) ( ρ ) (% ) u = + L v c,x, u = + L v c, 0 0 = 0 = 0 (( ) ( ) ) η η σ σ c c x % % ( c % c ) if v ( c,x ) if σ σ (4) % % = σ v ( c % ) = σ η ln c % c + ( η ) ln x % ln c if σ = % c if σ = ( ) ( ) η 0,, ρ > 0, σ > 0, c = + θ c, i =,. i i i The shopping baske of homes in counry is composed of consumpion good, c%, and ourism services, x%. The shopping baske of counry is only composed of consumpion, c%. In wha follows he wiggle symbol ( ) will denoe demand. For our purposes we need a non-homoheic uiliy funcion for counry. However, he predicions from a model are informaive only if hey are compared o hose from an alernaive framework. This is he reason why we also consider he case of homoheic preferences. Thus, our heoreical srucure divides in wo differen models: Model : c > 0, i =,, i Model : c = 0, i =,. i (5) In model here is a Sone-Geary ype of relaionship beween consumpion good and ourism services, and hence he uiliy funcion counry is non-homoheic. We follow Chrisiano (989) and assume ha he minimum consumpion a he rae a which income per capia grows in he long run, i c grows a each period i θ. 8 This ype of preferences has wo desirable properies. Firsly, he marginal uiliy of consumpion 8 Alernaively, we could have followed Carroll e al. (000) and assumed ha he minimum consumpion is endogenously deermined hrough a habi formaion process. Since boh approaches virually have he same implicaions, we op by keeping he simples one.

14 XREAP goes o infiniy as i c% approaches i c, which discourages saving. As repored by Chrisiano (989), his propery is crucial for explaining he ime behaviour of counries saving rae, because i allows explaining he fac ha homes save lile and consume a lo when hey are near he minimum consumpion, ha is, when hey are poor. Since in our model he shopping baske of counry is composed of wo goods, his approach has a second implicaion, namely a consumpion-dependen elasiciy of subsiuion ( ES ) beween he goods: ( ) where MRS ( c,x ) ( ) (% % ) ( ) d c % x % MRS c %,x % c ES c %, c c %, = = ( η ) < d MRS c,x c % x % c % % % denoes he marginal relaionship of subsiuion, and consumpion is always higher han he minimum level. 9 This elasiciy is lower han he uni and rises as consumpion does. Therefore, he share of expendiure devoed o consumpion in counry is high when homes are near (6) c. Moreover, in a siuaion like ha he households would be lile willing o subsiue ourism services for consumpion. As consumpion moves up is minimum level he household becomes progressively more willing o subsiue ourism services for consumpion. Consequenly, a greaer proporion of expendiure is devoed o he former good han o he laer one. Therefore, his uiliy funcion implies ha consumpion is a good of firs necessiy, while ourism services are a luxury good. In model he elasiciy in (6) is uniary and hus consumpion and ourism expendiure evolves a he same pace as home s expendiure. Households in counry and receive capial and labour income and face he budge consrains: Counry ( ) + ( ) + n k = + r k + w p c % p x %, Counry c, x, ( + ) + ( ) + n k = + r k + w p c %, c, (7) 9 The fulfilmen of his condiion requires a high enough iniial endowmen of capial per capia. 3

15 XREAP where i k, i =, is he capial sock of he economy, which is equal o household s wealh a. A he iniial period, homes are endowed wih a posiive amoun of capial ha consiues heir iniial wealh: i k0 > 0, i =,. (8) 4. The Equilibrium of he Two-Counry Economy In his secion we firs characerize he compeiive equilibrium, and hen sudy he behaviour of he wo-counry economy in he long run. There is no need for analysing each model separaely since model is a paricular case of model. The resuls can be obained using sandard echniques, so we op by confining he deails on calculaions in hree appendices. 4. The Compeiive Equilibrium Given he iniial endowmens k0 > 0 and k0 > 0, he compeiive equilibrium of he wo-counry economy is characerized by a se of allocaions { l,l,k +,k + } prices { c, x, c, } 0,,,... = 0,,,... p,r,w, p, p,r,w = ha solve firm and household problems, as described in Appendix A, clear all markes and balance he rade balance. and The clearing condiions of labour markes have been already inroduced in he models. The res of condiions are as follows: Asses: k = k + k, k = k + k, z, c, x, c, α % + % = = ( + γ ) ( ) ( ) α α % = = ( x, ) ( ) ( γ ) ( ) ( ) ( ) ( ) α z, Capial good (in aggregae erms): z L z L z L k l L, Tourism (in aggregae erms): x L x L k l L, Consumpion: α α α = = + c, α = = c, c % c k l, c % c k l. (9) where z% and z% denoe invesmen demands of counry and, respecively. Noe ha he clearing condiions of capial good and ourism services markes are expressed in aggregae erms insead of in per capia erms. This adjusmen is necessary because 4

16 XREAP counries differ in populaion size. In each counry he aggregae expendiure a period ( ae ) exhauss gross domesic income a ( gdi ): ae = gdi p c % + z % + p x % = z + p c, c, x, c, ae = gdi p c % + z % = p x + p c. c, x, c, (0) In addiion, he rade balance mus be in equilibrium a every, which requires ha: In aggregae erms z % L = p x L = p x % L, x, x, L In per capia erms of counry z % = p x = p x, % x, x, L () where he firs equaion in () is expressed in aggregae insead of per capia erms o accoun for counries differences in populaion size. The equilibrium in he rade balanced expressed in per capia erms of counry reveals ha gross invesmen per capia of his economy is deermined by ourism expendiure per capia and he relaive size of counry. This resul has wo imporan implicaions. Firs, ourism demand per capia is no wha really maers for promoing growh of counry, bu ourism expendiure per capia because of he effecs of he relaive price of ourism. Second, a lile ourism expendiure per capia can be compensaed by a large relaive size of counry. From profi-maximising behaviour of firms, we obain ha ineres rae and he wage are equal o capial and labour marginal produciviies, respecively: Counry p c p c r, w, z c, z c, = α δ = α δ = ( α ) = ( α ) kz, kc, l l Counry p x p c p x p c r, w. x, c, x, c, = α δ = α δ = ( α ) = ( α ) kx, kc, l l () The equalisaion of ineres rae and he wage beween secors yields he resource allocaion in boh economies: 5

17 XREAP Counry Counry k = l k, k = l k, z, x, ( ) ( ) k = l k, k = l k. c, c, (3) Since echnologies are equally inensive in capial and labour, facor inpus are allocaed o each secor in he same proporion. The resuls in (3) and he expressions for ineres rae of counries in () yield he relaive prices: Counry Counry p =, p = p. c, x, c, (4) In counry, he relaive price of consumpion equals one given ha boh goods are produced wih he same ype of echnology. In counry he goods are also produce wih he same kind of echnology, and as a resul he relaive prices of goods are idenical. The resuls in (3) and (4) allow gross domesic income per capia of counries o be wrien as: Counry Counry ( γ ) ( ) α ( ) ( ) α x, x, gdi = c + z = + k, gdi = p c + x = p k. (5) Since ourism expors are enirely devoed o impor capial good, he resuls in (3) and (5) imply ha he saving rae of counry is equal o l. The equilibrium condiions in (9) and (), and he resuls in (3) allow he capial accumulaion of counries o be expressed as: Counry ( + ) + = % + ( δ ) n k z p x k, Counry x, L n k p x k p l k k. x, x, L 443 x α ( + + ) + = % + ( δ ) = ( ) + ( δ ) (6) The expression (6) makes clear ha he capial accumulaion of counry crucially depends on he ime evoluion of is erms of rade. The accumulaion of capial in counry is no characerised by decreasing reurns, since he TFP in his secor grows 6

18 XREAP a he rae γ. However, counry would need coninuous improvemens in is erms of rade for overcoming decreasing reurns and hence sagnaion in he long run. The spli of expendiure beween consumpion and ourism services in counry is obained from he firs-order condiions of home s problem: ( η ) c % = ηe + c η % x, = (% ) η px, x % = e c p x c c ( η )( ) (7) where e denoes household s expendiure, ha is, e c % + p x %. The equaions in x, (7) show ha, in model, he raios of consumpion and ourism expendiure o home s expendiure are no consan. The former raio increases and he laer one falls as e rises. This behaviour is a consequence of he chosen Sone-Geary uiliy funcion. Moreover, i is worhwhile o noe ha he expendiure-saving decision is ineremporal, while he decision on expendiure allocaion beween he goods in (7) is an inra-period one. This means ha he home firs decides how much income o spen and save in, which hinges on he whole ime-pahs of all prices from he period o infinie. Then, i chooses how o spli up expendiure beween consumpion and ourism services in he curren period, which only depends on variables in. Therefore, he income-elasiciy of consumpion and ourism expendiure canno be analyically compued, since i involves ineremporal decisions. The expendiure-elasiciy, however, can be easily compued using he equaions in (7): ε ( x, x % ) dc % e = ηe < d p e e, = >, c,e ε px x,e de c % ηe + ( η ) c de px, x % e c (8) where e > c provided ha c % > c. The expendiure-elasiciy of consumpion ( ε ) c,e and ourism expendiure ( ε px x,e ) are lower and higher han he uni, respecively. In his sense, we have defined ourism services as a luxury good and consumpion as a good of firs necessiy, respecively. In model, however, he raios of consumpion and ourism expendiure o home s expendiure are consan and he elasiciies in (8) are equal o he uni. 7

19 XREAP The equaions governing consumpion of counry and and he ourism expendiure hrough ime are obained from he firs-order condiions of he household problem in boh economies: Counry ( σ )( η ) σ p σ + x, = + x, + ρ c % r c c, c % p c % c % ( σ )( η ) σ % σ x, + + x, = px, x % p x, + ρ p x p r, (9) Counry σ p + c, + + σ + c c = p + c, + ρ c % c % c % r. c % The firs and he hird equaions in (9) reveal ha he minimum consumpion level affecs he ineremporal elasiciy of subsiuion of consumpion (IESC). Indeed, he nex and he curren period consumpion are close o one anoher if curren consumpion is near he minimum level. The home becomes more willing o swich consumpion hrough ime as his variable moves up is minimum level. This effec is absen in model. Moreover, looking a he firs wo equaions in (9), one can see ha in boh models he ineremporal allocaion of expendiure in counry is independen from he ime evoluion of p x, if σ is equal o he uni. Therefore, holding ineres rae consan, he price-elasiciy of ourism demand would be uniary. This seems an ineresing case for our analysis, since i allows isolaing he effec of an increase in counry s income on is ourism expendiure and he economic growh of counry. In addiion, ourism demand would be elasic and inelasic if σ was lower and higher han one, respecively. In model, he firs wo equaions in expression (9) show ha if boh expendiures grew over ime, ourism expendiure would grow a a higher rae han consumpion. In model, however, boh ypes of expendiures would grow a he same rae. The consrucion of he sysem of equaions ha characerizes he dynamic behaviour of he wo-counry economy is described in Appendix B. 8

20 XREAP The Long Run Equilibrium In his sub-secion we will show ha he long run equilibrium of he wo-counry economy is characerised by a balanced growh pah (BGP), in which counries populaion grows a he same rae and he growh raes of variables are consan. Since he variables l and l ake values in he inerval ( 0, ), heir growh rae mus be equal o zero. We sar analysing he behaviour of he economy of counry. The ineres rae is consan in he long run and hence he variables and gdi grow a he same consan rae: ( ) θ γ α k, z, z%, c, p x% x, = +. (0) In counry a consan ineres rae in he long run requires gross invesmen, z % = p x, o grow a he same rae as x, a he same consan rae: k. Therefore, k, p x, x, p c and c, gdi grow θ = θ θ. () The previous resuls imply ha he producion and he relaive price of ourism services (and consumpion) grow a he raes: x x c c p p α = = + θ, = + θ. () + + x c px, α x,+ x, ( ) ( ) We hen obain ha susained growh is ransmied from counry o counry hrough rade. As we anicipaed in he preceding sub-secion, he permanen improvemens in counry s erms of rade, p x, equilibrium expressions of ineres rae:, consiue he mechanism of ransmission. Indeed, he 9

21 XREAP Counry α k ( ) α + ( ) α k r = α k + γ δ = + γ = + θ, Counry α α k p α + x, + ( x, ) k px, r = α k p δ = = + θ, (3) show ha he marginal produciviy of capial in counry holds consan when capial per capia grows unboundedly, given ha his economy posses an own source of permanen growh. There are no increases in TFP of counry, and hence he marginal produciviy of capial falls as capial accumulaes. However, he permanen improvemens in counry s erms of rade compensaes he fall in he marginal produciviy of capial and, as a resul, he value of capial marginal produciviy approaches o a consan value in he long run. Therefore, counry overcomes decreasing reurns o capial accumulaion and can enduringly grow because he erms of rade becomes more and more favourable o his economy. 0 A more deailed analysis of he long run equilibrium can be found in Appendix C. 5. Calibraion of he Models and he Balanced Growh Pah We have jus showed ha counry can impor susained growh by rading. This resul has o do wih he long-run behaviour of he wo-counry economy. In his paper we are also concerned wih offering an answer o he quesion on why small ourism counries have been growing a higher raes han oher economies. This quesion is noiceably relaed o he ransiional behaviour of he wo-counry economy. We make use of numerical examples o illusrae he predicions from he models. More specifically, we 0 Hazari, Nowak and Sahli (003) also obained ha a ourism economy can impor susained growh whenever is erms of rade improve. Moreover, Álvarez-Albelo and Pigem-Vigo (007) and Álvarez- Albelo and Perera-Tallo (007) esablished condiions under which susained growh is ransmied hrough erms of rade improvemens. 0

22 XREAP proceed in wo sages. We firs parameerise he models o characerise he BGP, and hen solve hem. This secion covers he firs sage. Table 3: Empirical Facs of OECD High Income Counries (HIC) and Small Tourism Counries (STC) OECD High Income Counries (4) Populaion growh rae, a 0.66 Raio of HIC populaion o STC populaion, a 63 Growh Rae of Real GDP pc a.3 HIC Tourism Expendiure in STC over GDP Small Tourism Counries (3) Populaion growh rae, a. Growh Rae of Real GDP pc, a.4 STC GDP over HIC GDP a 0.65 Inernaional ourism receips over GDP (curren US$), b 6. Real GDP pc of STC over real GDP pc of HIC, a 43. Noes: The HIC are hose included in he World Developmen Indicaors, 006 consruced by he World Bank. The STC are hose included in Brau, Lanza and Pigliaru (007), excep Seychelles because of missing daa. The values are means of he period. Variables are in percenage form, excep he raio of HIC populaion o STC populaion. The variable GDP pc refers o real Gross Domesic Produc per capia in purchasing pariy power. The variable HIC Tourism Expendiure in STC over GDP is equal o Sources: a Penn World Table 6.; b Brau, Lanza and Pigliaru (007). We choose parameer values for he models o deliver an empirically plausible BGP. We will use daa of weny four OECD high income counries (HIC) and hireen small ourism counries (STC) in Table 3 o calibrae some parameers of he models. The HIC and he STC as a group will represen counry and, respecively. Table 4 conains he parameer values and he implied BGP. The calibraion arges appear in bold in Table 4. The daa used o consruc variables in Table 3 reveal ha HIC and STC were no in heir long run equilibrium during he considered ime period. This fac obligaes us o esablish some compromise crieria o calibrae he models. In his regard, we will consider he mean of he period of some variables as long run values. We use he Gauss-Seidel mehod o solve he models. The code and he resuls are available upon reques via o he auhors.

23 XREAP Table 4: Parameer Values and he Balanced Growh Pah Parameer Values Populaion: n = n = , L L = 63 Technology: γ = 0.07, α = 0.4 a, δ = Preferences: σ =, ( θ ) = = = = Model : c = c = 0, η = , ρ = 0.46 Balanced Growh Pah Growh raes (%) θ θ = θ =.3, θ p =.7, θ = θ = 0.84 x x c Variables in he dynamic sysem k + = 7.877, l a Model : c, c 0.43, η , ρ 0.46 =, ( ) k + = 3.377, l = 0.6 θ Ineres raes and saving raes (%) z % p x, x z % r = r = 6.85, s = 6., s = = 6.% gdi gdi gdi Income and expendiure over gross domesic income (%) z c p x, x % px,c = 6.43, = , = 0.043, = 73.9 gdi gdi gdi gdi Sources: a Cooley and Presco (995) Differences in per capia income (%) gdi gdi = 43. The populaion growh rae of boh economies is se o n = n = 0.66%, where he omission of ime denoes saionary value. During he considered ime period in Table 3 counries relaive sizes were no consan. As a compromise soluion, we op by seing he long run relaive size of counry in he models, HIC in Table 3 (63). L L, equal o he relaive size of The growh raes of income per capia of counries will evenually equalise, ha is, θ = θ = θ. The measure of income per capia in he model maches wih real GDP per capia in purchasing pariy power (PPP). The daa show ha income per capia grew a a higher rae in he STC (.4) han in he HIC (.3). Thus, we calibrae α and γ for θ o be equal o he growh rae of he HIC. Cooley and Presco (995) calibraed α for

24 XREAP he American economy and found a value of 0.4. We consider ha value as a good esimae for α. Then, we find ha γ = 0.07 allows replicaing a growh rae of.3%. The depreciaion rae of capial is equal o ha calibraed by Cooley and Presco (995) for he US economy ( δ = ). We impose a uniary price-elasiciy for ourism demand, ha is, σ =, and hus ourism expendiure is independen from movemens in he relaive price of ourism services. We consider his choice as appropriae by wo reasons. Firs, i is no agains he empirical evidence regarding he price elasiciy of ourism demand (Smeral, 004) and, second, i allows isolaing he effec of income increases on ourism expendiure of counry and hence on growh of counry. In model, we calibrae he parameers c and c for hem o reflec differences in per capia income of counries in he long run. More concreely, we se c = and c = This choice makes sense when boh c and c are posiive, since he minimum consumpion depends on he relaive developmen level of counries. In he model, counry is richer han counry and, consequenly, wha he former economy considers as a level of minimum consumpion resuls o be oo high for he laer one. We hen seek values for ρ and η o replicae hree figures ain Table 3: ourism expendiure over income of HIC (0.043), he raio of ourism expors o income of STC (6.), and he raio of income per capia of STC o income per capia of HIC (43.). In he model c = c = 0 and hus he expendiure elasiciy of ourism expendiure is equal o he uni. We hen look for he values of ρ and η for he model o replicae he same hree figures in Table 3 as before. The 990 World Bank Developmen Repor (pp. 6-7) saes ha: A consumpion-based povery line can be hough of as comprising wo elemens: he expendiure necessary o buy a minimum sandard of nuriion and oher basic necessiies and a furher amoun ha varies from counry o counry, reflecing he cos of paricipaing in he everyday life of sociey. The firs par is relaively sraighforward. The cos of minimum adequae caloric inakes and oher necessiies can be calculaed by looking a he prices of foods ha makes up he dies of he poor. The second par is far more subjecive; in some counries indoor plumbing is a luxury, bu in ohers is a necessiy. 3

25 XREAP Our calibraion crieria have he advanage of giving rise o he same long run equilibrium in boh models. This allows he ransiional behaviour of models and o be easily compared. In counry, he producions of ourism services and consumpion good grow a 0.84%, while he erms of rade grow a.7%. As we show in Appendix C, capial per capia of counry ( ( + θ ) ) is higher han counry s ( 3.377( + θ ) ) because ourism expendiure of counry is quie low, which makes he invesmen per capia of counry relaively smaller han counry s in spie of he populaion size differences beween counries. In counry and he 6.4% and he 6.% of boh capial and labour are allocaed o he producion of capial goods and ourism services, respecively. Counry spends he 0.043% of is income on ourism services and, as a resul, he 6.% of income is devoed o gross invesmen (saving). Consisenly wih our analysis in Appendix C, ineres raes, and also he saving raes, of counries equalise in he long run if σ =. The characerisaion of he ransiional behaviour of he wo-counry economy requires aking concree values for n, ϕ, L0 L 0, k 0 and k 0. These values appear in Table 5. Table 5: Populaion and Iniial Endowmens of Capial Populaion n = 0.0, ϕ = 0.98, L0 L0 = Iniial endowmens of capial per capia k0 =.45, k0 = We se n equal o he populaion growh rae of STC in Table 3. Moreover, we se ϕ = 0.98 and hence i akes abou wo hundred periods for he populaion growh raes of counries o equalise. This slow convergence is consisen wih he observed behaviour of he populaion growh rae of STC and HIC during he period These crieria lead o an iniial relaive size of counry of

26 XREAP The economy of counry does no possess an inernal source of susained growh. Therefore, i is reasonable o assume ha when counries sared rading he endowmen of per capia capial of counry was smaller han counry s. Noneheless, he lack of saisical informaion prevens us from exacly compuing he differences in capial per capia beween HIC and STC. To overcome his difficuly we choose k 0 0 k o be equal o HIC GDP per capia over STC GDP per capia in 970 (.45), and hen se k0 = and k0 = The Transiional Dynamics of he Two-Counry Economy This secion deals wih he second sage, which consis of solving he wo models and comparing heir predicions regarding economic growh of he economies. 6.. Model : Tourism Services as a Luxury Good Figure displays ime pahs of significan variables of he model. INSERT FIGURE The ime pah of saving rae is driven by he offseing impacs of an income effec and a subsiuion effec (Barro and Sala, 995, pp ). The firs effec relies on homes willingness o smooh consumpion hrough ime. When income is below is long run level homes prefer o devoe a high proporion of income o consumpion, and hus he saving rae is small a he sar of he ransiion. As income increases, he raio of consumpion o income falls, while he saving rae rises. The subsiuion effec operaes in he opposie direcion and depends on ineres rae movemens. An iniial low level of income per capia means ha he economy has a small amoun of capial per capia. As a resul, he ineres rae is high and hus curren consumpion is expensive in relaion o he consumpion of he nex period. Therefore, he saving rae is iniially high and decreases as he ineres rae falls. As we commened in Secion 3, he inroducion of a minimum consumpion allows he ime behaviour of he saving rae o be consisen wih ha observed in real economies. The income effec overcomes he subsiuion effec when income per capia is low. 5

27 XREAP This occurs because homes are no very willing o swich consumpion hrough ime when consumpion is near is minimum level. Thus, he saving rae ime pah is iniially upward sloping. As capial accumulaes, he subsiuion effec surpasses he income effec and he saving rae declines. The predicions from our model in panel (a) are hen consisen wih his observed fac. Neverheless, i is imporan o realise ha counry s invesmen is deermined by ourism impors of counry, insead of by agen decisions in counry, so he previous explanaion only applies for counry. The presence of a minimum consumpion level in he uiliy funcion of counry affecs he degree of subsiuabiliy beween he goods. According o our explanaion in Secion 3, homes are lile willing o subsiue ourism services for consumpion when consumpion is close o is minimum level. The degree of subsiuabiliy beween he goods increases as consumpion rises above is minimum level, hereby provoking an increase in expendiure devoed o ourism services, and a decrease in consumpion goods during he ransiion. In his sense, we have defined ourism services as a luxury good. The relaionship beween ourism expendiure and income is less obvious han ha of ourism expendiure and home s expendiure, because income is no jus spen, bu also saved a each period. In our numerical example here is a posiive relaionship beween ourism expendiure and income of counry (panel (b)). The reason for his resul can be easily undersood by rewriing he equaions in (7): c % e c, gdi gdi gdi = η + ( η ) c % e c, = η + ( η ) e px, x % e c = ( η ). gdi gdi gdi (4) (5) (6) The saving rae increases a he beginning of he ransiion, so he raio of expendiure o income ( e gdi ) decreases. Along he ransiion c grows a he rae θ and grows a a higher rae han θ (panel (f)). Therefore, from equaion (4) i follows ha c % gdi declines as he saving rae increases. Moreover, he equaion (5) indicaes ha gdi 6

28 XREAP e grows a a higher rae han θ as long as c % e falls along he ransiion. This resul and he equaion (6) indicae ha p x % gdi rises as he saving rae does. The x, equaion (4) is silen abou how c % gdi behaves as he saving rae declines. In our numerical example η is near one, which resuls in c % gdi increasing as he saving rae declines. Lasly, a look a he equaion (6) reveals ha saving rae declines. p x % gdi rises while he x, The income elasiciy of ourism impors, compued as he raio of ourism impors growh rae o income growh rae, is displayed in panel (c). This elasiciy, which is abou 3% a he beginning of he ransiion, declines as income per capia increases and evenually converges o he uni. This range of values is consisen wih he esimaes for his variable. The growh performance of counry is unaffeced by he growh one of counry. The engines of growh of counry during he ransiion are he accumulaion of capial per capia and TFP increases. The accumulaion of capial per capia depends posiively on he raio of saving o capial, while he TFP grows a a consan rae. The behaviour of he saving rae in panel (a) implies ha capial accumulaes slowly, and hus i akes abou seveny five periods for he growh rae in panel (f) o reach he BGP. The engines of growh of counry during he ransiion are he accumulaion of capial per capia and he erms of rade improvemens. The accumulaion of capial hinges on ourism expendiure and he relaive size of counry, and he populaion growh rae of counry. The erms of rade changes are deermined by he scarciy of ourism services in relaion o capial goods. I is clear ha he growh possibiliies of counry depend on counry s economic decisions. Consequenly, he growh of income per capia differ beween counries because of differences in he growh of capial per capia, TFP and he erms of rade. The nex expression specifies he variables displayed in panels (d) and (e): 7

29 XREAP α ( k + k+ ) ( k k ) α ( ) α α panel ( d ):, gdi k p x, k k = gdi k ( + γ ) px, + ( + γ ) px, panel ( e ):. px, (7) The growh raes of capial per capia are useful for undersanding he ime pah in panel (d): Counry Counry z p x % p x % L L ( δ + n ) ( δ + n + ) k k k k k k,. x, x, + + = = k + n k + n + (8) Iniially, capial per capia grows faser in counry han in counry, bu he resul reverses afer he period welfh. Noe ha ourism expendiure and hus invesmen of counry sar low, in spie of he fac ha L L akes he highes value a he beginning of he ransiion. Moreover, n doubles n. As ime passes, ourism expendiure grows much faser han income of counry and, in addiion, n + approaches fall in L counry s. n. As a resul, he invesmen of counry rapidly increases regardless he L, and he capial per capia of counry evenually grows faser han The nex equaion is helpful for undersanding he ime pah displayed in panel (e): η α ( ) ( )( ) ( ) + γ l k c + γ α L L px, x % L L η x, = = x α l k p. ( ) (9) The relaive price of ourism services increases along he ransiion because of counries differences in produciviy. The producion of ourism services is unable o increase as does ourism expendiure, which resuls in a rise of he price of ourism services. This is he reason why counry s erms of rade grow faser han TFP of counry during he ransiion. Moreover, he fac ha in he model ourism increases much faser han income leads o a much higher increase in p x,. The ourism expendiure evenually 8

30 XREAP grows as income of counry, and hus he differenial beween he growh raes of and TFP declines over ime and becomes nil in he long run. p x, The ime pahs in panel (f) show ha he growh rae of income per capia of counry is well above ha of counry along he ransiional period. During he firs period of he ransiion he higher growh of counry is due o he improvemens in he erms of rade, which more han compensae he negaive differenial displayed in panel (e). 6.. Model : Uniary Expendiure-Elasiciy of Tourism Impors Figure 3 displays he same ime pahs as Figure. INSERT FIGURE 3 The absence of minimum consumpion makes he model unable o deliver hump-shaped saving raes. The subsiuion effec overcomes he income effec because he preference for smoohing consumpion is lower in his model han in model. Accordingly, he panel (a) shows ha saving raes sar high and decrease down o he BGP. However, a he beginning of he ransiion he saving rae of counry barely increases and is lower han counry s. This behaviour is due o he fac ha invesmen of counry is enirely deermined by ourism impors of counry, insead of by agen decisions in he former economy. The eliminaion of he minimum consumpion in equaions (4) hrough (6) reveals ha consumpion and ourism expendiure over home s expendiure evolve hrough ime a he same pace. Proceeding as in he previous subsecion, i is easy o check ha he raios of consumpion and ourism impors o income of counry rise a he same rae along he ransiion. The raio of ourism impors o income in panel (b) sars being higher han in model simply because he elasiciy of subsiuion of goods in he uiliy funcion of counry is consan and uniary. Consequenly, panel (c) shows ha he income elasiciy of ourism impors is much lower han ha delivered by model. More specifically, i ranges from.3 o. The descripion of he engines of growh of counries during he ransiion in he previous sub-secion also applies here. Neverheless, he behaviour of counry s 9