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ETLA ELINKEINOELÄMÄN TUTKIMUSLAITOS THE RESEARCH INSTITUTE OF THE FINNISH ECONOMY Lönnrotnkatu 4 B Helsnk Fnland Tel Telefax World Wde Web: Keskusteluaheta Dscusson papers No. 962 Kar E.O. Alho* A GRAVITY MODEL UNDER MONOPOLISTIC COMPETITION** Frst verson 31 December 2004 Ths revsed verson 18 February 2005 * ETLA, The Research Insttute of the Fnnsh Economy, and Unversty of Helsnk, Address: ETLA, Lönnrotnkatu 4 B, Helsnk, Fnland, E-Mal: ** Acknowledgement. Ths s a part of the proect Integraton, Locaton and Growth wthn the Northern Dmenson, carred out ontly by ETLA and Turku School of Economcs, and fnanced by the Academy of Fnland (Grant No ). Comments by Professor Mka Wdgrén of Turku School of Economcs, CEPR, CESfo and ETLA and partcpants of the XXVII Annual Meetng of Fnnsh Economsts are gratefully acknowledged. The usual dsclamer apples. ISSN ALHO, Kar E.O., A GRAVITY MODEL UNDER MONOPOLISTIC COMPETITION. Helsnk: ETLA, Elnkenoelämän Tutkmuslatos, The Research Insttute of the Fnnsh Economy, 2005, 17 p. (Keskusteluaheta, Dscusson Papers, ISSN, ; no. 962). ABSTRACT: The paper presents an alternatve dervaton of the gravty equaton for foregn trade, whch s explctly based on monopolstc competton n the export markets and whch s more general than prevously n the lterature. In contrast to the usual specfcaton, our model allows for the realstc assumpton of asymmetry n mutual trade flows. The model s estmated for trade n Europe, producng evdence that trade flows and barrers do, ndeed, reveal strong asymmetry. We then carry out a smulaton, based on the estmated model, of general equlbrum effects, through trade, of possble UK entrance nto EMU. Key words: Gravty model, trade barrers, asymmetry JEL classfcaton: F12, F15 ALHO, Kar E.O., A GRAVITY MODEL UNDER MONOPOLISTIC COMPETITION. Helsnk: ETLA, Elnkenoelämän Tutkmuslatos, The Research Insttute of the Fnnsh Economy, 2005, 17 s. (Keskusteluaheta, Dscusson Papers, ISSN, ; no. 962). TIIVISTELMÄ: Paperssa estetään ulkomaankaupan gravtaatomalln vahtoehtonen ohtamnen, oka perustuu eksplsttsest monopolstsen klpaluun ventmarkknolla a oka on ylesemp kun aemmn krallsuudessa. Pänvaston kun tavanomasest, paperssa ohdettu mall sall realstsen oletuksen epäsymmetrsstä kesknässtä kauppavrrosta. Mall estmodaan Euroopan kauppavrrolle, a estmonttulos antaa vahvstusta slle, että kauppavrrat a kaupanesteet ovat todellakn selväst epäsymmetrsä. Sen älkeen malln avulla laadtaan smulont stä, mllaset ylesen tasapanon mukaset vakutukset ovat ulkomaankaupan muutosten kautta Ison-Brtannan mahdollsesta lttymsestä EMUun. Kysymys kaupan esteden asymmetrasta on älleen varsn merkttävä tekä ntegraatopoltkan vakutusten selvttämsessä. Asasanat: Gravtaatomall, kaupan esteet, epäsymmetra 1. INTRODUCTION The analyss of trade usng the classcal gravty model has been very ntense durng the recent years, to analyze, e.g., the trade effects of currency unons. There are, however, two shortcomngs n these applcatons. Frst, t s commonly assumed that trade barrers are symmetrc,.e., dentcal n trade from country to and n trade from to, and no emphass s pad to dfferences n exports and mports and the factors underlyng them. Secondly, the theoretcal bass of the estmated gravty model s nsuffcent and often lackng totally. Ths assumpton of symmetry s very domnatng n the emprcal applcaton of the gravty model, 1 but t s n sharp conflct wth the actual stuaton. Take, for nstance, trade flows wthn Europe. In 1999, the average absolute dfference between the logs of the blateral trade flows of 27 European countres was as hgh as 0.66, whch mples that, on average, the smaller of the blateral trade flows s only 52 per cent of the bgger. Therefore, t s not surprsng that usng a gravty model to explctly test for the symmetry of trade barrers n Europe produces the outcome that they are strongly asymmetrc (see Alho, 2003). James E. Anderson and Erc van Wncoop (2003) presented an mportant and novel analyss whch clams to solve the famous border puzzle concernng the effects of a border on trade, orgnally found by McCallum (1995) to be extremely large wth respect to the U.S. and Canada. They buld on the early dervaton of the gravty model by Anderson (1979). Assumng CES-preferences, symmetrc trade barrers, and mposng the general equlbrum constrant for trade,.e., that total sales equal total producton, Anderson and van Wncoop explctly derve the followng gravty equaton for blateral trade, 1 For nstance, the recent analyses of the mpact of EMU on trade by Mcco et al. (2003) and Barr et al. (2003) both buld ther trade model on the sum of exports and mports and thereby omt the dfferences exstng between them. 2 (1) Y Y 1 σ X = ( ). YW P P t Here X s exports from country (regon) to country, Y s the ncome (GDP) of country, Y W denotes that for the whole world, t s the trade barrer factor (nverse of unty mnus the ad valorem barrer per unt of exports) between countres (regons) and, assumed to be the same as t, and P s ther key noton of aggregate trade resstance, or smply, the consumer prce ndex of country. The parameter σ s the elastcty of substtuton between mports from varous orgns. The authors estmaton results of (1) produce a much smaller effect of the US-Canada border on trade than what was found out by McCallum. What s strkng about (1) s that t mples total symmetry n trade flows,.e., X = X, whch does not preval n realty, as mentoned above. Therefore, a more general approach s n place. In ths paper we derve a model for blateral trade flows, expandng on the framework used by Anderson and van Wncoop, by explctly ntroducng monopolstc competton n the export market, and by also allowng for asymmetry n trade. We estmate the model for trade flows between European countres to determne the factors behnd the trade asymmetres. The paper proceeds as follows. The gravty model s derved n Secton 2 and n Secton 3 we present ts estmaton for trade flows between 27 European countres n Secton 4 llustrates, how to use the estmated model to derve general equlbrum effects of trade polces, whch s then appled to evaluate the effect, through trade, of possble UK onng EMU. Here agan, the ssue of asymmetry turns out to be qute crucal as to the magntude of the effects of ntegraton polces. 3 2. A MODEL OF BILATERAL TRADE The specfcaton of the demand for mports from varous countres here follows that of Anderson and van Wncoop, wth some mnor modfcatons. The mport demand functons n country, = 1,,N, are derved from a CES utlty functon for aggregate consumpton D, (2) σ /( σ ) N 1/ σ ( σ ) / σ D = a Q, σ 0, = 1 where Q s the volume of exports from country to, the a s are the country-specfc postve preference (dstrbuton) parameters summng to unty and σ s, agan, the elastcty of substtuton between mports from varous orgns. The mport demand functons are then (3) p σ Q = a D ( ), P where p s the prce set by the exporters of country n the market of country, nclusve of the cost of trade barrers and, beng dual to the quantty ndex (2), P represents the CES prce ndex of the consumpton basket n country, (4) 1/(1 σ ) 1 σ = N P a p. = 1 From (3) we can derve the market share of the value of exports X = p Q n country, n relaton to ts GDP, yeldng (5) X Y p = a ( P ) 1 σ, where Y s the GDP (n nomnal terms) of country and the budget constrant Y = P D s mposed. 4 We next consder the export supply decson of a monopolstc frm of country n the market of country. For ths we need to specfy that aggregate demand D s gven by the functon ε (6) D = b P, ε 0, where b s a scale factor representng the sze of the country concerned. Note that typcally ε σ. Let there be K dentcal exportng frms n country. The optmal supply decson of an exporter n country maxmzng proft n market s gven by (7) p 1+ ε ( p, Q )) = t c, ( k where c s the margnal cost of producton n country and Q k denotes the volume of exports of frm k of country n the market of country, t s, as n Eq. (1), the trade barrer factor (nverse of unty mnus the ad valorem barrer per unt of exports) between countres (regons) and, and ε(z,z ) denotes the elastcty of the varable z wth respect to the varable z. Usng (3), (6) and the general result from ndex number theory that ε(d,q k ) = s k = X k /Y,.e., the market share of exporter k n the market of country, and summng over the dentcal K frms, we get the followng from (7), p K (1 σ ) + ( σ ε )( s + h (1 s )) = K c t. (8) [ ] Here h s the conectural varaton parameter n the proportonal output game 2 (see e.g., Smth and Venables, 1988 and Alho, 1996 and the appendx for more detals) and s s the aggregate market share of country n the market of country, s = K s k k = 1 = X /Y. The supply equaton (8) allows for prce dscrmnaton between varous export markets. It s therefore more general than the approach of Anderson and van Wncoop, who assume un- 2 I.e., the parameter h s n relatve terms the output response by the compettors to a one percent rse n the output of the frm concerned n market. If h s, e.g., zero, we have the case of Cournot competton. 5 = form prcng, whch takes place when competton s perfect ( h s (1 s ) and σ approaches nfnty). Note that under perfect competton, the export prce only depends on the unt cost and the respectve trade barrer. But otherwse under mperfect competton, the bgger the country, measured by the number of frms, the lower the export prce whch ts frms charge. We next need a model for the determnaton of the cost levels c and ntroduce therefore the followng framework. Assume smply that labour L s the only factor of producton and that there are constant returns to scale, Q = A L, where Q s the volume of GDP. Let the utlty functon U of workers be smply, n a standard manner, U 1 ν = log( D ) L, where ν ν 0. Now optmzng under the budget constrant P D = W L + π, where W s the wage rate and π aggregate profts, we get the result for wage formaton, (9) W = P D L. ν 1 ν = Y L In the next step, n dervng the unt cost c = W /A, we could take two approaches. Frst, we could take the technology, as ncorporated n the parameter A, to be dentcal n all the countres. But, as the countres n our emprcal sample of European countres, on whch we shall estmate the gravty model, are wdely apart from each other as to ther ncome levels and thereby productvtes, ths assumpton of unformty s not very sensble. Therefore, we allow for dfferences n productvtes and wrte A, beng the average labour productvty, as A = Q /L = Y /P L. 3 So, we get for the unt cost (10) c = W / A = P L. ν 3 Note that as aggregate demand s dentcally equal to aggregate supply (GDP),.e. P Q Q = P D Q Q where P s the prce on GDP, these prces P and P are also dentcal. 6 It depends smply on the prce level n the country and postvely on the sze of the country, f ν s postve, measured by the labour force, whch wll be below captured by populaton. We further assume that that the average sze Q of the frms s dentcal n all the countres, so that K Q = Q = Y /P. Normalse then ths average sze to unty, and nsert ths result and (10) nto (8). We can, by equatng export demand (4) wth supply (8), solve then for export prce p from the equlbrum condton, (11) ν 1 σ AY P (1 σ ) = a ( ), p 1 h P t L h p where A = (ε -1 σ -1 )(1 h ) 0. Insert next ths equlbrum soluton (11) for the export prce n market nto the export demand equaton (5). Usng the approxmaton that log(x + y) log(x) + log(y) + o(x 2 ) + o(y 2 ), we can solve for the blateral exports to be as follows, returnng back to a power functon specfcaton, µ µ µ Y Y t a (12) X =, where µ = σ ( σ ). µ µ µν P P L The parameter µ s thus postve and smaller than unty, f the elastcty of substtuton σ s hgher than unty. In addton, the functon (12) ncludes hgher order terms for Y, P, and P and the parameter h s assumed to be unform n all markets. Note that, as mentoned above, under perfect competton, the Y varable s not present n (11), and not n (12), ether. There are several dfferences between specfcatons (12) and (1). The coeffcents of Y and Y are normally dfferent from each other n (12), and the coeffcents of the prce level n the exportng and mportng countres are now also equal, but of opposte sgn, n contrast to Eq. (1) where they are dentcal. 7 3. ESTIMATION AND TESTING FOR ASYMMETRY IN EUROPEAN TRADE As an llustraton, let us estmate the basc trade equaton (12) for trade flows between 27 European countres n 1999, the frst year of Economc and Monetary Unon (EMU), and compare t to the specfcaton (1) of Anderson and van Wncoop. We consder the followng regons of countres n our estmatons wth dfferent trade barrers between them: those countres belongng to EMU, the EU, EU Accesson Countres n Central and Eastern Europe, EFTA and Russa. We specfy the preference parameters a to be smply a functon of common language, representng a common culture n the exportng and mportng country. The trade barrers are captured by the followng specfcaton, (13) t ςb + δn + φn + βkmr ( k, m) λ = cd km, e. Here d s the dstance between countres and, b s the common-border ndcator, equal to unty f countres and share a common border and zero otherwse, and n s unty f s an sland. The term r (k,m) s the regonal ntegraton ndcator for exports from the regon of countres k to regon m, and equals unty f country belongs to regon k and country belongs to regon m, and zero otherwse. So, we allow for trade barrers to be potentally asymmetrc n exports from regon k to m and from m to k,.e. that β km may be dfferent from β mk. 4 Trade wthn the EU Internal Market s the reference pont. The relatve prce ndces, P relatve to that n other countres, are here calculated from measured prce data as the relaton between the current exchange rate of the currency concerned n terms of USD and ts correspondng purchasng power party (PPP) rate. Anderson and van Wncoop (2003) recommend aganst usng measured prces because they are 4 EMU s a subset of the EU, whch has to be taken nto n the nterpretaton of the coeffcents of the respectve dummy varables. 8 largely based on prces of nontradables. However, normally nontradables and tradables prces are postvely related to each other. On the other hand, ths nformaton on relatve prces between the countres s readly avalable. Ther use also offers a neat way to carry out general equlbrum type of smulatons related to changes n trade barrers, see Secton 4. The estmaton results, usng SUR, are the followng. The common culture varable dd not turn out to be sgnfcant, and s therefore omtted from the results. The ncluson of the labour force n the exportng country, captured here by populaton, whch should have a negatve coeffcent, see (12), was met as to ths property, but otherwse ths specfcaton was not satsfactory n the sense that then the coeffcent of the ncome varable Y got a coeffcent whch s hgher than unty and whch s aganst our theoretcal model (12). Therefore, we mposed n Table 1. Estmaton of the blateral trade model for European countres (the log of the market share of blateral exports X /Y as the dependent varable) Explanatory varable Model 1 (Eq. (1)) Coeff. (St. error) Model 2 Coeff. (St. error) Model 3 (Eq. (12)) Coeff. (St. error) Constant (0.143) (0.259) (0.831) Log(Y ) (0) (0.019) (0.037) Log(P ) (0.026) (0.022) (0.037) Log(P ) (0.026) (0.052) (0.037) 2 Y (0.136) ) Log(dstance).231 (0.020).313 (0.016).164 (0.062) Common border (0.031) (0.104) sland (0.079) (0.110) sland (0.052) (0.122) Regonal ntegraton 2 P 2 P dummes Yes* No Yes 2 R C F-test of symmetry of regonal trade barrers ** ** F-test of coeff. of Y beng untary ***. * The barrers are constraned to be symmetrc, β km = β mk for all k, m, n Eq. (12), smlarly as n Eq. (1) ** p *** p The t-statstc of ths coeffcent s 1.8. 9 (12) the constrant that the dsutlty of labour parameter ν goes to zero, whch removes the labour force from the unt cost c, see (9) above. The estmaton results n Table 1 are presented usng ths specfcaton. We see that Anderson s and van Wncoop s model, presented n Equaton (1) above, s not very well supported by the data, see Model 1 n Table 1 and ts rather weak explanatory power n comparson to the other models. Models 2 and 3 are, nstead, based on our preferred specfcaton n Equaton (12) and ts versons. Model 3 s based on our gravty equaton as specfed above n (12) and ts constrants mposed. The hypothess that trade barrers representng the varous stages of regonal economc ntegraton are symmetrc,.e., that β km = β mk for all pars of k and m, s clearly reected, as shown n the estmaton results of Model 3 and also Model 1. Also the coeffcent of Y dffers sgnfcantly from unty, whch ponts to another asymmetry n the specfcaton of the trade equaton, n contrast to Equaton (1). The effect of a common border on mutual trade s found to be 21 percent, whch s smlar to the estmate by Anderson and van Wncoop concernng the effect of the Canada-US border on trade. The estmate of the elastcty of substtuton, σ, s 6.5 on the bass of Model 3, as solved from Eq. (12) above. 4. SIMULATION OF A CHANGE IN TRADE POLICIES Smulatng changes n trade barrers t, so that ther general equlbrum effects through the prce varables and ncome levels are taken nto account, s an mportant ssue rased by Anderson and van Wncoop. We suggest a computatonally straghtforward way to carry ths out. Lke Anderson and van Wncoop, we frst need to make an assumpton about the elastcty of substtuton σ. But what s neat n our model, s that t the estmaton of t, at 10 the same tme, produces us an estmate of σ, see (12). The change n the trade barrer t has both a drect mpact on trade, and an ndrect one through a change n the prce level P. The latter s a result of the fact that also the equlbrum export prce p changes as a reacton to a change n exports caused by a change n the trade barrer t. To fnd out ths ndrect effect, we frst solve from (5) the nduced change n the prce rato p /P from the change n the market share of exports X /Y resultng,.a., from a change n t. The elastcty of the relatve prce (p /P ) wth respect to the export market share X /Y can be solved from Equaton (5) to be (1 σ). Next, we take nto account that also the aggregate prce level P changes as p changes. Ths can presented by solvng for the elastcty ε(p,x ) from the dentty (14) ε( P, X ) = ε( P, p ) ε( p, X ) = s ((1 σ) + ε( P, X )), where we have used, agan, the above-mentoned general property n ndex number theory that ε(p,p ) = s. 5 From (14) we can solve for the expresson needed n the general equlbrum smulatons of changes n trade barrers, (15) s (1 σ ) ε( P, X) =. 1 s Ths allows us to take nto account the ndrect effect of a change n t on P and further to the trade flow, usng the gravty model, n addton to the drect effect estmated above. The elastcty n (15) s n general negatve ndcatng that lower mport barrers lead to a lower prce level. The changes n the trade barrers have an mpact on the ncome levels, too. These can be presented usng the dentty, see Eq. (6) above, (16), dy = dx + dx = dx + (1 ε ) d log( P ) Y dx,,, 5 In dervng the last step of Eq. (14), we use the dentty p = ( p / P ) P. 11 as the rse n total mports to country captures the rest of the ncrease n the total demand n ths market not met by supples of the domestc frms. Let us now use ths framework, and the estmated gravty model, to make an analyss of the general equlbrum effects of possble UK onng EMU. For ths smulaton, we take the trade equaton as estmated n Model 3 n Table 1 and combne t wth the prce mpact as shown n (15) and the ncome dentty n (16). We dsaggregate the countres nto three groups: the UK, the Euro Area and the rest of Europe. We allow for the trade barrer to be dsmantled from UK exports to the Euro Area and respectvely n exports from the Euro Area to the UK, f such barrers exst. The relevant mpacts of the trade barrers n the trade between the UK and Euro Area are the estmated coeffcents, see the defnton n (13) above, β EMU,EU, β EMU,EMU and β EU,EMU. The total ntal mpact on UK exports of onng EMU s then
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