Review of Gravity Model Derivations

Transcription

1 Mathematcal Theory and Modelng ISSN (Paer) ISSN (Onlne) Revew of Gravty Model Dervatons Muhammad Tayyab 1, Ayesha Tarar 2 and Madha Raz 3* 1. Assstant Executve Engneer,Resgnallng Proect, Pakstan 2. Lecturer at Federal Scence College,Guranwala,Pakstan 3. PhD Canddate, School of Socal Scences, Unversty Sans Malaysa * E-mal of the corresondng author: mdhtarar@gmal.com Abstract The gravty model of nternatonal trade flows s a common aroach to modelng blateral trade flows. But t s crtczed on the ground of weak theoretcal base and oor mcro-foundaton. The gravty equaton for descrbng trade flows frst aeared n the emrcal lterature wthout much serous attemt to ustfy t theoretcally. The theoretcal suort for the gravty model was orgnally very oor, but after the second half of the 1970s, several theoretcal develoments have flled ths ga.in ths study we also endeavor to ustfy the Gravty model secfcaton and derve gravty equaton from dfferent ersectve. We nfer from lterature and fnd t a strong emrcal tool of analyss for nternatonal trade flows even though of some weakness t nnate. Moreover, multlateral trade resstance factors may be added n the emrcal estmaton to correctly estmate theoretcal gravty model. Keywords: Gravty Model, Anderson Gravty Model, Tnbergen Gravty Model, Newton s Bascs 1. Introducton A consderable amount of lterature has been ublshed on the gravty model. In early versons of the model, Tn Bergen (1962) and Poyhonen (1963) conclude that exorts are ostvely affected by ncome of the tradng countres and that dstance can be exected to negatvely affect exorts. Some studes attemt to add addtonal structural elements to the gravty model to better reflect real word observatons. A Parallel search of a sold theoretcal foundaton for the gravty model addressng several ssues related to theoretcal weakness has been started snce 1970 s. Researchers have examned the econometrc ssues of what s the correct way of secfyng and estmatng a gravty equaton, to show how the secfc effects turn out to be sgnfcant n emrcal analyss. In the last decade, a lot of effort has been made n emrcal research on nternatonal trade to exlan the blateral volume of trade through the estmaton of a gravty equaton [Dsder and Head (2004)]. As a remnscence of Isaac Newton's law of gravty, the trade verson reresents a reduced form whch comrses of suly and demand factors (GDP or GNP and oulaton) as well as trade resstance (geograhcal dstance, as a roxy of transort costs and home bas) and trade reference factors (referental trade agreements, common language, common borders). Anderson (1979) make the frst formal attemt to derve the gravty equaton from a model that assume roduct dfferentaton, Bergstrand (1985, 1989) also exlore the theoretcal determnaton of blateral trade n a seres of aers, n whch gravty equatons are assocated wth smle monoolstc cometton models. Helman (1987) use a dfferentated roduct framework wth ncreasng returns to scale to ustfy the gravty model. Moreover, Deardorff (1995) has roven that gravty equaton characterzes many models and can be ustfed from standard trade theores. Anderson and Wn coo (2003) derve an oeratonal gravty model based on the manulaton of the CES exendture system that can be easly estmated and that hels to solve the so-called border uzzle. In order to comle the ssues of Gravty model we desgn ths study, we are gong to dscuss the exstng lterature on roer econometrc secfcaton of the gravty model and ts mortance for the dervaton of blateral trade flows, vs-à-vs a healthy arecaton on ts modelng and secfcaton. 82

2 Mathematcal Theory and Modelng ISSN (Paer) ISSN (Onlne) 2. Dervaton of Gravty model Numerous emrcal studes such as Tnbergen (1962) and Lnnemann (1966), showed that trade flows follow the hyscal rncles of gravty: two ooste forces determne the volume of blateral trade between countres - the level of ther economc actvty and ncome, and the extent of medments to trade. The latter nclude n artcular transortaton costs, trade olces, uncertanty, cultural dfferences, geograhcal characterstcs, lmted overla n consumer reference schemes, regulatory bottlenecks, etc. Natonal borders are among these medments, even for ndustralzed countres (Anderson and van Wncoo, 2003). Trade otental s the result of matched exort caactes and mort demands at the mcroeconomc level. On a more aggregated level of analyss roxmty n demand, er cata ncome, sace, and culture, are key macroeconomc determnants of exort otentals. Thus varous combnatons of macroeconomc varables, such as gross domestc roduct and oulaton wth geograhc dstance, are owerful redctors of trade otentals. Hence, gravty equatons have been used extensvely n the emrcal lterature on nternatonal trade (Havrylyshn and Prtchett, 1991; Frankel and We, 1993; Bayoum and Echengreen, 1997; Evenett and Hutchnson, 2002). Wthn ths extensve lterature, gravty equatons share common features that can be customzed for dfferent uroses. Frst, a gravty equaton s blateral. It exlans a trade-related deendent varable by the combnaton of macroeconomc varables, such as country sze, ncome, exchange rates, rces etc., for both countres. Moreover, ndcators of transortaton costs between the two countres and more general market access varables are commonly added. Second, gravty equatons can be derved from varous theoretcal trade models (Deardorff, 1995). Indeendent from the underlyng trade model chosen, they reresent a condtonal general equlbrum f multlateral (rce) resstance terms are taken nto account. Inference about determnants of trade flows can be drawn due to ther roerty of searablty (Anderson and van Wncoo, 2003). Ths means that trade flows across countres are searable from the allocaton of roducton and consumton between countres. Thus, gravty equatons establsh a lnk between trade and ts determnants condtonal on the observed roducton and consumton atterns, whch draws nference on trade flows from the underlyng general equlbrum structure determnng roducton and consumton allocatons. In addton, due to the searablty roerty, the gravty equaton s not affected by the resence of non-tradable sectors n the economy, as non-tradable do not affect the margnal roductvty of tradable goods wthn a sector (Anderson and van Wncoo, 2003). Thrd, a gravty equaton may be used n order to estmate ether determnants of the volume or determnants of the nature of trade flows. In the latter case, the urose s to use an ndex of ntra-ndustry trade as the deendent varable. However, there s nevtably a dscreancy between the model aled and the deal equaton that would ft secfc eculartes of the data well. Border trade, seasonal trade, trade references or regonal ntegraton may be controlled for wth secfc effects by ar of country; such a soluton however eoardzes any attemt to use the model for forecastng uroses. Basc Gravty model The Newtonan hyscs noton s the frst ustfcaton of the gravty model. In 1687, Newton roosed the Law of Unversal Gravtaton whch states that the forces of attracton between two obects and s gven by M M D F = G, (1) 2 Where notaton s defned as follow: F s the attractve force, M and M are the masses, D s the dstance between the two obects and G s a gravtatonal constant deendng on the unts of measurement for mass and force. 2.1 GRAVITY MODEL OF TINBERJEN (1962) 83

3 Mathematcal Theory and Modelng ISSN (Paer) ISSN (Onlne) Economsts dscovered Gravty n trade n 1962, Tnbergen (1962) roosed that roughly the same functonal form could be aled to nternatonal trade flows. However, snce t has been aled to a whole range of what we mght call socal nteractons ncludng mgraton, toursm, and foregn drect nvestment. The general gravty law for socal nteracton may be exressed n roughly the same notaton F α M M D β = G (2) θ where Fs the flow from orgn to destnaton alternatvely, M and M are the relevant economc szes of the two locatons. If F s measured as a monetary flow (e.g. exort values), then M s usually the gross domestc roduct (GDP) or gross natonal ncome (GNI) of each locaton. For flows of eole, t s more natural to measure M wth the oulatons. D s the dstance between the locatons (usually measured from center to center) 2.2 GRAVITY MODEL OF LINNEMANN (1966) The gravty equaton can be analyzed n the lght of a artal equlbrum model of exort suly and mort demand by Lnneman (1966). The study classfed factors contrbutng to trade flows between any ar of countres n three categores. a. Factors that ndcate total otental suly of country A- the exortng country-to the world market; b. Factors that ndcate total otental demand of country B- the mortng country to the world market; c. Factors that reresent the resstance to a trade flow from otental suler to Potental buyer B. The resstance factors are cost of transortaton, tarff wall, quota, etc. The otental suly of any country to the world market s lnked systematcally to() The sze of a country s natonal or domestc roduct (smly as a scale factor), and () the sze of a country s oulaton. The level of a country s er cata ncome may also be consdered as a thrd factor though ts nfluence wll be very lmted, at most. If the thrd factor ndeed had no effect at all, then the factors () and () would obvously be comletely ndeendent of each other as exlanatory varables, on theoretcal grounds. On the other hand, f the thrd factor dd have an effect, then the three exlanatory factors would not be ndeendent of each other, as a change n one of the three would necessarly be assocated wth a change n at least one of the other two varables. For statstcal exercses ths has mortant mlcatons because t would mly certan roblems of dentfcaton. In the equlbrum stuaton otental suly and otental demand on the world market have to be equal. For ths, a rerequste must be that the exchange rate s fxed at a level corresondng wth the relatve scarcty of the country s currency on the world market. Equalty of suly and demand on the world market mles that every country has a moderate rce level n the long run. If the rce level s too hgh or too low, there would be a ermanent dsequlbrum of the balance of ayments. Adustment through a change n the exchange rate wll necessarly take lace. Therefore, the general rce level wll not nfluence a country s otental foregn suly and demand excet n the short-run. If we assume a constant elastcty of the sze of the trade flow n resect of otental suly and otental demand ndcatng the trade flow from country to country byχ, the trade flow equaton would then combne the three determnng factors n the followng way: 0 β1 ( E ) ( M ) β ( R ) 3 β 2 Χ β (3) = 84

4 Mathematcal Theory and Modelng ISSN (Paer) ISSN (Onlne) Ε andμ are total otental suly and demand resectvely. R s Resstance.Aarently the trade flow from country to country wll deend on Ε andμ. In ts smlest form, all exonents equal to 1. The above three exlanatory factors n (3) should now be relaced by the varables determnng them. Therefore we now ntroduce the followng notatons. Y= Gross natonal roduct N= Poulaton sze y = Per cata natonal ncome (or roduct) D = Geograhcal dstance P = Preferental trade factor Ε s a functon of Y and N, and ossbly of y. Thus we may wrte In whch γ1= 1 and γ2 s negatve It was assumed that the same s true for the otental suly Μ whch s determned by dentcal forces.the trade resstance factor R can be relaced by two varables D wth a negatve exonent and P wth a ostve exonent. For the latter varable several other varables may be substtuted f we want to dstngush between varous tyes of referental tradng areas. Here we dsregard ths comlcaton for the sake of smlcty of the model. Therefore trade flow equaton runs as follows: (4) X = δ o Y N δ 1 δ 2 Y N δ 3 δ 4 P δ 6 D δ 5 (5) Where Ρ s varous tyes of referental tradng areas. 2.3 GRAVITY MODEL OF ANDERSON (1979) The model roosed by Anderson (1979) s manly based on Cobb-Douglus or CES reference functon. Usng a trade share exendture system, Anderson derves the gravty model, whch ostulates dentcal Cobb- Douglas or constant elastcty of substtuton (CES) reference functon for all countres and weakly searable utlty functons between traded and non-traded goods. Here utlty maxmzaton wth resect to ncome constrant gves traded goods shares that are functons of traded goods rces only. Prces are constant n cross-sectons; so usng the share relatonshs along wth trade balance dentty, country s morts of country s goods are obtaned. Then assumng log lnear functons n ncome and oulaton for shares, the gravty equaton for aggregate morts s obtaned. Anderson roosed the followng assumtons and derves the Gravty model. Assumtons: 85

5 Mathematcal Theory and Modelng ISSN (Paer) ISSN (Onlne) Preferences are homothetc and dentcal across regons. Products are dfferentated by lace of orgn. Pure exendture system s such that the share of natonal exendture accounted for by sendng on tradable s a stable undentfed reduced form functon of ncome and oulaton. Suose, each country s comletely secalzed n the roducton of ts own good. So there s one good for each country. There are no tarffs or transort costs. The fracton of ncome sent on the roducton of country s denoted by b and s the same n all countres. Ths mles dentcal Cobb-Douglas references everywhere. Prces are constant at equlbrum values and unts are chosen such that they are all unty wth cross-secton analyss. Consumton of good (n value and quantty terms) n country (morts of good by country ) s thus M = b Y (7) WhereY s ncome n country. The requrement that ncome must equal sales mles that Y ( Y ) = b (8) Where b s the fracton of ncome sent on roducton of country. Solvng (8) for b and substtutng nto (7) we obtan M YY = (9) Y Ths s the smlest form of gravty model. If error structure s dsregarded, a generalzaton of equaton (9) can be estmated by OLS, wth exonents on Y, Y unrestrcted. In a ure cross secton, the denomnator s an rrelevant scale term. The ncome elastcty roduced should not dffer sgnfcantly from unty. An unrestrcted gravty equaton s obtaned f Cobb-Douglas exendture system for traded- non traded goods slt s added. Traded goods shares of total exendture dffer wdely across regons and countres. Per cata ncome s consdered as exogenous demand sde factor, and oulaton (country sze) s consdered a suly-sde factor. Trade share should ncrease wth er cata ncome and decrease wth sze. Takng the trade-share functon as stable, the exendture system model combnes wth t to roduce the gravty equaton. Suose, all countres roduce a traded and a non-traded good. The overall reference functon assumed n ths formulaton s weakly searable wth resect to the artton between traded and non-traded goods: U = u (g (traded goods), non traded goods). Then gven the level of exendture on traded goods, ndvdual traded goods demands are determned as f a homothetc utlty functon n traded goods alone g( ) s maxmzed subect to a budget constrant nvolvng the level of exendture on traded goods. The ndvdual traded goods shares of total trade exendture wth homothetcty are functons of traded goods rces only. To make t smle, t s assumed that g( ) has the Cobb-Douglas form. Snce references are dentcal, exendture shares for any goods are dentcal across countres wthn the class of traded goods. So for any 86

6 Mathematcal Theory and Modelng ISSN (Paer) ISSN (Onlne) consumng country, θ s the exendture on country s tradable good dvded by total exendture n on tradable;.e. θ s an exonent of g ( ). Let φ be the share of exendture on all traded goods n total exendture of country and φ = F Y, N. ( ) Demand for s tradable good n country ( s morts of s good) s M = θφ Y (10) The balance of trade relaton for country mles that ( Y φ J ) θ YΦ = (11) Value of morts of Value of exorts of Plus domestc sendng = Plus domestc sendng on domestc tradable on domestc tradable solvng (11) for θ and substtutng nto (10) we have M φ Y φ Y φ Y φ Y Y M = = φ A log-lnear form of equaton (12) s the determnstc form of the gravty equaton wth the dstance term suressed and a scale term added. In the same way, the gravty equaton can be derved assumng ether erfect cometton or monoolstc market structure. 2.4 GRAVITY MODEL UNDER MONOPOLISTIC COMPETITION Anderson and Wncoo (2003) resented an mortant and novel analyss, assumng CES-references, symmetrc trade barrers and mosng the general equlbrum constrant for trade,.e. that total sales equal total roducton, Anderson and Wncoo exlctly derve the followng gravty equaton for blateral trade, (12) Here Χ s exorts from country (regon) to country, Y s the ncome (GDP) of country, Υ w s the world GDP, t s the trade barrer factor (nverse of one mnus the ad valorem tax er unt of exorts) between countres (regons) and, assumed to be the same as t, and P s aggregate trade resstance, or smly, the consumer rce ndex of country. The arameter σ s the elastcty of substtuton between morts from varous orgns. The mort demand functons n country, = 1 N, are derved from a CES utlty functon for aggregate consumton D. 87 (13)

7 Mathematcal Theory and Modelng ISSN (Paer) ISSN (Onlne) Here Q s the volume of exorts from country to, a s the country-secfc ostve reference (dstrbuton) arameters summng to unty and σ s, agan, the elastcty of substtuton between morts from varous orgns. The mort demand functons are then (14) (15) Where Ρ the rce s set by the exorters of country n the market of country, nclusve of the cost of trade barrers and, beng dual to the quantty ndex (14), P reresents the CES rce ndex of the consumton basket n country, (16) From (16) we can derve the market share of the value of exorts yeldng Χ = Ρ Q n country, n relaton to ts GDP, (17) Where Y s the GDP (n nomnal terms) of country and the budget constrant Y = P D s mosed. We next consder the exort suly decson of a monoolstc frm of country n the market of country. For ths we need to secfy that aggregate demand D, whch s gven by the functon (18) Where b s a scale factor reresentng the sze of the country concerned. Note that tycally ε < σ. Let there be K dentcal exortng frms n country. The otmal suly decson of an exorter n country maxmzng roft n market s gven by 88 (19)

8 Mathematcal Theory and Modelng ISSN (Paer) ISSN (Onlne) Where C s the margnal cost of roducton n country and Q k denotes the volume of exorts of frm k of country n the market of country, t s as n equaton (13), the trade barrer factor between countres (regons) and, and ε ( z, z ) denotes the elastcty of the varable z wth resect to the varable z. Usng (15), (18) and the general result from ndex number theory.e. the market share of exorter k n the market of country, and summng over the dentcal K frms, we derve the followng from (19), Here h s the conectural varaton arameter n the roortonal outut game 1 (see Smth and Venables,1988 and Alho,1996) and s s the aggregate market share of country n the market of country,.e. (20) The suly equaton (20) allows for rce dscrmnaton between varous exort markets. Note that under erfect cometton, the exort rce only deends on the unt cost and the resectve trade barrer. But otherwse under merfect cometton, the larger the country, measured by the number of frms, the lower wll be the exort rce that frms charge. We next need a model for the determnaton of the cost levels C and therefore ntroduce the followng framework. Assume smly that labour L s the only factor of roducton 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: where ν > 0 and D s total suly. Now otmzng under the budget constrant P D = W L + π, where W s the wage rate and π aggregate rofts, we derve the result for wage formaton, (21) W In the next ste, n dervng the unt cost C =, we could take two aroaches. A 1 The arameter h s n relatve terms the outut resonse by the comettors to a 1% rse n the outut of the frm concerned n market. f be zero, we have the case of Cournet cometton. 89 h s set to

9 Mathematcal Theory and Modelng ISSN (Paer) ISSN (Onlne) Frst, we could take t that technology, as ncororated n the arameter A, s dentcal n all the countres. But, ths assumton of unformty s not very sensble. Therefore, we allow for dfferences n roductvtes and wrte A, beng the average labor roductvty, as Q A = Y = 2. So, we derve for the unt cost L P L (22) Where ν s ostve and deends smly on the rce level n the country and ostvely on the sze of the country measured by the labor force, whch s catured below by oulaton.we further assume that that the average sze Q of the frms s dentcal n all the countres, so that KQ = Q = Y/P. Then normalze ths average sze to unty and nsert ths result and (22) nto (20). By equatng exort demand (16) wth suly (20), we can then solve for exort rce P from the equlbrum condton, (23) Next nsert ths equlbrum soluton (23) for the exort rce n market nto the exort demand equaton (17). 2 2 Usng the aroxmaton that log( x + y) log( x) + log( y) + o( x ) + o( y ). We can solve for the blateral exorts to be as follows, returnng back to a ower functon secfcaton, (24) The arameter µ s ostve and smaller than unty, f the elastcty of substtuton σ s greater than unty. In addton, functon (24) ncludes hgher order terms for Y, P and P. The arameter h s assumed to be unform n all market The above model gves the secfcaton of Gravty model under monoolstc cometton, whch exsts n the whole world. 2 Note that as aggregate demand s dentcally Equatonual to aggregate suly (GDP),.e. Q Q P s the rce on GDP. These rces P and P are dentcal. 90 P Q = P D Q

10 Mathematcal Theory and Modelng ISSN (Paer) ISSN (Onlne) FIRST-PASS GRAVITY EQUATION FOR BILATERAL TRADE The exendture share dentty The frst ste s the exendture share dentty for a sngle good exorted from the orgn naton to the destnaton naton s P x = Share E (25) (where X s the quantty of blateral exorts of a sngle varety from naton to naton, P s the rce of the good nsde the mortng naton also called the landed rce,.e. the rce of the morted good that s faced by customers n the mortng naton; ths s measured n terms of the numerare. Of course, ths makes x the value of the trade flow measured n terms of the numerare. Ε s the destnaton naton s exendture (agan measured n terms of the numerare) on goods that comete wth morts,.e. tradable goods. By defnton, share s the share of exendture n naton on a tycal varety made n naton-. The exendture functon Mcroeconomcs tells us that exendture shares deend uon relatve rces and ncome levels. The exendture share s assumed to deend only on relatve rces. Adotng the CES demand functon and assumng that all goods are traded, the morted good s exendture share s lnked to ts relatve rce by: 1 σ 1 R 1 σ ( n ( ) ) ( σ ), σ > 1 P Share, 1 wherep k= 1 k kd (26) P Where /P s the real rce of. Also, P s naton- s deal CES rce ndex (assumng all goods are traded), R s the number of natons from whch naton- buys thngs (ths ncludes tself), and σ s the elastcty of substtuton among all varetes (all varetes from each naton are assumed to be symmetrc for smlcty); n k s the number of varetes exorted from naton k. We assume symmetry of varetes by source- naton to avod ntroducng a varety ndex. As always, all rces here are measured n terms of the numérare. Combnng (25) and (26) yelds roduct secfc mort exendture equaton Addng the ass-through equaton The landed rce n naton- of goods roduced n naton- are lnked to the roducton costs n naton-, the blateral mark-u, and the blateral trade costs va = µ τ (27) Where s the roducer rce n naton-,µ s the blateral marku and τ reflects all trade costs, natural and manmade. Ths assumes that the rce-cost marku s a arameter. To kee thngs smle, we takeµ = 1. 91

11 Mathematcal Theory and Modelng ISSN (Paer) ISSN (Onlne) Aggregatng across ndvdual Varetes We have exorts of ndvdual varetes. To get total blateral exorts from to, we multly the exendture share functons across the number of symmetrc varetes that naton has to offer, namely n. Usng uer case V to ndcate to total value of trade, we have V n s Ε And V =n ( τ ) 1-σ 1-σ E /P (28) Lackng data on the number of varetes n and roducer rces, we comensate by turnng to naton- s general equlbrum condton. General equlbrum n the exortng naton Usng general equlbrum n the exortng naton to elmnate the nomnal rce the roducer rce n the exortng naton- must adust such that naton- can sell all ts outut, ether at home or abroad. Exresson (28) gves us naton- sales to each market. Summng over all markets, ncludng s own market, we get total sales of naton- goods. Assumng markets clear, naton s wages and rces must adust so the naton- s roducton of traded goods equals ts sales of trade goods. In symbols, ths requres. R Y = d= 1 V, where Y s naton- s outut measured n terms of the numérare. RelatngV to underlyng varables wth (28), the market clearng condton for naton- becomes: E 1 σ R 1 σ = n d= 1 τ 1 σ Y (29) where the summaton s over all markets (ncludng s own market). Solvng ths for n wll yelds, 1 σ 1 σ Y R 1 σ E n = Ω where = 1 τ (30) 1 σ Ω Here Ω measures the market otental. A naton s market otental s often measured by the sum of ts trade artners real GDPs dvded by blateral dstance. The catal-omega s a used for oenness snce t measures the oenness of naton- s exorts to world markets. 92

12 Mathematcal Theory and Modelng ISSN (Paer) ISSN (Onlne) A frst-ass gravty equaton Substtutng (30) nto (28), we get our frst-ass gravty equaton: V =τ 1-σ (Y E /Ω P 1-σ ) (31) Note that all varables are measured n terms of the numérare. Exresson (31) s a mcrofounded gravty equaton. Takng the GDP of naton- as a roxy for ts roducton of traded goods, and naton- s GDP as a roxy for ts exendture on traded goods, equaton (31) can be re-wrtten to look ust lke the hyscal law of Blateralt rade Y Y = G elastcty 1 12 gravty. ( dst ) ; 1 1 G 1 elatcty Ω where the Y s are the natons GDPs and t s assumed that blateral trade costs deend only uon blateral dstance n order to make the economc gravty equaton resemble the hyscal one as closely as ossble. Imortantly, G here s not a constant as t s n the hyscal world. It wll vary over tme. Smlarly Eaton and Kortum (1997) also derve the gravty equaton from Rcardan framework, whle Deardorff (1997) derves t from an H-O ersectve. Where as t s shown by Evenett and Keller (1998) that the standard gravty equaton can be obtaned from the H-O model wth both erfect and merfect roduct secalzaton. Many economsts beleve that gravty model s a successful model to estmate the flow of nternatonal trade. However, there s a great deal of ambguty regardng the theoretcal foundatons of Gravty model whch can be categorzed nto economc and non-economc exlanatons. Among the ustfcatons based on formal economc theory, we can cte Anderson (1979), Bergstrand (1985, 1989) and Deardoff (1995), Helman (1987), Helman and Krugman (1985). Emrcally, t has been notced that R-square n gravty equaton turns out to be n between 0.65 and 0.95, deendng uon the secfcaton of the equaton (Harrgan, 2002). But many economsts have the argument that the gravty equaton does not have much lnk wth the neoclasscal trade theory as t does not ncororate the role of comaratve advantage or mortance of relatve factor endowments or relatve level of technology among the tradng countres.a related observaton s that, neoclasscal trade theory s generally not concerned wth blateral trade: rather a country s trade s determned by ts dfference from the rest of world. However, t s common to augment the basc gravty model through addtonal blateral varables. For nstance varables are added to control for common language, common border, common colonal hstory, common currency, land-locked ness, and solaton. Usually these varables are ntroduced as bnary varables n the gravty equaton. Generally the gravty equaton s secfed as M k α k y y N N d β 1 k β 2 k β 3 k β 4 k β 4 k = (32) U k M k s the dollar flow of good or factor k from country or regon to country or regon, and, term N and y and y are ncomes n N are oulaton n and, and d s the dstance between countres (regons) and. The E InU =.Most often the flows are aggregated across goods. U s a log normally dstrbuted error term wth ( ) 0 93

13 Mathematcal Theory and Modelng ISSN (Paer) ISSN (Onlne) Concluson From above dscusson we deduce that Gravty equaton s dervable n dfferent condtons under dfferent assumtons. So gravty model s usable to measure blateral trade flows n all tyes of market structure and condtons. There are dfferent categores of emrcal alcatons of the Gravty equaton, whch can be mentoned to nvestgate ssues n nternatonal trade: that are estmatng the cost of a border, exlanng trade atterns, dentfyng effects related to regonalsm and lastly tabulatng trade otentals. Because of ts aeal as an emrcal strategy the alcaton of gravty model s becomng enormously oular. Quotng Echengreen and Irwn (1997), the gravty model s nowadays "... the workhorse for emrcal studes..." n nternatonal trade. Snce the early 1990s, the large avalablty of nternatonal data necessary to fll the standard secfcaton of the model, the relatve ndeendence from dfferent theoretcal models, and a bandwagon effect make the gravty model the emrcal model of trade flows (Evenett and Keller, 2002). References Anderson, J.E (1979), A Theoretcal Foundaton for the Gravty Equaton, The Amercan Economc Revew, Vol. 69: Anderson, J.E. and Wncoo E. V (2003), Gravty wth Gravtas: A Soluton to the Border Puzzle, The Amercan Economc Revew, Vol. 93, ssue 1, , Nashvlle. Bergstrand J.H (1989), The Generalzed Gravty Equaton, Monoolstc Cometton, and the Factor Proorton Theory n Internatonal Trade, Revew of Economcs and Statstcs: Bergstrand, J.H 1985, The Gravty Equaton n Internatonal Trade: Some Mcroeconomc Foundatons and Emrcal Evdence, The Revew of Economcs and Statstcs, Vol. 67: Harvard Unversty Press. Deardorff, A. (1997), Determnants of Blateral Trade: Does Gravty Work n a Classcal World?, In The Regonalzaton of the World Economy, ed. by Jeffrey Frankel. Chcago: Unversty of Chcago Press. Egger, P. and Pfaffermayr, M (2000), The Proer Econometrc Secfcaton of the Gravty Equaton: A Three Way Model wth Blateral Interacton Effects, Workng Paer, Austran Insttute of Economc Research, Venna, Austra. Evenett, S.J. and Keller, W (1998), On the Theores Exlanng the Success of the Gravty Equaton, n NBER Workng Paer, No. 6529, Cambrdge, MA: Natonal Bureau of Economc Research. Frankel, J. and We, S.J (1993), Emergng Currency Blocs, Mmeo, Unversty of Calforna- Berkeley. Frankel, J.A. (1997), Regonal Tradng Blocs n the World Economc System, Insttute for Internatonal Economcs, Washngton, D.C. Helman, E and Krugman, P. (1985), Market Structure and Foregn Trade, Cambrdge, MA: MIT Press. Hummels, D. and Levnsohn, J (1993), Product Dfferentaton as a Source of Comaratve Advantage, Amercan Economc Revew, Paers and Proceedngs, LXXXIII: Head,K. and Mayer. T (2000), Non-Euroe: The Magntude and Causes of Market Fragmentaton n the EU, Weltwrtschaftlches Archv, 136(2): Harrs, Mark N and Lázlo Mátyás (1998) The Econometrcs of Gravty Models, Workng Paer No. 5/98, Melbourne Insttute of Aled Economc and Socal Research. Head, K (2003), Gravty for Begnners, Unversty of Brtsh Columba, Vancouver. Hummels, D (1999), Have nternatonal transort costs declned? workng aer. Krugman, P. (1979), Increasng Returns, Monoolstc Cometton, and Internatonal Trade, Journal of Internatonal Economcs, Vol. 9: Lnder, S. B. (1961), An Essay on Trade and Transformaton, New York: John Wley and Sons. Lnneman, H. (1966), An Econometrc Study of Internatonal Trade Flows, North Holland, Amsterdam. Mátyás, L. (1997), Proer Econometrc Secfcaton of the Gravty Model, The World Economy, Vol. 20, No3. Oguledo, V.I. and Machee, C.R. (1994), Gravty Models: A Reformulaton and an Alcaton to Dscrmnatory Trade Arrangements, Aled Economcs, 26: Paas, T. (2000), Gravty Aroach for Modelng Trade Flows between Estona and the Man Tradng Partners, Workng Paer, No. 721, Tartu Unversty Press, Tartu. Poyhonen, P. (1963), Toward A General Theory of Internatonal Trade,Ekonomska Samfundets Tdskrft, Trede seren, Argang 16: Rauch, J.E (1996), Networks Versus Markets n Internatonal Trade, Workng Paer 5617, Natonal Bureau of Economc Research. Rauch, James E. and Trndade, V (2002), Ethnc Chnese Networks n Internatonal Trade",Revew of Economcs and Statstcs, 84:

14 Mathematcal Theory and Modelng ISSN (Paer) ISSN (Onlne) Santos Slva J.M.C. and Tenreyro S (2004), The Log of Gravty, FRB Boston Seres, aer no.03-1 (2003). Sachs, J.D and Andrew.M.W (1995), Natural Resource Abundance and Economc Growth, Workng Paer 5398, Natonal Bureau of Economc Research. Tnbergen, J. (1962), Shang the World Economy: Suggestons for an Internatonal Economc Polcy. The Twenteth Century Fund, New York. 95

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