On Theories Explaining the Success of the Gravity Equation

Transcription

1 On Theores Explanng the Success of the Gravty Equaton Smon J. Evenett World Trade Insttute and Centre for Economc Polcy Research Wolfgang Keller Unversty of Texas, Natonal Bureau of Economc Research, and Centre for Economc Polcy Research We examne whether two mportant theores of trade, the Heckscher- Ohln theory and the ncreasng returns theory, can account for the emprcal success of the so-called gravty equaton. Snce versons of both theores can predct ths equaton, we tackle the model dentfcaton problem by condtonng blateral trade relatons on factor endowment dfferences and on the share of ntrandustry trade. Only for large dfferences n factor endowments does the Heckscher-Ohln model predct perfect producton specalzaton n dfferent countres as well as the gravty equaton, and trade s purely n goods produced wth dfferent factor ntenstes. Our emprcal analyss yelds three fndngs. Frst, the predctons of the perfect specalzaton versons of both theores are rejected by the data and so are unlkely explanatons for the emprcal success of the gravty equaton. Second, a model of mperfect specalzaton that ncludes both ncreasng re- We have benefted from comments at semnar presentatons at Berln (Humboldt), Boston Unversty, Brown, Dartmouth, Columba, Geneva (Graduate Insttute), Harvard, New York Unversty, Penn, Toronto, Unversty of Calforna (San Dego and Santa Cruz), Wsconsn, and Yale, as well as from partcpants at the 1998 Mdwest Internatonal Economcs Conference n Ann Arbor, the 1997 NBER Summer Insttute, the August 1997 European Economc Assocaton meetng at Toulouse, the September 1997 conference of the European Research Workshop n Internatonal Trade/Centre for Economc Polcy Research n Helsnk, and the Emprcal Trade Conference 1996 at Purdue Unversty. Specal thanks go to Don Davs, Peter Debaere, Mahmoud El-Gamal, Gordon Hanson, Elhanan Helpman, Dan Trefler, Lars Peter Hansen as the edtor, and especally to an anonymous referee. We also thank Jm Rauch and Karl Agnger for provdng data used n ths paper. [Journal of Poltcal Economy, 2002, vol. 110, no. 2] 2002 by The Unversty of Chcago. All rghts reserved /2002/ $

2 282 journal of poltcal economy turns and factor endowments as sources of trade has a mxed performance: t correctly predcts producton of more dfferentated goods when the level of ntrandustry trade s greater; however, the predcted lnk to factor proportons s tenuous. Thrd, the predctons of a model wth mperfect specalzaton that reles solely on dfferences n factor endowments fnd support n the data. These results suggest that factor endowments and ncreasng returns explan dfferent components of the nternatonal varaton of producton patterns and trade volumes. The so-called gravty equaton of trade predcts that the volume of trade between two countres s proportonal to ther gross domestc products and nversely related to trade barrers between them. Emprcal research has found that varous versons of the gravty equaton can account for the varaton n the volume of trade across country pars and over tme (see Leamer and Levnsohn 1995). Snce Anderson (1979), t has been ncreasngly recognzed that the gravty equaton can be derved from very dfferent models, ncludng Rcardan, Heckscher-Ohln, and ncreasng returns to scale (IRS) models (Helpman and Krugman [1985], Bergstrand [1990], Markusen and Wgle [1990], Eaton and Kortum [1997], and Deardorff [1998]; see also the recent survey by Helpman [1998]). Many of these models have one characterstc n common: perfect specalzaton, where each commodty s produced n only one country. Ths multtude of models has led some to argue that the gravty predcton cannot be used to test any one of these trade theores (Deardorff 1998). Yet the gravty equaton consttutes, perhaps along wth the Heckscher-Ohln-Vanek factor servce trade predcton, one of the most mportant results about trade flows. Therefore, major nsghts nto the causes of nternatonal trade mght be ganed f t could be determned whch theory actually accounted for the success of the gravty equaton n a gven sample of data an emprcal challenge we refer to as a model dentfcaton problem. We address ths dentfcaton problem by notng that, n a constant returns to scale (CRS) Heckscher-Ohln world, perfect specalzaton results only when blateral dfferences n factor proportons are large enough. In contrast, when product specalzaton s the result of IRS, the gravty predcton can be obtaned even f there are no dfferences n factor proportons. Furthermore, these models predct dfferent types of trade: n the Heckscher-Ohln model, trade occurs exclusvely n goods produced wth dfferent factor ntenstes (nterndustry trade). In contrast, n the IRS model, some, and potentally all, trade s ntrandustry. Consequently, we shall take samples wth hgh shares of ntrandustry trade n total trade as those n whch IRS-based specalzaton mght drve the gravty equaton. Furthermore, those samples wth low

3 gravty equaton 283 shares of ntrandustry trade n total trade and large dfferences n factor proportons are those n whch a model of Heckscher-Ohln-based specalzaton mght be behnd the gravty equaton. In prncple ths could lead to a sample-by-sample reconclaton of the perfect specalzaton models of the Heckscher-Ohln and IRS trade theores. However, no such reconclaton emerges from our analyss of a large and heterogeneous set of blateral trade relatons n There s strong evdence that perfect specalzaton due to dfferences n factor proportons cannot explan the success of the gravty equaton. The IRS model of perfect specalzaton performs only slghtly better n our analyss. Our results suggest that perfect specalzaton models, whch predct a strct proportonalty of trade wth GDP, overpredct the volume of trade compared to what s actually observed by a large amount. Ths renforces the case for consderng trade models n whch producton s mperfectly specalzed. The prmary contrbuton of ths paper s that we evaluate gravty equatons based on mperfect specalzaton of producton. The mperfect specalzaton models presented here predct a factor of proportonalty of trade wth GDP of less than one. By predctng a lower level of trade, all else equal, these models are, a pror, better canddates to emprcally match the trade volumes that are observed. Moreover, n these models the degree of specalzaton s a functon of relatve factor abundance, a key exogenous varable. Wth estmates of the former and data on the latter, we have the means to evaluate these models. We fnd that trade among the ndustralzed countres ( North-North trade) can be partally captured by a model that combnes trade n perfectly specalzed dfferentated goods and homogeneous goods. Moreover, trade between less developed and ndustralzed countres ( North- South trade) s qute well explaned by an mperfect specalzaton Heckscher-Ohln model of trade n homogeneous goods. Our analyss also sheds new lght on the emprcal relevance of the IRS trade models n general. The nfluental fndng of Helpman (1987), that key mplcatons of the IRS model are consstent wth trade data for Organzaton for Economc Co-operaton and Development (OECD) countres, has been called nto queston. Hummels and Levnsohn (1995) repeated Helpman s analyss wth a set of non-oecd countres, whose blateral trade was not expected to contan much IRS-based trade. They showed that many correlatons found by Helpman contnue to hold. Rather than provdng broad evdence aganst IRS trade models and, n partcular, that these models cannot be responsble for the emprcal success of the gravty equaton (see Hummels and Levnsohn 1995, p. 828), ther fndngs hghlght the mportance of the model dentfcaton problem. Ths paper accounts for both Helpman s and Hummels and Levnsohn s fndngs by suggestng that Helpman ob-

4 284 journal of poltcal economy taned hs results because IRS-based trade s mportant among OECD countres, whereas Hummels and Levnsohn found a smlar correlaton among non-oecd countres because of specalzaton drven by dfferences n factor proportons. Our results underscore the mportance of both relatve factor abundance and IRS as determnants of the extent of specalzaton and nternatonal trade, wth ther relatve mportance dependng on the partcular sample n queston. Ths s n lne wth the results of Antweler and Trefler (1997), who estmate IRS and CRS models nested n the Heckscher-Ohln-Vanek factor servce trade expresson. They fnd that although a majorty of ndustres seem to be well characterzed by the assumpton of CRS, there s evdence for IRS n a number of sectors. The remander of the paper s organzed as follows. We present the gravty equaton predctons of four dfferent trade models n Secton I. Secton II descrbes n more detal how we dentfy a partcular model n our emprcal analyss. Secton III dscusses the data set employed n ths study, and Secton IV presents the emprcal results. Secton V presents conclusons. The senstvty of our results s dscussed n the Appendx. I. The Gravty Equaton: Theores A. The Gravty Equaton wth Perfect Specalzaton of Producton Throughout the paper, we assume that there s balanced trade, zero trade and transport costs, no trade n ntermedate goods, and two countres wth dentcal producton technologes and that consumers n both countres have dentcal homothetc preferences. Frst, we consder a typcal IRS model as lad out n Helpman and Krugman (1985, chap. 8.1), where there are two countres, c p, j, and two goods, g p X, Z. Both X and Z come n many dfferentated varetes, whch are dentcally produced wth ncreasng returns to scale. Wth preferences valung product varety, a country wll demand all foregn varetes accordng to the country s GDP as a share of world GDP. Let the GDPs of countres j and j be denoted Y and Y, respectvely, and denote the GDP of the w world by Y. Gven that IRS leads to perfect specalzaton of producton for every varety, t can be shown that country s mports from j, denoted j M, are gven by j YY j M p. (1) w Y Here mports are strctly proportonal to the GDPs, and so ths IRS trade

5 gravty equaton 285 model s a potental canddate to explan the success of the gravty equaton. 1 Equaton (1) s very general snce ts dervaton does not requre assumptons on factor prce equalzaton, dfferences n factor endowments across countres, factor ntenstes n the producton of goods X and Z, or even the number of sectors, factors, and countres (Helpman and Krugman 1985). Equaton (1) holds whenever there s perfect specalzaton n equlbrum, all consumers face the same goods prces and have dentcal homothetc preferences, and trade s balanced. Also, when nternatonal dfferences n factor endowments are large enough across countres (compared to dfferences n the goods factor nput requrements), perfect specalzaton can result. Thus a Heckscher- Ohln model can also generate the gravty equaton (1). In the twocountry, two-good, two-factor (2#2#2) case, ths requres that the countres relatve endowment ratos dffer by at least as much as the goods relatve nput ratos, whch are consstent wth dversfed producton and factor prce equalzaton through trade. In the emprcal analyss below, we shall refer to ths as the multcone Heckscher-Ohln model. B. Gravty Equatons wth Imperfect Specalzaton of Producton Frst, we present the gravty equaton for a model n whch one sector (Z) produces a homogeneous good under CRS, whereas a second sector (X) produces a dfferentated good under IRS (Helpman [1981]; see also Helpman and Krugman [1985, chaps. 7, 8]). Ths model wll be referred to as the IRS/uncone Heckscher-Ohln model. There are two countres ( and j) and two factors, captal (K) and labor (L). Assume that the homogeneous good s more labor-ntensve n producton and c that country s captal-abundant. Let g be the share of good Z n c c c c country c s GDP, g p Z/(pX x Z ), where p x s the relatve prce of good X. For endowments n the two countres that are suffcently smlar that factor prce equalzaton through trade can be acheved, country exports only the captal-ntensve X varetes. Country s share of X varetes n GDP s equal to 1 g, so the value of producton on whch country j draws for ts mports s gven by (1 g )Y. The assumpton of homothetc preferences means that country j purchases X varetes from abroad accordng to ts share n world GDP, whch s equal to Y/Y j w. 1 Ths gravty predcton, as well as those below, s readly generalzed to the case n whch tradable goods make up a share l, 0 l 1, of GDP that s common to all countres. j j w In that case, one obtans M p l(y Y/Y ).

6 286 journal of poltcal economy Together wth balanced trade ths means that country s mports from j are gven by j YY j M p (1 g ). (2) w For any value g 1 0, the level of blateral mports s lower than n the case n whch both goods are dfferentated (compare eqq. [2] and [1]). Furthermore, as the share of homogeneous goods n GDP declnes, the predcted level of mports rses; n the lmt, as g r 0, the generalzed gravty equaton (2) reverts to the smple gravty equaton (1) above. Therefore, the hgher the volume of trade, the lower the share of homogeneous goods n GDP. 2 Second, we present the partcular form of the gravty equaton n the case of a 2#2#2 uncone Heckscher-Ohln model, where both good Z and good X are homogeneous and are produced under CRS n both countres. If country s relatvely captal-abundant and good Z s relatvely labor-ntensve, country s mports from j are equal to p x[x w w w (Y/Y )X ], where X s the world s producton of good X. Usng the w j w defnton of g and the fact that Y/Y p 1 (Y/Y ) leads to Y j j YY YY j j j M p [(1 g ) (1 g )] p (g g ). (3) w w Y Y As the captal-labor ratos n the two countres converge, so do g j and g. In the lmt, when the factor proportons n and j are equal, we j have that g p g, n whch case equaton (3) gves the famlar result that there s no trade n a Heckscher-Ohln model when factor proportons are dentcal. Equaton (3) ncludes as a specal case the predcton about the volume of mports of the multcone Heckscher-Ohln model gven n (1) because as dfferences n factor proportons between j and j ncrease, the share of good Z n country j s GDP, g, approaches one, whereas the share of good Z n the GDP of country, g, tends to zero. If we denote the predcton about the volume of mports for the case n whch the producton of both goods s perfectly specalzed, equaton (1), by M S ; the IRS/uncone Heckscher-Ohln case wth specalzaton for one good, but not for the other good (eq. [2]), by M IH ; and the uncone Heckscher-Ohln case n whch both countres produce both 2 Ths fndng s n part due to Heckscher-Ohln reasons because g s nversely related to country s captal-labor rato. A declne n g therefore mples an ncrease n the volume of mports due to an ncrease n the countres dfferences n factor proportons. What we emphasze s that for gven dfferences n factor proportons, the more specalzaton there s, the hgher the level of mports; see below.

7 gravty equaton 287 goods, equaton (3), by M H, the followng nequaltes hold, ceters parbus: M 1 M 1 M. (4) S IH H Ths confrms that the blateral volume of mports s hgher the more product specalzaton there s. In summary, the observable mplcatons of these trade models are as follows. Both perfect specalzaton models predct that blateral mports are drectly proportonal to the product of the GDPs. For the IRS/uncone Heckscher-Ohln model, mports are less than proportonal to ths product, and the extent of the shortfall depends on the sze of the dfferentated goods sector n GDP. All else equal, the uncone Heckscher-Ohln model predcts the smallest factor of proportonalty of mports wth GDP, and ths factor s predcted to rse when dfferences n factor proportons across trade partners are larger. II. Model Identfcaton In the precedng secton, we dscussed the specfc form of the gravty equaton of trade for four models. From now on, we consder only 2#2#2 models. It s unlkely, however, that any of the observed trade flows are solely determned by any one of these four archetypcal models. Frst, the data come from a world wth more sectors, countres, and factors than exst n our 2#2#2 models. Second, there may be postve amounts of IRS-based trade even between countres wth the lowest recorded shares of IRS-based trade, and lkewse for factor proportons based trade. However, n dfferent crcumstances (such as dfferent degrees of product dfferentaton n the goods that are traded), we expect that the volume of trade s better accounted for by one partcular model than another. Ths s the bass for our model dentfcaton strategy. Consder a cross secton of country pars n whch there s lttle (or no) specalzaton due to IRS, but the absolute dfference between the two countres factor proportons, denoted FDIF, vares from one par to another. If Heckscher-Ohln forces are at work, then we expect, ceters parbus, more specalzaton n a par n whch FDIF s larger than n another country par n whch FDIF s smaller. Ths observaton allows us to dentfy the Heckscher-Ohln motvaton for specalzaton and the gravty predcton. We employ the ndex proposed by Grubel and Lloyd (1975) to ndcate the extent of IRS-based trade. As a result of trade due to IRS and product dfferentaton, a country smultaneously mports and exports

8 288 journal of poltcal economy varetes of a partcular product (ntrandustry trade). 3 The ndex, denoted GL j, measures the share of ntrandustry trade n total trade: j j g FM g MgF j j GL p 1 [, 0 GL 1. (5) j j ] g g g (M M ) In the extremes, when every good g s ether exported or mported (no ntrandustry trade), the Grubel-Lloyd ndex wll be equal to zero, whereas t s equal to one f a country s mports and exports of all goods are equal (only ntrandustry trade). Ths ndex s not a perfect ndcator for the share of trade based on IRS. Fnger (1975) has emphaszed that ndustry classfcatons often contan qute dfferent products, and clearly a hgh degree of dsaggregaton s desrable when measurng ntrandustry trade. Recently, researchers have emphaszed the mportance of trade n ntermedate goods n accountng for hgh values of GL j (Greenaway, Hne, and Mlner 1994; Fontagne, Freudenberg, and Perdy 1998), whch can n prncple be due to IRS and other reasons. Moreover, a sgnfcant part of trade that s classfed as nterndustry trade mght nvolve IRS, such as wde-boded arcraft exports from the Unted States to most other countres. 4 After dscussng ths ssue n some detal, Krugman (1994, p. 23) concludes that although GL j does not precsely measure the share of nternatonal trade that s due to IRS, there s no ndcaton that there s an mportant upward or downward bas. We expect that the IRS model accounts for the performance of the gravty equaton n those samples n whch the blateral Grubel-Lloyd ndces are relatvely large, ndcatng that a relatvely large proporton of blateral trade s two-way trade n dfferentated products. In Secton IVA1, we examne whether n fact the predcton M S (of the IRS model) s accurate n samples wth relatvely hgh Grubel-Lloyd ndces. We emphasze that predcton M S s common to both the multcone Heckscher-Ohln and the IRS models. However, should we fnd that the predcton M S s not rejected by the data n samples wth relatvely hgh Grubel-Lloyd ndces, then t would be ncorrect to nterpret ths fndng as evdence n favor of the multcone Heckscher-Ohln theory, whch predcts no ntrandustry trade. In the followng secton, we brefly dscuss the data that wll be used. 3 We defne ntrandustry trade as trade n goods wth dentcal factor nput requrements; for our emprcal analyss, though, ntrandustry trade s taken as two-way trade of goods n the same four-dgt Standard Internatonal Trade Classfcaton (SITC) class. 4 The only mportant producer of such arcraft (made by Boeng) outsde the Unted States s the European jont venture Arbus, so that Boeng exports to any country other than the Arbus maker countres are classfed as nterndustry trade. Ths s an example gven n Krugman (1994).

9 gravty equaton 289 III. Data We have assembled a cross-sectonal data set for 58 countres n the year The data set ncludes all countres wth GDPs above U.S.$1 bllon and n whch nternatonally comparable estmates of captal per worker are avalable. These 58 countres accounted for 67 percent of world mports and 79 percent of world GDP. The data set ncludes nearly all the ndustralzed countres but relatvely fewer of the less developed countres, reflectng the paucty of avalable captal stock estmates for the latter (see table 1). The source of data on GDP and captal per worker s the Penn World Table (verson 5.6) database (see Summers and Heston 1991). Both varables are reported n nternatonally comparable and purchasng power adjusted real U.S. dollars. The total value of blateral mports data comes from the NBER World Blateral Trade Database (see Feenstra, Lpsey, and Bowen 1997). The qualty of the data s lkely to be lower for the poorer countres n the sample. Ths dfferental degree of measurement error requres cauton when results for hghly ndustralzed countres are compared wth those obtaned from samples that nclude poorer countres. The blateral Grubel-Lloyd ndces, GL j, are calculated usng data on all goods trade at the four-dgt SITC, and therefore, n contrast to most reported GL j ndces, we do not confne ourselves to manufacturng goods trade. The Grubel-Lloyd ndex can be calculated only for country pars n whch there are postve amounts of trade, whch s the case for 2,870 observatons, or 87 percent of the possble 3,306 blateral mport relatons among 58 countres. The number of blateral mport relatons vares across countres from a low of 27 for Nepal to the maxmum of 57 for most ndustralzed countres. Furthermore, the average number of four-dgt SITC categores that a country trades blaterally vares consderably as well. At one end, Maurtus trades, on average, 36 categores wth ts partners, whereas at the other end, the Unted States trades, on average, 332 categores of goods wth ts tradng partners. Across each of ther respectve tradng partners, Bolva has the lowest average Grubel-Lloyd ndex, wth a value of.0006; the Unted Kngdom has the hghest value of Each country s average Grubel-Lloyd ndex s shown n table 1, along wth the country s GDP per capta, the number of blateral relatons the average s computed from, and the average number of goods categores n whch there s trade. In table 2 we report the correlaton coeffcents among the varables of table 1. They are all postve; n partcular, the correlaton of the average Grubel- Lloyd ndex wth GDP per capta s.78, and the correlaton between the average Grubel-Lloyd ndex and the average number of goods traded s.93. The dstrbuton of blateral Grubel-Lloyd ndces s very skewed:

10 TABLE 1 Summary Statstcs 290 Country GDP per Capta ($ U.S.) GDP (Bllon $ U.S.) Captal per Worker ($ U.S.) Number of Blateral Relatons Average Number of Industry Classes Traded Average Grubel-Lloyd Index Unted States 16,570 3, , Canada 15, , Swtzerland 14, , Norway 14, , Australa 13, , Sweden 13, , Denmark 12, , West Germany 12, , Belgum-Luxembourg 12, , Iceland 12, , France 12, , Fnland 12, , Japan 11,771 1, , Netherlands 11, , New Zealand 11, , Unted Kngdom 11, , Austra 11, , Italy 10, , Hong Kong 10, , Israel 8, , Span 7, , Ireland 7, , Venezuela 6, ,

11 291 Greece 6, , Mexco 5, , Tawan 5, , Argentna 5, , Portugal 5, , Syra 4, , Maurtus 4, , South Korea 4, , Iran 4, , Panama 3, , Chle 3, , Turkey 3, , Colomba 2, , Ecuador 2, , Peru 2, , Thaland 2, , Jamaca 2, , Domncan Republc 2, , Guatemala 2, , Paraguay 2, Sr Lanka 2, , Morocco 1, , Bolva 1, , Ivory Coast 1, , Phlppnes 1, , Honduras 1, , Zmbabwe 1, , Ngera 1, , Inda 1, , Nepal Serra Leone Zamba , Kenya , Madagascar ,

12 Country GDP per Capta ($ U.S.) TABLE 1 (Contnued) GDP (Bllon $ U.S.) Captal per Worker ($ U.S.) Number of Blateral Relatons Average Number of Industry Classes Traded Average Grubel-Lloyd Index Malaw Average 6, , Medan 4, , Standard devaton 4, ,

13 gravty equaton 293 GDP per Capta GDP TABLE 2 Correlaton Matrx Captal per Worker Number of Blateral Pars Average Number of Industres Average Grubel-Lloyd Index GDP per capta 1 GDP.41 1 Captal per worker Number of blateral pars Average number of ndustres Average Grubel-Lloyd ndex percent of all ndces are equal to zero, and 78 percent of all 1,120 country pars have a value of.05 or less. In the emprcal analyss below, we shall treat these 1,120 country pars or 2,240 observatons as trade relatons n whch there s lttle or no IRS-based trade. The remanng j 315 country pars (where GL 1.05) are those n whch IRS-based trade s thought to be present; they account for 87.1 percent of all the mports n our sample. In the IRS/uncone Heckscher-Ohln model, the blateral mports predcton depends on whether the dfferentated good s relatvely captal- or labor-ntensve. We follow Helpman and Krugman (1985) and others n assumng that the dfferentated good s relatvely captalntensve. However, we have examned ths queston n some detal and concluded that the assumpton may not hold emprcally. 5 For ths rea- 5 Rauch (1999) has computed the extent to whch an ndustry produces goods that are reference prced on organzed exchanges, denoted r. It s plausble to assume that ths s nversely related to the degree of product dfferentaton. We have correlated r wth ndustry-level data on captal-labor ntensty n producton from seven major ndustralzed countres (from Keller [2002]) as well as wth more dsaggregated U.S. data (from Bartelsman and Gray [2000]), fndng a zero or postve correlaton. As an alternatve measure of product dfferentaton, we have consdered the standard devaton of unt mport values, expectng a postve relatonshp (Austran Insttute for Economc Research 1999). Ths varable s not sgnfcantly related to the rato of captal to labor share n value added across ndustres (data from Peneder [1999]). Because of lmted data avalablty, ths analyss covers only manufacturng products (detals are avalable from the authors on request). The fndngs may well change when nonmanufacturng sectors and broader defntons of captal, especally ncludng research and development, are adopted. However, wthn manufacturng, there are a number of hghly captal-ntensve ndustres that produce homogeneous goods (e.g., petrochemcals) as well as labor-ntensve ndustres that produce farly dfferentated goods (e.g., apparel), explanng the mxed results.

14 294 journal of poltcal economy son we also consder the alternatve case n our analyss below, n whch the dfferentated good s relatvely labor-ntensve. Fnally, the data on blateral dstance between countres used below are the smallest arc tan dstance between captal ctes, measured n klometers (source: Haveman 1998). IV. Emprcal Results We splt the 2,870 blateral mports observatons nto two subsamples accordng to an arbtrarly chosen crtcal level of ntrandustry trade, j denoted GL. Those pars n whch GL GL belong to what s referred to as the low-grubel-lloyd sample, and the remanng observatons are part of the hgh-grubel-lloyd sample. The samples dffer n that we expect substantal amounts of trade based on product dfferentaton and IRS n the latter but not n the former. Gven the crtcal level GL, t wll be useful to sort the data, and form classes, accordng to each observaton s dfferences n factor proportons. Lkewse, we sort the observatons n the hgh-grubel-lloyd sample accordng to ther level of ntrandustry trade (measured by GL). Denote by V the number of classes nto whch the sorted observatons are allocated. In the benchmark case that s dscussed frst, GL s chosen to equal.05, and there are V p 5 classes of equal sze. We then present results for two alternatve cases. In one we adopt a crtcal level of GL p.033, whch shfts more blateral trade relatons nto the sample n whch product dfferentaton/irs-based trade s thought to be present. In the other case, we report results from regressons n whch the class sze s endogenously chosen so as to maxmze the ft of the regresson. Ths s complemented by a number of addtonal results and senstvty analyses reported n the Appendx. A. Benchmark Case The choce of GL p.05 results n 2,240 observatons n the low-grubel- Lloyd sample and the remanng 630 observatons n the hgh-grubel- Lloyd sample. We frst dscuss results for the two perfect specalzaton models before we turn to the two mperfect specalzaton models. 1. IRS-Based Perfect Specalzaton (Hgh-Grubel-Lloyd Sample) The model consdered frst s the IRS model, where both goods are dfferentated and produced wth scale economes. As dscussed above, j j w the model has a predcton of volume of mports of M p YY/Y. To ensure comparablty wth the results for the mperfect specalzaton models shown below, we allocate the 630 observatons nto V p 5 classes,

15 gravty equaton 295 wth GL j rsng from class v p 1,, V. The followng equaton, based on (1), s estmated: j YY j v v j v v w v M p a e (6) Y j for each v. The dsturbance e v s assumed to have mean zero but mght be heteroskedastc. In ths and all followng regressons, we assume that the varance of e j 2 j 2 s equal to j (Z ), where Z j s a vector that ncludes j fve varables: Y, Y, the sums of mports of country and exports of j country j, and the blateral dstance between and j (denoted D ). Let j j the predcted values from regressng log Feˆ F on a constant and log Z j be gven by log e ; the parameter a s then estmated by ordnary least j j j w j squares (OLS) wth the scaled varables M /e and (YY/Y )/e. 6 The results for these regressons can be found n table 3. The estmated a v s vary n the range from to 0.139, where the largest mport parameter s estmated for an ntermedate level of product dfferentaton ( v p 3). The table also reports standard errors (n parentheses) and the symmetrc 90 percent confdence ntervals of the pont estmates. 7 In addton, we test the hypotheses that the mport parameters of all fve classes are dentcal and whether a1 p a5 (a 10 percent sgnfcance level s adopted for all hypothess tests). Although the estmated a v s are larger for classes wth hgher levels of product dfferentaton, t s clear that all the a v estmates fall well short of the theoretcally predcted value of one at standard levels of sgnfcance. The sxth row of table 3 shows the results of usng all 630 observatons. Wth an a estmate of 0.087, ths regresson confrms that the IRS model overpredcts the level of blateral trade across countres substantally. We now turn to the multcone Heckscher-Ohln model. 8 6 Moreover, the gravty equaton s potentally a relatonshp between two endogenous varables, so the results mght be affected by smultanety bas (e.g., Saxonhouse 1989). We have also consdered regressons wth mports over the product of the GDPs as the dependent varable. Ths leads to the same qualtatve results (see App. table A2). See, e.g., Harrgan (1996), who pursues ths ssue further. 7 The standard errors and confdence ntervals are based on bootstrap technques (see Bckel and Freedman 1981; Efron 1982); they tend to be larger and appear to be preferable n ths case to those obtaned from standard asymptotc results. 8 Equaton (6) does not nclude a constant, whch means that OLS estmates are nconsstent f E[e contrary to the assumpton. Whle the mean of the ftted e j v ] ( 0, s j typcally small relatve to ts standard devaton, we have nevertheless estmated all four models also wth a constant. The pattern of how a v vares wth v remans the same (see App. table A1).

16 296 journal of poltcal economy TABLE 3 Benchmark Case IRS/Heckscher-Ohln Model: Hgh-Grubel-Lloyd Sample (GL 1.05) IRS Model (IRS/IRS Goods) IRS/Uncone Heckscher- Ohln Model (IRS/CRS Goods) Heckscher-Ohln Model: Low-Grubel-Lloyd Sample (GL!.05) Multcone Heckscher- Ohln Model (CRS/CRS Goods) Uncone Heckscher- Ohln Model (CRS/CRS Goods) a v 95% a v 95% a v 95% a v 95% 5% 5% 5% 5% Ranked by Grubel-Lloyd Index Ranked by FDIF vp1.016 (.012) (.005) (.007) (.004) vp2.044 (.005) (.005) (.014) (.008) vp3.139 (.013) (.009) (.005) (.008) vp4.069 (.017) (.005) (.003) (.006) vp5.099 (.015) (.006) (.004) (.007) All observatons.087 (.009) (.004) (.003) (.003) Only perfect specalzaton of producton yes no yes no H 0 : a pa G reject reject reject reject H 0 : a 1 pa 5 reject reject do not reject reject Share of blateral comparsons correct N.A. 9/10 N.A. 9/10 Note. Standard errors are n parentheses. 2. Heckscher-Ohln-Based Perfect Specalzaton (Low-Grubel-Lloyd Sample) Recall that n the multcone Heckscher-Ohln model, all trade s n homogeneous, perfectly specalzed products. The mports predcton j j w s gven by equaton (1): M p YY/Y. Therefore, the only parameter a v s predcted to equal one. We estmate j YY j v v j v v w v M p a e (7) Y for each v, v p 1,, 5. Dfferences n factor proportons are lowest for v p 1 and hghest for v p 5; wth 2,240 observatons n the low-grubel- Lloyd sample, each class has 448 observatons. Table 3 shows the results. The largest parameter, wth 0.111, s estmated for class v p 2, whereas

17 gravty equaton 297 the a estmates for the four other classes are between and All parameters are less than the theoretcally predcted value of one at standard levels of sgnfcance. In addton, when the entre low-grubel- Lloyd sample s used to estmate the coeffcent a, the resultng parameter estmate s (see the sxth row of table 3). Thus, n ths sample, the multcone Heckscher-Ohln model grossly overpredcts the volume of blateral trade. In summary, the predctons of the multcone Heckscher-Ohln model are rejected by the data. The evdence for the IRS model, whch overpredcts blateral trade somewhat less (wth a p n the regresson wth all observatons), s slghtly stronger. Care must be taken, though, not to overnterpret ths small dfference snce, as we have noted above, the data qualty for the hgh-grubel-lloyd sample s hgher than for the low-grubel-lloyd sample. The man result from our analyss thus far s that models of perfect specalzaton do not appear to be mportant n explanng the success of the gravty equaton. Ths mght n part be related to the fact that the predcton of trade volume of both of these models holds only f the producton of all goods s perfectly specalzed, whch s unlkely. We now turn to estmatng the predctons of mport volume of the two models that ncorporate mperfectly specalzed producton, wth mport predcton M IH for the IRS/uncone Heckscher- Ohln model and predcton M H for the uncone Heckscher-Ohln model. 3. IRS Model Incorporatng Imperfect Specalzaton (Hgh-Grubel- Lloyd Sample) The model consdered here s the IRS/uncone Heckscher-Ohln model. The regresson equaton when country s captal-abundant relatve to j s for each v, v p 1,, 5, and j YY j v v j v v e w v M p (1 g ) Y j YY j j v v j v v e w v M p (1 g ) f country j s relatvely captal-abundant. The number of estmated parameters (1 g v ) vares by class v. Moreover, the number of tmes that a gven country s parameter s estmated n a gven class changes as well. In table 3 we report the medan of the predcted values (1 g v), whch s weghted to take nto account the number of observatons that are Y

18 298 journal of poltcal economy used to estmate any one parameter ( 1 g v ). Ths statstc s denoted by a v. The medan predcted value vares across classes from to A nonstructural nterpretaton of a v s that t estmates the average sze of the dfferentated goods sector. Ths average should, frst, be nonnegatve, and the results confrm that. Second, n ths model, hgher values of the Grubel-Lloyd ndex (and hence class v) should be assocated wth hgher estmates of a v because a hgher share of dfferentated goods n GDP gves rse to a hgher share of ntrandustry trade n total trade. The a v estmates rse from for v p 1 to for v p 5, wth a nonmonotoncty at v p 2(a2 p 0.053). Ths pattern s broadly n accordance wth the model s predcton. For the two mperfect specalzaton models, we are nterested n seeng whether a v ncreases as v ncreases, that s, whether the pont estmate s greater n classes n whch the extent of specalzaton should be greater. Thus we report as an addtonal, albet rough, ndcator of model performance the number of blateral comparsons of a v s that are n lne wth these prors. That s, we ask whether a 2 exceeds a 1, whether a 3 s larger than a 1, whether a 3 exceeds a 2, and so on. As ndcated n the table, only one out of 10 blateral comparsons of a v s s ncorrect for the uncone/ IRS model. The confdence ntervals suggest that some but not all dfferences of mport parameter estmates across Grubel-Lloyd classes are also statstcally sgnfcant. In partcular, the medan mport parameter for ntermedate levels of the Grubel-Lloyd ndex (v p 3) s statstcally ndstngushable from that for the hghest Grubel-Lloyd class. At the same tme, we strongly reject both the null hypothess that the fve a v are the same and the null that a1 p a 5. Overall, ths provdes some support for the IRS/uncone Heckscher-Ohln model. We now turn to the uncone Heckscher-Ohln model. 4. Heckscher-Ohln-Based Imperfect Specalzaton (Low-Grubel- Lloyd Sample) We return to the sample of blateral pars n whch the computed Grubel- Lloyd ndex s.05 or less. Here we estmate the uncone Heckscher- Ohln model, where two homogeneous goods are produced n both countres. As dscussed n Secton I above, the model s mport predcton j j j w M H s equal to M p (g g )(YY/Y ) f country s captal-abundant. We estmate j YY j j v v j v v v e w v M p (g g ) Y

19 gravty equaton 299 for each v, v p 1,, 5, and j YY j j v v j v v v e w v M p (g g ) Y f country j s captal-abundant. In each class v, there are up to 58 countres. Out of 58 parameters g, only 57 are dentfed. We arbtrarly set the g for the country wth the lowest captal-labor rato n the sample (Serra Leone) equal to one n each class v. Because the composton of the classes vares n terms of countres, we also report here the medan ĵ of the predcted (net) mport parameter, gven by gv gv and denoted by a v. A nonstructural nterpretaton s that t represents the dfference between the sze of the labor-ntensve sector n the labor- and n the captal-abundant country. We expect that a v s postve and that t tends to rse when blateral dfferences n factor proportons ncrease. Table 3 shows that a v for the uncone Heckscher-Ohln model s estmated to le between and 0.080, whch together wth the confdence ntervals suggests that a v s postve for all classes. The medan ĵ value of g g when all 2,240 observatons are used n the estmaton s 0.04 (sxth row). Further, a v s generally rsng wth dfferences n factor proportons across classes, although there s one nonmonotoncty at class v p 4. Nne out of 10 blateral comparsons are correctly pre- dcted by the uncone Heckscher-Ohln model. The confdence ntervals also allow us to reject the null hypothess that all a v s are dentcal as well as the hypothess that a1 p a 5. Thus we fnd support n favor of the uncone Heckscher-Ohln model. Interestngly, although we fnd a nonmonotoncty for a v at a relatvely hgh FDIF level ( v p 4), the un- cone Heckscher-Ohln model works well even for the class wth the largest factor proporton dfferences. A pror, one mght have thought that the assumpton of a common cone of producton dversfcaton s then mplausble. We shall take up ths ssue agan n subsecton 6. In summary, from ths analyss of these mperfect specalzaton models, we fnd evdence supportve of both the IRS/uncone Heckscher- Ohln model and the uncone Heckscher-Ohln model. 5. Comparng the Perfect and Imperfect Specalzaton Models n Terms of Ft In ths subsecton we examne whether the perfect and mperfect specalzaton models dffer consderably n terms of emprcal ft. Table 4 shows a number of wdely used model selecton crtera for the benchmark case. The R s computed usng the expresson yy/yy, ˆˆ where yˆ and 2 y are the devatons from the means of the predcted values of the

20 TABLE 4 Measures of Ft for the Benchmark Case IRS/Heckscher-Ohln Model: Hgh-Grubel- Lloyd Sample (GL 1.05) IRS Model (IRS/IRS Goods) IRS/Uncone Heckscher-Ohln Model (IRS/CRS Goods) Heckscher-Ohln Model: Low-Grubel-Lloyd Sample (GL!.05) Multcone Heckscher-Ohln Model (CRS/CRS Goods) Uncone Heckscher-Ohln Model (CRS/CRS Goods) ln (e e) AIC R 2 ln (e e) AIC R 2 ln (e e) AIC R 2 ln (e e) AIC R 2 Ranked by Grubel-Lloyd Index Ranked by FDIF vp vp vp vp vp All observatons Only perfect specalzaton of producton yes no yes no

21 gravty equaton 301 ndependent varable and the actual value of the ndependent varable, respectvely. Akake s Informaton Crteron (AIC) s defned as ee ( ) 2Q AIC p ln, N N where ees the resdual sum of squares, N s the number of observatons, and Q s the number of estmated parameters. Also the unadjusted log 2 of ee s reported. In the regresson wth all 630 observatons, the R for the IRS model s.280, whereas for the IRS/uncone Heckscher-Ohln model, t s Also, accordng to the AIC, the perfect specalzaton model s preferred to the mperfect specalzaton model n the hgh- Grubel-Lloyd sample. The same qualtatve results are contaned for the two other models n the low-grubel-lloyd sample. Overall, t appears that our analyss of emprcal ft does not lead to major conclusons, except perhaps that the reducton n the resdual sum of squares that the mperfect specalzaton models generate s small relatve to the addtonal number of parameters that are estmated. We conclude the analyss of the benchmark case by examnng the countryspecfc estmates of the two mperfect specalzaton models. 6. Country-Specfc Estmates of the Imperfect Specalzaton Models In ths subsecton we dscuss the estmates of 1 g and g from the IRS/uncone Heckscher-Ohln and uncone Heckscher-Ohln models, respectvely. The results are collected n table 5. In the case of the IRS/ uncone Heckscher-Ohln model, 35 country-specfc parameters are estmated. The remanng 23 countres have no trade relatons n whch the level of ntrandustry trade exceeds the crtcal value of GL p.05. These countres are prmarly developng countres, as table 5 shows. The parameter 1 g denotes the share of the dfferentated goods sector n GDP n the captal-abundant country, whch should be bounded between zero and one. Moreover, under the assumpton that the dfferentated good s relatvely captal-ntensve, the model mples that the share of dfferentated goods n GDP ncreases wth the relatve abundance of captal to labor, ceters parbus. Under these condtons, one expects the correlaton of K/L and 1 g to be postve. As reported n table 5, 32 out of 35, or 91 percent, of the 1 g estmates satsfy the restrcton of beng between zero and one. We estmate values above 9 It s sometmes suggested to compute y and as devatons from zero when the reŷ gresson does not contan a constant (e.g., Kennedy 1992, p. 27). Ths changes lttle n the present context, though.

22 TABLE 5 Country Parameter Estmates for the Imperfect Specalzaton Heckscher- Ohln Models Country GDP per Capta (1) K/L (2) IRS/Uncone Heckscher- Ohln Model 1 g (3) Standard Error (4) p-value (5) g (6) Uncone Heckscher- Ohln Model Standard Error (7) p-value (8) Serra Leone N.A. N.A. Malaw Nepal Paraguay 2, Ngera 1,062 1, Ivory Coast 1,545 1, Kenya 794 1, Inda 1,050 1, Madagascar 769 1, Zamba 808 1, Maurtus 4,226 2, Morocco 1,956 2, Jamaca 2,215 3, Guatemala 2,090 3, Thaland 2,463 4, Phlppnes 1,542 4, Honduras 1,387 4, Domncan Republc 2,111 5, Zmbabwe 1,216 5, Bolva 1,754 6, Turkey 3,077 6, Chle 3,467 7, Sr Lanka 2,045 8, Peru 2,565 9, Portugal 5,070 9, Iran 4,043 10, Hong Kong 10,599 11, Republc of Korea 4,217 12, Argentna 5,324 12, Colomba 2,968 12, Mexco 5,621 14, Ecuador 2,913 15, Syra 4,240 15, Iceland 12,209 15, Panama 3,499 16, Unted Kngdom 11,237 17, Tawan 5,449 19, Venezuela 6,225 20, Ireland 7,275 20, Span 7,536 21, Greece 6,224 22, Israel 8,310 22, Japan 11,771 28, Italy 10,808 28, Denmark 12,969 29, Netherlands 11,539 29, Austra 11,131 29, Unted States 16,570 29, New Zealand 11,443 30, Sweden 13,451 31, France 12,206 31,

23 gravty equaton 303 TABLE 5 (contnued) Country Parameter Estmates for the Imperfect Specalzaton Heckscher- Ohln Models Country GDP per Capta (1) K/L (2) IRS/Uncone Heckscher- Ohln Model 1 g (3) Standard Error (4) p-value (5) g (6) Uncone Heckscher- Ohln Model Standard Error (7) p-value (8) Belgum- Luxembourg 12,230 33, Australa 13,583 33, Canada 15,589 34, Fnland 12,051 38, Norway 14,144 44, West Germany 12,535 47, Swtzerland 14,864 62, N.A one, whch would mean a negatve share of the homogeneous goods sector, for Honduras, Zmbabwe, and the Republc of Korea. The table also reports the standard errors of the 1 g as well as p-values, both of whch are computed usng bootstrap technques. The p-values ndcate the probablty that a gven country s 1 g exceeds that of Swtzerland, the country wth the hghest relatve captal endowment n the sample. The estmate for Swtzerland s equal to.091. The 1 g estmates often have relatvely small standard errors; however, t s not the case that most of these estmates are smaller than 0.091: at a 10 percent level, only 13 out of 34, or 38 percent, of the parameters are sgnfcantly smaller than that of Swtzerland. Thus t s not surprsng that we do not fnd the postve correlaton between 1 g and K/L that the model predcts. As reported n table 6, the smple correlaton of 1 g and K/L s negatve. The result s further confrmed by re- gressng the 1 g on a constant and K/L usng OLS: the t-statstc of the slope parameter n ths regresson s equal to The analogous correlatons wth GDP per capta are not much dfferent. These estmates do not provde support for the IRS/uncone Heckscher-Ohln model. Gven our dffculty of establshng whether the dfferentated good s relatvely captal-ntensve or not, we have also consdered the alternatve assumpton, that the homogeneous good s relatvely captal-ntensve. It can be shown that, on the mantaned assumpton that country s relatvely captal-abundant, the mport predcton becomes M p (1 g )(YY/Y ). That s, the regresson paramj j j w eter estmates country j s share of the dfferentated good n GDP nstead 10 We have also weghted each observaton by the nverse of the standard error of 1 g ; the results of that regresson do not provde more support for the model. When the three cases n whch 1 g exceeds one are dropped from the regresson snce they do not satsfy the restrcton that 1 g s a share, the t-statstc drops to 0.60.

24 304 journal of poltcal economy TABLE 6 Relaton of Captal-Labor Endowment Rato to 1 g and g IRS/Uncone Heckscher- Ohln Model Correlaton OLS t-statstc R 2 Correlaton Uncone Heckscher-Ohln Model OLS t-statstc R 2 Captal-labor endowment rato (K/L) GDP per capta of country s share. However, estmatng ths alternatve predcton also fals to confrm the theoretcal relatonshp n the IRS/uncone Heckscher-Ohln model between the sze of the dfferentated goods sector and factor endowments. 11 In the case of the uncone Heckscher-Ohln model, we estmate 57 parameters g, the share of the labor-ntensve good n GDP. The as- sumpton of mperfect specalzaton means that g should be greater than zero for all countres, and our estmates are consstent wth that (condtonal on the set value of g p 1 for Serra Leone). The range of the estmates s relatvely small, from a low of for Belgum-Luxembourg to a hgh of for Maurtus. Because some nternatonal dfferences n the sze of the homogeneous goods sector n GDP are lkely to be larger than (approxmately) 17 percentage ponts, the g estmates should not be nterpreted too lterally. Nevertheless, t s nterestng to see how dfferent the pont estmates are relatve to the set value for Serra Leone. The p-values n column 8 of table 5 report the probablty that the g of a gven country s at least as large as that of Serra Leone. For 36 out of 57 countres, or 63 percent, we can reject the null hypothess that g p 1. Moreover, none of the g are estmated sgnfcantly hgher than one at standard levels. We now examne the correlaton of relatve captal endowments and the estmated g s. All else equal, the hgher a country s relatve captal endowment, the more t wll specalze n the producton of the captalntensve good, mplyng a lower share of the labor-ntensve goods sector n GDP. Thus we expect a negatve correlaton of g and K/L. As reported n table 6, ths s what we obtan, wth a correlaton of.80. The result s strongly confrmed by an OLS regresson of g on a constant and 11 j We estmate 47 (1 g ) parameters, all postve, and three parameters exceed one (for Malaw, Iceland, and West Germany). If the homogeneous good Z s relatvely captalntensve, the model predcts a postve correlaton of g, Z s share n GDP, and K/L (or, j j j j equvalently, a negatve correlaton of 1 g and K /L ). Regressng 1 g on a constant j j and K /L, we fnd a t-statstc for the slope parameter of 0.35, whch changes to 2.06 once the three estmates above one are dropped.