Revisiting the Revisited: An Alternative Test of the Monopolistic Competition Model of International Trade

Transcription

1 Revstng the Revsted: An Alternatve Test of the Monopolstc Competton Model of Internatonal Trade Isao Kamata Unversty of Wsconsn Madson March 1, 2013 Abstract Ths paper proposes an alternatve test of the monopolstc competton model that has conventonally been examned for aggregate trade. The mpled relatonshp between the volume of trade and sze smlarty among tradng countres s reexamned consderng the degree of product dfferentaton; and the redefned relatonshp s tested usng sectorally dsaggregated data on producton and trade, employng non-lnear estmaton methods to handle zero-trade observatons. The result confrms the model s mplcaton for product-dfferentated sectors for both OEC and non-oec countres, but also ndcates that for non- OEC countres the trade-smlarty correlaton s more pronounced n non-dfferentated sectors, whch rases a puzzle to the model. Keywords: New Trade Theory; Monopolstc competton; Product dfferentaton; Gravty; Posson regresson JEL Classfcaton: C13, 43, F10, F12 I am partcularly grateful to Alan eardorff and Juan Carlos Hallak for extensve advce and dscussons. I would also lke to acknowledge Gary Saxonhouse for nvaluable comments on an earler verson of ths work. I also thank partcpants n the Mdwest Internatonal Economcs Group Fall 2009 Meetng for valuable feedback to an earler verson. I am solely responsble for all remanng errors. Isao Kamata, the Unversty of Wsconsn Madson, Robert M. La Follette School of Publc Affars; 1225 Observatory rve, Madson, WI 53706, U.S.A. Tel: (+1) ; Fax: (+1) ; E-mal: kamata@lafollette.wsc.edu 1

2 1. Introducton New Trade Theory s characterzed by a model of nternatonal trade wth monopolstc competton among the varetes of dfferentated products n an ndustry. Ths theory was orgnally motvated by the fact that a large part of nternatonal trade s ntra-ndustry rather than nter-ndustry, a characterstc that neo-classcal trade theory such as the Heckscher-Ohln Model or the Rcardan Model cannot explan. The monopolstc competton models of nternatonal trade, frst presented n the works of Krugman (1979, 1980) and Helpman (1981), have been wdely employed and appled n numerous studes of nternatonal trade. Ths type of model has mplcatons for the volume of trade; n partcular, as Helpman and Krugman (1985) have demonstrated, the volume of trade among a group of countres, as a share n the total ncome of the country group, wll be larger as the szes the economes of ndvdual countres n the group are more smlar to each other. In other words, f two regons have the same total szes of ther economes and consst of the same number of countres, the regon n whch countres are more equal n GP wll trade more wthn that regon. Although ths theoretcal mplcaton s clear-cut and has an emprcally testable form, only a few studes have drectly examned ths mplcaton emprcally. Helpman (1987) employed tme-seres data on 14 OEC countres and graphcally showed the postve relatonshp between the volume of trade among the countres as a fracton of ther total GP and the smlarty n ther respectve GPs. Hummels and Levnsohn (1995) performed more formal emprcal tests usng panel data on blateral trade flows between pars of the same 14 OEC countres, as well as those of another 14 non-oec countres. They expected that the data on trade between the OEC countres would ft the monopolstc competton model whle t would not be the case for trade between the non-oec countres, because the former was lkely to be more ntra-ndustry trade of horzontally dfferentated products 1 that the theoretcal model 1 In lterature two types of product dfferentaton are dstngushed: horzontal product dfferentaton and vertcal product dfferentaton. The former arses when products of a smlar qualty vary n certan characterstcs, whle the latter arses when products dffer n qualty. The product dfferentaton dscussed n the current paper s horzontal dfferentaton, whch the monopolstc competton model consders. 2

3 consders, whle the latter dd not seem to be characterzed as such. Ther results, however, showed that GP smlarty between two tradng countres well explaned the volume of blateral trade between them, both for the OEC and non-oec countres, whch left a puzzle. ebaere (2005) re-examned the study by Hummels and Levnsohn, and clamed that ther emprcal approach may not have been able to properly assess the mpact of the ncome smlarty on blateral trade, and ths was why ther results were puzzlng. He thus presented a modfed equaton explanng the relatonshp between the volume of trade and GP smlarty between countres, and estmated t usng updated data for the same set of OEC and non-oec countres. From the estmaton results he concluded that postve correlaton between the volume of trade and sze smlarty among tradng countres was sgnfcant only for the OEC countres but not for the non-oec countres, and thus the puzzle was not present any more. These studes attempted to test the monopolstc competton model n the context of aggregate trade, whch ncludes all types of traded goods. However, not all goods that are nternatonally traded are dfferentated products, and the trade of those non-dfferentated products may be drven by other mechansms than the one that s descrbed by the monopolstc competton model. In fact, to expand the tested mplcaton that the volume of trade wll ncrease as tradng economes become more equal n sze to the level of aggregate trade, they assumed that all ndustres were nternally dfferentated n terms of product varetes, or alternatvely that perfect specalzaton of producton took place n every sector. These assumptons are very restrctve and thus may not be realstc. In ths paper, I propose an alternatve emprcal approach to testng the mplcaton of the monopolstc competton model for the volume of trade among countres. The key s to focus on the trade of dfferentated products. I revew the model and derve the equaton for the volume of blateral trade of dfferentated products wthout mposng such restrctve assumptons as those mentoned above. The derved alternatve equaton suggests that the smple GP smlarty between tradng economes does not predct the volume of blateral trade of dfferentated products. The equaton, however, mples that the volume of blateral trade of dfferentated products, as a share n the domestc producton of these products n the two tradng countres, wll be proportonal to the two countres GP smlarty adusted 3

4 for how symmetrc the countres are n ther producton structure. In other words, the volume of trade of dfferentated products between two countres wll be larger as the countres are more smlar n GP, as well as n the share of the dfferentated sectors n GP. Ths mplcaton must be tested wth data on trade and producton n the sectors of dfferentated products. Therefore, n addton to data on aggregate trade and GP such as those used n the prevous studes, I employ dsaggregated data on trade and producton n manufacturng ndustres for a range of countres. I also use the nformaton on product characterstcs classfed by Rauch (1999) to defne the dfferentated sectors. Furthermore, to handle zero-trade observatons n the data, I apply non-lnear estmaton methods n addton to the benchmark OLS estmaton of log-lnear forms of the volume-oftrade equatons. The emprcal analyss, especally the result of the estmaton wth a non-lnear method that handles zero-trade observatons, shows that the tested mplcaton of the monopolstc competton model that the volume of blateral trade per producton wll be larger as two tradng countres are more smlar n GP and more symmetrc n producton structure s supported by the data for both OEC and non-oec countres, not only for the dfferentated-sector trade but also for aggregate trade. Therefore, n terms of the relatonshp between the volume of trade and the sze smlarty, we go back to Hummels and Levnsohn s puzzle, contrary to ebaere s concluson. However, usng a unque approach that separates trade of dfferentated products from aggregate trade, ths paper also demonstrates two other thngs: () blateral trade flows among OEC countres, especally n the sectors of dfferentated products, are well explaned by the monopolstc competton model; but () trade flows among non- OEC countres are not equally well-explaned by the model. Ths fndng suggests that there should be some other mechansm that makes trade patterns among lower-ncome countres dfferent from those among rch countres. Ths study offers some nsght for a seres of emprcal studes on the gravty equaton, to whch the monopolstc competton model provdes a theoretcal bass. Most studes have estmated the gravty equaton for aggregate trade. For example, Feenstra, Markusen and Rose (2001), Evenett and Keller 4

5 (2002), and Haveman and Hummels (2004) use the gravty equaton for aggregate trade to test whch theory of nternatonal trade s the most lkely to explan the actual trade flows, followng eardorff (1998) pontng out that multple trade theores can derve the gravty equaton. The pont of Feenstra et al. s the exstence of a home-market effect that may dstngush the monopolstc competton model from others, whle Evenett and Keller, as well as Haveman and Hummels, focus on the elastcty of natonal ncome wth respect to the volume of trade, whch wll be smaller than unty f specalzaton n producton s ncomplete. However, aggregate trade nvolves the trade of varous products, some of whch the monopolstc competton model fts well, but others may be characterzed by product homogenety and ncomplete specalzaton; thus all trade should not be explaned by a sngle model n a unfed manner. 2 In contrast, Harrgan (1994) and Jensen (2000) have estmated the gravty equaton at the sectoral level usng data on trade and producton n manufacturng ndustres. 3 They, however, do not explctly consder dfferences n product characterstcs (dfferentated versus homogeneous) across manufacturng ndustres, to whch ths paper pays careful attenton. 4 The remander of ths paper s organzed as follows. The next secton derves the equaton explanng the volume of trade n the dfferentated sectors, and dscusses ts mplcaton n comparson wth the equaton for aggregate trade that has been used n the exstng lterature. The secton presentng the emprcal approaches follows. The data employed for the emprcal analyss are descrbed n secton four. The results of the analyss are presented and dscussed n the ffth secton, whch s followed by the concludng secton. 2 Feenstra, Markusen and Rose (2001) also dvde trade nto three categores accordng to Rauch (1999) to estmate ther gravty equaton, but the explanatory varables are for the aggregate;.e., GPs of exporter and mporter countres. 3 Harrgan (1994) ntroduces a varety of proxes for scale economes n hs equaton to see whether the homemarket effect would be sgnfcant, whch would ndcate a monopolstc competton rather than Armngton preference for natonal varetes. The nterest of Jensen (2000) s n the sze of the estmated elastcty of volume of mports to the mporter s ncome. 4 Other emprcal work such as Anderson and van Wncoop (2003) carefully derves a structural gravty-type equaton from a generalzed monopolstc competton model, but due to the unobservablty of varables, ther attenton s lmted to a certan factor such as dstance or trade cost. La and Zhu (2004), on the other hand, have made an extended effort to measure as many varables as possble to estmate ther structural and generalzed volume-of-trade equaton wth data. 5

6 2. Monopolstc Competton Model and Volume of Trade In ths secton, to account for the volume of trade I derve two formulas from the monopolstc competton model of nternatonal trade ntroduced by Helpman and Krugman (1985). Ths model s characterzed as follows: () some sectors have a number of product varetes (I herenafter call these sectors dfferentated sectors ); () each of the product varetes n a dfferentated sector s produced monopolstcally compettvely by a sngle frm; and () consumers throughout the world have dentcal preferences that are characterzed by a two-ter utlty functon: the upper-ter utlty s homothetc, and the sub-utlty over product varetes wthn a sector takes a CES functonal form. Here I consder an equlbrum of frctonless trade so that the prce of each good or horzontally dfferentated product s equal throughout the world. In ths free-trade equlbrum, every product n the dfferentated sectors produced n each country wll be dvded among all consumers worldwde, accordng to ther share of world ncome. The volume of exports from one country to another s thus expressed as follows: s EX y psqs, EX s,, (1) s H where : group of the dfferentated sectors; H: group of homogeneous sectors;, : scrpts for countres ( ); EX s, : exports from Country to Country n Sector s; Q s, : Country s producton n Sector s; p s : equlbrum prce of (dfferentated) products n Sector s y : Country 's GP share n the world (= Y /Y w ) Note that the volume of trade between a specfc par of countres n the sectors of homogeneous products (or homogeneous sectors ), EX for s H, s ndetermnate. That s, although a country wll export a s, homogeneous product when the amount of the product that the country domestcally produces s greater than the amount t consumes, how much of the country s product wll be exported to whch country(es) 6

7 cannot be determned because, n the free-trade equlbrum, mportng countres wll be ndfferent about from whch country(es) they mport the homogeneous product to supply ther domestc demand Aggregate volume of trade The verson of the formula for the aggregate volume of trade, whch has been employed n studes such as Helpman (1987), Hummels and Levnsohn (1995), and ebaere (2005), further assumes the followng: (A1) Each country n the world s also completely specalzed n producton n the homogeneous sectors. That s, every homogeneous product s produced by no more than one country. Under ths assumpton, any product produced by a sole producer country (.e., a sole exporter) wll be mported by all other countres, and how much each country mports wll be determned accordng to the country s share of world ncome. Therefore, no ndetermnacy wll be left for the quanttes of blateral trade, and the volume of exports n both homogeneous and dfferentated sectors from Country to Country s expressed as follows: EX s y H psq., s, (A2) Products n any sector are tradable,.e., there exst no non-traded sectors. 5 Under ths assumpton, the aggregate value of a country s producton over the sectors equals ts ncome, or GP. That s; p Q Y s, H s s, ; EX y Y where Y s GP of Country. Therefore, followng Helpman (1987), the aggregate blateral trade volume between Countres and s expressed as follows: VT EX EX y Y y Y 2Y Y / Yw y 2( YY / Y) 5 Ths assumpton (A2) can be replaced wth the followng weaker assumpton (A2 ) to derve Equaton (2) below: (A2 ) Every country has an equal share of non-traded sectors n ts GP. 7

8 VT / Y y [1 ( Y / Y ) 2 ( Y / Y ) 2 ] where Y = Y + Y : Country - par s total GP y = Y /Y w : Country - par s share of world GP The term n the square brackets on the rght-hand sde of the second equaton ndcates the smlarty of GPs, or the smlarty of the szes of the economy, of two tradng countres. Ths term takes a greater value as the sze of the two countres become more equal, and takes the maxmum value of 0.5 when the two countres are exactly equal n GP;.e., Y /Y = Y /Y = 1/2. Usng ths ndex of sze smlarty, 6 the equaton s expressed as follows: VT / Y y sm, (2) 2 2 where sm [1 ( Y / Y ) ( Y / Y ) ]. Ths Equaton (2) mples that the volume of aggregate blateral trade, as a share n the total ncome (GP) of the two tradng countres, wll be greater as ther respectve natonal ncomes are more smlar Volume of Trade n the fferentated Sectors The two assumptons A1 and A2 are very restrctve. Snce Equaton (2) can be derved only wth these restrctve assumptons, ts valdty should be lmted accordngly. However, by focusng our attenton on the dfferentated sectors, t s possble to derve an alternatve formula that can explan the volume of trade n such sectors n a smlar way but wthout mposng these assumptons. Snce countres are consdered to be completely specalzed n producton of unque varetes n the dfferentated sectors, by takng the frst term of Equaton (1), export from Country to Country n the dfferentated sectors s descrbed as follows: EX, s y psqs, y X, 6 Helpman (1987), as well as Hummels and Levnsohn (1995), calls ths term the dsperson ndex, whle ebaere (2005) names t the smlarty ndex. I follow the latter snce ths ndex beng larger means two countres beng more smlar n terms of the sze of the economy. 8

9 where EX, : export n the dfferentated sectors from Country to Country X : value of Country 's domestc producton n the dfferentated sectors: X p Q. s s s, Therefore, the volume of trade n the dfferentated sectors between Countres and s expressed as follows: VT EX EX y X y X y {( Y / Y ) X ( Y / Y ) X,, } VT X where X y 1 X Y Y X X Y Y y X 1 X / Y / Y Y Y 2 X / Y X / Y Y Y 2, VT : volume of trade n dfferentated sectors between Countres and X : Countres and s total domestc producton n the dfferentated sectors (X X + X ). The term n the square brackets n ths equaton s smlar to the sze smlarty ndex n Equaton (2) for aggregate trade, but ths term depends not only on two countres relatve ncome szes but also on the szes of producton n the dfferentated sectors of the countres (X, X ). The GP share term for each country ((Y /Y ) 2 or (Y /Y ) 2 ) s weghted by the term (X /Y )/(X /Y ), and ths weght term ndcates how large the share of the dfferentated sectors n GP s n each country, relatve to the overall GP share of the dfferentated sectors n the two countres. In other words, ths term ndcates GP smlarty between two countres adusted for how symmetrc the two countres are n ther producton structure. Ths term takes a larger value as two countres are more smlar n the sze of ther economes and more symmetrc n producton structure. I thus call ths term the producton structure-adusted sze (or GP) smlarty, and re-wrte the equaton as follows: VT * / X y sm (3) where 2 2 * X / / Y Y X Y Y sm 1. X / Y Y X / Y Y 9

10 Equaton (3) mples that the volume of blateral trade n the dfferentated sectors, as a share n the two countres total producton n those sectors, s predcted by the sze smlarty between the two tradng countres adusted for how symmetrc ther producton structures are. That s, two countres wll trade more n the dfferentated sectors as the two countres are more smlar n GP and more symmetrc n producton scusson on Producton Structure-adusted Sze Smlarty As mentoned above, the volume of blateral trade n the dfferentated sectors, as a share n the two countres domestc producton n those sectors, s proportonal to the smlarty n sze between the countres that s adusted for the symmetry of the country par s producton structure. Ths adusted ndex of GP smlarty takes a larger value as two tradng countres are more smlar n GP and more symmetrc n producton structure. Ths s true n general,.e., for more common cases n whch a country wth larger GP s a larger producer n the dfferentated sectors than the other country. However, ths ndex s n fact even greater for less common cases n whch a country wth smaller GP s a larger producer n the dfferentated sectors;.e., the two countres are dssmlar or asymmetrc n an extreme manner. 7 Ths s because, accordng to the monopolstc competton model of trade, a trade flow between countres wll be larger when the exporter has larger producton and the mporter has larger ncome. Therefore, havng the szes of GP and sectoral producton adusted (or normalzed), the trade flow n the sector wll be larger when one country mports the whole domestc producton of the other country (for a hypothetcal case n whch one country has 100% of a country par s GP but no producton n the consdered sector, whle the other country has zero ncome but 100% of the country par s producton n that sector), rather than when two countres exchange a half of ther respectve producton (for another hypothetcal case n whch two countres are exactly equal n both GP and sectoral producton). 7 In such a case the adusted smlarty ndex takes a value over 0.5 and up to 1, compared to the case n whch two countres are perfectly smlar and symmetrc (sm * = 0.5). In the data used n the current study, the number of such uncommon cases for the OEC countres s 228 out of the total 3,630 observatons; and 2,144 out of 14,565 for the non-oec countres. See Secton 4 for the detaled descrpton of the data. 10

11 3. Emprcal Approaches to Estmate Volume-of-Trade Equatons In ths secton, I descrbe emprcal specfcatons to estmate the volume-of-trade equatons derved n the precedng secton, to test how well blateral trade s explaned by the sze smlarty of two tradng economes. Each approach s taken to estmate both Equaton (2) for aggregate trade and Equaton (3) for trade n the dfferentated sectors. The results of the estmaton from each approach, whch s presented n the ffth secton, are compared to examne how the proposed alternatve model for the dfferentated-sector trade dffers from the conventonal model for aggregate trade OLS Estmaton of Log-lnearzed Form As a benchmark, I frst estmate the volume-of-trade equatons n a log-lnearzed form by the OLS. Recallng Equatons (2) and (3) but also takng nto account other potental factors that may affect blateral trade flows, the followng two equatons are now consdered: 8 For aggregate trade, VT t t 1 t t 2 / Y sm y (4) t For dfferentated-sector trade, VT t t * 1 t t 2 / X sm y (5) t Although the underlyng monopolstc competton model explans a core mechansm determnng the volume of trade as Equatons (2) and (3) suggest (wth both β 1 and β 2 equalng one), real trade flows may be affected by other factors. For example, the lterature on the gravty equaton suggests that blateral trade flows wll be affected by geographc factors such as dstance, border sharng, and commonness of language. The term μ s ncluded n the equatons to capture these factors that are specfc to country pars, as well as other unobserved potental country par-specfc (but tme-nvarant) factors affectng 8 Snce panel data are used for the estmaton, here and n the rest of ths paper, varables n the equatons are expressed wth scrpt t to denote a tme perod. 11

12 blateral trade flows. The last term ε t captures dosyncratc dsturbances to recorded trade flows or measurement errors n data, whch are assumed to be log-normally dstrbuted. Takng the logarthm of both sdes of the two equatons (4) and (5), respectvely, yelds the followng lnearzed equatons: log( VTt / Yt ) 1 log( smt ) 2 log( yt ) t (6) * log( VTt / X t ) log( smt ) 2 log( yt) (7) 1 t Equaton (6) for the volume of aggregate blateral trade s the same as the man emprcal specfcaton that s employed by ebaere (2005). Equaton (7), whch s desgned to account for the volume of blateral trade n the dfferentated sectors, s an alternatve emprcal approach that ths paper proposes. Both equatons are estmated by OLS regresson wth country par-specfc dummes (μ ). Year-specfc dummes are also ncluded for the estmaton n order to capture any trend n or shocks to trade flows that are common for all countres n the world. Equatons (6) and (7) are estmated separately for the samples of OEC and non-oec countres. 9 Ths s to examne whether trade among OEC countres and trade among non-oec countres are equally well explaned by the volume-of-trade equatons, followng the studes by Hummels and Levnsohn (1995) and ebaere (2005). These studes separated a group of OEC countres from that of non-oec countres for estmaton, based on the understandng that ntra-ndustry trade of dfferentated products, whch the monopolstc competton model prmarly ams to explan, s domnant n trade among OEC countres, whle trade among non-oec countres should not be manly characterzed by horzontal product dfferentaton. Ther expectaton was thus that the aggregate verson of the volume-of-trade equaton (6) would descrbe blateral trade well for OEC countres but not for non-oec countres. Although Hummels and Levnsohn found a result that was counter to ths expectaton (.e., the data support the model for both country groups), ebaere s re-examnaton found emprcal support for the model only for OEC countres, as ntally expected. In contrast, the current study focuses on trade of dfferentated products, whch the monopolstc competton model ams to 9 See the next secton for the lst of the countres ncluded n each sample. 12

13 explan for any country group. Therefore, t s expected that the proposed equaton (7) for the dfferentated-sector trade should explan both trade among OEC countres and trade among non-oec countres equally well, whle the conventonal equaton (6) for aggregate trade would not. An emprcal ssue here n estmatng Equatons (6) and (7) s the treatment of zero-trade observatons. A consderable number of country pars n both OEC and non-oec groups have no blateral trade n the dfferentated sectors n certan years. In the data used n ths study, observatons wth no dfferentated-sector trade are less than one percent of all the observatons n the OEC sample, whle such zero-trade observatons comprse more than 60% n the non-oec sample. For the estmaton of the log-lnear equatons, these zero-valued observatons brng the problem of undefned logarthmc values n the left-hand sde. To handle ths problem, for the benchmark estmaton I use the followng two technques: () omttng the zero-trade observatons and usng only observatons wth postve dfferentated-sector trade; and () ncludng the zero-trade observatons for estmaton by replacng zero 10, 11 wth a very small postve number Non-lnear Model for Zero-trade Observatons: Posson Quas-maxmum Lkelhood Estmaton Although replacng zero wth a small postve number has been a conventon n estmatng a logarthmc form, t s not deal. It s more desrable f there exsts an other approprate alternatve estmaton method that can treat zero n the value of trade as t s. Hummels and Levnsohn (1995) estmated (by the OLS) ther volume-of-trade equaton n a level form, nstead of a logarthmc form, for ther non-oec sample to avod omttng zero-trade observatons. ebaere (2005) also employed smlar level specfcatons 12 and estmated the equatons by the Tobt method to keep zero-trade observatons n 10 ebaere (2005) also apples a smlar procedure to handle zero-trade observatons n estmatng hs log-lnear model. 11 Ths number must be at least smaller than the mnmum non-zero value of trade n the used data. The mnmum value of the blateral trade per producton (the left-sde varable of Equaton (5)) n the data s 9.4e-9, and I thus chose 10-9 (1.0e-9) for the postve small number replacng zero. 12 The level forms of the volume-of-trade equaton n the two studes are not the same. Hummels and Levnsohn (1995) used the value of aggregate trade as the dependent varable, whle ebaere (2005) employed the volume of aggregate trade as the share n GP. Hummels and Levnsohn s approach thus left the term of the country par s 13

14 hs non-oec data. The cost of usng such level forms of the equaton was that () they had to gve up estmatng separately the mpact of the two varables of nterest, the country par s sze smlarty and the country par s share of the world GP; or () as n one of ebaere s two level specfcatons, for separate estmaton of the effects of the two varables they had to abandon the strct consstency of a regresson equaton wth the theoretcal monopolstc competton model. In the current paper, I employ an alternatve method to handle zero-trade observatons, whch can both mantan the structural consstency of the regresson equaton wth the theoretcal model and separately estmate the mpacts of the two varables of nterest. The alternatve s the (fxed-effect) Posson quas-maxmum lkelhood (PQML) estmaton. The Posson regresson s usually appled for count data, but t s also applcable to non-negatve contnuous varables. Hausman, Hall and Grlches (1984) developed the condtonal fxed-effect PQML method n the panel data context, whch has been shown by Wooldrdge (1999) to be consstent and robust across dstrbutonal assumptons when the condtonal mean of the dependent varable s an exponental-class functon of the lnear combnaton of regressors. The PQML method has also been appled to the estmaton of the gravty equaton by Slva and Tenreyro (2006) for cross-sectonal data and by Westerlund and Wlhelmsson (2006) for panel data. These studes have shown by smulaton that wth zero-trade observatons the PQML method has the advantage of smaller potental estmaton bas compared to the OLS estmaton of a logarthmc form of the equaton. I thus employ the PQML method and estmate the followng form of the volume-of-trade equatons: For aggregate trade, VT t / Y 1 2 t smt yt t VT ] t / Yt exp[ 1 log( smt ) 2 log( yt) t (8) For dfferentated-sector trade, GP n the rght-hand sde of the equaton, about whch ebaere argued n terms of ts relevance for assessng the mpact of the sze smlarty between tradng countres. 14

15 VT t / X t * 1 2 smt yt t VT ] * t / X t exp[ log( smt) 2 log( yt) (9) 1 t The man dfference from the benchmark log-lnear form (6) or (7) s that n the above form the stochastc error term ε t s addtve, nstead of multplcatve as n Equatons (4) and (5) Tobt Estmaton of Log-lnearzed Form For the purpose of robustness check of the OLS estmaton of the log-lnear form, I also apply the Tobt regresson to estmate the volume-of-trade equatons. Even for the Tobt estmaton, zero-trade observatons n the data brng the ssue of the undefned logarthm of zero n prncple. However, n the specfc data used n the current study, blateral trade s recorded n thousands of U.S. dollars, and thus no (or zero) value s recorded when the value of blateral trade s less than $500 (rounded to zero thousands). Usng ths feature of the employed data, I apply the Tobt estmaton to the followng log-lnear specfcaton, whch s slghtly dfferent from Equatons (6) and (7): For aggregate trade, log( VTt ) log( Yt ) 1 log( smt ) 2 log( yt) t (10) log(vt t ) = log(vt * t ) f VT * t > 0.5 ($500) log(vt t ) = log(0.5) f VT * t 0.5 ($500) For dfferentated-sector trade, * log( VTt ) log( X t) 1 log( smt) 2 log( yt) t (11) log(vt t ) = log(vt * t ) f VT * t > 0.5 ($500) log(vt t ) = log(0.5) f VT * t 0.5 ($500) where VT t or VT t s the observed or recorded value of blateral trade n the data, whle VT * t or VT * t s the underlyng actual trade value. 13 The followng two thngs should be noted for ths estmaton approach. 13 It should be noted that the uncondtonal fxed-effect Tobt model wll generally be based due to the problem of ncdental parameters (Hsao 2003, pp.48-9 and p. 243). 15

16 Frst, a country par s total producton (X t n the dfferentated-sector equaton or Y t n the aggregate equaton) s now moved from the denomnator of the left-hand sde to the rght-hand sde of the equaton. The varable s thus ncluded as one of the regressors, but the coeffcent for ths varable s restrcted to be one for estmaton. Secondly, all the zero values for blateral trade n the data are replaced wth $500 or 0.5 n thousands of dollars. 4. The ata To estmate Equatons (6) through (11) presented n the prevous secton, data on trade, GP, and ndustral producton have been collected for varous countres. The data on blateral trade are from the NBER-Statstcs Canada Trade ata compled by Feenstra, Lpsey, and Bowen (1997) for the perod , and the UC-Statstcs Canada Trade ata that s compled by Feenstra (2000) to supplement for the perod up to The dataset contans trade flows between each par of countres. Goods n the trade flows are classfed accordng to the four-dgt Standard Internatonal Trade Classfcaton (SITC, Revson 2). The value of each trade flow s recorded n thousands of nomnal U.S. dollars. The data on GP measured n current U.S. dollars are from the World evelopment Indcators (World Bank, 2005). Both GP of each country and the world total GP have been collected to compute the world ncome (GP) share of each country par (y ). 14 The data on ndustral producton are from the Unted Naton s Industral Statstcs atabase (INSTAT3, UNIO 2003), whch contans the annual data on manufacturng producton n countres for the years of Manufacturng ndustres are classfed accordng to the three-dgt Internatonal Standard Industral Classfcaton (ISIC, Revson 2). The data on gross output n nomnal U.S. dollars are used. 14 For the computaton of ths country-par GP share, I use the world GP that also counts the GPs of countres whch are not ncluded n the 89 sample countres lsted n Table 1. Therefore, the world GP s greater than the sum of the GPs of the 89 sample countres. 16

17 The data for the current study cover 89 countres for the years 1970 through These countres all have populaton above one mllon as of the year The countres are dvded nto two groups, OEC countres and non-oec countres, accordng to the actual OEC membershp as of the year As a result, the data nclude 20 countres (190 blateral pars) n the OEC group and 69 countres (1,808 pars 16 ) n the non-oec group. Table 1 lsts the countres and years ncluded n the data for each group. The blateral trade flows between the OEC countres represent 33.8% of the world total flows on average over the perod (wth an annual share rangng 0.3% through 62.0%); and the flows between the non-oec countres represent 1.0% on average over the perod (wth an annual share rangng 0.5% through 1.5%). The panel data are kept unbalanced to retan as many observatons n the data as possble. [TABLE 1 HERE] 4.1. Industry/commodty classfcatons for the producton data and trade data Snce the trade data and the producton data are based on dfferent classfcaton schemes, mappng one classfcaton onto the other s requred to merge the two datasets usng a common classfcaton. 17 In the producton data 28 manufacturng ndustres are classfed accordng to the threedgt ISIC, whle n the trade data goods are classfed nto over a thousand categores accordng to the four-dgt SITC. The mappng thus requres condensng the four-dgt SITC (Revson 2) nto the threedgt ISIC (Revson 2). I have mapped the trade data onto the three-dgt ISIC usng the concordance s the year n whch New Zealand oned the OEC. New Zealand was the newest member untl Mexco oned n The number of country pars n the data s less than 69 C 2 = 2,346. Ths s because the 69 countres nclude countres that appear n the data as one of a country par n any year(s), whle some country pars have no years for whch producton or GP data are avalable for both countres. For nstance, the data for Mexco are avalable only for whle the data for Hong Kong are avalable only for As a result, blateral trade between these two countres s not ncluded n the data for any year. 17 Whle the ISIC for the producton data s based on ndustral actvtes, the SITC for the trade data s based on commodty characterstcs. Snce the two classfcatons are based on dfferent prncples, the mappng cannot necessarly be one-to-one. 17

18 nformaton sourced from the OEC, whch s avalable on Jon Haveman s Industry Concordances web page. 18 Next, to separate the dfferentated sectors from other (non-dfferentated) sectors, I follow Rauch (1999), whch classfes the four-dgt SITC commodtes nto three categores based on the degree of product dfferentaton: goods traded on an organzed exchange (homogeneous goods), reference prced goods, and dfferentated goods. Although the producton data, whch are classfed accordng to ISIC, cannot be smply mapped onto Rauch s three categores, there are ten three-dgt ISIC manufacturng ndustres whose correspondng four-dgt SITC categores are all classfed as Rauch s dfferentated goods. These ndustres are: 322 (wearng apparel), 324 (footwear), 332 (furnture), 355 (rubber products), 356 (plastc products), 361 (pottery, chna, and earthenware), 362 (glass and products), 382 (non-electrc machnery), 384 (transport equpment), and 385 (professonal and scentfc equpment). I therefore group these 10 three-dgt ndustres as representatve of the dfferentated sectors, and accordngly compute blateral trade and producton n these dfferentated sectors for each country par for each year. These 10 dfferentated manufacturng ndustres comprse 31.2% of the world aggregate trade on average, wth the share n each year rangng from 24.3 to 37.0% durng the perod of These shares n the total trade flows among the 89 sample countres are: 41% on average wth annual shares rangng 33 through 49% for the OEC countres; and 13% on average wth annual shares rangng 9 through 21% for the non-oec countres Zero-trade Observatons In the OEC group, whle all country pars have postve blateral trade flows n all the 28 years, 28 out of 3,630 observatons (for 190 country pars for 28 years) have zero trade n the dfferentated 18 The orgnal mappng s from the fve-dgt SITC to the three-dgt ISIC. However, snce the trade data have only the detal of the four-dgt classfcaton, I dsregarded the detals of the fve-dgt SITC n the orgnal concordance. 19 The dfferentated-sector ndustres n ths study are selected only from manufacturng ndustres. 18

19 sectors. In the non-oec group, 4,551 out of 14,565 observatons (for 1,808 country pars for 28 years) have no trade flows, and addtonal 2,798 observatons have zero flows n the dfferentated sectors. Fgures 1 through 4 plot blateral trade per producton aganst the sze smlarty ndex wth a trend lne ftted by locally weghted regresson. 20 Fgures 1 and 2 are for the OEC countres, and 3 and 4 are for the non-oec countres. Fgures 1 and 3 plot the value of aggregate trade per GP aganst the ndex of GP smlarty between two countres (sm t ). Fgures 2 and 4 plot the value of trade per producton n the dfferentated sectors aganst the ndex of producton structure-adusted GP smlarty (sm * t). All the varables are n logarthms and mean-dfferenced, whch correspond to the benchmark OLS estmaton wth dummes. The vertcal and horzontal lnes ndcate zeros, whch are the means of the mean-dfferenced varables. Whle the trend lne exhbts some postve slope on all the fgures, the postve relatonshp between the two varables does not seem to be very clear except for Fgure 1 for aggregate trade between the OEC countres. [FIGURES 1 THROUGH 4 HERE] 5. Emprcal Results 5.1. OLS Estmaton of Log-lnear Form The results of the benchmark OLS estmaton of the log-lnear form of the volume-of-trade equatons are presented n Tables 2 and 3. In each table, the second through fourth columns show the results for the OEC countres, and the ffth through seventh columns show the results for the non-oec countres. For each country group, one column shows the result of the estmaton of Equaton (6) for aggregate trade, and one column shows the result of the estmaton of Equaton (7) for the dfferentatedsector trade. For the purpose of comparson, the sectoral equaton (7) s also estmated for a group of three-dgt ISIC manufacturng ndustres that are not ncluded n the dfferentated sector. 21 The 20 Locally weghted scatterplot smoothng or lowess. The smoothng parameter (or bandwdth) s 0.8 for the trend lne n these fgures. 21 The non-dfferentated sector group conssts of the followng 17 three-dgt ISIC ndustres: 311 (food products), 313 (beverages), 314 (tobacco), 321 (textles), 323 (leather products), 331 (wood products), 341 (paper 19

20 estmaton result for these non-dfferentated sectors s shown n another column for each country group. The lower part of the tables shows the results of the tests, n the p-values, of the hypotheses that () the coeffcent for the ndex of sze smlarty equals one; () the coeffcent for a country par s world GP share equals one; and () these two coeffcents are ontly equal to one. These hypotheses are what the monopolstc competton model suggests when nternatonal trade s frctonless. It should be noted, however, that n realty varous knds of trade frcton exst, and not all of them may be controlled for by country-par specfc dummes n the estmaton. Havng such trade frcton, the coeffcent estmates may be dfferent from (smaller than) one even though the estmaton suggests a postve and sgnfcant relatonshp between the volume of trade and the respectve determnants. [TABLES 2 AN 3 HERE] Table 2 shows the result of the OLS estmaton usng observatons wth postve trade values but excludng zero-trade cases. In the followng, to focus on the tested predcton on the relatonshp between the volume of blateral trade per producton and the sze smlarty between tradng countres, I put my man focus on the estmate of the coeffcent for the smlarty ndex (β 1 ). The result ndcates that among the OEC countres the postve relatonshp between the volume of trade per producton and the sze smlarty ndex s sgnfcant for both aggregate and dfferentated-sector trade. Ths relatonshp s also postve for trade n non-dfferentated sectors but less sgnfcant. In addton, the sze of the coeffcent estmate s the largest for the dfferentated sectors ( ˆ 1 =.858), t s smallest for the non-dfferentated sectors ( ˆ 1 =.312), and the case for aggregate trade falls n between ( ˆ 1 =.422). The dfference between the estmate for the dfferentated-sector case and those for the other two cases s sgnfcant. 22 On the other hand, for the non-oec countres, the coeffcent s estmated to be postve and sgnfcant (at the and products), 342 (prntng and publshng), 351 (ndustral chemcals), 352 (other chemcals), 353 (petroleum refneres), 354 (mscellaneous petroleum and coal products), 369 (other non-metallc mneral products), 371 (ron and steel), 372 (non-ferrous metals), 381 (fabrcated metal products), and 383 (electrc machnery). The mscellaneous category 390 s excluded from both dfferentated and non-dfferentated groups. 22 The hypothess that ˆ s the same between the aggregate case and the dfferentated-sector case s reected at the 1 5% level of sgnfcance. 20

21 1% level) for all the three cases; but the dfference n the value of the estmate s not sgnfcant across the cases. 23 The same equatons (6) and (7) are also estmated by OLS usng all the observatons wth zerotrade values beng replaced wth a small postve number (10-9 ). Equaton (7) s also estmated for the non-dfferentated sectors. The result s shown n Table 3. For the OEC countres, the overall result s the same as the prevous case, except that now the estmate for the non-dfferentated sector s not sgnfcant even at the 10% level. However, for the non-oec countres, the coeffcent estmate s nsgnfcant for all the three cases. The pont estmate for dfferentated-sector trade s larger than that n the other two cases, but the dfference s not sgnfcant. 24 In other words, for the non-oec countres, the OLS estmaton of the log-lnear form of the volume-of-trade equaton gves a dfferent pcture dependng on whether zero-trade observatons are excluded or ncluded Alternatve Estmaton of the Log-lnear Form: Tobt The Tobt estmaton of the log-lnear equatons s also performed to see the robustness of the result when both zero- and nonzero-trade observatons are ncluded. Equatons (10) and (11) are estmated for aggregate and dfferentated-sector trade, respectvely. As n the OLS estmaton, Equaton (11) s also estmated for the non-dfferentated sectors. The result s shown n Table 4. The overall pcture s smlar to Table 3 for the OLS estmaton havng zero-trade observatons ncluded, but the coeffcent estmate ˆ 1 ncreases ts sgnfcance n the dfferentated-sector equaton (11) for both country groups. In partcular, for the non-oec countres the estmate s weakly sgnfcant (at the 10% level) n the dfferentated sectors whle t s nsgnfcant n the other two cases: aggregate trade and the non- 23 The p-value of the test of ˆ beng equal between the dfferentated-sector case (wth the largest value) and the 1 non-dfferentated-sector case (wth the smallest value) s The p-value of the test of ˆ beng equal between the dfferentated-sector case (wth the largest value) and the 1 non-dfferentated-sector case (wth the smallest value) s

22 dfferentated sectors. 25 Ths result ndcates that the separaton of the dfferentated sectors n estmatng the volume-of-trade equaton, whch the current paper proposes, gves evdence of the predcton of the monopolstc competton model more clearly than the conventonal aggregate trade approach does. [TABLE 4 HERE] 5.3. Posson Quas-maxmum Lkelhood (PQML) Estmaton The above three estmaton methods do not treat the zero value n the trade data as t s. On the other hand, the proposed estmaton of Equatons (8) and (9) by the Posson quas-maxmum lkelhood (PQML) procedure can treat zeros n observatons as they are. Table 5 presents the result of the PQML estmaton. Equaton (9) s also estmated for the non-dfferentated sectors. [TABLE 5 HERE] The result for the OEC countres s consstent wth the estmaton results by the prevous three methods, whle the estmated coeffcent for the smlarty ndex s sgnfcant at the 1% level not only n the aggregate and dfferentated-sector equatons but also n the non-dfferentated-sector equaton. In other words, the estmaton shows that among the OEC countres the postve correlaton between the volume of trade per producton and the adusted sze smlarty s ndcated even n the non-dfferentated sectors. However, ths may be because these non-dfferentated sectors comprse manufacturng ndustres. These ndustres are excluded from the pure dfferentated sectors, but that does not mean that products n these ndustres are all homogeneous. A more mportant thng n the estmaton result s that the sze of the estmated coeffcent s the largest for the dfferentated-sector trade, the medan for the aggregate trade, and the smallest for the non-dfferentated sectors. The coeffcent estmate n the dfferentated-sector equaton s sgnfcantly larger than the estmate n the other two equatons However, the dfference n the estmate across the three cases s not sgnfcant for the non-oec countres. On the other hand, for the OEC countres, the estmate n the dfferentated-sector equaton s sgnfcantly larger than that n the other two cases at the 1% sgnfcance level. 26 The dfference s sgnfcant at the 10% level between aggregate trade and dfferentated-sector trade, and at the 5% level between the dfferentated sectors and non-dfferentated sectors. 22

23 For the non-oec countres, the coeffcent estmate s also sgnfcant n all the three cases, at least at the 5% level. However, the estmate for the dfferentated sector s the smallest and least sgnfcant, 27 whch s counter to the expectaton from the theory. In other words, the result of the PQML estmaton mples that, among the non-oec countres, the postve correlaton between the volume of trade per producton and the sze smlarty between countres s more strkng as nternatonal trade contans more non-dfferentated products Comparson of Four Approaches to Estmaton The above four estmaton approaches gve consstent results for the OEC countres, but for the non-oec countres they provde dfferent results from each other. To see whch method descrbes the data, especally for the non-oec countres, better than the others, I use the Akake Informaton Crtera (AIC, by Akake 1974) for the four estmaton specfcatons. The AIC measures the goodness of ft of an emprcal model, and a model wth a lower AIC value s preferred to that wth a hgher AIC value. Table 6 compares the value of the AIC of each estmated model for the two country groups and the three cases: aggregate trade, dfferentated-sector trade, and non-dfferentated-sector trade. For any country group and any case, the estmated model by the PQML has the lowest AIC value, the OLS wth only postve-trade observatons gves the next lowest, the Tobt gves the thrd, and the estmated model by the OLS ncludng (value-replaced) zero-trade observatons has the hghest AIC value. Ths comparson ndcates that, for any case, the equaton estmated by the PQML descrbes the data the best. [TABLE 6 HERE] 5.5. Summary and scusson As descrbed above, the result for the OEC countres s consstent across the four estmaton approaches. The estmated coeffcent for the sze smlarty ndex s postve and sgnfcant not only n 27 However, the dfference of the estmate between dfferentated-sector trade and the other two cases s not sgnfcant (the p-value s 0.15). 23

24 the dfferentated-sector-trade equaton but also n the aggregate-trade equaton. The estmate for the dfferentated sectors, however, s sgnfcantly larger than that n the other cases, and s also close to one. 28 On the other hand, the estmaton for the non-dfferentated sectors gves a smaller and less sgnfcant coeffcent estmate than the other two cases, mplyng that the monopolstc competton model does not descrbe trade n the non-dfferentated sectors as well as t does trade n the dfferentated sectors. Therefore, ths study, by separatng dfferentated (and non-dfferentated) sectors from aggregate trade n estmaton, clearly demonstrates that the postve correlaton between the volume of trade among OEC countres and sze smlarty among the countres, whch has been found n the prevous studes, s drven by such correlaton n trade of the dfferentated products, as the monopolstc competton model suggests. On the other hand, for the non-oec countres, the results are mxed n the four approaches. Some methods estmate the coeffcent for the smlarty ndex beng nsgnfcant even n the dfferentated-sector equaton, but other methods estmate the coeffcent beng sgnfcant even for the non-dfferentated sectors. However, the estmaton by the PQML, whch has econometrc advantages (small potental estmaton bas wth zero-valued data) and better descrbes the data wth a lower AIC value than the other three approaches, shows that the coeffcent for the sze smlarty ndex s sgnfcant regardless of whether the traded sectors are dfferentated or not. Ths result brngs us back to Hummels and Levnsohn s puzzle; and also mples that ebaere s fndng may be due to hs way of handlng zerotrade observatons n estmaton. Moreover, the current study deepens the puzzle. That s, the estmaton ndcates that for the non-oec countres the correlaton between the volume of trade and the sze smlarty between tradng economes s weaker n the dfferentated sectors than n the less dfferentated sectors, whle the correlaton should be drven by product dfferentaton f the monopolstc competton model apples. The current study thus mples that some dfferent mechansm from horzontal product 28 The p-value of the test of the hypothess that the coeffcent equals zero ranges from 0.38 through 0.85 across the four estmaton methods. 24