Measuring Comparative Advantage: A Ricardian Approach

Transcription

1 Measurng Comparatve Advantage: A Rcardan Approach Johannes Moenus Unversty of Redlands Prelmnary, please do not cte comments hghly apprecated 06/12/2006 ABSTRACT In ths paper, we derve and compare several producton- and export-based measures of comparatve advantage wthn a Rcardan framewor. We frst sort commodtes nto ndustres n order to obtan ndustry-specfc ndcators of comparatve advantage. We then compare these measures aganst a smple theoretcal benchmar. Frst, we show that theoretcally correct producton- and export-based ndcators are equvalent when there are no trade costs such as transport fees, nsurance and tarffs. However, n the presence of trade costs, most measures perform poorly, and the more mportant trade costs are, generally the poorer the performance. Second, Balassa's (1965, 1979 export-based ndex of Revealed Comparatve Advantage s generally not a vald measure of comparatve advantage across ndustres or over tme. It s only a vald measure wthn an ndustry for a gven perod. However, we derve structural estmaton equatons for how t can be approprately used for regresson analyss of comparatve advantage. Fnally, we suggest how export-based measures may be decomposed nto two components, one measurng relatve technology n producton and the other measurng relatve trade costs, mprovng the performance of measures when trade costs are present. These allow us to study factors that nfluence comparatve advantage and costs of trade at the same tme. School of Busness, Unversty of Redlands, Redlands, CA , johannes_moenus@redlands.edu. I am ndebted to Leonard Dudley for help on an earler verson of the paper. Semnar partcpants at Northwestern Unversty, Unversty of Texas, Austn and the Mdwest Trade Meetngs provded helpful comments. All remanng errors are mne.

2 Measurng Comparatve Advantage: a Rcardan Approach page 2 1. INTRODUCTION How should comparatve advantage be measured? The conventonal wsdom s that the answer depends on one s research objectve. If the goal s to test between competng statc theores of nternatonal trade, then the preferred approach has been to use net factor flows or ndustry shares of GDP. If nstead, the objectve s to explan the effects of commercal polcy, transport costs or other shocs on the compettve stuaton of a set of countres, the usual method has been the gravty model. An popular but recently contested approach to estmatng the effect of technology and factor supples on comparatve advantage uses Balassa s (1965, 1979 measure of Revealed Comparatve Advantage RCA. However, a systematc evaluaton and comparson of these measures as well as how they perform n the presence of trade costs s mssng. Wth excepton of net factor flows, almost all currently used measures of comparatve advantage 1 are derved from commodty exports or producton. We construct these commodty based measures from a Rcardan model. We also establsh a theoretcal benchmar measure of comparatve advantage and show that wth excepton of RCA, all measures reflect comparatve advantage accurately n the absence of trade costs. RCA only reflects comparatve advantage accurately for a gven ndustry and perod across countres. Next we generate producton volumes and exports n the presence of trade costs from the model. We calculate the measures from ths artfcal data and correlate them wth the theoretcally correct benchmar suggested by the model. All measures perform rather poorly. Generally, the hgher the trade costs, the smaller the country and the lower ts average technologcal poston, the poorer the performance of the measures. We therefore suggest a smple procedure based on the gravty model to mprove the performance of these measures. 1 Throughout the paper, we use the orgnal Rcardan (1817 defnton of comparatve advantage, whch states that a country has comparatve advantage n an ndustry f ths ndustry has relatvely lower labor nput requrements than another one. For an extensve dscusson of dfferent defntons of comparatve advantage, see Deardorff (2004.

3 Measurng Comparatve Advantage: a Rcardan Approach page 3 Much emprcal research on trade has been devoted to testng theores of comparatve advantage. A wdely used approach s the technque poneered by Leontef (1953 over a half century ago and extended more recently by Trefler (1993, Usng nput-output tables, Trefler calculated the net trade n the servces of each producton factor for a group of tradng economes. Comparng these flows wth factor abundance by country and allowng for dfferences n tastes and productvty, he was able to fnd emprcal support for both the technologcal and factorendowments theores of comparatve advantage. Unfortunately, ths approach has lttle to say about nternatonal exchange of commodtes as opposed to factors. In addton, snce t does not tae account of trade costs such as tarffs, non-tarff barrers and transport costs, t tends to overestmate the amount of trade. Harrgan (1997 proposed an alternatve measure of comparatve advantage, namely, the share of each ndustry n a country s GDP. Although hs specfcaton does not deal explctly wth ntermedate nputs, t has the advantage of allowng productvty dfferentals to vary across ndustres. He too found that comparatve advantage depends on both factor abundance and dfferences n productvty. However, as he hmself admtted, hs estmates had low predctve power. Harrgan and Zarajse (2000 obtaned smlar results usng a larger and more vared sample of countres but wthout drectly estmatng technology dfferences. One problem wth ths approach s the assumpton that trade costs have no effect on producton patters. Two recent studes by Anderson and van Wncoop (2004 and Hanson (2004 have concluded that such costs can have a major mpact on the goods a country produces. If the objectve s to explan observed flows of commodtes, the most frequently used approach has been the gravty equaton. Here the dependent varable s the blateral trade between two countres, ether aggregated or by commodty. Evenett and Keller (2002 used a verson of ths technque n whch trade flows are dsaggregated by sector to test alternatve trade theores. Although the gravty model provdes a good explanaton of blateral trade flows, t s not easy to nfer ts mplcatons for the determnants of a country s relatve tradng poston.

4 Measurng Comparatve Advantage: a Rcardan Approach page 4 Balassa s (1965 ndex of Revealed Comparatve Advantage seemed to provde a cure for these shortcomngs, snce the normalaton should allow for comparsons over tme and across ndustres. The Balassa ndex s defned as the rato of a country s share n world exports of a gven ndustry dvded by ts share of overall world trade. It owes ts popularty to several advantages t has compared wth those we have examned. As wth the gravty model, the data are readly avalable. However, unle the gravty model, the normaled dependent varable may be nterpreted drectly as a measure of a country s relatve tradng poston. Recently, many researchers have been reluctant to use ths measure snce, as Harrgan and Zarajse (2000 observe, RCA s consdered to be an ad hoc specfcaton wth no theoretcal foundaton. 2 In ths paper, we show under whch condtons the Balassa Index s a vald measure. The purpose of ths paper s to derve and evaluate the producton and export-based measures of comparatve advantage dscussed above. We evaluate the qualty of an emprcal measure of comparatve advantage by ts correlaton wth a correspondng theoretcal benchmar, where we generate the data for both the benchmar and the emprcal measure from a rcardan model. We conduct the exercse both n the absence as well as presence of trade costs. Because of ther popularty, we focus on the measures suggested by Balassa (1965 and Harrgan (1997. We do so n three steps: Frst, we show how the Rcardan specfcaton of Dornbusch, Fscher and Samuelson (DFS, 1977 may be extended n order to group products nto ndustres. 3 Products are sorted accordng to comparatve advantage and then grouped nto ndustres. The overall model for the country s dentcal wth the orgnal DFS verson. Once the overall equlbrum s determned, the products get reshuffled and sorted nto ther respectve ndustres, but wth the orgnal ran- 2 There s a large lterature that recognes problems wth and suggests mproved versons of the Balassa-Index, see for example Bowen (1973 Kunmoto (1977 Hllman (1980, Yeats (1985 and Vollrath (1991. Newer applcatons of the Balassa-Index le Proudman and Reddng (2000 and Pham-S (2004a, b are aware of these problems and consequently suggest alternatves or robustness checs to mtgate the problem. However, none of these studes nvestgates the drect correspondence between comparatve advantage and the Balassa-Index. 3 The Rcardan framewor s deal for our purposes snce autary prces and free trade prces have a drect correspondence to each other, avodng the complcatons llustrated by Hllman (1980.

5 Measurng Comparatve Advantage: a Rcardan Approach page 5 orderng from the overall model. Then n each ndustry there exsts a unque cut-off pont such that all products on one sde are produced at home and those on the other sde are produced abroad. Our theoretcal benchmar of comparatve advantage s the number of commodtes n an ndustry that a country produces at lower unt producton cost as ts compettors. 4 Ths can be normaled by the total number of commodtes a country produces as well as by relatve ndustry se, provdng theoretcal equvalents to shares and normaled shares of producton and exports. We calculate the emprcal measures and smulate the model for a broad range of parameters. The resultng correlaton coeffcents between the emprcal measures generated from the model and the theoretcal benchmar serve as our measure of qualty. In the absence of trade costs, we fnd that the correlaton between producton shares and export shares and the theoretcally correct measure s equal to one n the model. Consequently all three perfectly reflect comparatve advantage when no trade costs are present. Whle the normaled producton shares also perfectly correlate wth ther theoretcal counterpart, the Balassa-ndex only does so when both country se and average technology are the same across countres. Ths suggests RCA to be a msnomer. However, ths s not correct. The Balassa ndex s stll a vald measure of comparatve advantage wthn ndustres across countres. It also by defnton stll correctly reflects relatve export performance across countres, ndustres and tme and as such s stll useful for country analyss. Next we ntroduce ceberg transport costs, as n the orgnal DFS-model. We allow these costs to be ether unform or ndustry-specfc. We demonstrate that export shares and producton shares are no longer perfectly correlated wth ther theoretcal counterparts. Consequently, n general, nether measure wll correctly reflect comparatve advantage due to the exstence of non-traded goods. Moreover, none of the measures unformly domnates all others under the condtons we smulated. Nevertheless, for any gven relatve wage, export based measures can be easly modfed 4 The deal theoretcal measure, of course, would be a measure of relatve unt producton costs. However, as t s well-nown, these have no observatonal equvalence n real data for traded goods wth complete specalaton.

6 Measurng Comparatve Advantage: a Rcardan Approach page 6 to resemble ther theoretcal counterparts for traded goods. Ths modfcaton also allows us to decompose export based measures nto a comparatve-advantage component and a relatve-tradecost component. Interpretng trade costs broadly, we can examne how frctons le transportaton costs, language dfferences, nsttutons and preferences for home goods together nfluence realed comparatve advantage. Fnally, we tae the export-based measures to the data. We show that the emprcal verson of the decomposton yelds a comparatve-advantage component, a relatve-trade-cost measure and an error component. However, snce we cannot dsentangle the trade-cost measure from the error component, we are left once agan wth two components. We then use the gravty-model framewor to construct counter-factual blateral exports by ndustry under the assumpton that trade costs are ero. These estmates are used to construct trade cost-free values of the Balassa Index. Dvdng the orgnal observed ndex by ths constructed ndex, we obtan the relatve trade cost measure. The paper proceeds as follows. The next secton ntroduces the extended DFS model graphcally and uses t to derve the varous measures. In the followng secton, we compare the performance of dfferent measures of comparatve advantage both wth and wthout trade costs. Fnally, we demonstrate the usefulness of ths approach wth actual data. 2. THE DFS-MODEL WITH COMMODITES GROUPED INTO INDUSTRIES In ths secton, we frst show how the measures can be derved theoretcally usng a smple graphcal analyss. We then complement ths analyss wth formal dervatons from a Rcardan trade model. 2.1 Graphcal Analyss In ther extenson of Rcardan trade theory, Dornbusch et al. (1977 assumed a contnuum of ndustres raned n terms of decreasng comparatve advantage of the home country relatve to the

7 Measurng Comparatve Advantage: a Rcardan Approach page 7 rest of the world. They then drew up two schedules, one reflectng supply and the other demand. In Fgure 1, goods are arrayed on the horontal axs by decreasng comparatve advantage of the home country. The home country s relatve wage s measured on the vertcal axs. The negatvelysloped A-schedule captures the effects of technology on the supply sde. Under dentcal Cobb- Douglas preferences, the postvely sloped B-schedule represents the dstrbuton of demand. The ntersecton of the two schedules determnes the relatve wage as well as whch goods are produced at home and whch n the foregn country. A-schedule B-schedule Pecewse Comparatve Advantage ω Industres 1,2,3 Fgure 1. The smple Dornbusch-Fscher-Samuelson (1977 model In the real world, commodtes are produced by ndustres, each of whch may produce more than one good. It s therefore approprate for us to amend the DFS model, eepng the basc assumpton of a contnuum of goods, but regroupng commodtes nto ndustres. For later emprcal mplementaton, one may thn of all nternatonal transactons beng sorted accordng to some ndustry classfcaton le the Standard Internatonal Trade Classfcaton (SITC. To llustrate the pont, we assume that ndustres whch are adjacent to each other n the classfcaton have smlar levels of relatve labor productvtes and are therefore located next to each other on the A-Schedule. Such a stuaton s depcted n Fgure 2.

8 Measurng Comparatve Advantage: a Rcardan Approach page 8 The dfferent ndustres may easly be located on the A-schedule, each country havng pecewse comparatve advantage n certan ndustres. The A- and B-schedules stll jontly determne the cutoff pont that determnes whch ndustres of the contnuum wll be producng n the home country and whch ones wll be producng n the foregn country. Gven the general cut-off pont n Fgure 1, we can determne the ndustry-specfc cutoff ponts n Fgure 2, where [1,2,3]. Note that n general there wll be ntra-ndustry trade snce n each branch, the commodtes to the left of wll be produced n the home country and those to the rght abroad. Industry 1 Industry 2 Industry 3 ω Fgure 2. A-schedules by ndustry It s clear from these graphs that n order to calculate both producton and export shares, each commodty on the contnuum needs to carry two ndces. One ndex must ndcate the commodty s ran-order on the A-schedule and a second must show the ndustry category to whch t belongs. The model may also be extended to allow country- and ndustry-specfc trade costs. As we wll show below, trade costs create problems when one compares any of the measures across countres. However, country-ndustry-specfc trade costs are hard to handle wthn the graphcal analyss. Therefore, we ntroduce two smplfyng assumptons. Frst, the commodtes wthn an ndustry category are dstrbuted randomly along the A-schedule. Instead of the stuaton n Fgure 1, we then have that llustrated n Fgure 3.

9 Measurng Comparatve Advantage: a Rcardan Approach page 9 A-schedule B-schedule ω Fgure 3. Randomly dstrbuted ndustres Second, we assume that transport costs are unform but specfc to each ndustry. 5 The frst assumpton allows drawng up contnuous schedules of relatve unt producton costs, as llustrated by the sold downward-slopng curves n Fgure 4. The second assumpton allows addng correspondng schedules of producton plus transport costs for each country, as llustrated by the dotted curves n the same fgure. Wthn each ndustry, the dotted curve on the left shows the lmt to the goods that the home country can produce for export, whle that on the rght s the lmt to those that the foregn country can export. Between the two curves are the non-traded goods n each ndustry. 5 Ths assumpton s relaxed n the smulaton analyss below.

10 Measurng Comparatve Advantage: a Rcardan Approach page 10 Industry 1 Industry 2 Industry 3 ω Non-traded Goods Fgure 4. Industry-specfc transport costs Combnng our dscusson wth the graphs above, we summare as follows: (1 In the DFS model, both wth and wthout transportaton costs, producton and exports are not perfectly correlated, not even for all traded goods. A small country that exports a certan good does so proportonally to the se of the rest of the world, whle t mports proportonally to ts own se. However, producton and export shares are perfectly correlated n the absence of trade costs, snce the relatve se of a country does not matter for shares. (2 In the presence of transport costs, due to the exstence of non-traded goods wthn each ndustry, both measures are mperfect reflectons of actual comparatve advantage. (3 The greater the asymmetres of transport costs across countres and ndustres, the greater are the dstortons that separate observed producton and exports from the underlyng relatve unt producton costs. Eaton and Kortum (2002 have proposed a counterfactual method that allows estmatng trade flows n the absence of such transport-cost asymmetres. However, ther procedure cannot be easly appled to the non-traded goods wthn each ndustry.

11 Measurng Comparatve Advantage: a Rcardan Approach page 11 Next we derve these results formally n the context of the DFS (1977 model, whch can be spped at a frst read. Then we use counterfactuals to construct mproved measures of comparatve advantage. 2.2 Technology The world economy, consstng of two countres, produces consumer products whch wll be ndexed by, [1, N], where N ndcates the total number of products that are ether produced at home or abroad. Any reader famlar wth DFS (1977 can sp ths and the next secton, snce I merely replace the contnuum of products n the DFS (1977 framewor wth dscrete products. Later on, I wll addtonally group the commodtes nto ndustres. For a gven, a( and a( are the home and foregn countres respectve unt labor requrements. Each good can then be charactered by ts relatve unt labor-requrement a(/a(. Home and foregn worers receve wages w and w determned by the condton that trade between the two countres be balanced. In the absence of trade costs, the home country wll produce a certan good f t s the low-cost producer: a( w a ( w. [1] However, wth trade costs the stuaton changes, snce only a fracton of the goods produced wll survve ceberg trade costs. Let g(. and g(. be the fractons of FOB value that survve after shpment to ther destnaton n the foregn and home country respectvely. These costs can n prncple be country-par or ndustry-specfc and are assumed to be a functon of dstance, tarffs, nsttutons and the le. 6 However, n what follows we wll assume that they are country specfc 6 Snce the use of tarff ncome s rrelevant for the queston we address, we assume no redstrbuton of tarff ncome as wages. For a detaled dscusson of the effect of ths redstrbuton, see DFS(1977.

12 Measurng Comparatve Advantage: a Rcardan Approach page 12 for ease of exposton. 7 Snce there exst only two countres n our world, we ndex trade costs only by the country of orgn. The home country wll therefore produce commodty only as long as a ( w a( w [2] g (. Consder frst the stuaton n whch commodtes are sorted by decreasng order of the home country s comparatve advantage amended for trade costs. The relatve comparatve advantage of the foregn country n the home country s maret can be charactered by the followng dscrete functon: a ( / g (. A (, A ( + 1 < A (. [3] a( where we assume that the rato A ( s unque for all to smplfy the soluton of the model. Smlarly, exports from the home country wll be too expensve and therefore the foregn country wll produce commodty as long as a( w a ( w [4] g ( Consequently, the home country's comparatve advantage adjusted for costs of trade can be charactered by: a ( A (, A( + 1 < A( a( / g( Wthout loss of generalty, we assume that the costs of trade are determned by exportng country factors le shppng and transacton technology. The home country produces a range of commodtes ndexed from 1 to some borderlne commodty ( ω, g (, whch s defned by: 1 ( A (, g < + 1 ω [5] 7 As mentoned earler, n the smulaton we allow g and g to be also ndustry-specfc. However, ths only poses complcatons n terms of ndexng the products and therefore the graphcal representaton, snce the orderng n terms of lowest producton- and trade costs combned may vary across countres.

13 Measurng Comparatve Advantage: a Rcardan Approach page 13 where A 1 ( s the nverse functon of A ( and ω = w commodtes rangng from ( ω, g to N wth and. 1 ( A(, g < + 1 w. The foregn country produces ω [6] Ths stuaton can be depcted as n Fgure 5, where we approxmate usng contnuous functons: Transport Costs A( A ( ω Produced at Home Non-Traded Produced n Foregn Fgure 5. Transport costs Equatons [4] and [5] together wth Fgure 5 reveal that the home country's export performance s jontly determned by the relatve unt labor costs and trade costs of both countres. However, the borderlne good that the home country exports s determned by ts own technologcal advantage and trade cost. The borderlne commodty,, n whch the home country has a comparatve producton dsadvantage but that t nevertheless produces s determned by the foregn country's trade cost. For gven technologes and trade costs, t follows that the relatve wage has to fall wthn the followng nterval:

14 Measurng Comparatve Advantage: a Rcardan Approach page 14 a ( j a ( / g (. ω,, j. [7] a( j / g(. a( Adjusted for trade costs, the home country has a comparatve advantage n all goods ndexed on the rght sde of ths nequalty whle the foregn country has a comparatve advantage n the goods ndexed j on the left hand sde of the nequalty. 2.3 Demand For smplcty, let us assume dentcal Cobb-Douglas preferences. Less restrctve assumptons do not yeld very dfferent results as long as preferences are homothetc (Dornbusch et al., 1977, 826, n. 3. Cobb-Douglas preferences guarantee constant expendture shares. Defne b( as the share of domestc ncome, Y, spent on good : p( c( b( = > 0, [8] Y where c( s domestc consumpton for commodty and p( s ts prce. There s postve demand for all goods. By defnton, N = 1 b ( = 1. [9] Identcal preferences n the two countres then guarantee that b ( = b (. [10] The share of foregn ncome Y spent on mported goods s defned as λ = = 1 b( [11]

15 Measurng Comparatve Advantage: a Rcardan Approach page 15 where s the borderlne good that s no longer exclusvely produced n the home country and λ = λ( ω, g. The share of domestc ncome Y spent on goods produced n the foregn country s therefore N λ = b(, = + 1 [12] where denotes the hypothetcal ncremental commodty that s no longer produced at home and λ = λ ( ω, g. The actual "borderlne" commodtes wll be determned n equlbrum. Equlbrum requres that domestc labor ncome equals world spendng on domestcally produced goods: ( 1 wl + w L wl = λ λ [13] where L and L are the labor supples n home and foregn respectvely. [13] can be rewrtten as: λ L L ω = B,, [14] λ L L snce and determne λ and λ. The functon B(. characteres the demand-sde of the model. For gven relatve labor endowments, t represents relatve factor ncomes ω that are consstent wth patterns of trade as determned by and. It s ncreasng n the share of ncome foregners spend on goods produced at home and vce versa. Snce all ncome s spend on commodtes n our model, relatve factor-ncomes also determne relatve demands for products, and B(. s therefore commonly referred to as the demand schedule. Equlbrum s then charactered by: λ L L A( ω = = B ; ; A ( L L, [15] λ where the bars over varables ndcate ther equlbrum values.

16 Measurng Comparatve Advantage: a Rcardan Approach page MEASURES OF COMPARATIVE ADVANTAGE In ths secton, we frst present theoretcal measures of comparatve advantage based on our model. Then we derve commonly used emprcal measures of comparatve advantage from our model. Fnally we study how these relate to each other. 3.1 A Theoretcally Correct Measure of Comparatve Advantage Relatve unt producton costs are unobservable n a world where all goods are traded and producton s completely specaled. Therefore, theoretcal measures based on relatve unt producton costs may be elegant, but emprcal counterparts are nonexstent for traded goods. To study the emprcal performance of currently used emprcal measures, we turn to a smpler alternatve that follows drectly from the theory: A country has a comparatve advantage n producng a certan good f t s relatvely better at producng ths good than a competng country. It s therefore evdent that at the product level, comparatve advantage can be represented by a bnary measure: a country ether has a comparatve advantage or t does not. In the absence of trade costs, there s complete specalaton at ths level. At the ndustry level, such complete specalaton s not lely to be the case: some commodtes wthn an ndustry may be produced n the home country, some n the foregn country. Consequently a country may have a comparatve advantage n some but not all of the goods n an ndustry. A frst approach to measure comparatve advantage on the ndustry level s therefore to smply count the number of goods wthn ndustry that a country produces, whch I wll call n and n for the home and foregn country respectvely. However, unless both countres are of the same se and ndustres are defned n a way that each one covers the same number of products, ths measure does not lend tself easly to comparsons across ndustres and countres. To allow for easer comparsons across countres, n can be adjusted for country se. The equvalent of country se s the number of commodtes produced n a country, n and n. If n

17 Measurng Comparatve Advantage: a Rcardan Approach page 17 addton one controls for the number of commodtes n an ndustry relatve to all commodtes n the world, one obtans the formal equvalent of commodty counts to the Balassa-Index. If there are postve trade costs an addtonal complcaton arses: namely, the presence of nontraded goods. Whle t s stll easy to determne whch country has a comparatve advantage at the product level for traded goods, ths dstncton s not as smple for non-traded goods. Recall that whether a country has comparatve advantage n producng a good s determned by the exogenously gven relatve technologes as well as the endogenously determned relatve wage. The relatve wage s not only nfluenced by factor avalablty and technology, but also by trade costs snce they determne the share of non-traded goods. 8 For any gven relatve wage, we can calculate domestc prces for all non-traded goods n home and foregn marets. The home country has a comparatve advantage n producng those non-traded goods whose domestc prce s lower than the prce n the foregn maret. For all other non-traded goods, t has comparatve dsadvantage. Snce ths cut-off pont depends on the relatve wage, t s clear that changes n transportaton costs nfluence the wage and may also change the set of non-traded commodtes n whch a country has a comparatve advantage. To summare, the model mples theoretcally correct measures of comparatve advantage. At the product level, a country has a comparatve advantage f t ether exports the product or has a lower domestc prce. To fnd a comparable measure at the ndustry level, we count the number of products n the ndustry n whch a country has a comparatve advantage. We can then adjust for country and ndustry se. Table 1 dsplays these measures of comparatve advantage based on our model at the product and ndustry level. 8 Strctly speang, we therefore can never exactly determne comparatve advantage unless we now unt costs under autary. All we can do s therefore determne comparatve advantage tang the relatve wage as gven, despte the fact that t s endogenously determned.

18 Measurng Comparatve Advantage: a Rcardan Approach page 18 Table 1. Benchmar measures of comparatve advantage Product level Absolute { 0,1} Share Industry level I n = I = I, T + I ϕ = Normaled ( I + I ( n + n HI = I n ϕ HI n = 1 = = 1 ϕ = n n ', NT = + 1 ( n + n ( n + n where the summatons are over all products that belong to the -th ndustry or alternatvely, s the ndustry nto whch the -th product has been sorted. The producton share of product, φ and relatve producton shares, HI are lsted only for reference. From the perspectve of the home country, n conssts of two components: all exported goods n the nterval from 1 to and some of the non-traded goods n the nterval between +1 and, namely those whch home has the lower domestc prce for, where ' denotes the borderlne good for whch ths requrement s fulflled. I wll call those counts of ndustres n,t and n,nt respectvely. ϕ 3.2 Modeled Equvalents of Emprcal Measures of Comparatve Advantage In prevous research, two types of emprcal measures of comparatve advantage have been suggested. One uses producton data (e.g. Harrgan, 1997, and the other export data (e.g. Balassa, We construct the model equvalents of each of these measures and then compare the resultng ndcators wth the theoretcally correct measures presented n Table 1. We start by assumng no trade costs, but wll later drop ths restrcton. Begnnng wth producton measures, we wll examne the followng ndcators: ndustry producton, share of ndustry producton n country producton (producton shares as well as the latter normaled by the relatve se of the ndustry wthn the world. 9 We wll then examne the 9 See Overman et. al (2001 for a survey of how ths measure was used n emprcal research.

19 Measurng Comparatve Advantage: a Rcardan Approach page 19 followng export-based measures of comparatve advantage: ndustry exports, share of ndustry exports n country exports (export shares, and the latter normaled by the share of ndustry exports n world exports, commonly referred to as the Balassa Index. In the dervatons that follow, we wll focus on the home country at the ndustry level. As before, each commodty wll be sorted nto an ndustry. We therefore add ndustry ndces. Then we analye the relatonshp of the dfferent measures of comparatve advantage to one w other. We normale world ncome to Y = 1. Let the home country's share n world ncome be θ. Consder frst the commodty level. Defne ϑ as the home country's producton of commodty as a fracton of world ncome (or producton. ϑ = b( f s a traded good and ϑ = θ b( f t s non-traded. Now move up to the ndustry level. The home country's producton of ndustry as a b, T, NT = fracton of world ncome s θ ( + θ b ( = θ + θ =, where we have now added the second ndex to ndcate that each good belongs to an ndustry. T and NT ndcate traded and non-traded goods respectvely. Let the home country's share n world producton overall be θ = M = 1 θ, where M denotes the number of ndustres. Industry 's producton as a share of total home country producton s then defned as: φ= θ θ. FOB exports of tradable commodty are e( = (1 θ b(. Therefore, ndustry s exports are e = ( 1 θ b (. The home country s total exports (FOB are e = M = 1 e M = 1 = 1 = 1 = ( 1 θ b ( and world exports are e w = e + e. Fnally, the home country's exports n ndustry as a share of the country s total exports are χ = e e. It θ, T follows, that even wth country-ndustry specfc ceberg trade costs that χ =, snce foregners θ pay the domestc prce, but quanttes are melted away, whch leads them to pay an "mplct" hgher prce. The other measures follow analogously. We can therefore summare our measures on the ndustry level before we move forward to compare them to one other: n, T

20 Measurng Comparatve Advantage: a Rcardan Approach page 20 Table 2. A comparson of modeled emprcal measures of comparatve advantage Producton Exports Absolute a Share ϕ HI Normaled θ + θ θ ( 1 θ e = θ, T θ ϕ = e θ, T χ = = θ e θ n, T = BI = = w w w w e e e e e e χ a wth world ncome normaled to one, as n DFS (1977. We are now ready to study how these measures compare to our theoretcally correct measure and how they are related to one other. 3.3 Comparsons between the Measures In ths secton, we compare the emprcal measures generated by the model wth ther theoretcal benchmars. We do so by generatng correlaton coeffcents between the benchmars and emprcal measures by smulatng the model numercally. Whle analytcal solutons can be derved for smple (e.g. unform trade costs, ths s mpossble for complex structures of trade costs, for example when trade costs are ndustry-specfc. The specfc functonal forms for technology, the costs of trade as well as parameter values employed can be found n appendx A. We analye potental nfluences on the behavor of these measures, namely technologcal advantage, country se, the number of ndustres, how evenly commodtes are dstrbuted across ndustres as well as unform and ndustry-specfc trade costs. The results are presented n table 3 and 4 n appendx B. The tables reveal three major results: (1 Producton shares, export shares and relatve producton shares are all perfectly correlated wth ther correspondng benchmar measures from table 1, regardless of country se and relatve technology level. (2 The Balassa-ndex s only correlated wth ts theoretcal equvalent when countres are of equal se and none of them has a

21 Measurng Comparatve Advantage: a Rcardan Approach page 21 technologcal advantage on average. (3 All measures perform more or less poorly when trade costs are present. There s no domnant measure that outperforms all others n all stuatons. The frst result s demonstrated n the frst row of tables 3 and 4. It s what one should expect based on the wor by Harrgan (1997. Extendng hs argument to export shares s straghtforward, snce normalng a country's export n an ndustry wth overall country exports elmnates the nfluence of country-se. It s not as straghtforward that the same holds for relatve producton shares, but can be understood from the explanaton of the second result. The frst row of quadrants n tables 3 and 4 also reveal that the Balassa-ndex (shaded n gray s not perfectly correlated wth ts theoretcal benchmar unless the home and foregn country are of the same se and there s no technologcal advantage on average for ether country. Ths can be explaned by the followng experment: assume that a small country loses comparatve advantage n one good n a partcular ndustry and gans comparatve advantage n one good n another ndustry. Ths only changes n and n, but not ( n + n n the correspondng measure n table 1. Therefore, only the numerator of the measure n table 1 changes. However, n the Balassa-ndex, the numerator and the denomnator change smultaneously n both ndustres. Ths s due to the fact that the small country exports proportonally to the rest of the world's se, whle t mports proportonally to ts own se. Consequently, n the ndustry that loses one commodty from the small country's perspectve, world exports declne snce the large exports from the small country to the rest of the world are replaced wth small exports from the rest of the world to the small country. The opposte s true for the other ndustry nvolved. Consequently, the Balassa ndex cannot be perfectly correlated wth the measure based on ndustry counts. Technologcal advantage has a smlar nfluence, snce an ncrease n average technologcal advantage ncreases the economc se of a country and also maes exports and mports for the two countres asymmetrc. Note, however, that ths only matters across ndustres, not wthn ndustres across countres. Consequently, the Balassa-Index s stll a vald measure of comparatve advantage for a partcular ndustry across countres, snce t s perfectly correlated wth export shares across countres n any gven ndustry

22 Measurng Comparatve Advantage: a Rcardan Approach page 22 and year. But comparsons across ndustres and tme do not reflect comparatve advantage accurately. However, the ndex by defnton stll measures relatve export performance correctly, even across ndustres and tme, and ths can stll be a useful measure for country analyss. Snce the ndex of relatve producton shares s mmune to these problems, t suggests tself for comparsons across ndustres and countres as a means of comparson of comparatve advantage. The thrd result has to be taen wth a gran of salt, snce t lely s the one most specfc to the Rcardan model employed. However, the observatons may be nterestng enough to warrant more general nvestgaton. The thrd result can be seen by comparng correspondng rows n tables 3 and 4: when trade costs are present, the model does not delver a "champon": There s no sngle measure that consstently outperforms all others. But comparng correspondng columns n both tables suggests drectons for future research: t seems that relatve producton shares outperform all other measures for small countres, or more precsely, when there are large asymmetres between small and large countres and the research nterest s on the small countres. Export shares perform reasonably well when trade costs are not too "large". If the home country has a technologcal advantage on average, then all measures tend to be more accurate even n the presence of trade costs. All these effects are caused by the same drvng force: whatever maes the analyed country resemble the world economy more closely ncreases the correlaton between the emprcal measures and ther theoretcal counterparts (wth excepton, of course, of the Balassa-ndex. Consequently, a larger country, hgher relatve technology and lower, more evenly dstrbuted trade costs across ndustres all tend to mprove the accuracy of the measures. Fnally, usng a fner ndustry classfcaton tends to mprove performance. Uneven dstrbuton of commodtes across ndustres (mplyng relatvely small and large ndustres surprsngly doesn't seem to hurt, but rather to help accuracy of the measures. Whle ths may be due to smple aggregaton effects, ths needs to be explored n more detal. The results from ths secton suggest that the Balassa-ndex s napproprate for analyss of comparatve advantage across ndustres. Ths seems to suggest employng producton based

23 Measurng Comparatve Advantage: a Rcardan Approach page 23 measures whenever avalable. However, f nternatonal trade costs could be accounted for, exportbased measures would be preferable at least for traded goods. We wll suggest such a procedure based on Eaton & Kortum (2002. We wll also show that t s possble to obtan a general and theoretcally correct measure of comparatve advantage from the Balassa-Index through regresson analyss. Combnng the theoretcally correct measure derved from the Balassa-Index wth the procedure that accounts for trade costs allows studyng nfluences on comparatve advantage and costs of trade separately. We therefore derve estmaton equatons for the Balassa-Index next. 4. ESTIMATING MODELS OF COMPARATIVE ADVANTAGE AND RELATIVE EXPORT PERFORMANCE Rewrtng the expresson for exports, solvng t for c and nsertng t bac nto the export equaton provdes us wth the followng expresson for exports: ( ( ( (1 ( ( (1 p a w b b e θ θ = = [16] Insertng [16] bac nto the formula for the Balassa-Index and smplfyng leads to: + + = = + = = = + = = = = = M N M N M p a w p a w p a w p a w p a p a BI ( ( ( ( (1 ( ( ( ( (1 ( ( ( ( θ θ θ θ [17] If all the requred data s avalable, [17] can be estmated drectly by tang logs on both sdes. Smplfyng ths expresson, however, [17] can be rewrtten as: ( ( (1 1 ( λ θ λ θ σ θ σ θ λ σ + + = BI [18] where σ s the share of ndustry n all commodtes that fall nto the nterval from 1 to, and σ s the share of ndustry n all commodtes that fall nto the nterval from + 1 to N. Tang logs on both sdes, we obtan:

24 Measurng Comparatve Advantage: a Rcardan Approach page 24 ((1 θ σ + θ σ + ln( (1 θ λ + θ λ ln( BI ln( σ ln( λ ln [19] = Estmatng [19] reveals that under the assumpton that the data s generated by a rcardan model as specfed above, n a regresson of the Balassa-Index on a constant, country- and ndustry dummes the error term ε of ths regresson provdes a measure proportonal to the number of products a country produces n ndustry. ln( BI = α + β1dc + β1di + ε [20] It follows from [17] that ε = β 0 a( ln + e p, and from the Frsh-Waugh-Lovell-Theorem that ( [20] can therefore be wrtten n the followng form, a( ln( BI α β = + 0 ln + β1dc + β 2DI + ε [21] p( where the second term s proportonal to ln(σ agan. Consequently, [21] can be used to estmate nfluences on comparatve advantage drectly, despte the fact that the Balassa-Index tself s generally not a vald measure of comparatve advantage. We wll provde an example of ths n secton 5.3 of the paper. Alternatvely, of course, t s also vald to use the followng estmaton to obtan dentcal results: a( ln( χ α β = + 0 ln + β1dc + ε [22] p( where we replaced the left hand sde wth export shares. The defnton of exports [16] can also be estmated. Its smple structure s dentcal to a very smple verson of the gravty model n emprcal trade. Snce ndustry-specfc factors on the rght hand sde are the man drvers of exports n ths model, whle all other nfluences are absorbed n dummy-varables, one can nterpret the estmaton technque that results from our theoretcal model as an amended verson of the gravty equaton. In fact, Feenstra (2004 has suggested usng country-specfc dummy-varables to replace the multlateral resstance terms derved n Anderson and van Wncoop (2004. We fnd smlar terms n our regresson. However, snce our analyss s ndustry-specfc, country- and

25 Measurng Comparatve Advantage: a Rcardan Approach page 25 ndustry specfc prce-terms have to be ncluded n the regresson n order to avod omtted varable bas. In prncple, the framewor above can easly be adapted to blateral aspects of comparatve advantage based on the wor of Eaton and Kortum (2002 and Deardorff (2004b. Fnally, the above analyss suggests that the orgnal specfcaton of Balassa (1965 was nvald. 5. DISENTANGLING COMPARATIVE ADVANTAGE AND COSTS OF TRADE Whle the assumpton of ceberg transportaton costs s techncally elegant, t does not reflect the actual organaton of transactons. The specfcaton above harbors a major problem: FOB exports are not equvalent to the true value purchased by foregners before meltng, they are the true value equvalent before addng costs of nternatonal trade. I ntroduce a smple verson of ths next. 5.1 Trade Costs as Mar-Ups I eep the smple assumptons about preferences but change the notaton such that trade costs are a country-par and ndustry-specfc marup over regular FOB values. Consequently, the FOB export data we observe s ( = p( c (. The survval fracton g ( of the prevous sectons s e o smply the nverse of the marup, therefore: ( e, o p( = c ( = b g ( g ( ( (1 θ [23] Under the assumpton that a soluton for the relatve wage and the relatve prces exst, [23] can be wrtten as: e, o ( = b( b( w a ( (1 θ g ( (1 θ g ( = [24] p( Implementng ths nto the Balassa-Index yelds n ts smplest verson:

26 Measurng Comparatve Advantage: a Rcardan Approach page 26 BI, g = (1 θ = 1 g ( + θ = 1 N g = + 1 g ( ( M = 1 = 1 g (1 θ ( M = 1 = 1 g ( + θ M N g = 1 = + 1 ( [25] Ths expresson cannot be smplfed f g ( are country-par and ndustry-specfc. However, several cases are possble n whch the above expresson can be smplfed, for example f g ( = g ( = g, then BI,g = BI. Generally, however, we can mplctly defne BI, g = BI G, where G = f(g ( s a scalng factor whch s a functon of the trade costs for each commodty. From the expresson above, t s hard to solve for G analytcally. However, G can be approxmated usng a statstcal method proposed by Eaton and Kortum (2002. We turn to ths procedure next. 5.2 Counterfactual Estmates Recall from above that observable exports can be wrtten as: e ( b( (1 g ( = θ [26], o Tang logs on both sdes, ths can be wrtten as the followng estmaton equaton: ( e ( = ln( b( + ln( 1 θ + ln( g ( + ε ln, o In order to estmate ths model, we wll mae the followng dentfyng assumpton: g ( s assumed to be country-par specfc n the sense that t s a functon of dstance and the country of orgn. We therefore actually estmate the followng model: ( ( α + β D + β D + γ d + ε ln [27] e h, f = h h f f h hf where h, f ndcate the home and the foregn country respectvely, D h s a dummy varable that assumes the value 1 for country h and ndustry and ero otherwse, D f s a dummy varable that assumes the value 1 for country f and ero otherwse, and d hf s the dstance between the two countres. We then construct counterfactuals as n Eaton and Kortum(2002, where we calculate eˆ hf ( for the case of ero dstance between the two countres. These estmates are then agan used

27 Measurng Comparatve Advantage: a Rcardan Approach page 27 to construct export-based measures of comparatve advantage. In partcular, we wll calculate the Balassa-Index for ero trade costs, BI 0. We wll use ths ndex to recover the trade-cost ndex G = BI BI 0. BI 0 and G can be used to study nfluences that may affect comparatve advantage (new technology, the costs of trade (length of the coastlne, number of ports or both (nsttutons. For our demonstraton exercse, I only use three wdely used ndustry-categores suggested n Rauch(1999: He sorted four dgt SITC ndustres nto those that are traded on organed exchanges, those that are reference prced and those that are nether. In recent wor (Berowt et. al. 2004, the frst and the last category are referred to as smple and complex goods respectvely. Complex vs. Smple Smple Complex Eaton and Kortum (2002 demonstrated how to estmate ths rcardan model n a mult-country settng. In order to get more relable results, we therefore estmate blateral trade relatonshps and construct counterfactuals for the 55 countres lsted n table 5 n appendx B for the years 1982 and Trade data comes from the World Trade Database of Statstcs Canada. Blateral dstances are the same as n Rauch (1999. For those three ndustry categores, we plot the relatonshp between BI and BI 0, whch are labeled RCA and CA respectvely n the followng graphs. Each pont represents a country.

28 Measurng Comparatve Advantage: a Rcardan Approach page 28 CA CA RCA RCA BI and BI 0 for goods traded on organed exchanges n 1982 (left panel and 1992 (rght panel CA CA RCA RCA BI and BI 0 for reference prced goods n 1982 (left panel and 1992 (rght panel CA CA RCA RCA BI and BI 0 for goods that fall n nether category n 1982 (left panel and 1992 (rght panel

29 Measurng Comparatve Advantage: a Rcardan Approach page 29 Snce we plot all measures by ndustry, RCA and CA can be used to measure comparatve advantage. 10 Recall that for both measures BI (=RCA and BI 0 (= CA, hgher values ndcate hgher comparatve advantage. As expected, there s a clear postve correlaton between the two varables. An astonshng pattern emerges: whle n 1982 relatve export performance as measured by the unadjusted Balassa-Index overstated true comparatve advantage n smple goods, t underrepresented t n complex goods! By the year 1992, these dfferences seemed to have been roned out and the Balassa-Index seems to be a farly decent representaton of "true" comparatve advantage. Another nterestng fact s that there are a number of country-ndustry combnatons where the Balassa-ndex ndcates (revealed comparatve advantage, whle the corrected measure does not. Avodng these msclassfcatons can be potentally mportant for locaton-analyss. It s also nstructve to study the relatonshp between the relatve trade cost ndex and the comparatve advantage ndex: TCI TCI RCA RCA BI 0 and G for goods traded on organed exchanges n 1982 (left panel and 1992 (rght panel 10 Export shares and the Balassa ndex are always perfectly correlated wthn ndustry for a gven year by constructon. However, ths s not the case across ndustres. For example, n our data the correlaton coeffcent between RCA and export shares n the year 1992 s 0.82.

30 Measurng Comparatve Advantage: a Rcardan Approach page 30 TCI TCI RCA RCA BI 0 and G for reference prced goods n 1982 (left panel and 1992 (rght panel TCI TCI RCA RCA BI 0 and G for goods that fall n nether category n 1982 (left panel and 1992 (rght panel For the measures BI (=RCA and G (= TCI, hgher values ndcate hgher comparatve advantage and lower relatve trade costs respectvely. In a compettve world, only countres wth relatvely low trade costs are able to export f they have low comparatve advantage. Ths s reflected n all graphs above. Relatve trade-cost dfferences decreased for smple goods, but ncreased somewhat for complex goods. For all three categores, the dfferences are the hghest for countres that have comparatve dsadvantage n that category. Countres wth hgh relatve export performance generally have somewhat hgher than average trade costs, lely reflectng the fact that they have to export to many and potentally also dstant countres.

31 Measurng Comparatve Advantage: a Rcardan Approach page 31 In the next secton, we wll use these measures as left-hand sde varables n order to estmate nfluences on comparatve advantage and costs of trade jontly. 5.3 Estmatng Influences on Comparatve Advantage and the Costs of Trade The two ndces derved above, BI 0 and G, can now be used to study nfluences on comparatve advantage and relatve costs of trade. The regresson equatons are analogous to the ones n [21]: a( ln( BI α β 0 = + 0 ln + β1dc + β 2DI + ε [28] p( ( g( + β D + β D ε ln( α + β ln + [29] G 0 = 0 1 C 2 I Note that ndustry-dummes are ncluded on the rght hand sde, whch allows us to nclude all ndustres n the sample. As a smple example, researchers have postulated that remoteness of a country affects ts trade, where remoteness s measured as GDP-weghted blateral dstances (We Remoteness should not affect technology, but should affect the prces charged, snce frms n a remote locaton are somewhat shelded from competton. It should also nfluence relatve trade costs, snce long-hauls cost less per unt of dstance than short hauls of freght. Wth the framewor developed here, we can estmate those effects drectly. We do so for Balassa's relatve export performance as well as the two new measures developed n ths paper. Snce we only have one parameter of nterest, we only nclude ths parameter for smplcty. 11 The coeffcent states the dfferental effect of remoteness on complex versus smple goods. It ndcates the percentage change n the left-hand sde measure gven a one percent ncrease n the remoteness measure relatve to the other goods categores. We do the estmaton for all years combned 12 as well as the begnnng and the end of the sample perod. The results are presented n the followng table: 11 Recall from above that the derved specfcaton requres prce-data, whch was not avalable to us for all countres. Unfortunately, ths mples that the presented results are lely based due to omtted varable bas. However, snce these regressons only serve llustratve purposes, we are not concerned about ths ssue here. 12 Ths requres to replace the ndustry dummes n [28] and [29] wth ndustry-year dummes.