Technology, Geography, and Trade Jonathan Eaton and Samuel Kortum Econometrica, Volume 70 September 2002 Prepared by Pavel Vacek, November 15, 2004

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1 Technology, Geography, and Trade Jonathan Eaton and Samuel Kortum Econometrca, Volume 70 September 2002 Prepared by Pavel Vacek, November 15, 2004

2 Technology, Geography, and Trade Jonathan Eaton and Samuel Kortum Econometrca, Volume 70 September 2002

3 1 Goal Develop a model ncorporatng realstc geographc features nto General Equlbrum Derve structural equatons for blateral trade Estmate parameters of the model Counterfactuals

4 2 Eaton and Kortum are not the frst to gve the gravty equaton a structural nterpretaton. Helpman (1987) assumes monopolstc competton wth frms n dfferent countres choosng to produce dfferentated products. Implcaton s that each source should export a specfc good everywhere. Haveman and Hummels (2002) report evdence to the contrary. In Eaton and Kortum (2002), more than one country may produce the same good, wth ndvdual countres supplyng dfferent parts of the world.

5 3 Model Buldng on Dornbusch, Fscher, Samuelson (1977) model of Rcardan trade wth a contnuum of goods, 2 country model only. Countres have dfferental access to technology, effcency vares across commodtes and countres. Denote country s effcency n producng good j [ 0,1 ] as z ( j). Denote nput cost n country as c (Later c wll be broken nto the cost of labor and of ntermedate nputs).

6 4 Cost of a bundle of nputs s the same across commodtes wthn a country (because country nputs are moble across actvtes and actvtes do not dffer n ther nput shares). Wth CRS, the cost of producng a ut of good j n c z j. country s ( ) Geographc barrers: Iceberg transportaton cost, delverng a ut from country to country n requres producng d uts n, ( d =1 for all, d > 1 for n. ). Assume the trangle nequalty, for any 3 countres, k and n holds: d d d. nk k

7 5 Delverng a ut of good j produced n country to country n costs: ( ) c p j = d z ( j) Perfect Competton: p ( j) s what buyers n country n would pay f they chose to buy good j from country. Shoppng around the world for the best deal, yelds prce of j: { p ( j) = mn p ( j), = 1,... N, n where N s the number of countres. }

8 6 Facng these prces, buyers (fnal consumers or frms buyng ntermedate nputs) purchase goods n amounts Q(j) to max CES objectve: σ σ 1 σ 1 σ 1 U = Q( j) dj 0 where s>0 s the elastcty of substtuton. Maxmzaton s subject to a budget constrant. It aggregates across buyers n country n to X n, country n s total spendng.

9 7 Probablstc representaton of technologes: country s effcency n producng good j s the realzaton of a random varable Z. Z s drawn ndependently for each j from ts country specfc dstrbuton: F( z) = Pr[ Z z]. The cost of purchasng a partcular good from country n country n s the realzaton of the random varable: c P ( j) = d Z The lowest prce s the realzaton of: P( j) = mn P ; = 1,... N}. n {

10 8 π s the probablty that country supples a partcular good to country n (probablty that s prce turns out to be the lowest). Probablty theory of extremes provdes a form for that yelds a smple expresson for π and for the resultng dstrbuton of prces. F( z)

11 9 Asde: Kortum (1997) and Eaton and Kortum (1999) show how a process of nnovaton and dffuson can gve rse to Frechet dstrbuton, wth T reflectng a country s stock of orgnal or mported deas. Snce the actual techque that would ever be used n any country represents the best dscovered to date for producng each good, t makes sense to represent technology wth an extreme value dstrbuton.

12 10 The dstrbuton of the maxmum of a set of draws can converge to one of only three dstrbutons: - the Webull - the Gumbell - the Frechet Only for Frechet does the dstrbuton of prces nhert an extreme value dstrbuton. Therefore t was chosen.

13 11 Frechet dstrbuton: F( z) T z θ = e, where T >0 and q>1. Theta=1.2 T=100

14 12 F( z) T z θ = e where T >0 and q>1 Treat the dstrbutons as ndependent across countres. T s country specfc parameter governg the locaton of the dstrbuton. (A bgger T mples that a hgh effcency draw for any good j s more lkely). Thnk about T as country s state of technology reflectng country s absolute advantage across a contnuum of goods.

15 13 F( z) T z θ = e where T >0 and q>1 q parameter s common to all countres and reflects the amount of varaton wthn dstrbuton. (Bgger q mples less varablty.) Thnk about q as a parameter regulatng heterogenety across goods n countres relatve effcences. It governs comparatve advantage wthn a contnuum of goods.

16 14 Resultng dstrbuton of prces n dfferent countres: Country presents country n wth a dstrbuton of prces: c d G ( p) = Pr[ P p] = 1 F( ) p G ( p) = 1 e [ T( c d) θ ] p θ

17 15 How to get t: Recall: P = c d Z T z θ and F( z) = Pr[ Z z] = e. Defne: G ( p) = Pr[ P p] c d c d n G ( p) = Pr[ p] = 1 Pr[ Z ] Z p c d = 1 F[ ] p θ cd T p θ T ( c d ) p = 1 e = 1 e θ

18 16 The lowest prce for a good n country n (P n ) wll be less than p unless each source s prce s greater than p. Therefore: the dstrbuton G ( p) = Pr[ P p] n n country n actually buys s: for what G ( p) = 1 [1 G ( p)] n N = 1 Insertng G, prce dstrbuton nherts form of G (p): G ( p) = 1 e n φ n p θ where φ = T ( c d ) N n = 1 θ

19 17 The prce parameter N θ φ = Tc ( d) summarzes how: n = 1 1. states of technology around the world, 2. nputs costs around the world, 3. and geographc barrers govern prces n each country n. Specal cases: a) n zero-gravty world wth no geographc barrers d =1 for all n and F s the same everywhere and the law of one prce holds for each good

20 18 b) n autarky, wth prohbtve geographc barrers F n reduces to T c θ n n Country n s own state of by ts nput cost. technology downweghted Prce dstrbuton has 3 mportant propertes: 1. π (the probablty that country provdes a good at the lowest prce n country n) { } π = Pr[ P ( j) mn P ( j), s ] π ns T ( c d ) = φ n θ

21 19 Contnuum of goods mples, π s also the fracton of goods that country n buys from country. 2. Can be shown: The prce of a good that country n actually buys from any country also has the dstrbuton G n. Pr[P < p P = P ] = G ( p). n n n For goods that are purchased, condtong on the source has no bearng on the good s prce.

22 The prces of goods actually sold n a country have the same dstrbuton regardless of where they come from. Corollary: Country n s average expendture per good does not vary by source. Hence the fracton of goods that country n buys from country, π s also the fracton of ts expendture on goods from country : π θ X T( c d ) T( c d ) = = = N X φ T ( c d ) n n k k nk k = 1 where X n s country n s total spendng and X s spent (c..f.) on goods from. θ θ 20

23 θ X T( c d ) T( c d ) = = N X φ T ( c d ) n n k k nk k = 1 Notce: ths already resembles gravty equaton. θ θ Blateral trade s related to the mporter s total expendture and to geographc barrers The exact prce ndex for the CES functon s: 1/ θ p n = γ φ n where 1 1 σ 1 σ θ γ = + Γ θ and G s the Gamma functon.

24 22 Connecton between trade flows and prce dfferences: Dvde X X X by n X and substtute for F from prce ndex p n. X / X φ n θ p d = d = X / X φ p n n θ (Notce: p and p n above are prce ndces for country and n, not prces of some sngle good.) Call the left hand sde country s normalzed mport share n country n. (Trangle nequalty mples, t never exceeds one.)

25 23 X / X φ n θ p d = d = X / X φ p n n θ As overall prces n market n fall relatve to prces n market or as n becomes more solated from (hgher d ) s normalzed share n n declnes. As the force of comparatve advantage weakens (hgher q), normalzed mport shares become more elastc w.r.t. the average relatve prce and to geographc barrers. A hgher q means relatve effcences are more smlar across goods. There are fewer effcency outlers that overcome dfferences n average prces or geographc barrers.

26 24 Emprcal exploraton of the trade-prce relatonshp: X / X φ n θ p d = d = X / X φ p n n θ A) Measure left-hand sde by data on blateral trade n manufactures among 19 OECD countres n (normalzed mport shares never exceed 0.2) Crude proxy for d s dstance.

27 25 Normalzed mport shares aganst dstance between the correspondng country-par (logarthmc scale). Ignorng the prce ndces n θ X / X φ n θ p d = d = X / X φ p n n. We wll see the resstance that geography mposes on trade. Inverse correlaton.

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29 27 X / X φ n θ p d = d = X / X φ p n n θ B) Retal prces n each of 19 OECD countres of 50 selected manufactured products were used to construct prce measure. Prce measure: ln p d p n Negatve relatonshp between normalzed mport shares aganst prce measure as model predcts.

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31 Equlbrum nput costs (so far nput costs c were taken as gven). Strategy: 1. Decompose the nput bundle nto labor and ntermedates. 2. Determnate prces of ntermedates, gven wages. 3. Determnaton of wages. 29

32 Producton Producton combnes labor and ntermedate nput, wth labor havng a constant share b. Intermedates comprse the full set of goods combned accordng to the CES aggregator. The overall prce ndex n country, p, becomes approprate ndex of ntermedate goods prces there. The cost of an nput bundle n country : c = w p, β 1 β where w s the wage n country. N θ Notce: c (F ) through p and F ( T ( c ) ). = 1 30

33 31 Determnaton of prce levels around the world: Substtutng c = w p nto β 1 β 1/ θ p n = γ φ n, we can get system of equatons: N θ φ = Tc ( d) and applyng n = 1 p = N γ β 1 β θ T( d w p ) n = 1 1/ θ Numercal methods necessary.

34 32 Plug c = w p nto β 1 β θ X T( c d ) T( c d ) = = N X φ T ( c d ) n n k k nk k= 1 to get expresson for trade shares as functons of wages and parameters of the model: θ θ X X β 1 β π T n γ d w p = = p n θ

35 33 Labor market equlbrum (They show how manufacturng fts nto the larger economy.) Denote: L manufacturng workers X n total spendng on manufactures. wl = β N π X n n= 1 Manufacturng labor ncome n country s labor s share of country s manufacturng exports around the world, ncludng sales at home.

36 34 Denote Y n aggregate fnal expendtures and a the fracton spent on manufactures. Total manufacturng expendtures are: 1 β X = w L + α Y β n n n n Demand for manufactures as ntermedates by the manufacturng sector tself. Fnal consumpton of manufactures.

37 35 Aggregate fnal expendtures Y n consst of value-added n manufacturng w n L n plus ncome generated n nonmanufacturngy O. n Y wl n n n Y O n = +. Assume nonmanufacturng output can be traded costlessly (not nnocuous), and use t as numerare.

38 36 To close the model smply, consder two polar cases: 1. Labor s moble (Workers can move freely between manufacturng and nonmanufacturng.) Wage w n gven by productvty n nonmanufacturng and total ncome Y n s exogenous. Combng equatons get N N = β π X nand n= 1 wl wl = π [(1 β) wl + αβy ] n n n n= 1 that determnes manufacturng employment L. 1 β X = wl + αy β n n n n

39 2. Labor s mmoble The number of manufacturng workers n each country s fxed at L n. O Nonmanufacturng ncome s exogenous. Combng we get: N = β π X nand n= 1 wl Y n 1 β X = wl + αy β n n n n N O = π β + αβ + αβ n n n n= 1 wl [(1 ) wl Y ] whch determnes manufacturng wages w. The full general equlbrum s comprsed by: 37

40 38 p = N β 1 β θ γ T( d w p ) n = 1 1/ θ X X β 1 β π T n γ d w p = = p n θ N wl = π [(1 β ) w L + αβ Y ] n n n n = 1 (Manufacturng employment for labor moblty.) N O = π β + αβ + αβ n n n n= 1 wl [(1 ) wl Y ] (Manufacturng wages for mmoble case.)

41 39 Rch nteracton among prces n dfferent countres makes analytc soluton unattanable.

42 40 Estmates Estmates wth source effects (characterstcs of tradng partners and dstance between them). X X β 1 β π T n γ d w p = = p n From estmatng t, we can learn about states of technology and geographc barrers. Normalze by the mporter s home sales (dvde by X nn /X n ) θ X T w p = X T w p nn n n n ( 1 ) θβ θ β d θ

43 41 After a few other rearrangng steps, fnally get equaton to estmate: where: X 1 T w ln = ln + ln ln X T w ' 1 β X ln X ln X ln β X. 1 Defng S ln T θ ln w β ' ' θ d θ β nn n n Thnk of S as a measure of country s compettveness, ts state of technology adjusted for ts labor costs.

44 42 ' X ln θ ln d S S ' = + X nn n Left-hand sde s calculated: The same data on blateral trade of 19 OECD countres. (How many observatons? 19*19-19=361-19=342. Set b=0.21 (the average labor share n gross manufacturng producton n the sample). X n ncludes mports from all countres n the world snce prce of ntermedates reflect mports from all sources.

45 43 ' X ln θ ln d S S ' = + X nn n Rght-hand sde s calculated: S captured as the coeffcents on source-country dummes. Proxes for d (reflectng proxmty, language and treates). For all n we have: lnd = d k + b+ l+ e h + m n + δ

46 44 lnd = d k + b+ l+ e h + m n + δ where dummes are: d k (k=1,.6) s the effect of dstance between n and lyng n the k th nterval, b s the effect of n and sharng a border, l s the effect of n and sharng a language, e h (h=1,2) s the effect of n and both belongng to tradng area h (EFTA and EC), m n (n==1, 19) s an overall destnaton effect, δ s error term capturng geographc barrers arsng from all other factors.

47 45 Error term δ s decomposed to capture potental recprocty n geographc barrers: δ = δ + δ δ the country-par specfc component affects twoway trade, such that δ 1 δ affects one-way trade. δ =, 2 2 n

48 46 GLS estmaton of: ' ln X = S S θm θd θb θl θe + δ + δ ' X nn 2 1 n n k h Results: estmates of S ndcate Japan s the most compettve country n 1990, Belgum and Greece the least compettve. Dstance nhbts trade a lot. The EC and EFTA do not play a major role.

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50 48 Counterfactuals: Hghly stylzed model (suppressed heterogenety n geographc barrers across manufacturng goods) The Gans From Trade The Benefts of Foregn Technology Elmnatng Tarffs Trade dverson n the EC US Ulateral Tarff Elmnaton If US remove tarffs on ts own, everyone benefts except the USA. Bggest wnner s Canada f labor s moble. General Multlateral Tarff Elmnaton

51 Technology vs. Geography For smaller countres manufacturng shrnks as geographc barrers dmsh from ther autarky level. Producton shfts to larger countres where nputs are cheaper. As geographc barrers contnue to fall, however, the forces of technology take over and the fracton of the labor force n manufacturng grows, often exceedng ts autarky level. 49

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53 51 Concluson Rcardan model capturng the mportance of geographc barrers n curtalng trade flows. The model delvers equatons relatng blateral trade around the world to parameters of technology and geography.