Home Market E ect and its Extensive and Intensive Margins: The Role of Factor Endowments.

Transcription

1 Home Market E ect and ts Extensve and Intensve Margns: The Role of Factor Endowments. Arnab Nayak Auburn Unversty October 2011 Abstract Ths paper develops a factor proportons drven monopolstc competton model of trade to examne how home-market e ects (HME) vary across countres and ndustres. I extend the mult-sector framework of Hanson and Xang (AER 2004) to a two factor case where xed cost of startng a busness s more captal ntensve than the margnal cost. Countres wth d erent factor endowments have d erent extensve and ntensve margns of output growth n every sector due to factor prce d erences. Most mportantly, rch and poor countres experence HME n d erent sectors. For large captal abundant countres, the HME ncrease n ndustres exhbtng hgh trade cost and more d erentated products. Ths s drven by ncreasng proportons of extensve margns (new varetes) n these sectors. For large labor abundant countres, the HME rse n sectors wth hgh trade costs and less d erentated products. Ths s drven by ncreasng proportons of ntensve margns (quantty per varety) n these sectors. I con rm the predctons of the model from blateral exports data usng Hanson and Xang s d erence-n-d erence gravty spec caton. I nd strong evdence that rch and poor countres exhbt HME n mutually exclusve sectors and that these e ects are drven by d erent degrees of extensve and ntensve margns.(jel F1, R1) 1 Introducton Internatonal trade theory predcts that ndustres whch produce d erentated goods and are subject to ncreasng returns tend to concentrate n larger economes when trade s costly. Ths s known as the home market e ect (henceforth, HME; Krugman, 1980). HME occurs because rms Department of Economcs, Auburn Unversty, 0326 Haley Center, Auburn, Al E-mal: azn0018@auburn.edu. Ths paper s a part of my PhD dssertaton, whch was defended n July 2011 at Purdue Unversty. I am especally grateful to my advsor Davd Hummels for hs contnuous support and gudance. I am ndebted to Davd Hummels and Chong Xang for provdng ther data and estmaton codes. I am also grateful to Chong Xang for hs helpful comments and suggestons. I thank my dssertaton commttee members Thomas Hertel and Ralph Sebert for ther contnued support and suggestons. 1

2 gan from scale economes by producng n a sngle locaton and locatng n the larger economy mnmzes ther transportaton costs. Understandng the true nature of ndustry expanson across growng economes s mportant n plannng for growth and for related expansonary polces. Most of the lterature lookng at home market e ects uses a model wth a sngle factor (labor), a freely traded homogeneous product ndustry and a sngle monopolstcally compettve, ncreasng returns to scale manufacturng ndustry facng trade costs (see Krugman and Venables (1995) for example). Free trade n the homogeneous sector and ncomplete specalzaton ensure that wages are equal across countres. The sngle factor of producton mples that HME are dentcal and ndependent of the countres factor proportons. Hanson and Xang (2004) develop a model wth a contnuum of d erentated goods sectors wth ncreasng returns, but gnore d erences n factor proportons. In ther model, the larger country has a hgher wage and there s dentcal patterns of HME and ndustralzaton n every growng country. To the best of my knowledge there s no emprcal or theoretcal work on how factor endowment d erences can a ect the patterns of HME across countres. Davs and Wensten (1999 and 2003) use a framework that nests an ncreasng returns model featurng HME wth that of a Heckscher- Ohln model to assess the relatve mportance of these two theores n accountng for producton patterns and trade. They show that both HME and factor proportons play mportant roles n determnng OECD producton patterns. Ths paper advances our knowledge of HME by nvestgatng how the patterns of HME across countres are a ected by the factor endowment d erences across countres. To undertake ths analyss, ths paper makes two changes to the standard lterature. It extends the mult-sector framework of Hanson and Xang (2004) to a two factor case and also assumes that xed costs of startng busnesses are more captal-ntensve than varable costs. Recent emprcal research by Hummels and Klenow (2005) and Nayak (2011) show evdence respectvely from countres trade ows and ndustry data that output growth n captal and laborabundant countres are drven by d erent rates of expanson of the number of new rms n the market (the extensve margn) and the ncrease of output of exstng rms (the ntensve margns). The lterature usng a two factor monopolstc competton model followng Helpman and Krugman (1985) cannot match ths emprcal fact as t assumes a homothetc cost functon wth xed costs and margnal costs havng dentcal captal labor rato n all countres. Ths mples that rm szes are dentcal across all countres and t s only the growng number of rms that drves output 2

3 growth. The assumpton of homothetc cost s hghly stylzed as Helpman and Krugman (1985) note: "... t [the cost functon] mples that the relatve factor ntensty n actvtes that generate xed costs are the same as n actvtes that generate varable costs. Thus t does not allow for the exstence of nputs, lke buldngs, sghts, large scale equpment...whch generate manly xed costs and contrbute neglgbly to varable costs." The model n ths paper extends the Helpman and Krugman (1985) model of monopolstc competton by assumng that xed costs are more captal-ntensve than margnal costs. 1 In a related paper usng smlar assumptons, Nayak (2011) shows ths technology mples that captal-abundant countres have a comparatve advantage n startng new busnesses. Thus, captalabundant countres expand output prmarly through extensve margn growth. A panel data analyss on how rm szes and number of rms change wth captal accumulaton across countres provdes support for ths theoretcal conjecture. Nayak (2011) shows the mplcatons of ths technology assumpton on patterns of trade and producton when countres d er n relatve factor endowments. Smlar to Nayak (2011), ths paper shows that when xed costs are more captal-ntensve than margnal costs, countres wth d erent endowments face ex ante dentcal technologes but choose d erent technques of producton drven by factor prce d erences. Factor endowment d erences n the model also lead to d erences n the extensve and ntensve margns of output between countres and between d erent sectors wthn a country. Most mportantly, factor prce non-equalzaton leads to an nteracton of comparatve advantage forces wth scale e ects, predctng that HME s stronger n the more d erentated, hgh trade cost sectors n captal-abundant countres and t s stronger n less d erentated, hgh trade cost sectors n labor-abundant countres. These predctons, are based on a model that ntegrates the Heckscher-Ohln model wth the multple sector model by Hanson and Xang (2004). In the one-factor model of Hanson and Xang (HX henceforth), agglomeraton forces rase demand, generatng hgher factor prces n larger countres. Snce prces are a markup over costs n monopolstc compettve models, larger countres also have hgher product prces n all sectors. More d erentable sectors beng less senstve to 1 Smlar assumptons have been used by the footloose captal (FC) models n the new economc geography lterature, though all Heckscher-Ohln motves of trade are avoded n the FC model by ncorporatng a costlessly traded homogeneous good and dentcal factor proportons across countres. 3

4 hgh prces, larger countres have more HME n more d erentable sectors. Integratng Heckscher Ohln wth the HX framework mples that the captal-abundance of a country exerts a second force on the relatve wages of countres along wth agglomeraton forces. In ths two-factor case, large captal-abundant countres always have hgher wages than small labor-abundant countres as both captal-abundance and agglomeraton forces rase wages. So the HME for large captal-abundant countres s dentcal to HME n the HX case. However, when a large labor-abundant country has a lower wage than a small captal-abundant country, ts comparatve advantage s no longer n the more d erentated sectors. Snce labor-abundant countres also have a comparatve dsadvantage n startng new busnesses as xed costs are more captal-ntensve, agglomeraton forces are stronger n labor-abundant countres n less d erentated sectors wth hgh trade costs. Therefore, the Hanson and Xang model can be seen as a lmtng case of the model n ths paper when factor proportons are equal across large and small countres, and the two factors can be reduced to one. The emprcal ver caton of the HME reles on the d erence-n-d erence technques developed by Hanson and Xang (2004). The tests for HME are conducted separately for large captalabundant and large labor-abundant countres, searchng HME n d erent sectors n each case. Analyzng the HME n captal-abundant countres nvolves comparng blateral exports of large captal-abundant countres such as the US, Germany and Japan, relatve to those of smaller laborabundant countres lke Guatemala, Morocco and Peru. The large captal-abundant countres are expected to have greater HME n more d erentable, hgh trade cost sectors such as ron and steel and ceramcs, relatve to more homogeneous low trade cost sectors such as watches and rados. For HME n large labor-abundant countres, the d erence-n-d erence test nvolves comparng the exports of large labor-abundant countres, such as Chna and Inda, wth exports of smaller captal-abundant countres, lke Ireland and New Zealand. The large labor-abundant countres are expected to get more HME n less d erentable, hgh trade cost sectors such as textles and yarns, than n more d erentable low trade cost sectors such as electronc dagnostc apparatuses and precson machne parts. Fgure (1) summarzes ths separaton of countres and ndustres for testng HME n captal and labor-abundant countres nto two cases. Case I n Fgure (1) depcts the test for HME n captal-abundant countres. For labor-abundant countres, test strategy s represented n Fgure (1) as Case II. I test and con rm these predctons usng countres trade ows data followng Hanson and 4

5 Xang s methodology. Crucally, not only do the tests con rm that captal-abundant and laborabundant countres exhbt HME n the d erent ndustres as predcted by the model, but also when the ndustres are swtched, they show no evdence of HME n sectors n whch they are not predcted to have HME. Ths con rms the role played by factor endowments n determnng the pattern of ndustry agglomeraton as a country grows bgger. To complete the analyss, I look at how the extensve and ntensve margns d er for the labor and captal-abundant countres n the sectors n whch they experence HME. Hummels and Klenow (2005) develop a methodology for measurng an ndex of a country s extensve (number of varetes) and ntensve (quantty per varety) margns. Ther aggregate measures of countres extensve and ntensve margns gve us valuable nsght nto how rch and poor countres expand ther aggregate producton along these two margns. Extendng ther methodology to get estmates of sectoral extensve and ntensve margns across countres, I analyze how captal and labor-abundant countres expand sectoral output along the two margns. I show that n captal-abundant countres, home market e ects are drven by larger proportons of extensve margns (new varetes), whereas n labor-abundant countres, home market e ects are drven by ncreasng proportons of ntensve margns (quantty per varety). Ths con rms further the assumpton that t s easer to expand the number of rms due to the ease of access to captal n rcher countres and thereby ndustry agglomeraton s also more conducve n these countres n more d erentable sectors. The paper s organzed as follows. In secton 2, I develop a general equlbrum model whch solves for the trade equlbrum across two countres d erng n factor endowments. Secton 3 de- nes HME and shows how the HME vary across countres d erng n szes and factor endowments. Secton 4 tests all HME predctons separately for large labor-abundant and captal-abundant countres. Subsecton 4.1 develops the d erence-n-d erence methodology, whle sub-secton 4.2 detals the results for the test of HME n separate samples of captal and labor-abundant countres and varous robustness exercses. Sub-secton 4.3 tests the extensve and ntensve margn predctons of HME n labor and captal-abundant countres. Secton 5 concludes. 5

6 2 Two Factor Mult-Sector GE Model The model assumes the world conssts of a large and a small country and departs from the standard models of home market e ects both n ncludng a second factor and n ts assumpton of the cost functon. The large country could be ether relatvely captal-abundant or t could be relatvely labor-abundant. Dependng on these two cases, I show how the sectors n whch the large country experences HME s d erent from the sectors n whch a large labor-abundant country experences HME. I call the two countres North (N) and South (S, S s varables are denoted by *). N and S d er n sze and factor abundance (K=L > K /L ). I assume preferences and technologes are dentcal across N and S. Both labor and captal are allowed to move freely across the sectors n a gven country, but not across countres. Ths model s solved n two steps. Frst, I solve the partal equlbrum n each ndustry, focusng spec cally on the relatve rm szes, number of rms, the extent and share of ntra-ndustry trade, and how these varables depend on relatve factor prces and country szes. GE factor prces are solved subsequently, whch enables us to analyze how home market e ects vary n labor and captalabundant countres Representatve Consumer s problem There s a contnuum of monopolstcally compettve d erentated goods ndustres denoted by [0; 1]. Each ndustry faces a constant-elastcty-of-substtuton (CES) demand curve wth elastcty of substtuton. The number of ndustry varetes produced n N and S s gven by n and n. The representatve consumer n each country has a two-ter utlty functon over the contnuum of ndustres on the nterval [0; 1]. Each representatve consumer has a Cobb Douglas upper-ter utlty functon wth a constant fracton of ncome b beng spent on the varetes of goods from ndustry. Eqn (1) below denotes the upper-ter utlty functon where the aggregate shares b sums to one, U = Z 1 0 b ln Q()d; Z 1 0 b d = 1 (1) In (2), Q() s the lower-ter CES sub-utlty functon denotng the composte consumpton from 6

7 all varetes n ndustry from N and S, 0 Q () n +n X j= q j A : (2) The quantty of each varety j consumed s denoted by q j. In equlbrum all rms are dentcal and each varety s produced by only one monopolstcally compettve rm. Therefore, I drop the ndex j for each ndvdual rm n an ndustry Equlbrum n an Industry From the utlty functon (equatons 1 and 2), the demand facng each North country rm s the sum of the domestc and foregn demands, q D = b p G 1 {z } Home Demand + 1 G 1 {z } Demand from S 1 A ; (3) where s ceberg trade cost n ndustry between N and S and the terms G and G are respectvely the ndustry prce ndexes n the N and S and are de ned as, G 1 = n p 1 + n p 1 1 ; and G 1 = n p 1 + n p 1 1 : (4) Representatve Frm Problem and Technology: There are two factors of producton, labor and xed captal. F unts of captal s used as nvestment n xed producton assets per rm n an ndustry and c s the varable labor nput requred to make each unt of output n sector. The rental rate for captal s r and the wage s w. Ths mples the cost functon, 2 C = c wq {z } + rf {z} : (5) Varable Costs Fxed Costs 2 Non-homothetcty of the two factor cost functon of the type assumed here has also been used n the new economc geography lterature. The footloose captal (FC) model by Martn and Rogers (1995) assumes a technology n the ncreasng returns sector dentcal to the one assumed here. Baldwn and Okubo (2006) extend the (FC) model to nclude rm heterogenety assumng that xed costs comprse captal only and varable producton costs and xed export costs use only labor. However, these models assume factor prce equalzaton due to the presence of a costlessly traded homogeneous product ndustry and free captal moblty. Heckscher-Ohln motves for trade s avoded by assumng that countres have same factor proportons, but d ers only n sze. Flam and Helpman (1987) also assumes a non homothetc cost functon n a Dxt Stgltz model. 7

8 For analytcal tractablty, I have assumed the smplest cost functon that makes the xed costs more captal-ntensve and the varable costs labor-ntensve. The resultng d erences wth the standard homothetc cost functon assumpton on equlbrum varables of the model, ncludng the predctons on HME, are hghlghted n appendx (A.1). Note also that none of the HME results derved below depend spec cally on ths smpl ed cost assumpton and I show n the appendx (A.2) that all the HME results derved below contnue to hold even when xed and varable costs nclude both factors, whle mantanng that xed costs are more captal-ntensve than margnal costs. 3 Gven ths cost functon, a representatve rm sets ts prce to maxmze pro ts, Max = p q c wq rf : (6) As n the Dxt-Stgltz (1977) model of monopolstc competton, each dentcal rm takes the ndustry prce ndex G as gven whle maxmzng (6) subject to the demand (3). The optmzed prce s a constant mark-up over margnal costs, p = n a country. 1 c w and re ects closely the cost of labor Zero Pro ts and Free Entry: Replacng the optmal prce from the rst order condton, the operatng pro t, whch s the total revenue mnus the varable costs of producton, s, (p q c wq ) = p q : (7) Free entry and ext mples that pro ts (6) for all rms n the ndustry must be zero n equlbrum. Then from (6) and (7) the quantty suppled by each producer s, q s = ( 1) F c r w : (8) As expected, rm scale n (8) ncreases n xed costs and falls n varable costs. 3 It s only for the dervaton of the general equlbrum condtons that the captal-abundant countres have hgher relatve wages, that we use the smpl ed cost structure to make the algebra easer. 8

9 Producton Technques: The captal ntensty of a rm (or ts technque) s de ned as the rato of the amount of captal used by a rm per unt of labor t uses,.e. quantty suppled from (8) we get rm technque n ndustry as, F c q s : Substtutng the optmal K L = w ( 1) r : (9) Because xed and varable cost components d er n factor ntenstes, optmal technque depends on rm scale, and rm scale depends on factor prces through equaton (8). Equlbrum Number of Frms and Industry Output Share of N and S: Quantty suppled (8) by each rm must be equal to quantty demanded (3) from each rm for markets to clear. Equatng free entry (zero pro t) level of output for a rm, q s, to ts aggregate demand, 4 p q s = b 1 p G + b p 1 : (10) G Replacng the equlbrum quantty suppled by each rm n N and S from equaton (8) nto equaton (10) and dvdng gves, p q s p qs = er = 1 1 ep e 1 + G G 1 1 G G 1 + G 1 e 1 : (11) G 1 e where a tlde ( ~ ), represents the rato of a N s varable relatve to ts Southern counterpart. 1 Smplfyng the value of G G usng (4) yelds, G G 1 = en 1 ep en ep : (12) 1 Solvng (11) and (12) smultaneously we get n n as, n n = en = ep 1 er ( e ) 1 (1 + e ) ep 1 ( e ) ep 2 2 er 1 (1 + e ) : (13) 4 Ths open economy soluton of number of rms and ndustry shares follows the analyss by Romals (2004) of the equlbrum wthout factor prce equalzaton under the changed cost functon. 9

10 Usng (13) we can derve condtons when ntra-ndustry trade exsts n ndustry. We can also nd N s share of producton n that ndustry. Notaton s smpl ed by de nng the expresson ep 1 er as e. Frst, usng (13), we can get the condton for n = 0,5 e = ep 1 er = 1 ( e! + 1) e 2 2 : (14) + 1 Ths happens when North s the sole producer n the sector and the aggregate world expendture n the sector b ( + ) goes fully to North s producers. Equaton (14) shows that f the elastcty of substtuton ; N s relatve prce ep (or relatve wage ew) and relatve rental rate er are not too hgh, then North could become the sole producer n the ndustry. Smlarly n = 0 and S captures the entre market f, e = ep 1 er = e ( e + 1).e., f N s relatve prce s hgh enough, ts rental rate s hgh enough and the ndustry s less d erentable (.e. s hgh), then S becomes the sole producer n an ndustry. Therefore when < < ; both North and South produce n a sector and we have ntra-ndustry trade n the sector. Assumng ntra-ndustry trade exsts between N and S; the next subsecton derves the share of each country n a sector. The appendx (A.3) further proves that < when > 1 and > 1: (15) North Frms Share of World Revenues : The North s share n total world output n any ndustry s v = n p q s (n p q s+n p qs ) ; where each N rm s revenue s p q and n s the total number of rms n N: Dvdng the numerator and denomnator by n p qs equlbrum quanttes suppled by each N and S rm usng (8), eq s world producton n an ndustry s, and replacng the rato of the = er ew, North s share of total v = en fp eq s (1 + enf p eq s ) = en er (1 + en er) : (16) Substtutng the value of fn from (13), usng the condtons for ncomplete specalzaton from above, denotng fp 1 er = e and + = W; where W s the aggregate world ncome, North s 5 Ths s derved from (13) so that n n! 1. 10

11 share of world revenues can be represented as, 8 >< v = >: 1 f e " # e 1 ( +1) f e 2 ; e + 1 f W f e : (17) Therefore, N s share of ndustry producton s a functon of ts relatve sze, trade costs and factor prces. Gven the equlbrum relatve wage and rental rate ~w and ~r; one can determne a country s share of world producton across ndustres as the relatve country sze changes and the substtuton elastcty ( ) of the ndustry () changes. In general equlbrum N s relatve wage must be greater than ts relatve rental rate ( ~w > ~r) for market clearance. I prove ths next and use (17) to derve how N s ndustry share of world producton vares across sectors as N s relatve sze changes and the sector s product d erentablty changes Equlbrum Factor Prces under Postve Trade Cost: The factor market clearance condtons n ths model for N and S are, Z n F d = K and Z n c q d = L (18) [0;1] Z [0;1] n F d = K ; and Z [0;1] [0;1] n c q s d = L : (19) When trade s costly, the general equlbrum of ths model generates the followng results for factor prces n the two countres: Lemma 1 When trade s costly, factor markets are cleared f and only f the relatvely captalabundant N has a hgher wage rental rato,.e. ~w > ~r. Proof. See the appendx (A.4). The result derves from the fact that factor prce equalzaton gves dentcal technques of producton across N and S, so the larger country demands proportonately larger quanttes of both factors under costly trade. So factor prce equalzaton cannot clear factor markets n both 11

12 countres and the only way the factor markets can clear s when the abundant factor s relatvely cheaper n both countres n equlbrum. 3 The Home Market E ect To test for a country s home market e ects n an ndustry, we need to compare the relatve ndustry szes to the relatve sze of the country. The relatve sze of the ndustry n a country s descrbed by the country s share of the product n the world market v n equaton (17). As seen from ths equaton, N s share n an ndustry depends on ts sze, the trade costs n the ndustry and the relatve factor prces. Controllng for trade costs and other forces of comparatve advantage; f a country s output share n a sector s larger than ts share of world GDP, the country s de ned to exhbt HME n the sector. Usng v = from (16), N s sad to experence HME n a sector f v > f (1 v ) > + : 6 n p q b ( + );.e. N s share of total world output n the sector + and S wll have HME n the sector Dependng on whether N or S s the larger country, we can separate the condtons for the larger country s havng HME as two dstnct cases. The left hand panel A of Fgure (1) class es the possble szes and per capta captal endowments of countres. It dvdes countres nto large and small (along the axs) and captal and labor-abundant (along the X axs). Panel B of the same gure class es ndustres by product d erentablty and by the degree of trade costs faced. n the followng analyss I show that large captal-abundant countres experence hgher HME relatve to small, labor-abundant countres n more d erentable, hgh trade cost sectors. Large labor-abundant countres experence hgher HME than small captal-abundant countres n hgh trade cost, less d erentable sectors. These two cases are depcted n panels A and B of Fgure (1) as Case I and Case II respectvely. 3.1 Case I : HME for K-abundant N Notng that N s share of world exports n ndustry s v = the sum of revenues from all sectors, n p q b ( + ); ts ncome can be wrtten as 6 Ths de nton also matches the de nton of revealed comparatve advantage (Balassa 1965) of a country n a gven sector. Here, however, the test of HME wll control for all endowments drven comparatve advantages to separate out only the role of a larger market drawng the ndustres. 12

13 Wrtng 1 (20) as, = Z 1 0 n p q d = Z 1 0 v b ( + )d: (20) = x to smplfy notaton, we can substtute the value for v from (17) to rewrte Z 1 0 b g d = 0; where, g = (x ~ 1) ~ : (21) (x ~ ) The appendx A.5 shows the steps n dervng (21) from (20). Gven and ; a soluton to above the equaton always exsts and we can solve for the equlbrum ~ and derve the followng result. Lemma 2 When N s the larger country,.e. > ; equaton (21) provdes a unque soluton for ~ ; such that 1 < ~ < mn [x ] : Proof. See appendx (A.6). Snce ~ = ~w ~r, and from Lemma (1) and Lemma (2) we know that ~w > ~r and ~ > 1, wages must be hgher n the larger captal-abundant N;.e. ~w > 1: Ths s the standard result that large captal-abundant countres have hgher absolute wages than small labor-abundant countres, snce both ts larger sze and ts captal-abundance pushes wages up n N. We can now derve condtons under whch the larger N wll face HME. When N s the larger country than S; N exhbts HME n the sector f, v > condton can be wrtten as, + : Ths [v ( + ) ] > 0: (22) Usng (20) and (21), the condton n (22) holds when g > 0 (see appendx (A.5)). Gven ~ = ~w ~r and x = 1 ; the dstrbuton of g wll depend on the parameters ; and b, and t s not possble to solve for analytcal condtons about the dstrbuton of g wthout de nng these dstrbutons. However, we can compare the values of g across ndustres and determne condtons under whch ndustres located n the captal-abundant N s more lkely to exhbt HME. Note that 13

14 we can rewrte the condton g > 0 n the followng form, ~w ~r g = (x ~w ~r 1) (x ~w > 0 (23) ~r) h x, ~w 1 > [x ~w ~r 1] (24) ~r, > ~w 2 ~r 2 + ~w ~r x ( ): (25) Gven that N s the larger country,.e. > and from Lemma (1) and (2) that the larger N has a hgher relatve and absolute wage,.e. ~w > ~r and ~w > 1; we can see that the left hand sde of (25) rses relatve to the rght hand sde as we move to lower and hgher trade cost x ndustres. Therefore from (25) we can say that as we move to more d erentable sectors, wth lower ; and hgher trade costs x ; we should see the larger N exhbtng ncreasng degrees of HME n that ndustry. The followng proposton summarzes ths. Proposton 3 When N s larger than S; N wll see ncreasng Home Market E ects n ndustres whch are more d erentated (lower ) and have hgher trade costs (x ). These condtons for HME n a large captal-abundant country from proposton (3) are summarzed n Fgure (1) as Case I. It shows that countres whch are large and captal-abundant (the upper rght quadrant of P anel-a) would show more agglomeraton e ects than smaller laborabundant countres (the lower left quadrant of P anel-a) n sectors whch are more d erentable and face hgh trade costs (the upper left quadrant of P anel-b) than n sectors whch are less d erentable and facng low trade costs (the lower rght quadrant of P anel-b). Ths predcton for HME n large captal-abundant countres s dentcal to the Hanson and Xang s (2004) predcton for HME n all large countres when factor proporton d erences are absent. As Case II below shows, ncludng factor proporton d erences however, changes the HME across N and S. Therefore, the current model nests the HX predctons as a specal case when factor proporton are equal across countres d erng only n sze. 14

15 3.2 Case II : HME for L-abundant S The S s share of world exports n ndustry s v = (1 v ): Its ncome can be wrtten as the sum of revenues from all sectors, Agan wrtng 1 = Z 1 0 n p q d =, W = W Z 1 0 Z 1 0 v b ( + )d: (26) v b ( + )d: (27) as x, we can see that ths equlbrum condton s dentcal to the N s equlbrum as expected n a two-country world and therefore we can wrte S s equlbrum dentcally to (21) as, Z 1 0 b g d = 0; where, g = (x ~ 1) ~ : (28) (x ~ ) Gven and ; a soluton to above the condton always exsts. However, snce we are nterested n learnng about HME n the S; we now need to assume that the S s the bgger country and solve for the equlbrum ~ that clears all markets. Solvng for the equlbrum ~ n ths case gves the followng result. Lemma 4 When S s the larger country,.e. > ; equaton (28) provdes a unque soluton for ~ ; such that max x 1 < ~ < 1: Proof. See appendx (A.7). From Lemma (1) we know that ~w > ~r. Combnng wth Lemma (4) that ~ = ~w ~r < 1 mples that relatve wage rental rato s hgher n the smaller captal-abundant N;.e. ~w=~r > 1, but absolute wages need not necessarly be hgher. Ths result arses because now the e ect of sze on wages partally dampens the smaller N s wages relatve to the larger S. Absolute wages could stll be hgher n the N,.e. ~w > 1; f the N s relatve cost of captal ~r s less than one and the condton ~w < (1=~r) 1= s sats ed. The de nton of the HME for the S s v > +, so when S s larger, to reveal HME n a sector t should have a greater share of the ndustry output than ts GDP share. In ths twocountry world, ths s dentcal to N s share of the ndustry s output beng less than ts GDP share, 15

16 v < = +. Ths s sats ed when g < 0. Therefore from (28) g < 0 mples, > ~w 2 ~r 2 + x ~w : (29) ~r Assumng that the smaller captal-abundant country s also rcher, so that ( ~w > 1), the RHS of (29) decreases as ncreases and the trade cost x n a sector rses. Therefore when comparng a large L-abundant country wth a smaller but rcher captal-abundant country, the large S wll experence ncreasng degrees of HME n more homogeneous sectors wth rsng and rsng trade costs x. We can summarze ths n the followng proposton. Proposton 5 When S s larger than N; S wll experence hgher degrees of home market e ects n ndustres whch are less d erentated (hgher ) and have hgh trade costs(x ), as long as N has hgher absolute wages. The condtons for HME for a labor-abundant country are summarzed n Fgure (1) as Case II. It shows that countres whch are large and labor-abundant (the upper left quadrant of P anel- A) would show more agglomeraton e ects than smaller, but rcher captal-abundant countres (the lower left quadrant of P anel-a) 7 n sectors whch are less d erentable and face hgh trade costs (the upper rght quadrant of P anel-b) than n sectors whch are more d erentable and face low trade costs (the lower left quadrant of P anel-b). When mplementng ths n the emprcal testng of HME for L-abundant countres, care s taken to choose the sample n such a way as to satsfy the clause that absolute wage s hgher n the smaller captal-abundant countres. 4 Emprcs The theory descrbes two dstnct cases for dentfyng HME n captal and labor-abundant countres. These two cases are summarzed n Fgure (1) as Case I and Case II. Large captal-abundant countres expect to see ncreasng HME relatve to small labor-abundant countres n more d erentable sectors wth hgh trade costs. Large labor-abundant countres expect to see ncreasng HME relatve to small captal-abundant countres n sectors whch are decreasngly d erentable and 7 P anel-a of gure (1) depcts the captal abundance but not the absolute wage d erental. The emprcal secton ncorporates the wage condton explctly. 16

17 have ncreasng trade costs. I follow Hanson and Xang s [HX] d erence-n-d erence strategy for mplementng the theoretcal predctons from the two-country world to the emprcal case where there are multple countres. I rst descrbe bre y the HX emprcal methodology of usng blateral trade ows to measure ndustry producton shares across countres and usng these measures to test HME. 4.1 D erence-n-d erence Technque for Identfyng HME from Blateral Trade Flows For country j; the total exports n ndustry m to mporter k s gven as, X mjk = n mj b m k p 1 m 1 mjk Gm mk ; where b m k s mporter k s total expendture n ndustry m and G mk s the ndustry m prce ndex n mportng country k, whch s a constant for all exporters to k. Therefore f we dvde the exports of two countres, j and h, to the common mporter k, we lter out these mporter xed e ects and only the exportng country varates are left behnd, X mjk = n mjp 1 X mhk n mh p 1 m mjk m mhk = n mj n mh wj : 1 m jk : w h hk The exporter j spec c term p mjk denotes the delvery prce of ndustry m products from country j to k; p mjk = w j : jk ; where w j s the margnal cost of producton n j. jk s the ceberg transportaton cost of delverng each unt from j to country k: Followng HX, I de ne ths ceberg transportaton cost as jk = dst m jk, where dst jk ncludes both dstance e ects and e ects of common border and language between j and k. Therefore, we can wrte the rst d erenced mport shares of countres j and h as, X mjk = n mjp 1 X mhk n mh p 1 m mjk m mhk = n 1 mj wmj n mh w mh m dstjk dst hk m(1 m) : (30) Fnally, we do not have a closed form soluton for the exact number of producers n ndustry m n country j; n mj, but we know from (13) that the rato n mj n mh depends on the relatve szes of both countres, the relatve product and factor prces between the countres, the trade cost n an ndustry, 17

18 the substtuton elastcty, and prce ndexes of both countres, whch n turn depend on the relatve number of rms n the two countres. Therefore we cannot predct how varatons n j = h a ect n mj n mh n a closed functonal form. But from propostons 3 and 5 we can tell for whch ndustres a large captal or labor-abundant country should face ncreasng HME and n whch ndustres they should face decreasng amounts of HME. The set of ndustres n whch a country faces ncreasng HME s termed treatment ndustres and the opposte set of ndustres n whch a country faces least HME s termed control ndustres. The d erence-n-d erence equaton from Hanson and Xang (2004) compares the rst d erence equaton from (30) wth the same two countres relatve exports to the same mporter k across treatment and control ndustres, X mjk =X mhk X ojk =X ohk = n mj=n mh n oj =n oh (w mj =w mh ) m (w oj =w oh ) o dstjk dst hk m(1 m) o(1 o) (31) In ths equaton we want to test whether, controllng for d erences n the two ndustres factor costs and trade costs, ncreases n the relatve sze of exporter j compared to exporter h rases j s share n k s mports more than proportonally n the treatment sectors (m) than the control sectors (o). In logarthmc form, Xmjk =X mhk dstjk ln = + f ( j = h ) + ( j h ) + ln + " mojhk ; (32) X ojk =X ohk dst hk the functon f ( j = h ) captures a lnear polynomal functon of the countres relatve szes j = h. j and h are vectors of factor endowments that a ect comparatve advantage through the relatve factor prce terms n (w mj =w mh ) and n mj =n mh n (31) and nally the dst jk dst hk term ncludes factors of geographc proxmty between each of the two exporters and the mporter k. Therefore, comparng exports n the rght combnaton of treatment (m) and control (o) ndustres for the rght combnaton of large and small countres, we can nd out f HME s present. Departure from Hanson and Xang (2004): Hanson and Xang (2004) use equaton (32) to test f larger countres have HME n treatment ndustres. However, n ther sngle factor model, absolute wage d erences are drven solely by sze and thereby all large countres experence HME n the same ndustres. Ths s exactly where the present model departs from HX s emprcal strategy. Due to factor proporton d erences n the current model, HME works n d erent ndustres for 18

19 countres that d er n factor abundance. In fact, n the lmtng case that factor proportons are dentcal for countres d erng n sze, the present model gves dentcal results for HME as n Hanson and Xang (2004). For the emprcal analyss, I wll separately use the double d erence technque from equaton (32) for large captal and labor-abundant countres and check f ndeed the predctons from propostons 3 and 5 hold n blateral exports data. Most mportantly, the tests for HME are also conducted by swappng the ndustres n whch the large captal and labor-abundant countres are predcted to have HME. If the theoretcal analyss s correct, we should nd no systematc evdence of HME when such swtched treatment and control ndustres are used. 4.2 Testng HME for K-abundant (Case I) and L-abundant (Case II) Countres The strategy for choosng the countres and ndustry pars for testng HME n captal and laborabundant countres s depcted respectvely n Fgure (1) as Case I and Case II. From proposton 3, large captal-abundant countres should experence ncreasng HME relatve to small laborabundant countres n more d erentated (low ) and hgh trade cost (x ) ndustres. From proposton 5, large labor-abundant countres should experence ncreasng HME relatve to smaller captal-abundant countres havng hgher absolute wages n less d erentated (hgh ) and hgh trade cost x ndustres. For the rst d erencng of Case I, large captal-abundant countres (upper rght quadrant of panel A n Fgure (1)) exports are compared wth exports from small labor-abundant countres (lower left quadrant of panel A n Fgure (1)). The next step s to choose the treatment and control ndustres to compare n the second d erence as explaned above for Case I. Panel B of Fgure (1) depcts the treatment (low and hgh trade cost x ) and control (hgh and low trade cost x ) ndustry for Case I: Sold arrows on Panel A and B of Fgure (1) show the choce of countres and treatment and control ndustres respectvely. For testng HME n large labor-abundant countres ( Case II ) I choose countres n the upper left quadrant of the left panel A n Fgure (1) and d erence these countres exports from exports of the smaller captal-abundant countres n the lower rght quadrant of panel A n the Fgure (1). For the second d erencng we need to compare the hgh and hgh trade cost (x ) treatment ndustres to low and low trade costs x control ndustres. Panel B of Fgure (1) depcts the 19

20 treatment and control ndustres respectvely on the upper rght quadrant of the and x plot and control ndustres on the lower left quadrant. The choce of countres and ndustres for Case II s ndcated by the dashed arrows on Panels A and B n the Fgure. Data: The data for the estmaton of (32) comes from the World Trade Flows database (Feenstra et al. 1997) for the year Data on per capta factor endowments and ncome s from the World Bank s WDI and the data on captal stock s generated usng the gross xed captal formaton seres from the WDI usng a perpetual nventory method. Dstances between countres and other geographc characterstcs are obtaned from the CEPII geography database. For a sample of large captal-abundant countres I select the 20 largest countres havng per capta captal stock above 75 percent of US per capta captal stock. 9 For the small labor-abundant countres I choose countres whch have less than 25th percentle of the US per capta captal stock. The lst of sample countres s tabulated n table (1). For a sample of the large L-abundant countres I select the 10 bggest countres havng per capta captal stock below the 25 percentle of US per capta captal stock. From proposton 5, the small captal-abundant countres must also have hgher absolute wages than all the L-abundant countres. I choose countres whch have per capta GDP hgher than all L-abundant countres and all have more than 50 percent of US per capta captal stock. The lst of sample countres s tabulated n table (1). Fgure (2) plots estmates of elastctes of substtuton and trade costs for d erent 3 dgt SITC ndustres and shows the selecton of treatment and control ndustres for testng HME n captal and labor-abundant countres based on the dstrbuton of ndustry freght rates and substtuton elastctes. Followng Hanson and Xang (2004), I use the Hummels (1999) estmates for elastctes of substtuton at the SITC 3 dgt level. For trade costs measures I also use Hanson and Xang s methodology of estmatng ndustres dstance elastcty of trade costs usng the transport charges of US mports from d erent countres and usng these measures to get a measure of freght rates for d erent ndustres. The rst two columns of tables (2) and (3) lsts respectvely the treatment ndustres and the correspondng control ndustres n case I and the last two columns lsts respectvely the treatment ndustres and the correspondng control ndustres n Case II. 8 Data s chosen for the year 1994 as t s the same data that Hanson and Xang (2004) used. 9 The samplng was also carred out usng per capta GDP to proxy for captal abundance. TThe results are unaltered f per capta GDP s used nstead of per capta captal stocks. 20

21 The sample of mporters are the bggest 21 mporters n the world. Whle ths sample s small, selectng the largest mporters nevertheless helps n avodng a lot of mssng observatons. Total mports n these 21 bggest mporters comprse more than 80 percent of world mports n the sample year. Estmaton Issues: Due to the level of dsaggregaton of the trade data (SITC 3 dgt), a large percentage of all possble trade ows turn out to be zero. Followng Hanson and Xang (2005), I ll out these zeros wth a one. Ths could lead to based estmates, however. Therefore, I also report the results of a truncated OLS estmaton usng just the rst stage d erencng and addng a dummy for the treatment ndustry, followng Pham, Mtra and Lovely (2009). I always keep the larger country on the numerator whle estmatng (32) to avod the knd of bas Pham, Mtra and Lovely (2009) talk about f the sample s not ordered thus. Results: The left panel ttled Case I of table (4) shows the results for the test of HME n captalabundant countres when I pool all the SITC 3 dgt sector combnatons of treatment and control ndustres and sample countres usng the d erence-n-d erence technques to estmate equaton (32). Followng Hanson and Xang (2004), I estmate equaton (32) wth d erent functonal forms for the relatve GDP of the two exporters. The f ( j = h ) measure s substtuted by lnear and polynomal functons of the d erence n the GDP across the two exporters and each of the columns (1) through (3) lsts results of usng d erent measures of f ( j = h ). The estmaton ncludes a number of controls for country endowments that could drve comparatve advantage across sectors and geographc factors, whch ncludes the dstances between the captals of the two exporters and common mporter and bnary varables for common border and common language wth the mporter. 10 The results show that s postve and sgn cant n all spec catons of the relatve GDP functon f ( j = h ). So, ndeed, captal-abundant large countres get a larger share of world mports n more d erentable sectors whch have hgh trade costs relatve to the less d erentable low trade cost control sectors. 10 The estmaton results reported do not show the controllng for human captal d erences. The results of the estmaton reman robust and sgn cant when ncludng human captal d erences n the test of HME for captal abundant countres. However, due to scarcty of educaton data, the HME estmaton for labor abundant countres could not be undertaken. 21

22 The rght panel ttled Case II of table (4) shows the results for testng HME (equaton 32) n labor-abundant countres usng the same set of controls and ndependent varables as n case I, but a d erent set of treatment and control ndustres as explaned above. The results n the last three columns of table (4) also show a postve and sgn cant e ect of rsng sze for large labor-abundant countres on ther export shares n treatment ndustres relatve to control ndustres n all spec catons of the relatve GDP functon f ( j = h ). So, laborabundant countres get a larger share of world mports n less d erentable, hgh trade costs sectors as predcted by the theory. Thus the separate estmatons of HME n case I and case II show that both N and S exhbt HME. As predcted by theory, they exhbt HME n d erent sectors, drven by ther correspondng strengths n product d erentaton and varable producton costs. Snce N has more xed captal whch s requred to make new varetes, sectors that support a larger set of varetes tend to agglomerate n N. S countres lke Chna and Inda also see HME or agglomeraton, but t s not n sectors whch are the most d erentable, but rather n sectors that face larger trade costs and that requre more labor-ntensve producton processes. Changng Treatment and Control Industres: The two tests predcted from theory do show HME for K and L-abundant countres n d erent sectors. But these tests do not con rm that these countres do not experence HME n sectors other than those predcted from theory. To con rm that labor and captal-abundant countres ndeed experence HME n dstnct sectors, I also conduct the tests for HME swtchng the ndustres n whch the large captal and labor-abundant countres are predcted to have HME. If the theoretcal analyss s correct, we should nd no systematc evdence of HME when such swtched treatment and control ndustres are used. Accordngly, I test whether large captal-abundant countres have HME n sectors n whch theory predcts that larger labor-abundant countres should exhbt HME. I call ths Case IA, where I take the theory predcted treatment (hgh and hgh trade cost) and control (low and low trade costs) ndustres for the large labor-countres and use these to test HME for large captal-abundant countres. Case IIA tests just the reverse case: whether the larger labor-abundant countres have HME n the sectors n whch theory predcts the larger captal-abundant countres should exhbt HME (see Case IA and Case IIA n Fgure 3). 22

23 The results of Case IA and Case IIA are represented n table (5). The left column of table (5) shows a postve but nsgn cant coe cent for Case IA; whereas the coe cent for for labor-abundant countres s negatve and sgn cant. That s, large captal-abundant countres have larger shares than smaller labor-abundant countres n sectors where labor-abundant countres are predcted to have HME, but the coe cent s very small and nsgn cant. Large labor-abundant countres on the other hand have a negatve HME n sectors where large captal-abundant countres exhbt HME. Therefore, tests for Case IA and IIA con rm that large K and L-abundant countres do not experence HME n sectors other than the ones n whch the theory predcts that they should experence HME. Takng Zeros nto Account: The d erence-n-d erence estmaton makes t d cult to take care of the zero trade ows, as normal Tobt estmaton cannot be used. To overcome ths problem, I use a dummy varable, sngle d erence methodology poolng both treatment and control ndustres as suggested by Pham, Mtra and Lovely (2009). In the followng regresson, the rst d erence lters out the mporter xed e ects and the d erence n the levels of HME, f any, s captured by ncludng a dummy varable for the treatment ndustry (T reat dummy ). ln (X mjk =X mhk ) = + 1 f ( j = h )+ 2 f ( j = h ) :T reat dummy + ( j dstjk h )+ln +" mjhk: : dst hk I estmate coe cents by allowng truncaton of trade ows. As seen from table (6), the coe cent on the treatment dummy s postve and sgn cant for both K and L-abundant countres. So both results from case I and case II from table (4) contnue to hold even when we spec cally adjust for truncaton of trade ows at zero Extensve and Intensve Margns of HME Prevous work on two factor models wth ncreasng returns to scale n manufacturng mostly assume a homothetc cost functon across xed and margnal costs and thereby, even when factor prces are unequal across countres, rm szes are dentcal. 12 So any ncrease n the world share 11 In analyss not reported here, I also repeat the d erence-n-d erence estmatons for both captal and labor abundant countres droppng all zeros. These estmatons also gve postve and sgn cant coe cents on the HME coe cent n all the spec catons reported n table (4). 12 See appendx (A.1) for a comparson of the current model wth the homothetc cost model. 23

24 of an ndustry s output must be due to the expanson of the number of rms n that ndustry (.e. only the extensve margn can cause HME). In the current model, however, rm szes vary by country due to varaton n factor prce ratos, q s = ( 1) F r c w : The precedng analyss dent es ndustres n whch large captal and labor-abundant countres have ncreasng degrees of HME. Here I analyze the roles that extensve and ntensve margns play n sectors where large labor and captal-abundant countres face HME. We know from (13) that the rato of extensve margns across N and S n a sector ( n n ) depends on the relatve szes n both countres, the relatve product and factor prces between the countres, the trade cost n an ndustry, the substtuton elastcty, and also the prce ndexes of both countres. Therefore we cannot predct how varatons n = a ect n n n a closed functonal form. But we can agan use the d erence-n-d erence technque to analyze how the relatve extensve margns change between a large and a small country, as the large country experences ncreasng HME n some sectors relatve to other sectors where t faces least HME. Gven that the shares of N and S respectvely n an ndustry s v = n p q b ( + ), the relatve shares of N and S can be wrtten as, ~v = n p q n p q n p q b ( + ) and v = = ~n ~p ~q and substtutng the relatve quanttes and prces we get ~v = ~n ~r. Takng a second d erence for the rato of the relatve shares of N and S across two ndustres, we can wrte, ~v m ~v o = ~n m ~n o : (33) That s, we see that when ether a large N or a large S country experences ncreasng HME n some ndustres m relatve to ndustres o, the HME s drven by the relatve extensve margn growth n that ndustry for the HME experencng country. Therefore the coe cent for relatve GDP should closely match the growth of extensve margns due to HME n the d erence-n-d erence exports equaton (32) we estmated earler. Usng estmates of sectoral extensve margns, we can further nvestgate whether the extensve margns of treatment ndustres grows relatve to the extensve margns of control ndustres as a large country experences more and more HME n ts treatment sectors. Extendng the methodology developed by Hummels and Klenow (2005) for measurng the extensve and ntensve margns of aggregate exports to a sectoral measure of extensve and 24

25 ntensve margns, we can estmate the followng d erence-n-d erence equaton, 13 EMmjk =EM mhk dstjk ln = + f ( j = h ) + ( j h ) + ln + " mojhk. (34) EM ojk =EM ohk dst hk Ths s dentcal to the d erence-n-d erence HME estmaton wth a measure of relatve GDPs, geographc and comparatve advantage characterstcs as dependent varables, but has d erences across relatve extensve margns across countres j and h n ther treatment and control ndustres respectvely. The results of estmatng ths equaton are summarzed n table (7). The results show that the relatve growth of HME n the treatment ndustres to control ndustres (ndustres n whch we expect least HME for a country) s ndeed drven by an ncrease n the number of rms. Even though the coe cent for the growth of relatve EM n the treatment ndustres relatve to control ndustres n labor-abundant countres s twce that of the same measure for captal-abundant countres, the measure also nvolves the relatve EM n the control ndustres and therefore does not represent whether the extensve margn plays a greater or smaller role n captal or laborabundant countres. To get a better measure of the splt of the HME n captal and labor-abundant countres, I summarze the average proportons of extensve and ntensve margns n the treatment ndustres for the large captal and labor-abundant countres n the sample n table (8). 80 percent of the growth of exports n the treatment ndustres for the captal-abundant countres s drven by the extensve margns, whereas the extensve margn drves 53 percent of the growth of the treatment ndustres n the labor-abundant countres. Therefore, extensve margns drve the HME n captal-abundant countres by a much hgher degree. Ths s because of ther abundance of captal resources whch s requred to start new busnesses n the more d erentated product ndustres. Labor-abundant countres have a comparatve advantage n makng less d erentated products, and experence HME drven by hgher ntensve margns n ther treatment sectors. 13 The estmaton of the sectoral extensve and ntensve margns from sector trade ows extendng the Hummels and Klenow (2005) method s descrbed n appendx (A.8). 25

26 5 Concluson When there are ncreasng returns to scale and trade s costly, rms locate n larger countres. Ths s known as the home market e ect. Most of the lterature lookng at home market e ects uses a sngle factor model, assumng cost functons are dentcal and homothetc across countres. These assumptons mply that rch and poor countres have HME n dentcal sectors. In ths paper I take a closer look at these assumptons as well as ther emprcal relevance. I develop a two-country, two factor monopolstc competton model wth a contnuum of ndustres, where factor ntenstes of margnal cost and xed cost are d erent. When trade costs are postve, ths non-homothetc cost functon allows countres to d er n technologes of producton and predcts that rch and poor countres experence HME n d erent sectors. For captal-abundant countres, the HME ncrease n sectors wth hgh trade costs and more d erentable products. For labor-abundant countres, the HME rse n sectors wth hgh trade costs and less d erentated products. I test and con rm these predctons by usng blateral exports data, showng that captal and labor-abundant countres experence home market e ects n dstnct sectors as predcted by theory and not n any other sectors. I also decompose home market e ects nto extensve and ntensve margns at the ndustry level for labor and captal-abundant countres. Even though the HME s drven by an ncrease n the number of rms n both captal and labor-abundant countres, extensve margns (new varetes) drve the HME n captal-abundant countres to a much larger extent than n laborabundant countres, where home market e ects are drven by ncreasng proportons of ntensve margns (quantty per varety). References [1] Alan Heston, Robert Summers and Bettna Aten, Penn World Table Verson 6.3, Center for Internatonal Comparsons of Producton, Income and Prces at the Unversty of Pennsylvana, August [2] Balassa, B., Trade Lberalzaton and Revealed Comparatve Advantage, The Manchester School of Economc and Socal Studes, Vol. 32, pp

27 [3] Baldwn. R. E., Okubo. T., "Heterogeneous rms, agglomeraton and economc geography: spatal selecton and sortng," Journal of Economc Geography, vol. 6(3), pages , June. [4] Crozet, M. and Tronfett, F Trade costs and the Home Market E ect, Journal of Internatonal Economcs, forthcomng ( [5] Davs, D., The home market, trade, and ndustral structure, Amercan Economc Revew 88, [6] Davs, D. and Wensten, D., Economc geography and regonal producton structure: an emprcal nvestgaton, European Economc Revew 43, [7] Davs, D. and Wensten, D Market Access, Economc Geography and Comparatve Advantage: An Emprcal Assessment, Journal of Internatonal Economcs, 59(1):1 23. [8] Dxt, A. and Stgltz, J. E. Monopolstc Competton and Optmum Product Dversty, Amercan Economc Revew, June 1977, 67(3), [9] Feenstra, Robert C., Robert Lpsey, and Charles Bowen World Trade Flows, , wth Producton and Tar Data. NBER Workng Paper No [10] Feenstra, Robert C., James R. Markusen, and Andrew Rose Understandng the Home Market E ect and the Gravty Equaton: The Role of D erentatng Goods. NBER Workng Paper No [11] Flam, H., Helpman, H., "Vertcal product d erentaton and North South trade". Amercan Economc Revew 77, [12] Hanson, G., Xang, C The home-market e ect and blateral trade patterns. Amercan Economc Revew 94, [13] Helpman, Elhanan 1984, The factor content of foregn trade, Economc Journal, 94: [14] Helpman, Elhanan, and Paul Krugman "Market Structure and Foregn Trade: Increasng Returns, Imperfect Competton, and the Internatonal Economy." Cambrdge, Mass.: MIT Press. 27

28 [15] Hummels, Davd Towards a Geography of Trade Costs. Mmeo. [16] Hummels, Davd, and Peter Klenow The Varety and Qualty of a Naton s Exports. Amercan Economc Revew, 95(3): [17] Krugman, Paul R., Scale Economes, Product D erentaton, and the Pattern of Trade, Amercan Economc Revew, 70, [18] Krugman, Paul R. and Venables, Anthony J., "Globalzaton and the Inequalty of Natons." Quarterly Journal of Economcs, November, 110(4), pp [19] Martn, P and C.A Rogers (1995) Industral locaton and publc nfrastructure, Journal of Internatonal Economcs 39: pp [20] Nayak, A., Does Varety Ft the Qualty Bll? Factor Endowments Drven D erences n Trade, Export Margns, Prces and Producton Technques. Mmeo, Purdue Unversty. [21] Pham, C, Lovely, M. E. & Mtra, D "The Home-Market E ect and Blateral Trade Patterns: A Reexamnaton of the Evdence," Economcs Seres 2009_12, Deakn Unversty, Faculty of Busness and Law, School of Accountng, Economcs and Fnance [22] Romals, J., Factor Proportons and the Structure of Commodty Trade, Amercan Economc Revew, XCIV, A Appendx A.1 Comparson of current and tradtonal IRS monopolstc competton models Most of the lterature usng the Dxt Stgltz (1977) model of monopolstc competton wth two factors assumes a homothetc cost functon of the Cobb Douglas type, C = (c q + F ) w r 1 ; where both xed costs and margnal costs use labor and captal n the same proporton of 1 : Ths assumpton helps to solve the general equlbrum, snce labor and captal n each ndustry 28

29 always get a xed proporton of the revenues. The assumpton however, s hghly stylzed. 14 The cost structure n (5) relaxes ths problem, but at the same tme keeps the model tractable for solvng the general equlbrum. The results comparng the equlbrum prces, number of rms and ther scales n the tradtonal model wth a homothetc cost functon and the current paper s model wth non-homothetc cost s gven below. p = w r 1 ; n = b 1 ( 1) F w r 1 ; q s = ( 1) F c : (Tradtonal Model) p = ( 1) w; n = b F 1 ; q s = ( 1) F r r c w : (Present Model) In the tradtonal model, rm sze are exogenous and dentcal across countres. In the present model, t s endogenously determned by the factor prce " rato n a country. Solvng# the tradtonal model further for N s share n an ndustry, v = W the condton for HME n N,.e. v > Z ;can be smpl ed as, ep 1 ( +1) ep + 1 fp ep b (x ep 1) (x ep d = 0; ) {z } ep = ~w ~r 1 % : Usng whch, Therefore we can wrte the condtons for HME n N and S as % > 0 and % < 0 respectvely. Therefore we can wrte the condtons for HME n N and S as, > ~w 2 ~r 2 (1 ) + ~w ~r (1 ) x ( ) and > ~w 2 ~r 2 (1 ) + x w r 1 : Comparng wth the current model s condton for HME n the N and S; we can see that we must mpose exogenous condtons between the captal ntensty and the product d erentablty of an ndustry to predct patterns of HME. The emprcal vablty of testng HME under such restrctons becomes qute d cult because both ndustry factor ntenstes and product d erentablty are calculated from dstnct supply and demand sde factors and t would be very d cult ndeed to get data on ndustry factor ntenstes for a large enough sample of countres. The emprcal 14 Please refer to secton 1 for Helpman and Krugman s (1985) pont of vew on the starkness of ths assumpton. 29

30 predctons from the current model, however, s much smpler and easer to mplement. Moreover, t also matches extensve and ntensve margns of growth across countres that grow n sze and have factor endowment d erences. A.2 Generalzed Cost Functon wth both Factors Enterng Fxed and Varable Costs In ths secton I generalze the assumpton n the man model that margnal costs comprse labor costs only and xed costs comprse captal expendtures only. All the results stll contnue to hold as long as the margnal cost s more labor-ntensve than xed costs and the relatve wage-rental rato s d erent enough. Let us assume a non-homothetc cost functon wth xed costs usng captal more ntensvely than the varable cost n ndustry, C = c wr q {z } + w rf {z } ; < 1: (36) Varable Costs Fxed Costs De ne relatve prces as, ~p = c wr c w r = ~w~r : Thus the N has a hgher relatve prce f s small, and ~w s large and/or ~r s not too small. The zero pro t condton yelds quantty suppled by each producer as, q s = ( 1) F r 1 : (37) c w As long as < 1,.e. as long as the xed costs are more captal-ntensve, the ntensve margn s smaller n the rcher country where r w s relatvely smaller. Solvng the equlbrum where the zero pro t quantty s also equal to the demand gven a prce, " we can solve the equlbrum # number of rms and also for N s share n an ndustry, v = W e 1 ( +1) e f Ths expresson s dentcal to the expresson for N s share n an ndustry to the case n the smpl ed cost functon n paper, but now e s de ned as ~w 1+ ~r ( 1)+1 nstead of the smpler term ~w 1 ~r: N s ncome can be wrtten as the sum of revenues from all sectors, = R 1 0 n p q d = R 1 0 v b ( + )d and wrtng 1 = x, we can 30

31 wrte ths condton by substtutng N s share v to get, Z 1 0 b g d = 0; where, g = (x ~ 1) ~ ; (38) (x ~ ) whch agan s dentcal to the smpl ed model n man text, but wth the changed ~. The condton for HME n N,.e. v > + ; can be smpl ed n the present case as, > ~w 2( +) ~r 2( +1) + ~w( +) ~r ( +1) x ( ) : As long as < 1 and > 1 and the condtons that the large captal-abundant country also has hgher relatve and absolute wages than the S, we can show that as ncreases and x ncreases, the HME ncreases n the N: Usng the same g functon, we can also derve that f the large labor-abundant country has smaller relatve and absolute wages than the smaller captal-abundant country, then t wll see ncreasng degrees of HME n less d erentable and hgher trade cost sectors. A.3 Proof that > Note that both = 1 (1+ ) = > 0 and = ( (1 + ) = ) > 0: Therefore, < > 1: But, (39) The rst two terms n the numerator and denomnator are dentcal, therefore > > ) > 0: Gven that costs trade are postve,.e. > 1; and gven > 1; the last condton s always sats ed. 31

32 A.4 General Equlbrum, Factor Prce Non-Equalzaton and Relatve Factor Prces Followng Romals (2004), I show that FPE cannot hold when trade costs are postve usng the method of contradcton. Suppose factor prce equalzaton (FPE) holds. Then rms technques n each sector are dentcal across N and S. Suppose country szes are also dentcal; then, by symmetry of trade costs, the number of rms s equal across N and S, so clearly factor prce equalzaton cannot clear factor markets. When relatve country szes d er, the bgger country has a larger number of rms. FPE mples that a bgger country demands more labor and captal n the same proporton rrespectve of ts factor endowments. Thus factor prce equalzaton would not clear factor markets as long as relatve factor abundance exsts. From equaton (13) when factor prces are equal, we can wrte en = ( e ) 1 (1+ e ) ( e ) 1 (1+ e ) : Note then en S 1 f e S 1: In each of these cases FPE contradcts the factor market clearng condtons (18): Case 1: When ~ = 1, or =, under factor prce equalzaton en = 1 and q s = qs n each sector : Therefore factor markets clear only when K = K and L = L : But ths contradcts the relatve factor endowments. Case 2: Under FPE, when >, ~n > 1 n all sectors. For tractablty I assume that for x = 1 s a constant (x) across all ndustres, so that ~n = 1 ndustres. 15 Ths mples, L L = R [0;1] R n qs [0;1] > 1 s a constant for all n q sd R n F d d = 1 ; and K K = [0;1] R n F d = 1 : (40) [0;1] Therefore, FPE and relatve factor abundance cannot hold n ths case. Case 3: ~ < 1. Ths s just the reverse of case 2 and factor prce equalzaton can be dentcally rejected n ths case too. Factor Market Clearance Condton ( w r < w r when K K > L L ): When FPE breaks down, factor markets clear only when the N has a hgher wage rental rato. Ths s because full employment 15 Ths s just a smplfyng assumpton and s not necessary for the non-equalzaton of actor prces. 32

33 of factors n the North occurs f () North uses captal more ntensvely n each sector than South, () t sells more varetes n > n for a gven sze of each sector, and/or () has larger shares of world exports n captal-ntensve sectors. From equaton (9) we know that condton () s sats ed only when N has a hgher w r sector s output, the rm sze q s = ( than S: For the number of rms to be larger n the N for a gven amount of a 1) F r c w must be smaller n the N, whch happens f w r > w r. For N to export larger shares n more captal-ntensve sectors the N must also have hgher wage rental rates (proved n secton 3.1 below). All of these results are reversed when w r only when w r < w r > w r. Hence, can the factor markets clear n the N; gven ts relatve captal-abundance. A.5 Dervaton of g functon The functon g s derved as follows, = Z 1 0 n p q d = Z 1 0 v b ( + )d (41) But 2 3 v = 4 ex 1 ( + ) + x ( + (42) ) e + 1 e x 1 + x v ( + ) = ex( + ) + x 2 + e + 1 e x + x (43), = Z 1 0 Z 1 0 v b ( + )d (44) b [v ( + ) ] d = 0, Z 1 b ex( + ) + x 2 + e + 1 e x + x d = 0 (45) () Z 1 b 0 ex( + ) + x 2 + e + 1 e x + x A = 0 (46) 33

34 A.6 Proof of Lemma 2 :, Z 1 0 ~ b d = 0 (47) (x~ 1) (x ~) {z } g Note that we assume and are gven and that the N s larger (.e. > ) throughout ths proof. Denote RHS of equaton (21) by (~): Takng dervatves of (~); t s easy to show 0 (~) < 0 for all values of ~, and : 1. When > ; t s easy to verfy that (1) > 0: If ~ > 1 and ~ s rsng towards mn [x ], ( ~) approaches 1 (as the second term rses and the rst falls). Therefore, equaton (21) wll always have a soluton when 1 < ~ < mn [x ] : 2. When ~ > max [x ] ; (~) > 0 and (~) s ll-de ned between mn [x ] < ~ < max [x ] snce 9 an for whch x ~ = 0: Therefore the only soluton for (~) s the one gven n (1) above. 3. When ~ < 1; t s easy to see the (0) 0 (snce when ~ = 0; at least ~w or ~r; or both are zero). As ~ rses from 0 towards the mn[x 1 ]; (~) falls towards 1 and as ~ falls from 1, towards max[x 1 ]; t goes from a postve number to +1: Between mn[x 1 ] < ~ < max[x 1 ]; (~) s agan ll de ned as 9 an for whch x ~ solves equaton (21). 1 = 0: Therefore, there s no ~ < 1 that A.7 Proof of Lemma 4 Note that we assume and are gven and that the S s larger (.e. > ) throughout ths proof. Denote RHS of equaton (28) by z(~): Takng dervatves of z(~); t s easy to show z 0 (~) < 0 for all values of ~, and : 1. When > ; t s easy to verfy that z(1) < 0: If ~ > 1 and ~ s rsng towards mn [x ], z (~) approaches 1. Therefore, equaton (21) wll have no soluton when 1 < ~ < mn [x ] : 2. When ~ > max [x ] ; z(~) > 0 8~ and z(~) s ll de ned between mn [x ] < ~ < max [x ] snce 9 an for whch x ~ = 0: Therefore no soluton for z(~) exsts for ~ 1. 34

35 3. When ~ < 1; t s easy to see the z (0) < 0 (assumng both factor prces are not zero). As ~ rses from 0 towards the mn[x 1 ]; z (~) falls towards 1. Therefore no soluton for z(~) exsts when 0 < ~ < mn[x 1 ]: Between mn[x 1 ] < ~ < max[x 1 ]; (~) s agan ll de ned as 9 an for whch x ~ 1 = 0: but as ~ falls from 1, towards max[x 1 ]; t goes from a negatve number to +1: Therefore, there the only soluton for z(~) exsts when max[x 1 ] < ~ < 1 that solves equaton (21). A.8 Methodology for Measurng Sectoral Extensve and Intensve Margns Here I adapt Hummels and Klenow s methodology to decompose sectoral exports of a country nto ts extensve and ntensve margns. The world trade ows database allows us to see n how many of the HS6 categores a country exports n a 3 dgt SITC sector to an mporter h, how many HS6 products are n that sector n market h, and the aggregate quanttes that the rest of world exports n each HS6 category to h. So t s easy to measure the extensve margn and ntensve margn of a country j s exports to h n sector m as follows, EM jhm = P I jhm X khm P I hm X khm ; IM jm = P I jhm X jhm P I jhm X khm ; EXP jhm = EM jhm IM jhm = P I jhm X jhm P I hm X khm where, k denotes the rest of the world, I jhm s the set HS6 varetes that country j sells to country h n sector m and I hm s the total number of possble HS6 categores avalable n market h n the sector m. The numerator of the extensve margn of j, EM jhm uses the rest of the world s exports to h as weghts for the product categores n whch j sells, and the denomnator has the total rest of the world s sales n all categores n that sector. The ntensve margn compares j s own sales to h; to the rest of the world sales n all categores that j exports to h: Once all the EM jhm and IM jhm measures are obtaned for all export of j n sector m; j s overall extensve and ntensve margn n the sector m s calculated as, EM jm = hh j (EM jhm ) jhm ; IM jm = hh j (IM jhm ) jhm where jhm s the logarthmc mean (the sum s normalzed to 1) of the shares of h n the overall exports of j and the rest of the world n sector m. 35

36 Table 1: Lst of Countres Large K-Abundant Large L-Abundant Small K-Abundant Small L-Abundant Australa Algera Bahran Bolva Austra Columba Cyprus Algera Belgum and Lux Chna Hungary Ecuador Canada Egypt Iceland Guatemala Denmark Indonesa Ireland Jordan Fnland Inda Macao Morocco France Pakstan Malta Peru Germany Phlppnes New Zealand Paraguay Hong Kong South Afrca Oman El Salvador Ireland Thaland Seychelles Tunsa Israel Trndad and Tobago Sr Lanka Italy Japan Netherlands Norway Sngapore Sweden Swtzerland UK USA A.9 Tables Standard errors n parentheses ** p<0.01, * p<0.05, + p<0.1 36

37 Table 2: Treatment Industres Treatment K-Abun Industry Name Treatment L-Abun Industry Name 674 Iron Sheets 511 Hydrocarbon Derv 671 Pg Iron and Ferro 512 Alcohols and Phenols 621 Rubber and Plastcs 592 Starches and Insuln 679 Iron Castngs 651 Textle arns 665 Glasswares 652 Cotton Fabrcs 663 Mneral Manuf 653 Woven Fabrcs 666 Pottery and Ceramcs 786 Tralers and Sems 678 Iron Tubes 656 Rbbons, Embrodery 642 Paper Products 654 Non-Cotton Spl Fab 812 Santary & Plumbng 657 Specal Textle Fab 625 Tres 658 Textle Materal NES 676 Steel Rals 659 Carpets & Flr Cover 641 Paper and Paper Brd 711 Bolers Large 677 Iron Ware 532 Synthetc Tannng Mat 672 Iron Ingots 635 Wood Manuf 673 Iron Bars 821 Furntures 634 Wood Panels 661 Cement Table 3: Control Industres Control K-Abun Industry Name Control L-Abun Industry Name 541 Pharmaceutcals 774 Elec Dagnos Apprts 752 Computers 776 Thermonc Cathodes 761 Televsons 771 Electrc Machnery 884 Optcal Lenses 695 Machne Parts, Tools 764 Audo Speakers 696 Cutlery 762 Rados 524 Inorganc Chemcals 759 Computer Parts 675 Alloys, Steel Flat 514 Ntrogen Comps 772 Electrcal Apprts 881 Cameras 751 O ce Machnes 882 Camera Supples 885 Watches, Clocks 726 Prntng Mach 37

38 Table 4: D erence-n-d erence Estmaton for Case I and Case II Dep Var Case I: HME n K-abun Countres z Case II: HME n L-abun Countres? z Treatment Industry (Low, Hgh trade cost)? Treatment Industry (Hgh, Hgh trade cost) z Control Industry (Hgh ; Low trade cost)? Control Industry (Low ; Low trade cost) D -In-D Import Shares (1) (2) (3) (4) (5) (6) ln(d n GDP) ** ** ** ** (0.002) (0.001) (0.006) (0.006) ln(d n GDP 2 ) ** ** (0.002) (0.007) D n GDP ** ** (0.000) (0.000) (D n GDP) ** ** (0.000) (0.000) ln(d n Dst) ** ** ** ** ** ** (0.002) (0.002) (0.003) (0.010) (0.010) (0.010) ln(d n Per Cap Land) ** ** ** ** ** ** (0.002) (0.002) (0.002) (0.007) (0.008) (0.007) ln(d n Per Cap K) ** ** ** ** ** ** (0.005) (0.002) (0.002) (0.007) (0.014) (0.013) Common_Lang ** ** ** ** ** ** (0.006) (0.006) (0.006) (0.013) (0.025) (0.024) Common_Border ** ** ** ** (0.012) (0.012) (0.012) (0.058) (0.058) (0.059) Constant ** ** * ** ** ** (0.075) (0.013) (0.012) (0.346) (0.039) (0.037) Observatons 1,799,889 1,799,889 1,799, , , ,692 R-squared Standard errors n parentheses ** p<0.01, * p<0.05, + p<0.1 38

39 Table 5: Reversng Treatment and Control Industres Dependent Varable Case IA: K-abundant y Case IIA: L-abundant? y Treatm ent Industry (H gh, H gh trade cost)? Treatm ent Industry (L ow, H gh trade cost) y C ontrol Industry (L ow ; L ow trade cost) D -n-d Imports (1) (2)? C ontrol Industry (H gh, L ow trade cost) ln(d n GDP) ** (0.001) (0.003) ln(d n Dst to Importer) ** ** (0.003) (0.006) ln(d n Land per Capta) ** ** (0.002) (0.004) ln(d n Captal per Capta) ** ** (0.005) (0.008) Common_Lang ** ** (0.006) (0.014) Common_Border ** ** (0.012) (0.034) Constant ** ** (0.013) (0.021) Observatons 1,077, ,534 R-squared Standard errors n parentheses ** p<0.01, * p<0.05, + p<0.1 39

40 Table 6: Consderng Zeros and Truncaton: HME Usng a Sngle D Equaton Dependent Varable Case I: HME K-abun Cty z Case II: HME n L-abun Cty? z Treatm ent Ind (L ow ; hgh trade cost)? Treatm ent Ind (H gh, H gh trade cost) z C ontrol Ind (H gh, low trade cost)? C ontrol Ind (L ow ; L ow trade cost) Sngle D Imports (1) (2) ln(d n GDP) ** ** (0.013) (0.039) Treatment Dummy ** ** (0.047) (0.124) ln(d n Dst to Importer) ** ** (0.019) (0.053) ln(d n Land per Capta) ** (0.012) (0.024) ln(d n Captal per Capta) ** ** (0.042) (0.057) Common_Lang ** ** (0.042) (0.103) Common_Border 1.038** 1.056** (0.073) (0.291) Constant ** (0.126) (0.206) Observatons Wald Ch2(7)

41 Table 7: Extensve and Intensve Margn of Sectoral trade Dependent Varable Case I: HME K-abun Cty z Case II: HME n L-abun Cty? z Treatm ent Ind (L ow ; hgh trade cost)? Treatm ent Ind (H gh, H gh trade cost) z C ontrol Ind (H gh, low trade cost)? C ontrol Ind (L ow ; L ow trade cost) D -In-D Extensve Margn (1) (2) ln(d n GDP) ** ** ln(d n Dst to Importer) ** * ln(d n Land per Capta) ** ln(d n Captal per Capta) ** ** Common_Lang * Common_Border ** Constant ** ** Observatons R-squared Table 8: Average Extensve and Intensve Margn n Industres exhbtng HME Treatment Sector Export Margn K-abun Cty HME Sectors z L-abun Cty HME Sectors? (Percentage) z Treatm ent Ind (L ow ; hgh trade cost)? Treatm ent Ind (H gh, H gh trade cost) Avg Extensve Margn Avg Intensve Margn

42 42 Fgure 1: Selecton of Country and Correspondng Treatment and Control Industres for Testng HME n K-abundant Countres (Case I) and L-abundant Countres (Case II)

43 Fgure 2: Selecton of Treatment and Control Industres for Testng HME (Case I and Case II) 43

44 Fgure 3: Testng HME wth Treatment and Control Industres Reversed (Case IA and Case IIA) 44