Technology and the law of comparative advantage

Transcription

1 Technology and the law of comparatve advantage Antono Navas The Unversty of Sheff eld PRELIMINARY AND INCOMPLETE. August 7, 2014 Abstract Ths paper explores how trade openness affects both product and process nnovaton n a standard model of trade wth frm heterogenety and factor-endowment-drven comparatve advantage. Trade openness expands the proft opportuntes of the most productve frms and expels the less eff cent frms out of the market, makng process nnovaton more attractve for the most productve frms n both ndustres. Incentves, however, are larger n the ndustry n whch the country has the comparatve advantage. Trade also ncreases the profts of prospectve entrants what t leads to an ncrease n product nnovaton n the comparatve advantage ndustry. In addton I obtan a non-monotonc relatonshp between trade costs and the country s trade pattern: When the level of trade costs are reasonably hgh, a reducton n trade costs leads to an ncrease n process nnovaton and R&D ntenstes n both ndustres, beng stronger n the comparatve advantage ndustry, however, f the trade costs are lower enough, the effect s stronger n the comparatve dsadvantage ndustry. Ths fnal result could ratonalze recent emprcal fndngs suggestng that n the last half century comparatve advantage has become weaker over tme. Keywords: Innovaton, Frm Heterogenety, Comparatve Advantage. JEL Codes: F12, F43 1 Introducton The Neoclasscal trade theores emphasze the role of dfferences n technology Rcardo 1817, Jones 1961, Dornbusch and Fscher, 1977 and a more recently contrbuton by Eaton and Kortum 2002 or dfferences n factor endowments Heckscher-Ohln 1933, and more recent formulaton by Vanek The author would lke to thank Chenglu L for excellent research assstantshp. Remanng errors are mne. 1

2 1968 to explan trade flows and trade patterns across countres. New trade theores have ncorporated scale economes at an ndustry and frm level to explan several features of the data that the neoclasscal theores were fndng dff cult to explan lke the ntra-ndustry trade phenomenon, or the fact that only a small proporton of frms wthn each ndustry are able to export Meltz 2003, Bernard, Jensen, Eaton and Kortum 2002, Meltz and Ottavano 2008, Chaney Whle these theores have dentfed dfferent nsttutonal factors that may bust or dampen trade volumes across countres and may affect a country s specalsaton pattern stll, technologcal and factor endowment dfferences across countres are at the heart of the determnants of trade specalsaton patterns. At the emprcal level, several studes have tred to dllucdate how these two channels are able to account for trade patterns and trade volumes across countres. Trefler 1993a, The new new trade theory based on nternal scale economes developed by Meltz 2003 and Meltz and Ottavano 2008, has outlned a new mechansm through whch trade ncreases welfare n tradng countres: The mpact of trade on technology through selecton. Trade through tougher competton expels the less eff cent frms out of the market reallocatng market shares across the most productve survvng ncumbents. By concentratng the producton n the most eff cent ndustry unts, ths ncreases an ndustry s average productvty. A recent paper by Bernard, Reddng and Schott 2007 outlnes the mportance of ths mechansm to establsh a lnk between the prevously dscussed two potental sources of comparatve advantage: Dfferences n factor endowments through selecton generates a Rcardan comparatve advantage. Tougher selecton n the comparatve advantage ndustry leads to a relatvely larger ncrease n the average productvty of that ndustry after trade openness. In ths paper I want to explore further the lnk between technology and factor endowments, by expandng a 2x2x2 standard model of trade, factor proportons and frm heterogenety to allow frms to upgrade ther current state of technology. In our setup there are two fnal good ndustres producng each of them a contnuum of dfferentated goods. The structure of each of the two ndustres, s smlar to Meltz 2003: Frms pay a fxed cost to create a new varety whch allows them to enter n the market. Assocated wth ths varety the frm uses a lnear technology to produce that nvolves the use of an ndustry specfc ntermedate nput. However, the untary nput requrements are uncertan for the frm at the moment of entry. The ndustry-specfc ntermedate nputs are produced accordng to a Cobb-Douglas producton functon that uses both sklled and unsklled labour n dfferent proportons across both fnal goods. After entry, the ntermedate nput untary requrements are revealed to the frm and the frm chooses whether to stay n the market and payng a per perod fxed cost to produce. Once the frm has decded to stay, I assume that t has the opton to upgrade ts current state of technology by payng a fxed cost. In ths framework I dstngush between process nnovaton technology 2

3 upgradng and product nnovaton the creaton of new varetes. Our results suggest that the selecton effect found Meltz 2003 or Meltz and Ottavano 2008 leads to a rse n technology upgradng n both ndustres. Interestngly, technology upgradng s stronger n the ndustry n whch the country has a comparatve advantage. The reason behnd ths result s the fact that trade expands the busness opportuntes for the most productve frms n both sectors. However, trade expands t to a greater extent n the comparatve advantage ndustry snce the economy s able to offer these goods relatvely cheaper than the foregn counterpart. Ths rses the expected profts of prospectve entrants and nduces a dsproportonate entry n the comparatve advantage ndustry. As a consequence, the relatve demand for the abundant factor rses what t has a postve mpact on the relatve factor remuneraton. Domestc frms see ther profts reduced and need to ext. The combnaton of a stealng busness effect n the foregn country and a reallocaton of market shares from the less eff cent frms whch ext, towards the most productve ones, nduce a larger proporton of frms to upgrade ther technology. Overall technology upgradng rses n both ndustres and the comparatve advantage ndustry enoys more product and process nnovatons compared to an autarkc scenaro. Usng R&D ntenstes as a measure of nnovaton actvty, my model predcts that trade openness ncreases the relatve R&D ntensty favourng the comparatve advantage ndustry one. These last results renforce the Rcardanled-factor endowment comparatve advantage by havng a postve effect on the wthn plant productvty mprovements. In a further secton n the paper, I explore the evoluton of the comparatve advantage by consderng a reducton of trade costs when both ndustres are opened to trade. The results establshes a non-monotonc relatonshp between the level of trade costs and the evoluton of comparatve advantage: When the trade costs are hgh, a reducton n trade costs ncreases technology upgradng and R&D ntenstes relatvely more n the comparatve advantage ndustry. Ths nduces TFP dvergence across sectors. However, f the trade costs are lower enough a reducton n trade barrers ncreases technology upgradng and R&D ntenstes n the comparatve dsadvantage ndustry leadng to TFP convergence across ndustres. Overall the average productvty, the proporton of frms that upgrade ther technology and the R&D ntenstes ncreases n both ndustres as trade costs fall. However, provded that there s self-selecton nto exportng markets, these three dmensons are always larger n the comparatve advantage ndustry. Ths suggests that a gradual reducton n trade costs may eventually strengthened the pattern of comparatve advantage at the ntal stages whle reducng t when the trade costs become suff cently low. Ths paper s related to several lteratures. The frst one s the lterature on the effects of trade openness and trade lberalsaton on nnovaton. A recent lterature based on models wth frm heterogenety outlnes the mportance of selecton effects n promotng process nnovaton Atkeson and Bursten 2011, 3

4 Bustos 2011, Impullt and Lcandro 2011, Navas and Sala 2013 and Long et al among others. Unlke those papers we study the role played by factor endowments n determnng the effect that trade has on nnovaton at the ndustry level. My model suggests that dfferences n factor ntenstes across ndustres and the vector of local factor endowments the home country enoys relatve to ts trade partners, may generate asymmetres n productvty and nnovaton across ndustres that n an autarkc equlbrum exhbt dentcal productvty dstrbutons. The second dmenson s clearly a determnant of the dynamc evoluton of the ndustry s average productvty. Ths paper s related to the lterature that ncorporates dfferences n factor endowments n models of trade wth economes of scale.krugman 1981, Helpman and Krugman 1985 HK. Those papers obtan the nterestng result that most of the fndngs n the Heckscher-Ohln model are also present n an envronment n whch there are ncreasng returns to scale at the frm level. More recently, Bernard, Reddng and Schott 2007 BRS ncorporates a factor proportons theory nto a standard Meltz 2003 model of trade wth frm heterogenety and fnds that the same H-O results are also present when we allow productvty to vary across frms. They also fnd that dfferences n factor endowments together wth trade openness can generate a Rcardan comparatve advantage as explaned above. My paper goes n lne wth the above papers and renforces the dea that the H-O results are robust to rcher envronments. In addton, by ncludng the possblty of frms to technology upgrade, ths paper fnds that dfferences n factor ntenstes across ndustres and factor endowments across countres generates a dfferent mpact on trade-nduced plant productvty mprovements across frms wth the same ntal productvty. Ths result renforces the early fndngs by BRS on Rcardan-led-factor endowment comparatve advantage by havng an mpact on average ndustry productvty whle t also suggests that ths Rcardan advantage may persst along tme. Fnally, ths paper s related to a recent lterature that nvestgates the evoluton of comparatve advantage. In a very nterestng study, Levchenko and Zhang 2013 obtan that, contrary to the common knowledge, n the last 50 years on average, productvty has ncreased by more n the countres revealed comparatve dsadvantage ndustres. Our paper suggests a non-monotonc relatonshp between trade costs and the pattern of comparatve advantage and for suff cently low level of trade costs, a reducton n trade barrers may beneft the comparatve dsadvantage ndustry, narrowng the dfferences n TFP across ndustres wthn a country. The evdence of Levchenko and Zhang 2013 could be consstent wthn ths framework wth a gradual reducton n trade barrers across countres provded that the ntal level of trade costs were suff cently low n the 1960s. Secton 2 of the paper descrbes the man elements of the model n autarky. On secton 3, I dscuss the man propertes of the model n free trade, obtanng that as n BRS and HK the man results for the Heckscher-Ohln model are held 4

5 n ths envronment. In secton 4 I dscuss the most realstc case n whch the economy s open to trade but trade s costly both n varable and fxed trade barrers. In secton 5 I analyze the effect of trade lberalsaton understood as a reducton n trade barrers. Secton 6 concludes. 2 The model Consder an economy nhabted by a contnuum of consumers. There are two fnal goods. Let denote wth C the consumpton of good = 1, 2. Each C s a composte good defned over a contnuum of varetes belongng to the set Ω. Preferences over these goods are gven by the followng utlty functon: UC 1, C 2 = C 1 α C 2 1 α C 1 = q 1 ω σ dω σ ωɛω 1 C 2 = q 2 ω σ dω σ ωɛω 2 Solvng the consumer s problem we arrve to the standard CES aggregate demand system for each varety of the composte good: q ω = R σ p ω P P where R denotes consumer s expendture dedcated to good. Under Cobb- Douglas preferences R = α R where R denotes total revenue. To produce, frms use an ntermedate nput x that s homogeneous to all products wthn the same ndustry but dffer across ndustres. Ths ntermedate nput s produced compettvely combnng both captal and labor usng the followng Cobb-Douglas technology: x 1 = A 1 S 1 β 1 L 1 1 β 1 wth A = β β 1 β 1 β. x 2 = A 2 S 2 β 2 L 2 1 β 2 We assume wthout loss of generalzaton that β 1 > β 2 that s the ndustry 1 uses ntermedate nputs that are more sklled labour ntensve. Perfect competton n the ntermedate nput sector mples that: p m = w s β w l 1 β 5

6 The producton sde n the fnal good sector s dentcal to Meltz To enter n the market, a frm needs to nvest f e unts of the ntermedate nput to create a new varety. Once the frm has created ths varety the frm bbtans the monopoly rghts to produce t. Assocated wth ths varety there s a technology to produce whch s lnear n the ntermedate nput. More precsely: q ϕ = ϕ x However, frms productvty ϕ s unknown before the creaton of ths new varety. More precsely, the frm knows that the productvty parameter ϕ follows a random process wth support [0, and a cumulatve contnuous dstrbuton functon Gϕ. After the nvestment n the creaton of ths varety s undertaken, the productvty s revealed to the frm. The creaton of new varetes of the same composte good s consdered here as product nnovaton. To operate the technology the frm needs to pay a per perod fxed nvestment of f d unts of the ntermedate nput. At ths moment she needs to decde whether to stay and produce. Once the frm decdes to stay and produce we are gong to consder that the frm has the possblty to adopt a new technology whch mproves ther productvty by a factor of θ by nvestng a fxed amount f I of the ntermedate nput of unts. The process of a frm s technology upgradng wll be denoted as process nnovaton. In ths verson of the model we consder that all actvtes wthn an ndustry product, process nnovaton, producton and exportng when apples uses the same ntermedate nput. Consequently, all actvtes wthn an ndustry has the same factor ntensty. However, these actvtes dffer n factor ntenstes across ndustres. The frms problem s solved by backward nducton. Frst, I solve for the frm s decson of technology upgradng. Then I solve for the the frm s decson of stayng n the market takng nto account ts future decson of technology upgradng. Fnally, I solve for the frm s entry decson, takng nto account the flow of expected profts n the ndustry. Snce the varety produced by each frm s unque, a frm charges the standard monopoly prce: p ϕ = σ p m σ 1 ϕ = σ ω σ 1 θ d ϕ where d s the ndcator functon takng the value of 1 f the frm adopts the new technology and ω = w s β w l 1 β. The varable proft assocated to a frm wll be gven by the followng expresson: R π v ϕ = σ P 1 σ ρ θ d ϕ ω 1 σ = r dϕ. σ Notce that the rato between the revenue of two non nnovatve frms s gven by productvty rato as n Meltz 2003 r dϕ r d ϕ = ϕ. ϕ 6

7 A frm decdes to adopt the new technology ff: θ r d ϕ 1 δf I ω 1 σ wth equalty f the frm s ndfferent between adoptng the technology or stayng wth ts current technology. Let denote wth ϕ I the value of the productvty of the ndfferent frm, whch we call the margnal nnovator. The frm s ndfferent between stayng or extng the market when: r d ϕ d σ = f D ω 2 Ths condton s known n the Meltz 2003 model as the ZP condton. Dvdng 1 and 2 we have that: ϕi ϕ D = δfi f D 1 θ 1 Notce that the proporton of survvng frms undertakng process nnovaton s ndependent of the factor prces and therefore on factor endowments n autarky. Ths s the consequence of the fact that both actvtes are usng the same ntermedate nput and therefore they use the producton factors wth the same ntensty. Allowng for dfferences n factor ntenstes across actvtes wthn an ndustry breaks ths result. We leave ths possblty for future research. Fnally, a frm decdes to enter n the ndustry ff EV f e ω. In ths model we focus on steady state solutons. In steady state a frms value functon s gven by the followng expresson: { V = max 0, π v ϕ, π } v θϕ f I ω δ δ Equlbrum n a Closed-Economy Model One of the nterestng propertes of the Meltz-type models s that the equlbrum of the economy, n our case perfectly characterzed by the two productvty thresholds ϕ I, ϕ D, can be summarsed wth two condtons: the Zero Proft Condton ZP Condton 2 n our model and the Free Entry condton FE. In ths framework however, we need an extra equaton that comes from the Zero Innovaton Profts condton Condton 1 n our model. The FE condton n ths model becomes: ϕd 1 ϕ D f D + 1 Gϕ I 1 G ϕ D ϕi 1 δf I = ϕ I δf e 1 Gϕ D. 7

8 The left hand sde lhs of our FE condton s smlar to a standard heterogenousfrm trade model. There s, however, an extra term, the second one, whch represents the nnovaton profts. The possblty of technology upgradng ncreases the expected value of profts from entry by ncreasng the profts of the most productve frms. The appendx shows that there exsts a unque productvty threshold level ϕ D and consequently a unque value for ϕ I. Compared to Meltz 2003, the possblty of technology upgradng reallocates market shares from the less productve frms to the most productve ones, makng survval more dff cult n ths economy. Consequently, ϕ D s larger n ths case. Despte the fact that ths model exhbts a larger average productvty due to the frm s possblty of technology upgradng, both sectors share the same productvty thresholds, ϕ D, ϕ I and consequently the same average productvty, provded that the rest of the parameters are dentcal n both ndustres. In autarky, dfferences n factor endowments across countres are not generatng dfferences n average productvty across ndustres. 1 In the sklled-labour abundant country, ntally frms have larger expected benefts n the comparatve advantage ndustry Industry 1 because margnal costs of producton n that ndustry are relatvely smaller. Consequently, frms can charge relatvely lower prces and have relatvely larger sales. However, the costs of entry are also smaller n that ndustry, and ths together wth the rse n the expected profts of the representatve frm ncreases entry. These two effects offset the postve effect that the comparatve advantage mechansm s havng on frms profts. However, as dscussed above, there s more entry n the ndustry n whch the economy has the comparatve advantage. Thus, the model generates dfferences n the mass of survvng frms n equlbrum. To see ths, notce that: M 1 M 2 = R 1 R 2 r 2 r 1 = α 1 α ϕ1d ϕ 1D σf1d ω 1 ϕ2d ϕ 2D σf2d ω 2 = α β2 β ws α w L Our country s sklled-labor abundant. We show n the appendx that ths mples that: w H s w F < s. w H L w F L Ths mples that: M H 1 M H 2 > M F 1. M2 F Ths result s already present n standard models of trade wth mperfect competton and ncreasng returns to scale Helpman and Krugman, Unlke exstng work, the nnovaton resources n ths economy are not constant across ndustres. The comparatve advantage ndustry nvests more resources n both product and process nnovaton. R&D expendtures n each sector are gven by: 1 The same result has been found n Bernard, Reddng and Schott

9 R&D exp = f e M e + δf I M I }{{} amount of resources ω }{{} Resource cost Consderng the statonarty condton for each sector and rearrangng terms: δf e R&D exp = 1 Gϕ D + δf 1 Gϕ I I M ω 1 G ϕ D Snce ϕ D, ϕ I are dentcal across ndustres, consderng the rato of R&D exp across ndustres we have that: R&D exp 1 = M β1 β 1 ws 2 = α R&D exp 2 M 2 w L 1 α. Whle the relatve R&D expendtures ust depend on the sze of the sector α the amount of resources nvested s larger n the ndustry n whch the economy has a comparatve advantage. To see ths, consder the smpler case n whch α = 1 2. In ths case the economy s nvestng the same amount of ncome n nnovaton n both ndustres. However, n the ndustry n whch the economy has the comparatve advantage, the cost of resources s cheaper, and consequently ths ndustry s nvestng n more resources. A common measure to explore the presence of nnovaton actvtes wthn an R&D expendtures ndustry used n the emprcal lterature s R&D ntenstes sales. Ths measure s used to avod the fact that R&D expendtures are larger because the ndustry s larger n the economy. The model suggests that R&D ntenstes are dentcal across ndustres as t can be seen below. 3 Costless Trade R&Dnt 1 R&Dnt 2 = R&D exp 1 R&D exp 2 R 2 R 1 = 1. In ths secton I explore the mplcatons of the model for nnovaton when we consder a movement from autarky to free trade. Common to the new lterature on frm-heterogenety and factor endowments, ncludng nnovaton n ths envronment does not alter the man propertes of the Heckscher-Ohln model. Moreover, R&D ntenstes are stll nvarant across ndustres and nnovaton does not have any mpact on average productvty. In contrast to the one derved n ths secton, under costly trade, R&D ntenstes dffer accordng to the comparatve advantage. Ths has a clear mpact on average productvty across ndustres. Consder the possblty that the frm can serve the foregn market at no cost. The varable proft of a domestc frm n the domestc market s now gven by: 9

10 rd Hϕ = R ω H ρ θ σp H 1 σ d H 1 σ ϕ and the varable proft of a domestc frm n the foregn market s gven by: rd F ϕ = R ω F ρ θ σp F 1 σ d H 1 σ ϕ. The margnal nnovator n the Home country H must satsfy the followng condton: 1 + RF P F R H θ P H 1 rd ϕ I σ = δf I ω H where r d ϕ I = ρϕ I ω H 1 σ R H P H 1 σ The margnal survvor, the one ndfferent between stayng on leavng the market s defned by the followng condton: 1 + RH r d ϕ d R F σ = f d ω H P H P F Then we have that: ϕi ϕ D = δfi f D 1 θ 1 whch s the same as n autarky. In fact snce the varable proft for each frm s a constant tmes the varable proft n autarky we have that the FE condton s gven by: ϕd 1 f D + 1 Gϕ I ϕi 1 δf I = 1 G ϕ D ϕ D ϕ I 5 δf e 1 Gϕ D 6 whch s dentcal to the one n autarky. Therefore productvty thresholds are unchanged after trade openness when trade s costless. Ths mples that the productvty dstrbutons reman unchanged after trade openness but costless trade. The standard results n the Heckscher-Ohln model are held n ths envronment. Factor Prce Equalsaton holds provded that we do not have factor ntensty reversals.e. factor endowments not to be very dfferent across countres. Unlke prevous studes, trade has an mpact on nnovaton. Trade promotes nvestment n product nnovaton n those ndustres n whch the country has a comparatve advantage. In contrast, the relatve R&D ntenstes wll be unchanged after trade openness. To see ths notce that the R&D ntenstes rato s gven by: R&Dnt 1 = M β2 β 1 R 2 ws 1 R&Dnt 2 M 2 R 1 w L But R = M r, then substtutng we have that: 10

11 β1 β R&Dnt 1 R&Dnt 2 = r2 w 2 s r 1 w L R&Dnt 1 R&Dnt 2 = ϕ2d ϕd ϕ 2D σf 2D + 1 Gϕ 2I 1 Gϕ 2D ϕ D σf 1D + 1 Gϕ 1I 1 Gϕ 1D ϕ2i ϕ σf2i ω 2 2I ϕ1i ϕ σf1i ω1 1I ω 1 = 1 ω 2 Costless trade does not have any mpact on process nnovaton because t does not alter the dstrbuton of profts wthn the ndustry. When trade s costless, trade openness wdens the proft opportuntes of all frms although ths ncrease s more pronounced n the ndustry n whch the country has the comparatve advantage because the relatve cost of factors s cheaper. Ths nduces entry and an ncrease n the relatve demand for sklled labour. The ncrease n entry perfectly offsets the ncrease n proft opportuntes and leaves the market share of each frm n each market unaltered. Snce the global sze of the frm s unchanged under ths settng, frms ncentves to undertake process nnovaton actvtes have not been altered Ths result s challenged n the next secton. 4 Costly Trade The recent lterature on trade and frm heterogenety has suggested that both fxed and varable trade costs are mportant n nternatonal trade actvtes Roberts and Tyebout, In ths secton, I ntroduce both types of costs and show that the man mplcaton of t, self-selecton nto exportng markets, together wth dfferences n factor endowments generate mportant consequences for nnovaton. Self-selecton nto exportng creates asymmetres across frms wthn an ndustry. Dfferences n factor endowments create asymmetres across sectors. The nteracton between both expand busness opportuntes of the most productve frms to a larger extent n the comparatve advantage ndustry. Ths nduces dfferences n nnovaton outcomes across ndustres and consequently dfferences n the average productvty across ndustres. Unlke BRS these dfferences n productvty arse through two channels: an effect on the survval productvty threshold due to tougher selecton whch creates a reallocaton effect towards most productve plants, and an effect on the wthn-plant productvty. In ths economy, to get one unt of the product sold n the foregn market, a frm must shp τ 1 unts of the product ncurrng nto a varable trade cost of τ 1. To serve the foregn market the frm needs to ncur also n a fxed cost f x unts of the ntermedate nput used n producton. As commented before, we assume that exportng actvtes uses the same ntermedate nput as nnovaton and producton actvtes wthn the same ndustry. A great part of ths 11

12 fxed cost of exportng conssts on advertsement and complyng wth regulaton standards. I assume that these costs are proportonal to the untary producton cost. To outlne the role played by factor endowments on nnovaton outcomes, we assume that sectoral structural parameters other than factor endowments are dentcal across countres. As t s dscussed n Navas and Sala 2013 ths model exhbts dfferent equlbra dependng on the parameter confguraton. These are assocated wth dfferent parttons of frms accordng to nnovaton and export status. In the world I descrbe here, the varety of equlbra becomes more nterestng snce dfferent ndustres could n prncple sustan dfferent type of equlbra dependng on the value of fxed costs of exportng, nnovaton and trade barrers. Rather than descrbng a large varety of cases, n ths paper, I focus on a symmetrc equlbrum n whch all ndustres share the same structural parameters and an equlbrum n whch nnovators are a subset of the most productve exporters for both ndustres and countres, n lne wth recent evdence found by Aw, Roberts and Xu Consequently, both ndustres are characterzed by a partton of frms across status gven by the followng herarchy: Innovators and exporters the most productve ones, exporters and domestc frms. In a further secton I descrbe the condtons under whch ths equlbrum holds, and through smulatons we show that ths equlbrum holds provded that the level of varable trade costs are low enough. 2 For further analyss we denote wth superscrpt = H, F the varables assocated wth the home country and wth superscrpt k = H, F the varables assocated wth the destnaton country both of them can be ether Home H or Foregn F. In ths equlbrum, the margnal nnovator s an exporter. Consequently, the margnal nnovator n country and ndustry s defned by the followng condton: 1 + τ 1 σ R k R P k P θ 1 r d ϕ I = δf I ω σ where we have used the fact that R 1 = αr and R1 k = αr k exporter n country s descrbed by the followng expresson: τ 1 σ R k P k r d ϕ x R P = f x ω σ and the margnal survver s gven by the followng condton: r d ϕ I = f d ω σ = 1, 2 7 The margnal 2 Robustness checks analyse how the results vary under symmetry wth dfferent herarchcal structures

13 Dvdng 8 and 9 we fnd that: ϕ x ϕ d P 1 R f x = τ P k R k f d }{{} Λ 10 Dvdng 7 and 9 I obtan: ϕ I ϕ d δf I = f d θ σ 11 Λ fx fd Notce that as a consequence of trade openness, there s a larger proporton of frms undertakng process nnovaton n both ndustres, and ths result s ndependent of factor endowments. Ths s the consequence of the fact that nnovators have access to a larger market where they can take advantage of the ncreasng returns to scale nature of nnovaton. Takng the rato across ndustres we have that: ϕ 1 σ 1I 1 + Λ fx 2 ϕ fd 1d ϕ = 1 σ 12 2I 1 + Λ1 fx fd ϕ 2d ϕ 1I ϕ 1d ϕ and therefore we can conclude that < 2I ϕ ff Λ 1 < Λ 2. Ths 2d mples that those ndustres exhbtng a larger proporton of frms nnovatng are also those ndustres n whch there s a larger proporton of frms exportng. In the appendx I dscuss the aggregaton propertes of the model under costly trade. Compare to the benchmark case of frm heterogenety wthout technology upgradng, I observe that the dfference n profts between autarky and trade s larger n ths setup due to the effect that trade has on process nnovaton. Trade openness ncreases the sze of the market for the most productve frms and consequently ther sales. For a gven nnovaton productvty threshold, the nnovators are able to explot ther knowledge advantage across more producton unts snce they are able to sell more. Ths ncreases profts. Substtutng the expresson for profts n the Free Entry condton and rearrangng terms t can be obtaned: [ ] π d + p x π x + p I π I = δf e 1 Gϕ D 13 Lookng at ths condton we can deduct several propertes. Frst, trade openness mproves the average productvty n both ndustres by ncreasng the productvty threshold to survve n the market. Second the ncluson of process 13

14 nnovaton ncreases the effect that trade has on average productvty. Ths s due to the fact that nnovaton opportuntes nteractng wth trade creates new opportuntes to the most productve frms helpng them to ncrease ther market share n detrmental of the local compettors. Specfc to ths paper s the asymmetrc mpact on nnovaton across ndustres. More precsely I show n the appendx that: Proposton 1 Under costly trade: 1. The ncrease n the survval productvty threshold s larger n the ndustry n whch the economy has a comparatve advantage. 2. In the ndustry n whch the economy has a comparatve advantage there s a relatve larger share of ncumbent frms undertakng process nnovaton. 3. Assumng a Pareto-Dstrbuton for productvty, the R&D ntenstes are larger n the sector n whch the economy has comparatve advantage and ths s due to a ont effect of more product and process nnovaton. Proof. See Appendx. The ntuton behnd these results underles on the fact that when the economy opens to trade, frms are asymmetrcally exposed to dfferent ndustry opportuntes. In the home sklled-abundant country, the margnal cost of producton n ndustry 1 s lower than n the Foregn Country. When the economy opens up to trade, frms see ther opportuntes expanded n trade because the access to a larger market allows them to explot the ncreasng returns to scale assocated wth both producton and nnovaton. However, these proft opportuntes are larger n the ndustry n whch the economy has the comparatve advantage snce ths ndustry s able to offer the good cheaper than ts analogous counterpart n the foregn country Industry 1. Ths promotes a dsproportonate entry, and consequently more product nnovaton. The massve entry of frms makes profts fall and t becomes more dff cult to survve. The less productve frms can no longer make postve profts and consequently the productvty threshold needed to survve n the market ncreases. The expulson of the less eff cent frms generates a reallocaton of market shares across the most productve frms. Ths ncreases process nnovaton due to a combnaton of larger opportuntes and market share reallocaton. For ths equlbrum to hold the followng parameter constrants need to be satsfed: ϕ I 1. The margnal nnovator must be an exporter..e. ϕ > 1. Ths X mples: Λ fd δf I + 1 < fx f x θ 1 14

15 Substtutng 10 and rearrangng terms, we have that: τ R P R k P k < δf I 1 f x θ 1 2. The productvty threshold of an exporter must be larger than the domestc one whch mples > 1 ϕ : X ϕ D τ R P R k P k > f d f x Wrtng both condtons together we have that: f d < τ f x R P R k P k < δf I 1 14 f x θ 1 If the followng condton s satsfed: τ R P R k P k < f d f x then all frms wll be able to export. In that case the economy wll be n an equlbrum wth costly trade but no selecton nto exportng markets. Condton 14 depends on four endogenous varables and the model does not exhbt a closed form soluton for these varables. The next smulaton exercse suggests that ths equlbrum holds provded that transportaton costs are not large enough and there are no substantal dfferences n factor endowments across countres. In the next secton I look at the propertes of ths equlbrum. As t becomes apparent, whle trade has ntroduced technologcal dvergence across ndustres, due to a combnaton of trade barrers and dfferences n factor ntensty usage, these technologcal dfferences across ndustres could become smaller as the trade costs are reduced. Ths suggests that whle trade openness create a rcardan comparatve advantage across ndustres, the wdth of the comparatve advantage depends clearly on the level of trade costs. If the ntal stuaton s one of low trade costs, ths comparatve advantage becomes weaker over tme, provded that trade costs are reduced over tme. Ths could be consstent wth recent emprcal evdence found by Levchenko and Zhang

16 Paremeter Autarky Free Trade Percentage Varaton ϕ 1D ϕ 2D ϕ 1I ϕ 2I ϕ ϕ M M M1 e M2 e Table 1: A movement from autarky towards FreeTrade 5 Smulaton Exercses In ths secton I undertake several smulaton exercses whch corroborates the results dscussed n the theoretcal part. Frstly, I compare the results n autarky wth the results n Free Trade and second, I dscuss the effects of a partal trade lberalsaton experment a reducton n trade costs. In ths subsecton we depart for the parameter values provded by Bernard, Reddng and Schott These ones can provde us wth a better comparson between the two models and the role played by nnovaton n the productvty convergence across ndustres. Table 1 shows the results n autarky and free trade for the home country smlar ones you can fnd for the foregn country. Notce that a movement towards free trade ncreases the survval productvty cutoff and reduces the nnovaton productvty cutoff promotng technology upgradng. However, these effects are not the same across ndustres. In the comparatve advantage ndustry there s more selecton due to an ncrease n the mass of entrants attracted by larger expected profts and a lower nnovaton productvty cutoff snce trade expand the busness opportuntes of local frms more n the comparatve advantage ndustry. The effects on the average productvty for the benchmark case are large takng nto account that under the current parametrzaton only 3.75 and 3.5% of the ncumbent frms undertake process nnovaton. In the comparatve advantage ndustry there s an ncrease n the mass of varetes created whle n the comparatve dsadvantage ndustry the mass of each perod new varetes s clearly reduced. Ths reflects the dfferences n proftablty between both ndustres whch reallocates potental entrants for the comparatve dsadvantage ndustry to the comparatve advantage one. However, although the proporton of survvng frms s clearly large n the comparatve advantage ndustry, there s a clear drop n survvng n both ndustres. 3 3 As commented above, I have used BRS paramter values for the common parameters n the 16

17 productvty 0.8 Zero proft and Export Productvty Cutoffs Varable Trade Costs tau Fgure 1: Export and domestc productvty cutoffs: The contnuous lne represents the survval productvty cutoffs for both ndustres whle the dscontnuous lne represents the export productvty cutoff for both ndustres. The red lne represents the ndustry n whch the economy has the comparatve advantage. As t can be seen, n the ndustry n whch the economy has the comparatve advantage the survval productvty threshold s defntely larger. However, the export productvty cutoff s smaller. 17

18 Fgure 1 shows the export and domestc productvty cutoffs for both ndustres n the home country. The contnuous lne dsplays the survval productvty thresholds for both ndustres whle the dscontnuous one shows the export productvty cutoffs. The red lnes represent the ndustry n whch the ndustry has the comparatve advantage ndustry 1 whle the green one does t for the ndustry wth the comparatve dsadvantage ndustry 2. It s clear that the survval productvty cutoff s larger and the export productvty cutoff s smaller n the ndustry n whch the economy has the comparatve advantage. The former reflects tougher competton n that ndustry due to the larger expanded opportuntes for frms n that ndustry. Compared to a model wthout nnovaton, the survval productvty cutoffs n both ndustres have ncreased consderably. In the comparatve advantage ndustry for the case of the trade costs equal to 20% the productvty cutoff s 3.8% larger whle n the comparatve dsadvantage ndustry t s 3.67% larger. Although small, we can also observe that when we ntroduce the possblty of frms to upgrade ther own technologes n a model wth frm heterogenety and comparatve advantage the dfference between productvty cutoffs due to comparatve advantage mechansms across ndustres exacerbates. Consderng a more general case n whch the fxed costs of exportng are not equal to the fxed costs of producton, ust confrm the qualtatve results that we have obtaned as the fgure 2 provdes. Fgure 3 dsplays the relatve survval productvty cutoffs of Industry 1 versus Industry 2 for both the home and the foregn country. It becomes apparent that for hgh level of transportaton costs a reducton n transportaton costs ncreases the survval productvty cutoff by more n the comparatve advantage ndustry. However for suff cently low levels of transportaton costs, the opposte happens. Ths suggests that when the trade costs are hgh selecton becomes tougher n the ndustres n whch the economy has the comparatve advantage but as the trade costs fall survval s more dff cult n the comparatve dsadvantage ndustry. Fgure 4 dsplays the nnovaton productvty cutoff across both ndustres for the home country. The contnuous lne represents the nnovaton productvty cutoff n the ndustry 1 whle the dscontnuous lne represents the productvty cutoff n ndustry 2 for dfferent values of trade costs. It becomes apparent that a reducton n trade costs, decreases the nnovaton productvty cutoffs n both ndustres, or n another words ncreases the mass of frms that upgrade ther technology. Yet, t can be also observed that the nnovaton productvty cutoff s smaller n the ndustry n whch the home country has the model. Ths provdes a more accurate nterpretaton of the results by comparng a model wth and wthout process nnovaton. For the value nnovaton ump we have used 20% θ = 1.2 and for the nnovaton cost we have used 25 tmes the cost of entry. Changes n the parameter values do not generate qualtatve changes n the results, provded that the economy s n the analysed equlbru. Robustness checks are avalable on request. 18

19 Productvty cutoffs productvty 1.3 Zero proft and Export P roductvty Cutoffs Varable Trade Costs tau Fgure 2: Export and domestc productvty cutoffs Selecton nto exportng wth τ = 1: The contnuous lne represents the survval productvty cutoffs for both ndustres whle the dscontnuous lne represents the export productvty cutoff for both ndustres. The red lne represents the ndustry n whch the economy has the comparatve advantage. As t can be seen, n the ndustry n whch the economy has the comparatve advantage the survval productvty threshold s defntely larger. However, the export productvty cutoff s smaller Relatve productvty cutoffs Varable Trade Costs tau Fgure 3: Relatve productvty cutoffs. The fgure dsplays the relatve productvty cutoffs of Industry 1 vs Industry 2 for both the home country contnuous lne and foregn country dscontnuous lne. 19

20 productvty 1.18 Innovaton P roductvty Cutoffs V arable Trade Costs tau Fgure 4: Innovaton Productvty Cutoffs: Industry1 productvty cutoff s represented by the contnuous lne whle the dscontnuous lne represents the ndustry 2 productvty cutoff. comparatve advantage and consequently the mass of frms engagng n process nnovaton s larger n the comparatve advantage ndustry. As commented n the sectons above ths result s the consequence of a tougher selecton process n ths ndustry. Fgure 5 represents nstead the relatve nnovaton productvty cutoffs ndustry 1 versus ndustry 2 for both the home country contnuous lne and the foregn country dscontnuous lne. The results suggest an nterestng fndng. Whle the relatve nnovaton cutoff s systematcally larger n each country s comparatve dsadvantage ndustry there s a non-monotonc relatonshp between the trade costs and the relatve evoluton of both cutoffs, whch s a measure of the process nnovaton actvty. When the trade costs are hgh, a reducton n trade costs decreases by more the nnovaton cutoff n the comparatve advantage ndustry, decreasng the relatve cutoff for ndustry 1 n the home country and ncreasng the relatve cutoff n the foregn country. However, when the trade costs are low enough we fnd the opposte result: A reducton n trade costs decreases the nnovaton cutoff more n the comparatve dsadvantage ndustry and consequently the relatve cutoff ncreases n the home country and decreases n the foregn country. These results suggest that a reducton n trade costs ncreases process nnovaton n both ndustres. When the trade costs are substantally hgh however, the reducton n trade costs favours the comparatve advantage ndustry and when the trade costs are low the trade cost reducton favours nstead the comparatve dsadvantage ndustry. The mplcatons for the evoluton of the average productvty across ndustres are straghtforward: A process of globalsaton nduces an ncrease n TFP n both ndustres provded that the trade 20

21 Innovaton cutoffs 1.01 Relatve Innovaton cutoffs Varable Trade Costs tau Fgure 5: Relatve Innovaton Cutoffs. Ths fgure dsplays the relatve nnovaton cutoffs Industry 1 vs Industry 2 for both the Home contnuous lne and the Foregn country dscontnuous lne as a functon of the trade costs. costs are not relatvely hgh we are n the parameter confguraton consstent wth ths equlbrum. Yet, globalsaton nduces TFP dvergence across sectors n countres relatvely less open to trade, but t nduces TFP convergence across sectors n countres relatvely more open to trade. Ths can ustfy the emprcal fndngs of Levchenko and Zhang Fgure 6 llustrates ths pont. Fgure 7 shows the effects of trade lberalsaton on product nnovaton n both ndustres. As t becomes apparent, product nnovaton s already larger n the comparatve advantage relatve to the comparatve dsadvantage ndustry n each of the countres. As trade costs are reduced the dfferences between product nnovaton across ndustres are enlarged: Product nnovaton becomes larger n the comparatve advantage ndustry for the home country and the same happens for the foregn country. Ths s the consequence of the fact that trade lberalsaton expands the opportuntes of the most productve frms n the comparatve advantage sector and the ncrease n the expected profts n ths sector promotes entry. In the comparatve dsadvantage sector domestc frms face dsproprotonate tougher competton, the average expected proft falls and consequently entrants shft away from the comparatve dsadvantage sector to the comparatve advantage one. A common measure of nnovatve actvty across ndustres s to look at R&D ntenstes. Fgure 8 dsplays the evoluton of the R&D ntenstes for both ndustres n the home country. Notce that R&D ntenstes ncrease n both ndustres as trade costs fall. Although the dfferences across ndustres are not substantally large there are stll dfferences n R&D ntenstes when 21

22 Mass of new varetes Productvty 1.15 Average Productvty Varable Trade Costs tau Fgure 6: Evoluton of the Average Productvty n Industry 1 Contnuous lne and Industry 2 Dscontnuous lne n the Home Country. 180 Product Innovaton Varable Trade Costs tau Fgure 7: Product Innovaton n the Home Country. Ths fgure dsplays the creaton of new varetes for dfferent varable trade costs for both ndustres, ndustry 1 contnuous lne and ndustry 2 dscontnuous lne. 22

23 Percent R&D Intenstes Varable Trade Costs tau Fgure 8: R&D ntenstes across ndustres n the home country. The fgure dsplays the R&D ntenstes for ndustry 1 contnuous lne and ndustry 2 dscontnuous lne for the home country. the economy s open to trade favourng the comparatve advantage ndustry n the home country. Ths s the consequence of the fact that n the comparatve advantage ndustry there s more product and process nnovaton. If we compare the relatve evoluton of R&D ntenstes n the home country contnuous lne and the foregn country dscontnuous lne we obtan a smlar message Fgure 9. The fgure dsplays a smlar functonal form to fgure 3. When the trade costs are large, a reducton n the trade costs ncreases the R&D ntensty by more n the comparatve advantage ndustry n each country. However, f the trade costs are suff cently small, the reverse happens and the R&D ntenstes ncreases by more n the comparatve dsadvantage ndustry. When trade costs are hgh further lberalsaton leads to dvergence n nnovatve actvty across ndustres but ths result s reversed f the trade costs are suff cently small. 6 Conclusons Ths paper ntroduces technology upgradng nto a standard model of trade, factor proportons and frm heterogenety to explore how factor endowments shape the mpact that trade has on nnovaton at an ndustry level. Our results suggest that factor endowments affect the dstrbuton of nnovatve actvty across ndustres wthn a country when the economy opens to 23

24 Relatve R&D ntenstes Relatve R&D ntenstes Varable Trade Costs tau Fgure 9: Relatve R&D ntenstes. Ths fgure dsplays Relatve R&D ntenstes Industry 1 vs Industry 2 for both the home contnuous lne and the foregn country dscontnuous lne. trade. More precsely, frms n the ndustry where the economy has a comparatve advantage undertake more product and process nnovaton. Ths renforces prevous results that outlne the mportance of the relatve factor endowments n generatng a rcardan comparatve advantage. In addton I explore how the evoluton of technology s affected by a reducton n trade costs under the presence of dfferences n factor endowments across countres and factor ntenstes across ndustres. The results suggest that the reducton n varable trade costs promotes technology upgradng and ncreases R&D ntenstes n both ndustres. However, the results establsh a non-monotonc relatonshp between the pattern of comparatve advantage and trade costs: When the trade costs are hgh, a reducton n trade costs pushes technology upgradng more n the comparatve advantage ndustry leadng to TFP dvergence across ndustres. However, when the trade costs are low enough, a reducton n trade costs pushes technology upgradng n the comparatve dsadvantage ndustry leadng to a process of TFP convergence across both ndustres. Ths paper could be extended n several drectons. Frst, the paper has consdered a smple process of technology upgradng where the degree of technology upgrade s fxed across frms. Generalsng the results to a rcher envronment n whch the frm can choose how much to upgrade s a promsng area for future research. Second, the paper could allow for a more complete and realstc de- 24

25 scrpton of the ntermedate nput sector and establshes the complementartes between mportng, exportng and nnovaton under the presence of dfferences n factor endowments. Both dmensons are currently takng part on my research agenda. 7 Appendx 7.1 Aggregaton n a Closed Economy Model Defne the followng productvty dstrbutons: { } gϕ Pr ϕ/ϕ ϕ D = µ D ϕ = 1 Gϕ D. f ϕ ϕ D 0 otherwse { } gϕ Pr ϕ/ϕ ϕ I = µ I ϕ = 1 Gϕ D. f ϕ ϕ I 0 otherwse the second one, that s more assocated to heterogenous frm models of process nnovaton wll be the ex-ante productvty dstrbuton of nnovators. We can show that paralell to the Meltz 2003 model the aggregaton property also holds n ths model. Ths allows to wrte the sectoral aggregate varables of the model as a functon of the average productvty of the sector. The rght average productvty of each ndustry s gven by the followng expresson: where: and ϕ = [ ϕ D + 1 Gϕ I 1 G ϕ D ϕ D = ϕ I = In equlbrum we must have that: [ θ 1 ϕ D ϕ µ ϕ dϕ ϕ I ϕ µ I ϕ dϕ EV = f e ω ] ϕ I ] Ths condton s known n the Meltz 2003 framework as the Free Entry condton FE. It can be rearranged to: nnovaton profts { EV = 1 Gϕ [ }}{ D δ π ϕ 1 Gϕ D + I ] θ r ϕi 1 f I = f 1 G ϕ D σ e ω } {{ } π 25

26 Compared to a standard model of frm heterogenety wthout technology upgradng, ths new FE condton exhbts a new element n the left hand sde of the equaton. More precsely, the second element captures the expected profts from technology upgradng whch are gven by the probablty of nnovate condtonal on survvng and the nnovaton rents. 8 Aggregaton n Costly Trade. Defne the followng productvty dstrbuton: { Pr ϕ/ϕ ϕ x = µ x ϕ = gϕ 1 Gϕ x f ϕ ϕ x 0 otherwse Ths s the condtonal productvty dstrbuton of exporters to country. Defne also the followng average productvty: ϕ x = ϕ µ x ϕ dϕ } ϕ x and consder as well the followng productvty averages: ϕ x = M x ϕ x + θ 1 M I ϕ I M x Then the aggregate prce ndex for each sector n each market wll reman as follows: P π x. 1 σ = [ M ] 1 σ p ϕ + M k x p k 1 σ ϕ x The expected profts from a potental entrant are gven by: EV = 1 Gϕ D δ π where π ϕ ϕ D = D ϕ D ϕ D + p x π ϕ x + p I 1 nnovaton profts {}}{ 1 σ θ Λ fx r ϕ I δf I f d σ } {{ } π 1 f D = π d and π ϕ ϕ x x = 1 f x = Compare to autarky ths equaton has two extra terms. The second term captures the profts from exportng. The thrd term captures the nnovaton ϕ x 26