Learning How To Export

Transcription

1 Learig How To xport Paul S. Segerstrom SS Igat Stepaok IfW Curret versio: September 6, 203 Abstract: I this paper, we preset a stadard quality ladders edogeous growth model with oe sigi cat ew assumptio, that it takes time for rms to lear how to export. We show that this model without Melitz-type assumptios ca accout for all the evidece that the Melitz (2003) model was desiged to explai plus much evidece that the Melitz model ca ot accout for. I particular, cosistet with the empirical evidece, we d that trade liberalizatio leads to a higher exit rate of rms, that exporters charge higher prices for their products as well as higher markups, ad that may large rms do ot export. We also d that trade liberalizatio promotes ecoomic growth ad that it has the opposite e ect of retardig ecoomic growth i a closely comparable growth model with Melitz-type assumptios. JL classi catio: F2, F3, F43, O3, O4. Keywords: Trade liberalizatio, heterogeeous rms, quality ladders, edogeous growth. Authors: Paul S. Segerstrom, Stockholm School of coomics, Departmet of coomics, Box 650, 383 Stockholm, Swede (-mail: paul.segerstrom@hhs.se, Tel: , Fax: ). Igat Stepaok, Kiel Istitute for the World coomy, Hideburgufer 66, D-2405 Kiel, Germay (-mail: igat.stepaok@ifw-kiel.de, Tel: ). We thak Frederic Robert-Nicoud, Rikard Forslid, Lars Ljugqvist ad Yoichi Sugita for helpful commets, as well as from semiar participats at the Stockholm School of coomics, the Kiel Istitute for the World coomy, the Stockholm-Uppsala Doctoral Studets Workshop i Uppsala, the NTR Jamboree i Toulouse, the Nordic Iteratioal Trade Semiars workshop i Helsiki, the uropea Trade Study Group meetig i Lausae, the Geeva Trade ad Developmet Workshop, the coometric Society uropea Meetig i Malaga, the Ceter for Market Studies ad Spatial coomics at the Higher School of coomics i St. Petersburg, the Royal coomic Society coferece at Royal Holloway, the ACS workshop at the Uiversity of Tartu, the Sprig Meetig of Youg coomists i Aarhus. Fiacial support from the Wallader Foudatio ad the Fritz Thysse Foudatio is gratefully ackowledged.

2 Itroductio The issue of which rms export is a importat oe ad has bee the topic of may recet papers i the iteratioal trade literature. The evidece idicates that eve i so-called export sectors, may rms do ot export their products. Research has cocetrated o two factors to explai the exportig behavior of rms: productivity di ereces amog rms ad the presece of xed costs to eterig foreig markets. It has bee widely documeted that persistet productivity di ereces exist amog rms operatig i the same idustry ad that the more productive ad larger rms ted to be the oes that export (see Berard ad Jese (999), Aw, Chug ad Roberts (2000) ad Clerides, Lach ad Tybout (998)). The presece of xed costs to eterig foreig markets has bee show i Berard ad Jese (2004a) ad Roberts ad Tybout (997). Furthermore, Pavcik (2002), Tre er (2004) ad Berard ad Jese (2004b) have documeted that trade liberalizatio leads to aggregate productivity gais. I a semial paper, Melitz (2003) developed the rst trade model that is cosistet with this empirical evidece. I this model, rms do R&D to develop ew product varieties ad the lear how costly it is to produce these ew products. Oce rms have leared what their margial costs of productio are, they decide whether or ot to icur the oe-time xed costs of eterig the local ad foreig markets. The xed cost of eterig the foreig market is assumed to be higher ad cosequetly, oly the most productive (lowest margial cost) rms choose to export their products. Whe trade liberalizatio occurs (the variable costs to trade fall), rms ear higher discouted pro ts from exportig ad more rms choose to become exporters. This leads to more competitio for all rms i their domestic markets ad raises the productivity level required for domestic productio. Thus, trade liberalizatio facilitates the etry of more productive ew rms ad give the exogeous death rate of old rms, leads to aggregate productivity gais. I this paper, we preset a model of iteratioal trade that yields Melitz-type results without the stadard Melitz-type assumptios. Istead of assumig that rms do R&D to develop ew product varieties, we study a quality ladders edogeous growth model where rms do R&D to develop higher quality products as i Grossma ad Helpma (99). Ad istead of assumig that rms lear their margial cost after developig a ew product, we assume that there is o ucertaity about the margial cost of a rm that iovates. Firm heterogeeity emerges aturally i our model because of ucertaity i R&D itself: some rms iovate more quickly tha other rms. Thus, at ay poit i time, di eret rms produce di eret quality products ad have di eret pro t levels. We show that this quality ladders growth model geerates the same empirically supported results about trade liberalizatio ad productivity as Melitz (2003) if it takes time for rms to lear how to export.

3 The model also has some importat properties that di eretiate it from Melitz (2003). First, the model has a edogeously determied rm exit rate that is a ected by trade liberalizatio. This edogeeity comes aturally, sice the model has a quality ladders structure. Firms do R&D to develop higher quality products, ad whe they succeed, they drive the previous quality leaders out of busiess. Iovatio is associated with a process of creative destructio, as was origially emphasized by Schumpeter (942). We show that trade liberalizatio (lowerig the variable costs to trade) leads to a icrease i the exit rate of rms. This result is cosistet with the evidece i Pavcik (2002), where it is reported that a period of trade liberalizatio i Chile ( ) was accompaied by a massive exit rate of rms. Gibso ad Harris (996) have similar digs for New ealad ad Gu, Sawchuk ad Reiso (2003) show a sigi cat icrease i the exit rate of rms as a result of tari cuts i Caada durig I Melitz (2003), a exogeous rm exit rate is assumed for rms that have already etered a market (sice there is o other reaso why rms would choose to go out of busiess) ad cosequetly trade liberalizatio has o e ect o the exit rate of rms that have already etered a market. Secod, the model implies that exporters charge higher prices o average for their products. There is evidece to support this result: Kugler ad Verhooge (2008) have foud that exporters charge higher prices usig Colombia data ad Hallak ad Sivadasa (2009) obtai the same result usig Idia ad US data. Theoretical models dealig with this empirical regularity either itroduce a secod source of rm heterogeeity beside productivity (Hallak ad Sivadasa 2009) or correlate a rm s margial cost with product quality (Baldwi ad Harriga 2007, Kugler ad Verhooge 2008). Neither approach is chose i this paper. xported products are cheaper i Melitz (2003), which is clearly at odds with the empirical evidece. Third, the model implies that exporters charge higher markups o average. Recetly evidece has emerged to support this result: lookig at Sloveia rm-level data for the period betwee 994 ad 2000, De Loecker ad Warzyski (202) d that exporters charge sigi catly higher markups o average compared to o-exportig rms. While several models have ow bee developed to explai why exportig rms charge higher markups, our model is distictive i that we ca explai this empirical regularity while assumig CS cosumer prefereces (ulike i Melitz ad Ottaviao (2008)), liear pricig (ulike i Sugita (20)) ad iceberg trade costs (ulike i Irarrazabal et. al. (202)). Feestra ad Ma (forthcomig) build a moopolistic competitio model with CS prefereces ad edogeous markups. I our model, there is less product market competitio associated with ew products ad rms that export ted to sell ew products, so these rms are able to charge higher markups (ad higher prices) tha o-exportig rms. All rms charge the same markup i Melitz (2003), which is clearly at odds with the empirical evidece. 2

4 Fourth, sice some rms lear to become exporters faster tha others, the model implies that at ay poit i time, there are some relatively large ad productive rms that do ot export their products. Berard et. al. (2003) ad Hallak ad Sivadasa (2009) have documeted that may large ad productive rms do ot export. The model does ot geerate a threshold productivity level like i Melitz (2003), where all the rms with productivity above the threshold export ad all the rms with productivity below the threshold do ot export. The Melitz model ca explai why may rms do ot export but it caot explai why may large rms do ot export. ve though this Schumpeteria growth model ca match several stylized facts, the questio remais, why develop a alterative to the Melitz model? Do we really eed a radically di eret model of iteratioal trade? Why does the Schumpeteria approach provide a fruitful etry ito the aalysis of rm-level trade data? These are importat questios ad the best aswer comes from cosiderig two recet papers that explore extesios of the Melitz model. I the origial 2003 paper, a very limited rage of issues are studied ad it is oly whe this model is exteded to study other issues that problems with the Melitz model become apparet. The rst paper by Gustafsso ad Segerstrom (200) exteds the Melitz model ito a model of ecoomic growth (the origial model has zero ecoomic growth). They show that, except whe the rate of ecoomic growth is very low, symmetric bilateral trade liberalizatio i this two-coutry model retards ecoomic growth ad makes all cosumers i both coutries worse o i the log ru (Theorem 3). This aalytically derived result is illustrated umerically i sectio 3. We show that whe parameter values for this Melitz model with ecoomic growth are carefully chose to satisfy various stylized facts [icludig a 2% steady-state rate of ecoomic growth, cosistet with the evidece i Joes (2005)], a 30% reductio i trade costs lowers log-ru cosumer welfare by % (Table 2). Whe we do the same exercise for the Schumpeteria growth model, choosig parameter values to satisfy the same stylized facts, we d that a 30% reductio i trade costs raises log-ru cosumer welfare by 48% (Table ). The gais from trade liberalizatio are much larger i our Schumpeteria growth model tha i this closely comparable growth model with Melitz-type assumptios. The secod paper by Segerstrom ad Sugita (203) exteds the Melitz model ito a model with multiple idustries (the origial model has just oe idustry). Ivestigatig the log-ru impact of the Caada-USA free trade agreemet o Caadia maufacturig idustries, Tre er (2004) estimated that the Caadia tari cuts icreased idustrial productivity by 5% i the most import-competig idustries (the idustries that experieced the biggest tari cuts). Doig the same exercise usig the calibrated Melitz model with multiple idustries, Segerstrom ad Sugita (203) show that Caadia tari cuts should 3

5 have decreased productivity i the most import-competig idustries by 0.3%. There is a big di erece betwee what Tre er ds empirically (+5%) ad what the Melitz model implies (-0.3%). Tre er s paper ad other closely related empirical studies are routiely cited by leadig scholars as evidece for the Melitz model [Berard, Jese, Reddig ad Schott, 2007, 202; Helpma, 20; Reddig, 20; Melitz ad Tre er, 202; Melitz ad Reddig, 202] but these studies actually represet evidece agaist the Melitz model. Not oly does the Melitz model predict productivity gais from trade liberalizatio that are much too small, it actually gets the sig wrog by predictig that idustrial productivity should have decreased i the idustries with the biggest tari cuts. Segerstrom ad Sugita (203) thus provide further motivatio for explorig alteratives to the Melitz model. The Schumpeteria approach is worth explorig because it has the potetial to geerate much larger ad more realistic gais from trade liberalizatio. The rest of this paper is orgaized as follows: I Sectio 2, we preset our model of iteratioal trade without Melitz-type assumptios. We show that this model has a steady-state equilibrium ad derive ve equilibrium properties (Propositios through 5). I Sectio 3, we solve the model umerically for plausible parameter values to obtai the e ects of trade liberalizatio o ecoomic growth ad welfare. I Sectio 4, we o er some cocludig commets ad i the Appedix, we preset calculatios doe to solve our model i more detail. 2 The Model 2. Overview The model preseted i this paper is essetially a two coutry versio of the Segerstrom (2007) quality ladders edogeous growth model with the ew assumptio that it takes time for rms to lear how to export. There are two symmetric coutries, Home ad Foreig. I both coutries, there is a costat rate of populatio growth ad the oly factor labor is ielastically supplied. Cosumers have costat elasticity of substitutio (CS) prefereces. Workers are employed i a productio sector ad i a R&D sector. There is a cotiuum of di eretiated products idexed by! 2 [0; ]. ach product! has di eret possible quality levels deoted by j. Higher values of j deote higher quality ad j is restricted to takig o iteger values. Firms are ivolved i R&D races to discover the ext higher quality product ad whe a rm succeeds, it replaces the previous icumbet who was sellig product! as a moopolist. Whe the state-of-the-art quality product is j, the ext quality level to be discovered is j +. Over time each product is pushed up its quality ladder. While holdig the patet for the Alteratively stated, if Tre er (2004) had foud that productivity decreases slightly i the Caadia idustries that experieced the biggest tari cuts, that would have bee evidece i support of the Melitz model. Istead, he foud a big productivity icrease. 4

6 state-of-the-art quality of product!, a rm starts to sell oly i its local market. To become a exporter it must ivest i learig how to eter the foreig market. ach rm operates util a higher quality versio of its product! is discovered by aother rm from its home market. No-exporters do ot have a icetive to improve o their ow products. xporters do ot have a icetive uder certai parameter coditios that we assume hold. As a result, oly followers do iovative R&D. We solve the model for a symmetric steady-state equilibrium. 2.2 Cosumers ad Workers The ecoomy has a xed umber of households. They provide labor, for which they ear wages ad save by holdig assets of rms that egage i R&D. ach household grows at the rate > 0, hece the supply of labor i the ecoomy at time t ca be represeted by L t = L 0 e t. ach household is modelled as a dyastic family that maximizes preset discouted utility U R 0 e ( )t l [u t ] dt, where the cosumer subjective discout rate satis es >. The static utility of a represetative cosumer de ed over all products available withi a coutry at time t is u t " 0 X j d(j;!; t)! d! j # : () This is a quality-augmeted Dixit-Stiglitz cosumptio idex, where d(j;!; t) deotes the quatity cosumed of a product variety! of quality j at time t, > is the size of each quality improvemet ad the product di eretiatio parameter 2 (0; ) determies the elasticity of substitutio betwee di eret products >. Sice j is icreasig i j, () captures i a simple way the idea that cosumers prefer higher quality products. Utility maximizatio follows three steps. The rst step is to solve the withi-variety static optimizatio problem. Let p(j;!; t) be the price of variety! with quality j at time t. Households allocate their budget withi each variety by buyig the product with the lowest quality-adjusted price p(j;!; t)= j. To break ties, we assume that whe quality-adjusted prices are the same for two products of di eret quality, each cosumer oly buys the higher quality product. We will from ow o write p(!; t) ad j(!; t) to deote the price ad quality level of the product withi variety! with the lowest quality-adjusted price. Demad for all other qualities is zero. The secod step is to d the demad for each product! give idividual cosumer expediture c t that maximizes idividual utility u t at time t. Solvig this problem yields 5

7 the demad fuctio d(!; t) = q(!; t)p(!; t) c t, (2) where d(!; t) is demad for the product withi variety! with the lowest quality-adjusted price, q(!; t) j(!;t) is a alterative measure of product quality, is a quality-adjusted price idex. P t 0 Pt q(!; t)p(!; t) d! > ad The third step is to solve for the path of cosumer expediture c t over time that maximizes discouted utility subject to the relevat itertemporal budget costrait. Solvig this itertemporal problem gives the stadard uler equatio _c t =c t = r t, implyig the idividual cosumer expediture grows over time oly if the iterest rate r t exceeds the subjective discout rate. A higher iterest rate iduces cosumers to save more ow ad sped more later, resultig i icreasig cosumer expediture over time. Sice _c t =c t must be costat over time i ay steady-state (or balaced growth) equilibrium, the iterest rate must be costat over time ad from ow o, we will refer to the iterest rate as r. A atural measure of productivity at time t is real output c t L t =P t divided by the umber of workers L t, or c t =P t. But c t =P t equals u t as Dixit ad Stiglitz (977) have show. Thus measurig productivity i this model is equivalet to measurig the static utility level of the represetative cosumer. 2.3 Product Markets We solve the model for a symmetric steady-state equilibrium where half of all products! origiate from Home ad the other half from Foreig. very product! will have a versio of it sold i both markets. Home origiatig products will either be exported to Foreig or produced there by Foreig s competitive frige. We assume that oce a better versio j of a product origiatig from Home is discovered, the blueprit of its previous versio j becomes commo kowledge i both Home ad Foreig, ad ca be produced by the competitive frige i Foreig. Productio by the competitive frige i Foreig cotiues util the ew icumbet i Home lears how to export, starts to sell that product of quality j i Foreig ad drives the competitive frige there with its j versio out of busiess. Thus some of the Home origiatig products havig a more advaced versio sold i Home ad with correspodig assumptios for the Foreig coutry, some of the Foreig origiatig products will have a oe step higher quality versio sold i Foreig. The productio of output is characterized by costat returs to scale. It takes oe 6

8 uit of labor to produce oe uit of a good regardless of product quality. The wage rate is ormalized to oe ad rms are price-setters. ach rm produces ad sells a uique product!. Pro ts of a producer deped o what it sells domestically ad what it sells abroad if it exports. We assume iceberg trade costs: a exporter eeds to ship > uits of a good i order for oe uit to arrive at the foreig destiatio. Let L (!; t) ad (!; t) deote pro ts from local sales ad from exportig, respectively, for a rm based at Home. d(!; t)l t deote demad for product! i the Home coutry. Kowig that lower quality products ca be produced by the competitive frige, the pro t-maximizig price that quality leaders ca charge at home ad abroad is the limit price if < =, where = is the moopoly price. If =, the iovatios are drastic ad rms d it optimal to charge the moopoly price = at home ad (for =) the moopoly price = abroad. Quality leaders disregard the competitive frige whe the iovatio step is large eough. We will assume that iovatios are ot drastic ( < =), which traslates ito quality leader rms chargig the limit price p L = p = both at home ad abroad. This price does ot deped o the quality level of a particular product relative to that of other products. Pro ts are the di erece betwee price ad margial cost times demad d(!; t)l t for product! at Home, that is, L (!; t) = ( )d(!; t)l t. Let R q(!; t)d! be the average quality 0 of all products sold i Home ad y(t) c t =P t Let be per capita demad for a product of average quality sold by a leader i Home. Substitutig for demad, we ca rewrite pro ts from sellig locally as q(!; t) L (!; t) = ( ) y(t)l t : Pro ts deped o the quality q(!; t) of the product sold. This depedece o the quality of the product comes from the demad fuctio, which is essetial for the existece of rm heterogeeity. Di eret product quality levels result i di eret pro ts. I compariso to Melitz (2003) ad Haruyama ad hao (2008) where heterogeeity of pro ts comes from di erig margial costs, we obtai heterogeeity from the reveue side of pro ts. If we had assumed a Cobb-Douglas utility fuctio ( = ) which results i uit-elastic demad, we would ot have that heterogeeity because pro ts would ot deped o product quality (remember that i the de itio q(!; t) j(!;t) ). I our model we will have a edogeous distributio of rm productivities ad pro ts that is geerated by the R&D process of creative destructio. The margial cost for sellig abroad is >. Assumig that the limit price rms ca charge is higher tha the iceberg trade cost ( > ), we ca express pro ts from exportig 7

9 as q(!; t) (!; t) = ( ) y(t)l t : The pro t ow from exportig is a icreasig fuctio of the per-uit pro t margi y(t)l t., the relative quality of the rm s product q(!; t)= ad the market size measure Sice it becomes commo kowledge how to produce a good after a higher quality versio is discovered, ay rm ca produce ad sell it. It follows that competitive frige rms price at margial cost ad ear zero pro ts. Therefore all products are either sold by leaders at price or sold by the competitive frige at price. 2.4 R&D Races ad the R&D Cost to Becomig a xporter. There is two R&D activities described by two distict R&D techologies: ivetig higher quality levels of existig products ad learig how to export. Labor is the oly iput used i both R&D activities. There are quality leaders, rms that hold the patet for the most advaced product withi a certai product variety ad followers, rm that try to improve upo the products that are sold by leaders. We solve for a equilibrium where Home rms do ot improve o products origiatig from Foreig ad Foreig rms do ot improve o products origiatig from Home. Leaders that produce for the local market do ot try to improve o their ow products. Give the same R&D techology as that of followers, they have a smaller icetive to iovate i compariso to followers. A o-exportig leader has strictly less to gai L (j + ) L (j) from improvig o its ow product (omittig! ad t for brevity) compared to a follower who would gai L (j + ), hece leaders ca ot successfully compete for R&D acig with followers. If a leader is a exporter, the gai will be L (j + ) + (j + ) L (j) (j). That gai is lower tha that of a follower L (j + ) if < 2. Give, for exportig leaders ot to have a icetive to improve o their ow products, we must have < 2. Limit pricig requires < = ad for rms to be able to exportrequires <. Hece we ca write our al assumptio o as < < mi =; 2. This guaratees that exportig leaders do ot try to improve their ow products. Followers are the oes that ivest i quality improvig R&D ad oce they discover a state-of-the-art quality product, they take over the local market from the previous leader. Let I i deote the Poisso arrival rate of improved products attributed to follower i s ivestmet i R&D. While we omit! as a subscript for brevity, oe should keep i mid that every rm s iovatio itesity is product variety speci c. The iovative R&D techology for 8

10 follower rm i is give by I i = A F l i j(!;t) ; where l i is the labor devoted to R&D by the follower, < is a R&D spillover parameter, ad A F > 0 is a R&D productivity parameter. The R&D spillover parameter ca be positive or egative but the restrictio < is ecessary to esure that the model has a ite equilibrium rate of ecoomic growth. The term j(!;t) i the R&D techology captures the idea that as product quality icreases over time ad products become more complex, further iovatio becomes icreasigly di cult. Veturii (202) ds that the R&D-drive growth models with the best empirical support assume icreasig R&D di culty. The returs to iovative R&D are idepedetly distributed across rms, across product varieties ad over time. Summig over all rms, the Poisso arrival rate of improved products attributed to all ivestmet i R&D withi a particular product variety! is give by I X i I i = A F l j(!;t) where l P i l i is the total labor devoted to iovative R&D. We solve the model for a equilibrium where the product iovatio rate I does ot vary across product varieties! 2 [0; ]. The secod R&D activity is that of leaders learig how to become exporters. This activity ca be see as learig to comply with foreig market regulatios, establishig a distributio etwork, ad more geerally, payig for the iformatio eeded to adapt to a less familiar eviromet. Muedler ad Molia (2009) provide evidece that rms ivest whe preparig to eter foreig markets. By hirig workers with previous experiece i exportig, rms icrease their probability of becomig exporters. The ivestmet each rm eeds to make i R&D labor to eter the foreig market is a type of xed cost of market etry, a commo feature i the heterogeous rm literature. The xed cost here is stochastic ad rms with more sophisticated products eed to ivest more i order to achieve the same arrival rate of the kowledge o how to eter the foreig market. Leaders ivest l uits of labor i a R&D techology which makes them exporters with a istataeous probability (or Poisso arrival rate) I = A l j(!;t)! ; (3) 9

11 where A is a R&D productivity parameter, 2 (0; ) measures the degree of decreasig returs to leader R&D expediture, ad is the same R&D spillover parameter. The term j(!;t) appears agai i the learig-to-export techology ad captures the idea that it is more di cult to lear how to export a more advaced product. There are four types of rms that sell products withi the Home coutry. First, there are Home leaders who export their products. The measure of product varieties produced by these rms is m L. Secod, there are Home leaders who do ot export their products. The measure of product varieties produced by these rms is m LN. Third, there are Foreig exporters. The measure of product varieties produced by these rms is m F. Fourth, there are competitive frige rms. If a better versio of a product is developed abroad ad the ew Foreig leader has ot yet leared how to export this product, the the ext lower quality versio of that product is produced at Home by competitive frige rms. The measure of product varieties produced by these rms is m CF. Sice all product varieties from both coutries are available to the cosumers i each coutry ad there is a measure oe of product varieties that cosumers buy, it follows that m LN + m L + m F + m CF = holds. Due to symmetry, the measure of product varieties produced by Home exporters equals the measure of product varieties produced by Foreig exporters, that is, m L = m F. Furthermore, half of all product varieties are produced by Home leaders at Home ad half of all product varieties are produced by Foreig leaders at Foreig, so m LN + m L = also holds. 2 Figure below describes what happes with a product sold iitially by a o-exportig rm. The state-of-the-art quality is produced by the o-exportig rm ad the competitive frige produces the ext lower quality versio of the same product abroad. Leaders do ot improve o their ow products, oly followers do. A o-exported product is improved o by some follower at the iovatio rate I (lower left arrow). Also, the curret o-exportig leader lears how to become a exporter at a rate I (lower middle arrow). Whe the product begis to be exported, the exportig leader takes over the foreig market. Products sold by exporters are state-of-the-art quality i both coutries. The competitive frige kows how to produce a oe step lower quality versio, but the exportig leader prices i such a way that it drives the competitive frige out of busiess. The exportig leader sells its product both at home ad abroad util its product is improved o by a follower at home, which happes at the rate I (upper middle arrow). The ew leader takes over the home market ad sells the better versio there, whereas the older versio is sold abroad at margial cost. The ew icumbet at home eeds to lear how to export i order to take over the foreig 0

12 market. Figure : Product Dyamics. 2.5 Bellma quatios ad Value Fuctios Firms maximize their expected discouted pro ts. Followers solve a stochastic optimal cotrol problem with a state variable j(!; t), which is a Poisso jump process of magitude oe. No-exportig leaders maximize over the itesity of R&D dedicated to learig how to export, where the kowledge arrives at a certai Poisso rate after which the rm becomes a exporter. The oly decisio exporters make is over what prices to charge i both markets. Other tha that, they exploit the market power they have util a better versio of their product! is discovered by a follower. Free etry ito iovative R&D races ad costat returs to scale i the R&D techology together imply that followers have zero market value. Let v F (j) = 0 be the value of a follower whe the curret state-of-the-art quality is j. All followers have the same zero value regardless of whether they are targetig exporters ad o-exporters. Let v LN (j) be the value of a leader that does ot export (omittig! ad t from the value fuctio for otatioal simplicity) ad let v L (j) be the value of a leader that does export. The Bellma equatio for follower rm i is rv F (j) = max li l i +I i v LN (j+). The follower ivests l i i R&D ad becomes a o-exportig leader with a istataeous probability I i. Substitutig for I i from the R&D techology equatio ad solvig gives the followig

13 expressio for the value of a o-exportig leader: v LN (j) = j(!;t) Q t A F : The value of the rm icreases i the quality of the product for which it holds a patet. The Bellma equatio for a o-exportig leader is give by rv LN (j) = max l L (j) l Iv LN (j) + I (v L (j) v LN (j)) + _v LN (j): (4) This equatio states that the maximized expected retur o the o-exportig leader s stock must equal the retur o a equal-sized ivestmet i a riskless bod rv LN (j). The retur is equal to a stream of pro ts L (j) mius ivestmet i R&D to eter the foreig market l, plus the arrival rates ad respective chages i value attributed to beig overtake by a follower Iv LN (j) ad becomig a exporter I (v L (j) v LN (j)), plus the capital gai term _v LN (j) because the value of the rm ca chage over time. No-exportig leaders make a decisio over l, how much to ivest i R&D to lear how to export. The Bellma equatio for a exportig leader is simpler i the sese that exportig rms do ot ivest i R&D. They oly exploit their quality advatage over other rms ad the kowledge how to export. They face the risk of beig replaced by a rm that lears how to produce a higher quality versio of the same product ad thus, the Bellma equatio for a exportig leader is rv L (j) = L (j) + (j) Iv L (j) + _v L : The value of a exportig leader is derived from (4), after substitutig for v LN (j) ad for l from (3). We obtai where ( v L (j) = j(!;t) Q t I + ; (5) A A F )= > 0. The value of a exporter icreases i the quality of the product it produces ad is also positively related to the rate at which rms become exporters I. 2.6 Fidig the Labor ad R&D quatios To solve the model, it turs out that a key variable is relative R&D di culty x(t) Q t =L t. L t is the size of the market ad Q is a icreasig fuctio of the average quality of all t available products. As this average quality icreases over time, iovatio becomes relatively more di cult. O the other had, as the size of the market icreases, there are more resources 2

14 that ca be devoted to iovatio. We will show that solvig the model reduces to solvig a simple system of two liear equatios i two ukows, where the two ukows are relative R&D di culty x(t) ad the cosumer demad measure y(t) c t =P. The two equatios are the labor equatio that describes whe there is full employmet of labor ad the R&D equatio that is derived from the pro t-maximizig decisios of rms. To d the labor equatio, we eed to rst itroduce some terms coected with product quality. Give that R q(!; t)d! is the average quality of all products sold i Home, let 0 Q L R m L q(!; t)d! be a quality idex of products produced by Home leaders that export, Q LN R m LN q(!; t)d! be a quality idex of products produced by Home leaders that do ot export, Q F R m F q(!; t)d! be a quality idex of products produced by Foreig exporters, ad Q CF R m CF q(!; t)d! be a quality idex of products produced by the Home competitive frige. These quality idexes are all fuctios of time but this is omitted to simplify otatio. They obviously satisfy = Q L + Q LN + Q F + Q CF : (6) Also let q L Q L =, q LN Q LN =, q F Q F = ad q CF Q CF =. ach of these terms represets the quality share of a particular group of rms i the total quality idex, where the share is determied ot oly by the average quality withi the group but also by the measure of rms costitutig the group. The quality shares satisfy = q L + q LN + q F + q CF ad must be costat over time i ay steady-state equilibrium. Give the symmetry coditio Q L = Q F, it follows that t = 2q L + q LN + q CF : (7) All labor i the Home coutry is fully employed i equilibrium ad is divided betwee employmet i the productio sector L P (t) ad employmet i the R&D sector L R (t). Startig with L P (t), demad by Home cosumers for a product sold by a Home leader is d(!; t)l t = q(!;t) c t Pt L t = q(!;t) y(t)l t. Demad for a exported product sold abroad is also d(!; t)l t, but d(!; t)l t eeds to be shipped, ad hece q(!;t) Q(t) y(t)l t is produced. Demad for a product produced by the competitive frige is d(!; t)l t = q(!;t) c t Pt L t = q(!;t) y(t) L t, where we multiply by to take ito cosideratio that the competitive frige prices at 3

15 margial cost, which is oe. Thus, total productio employmet L P (t) ca be expressed as L P (t) = d(!; t)l t d! + m L +m LN d(!; t)l t d! + m L d(!; t)l t d!: m CF Substitutig ad simplifyig gives L P (t) = (q L + q LN + q L + q CF ) y(t)l t : To solve for employmet i the R&D sector, we use the R&D techologies for quality iovatio ad learig how to export. Rearragig terms yields l = Ij(!;t) Q t A F = q(!; t)q t I=A F ad l = I= j(!;t) = q(!; t)q Q t A t I = =A : For half of all product varieties (m L +m LN = =2), Home follower rms do iovative R&D ad for varieties with a Home o-exportig leader, these leaders also do R&D to lear how to export. Thus, total R&D employmet L R (t) ca be expressed as ad after substitutig for l ad l, we obtai L R (t) = l d! + m L +m LN l d! m LN L R (t) = (q L + q LN )I=A F + q LN I = =A x(t)l t : Full employmet of labor implies that L t = L P (t) + L R (t). Dividig both sides by L t, we obtai the labor equatio: = (q L + q LN + q L + q CF ) y + (q L + q LN )I=A F + q LN I = =A x: (8) I order for equatio (8) to hold i steady state equilibrium, it must be the case that x(t) ad y(t) are both costat over time, ad therefore we will write them as x ad y. Oce we have solved for the equilibrium values of I, I, q L, q LN ad q CF, the labor equatio ca be graphed as a dowward slopig lie i (x, y) space (as illustrated i Figure 2). The iterpretatio of the slope is that whe R&D is relatively more di cult (higher x), more resources must be devoted to R&D activities to maitai the steady-state iovatio rate 4

16 ad less resources ca be devoted to producig goods, so cosumer demad y must be lower. To d the R&D equatio, we substitute ito (4) for l usig (3), for v LN (j) ad for v L (j) v LN (j) usig (5). This results i the R&D equatio r + I + _ = ( y )A F x + A F I = : (9) A Oce we have solved for the steady-state equilibrium values of I, _ = ad I, the R&D equatio ca be graphed as a upward slopig lie i (x, y) space (as illustrated i Figure 2). The iterpretatio of the slope is that whe R&D is relatively more di cult (higher x), cosumer demad y must be higher to justify the higher R&D expeditures by rms. 2.7 Quality Dyamics To determie the steady-state equilibrium iovatio rate I, we must rst study the dyamics of the di eret quality idexes. Sice x is costat over time i ay steady-state equilibrium, it follows from the de itio x Q t =L t that _x=x = ( ) Q _ t = = 0 ad Q _ t = = =( ). Also sice q L, q LN ad q CF are all costat over time i ay steady-state equilibrium, it follows that _q L =q L = _ Q L =Q L _ = = 0, ad correspodig calculatios yield _ = _ Q L Q L = _ Q LN Q LN = _ Q CF Q CF = : (0) I ay steady-state equilibrium, the quality idexes of all types of rms must grow at the same rate. The dyamics of Q L R m L j(!;t) d! is give by the di eretial equatio _Q L = j(!;t) I d! m LN m L j(!;t) Id!; where the rst itegral captures that o-exported products become exported products at the rate I, ad the secod itegral captures that exported products become o-exported products whe iovatio occurs, which happes at the rate I. Usig the de itios of the 5

17 quality idexes ad dividig by Q L, we obtai the growth rate of Q L : _Q L =Q L = (q LN =q L )I I: Proceedig i a similar fashio, the dyamics of Q LN is give by the di eretial equatio _Q LN = m LN j(!;t)+ j(!;t) Id! j(!;t) I d! + j(!;t)+ Id!; m LN m L where the rst itegral captures that o-exported products are improved o at the rate I, the secod itegral captures that o-exporters become exporters at the rate I ad the third itegral captures that exported products are improved upo at the rate I, after which these products become o-exported. This time dividig by Q LN, we obtai _Q LN =Q LN = ( )I I + (q L =q LN )I: The quality dyamics for the competitive frige at Home is depedet etirely o the dyamics of rms i Foreig. The i ow of product varieties ito the Home competitive frige is from all Foreig exporters whose products are improved upo at the rate I by Foreig followers. The out ow is from the group of Foreig o-exporters who lear to become exporters at the rate I ad take back the market of a product previously produced by the Home competitive frige. Thus, the dyamics of Q CF is give by the di eretial equatio _Q CF = j(!;t) Id! j(!;t) I d!: m L m CF Usig the de itios of the quality idexes ad dividig by Q CF, we obtai _Q CF =Q CF = (q L =q CF )I I : Give (0), we ca solve the two equatios _ Q L =Q L = (q LN =q L )I I = =( ) 6

18 ad _ Q LN =Q LN = ( )I I + (q L =q LN )I = =( ) for I ad the combie them to elimiate the I term. This yields a quadratic equatio i q LN =q L that has oly oe positive solutio. Pluggig this positive solutio back ito (q LN =q L )I I = =( ), we obtai the uique steady-state equilibrium iovatio rate: I = ( ) ( ) : The iovatio rate I depeds i the log ru o the populatio growth rate > 0, the R&D di culty growth parameter > ad the itertemporal R&D spillover parameter <. Idividual researchers become less productive with time ( > ) ad what keeps the iovatio rate steady i the log ru is the growig umber of people employed i the R&D sector, which is made possible by positive populatio growth ( > 0). Havig solved for the steady-state iovatio rate I, straightforward calculatios lead to the steady-state variety shares q L, q LN ad q CF. We obtai that q L = 2 + I I + I( I q LN = q L I I q CF = q L I( ) + I I ) + I All three variety shares are uiquely determied oce we have solved for the steady-state rate at which rms lear how to export I. 2.8 Fidig I Usig the symmetry coditio Q F = Q L, the quality-adjusted price idex P t satis es Pt = R q(!; t)p(!; 0 t) d! = Q L + Q LN + Q F + Q CF = (2q L + q LN + q CF ). It follows that Pt must grow at the same rate =( ) as i ay steady-state equilibrium. We have already established that y c t =P is costat over time, so it immediately follows that cosumer expediture c t must be costat over time. Thus, the cosumer optimizatio coditio _c t =c t = r implies that r = holds. Usig the Bellma equatio for a exportig leader, substitutig for L (j) ad (j), t 7

19 for v L (j) usig (5) ad the substitutig ito the R&D equatio (9) for y=x, we obtai A F = 2 I + + A A F I A r + I + _ = : () Takig ito accout that r =, I =, ad Q _ ( )( ) t = =, the RHS of () is a mootoically icreasig fuctio of I. Thus equatio () uiquely determies the steady-state equilibrium value of I. Furthermore, sice the RHS decreases whe falls holdig I xed, I must icrease to restore equality i (). We have established oe of the cetral results i this paper: Propositio Trade liberalizatio iduces a higher level of ivestmet i learig how to export ( # =) I "). This result is quite ituitive. Whe the barriers to trade are decreased, it becomes more pro table to be a exporter. Therefore rms ivest more i learig how to export. 2.9 The Steady State quilibrium Give that we have solved for the steady-state equilibrium values of I, I, q LN, q L ad q CF, the labor equatio (8) ca be graphed as a dowward slopig lie i (x, y) space. Give that we have also solved for the steady-state equilibrium values of r ad Q _ t =, the R&D equatio (9) ca be graphed as a upward slopig lie i (x, y) space. Both equatios are illustrated i Figure 2 ad keepig i mid that x ad y are costat i steady state, the uique itersectio of these two equilibrium coditios at poit A determies the steady- 8

20 state values of relative R&D di culty x ad cosumer demad y. Figure 2: The Steady-State quilibrium. We ca determie the rate of ecoomic growth i this steady-state equilibrium by studyig how cosumer utility chages alog the equilibrium path. Substitutig (2) ito () ad usig y c t =P t to substitute for c t, we obtai u t = y Q t (2qL + q LN ) + q CF : (2) Takig logs ad di eretiatig the above expressio with respect to time gives the utility growth rate g u _u t =u t = Q _ t =, which after substitutig for Q _ t = yields g u _u t =u t = ( )( ) : (3) The utility growth rate is proportioate to the populatio growth rate. Sice static utility u t is proportioal to cosumer expediture c t ad static utility icreases over time oly =( ) =( ) because Qt icreases, Qt is a measure of the real wage at time t. Thus the real wage growth rate is the same as the utility growth rate ad g u also represets the rate of ecoomic growth i this model. quatio (3) implies that public policy chages like trade liberalizatio (a decrease i ) 9

21 have o e ect o the steady-state rate of ecoomic growth. I this model, growth is semiedogeous. We view this as a virtue of the model because both total factor productivity ad per capita GDP growth rates have bee remarkably stable over time i spite of may public policy chages that oe might thik would be growth-promotig. For example, plottig data o per capita GDP (i logs) for the US from 870 to 995, Joes (2005, Table ) shows that a simple liear tred ts the data extremely well. Further evidece for equatio (3) is provided by Veturii (202). Lookig at US maufacturig idustry data for the period , he ds that semi-edogeous growth models (where public policies do ot have log-ru growth e ects) have better empirical support tha fully-edogeous growth models (where public policies have log-ru growth e ects). For the measures m LN ad m L to remai costat i steady-state equilibrium, the out ow of rms from m LN must be equal to the i ow, that is, m LN I = m L I. Substitutig for m LN usig m LN + m L = yields m 2 2 L I = m L I, from which it follows that m L = I =2 I+I ad m LN = I=2 I+I. The last two equatios show that a icrease i I leads to a icrease i the measure of products purchased from exportig leaders m L ad a decrease i the measure of products purchased from o-exportig leaders m LN. 2.0 Firm xit Whe a rm iovates ad becomes a ew quality leader, oe ca say that the birth of a ew rm has occurred. This birth is also associated with death, as the previous quality leader stops producig ad i a sese dies. We de e the rm exit rate or death rate D as the rate at which rms die i the Home coutry. To calculate the rm exit rate, we eed to rst specify how may rms produce a product whe it is produced by the competitive frige. Whe it becomes commo kowledge how to produce a product variety, ay rm ca produce it. We solve for a equilibrium where two rms actually do. Give that rms are price-setters, two rms is eough to geerate a perfectly competitive outcome with zero ecoomic pro ts (the Bertrad equilibrium), so there is o icetive for other rms that kow how to produce a product to eter ad start producig. This is a model with a i ite umber of equilibria. I markets where rms i the competitive frige produce, the umber of producig rms ca be two, three or oe billio. Give that the equilibrium price equals margial cost ad producig rms ear zero pro ts, competitive frige rms are idi eret betwee producig ad ot producig. However, all the equilibria look the same from the perspective of cosumers ad thus we choose to focus o oe particular equilibrium, the oe where two rms from the competitive frige produce whe a product is produced by the competitive frige. If oly oe competitive frige rm produces a product, the this rm maximizes its pro ts by chargig a price greater tha 20

22 margial cost. Other rms the have a icetive to eter ad charge a slightly lower price, so there is o equilibrium with just oe rm from the competitive frige producig. The rm exit rate is the give by D Im LN + Im L + (I + I)2m CF m LN + m L + 2m CF : For the measure of product varieties m LN +m L where there are Home quality leaders, Home iovatio occurs at the rate I ad results i the death of these rms. For the measure of product varieties m CF where there is a Foreig o-exportig leader ad a Home competitive frige (cosistig of two producers), both Foreig iovatio (which occurs at rate I) ad Foreig learig how to export (which occurs at rate I ) result i the death of the curret Home producers. Usig m L = I =2 I+I ad m LN = I=2 I+I steady-state rm exit rate = m CF, straightforward calculatios yield the D = 3I (I + I ) 3I + I : D =@I = 6I 2 = (3I + I ) 2 > 0, it follows that trade liberalizatio leads to a higher rate at which rms die, sice trade liberalizatio icreases I. We have established Propositio 2 Trade liberalizatio leads to a higher rm exit rate ( # =) D "). Pavcik (2002) studies a period of trade liberalizatio i Chile ( ) ad reports that it coicided with a massive exit rate of rms. Gibso ad Harris (996) preset evidece of icreasig rm exit as a result of trade liberalizatio i New ealad. Gu, Sawchuk ad Reiso (2003) show a sigi cat icrease i the exit rate of rms i 8 Caadia maufacturig idustries as a result of tari cuts. Iitially lower exit rates icreased after trade liberalizatio policies were itroduced. This paper presets the rst model that is cosistet with this evidece. Haruyama ad hao (2008) preset aother quality ladders growth model with edogeous rm turover but trade liberalizatio does ot a ect the rm exit rate i their setup. I Melitz (2003), a exogeous rm exit rate is assumed (sice there is o other reaso why rms would choose to go out of busiess) ad cosequetly trade liberalizatio has o e ect o the exit rate of rms that have already etered a market. 2. Comparig xporters ad No-xporters We ow examie whether exportig rms charge higher prices tha o-exportig rms. The average price charged by exportig rms is P m L+m F m L +m F =. The average price 2

23 charged by o-exportig rms is P N m LN +2m CF m LN +2m CF have established ad thus P > P N always holds. We Propositio 3 xportig rms charge higher prices o average tha o-exportig rms. A umber of recet papers poit out the correlatio of export status with prices charged by rms. Kugler ad Verhooge (2008) use data from Colombia to compare output prices (what rms charge o their home markets) ad export status of maufacturers. They d a positive relatioship, that is, exporters charge higher prices. Hallak ad Sivadasa (2009) also d a positive relatioship usig Idia ad U.S. data. I our model, exporters charge the price ad this is higher tha the average price of o-exporters, which is a covex combiatio of the price charged by o-exportig leaders ad the price oe charged by competitive frige rms. The Melitz (2003) model caot accout for the above-metioed evidece regardig the pricig behavior of exporters ad o-exporters. I Melitz (2003), it is the rms that charge the lowest prices that export. The rms that charge the lowest prices are the highest productivity rms ad the highest productivity rms are the rms that export. Baldwi ad Harriga (2007) develop a alterative model to accout for the evidece about the pricig behavior of exporters. margial cost ca also produce a higher quality product. I their model, ay rm that draws a higher The competitiveess of rms icreases with higher margial cost due to the lower quality-adjusted price that they charge. Baldwi ad Harriga assume that q = a +, where q is the quality level of a product, a its margial cost ad is a parameter that is restricted to be positive. Give > 0, quality icreases quickly eough so that the quality-adjusted price falls as margial cost icreases. xporters ed up producig higher quality products ad chargig higher prices. I our model by cotrast, all rms have the same margial cost of oe ad there is o coectio betwee margial cost ad the quality of products. Nevertheless, our model is cosistet with the evidece that exporters ted to charge higher prices. De Loecker ad Warzyski (202) study a pael of Sloveia rms for the period ad d that exporters charge sigi catly higher markups (of price over margial cost). Their measure of markups for exporters is a share weighted average markup across markets, where the weight by market is the share of a iput s expediture used i productio sold i that market. Usig that de itio i the setup of our model, the markup of the average exportig rm is +, which simpli es to + + = 2. No-exportig rms are + either o-exportig leaders or competitive frige rms (with two producig i equilibrium). m LN m LN +2m CF + 2m CF m LN +2m CF The markup of the average o-exportig rm is N. Usig m LN = m CF, this simpli es to N = +2 : Thus our model is cosistet with the evidece i 3 2 De Loecker ad Warzyski (202) ad satis es > N if : It is easy to show that 22 >

24 this is the case for all 2 (; 2) ad with the focus i this paper o o-drastic iovatios, 2 (; 2) is easily satis ed. 2 We ca therefore write: Propositio 4 xportig rms charge higher markups o average tha o-exportig rms. We ca also examie whether exportig rms are more productive tha o-exportig rms. For all rms, oe uit of labor produces oe uit of output but rms di er i the quality of products they kow how to produce. Thus, more productive rms i our model are rms that kow how to produce higher quality products. The average quality of products produced by exportig rms is Q Q L+Q F m L +m F = Q L m L = q L m L. The average quality of products produced by o-exportig rms is Q N Q LN +2Q CF m LN +2m CF = q LN +2q CF m LN +2m CF = q LN +2q CF 3m LN sice m LN = m CF. It is straightforward to verify that exportig rms sell higher quality products o average tha o-exportig rms ad hece have higher average productivity whe I is su cietly low: Propositio 5 xportig rms are more productive o average tha o-exportig rms ad Q > Q N holds if 3 > ad (3 )I > I. The coditio 3 > is easily satis ed for plausible parameter values. For example, if = :40, = 0:6 ad = =( ) = 2:5, the 3 > = :4 :5 :65. quatio () implies that (3 )I > I is satis ed whe A is su cietly small because the I is su cietly small. The coditio (3 )I > I holds whe the product iovatio rate I is sigi catly higher that the rate at which rms lear to become exporters I ad most rms are o-exporters i equilibrium. This is exactly what Berard et. al. (2003) d i their study of 200,000 U.S. maufacturig plats, where oly 2 percet reported exportig. Thus, we view (3 )I > I as beig the mai case of iterest, ad whe this coditio holds, the model has the implicatio that exportig rms are more productive o average tha o-exportig rms. I Melitz (2003), ot oly are exportig rms more productive o average tha oexportig rms, all exportig rms are more productive tha all o-exportig rms. There is a threshold productivity value which separates exporters from o-exporters, with all exporters havig productivity above the threshold ad all o-exporters havig productivity below the threshold. I our model by cotrast, there is o such threshold: there are exporters that are less productive tha certai o-exporters. Propositio 5 speaks about productivity o average withi the groups of exporters ad o-exporters. I support of 2 The iequality 2 + > +2 3 ca be rewritte as 5 > Sice <, the iequality holds if 5 > or 0 > ( 2)( ). We coclude that > N holds for all 2 (; 2). 23