DISCUSSION PAPER SERIES

Transcription

1 DISCUSSION PAPER SERIES No AGGLOMERATION AND REGIONAL GROWTH Richard Baldwi ad Philippe Marti INTERNATIONAL TRADE ABCD Available olie at:

2 ISSN AGGLOMERATION AND REGIONAL GROWTH Richard Baldwi, Graduate Istitute of Iteratioal Studies, Geeva ad CEPR Philippe Marti, Uiversité de Paris1, CERAS-ENPC ad CEPR Discussio Paper No July 003 Cetre for Ecoomic Policy Research Goswell Rd, Lodo EC1V 7RR, U Tel: (44 0) , Fax: (44 0) [email protected], Website: This Discussio Paper is issued uder the auspices of the Cetre s research programme i INTERNATIONAL TRADE. Ay opiios expressed here are those of the author(s) ad ot those of the Cetre for Ecoomic Policy Research. Research dissemiated by CEPR may iclude views o policy, but the Cetre itself takes o istitutioal policy positios. The Cetre for Ecoomic Policy Research was established i 1983 as a private educatioal charity, to promote idepedet aalysis ad public discussio of ope ecoomies ad the relatios amog them. It is pluralist ad o-partisa, brigig ecoomic research to bear o the aalysis of medium- ad log-ru policy questios. Istitutioal (core) fiace for the Cetre has bee provided through major grats from the Ecoomic ad Social Research Coucil, uder which a ESRC Resource Cetre operates withi CEPR; the Esmée Fairbair Charitable Trust; ad the Bak of Eglad. These orgaizatios do ot give prior review to the Cetre s publicatios, or do they ecessarily edorse the views expressed therei. These Discussio Papers ofte represet prelimiary or icomplete work, circulated to ecourage discussio ad commet. Citatio ad use of such a paper should take accout of its provisioal character. Copyright: Richard Baldwi ad Philippe Marti

3 CEPR Discussio Paper No July 003 ABSTRACT Agglomeratio ad Regioal Growth* We review the theoretical liks betwee growth ad agglomeratio. Growth, i the form of iovatio, ca be at the origi of catastrophic spatial agglomeratio i a cumulative process à la Myrdal. Oe of the surprisig features of the rugma (1991) model was that the itroductio of partial labour mobility i a stadard ew trade model with trade costs could lead to catastrophic agglomeratio. The growth aalog to this result is that the itroductio of edogeous growth i the same type of ew trade model ca lead to the same result. A differece with the labour mobility versio is that the results are easier to derive from the aalytical poit of view i the edogeous growth versio. We show that the relatio betwee growth ad agglomeratio depeds crucially o capital mobility betwee regios. The absece of capital mobility is at the heart of the possibility of spatial agglomeratio with catastrophe. I additio, growth alters the process of locatio eve without catastrophe. I particular, ad cotrary to the fudametally static models of the New Ecoomic Geography, spatial cocetratio of ecoomic activities may be cosistet with a process of delocatio of firms towards poor regios. Fially, the presece of localized techology spillovers implies that spatial agglomeratio is coducive to growth. JEL Classificatio: O40 ad R10 eywords: agglomeratio, capital mobility, geography ad growth Richard Baldwi Graduate Istitute of Iteratioal Studies 11A Aveue de la Paix CH-10 Geève SWITZERLAND Tel: (41 ) Fax: (41 ) [email protected] For further Discussio Papers by this author see: Philippe Marti CERAS-ENPC ENS 48 Boulevard Jourda Paris FRANCE Tel: (33 1) Fax: (33 1) [email protected] For further Discussio Papers by this author see:

4 *This is the draft of a chapter for the Hadbook of Regioal ad Urba Ecoomics: Cities ad Geography edited by Vero Hederso ad Jacques Thisse. We are grateful to our discussat Jacques Olivier for helpful commets ad especially to Jacques Thisse for detailed suggestios. This Paper is produced as part of a CEPR Research Network o The Ecoomic Geography of Europe: Measuremet, Testig ad Policy Simulatios, fuded by the Europea Commissio uder the Research Traiig Network Programme (Cotract No: HPRN-CT ). Submitted 06 Jue 003

5 1. Itroductio: why should we care about growth ad geography?. The basic framework of growth ad agglomeratio 3. The case without localized spillovers: growth matters for geography 3.1. The growth equilibrium Edogeous growth ad the optimal savigs/ivestmet relatio The role of capital mobility 3.. Perfect capital mobility: the locatio equilibrium Stability of the locatio equilibrium 3.. Does capital flow from the rich to the poor? 3.3. No capital mobility: ew growth ad ew geography Stability of the symmetric equilibrium 3.3. The core-periphery equilibrium 3.4. Cocludig remarks 4. The case with localized spillovers: geography matters for growth (ad vice versa) 4.1. Necessary extesios of the basic model 4.. The case of perfect kowledge capital mobility 4..1 Spatial equity ad efficiecy 4.. Welfare implicatios 4.3. The case without capital mobility: the possibility of a growth take-off ad agglomeratio The log-ru equilibria ad their stability 4.3. Possibility of catastrophic agglomeratio Geography affects growth Ca the Periphery gai from agglomeratio? 4.4. The geography of goods ad ideas: stabilizig ad destabilizig itegratio 5. Other cotributios 6. Cocludig remarks Globalizatio ad the ewly idustrialized coutries 4.4. The learig-liked circular causality

6 1. INTRODUCTION Spatial agglomeratio of ecoomic activities o the oe had ad ecoomic growth o the other had are processes difficult to separate. Ideed, the emergece ad domiace of spatial cocetratio of ecoomic activities is oe of the facts that uzets associated with moder ecoomic growth. This strog positive correlatio betwee growth ad geographic agglomeratio of ecoomic activities has bee documeted by ecoomic historias (Hoheberg ad Lees, 1985 for example), i particular i relatio to the idustrial revolutio i Europe durig the ieteeth cetury. I this case, as the growth rate i Europe as a whole sharply icreased, agglomeratio materialized itself i a icrease of the urbaizatio rate but also i the formatio of idustrial clusters i the core of Europe that have bee by ad large sustaied util ow. The role of cities i ecoomic growth ad techological progress has bee emphasized by urba ecoomists (Hederso, 1988, Fujita ad Thisse, 00), developmet ecoomists (Williamso, 1988) as well as by ecoomists of growth (Lucas, 1988). At the other had of the spectrum, as emphasized by Baldwi, Marti ad Ottaviao (001), the growth takeoff of Europe took place aroud the same time (ed of eighteeth cetury) as the sharp divergece betwee what is ow called the North ad the South: growth sharply accelerated (for the first time i huma ecoomic history) at the same time as a dramatic ad sudde process of agglomeratio took place at the world level. Hece, as put by Fujita ad Thisse (00), agglomeratio ca be thought as the territorial couterpart of ecoomic growth. Less dramatically ad closer to us, Quah s results (1996) suggest also a positive relatio betwee growth ad agglomeratio. He fids that amog the Cohesio group of coutries (Greece, Spai, Portugal ad Irelad, though there are o Irish regioal data), the two coutries that have achieved a high rate of growth ad coverged i per capita icome terms towards the rest of Europe (Spai ad Portugal) have also experieced the most marked regioal divergece, This is cosistet with the results of De la Fuete ad Vives (1995), for istace, buildig o the work of Esteba (1994) who suggest that coutries have coverged i Europe but that this process of covergece betwee coutries took place at the same time as regios iside coutries either failed to coverge or eve diverged. There are however few direct empirical tests of the relatio betwee agglomeratio ad growth. Ciccoe (00) aalyses the effects of employmet desity o average labor productivity for 5 Europea coutries at the Nuts 3 regioal level. He fids that a icrease i agglomeratio has a positive effect o the growth of regios. A idirect test of the relatioship is performed i the literature o localized techology spillovers. The presece of localized spillovers has bee well documeted i the empirical literature. Studies by Jacobs (1969) ad more recetly by Jaffe et al. (1993), Coe ad Helpma (1995), Coe et al. (1997), Ciccoe ad Hall (1996) provide strog evidece that techology spillovers are either global or etirely localized. The diffusio of kowledge across regios ad coutries does exist but dimiishes strogly with physical distace which cofirms the role that social iteractios betwee idividuals, depedet o spatial proximity, have i such diffusio. A recet study by eller (00) shows that eve though techology spillovers have become more global with time, techology is to a substatial degree local, ot global, as the beefits from spillovers are decliig with distace. The fact that techology spillovers are localized should i theory lead to a positive lik betwee growth ad spatial agglomeratio of ecoomic activities as beig close to iovatio clusters has a positive effect o productivity. Hece, these empirical results 3

7 poit to the iterest of studyig growth ad the spatial distributio of ecoomic activities i a itegrated framework. From a theoretical poit of view, the iterest should also be clear. There is a strog similarity betwee models of edogeous growth ad models of the ew ecoomic geography (NEG). They ask questios that are related: oe of the objectives of the first field is to aalyze how ew ecoomic activities emerge through techological iovatio; the secod field aalyzes how these ecoomic activities choose to locate ad why they are so spatially cocetrated. Hece, the process of creatio of ew firms/ecoomic activities ad the process of locatio should be thought as joit processes. From a methodological poit of view, the two fields are quite close as they both assume (i some versios) similar idustrial structures amely, models of moopolistic competitio which reflects the role of ecoomies of scale i both fields. I this chapter, we will attempt to clarify some of the theoretical liks betwee growth ad agglomeratio. Growth, i the form of iovatio, ca be at the origi of catastrophic spatial agglomeratio i a cumulative process à la Myrdal. Oe of the surprisig features of the rugma (1991) model, was that the itroductio of partial labor mobility i a stadard ew trade model with trade costs could lead to catastrophic agglomeratio. The growth aalog to this result is that the itroductio of edogeous growth i the same type of ew trade model ca lead to the same result. A differece with the labour mobility versio is that the results are easier to derive from the aalytical poit of view i the edogeous growth versio. I additio, growth alters the process of locatio eve without catastrophe. I particular, ad cotrary to the fudametally static models of the NEG, spatial cocetratio of ecoomic activities may be cosistet with a process of delocatio of firms towards poor regios. I commo with the static models (see the chapter by Ottaviao ad Thisse i this volume), the Home Market Effect plays here a crucial role to explai agglomeratio. The relatio betwee growth ad agglomeratio depeds crucially o capital mobility. Without capital mobility betwee regios, the icetive for capital accumulatio ad therefore growth itself is at the heart of the possibility of spatial agglomeratio with catastrophe. I the absece of capital mobility, some results are i fact familiar to the NEG (Fujita, rugma ad Veables, 1999): a gradual lowerig of trade costs betwee two idetical regios first has o effect o ecoomic geography but at some critical level iduce catastrophic agglomeratio. I the model preseted i this chapter, i the absece of migratio, catastrophic agglomeratio meas that agets i the south have o more private icetive to accumulate capital ad iovate. The circular causality which gives rise to the possibility of a core-periphery structure is depicted below ad as usual i ecoomic geography models is characterized by both productio ad demad shiftig which reiforce each other. The productio shiftig takes the form of capital accumulatio i oe regio (ad de-accumulatio i the other) ad the demad shiftig takes the form of icreased permaet icome due to ivestmet i oe regio (ad a decrease i permaet icome i the other regio). 4

8 North accumulates more capital Norther firm profits ad retur to capital rises Norther permaet icome icreases Norther market size icreases Figure 1: Demad-liked circular causality Capital mobility elimiates the possibility of catastrophic agglomeratio because i this case productio shiftig does ot iduce demad shiftig as profits are repatriated. It is therefore stabilizig i this sese. This is i sharp cotrast with labor mobility which we kow to be destabilizig. However, capital mobility also makes the iitial distributio of capital betwee the two regios a permaet pheomeo so that both the symmetric ad the core-periphery equilibria are always stable. I a secod sectio of this chapter, we will cocetrate o the opposite causality ruig from spatial cocetratio to growth. For this, we will itroduce localized techology spillovers which will imply that the spatial distributio of firms will have a impact o the cost of iovatio ad therefore the growth rate. This chapter uses modified versios of Baldwi (1999), Baldwi, Marti ad Ottaviao (000) ad Marti ad Ottaviao (1999). The first two papers aalyze models of growth ad agglomeratio without capital mobility. I cotrast to the first paper which uses a exogeous growth model, this chapter aalyses edogeous growth. I cotrast to the secod paper, we restrict our attetio to the case of global techology spillovers. The last paper presets a model of growth ad agglomeratio with perfect capital mobility. Baldwi et al. (003) also treat some commo themes i their chapters 6 ad 7.. THE BASIC FRAMEWOR OF GROWTH AND AGGLOMERATION May of the most popular ecoomic geography models focus o labor, examples beig rugma (1991), rugma ad Veables (1995), Ottaviao, Tabuchi ad Thisse (00) ad Puga (1999). These are usuited to the study of growth. The key to all sustaied growth is the accumulatio of huma capital, physical capital ad/or kowledge capital with the accumulatio of kowledge capital, i.e. techological progress havig a privileged positio. We thus eed a model i which capital exists ad its stock is edogeous. 5

9 To preset the basic elemets of this literature, we orgaize the discussio with the help of a workhorse model. As Baldwi et al (003) show, itroducig capital ito a geography model is relatively simple. The simplest way is accomplished by the footloose capital model (FC model) due to Marti ad Rogers (1995). The FC model, however, takes the capital stock as give. Gettig to a growth model requires us to add i a capital-producig sector. Specifically we deote capital by ad labor by L. The capital-producig sector is referred to as the sector I (for iovatio ad ivestmet, see below) ad this comes o top of the two usual sectors, maufactures M ad traditioal-goods T. The regios (two of them) are symmetric i terms of prefereces, techology ad trade costs. The usual Dixit-Stiglitz M-sector (maufactures) cosists of differetiated goods. Aother differece is that the fixed cost is i terms of. Each variety requires oe uit of capital which ca be iterpreted as a idea, a ew techology, a patet, machiery, etc.. Productio also etails a variable cost (a M uits of labor per uit of output). Its cost fuctio, therefore, is π +w a M x i, where π is 's retal rate, w is the wage rate, ad x i is total output of a typical firm. Traditioal goods, which are assumed to be homogeous, are produced by the T-sector uder coditios of perfect competitio ad costat returs. By choice of uits, oe uit of T is made with oe uit of L. The structure of the basic growth ad agglomeratio model is i figure. Regioal labor stocks are fixed ad immobile, so that we elimiate oe possible source of agglomeratio. Each regio's is produced by its I-sector. I is a memoic for iovatio whe iterpretig as kowledge capital, for istructio whe iterpretig as huma capital, ad for ivestmet-goods whe iterpretig as physical capital. Oe possible iterpretatio of the differece betwee the situatio of capital mobility ad oe of capital immobility is that i the first case is physical capital (mobility the meas the delocatio of plats) or as kowledge capital that is marketable ad tradable through patets. The secod case, capital immobility, would be more cosistet with the iterpretatio of huma capital. I this case, labor immobility implies capital immobility. The I-sector produces oe uit of with a I uits of L, so that the margial cost of the I sector, F, is w a I. Note that this uit of capital i equilibrium is also the fixed cost F of the maufacturig sector. As oe uit of capital is required to start a ew variety, the umber of varieties ad of firms at the world level is simply the capital stock at the world * level: W = +. We ote ad * the umber of firms located i orth ad south * respectively. As oe uit of capital is required per firm we also kow that: W = +. However, depedig o the assumptio we make o capital mobility, the stock of capital produced ad owed by oe regio may or may ot be equal to the umber of firms producig i that regio. I the case of capital mobility, the capital may be produced i oe regio but the firm that uses this capital uit may be operatig i aother regio. Hece, the umber of firms located i oe regio is, i the case of capital mobility, differet from the stock of capital owed by this regio. 6

10 L, umeraire, w=1 T sector (traditioal) - Walrasia (CRS& Perf. Comp.) - uit labor cost M-sector (Maufactures) - Dixit-Stiglitz moopolistic competitio - icreasig returs: fixed cost, 1 uit of - variable cost = a M uits of L No trade costs? p T =p T = w=w*=1 Iceberg trade costs North &ad South markets I-sector (Iovatio, Ivestmet ) - perfect competitio -itertemporal spillovers ( cases: global or localized) - variable cost for oe uit of = a I Trade i capital, cases: -perfect capital mobility - o capital mobility Figure : The basic structure of the growth ad agglomeratio model To idividual I-firms, the iovatio cost a I is a parameter. However, followig Romer (1990) ad Grossma ad Helpma (1991), a sector-wide learig curve is assumed. That is, the margial cost of producig ew capital declies (i.e., a I falls) as the sector's cumulative output rises. May justificatios of this itertemporal exterality, classic i the edogeous growth literature, are possible. Romer (1990), for istace, ratioalizes it by referrig to the o-rival ature of kowledge. We ca summarize these stadard assumptios of this literature by the followig: L & = a W W ; F = wa ; a = 1/ ; = I I I + I where ad * are the orther ad souther cumulative I-sector productio levels. Note that spillovers are global: the North lears as much from a iovatio made i the South tha i the North. Below, we itroduce localized techological spillovers. Followig Romer (1990) ad Grossma ad Helpma (1991), depreciatio of kowledge capital is igored. Fially, the regioal 's represet both regio-specific capital stocks ad regio-specific cumulative I-sector productio. Because the umber of firms, varieties ad capital uits is equal, the growth rate of the umber of varieties, o which we will focus, is therefore: & W W / = g. We assume a ifiitely-lived represetative cosumer (i each coutry) with prefereces: * (1) U * + ρt 1 α α 1 1 / σ = l ; ; C e Qdt Q = CT C M M = ci t= 0 i= 0 di / σ () See Baldwi et al. (003) for a similar aalysis with depreciatio. 7

11 where ρ is the rate of time preferece, σ is the costat elasticity of substitutio amog varieties, ad the other parameters have the usual meaig. Utility optimizatio implies that a costat fractio α of total orther cosumptio expediture E falls o M-varieties with the rest spet o T. Optimizatio by agets i the North also yields uitary elastic demad for T ad the CES demad fuctios for M varieties. The optimal orther cosumptio path also satisfies the stadard Euler equatio with log utility which requires 3 E & / E = r ρ (r is the orth's rate of retur o ivestmet) ad a trasversality coditio. Souther optimizatio coditios are isomorphic. O the supply side, free trade i T equalizes omial wage rates as log as both regios produce some T (i.e. if α is ot too large). Takig orther labor as umeraire the w=w*=1. As for the M-sector, uits are chose such that a M =1-1/σ so that producer prices of varieties are also ormalized to 1. With moopolistic competitio, equilibrium operatig profit is the value of sales divided by σ. Usig the goods market equilibrium ad the optimal pricig rules, the operatig profits are give by: E π = bb w w E π * = bb * ; w w ; B s B* s se + φ(1 s φse + φ(1 s φ(1 se ) + ) φs + 1 s 1 se + ) φ s + 1 s ; α b σ, φ τ where s E E/ E w is orth s share of world expediture E w ; s = /(+*) is the share of firms which are located i the orth, ad 0 = φ = 1 is the usual trasformatio of trade costs such that φ measures the free-ess (phi-ess of trade), with φ=0 implyig zero free-ess ad φ=1 implyig perfect free-ess (zero trade costs). Whe capital is immobile, this share is the share of capital owed by the Norther regio: s. Also, B is a memoic for the 'bias' i orther M-sector sales sice B measures the extet to which the value of sales of a orther variety exceeds average operatig profit per variety worldwide (amely, be w / w ). 1 σ (3) 3 See Barro ad Sala-I-Marti 1995 for a derivatio usig the Hamiltoia approach. Ituitively, the margial cost of postpoig cosumptio is ρ plus the rate of declie of margial utility which, give the log prefereces is just, E & / E. The margial beefit is r, the rate of retur o ivestmet. The optimal cosumptio path must be such that the two are equalized so that agets are idifferet to a small itertemporal reallocatio of cosumptio. 8

12 3. THE CASE WITHOUT LOCALIZED SPILLOVERS: GROWTH MATTERS FOR GEOGRAPHY We start with the simple extreme case cosidered by Grossma ad Helpma (1991) where spillovers are perfectly global. This assumptio is already embedded i equatio (1) The growth equilibrium Sice the locatio of iovatio ad productio are irrelevat to the iovatio process (kowledge spillovers are global ad deped oly o past I-sector productio), the worldwide equilibrium growth rate ca be determied without piig dow the spatial distributio of idustry (the locatio equilibrium). The easiest ad most ituitive way of solvig for growth equilibria is to use Tobi s q (Baldwi ad Forslid 000). The essece of Tobi's approach is to assert that the equilibrium level of ivestmet is characterized by the equality of the stock market value of a uit of capital which we deote with the symbol v ad the replacemet cost of capital, F. Tobi takes the ratio of these, so what micro ecoomists would aturally call the M-sector free-etry coditio (amely v=f) becomes Tobi's famous coditio q =v/f=1. Calculatig the umerator of Tobi's q (the preset value of itroducig a ew variety) requires a discout rate. I steady state, E & / E = 0 i both regios 4, so the Euler equatios imply that r=r * =ρ. Moreover, the preset value of a ew variety also depeds upo the rate at which ew varieties are created. I steady state, the growth rate of the capital stock (or of the umber of varieties) will be costat ad will either be commo (g=g* i the iterior case) or orth's g (i the core-periphery case). I either case, the steady-state values of ivestig i ew uits of are: π v = ρ + g ; v * * π = ρ + g It ca be checked that the equality, v=f, is equivalet to the arbitrage coditio preset i edogeous growth models such as Grossma ad Helpma (1991). The free etry coditio i the iovatio sector esures that the growth rate of the value v of capital is equal to growth rate of the margial cost of a iovatio, F, which due to itertemporal spillovers is g. With r =ρ, ad usig the defiitio of F we get the regioal q's: q = π ρ w + g ; q * * w π = ρ + g I the case of global spillovers, the commo growth rate is easy to fid because it does ot deped o geography. The reaso is simply that the cost of iovatio ad the total size of the market do ot deped o the locatio of firms. Hece, we ca just use the special case of the symmetric equilibrium where s E = s = 1/ to fid the growth rate. (5) (4) 4 w w To see this, use the world labour market equilibrium: L = ae (1 1/ σ ) + ( 1 a)e + g which says that world labour supply ca be used either i the maufacturig sector, the traditioal sector or the iovatio sector. It implies that a steady state with costat growth oly exists if E w itself is costat. 9

13 3.1.1 Edogeous growth ad the optimal savigs/ivestmet relatio Usig equatio (3) i that case ad imposig that Tobi's q is 1 i equatio (5), we get the followig relatio betwee growth ad world expediture E w : be w = g + ρ where b α/σ as is stadard i the growth literature. It just says that higher expediture by icreasig profits iduces more etry i the maufacturig sector, which implies a higher growth rate. The other equilibrium relatio betwee growth ad world expediture is give by the world labor market w w equilibrium: L = ae ( 1 1/ s ) + ( 1 a)e + g, which states that labor ca be used either i the maufacturig sector (recall the uit labor requiremet i this sector is ormalized to 1-1/σ), i w the traditioal sector or i the iovatio sector ( & is the productio of the sector per uit of time ad F=1/ w is the labor requiremet i the iovatio sector). Here the relatio is egative as higher expediture implies that labor resources are diverted from the iovatio sector to the maufacturig ad traditioal sector. Combiig the two we fid that the world level of expediture is simply give by: E w = L + ρ. Usig these equatios, the growth rate of the umber of varieties ad of the world capital stock is give by: g = Lb (1 b) ρ ; b α σ g depeds positively o the size of the world ecoomy (as measured by the edowmet of the primary factor) ad egatively o the discout rate as i ay edogeous growth model. Importatly, whe kowledge spillovers are global i scope, the equilibrium growth rate g does ot deped o geography. Fially, a simple equilibrium relatio exists betwee s E ad s, the orther share of expeditures ad the orther share of capital owership. It ca be show that optimizig cosumers set expediture at the permaet icome hypothesis level i steady state. That is, they cosume labor icome plus ρ times their steady-state wealth, F= s, ad, F*= (1- s ) i the orth ad i the south respectively. Hece, E = L+ρ s, ad E* = L+ρ(1-s ). Note that this is w aother way to check the level of world expediture as: E + E* = E = L + ρ. Thus, we get: s E E E w L + ρ s = L + ρ = 1 ρ + s L + ρ 1 This relatio betwee s E ad s, ca be thought as the optimal savigs/expediture fuctio sice it is derived from itertemporal utility maximizatio. The ituitio is simply that a icrease i the orther share of capital icreases the permaet icome i the orth ad leads therefore to a icrease i the orther share of expeditures The role of capital mobility Havig worked out the equilibrium growth rate, ad thus implicitly defied the amout of resources devoted to cosumptio, we ca tur to workig out the spatial divisio of idustry, i.e., the locatio equilibrium. From ow o two roads are ope: 1) we ca let capital owers decide where to locate productio. Capital is mobile eve though capital owers are ot, so that profits are repatriated i the regio where capital is owed. (6) (7) 10

14 I this case, s, the share of firms located i the orth ad s, the share of capital owed by the orth, may be differet. s is the edogeous ad determied by a arbitrage coditio that says that locatio of firms is i equilibrium whe profits are equalized i the two regios. Because of capital mobility, the decisio to accumulate capital will be idetical i both regios so that the iitial share of capital owed by the orth, s, is permaet ad etirely determied the iitial distributio of capital owership betwee the two regios. ) a secod solutio is to assume that capital is immobile. Presumably, this would be the case if we focus o the iterpretatio of capital beig huma (coupled with immobile agets). I this case, the locatio of productio, s, is pied dow by capital owership: s = s. As we shall see i detail below, the capital mobility assumptio is pivotal. Why is this? I stadard termiology, allowig capital mobility elimiates demad-liked circular causality (backward likages); capital moves without its owers, a shift i productio leads to o expediture shiftig because profits are repatriated. Whe capital is immobile, ay shock which favours productio i oe regio is satisfied by the creatio of ew capital i that regio. Sice the icome of the ew capital is spet locally, the productio shiftig leads to expediture shiftig. Of course, expediture shiftig fosters further productio shiftig (via the famous home market effect), so without capital mobility, the model features demad-liked circular causality. As is well kow, this form of likage is de-stabilizig, so as we shall see i detail below capital mobility i a growth model is a stabilizig force. Because the case of capital mobility is simpler, we start with it. 3.. Perfect capital mobility: the locatio equilibrium With capital mobility, a obvious questio arises: where does capital locate? Capital owed i oe regio ca be located elsewhere. Agai, the arbitrage coditio, which implies that profits across regios eed to be equal for firms to be idifferet betwee the two locatios, pis dow the equilibrium locatio of firms. Usig equatio (3), ad imposig the equality of profits, we get that there is o more icetive for relocatio whe the followig relatio betwee s ad s E is satisfied: s 1 1+ φ 1 = + se, 0 s 1 φ 1 where the equilibrium s equals uity or zero whe the s implied by (8) is outside the zero-uity rage. This is a example of the home market effect. Sice (1+φ)/(1-φ) is greater tha oe, this relatioship tells us that a chage i market size leads to a more tha proportioal chage i the spatial allocatio of idustry. Combiig equatios (7) ad (8), we get the equilibrium relatio betwee the share of firms located i the orth, s, ad the share of capital owed by the orth, s : s 1 ρ 1+ φ 1 = + s 0 s L + ρ 1 φ Note also that if the iitial distributio of capital i the orth is such that s > ½, the more firms will be located i the orth tha i the south: s > ½. A icrease i the share of capital i the orth, s, iduces relocatio to the orth as it icreases expediture ad market size there. Note also that lower trade costs (higherφ) will reiforce the home market effect, implyig that a 1 (8) (9) 11

15 uequal distributio of capital owership will traslate i a eve more uequal distributio of firms Stability of the locatio equilibrium It is easy to see that the divisio of idustry described above will ot chage over time. With perfect capital mobility, operatig profits have to be the same i both regios which also implies that the value of capital has to be the same i both regios. Hece, π =π* ad q=q*=1. This, together with the assumptio of costat returs to scale, ad the assumptio of global spillovers (implyig that the cost of iovatio is the same i both regios) meas that the two regios will accumulate capital at the same costat rate so that ay iitial distributio of capital is stable. Moreover, sice either backward or forward likages operatig i this model with capital mobility, o catastrophic agglomeratio sceario ca ufold (see Marti ad Ottaviao 1999). Hece, the equilibrium described by (9) is always stable. I particular, the symmetric equilibrium where s = s = 1/, is always stable for ay level of trade costs. To see this poit i more detail, oe ca aalyze the effect of a small icrease i s ad check the impact of this perturbatio o the ratio of profits i the orth to profits i the south. That is, we ask the questio whether a icrease i geographic cocetratio i the orth decreases or icreases the icetive to relocate i the orth. The symmetric equilibrium is stable if ad oly if (π/π*)/ s is egative. Ideed this is the case for all positive levels of trade costs sice, evaluated at the equilibrium geography: ( π ) ( 1 φ ) π * = s ( 1+ φ ) s E 1 (1 s E < 0 ) Evaluated at the equilibrium give by (9), a exogeous icrease i the share of firms located i the orth always decreases relative profits there, so that it leads firms to go back to the south. The locatio equilibrium determied i (9) is always stable. The reaso is that whe more firms locate i the orth, this icreases competitio there (ad decreases it i the south). 3.. Does capital flow from rich to poor? A iterestig questio that ca be aalyzed i this framework is: Do firms relocate towards the orth or towards the south? I ecoomic geography models without growth, idustrial cocetratio implies that firms are destroyed i the south ad built i the orth. Here, the relocatio story is richer because of the costat creatio of ew firms. To see what is the directio of relocatio we eed to look at the differece betwee the share of capital owed by the orth ad the share of firms located i orth. The expressio is easier takig ratios, so: s s L(1 φ) ρφ 1 = s ( 1 φ )(L + ρ) I the symmetric equilibrium, where both regios are edowed origially with the same amout of capital there is o relocatio of course. If the iitial distributio of capital is such that s >1/, so that the orth is richer tha the south, the the directio of the capital flows is ambiguous; it depeds o the sig of L(1-φ)-ρφ. If this expressio is positive, the s > s so that some of the capital owed by the orth relocates to the south. (10) 1

16 The ambiguity of the directio of capital flows stems from the fact that it is govered by two opposite effects, amely the market crowdig effect (which is a dispersio force that makes the poor capital regio attractive because firms istalled there face less competitio), ad the market access effect (which is a agglomeratio force that makes the rich regio attractive because of its high level of icome ad expediture). The first effect domiates whe trade is quite closed (φ is low). Note that whe the rate of time preferece is high or more geerally whe the retur to capital is high, the capital rich regio becomes more attractive because the market access effect is reiforced. There is a threshold level of trade costs that determies the directio of capital flows. It is give by: φ CP L = L + ρ Whe trade costs are below this level, relocatio takes place towards the south ad vice-versa. The reaso why we attach CP (for core-periphery) to this threshold will become clear later whe we aalyze the case of capital immobility, as we will see that this threshold value is the oe for which the symmetric equilibrium becomes ustable. A iterestig feature here is that cocetratio of wealth ad of ecoomic activities i the orth (s ad s >½), is compatible with relocatio of firms from orth to south (s <s ) whe φ <φ CP. This comes from the itroductio of growth ad the fact that a larger umber of ewly created firms are created ad owed by the orth tha by the south No capital mobility: "ew growth" ad "ew geography" The previous sectio described a growth ad geography equilibrium where agglomeratio forces were preset, 5 but where o "catastrophe" could take place sice all circular causality had bee ruled out. As discussed above, elimiatig capital mobility i a growth model is actually destabilizig sice aythig that chages the spatial allocatio of idustry ad thus capital will simultaeously chage that spatial allocatio of expediture. Ad, as is well kow, the home market effect meas that ay chage i expediture s spatial allocatio iduces a kock-o chage i the locatio of idustry. More formally, restrictig capital mobility (together with the assumptios of labor immobility) has two implicatios. First, the umber of firms ad the umber of uits of capital owed i a regio are idetical: s = s. Secod, because the arbitrage coditio of the previous sectio does ot hold, profits may be differet i the two regios. This i tur implies that, cotrary to the previous sectio, the two regios may ot have the same icetive to accumulate capital so that the iitial owership of capital does ot eed to be permaet. This meas that the aalysis will be quite differet from the previous sectio. We will ask the followig questios which are the usual oes i the NEG models. Startig from a equal distributio of capital, the symmetric equilibrium, we will determie uder which circumstaces it remais a stable equilibrium. The we will look at the core-periphery equilibrium ad agai ask whe this equilibrium is stable. (11) 5 We defie agglomeratio as the pheomeo where the cocetratio of ecoomic activity creates forces that foster the cocetratio of ecoomic activity. The home market effect, which did operate i the pervious sectio, shows agglomeratio forces are preset sice a divisio where s L =s >½ would ot be a equilibrium. Due to the home market effect, such a divisio would ecourage further cocetratio of ecoomic activity i the orth. 13

17 3.3.1 Stability of the symmetric equilibrium We first cosider iterior steady states where both regios are ivestig, so q =1 ad q * =1. Usig (3) ad (5) i (6), q = q * =1 ad imposig s = s we get: 1 1+ φ 1 s = + s E 1 φ which of course is just (8) with s replaced by s. I other words, it ow determies the locatio of capital owership as well as the locatio of productio. Together with equatio (7) which implied that productio shiftig led to expediture shiftig, this defies a secod positive relatio betwee s E ad s, i.e. expediture shiftig leads to productio shiftig. The ituitio is that a relative icrease i orther demad icreases profits i the orth ad therefore the margial value of a extra uit of capital. I other words, the umerator of Tobi s q icreases i the orth. Hece, this raises the icetive to iovate there ad the orth ideed icreases its share of capital s. The ituitio is therefore very close to the home market effect except that it iflueces here the locatio of capital accumulatio. Together with the optimal savig relatio of (7), it is easy to check that the symmetric solutio s E = s = ½ is always a equilibrium, i particular it is a equilibrium for all levels of trade costs. The symmetric equilibrium is the uique equilibrium for which both regios accumulate capital (q = q* =1). However, the fact that there are two positive equilibrium relatios betwee s E ad s, the share of expeditures ad the share of capital i the orth, should war us that the symmetric equilibrium may ot be stable. Ideed, i this model a 'circular causality' specific to the presece of growth ad capital immobility teds to de-stabilize the symmetric equilibrium because of the demad-liked cycle i which productio shiftig leads to expediture shiftig ad vice versa. The particular variat preset here is based o the mechaism first itroduced by Baldwi (1999) i a eo-classical growth model. There are several ways to study the symmetric equilibrium's stability. We ca first graph the two equilibrium relatios betwee s E ad s,, the Permaet Icome relatio (call it PI) give by equatio (7) ad the Optimal Ivestmet relatio (call it OI) give by equatio (1). I the case where the slope of the PI relatio is less tha the OI relatio we get the left-pael of Figure 3. At the right of the permaet icome relatio, s E, the share of expeditures i the orth, is too low give the high share of capital owed by the orth (agets do ot cosume eough). The opposite is true at the left of the PI relatio. At the right of the optimal ivestmet relatio, s, the share of capital i the orth, is too high give the low level of s E, the share of expeditures i the orth (agets ivest too much). The opposite is true is at the left of the OI relatio. This graphical aalysis suggests that i this case the symmetric equilibrium is stable. I the case where the slope of the PI relatio is steeper tha the OI the the same reasoig leads to the right-pael of the diagram. This suggests that i this case, the symmetric equilibrium is ustable. Accordig to this graphical aalysis, the trade cost below which the symmetric equilibrium becomes ustable is exactly the oe for which the slope of the PI curve equals the slope of OI curve. The slope of the PI curve is ρ/(l+ρ) which is the share of capital icome i total icome. The slope of the OI curve is: (1-φ)/(1+φ). The two slopes are equal for a level of trade costs which we saw above: it turs out to be the threshold level, which we defie as φ CP, give by equatio (11), amely φ CP =L/(L+ρ). Whe the "free-ess" of trade is higher tha this level, our graphical aalysis suggests that the stable equilibrium is ot stable. (1) 14

18 s E OI s E PI PI 0I 1/ 1/ 1/ s 1/ s Figure 3: The orther shares of expediture ad capital, stable ad ustable cases To gai more ituitio o this result, we ca also study the symmetric equilibrium's stability i a differet ad more rigorous way. We ca aalyze the effect of a exogeous icrease s, by a small amout ad check the impact of this perturbatio o Tobi s q, allowig expediture shares to adjust accordig to (7). The symmetric equilibrium is stable if ad oly if q/ s is egative: i this case, a icrease i the share of orther capital lowers Tobi's q i the orth (ad therefore the icetive to iovate) ad raises it i the south (by symmetry q/ s ad q * / s have opposite sigs). Thus whe q/ s <0, the perturbatio geerates self-correctig forces i the sese that the icetive to accumulate more capital i the orth falls ad icreases i the south. If the derivative is positive, the icrease i the share of capital i the orth reiforces the icetive to accumulate more capital i the orth: the symmetric equilibrium is ustable i this case. Differetiatig q with respect to s, we have: q / q s s = 1/ 1 φ s = 1 + φ s E s = 1/ 1 φ 1+ φ This expressio illustrates the two forces affectig stability. The first term is positive, so it represets the destabilizig force, amely the demad-liked effect. This effect was abset of the stability aalysis i the case of capital mobility because a icrease i profits i oe regio led to delocatio of capital but ot to more local capital accumulatio. I the case of capital immobility, the oly adjustmet mechaism whe profits icrease i oe regio is that agets i that regio accumulate more capital up to poit where the profits of accumulatig capital are drive to zero. This "local" accumulatio process geerates a higher permaet icome ad a higher level of expediture i oe regio oly which is the reaso for the circular causality. The egative secod term reflects the stabilizig market crowdig effect, which was the oly oe preset i the capital mobility case. Clearly, reducig trade costs (a icrease i φ) erodes the stabilizig force more quickly tha it erodes the destabilizig demad-likage. (14) 15

19 Usig (7) to fid s E / s = ρ/(l+ρ ), the critical level of φ at which the symmetric equilibrium becomes ustable is defied by the poit where (13) switches sig. It is easy to check that agai this critical level is give by φ CP of equatio (11). Whe trade costs are high the symmetric equilibrium is stable ad gradually reducig trade costs produces stadard, static effects more trade, lower prices for imported goods, ad higher welfare. There is, however, o impact o idustrial locatio, so durig a iitial phase, the global distributio of idustry appears uaffected. As trade free-ess moves beyod φ CP, however, the equilibrium eters a qualitatively distict phase. The symmetric distributio of idustry becomes ustable, ad orther ad souther idustrial structures begi to diverge; to be cocrete, assume idustry agglomerates i the orth. Sice s caot jump, crossig φ CP triggers trasitioal dyamics i which orther idustrial output ad ivestmet rise ad souther idustrial output ad ivestmet fall. Moreover, i a very well defied sese, the south would appear to be i the midst of a 'vicious' cycle. The demad likages would have souther firms lowerig employmet ad abstaiig from ivestmet, because souther wealth is fallig, ad souther wealth is fallig sice souther firms are failig to ivest. By the same logic, the orth would appear to be i the midst of a 'virtuous' cycle The core-periphery equilibrium I additio to the symmetric equilibrium, a core-periphery outcome (s = 0 or 1, but we will focus oly o the secod oe where the orth gets the core) ca also exist. For s =1 to be a equilibrium, it must be that q = v/f = 1 ad q* = v*/f* <1 for this distributio of capital owership: cotiuous accumulatio is profitable i the orth sice v=f, but v*<f* so o souther aget would choose to setup a ew firm. Defiig the core-periphery equilibrium this way, it implies that it is stable wheever it exists. Usig (3), (5) ad (6), (7), q* with s =1 simplifies to: (1 + φ ) L + φ q* = (L + ρ) φ ρ (14) If q* is less tha 1 whe s =1, the the core-periphery equilibrium exists ad is stable as there is o icetive for the south to iovate i this case. The threshold φ that solves q*=1 defies the startig poit of the core-periphery set. Agai, this threshold is φ CP of equatio (11). This implies that at the level of the trade costs for which the symmetric equilibrium becomes ustable, the core-periphery becomes a stable equilibrium. Whe trade costs are high eough, the core-periphery equilibrium is ot a stable equilibrium: i this case the south would have a icetive to iovate because the profits i the south are high eough. This is because eve though the souther market is small i this case (it has o capital icome i the core-periphery equilibrium), it is protected from orther competitio thaks to high trade costs. Whe trade costs are low eough, this protectio dimiishes ad the fact that the market i the south is small becomes more importat: i this case, above the threshold φ CP, it becomes o profitable to operate a firm i the south. Usig s =1, the remaiig aspects of the core-periphery steady state are simple to calculate. I particular, sice s =1, q=1, ad q*<1, we have that o labor is used i the iovatio or maufacturig sectors i the south ad all iovatio is made i the orth. 16

20 Note that the core-periphery outcome (s =1) is reached oly asymptotically. This is because we preset a simpler versio of the model where the stock of capital i the south does ot depreciate ad oce the level of φ CP is crossed, stays costat, whereas the stock of capital i the orth keeps growig at rate g. Figure 4 summarizes the model s stability properties i a diagram with φ ad s o the axes: 1 s Symmetric (stable) Core-Periphery (stable) 1/ Symmetric (ustable) 0 (o trade) φ CP 1 (free trade) φ Figure 4: Stability properties of the core-periphery equilibrium Followig the traditio of the NEG we have aalyzed here the existece ad stability coditios of the symmetric ad core-periphery equilibria. I this simple model we ca go further ad aalyze what would happe if we started from a situatio i which the orth had more capital tha the south (1/ <s <1). It ca be checked, usig equatios (3), (5) ad (6) that i this case q <1 (ad q*>1) if: 1 ( 1 s )( s )( 1 φ )[ ρ φ L( 1 φ )] < 0 that is, if φ <φ CP. Hece, i this case, the orth would ot iovate (the large stock of capital implies a high degree of market crowdig) ad the south would iovate. Hece, if we start from such a iterior asymmetric equilibrium the oe would coverge back to the symmetric equilibrium as log as trade costs are high eough. If φ > φ CP, the the ecoomy coverges to the core-periphery equilibrium Cocludig remarks Comparig perfect capital mobility to o capital mobility, we coclude that: - whe trade costs are high, the absece of capital mobility leads to covergece betwee the two regios: if oe regio starts with more capital tha the other the, the two regios coverge to the symmetric equilibrium. O the cotrary, with capital mobility, ay iitial distributio of capital owership becomes permaet. However, some of the firms owed by the orth will relocate ad produce i the south. This will produce some sort of covergece i terms of GDP but ot i terms of GNP. 17

21 - whe trade costs are low, the absece of capital mobility leads to divergece betwee the two regios: asymptotically, whatever the iitial distributio of capital, all the capital is accumulated ad owed by oe regio. 7 With capital mobility, as log as all the capital is ot etirely owed by the orth, some firms will still produce i the south. However, some of the souther capital will delocate to the orth. Hece, i the case of mobile capital (physical or tradable iovatios such as patets), the key parameter for regioal icome distributio is the iitial distributio of capital. I the case of immobile (huma) capital, the key parameter is the level of trade costs. The regioal distributio of capital affects the log term regioal icome distributio oly to the extet that it determies which regio becomes the core, through a small iitial advatage i capital edowmets for example. To simplify matters we have used a model where oly oe type of capital exists. To make it more realistic, i particular for the Europea case, it would be iterestig to exted it ad take ito accout the differet atures of capital so that part of the capital is mobile ad part is ot. Ca we derive some policy implicatios from this aalysis? Oe strikig result is that whe regios are ot well itegrated (high trasport/trade costs) capital immobility is coducive to regioal covergece. 9 However, whe regios are well itegrated, the opposite result is true. To the extet that public policies ca alter capital mobility, the policy implicatio is clear: capital mobility, both physical ad huma, should be facilitated betwee coutries which are well itegrated o the trade side. I the Europea cotext, this suggests that the "sigle market" was right to foster free movemet of goods ad capital at the same time. 7 This result however is ot geeral. Urba (00) itegrates a eo-classical growth model ito a static geography model without physical capital mobility. Cotrary to the models preseted here, he shows that lower trade costs lead to covergece betwee the poor ad the rich coutry. The reaso is that the classic local decreasig returs effect implies that there is more icetive to accumulate capital i the poor coutry ad i his model this effect does ot deped o trade costs. O the cotrary, the home market effect, the divergece force, decreases as trade costs dimiish. 9 Basevi ad Ottaviao (00) modify this type of model to ivestigate the itermediate situatio i which capital mobility is either abset or perfectly free. 18

22 4. THE CASE WITH LOCALIZED SPILLOVERS: GEOGRAPHY MATTERS FOR GROWTH (AND VICE VERSA) I the previous sectio, we showed that growth could dramatically alter ecoomic geography i the sese that the process of accumulatio of capital teamed with capital immobility could lead to catastrophic agglomeratio. However, geography had o impact o growth. This was due to the fact that we assumed global spillovers: the learig curve, which as i ay edogeous growth model, was at the origi of sustaied growth, was global i the sese that the orth ad the south would lear equally from a iovatio made i ay regio. I this sectio, we aalyze how localized spillovers give a role i growth to the geography of productio ad iovatio activities Necessary extesios of the basic model Itroducig localized techological spillovers requires a mior modificatio to oe of the assumptios made i the previous sectio 11. Equatio (1) that described the iovatio sector assumed global spillovers i the sese that the margial cost of a iovatio, idetical i both regios, was: F= wa I =1/ W, so that it was decreasig i the total stock of existig capital; i the Grossma ad Helpma (1991), spillovers were global. Grossma ad Helpma (1991) also cosider the other polar of extreme where kowledge spillovers are purely local. Sice the geography of kowledge is a importat topic for policy makers ad a subject that has attracted a great deal of empirical work (see the chapter of Audretsch ad Feldma i this volume), it is more coveiet to allow o-polar assumptios cocerig kowledge spillovers as itroduced by Baldwi ad Forslid (000). Specifically, suppose that these spillovers are localized i the sese that the cost of R&D i oe regio also depeds o the locatio of firms (stock of kowledge capital). Hece, the orther cost of iovatio depeds more o the umber of firms located i the orth tha i the south so that equatio (1) becomes (takig ito accout that the wage rate is equal to 1): F 1 = ai ; ai ; A s + λ ( 1 s ), 0 λ 1 W A (15) 10 Localized spillovers are ot the oly way that geography ca affect growth. Marti ad Ottaviao (001) geerate a feedback betwee growth ad agglomeratio by assumig vertical likages rather tha local spillovers i iovatio. Because the iovatio sector uses maufacturig goods as a iput, the locatio of maufacturig affects the cost of iovatio through trade costs. Yamamoto (00) presets a similar model with circular causatio betwee growth ad agglomeratio comig from the vertical likages betwee the itermediate goods sector ad the iovatio sector. A differet type of geography ad growth model where trade is abset is proposed by Quah (00). The kowledge spillovers are imperfect both across space ad time so that quite ituitively spatial clusters ca appear. The reasoig is ot very differet from Grossma ad Helpma (1991) who show that whe kowledge spillovers are localized the icreasig returs activity cocetrates i oe locatio. 11 Here, localized techology spillovers are assumed. Durato ad Puga (001) provide micro-foudatios for the lik betwee local diversity ad iovatio. Firms that iovate locate i diversified cities ad the relocate i specialized cities to commece mass productio. 19

23 where λ (a memoic for learig spillovers) measures the degree of to which learig from kowledge creatio i oe regio facilitates kowledge creatio i the other regio. The fully global spillovers case is where λ = 1; the fully local case is λ = 0. To put it differetly, the higher the trade costs o the mobility of ideas, techologies, ad iovatios. The cost fuctio of the iovatio sector i the south is isomorphic. Agai the case of perfect capital mobility is easier tha the case without capital mobility. Hece, we will start with the former followig some of the aalysis of Marti ad Ottaviao (1999) ad the describe the model without capital mobility followig Baldwi, Marti ad Ottaviao (001) The case of perfect kowledge capital mobility There are three edogeous variables that we are iterested i: the growth rate g which is commo to both regios i steady state; s, the share of firms that are producig i the orth; ad s E, the share of expediture i the orth which also ca be thought as a measure of icome iequality betwee orth ad south. Remember that with perfect capital mobility, s the share of capital i the orth is give by the iitial distributio of capital as the stocks of capital i both regios grow at the same rate. We wat to fid the differet equilibrium relatios betwee these three edogeous variables. Due to localized spillovers, it is less costly to iovate i the regio with the highest umber of firms (which represet also capital or iovatios). This implies that, because of perfect capital mobility, all the iovatio will take place i the regio with a higher umber of firms. Remember that due to perfect competitio the value of a iovatio is equal to its margial cost. The shares of firms are perfectly tradable across regios (perfect capital mobility) so the value of capital (or firms) caot differ from oe regio to aother ad o iovatio will take place i the south. But the south will be able to simply buy (without trade costs) iovatios or capital produced i the orth. Hece, i the case whe s > 1/, that is whe the iitial stock of capital is higher i the orth tha i the south, we kow from the previous sectio that this will imply that more firms will be located i the orth (s > 1/) so that all iovatio will take place i the orth. I this case the world labor market equilibrium will be give by: g σ 1 = + α + s + λ (1 s ) σ α W L E (1 ) E W Remember also that world expediture is give by E W = L+ρF W. The value ad margial cost of capital is give by F i (15). Usig this ad equatio (16), we get the growth rate of capital g as a fuctio of s, our first equilibrium relatio: g [ s + λ(1 s )] ρ(1 b) 1/ < s 1 = bl (16) (17) 13 The set of basic results is eriched by other cotributios. Ottaviao (1996) as well as Mazocchi ad Ottaviao (001) exted the model of Marti ad Ottaviao (1999) to a three-regio ecoomy. 17 These results of course deped o the assumptio that agglomeratio of ecoomic activities decreases the cost of iovatio. If cogestio costs exist whe the agglomeratio becomes too large, lowerig trade costs betwee regios may have very differet effects. Baldwi et al. (003) show i this case that lower trade costs may lead to a equilibrium with high spatial iequality, high icome iequality ad low growth. 0

24 Compared to the growth rate derived i the previous sectio, this oe differs because of the presece of localized spillovers: spatial cocetratio of firms (a higher s ) implies a lower cost of iovatio ad therefore a higher growth rate. Note also that for a give geography of productio (a give s ), less localized spillovers (a higher λ) also implies a lower cost of iovatio i the orth (as the iovatio sector i the orth beefits more from spillovers of firms producig i the south) ad a higher growth rate. The arbitrage coditio cosistet with the assumptio of perfect capital mobility requires profits to be equalized i the two locatios so that π =π*=be W / W. This gives the same equilibrium relatio betwee s ad s E as i the previous sectio (equatio 8). To fid the third equilibrium relatio, oe betwee s E ad g, remember that due to itertemporal optimizatio, E= L+ρv where v is the value of capital which itself is equal to the discouted value of future profits. Usig these relatios, it is easy to get the last equilibrium relatio: s = 1 ρ + b g + ρ E s 1 Note that icome iequality betwee the two regios is decreasig i the growth rate as log as the orth is iitially richer tha i the south i capital stocks (s > ½). This is because the value of capital decreases with growth due to faster etry of ew firms. The equilibrium characterized by these three relatios is stable for the same reasos as i the case of perfect capital mobility of the previous sectio. Capital mobility allows southerers to save ad ivest buyig capital accumulated i the orth (i the form of patets or shares). Hece, the lack of a iovatio sector does ot prevet the south from accumulatig capital: the iitial iequality i wealth does ot lead to self-sustaiig divergece. No circular causality mechaism which would lead to a core-periphery patter, as i the NEG models of the type of rugma (1991), will occur. Usig equatios (8), (17) ad (18), the equilibrium is the solutio to a quadratic equatio. Oe ca fid the trade cost such that relocatio goes from orth to south i the case where s > 1/ (which implies also that s > ½). s > s if: λl(1 s ) + Ls φ < λl(1 s ) + Ls + ρ Note that whe all the capital is owed by the orth (s =1), the the threshold level of trade cost is agai φ CP give i the previous sectio. Note also that i the less extreme case where s <1, less localized spillovers imply, everythig else costat, that relocatio will take place towards the south. The reaso is that less localized spillovers imply a lower cost of iovatio i the orth, ad therefore a lower value of capital of which the orth is better edowed with. Hece, less localized spillovers geerate, for a give distributio of capital, a more equal distributio of icomes ad expeditures ad therefore attract firms i the south. Oe could aalyze the properties of this equilibrium by aalyzig the equilibrium locatio s. However, it is more revealig to use a graphical aalysis. Equatio (8) provides a positive relatio betwee s ad s E, the well kow demadliked effect. I figure 5, this relatio is give by the curve s (s E ) i the NE quadrat. Equatio (18) 1

25 (17) provides a positive relatio betwee g ad s. This is the localized spillovers effect: whe idustrial agglomeratio icreases i the regio where the iovatio sector is located, the cost of iovatio decreases ad the growth rate icreases. This relatio is give by the lie g(s ) i the NW quadrat. Fially, equatio (19) provides a egative relatio betwee s E ad g. This is a competitio effect: the moopoly profits of existig firms decrease as more firms are created; as the orth is more depedet o this capital icome, the orther share of icome ad expeditures decreases. This relatio is described by the curve s E (g) i the SE quadrat. This graph ca be used to aalyze the relatio betwee the geography of icome, the geography of productio ad growth Spatial equity ad efficiecy A icrease i regioal iequality i capital edowmets s shifts to the right the s E (g) i the SE quadrat. The impact is therefore a icrease i icome iequality ad a icrease i spatial iequality i the sese that s icreases. However, because the ecoomic geography becomes less dispersed ad therefore more efficiet from the poit of view of localized techology spillovers, the growth rate g is higher. Hece the itroductio of growth ad localized spillovers i a geography model is at the origi of a trade-off betwee spatial equity ad efficiecy (see Marti 1999 for a aalysis alog these lies) which may have importat implicatios for public policies. Equilibrium growth, agglomeratio ad regioal icome iequality s s E g(s ) s (s E) s g s E s E(g) g g Figure 5: Spatial equity ad efficiecy

26 It is also easy to aalyze the impact of lower trade costs o goods (higher φ). For a give icome disparity, it icreases spatial iequality so that the schedule s (s E ) shifts up i the NE quadrat. This i tur icreases the growth rate which leads to lower icome iequality, a effect that mitigates the iitial impact o spatial iequality. Overall eve though spatial iequality has icreased, the growth rate has icreased ad omial icome disparities have decreased. 17, 18 It is also iterestig to aalyze the effects of a icrease i λ that is less localized techology spillovers. This ca be iterpreted as lowerig trade costs betwee regios o ideas ad iformatio. Public policies that improve ifrastructure o telecommuicatio, the iteret or educatio may be iterpreted as affectig λ. This shifts the g(s ) to the left i the NW quadrat so that growth icreases for a give geography of productio. This lowers icome disparities betwee the two regios as moopolistic profits are eroded by the etry of ew firms. This i tur brigs a decrease i spatial iequality o the geography of productio as s decreases. More geerally, a exogeous icrease i growth will lead to less spatial agglomeratio ad less regioal icome iequality. This is importat because it implies that, eve i the presece of localized techology spillovers, the sig of the correlatio betwee growth ad agglomeratio depeds o the ature of the forces at work. 4.. Welfare implicatios The structure of the model is simple eough so that it is fairly easy, at least compared to the other models, to preset some welfare implicatios. Oe questio we ca ask is whether the cocetratio of ecoomic activities, geerated by market forces, is too small or too importat from a welfare poit of view (see Baldwi et al. 003, chapters 10 ad 11 for a more detailed aalysis). Two distortios, which are directly liked to ecoomic geography, exist here. First, whe ivestors choose their locatio they do ot take ito accout the impact of their decisio o the cost of iovatio i the orth where the iovatio sector is located. Localized positive spillovers are ot iteralized i the locatio decisio ad from that poit of view the market ecoomic geography will display too little spatial cocetratio. Secod the locatio decisio also has a impact o the welfare of immobile cosumers which is ot iteralized by ivestors. This happes for two reasos. O the oe had a icrease i spatial cocetratio affects egatively the cost ad therefore the value of existig capital so that the wealth of capital owers i both regios decreases. This affects more the orth tha the south. O the other had, whe spatial cocetratio i the orth icreases, cosumers i the orth gai because of the lower trasport costs they icur. Symmetrically, cosumers i the south loose. V ad V*, the idirect idividual utilities of orth ad south respectively, as a fuctio of the spatial cocetratio s ad of the growth rate g are give by: V 1 ρ s = + l 1 + α α g C + l[ s + φ1 s )] + (19) ρ Ls σ(s 1) ρ ( σ 1) 18 Marti (1999) also shows that lowerig trasport costs iside the poor regio will have exactly the opposite effect as it leads firms to relocate ito that regio. 3

27 V * 1 ρ (1 s = C + l 1 + ρ Ls ) α + l 1 ρ( σ 1) [ s + φ s ] α g + ρ ( σ 1) where C is a costat. We ca aalyze how a chage i the spatial cocetratio s affects welfare i both regios: V s V s * Lα (1 λ) = - ρ σ ( σ - 1) L s Lα (1 λ) = - ρ σ ( σ - 1) L s s + ρs 1 s s + ρ(1 s α + ρ( σ - 1) s ) s 1 -φ + φ(1 s α 1 -φ ρ( σ - 1) 1 s + φs There are three welfare effects of a chage i spatial cocetratio. The first term is idetically positive i both regios: a icrease i spatial cocetratio icreases growth because, through localized spillovers, it decreases the cost of iovatio. The secod term is egative i both regios: the decrease i the cost of iovatio also dimiishes the value of existig firms ad therefore dimiishes the wealth of capital owers. Because the orth ows more capital tha the south, this egative effect is larger i the orth tha i the south. Fially, the last term represets the welfare impact of higher cocetratio o trade costs. This welfare effect is positive i the orth ad egative i the south. To aalyze whether the market geography displays too much or too little cocetratio i the orth implies to evaluate these two equatios at the market equilibrium. It ca be checked that as log as λ is sufficietly small (techological spillovers are sufficietly localized), the effect of a icrease i spatial cocetratio is always positive o the orth. It is iterestig that the orth will gai less by a icrease i geographical cocetratio if it ows a larger share of the capital. Aother way to say this is that capital owers may loose from geographical cocetratio i the orth. Geographical cocetratio i the orth may improve welfare i the south. This is i stark cotrast with static ecoomic geography models where the southerers always loose followig a icrease i cocetratio i the orth. Here the positive effect o growth may more tha compesate the egative impact of cocetratio o trade costs ad o wealth. This will be so if λ is sufficietly small (techological spillovers are sufficietly localized), ad if trade costs are low eough. ) (0) 4.3. The case without capital mobility: the possibility of a growth take-off ad agglomeratio As i the case of globalized spillovers, allowig perfect capital mobility stabilizes the localized spillovers model by elimiatig demad-liked circular causality. We tur ow to the opposite assumptio capital immobility. As we shall see, this opes the door to some spectacular iteractios betwee growth ad geography. Here we follow the aalysis of Baldwi, Marti ad Ottaviao (001). The model is idetical to the oe described i the previous sectio except for the itroductio of localized spillovers as described i sectio (4.). This has several cosequeces: the geography of productio has ow a impact o the cost of iovatio so that as i sectio (4.) the global growth rate is affected by geography. The value of capital, which ca differ i the two regios as capital mobility is abset, is itself affected by geography because the iovatio sector is 4

28 perfectly competitive. Hece, the margial cost of capital ad iovatio is equal to its value. I tur, this affects wealth ad expeditures i the two regios so that profits will deped o geography i this way too. This implies that the two relatios betwee the share of capital i the orth (s ) ad the share of expeditures i the orth (s E ) are goig to be much more complex tha i the case without localized spillovers The log-ru equilibria ad their stability The optimal savigs/expediture fuctio derived from itertemporal utility maximizatio, which we iterpreted as a permaet icome relatio i the previous sectio (equatio 8) becomes: ρλ(s 1) * { LAA + ρ[ A(1 s ) + A s ]} s E = 1/ + * (1) where A is give i (15) ad A* is the symmetric. The permaet icome relatio is such that s E is always icreasig i s : a icrease i the orther share of capital icreases the orther share of expeditures. Whe we cosider iterior steady states where both regios are ivestig (iovatig), so that q =1 ad q * =1, the secod relatio betwee s E ad s, which we called the optimal ivestmet oe, becomes, i the presece of localized spillovers: (s 1)( λ + λφ φ ) s E = 1/ + * 1 ( φ )[ A(1 s ) + A s ] Note of course that s E = s = ½, the symmetric equilibrium is a solutio to the two equilibrium relatios (3) ad (4). Two other solutios to this system may exist which are give by: s = 1/ ± 1 1+ λ 1+ λλ 1 λ 1 λλ ; ρφ(1- λφ) Λ 1- L( λ + λφ φ Both s E ad s coverge to ½ either as λ approaches 1 or as φ approaches the value: φ cat L(1 + λ) + ρ = λ (1 λ )[ L(1 + λ) + ρ] [ L(1 + λ) + ρ] from above. For levels of φ below φ cat, these two solutios are imagiary. I additio, for levels of φ above aother critical value: φ CP' L + ρ = (L + ρ) 4λ λ( L + ρ) L( L + ρ) oe of the solutios is egative ad the other oe is above uity. Sice both violate boudary coditios for s, the correspodig steady state outcomes are the corer solutios s = 0 ad s =1. Note that for λ = 1, φ cat = φ CP = φ CP as defied i the previous sectio. As i the case without localized spillovers, we ca study the stability of the coreperiphery equilibrium by aalyzig the value of q* at s =1: + λ ρ 1 () (3) (4) (5) 5

29 q * s λ = [ L(1 + φ ) + ρφ ] φ( = 1 L + ρ) Whe q* < 1, we the kow that the core-periphery equilibrium is stable as the south has o icetive to iovate ay more. It is easy to check that q*<1, whe φ > φ CP. The stability of the symmetric equilibrium ca be studied followig the same method as i the case without localized spillovers. We tur to sigig q/ s evaluated at the symmetric equilibrium. Differetiatig q with respect to s, we have: q s / q s =1/ 1 φ ds = 1+ φ d s E s =1/ 4 1+ φ + 1+ λ (1 + φ) (1 φ) 1 λ 1+ φ Usig (1) to fid s E / s = λρ /[(1 + λ)( L(1 + λ) + ρ) ], whe evaluated at s = ½, we see that the system is ustable (the expressio i (7) is positive) for sufficietly low trade costs (i.e. φ 1). The two effects discussed i the previous sectio i the case without localized spillovers are still preset. The first positive term is the demad-liked effect: a icrease i s icreases orth s capital icome, expediture share ad local profits so that the value of a iovatio (the umerator of Tobi s q) icreases. The last egative term is the stabilizig market crowdig effect. The secod (positive) term is ew ad ca be thought of as the localized spillovers effect: a icrease i s implies a lower cost of iovatio i the orth (the deomiator of Tobi s q) ad therefore icrease the icetive to iovate i the orth Possibility of catastrophic agglomeratio It is possible to show that φ cat < φ CP < φ CP. Hece, localized spillovers make the catastrophic agglomeratio possible for higher trade costs. The critical level at which the expressio i (7) becomes positive is φ cat. Stadard stability tests ivolvig eigevalues ca be used to derive the same result. Figure 6 summarizes the model s stability properties i a diagram with φ ad s o the axes. It shows that up to φ cat, oly the symmetric equilibrium exists ad is stable. Betwee φ cat ad φ CP, the symmetric steady state looses its stability to the two eighborig iterior steady states, which are thus saddle poits by cotiuity. After φ CP, oly the core-periphery equilibria are stable. Note that these ca be attaied oly asymptotically because, due to the absece of capital depreciatio, the south share of capital ever goes to zero eve after it stops ivestig (i.e. after φ CP ). (7) (6) 6

30 s 1 Symmetric (stable) Core- Periphery (stable) 1/ Symmetric (ustable) Iterior osymmetric(stable) φ 0 (o trade) φ cat φ CP 1 (free trade) Figure 6: Stability properties of equilibria i the presece of localized spillovers Geography affects growth Itroducig localized techology spillovers implies that ecoomic geography affects the global growth rate ad the model geerates edogeous stages of growth. I the versio with capital mobility, the result that geography affects growth was already preset. However, because of the absece of possible catastrophe, the relatio betwee geography ad growth was liear. This is ot the case here. There are differet stages of growth i the sese that if we thik that trade costs are lowered with time, the as ecoomic geography is altered i a o liear way, the growth rate itself chages i a o liear maer. Whe trade costs are high so that φ < φ cat, the equilibrium ecoomic geography is such that idustry is dispersed betwee the two regios. This implies that spillovers are miimized ad the cost of iovatio is maximum. Usig the optimal ivestmet coditio q = q* = 1, ad the fact that s = ½, it is easy to fid the growth rate (see also equatio (18) usig s = s = ½) i that first stage: g = bl( 1+ λ) ρ(1 b) The growth rate of course icreases with λ. Asymptotically, whe s = 1, spillovers are maximized so that the cost of iovatio is miimized. Agai usig equatio (18) with s = s = 1, the growth rate is i that stage: g = bl ρ (1 b) (9) which is, of course, idetical to the solutio whe spillovers are global sice i the core-periphery outcome, all iovators are located i the same regio so that learig is ot affected by the degree of localizatio λ. The growth rate i that fial stage is higher tha the growth rate i the first stage whe trade costs are high. I the former stage, iovatio has stopped i the south which the is (8) 7

31 etirely specialized i the traditioal good. I the itermediate stage, which we call the take-off stage, i.e. whe trade costs are such that φ cat < φ < φ CP, the growth rate caot be aalytically foud. However, it ca be characterized as a take-off stage as the bifurcatio of the system etails that the ecoomy leaves a eighborhood of the symmetric steady state to reach a eighborhood of the asymmetric steady state i fiite time. To sum up, we have see that a gradual lowerig of trade costs o goods (a icrease i φ) leads, oce the trade cost passes a certai threshold, to a catastrophic agglomeratio characterized by a sudde acceleratio of iovatio i oe regio (take-off) mirrored by the sudde halt of iovatio i the other regio. The orth (the take-off regio) eters a virtuous circle i which the icrease i its share of capital expads its relative market size ad reduces its relative cost of iovatio which i tur iduces further iovatio ad ivestmet. I cotrast, the south eters a vicious circle i which lower wealth leads to lower market size ad lower profits for local firms. It also leads to a icrease i the cost of iovatio so that the icetive to iovate dimiishes. Hece, growth affects geography which itself affects growth ad agglomeratio is drive by the appearace of growth poles ad siks Ca the Periphery Gai from Agglomeratio? I most geography models, agglomeratio is a wi-lose bargai. Residets of the regio that gais the idustry typically ejoys a icrease i welfare while those left i the periphery see their real icomes fall. Allowig for edogeous growth opes the door to a importat caveat to this pessimistic sceario. The cotiual lowerig of trade costs produces ueve spatial developmet real percapita icome rises i the core regio (sice it saves the trade costs o all M-varieties) ad falls i the peripheral oe (sice it pays the trade costs o all M-varieties). However, the emergece of regioal imbalaces is accompaied by faster growth i all regios (growth take-off). Of course, this is good also for the periphery ad creates a tesio betwee the static loss due to relocatio ad the dyamic gai due to faster growth. Thus, while the core is uambiguously better off, the take-off has ambiguous effects o the welfare of the periphery. Ituitio is served by Figure 7, which plots the log ru levels of welfare i the two regios as fuctios of trade freeess. I particular, it depicts a sceario i which lower trade costs drive all idustry towards the orth. Whe trade is sufficietly closed, freer trade raises welfare i both regios because it lowers the price of imported maufactured goods. As trade freeess rises above the break poit, orth ad south welfare levels diverge. The orth beefits from agglomeratio ad faster growth. The south beefits oly from the latter, while it is harmed by the former. This explais why the south s post-take-off welfare is always below the orth s. Oce full agglomeratio has bee reached (i.e., freeess has rise above the sustai poit), the orth s welfare is costat. The behavior of south s welfare is more complex. If the expeditures share of maufacturig goods µ is low eough, the icrease i the growth rate has oly a mild impact o welfare ad the static loss domiates. I this case, the South loses from the take-off. This case is show by the solid lie (the lowest oe i the diagram). O the cotrary, if the share µ is sufficietly large, the dyamic gai domiates ad the take-off beefits both regios, as show by the dotted lie. Fially, for itermediate values of µ, the south iitially loses but evetually 8

32 attais a welfare level that exceeds its pre-take-off situatio. This is illustrated by the dashed curve. Welfare orth South high µ south medium µ orth & south south low µ φ Β φ S 1 Free-ess of trade (φ) Figure 7: Agglomeratio, growth ad welfare Importatly, after the take-off lowerig trade costs always improves welfare i the south because it decreases the price of goods imported from the orth. Thus, eve though the south may have bee made worse off by agglomeratio i the orth, resistig further reductios i trade costs is ot welfare improvig The geography of goods ad ideas: Stabilizig ad destabilizig itegratio The mai focus i the NEG literature has bee o the cosequece of fallig trasactio costs o trade i goods. We have show that i a dyamic model with edogeous growth ad localized spillovers, lower trade costs o goods have a effect o idustry locatio but also o the growth rate. These effects ca be catastrophic or ot, depedig o the mobility of capital. Ecoomic itegratio, however, is a multi-faceted pheomeo. Up to this poit, we have look at two types of closer itegratio lowerig the cost of trade i goods, ad makig capital more mobility. There is aother aspect of itegratio, however, which ca also be importat, amely itegratio that results i lower barriers to the spatial diffusio of learig kowledge spillovers. What might be called the cost of tradig ideas. I the model itroduced above (localised spillovers ad immobile capital) we ca study the impact of makig trade i ideas freer by chagig the learig spillover parameter λ. 0 0 eller (00) shows that techology spillovers have ideed become cosiderably more global betwee 1970 ad

33 s Core-Periphery (stable) Symmetric (ustable) Iterior osymmetric (stable) 1/ Symmetric (stable) λ 0 (o spillovers) λ mir λ mir 1 global spillovers Figure 8: Fallig trasactio costs o ideas: Stability properties of equilibria i the presece of localized spillovers Globalizatio ad the ewly idustrialized coutries Oe exercise that illustrates the iteractios focuses o the fact that both φ cat ad φ CP are icreasig i λ. The ituitio is that as spillovers are becomig more global, a icrease i the orther share of capital does ot decrease much the relative cost of iovatio i the orth (a destabilizig effect), so that the capital icome effect (the stabilizig effect based o lower trade costs o goods) must be stroger. Oe importat implicatio is that from a situatio with full agglomeratio i the orth (s = 1) ad fixed trade costs o goods, a gradual icrease i λ (more globalized spillovers due for example to fallig telecommuicatio costs) iitially has o impact o souther idustry. However, because the cost of iovatio i the south decreases with λ, Tobi s q i the south icreases with λ. At some poit, whe λ is high eough, q* becomes more tha 1, ad the south begis to iovate. The value of this threshold level which we call λ mir (for miracle ) is: λ mir ( ρ) φ L + = L (1 + φ ) + ρφ As i the case of fallig trade costs o goods, there is a secod critical value where the symmetric equilibrium becomes stable. This value, deoted as λ mir is the level of λ such that q/ s evaluated at the symmetric equilibrium becomes egative. As with the orth take-off, the (30) 30

34 miracle i the south would appear as a virtuous circle: as it starts ivestig, its wealth ad permaet icome rise so that market size i the south ad profits made by local firms icrease. I tur, as the umber of iovatios made i the south icreases, the cost of future iovatios decreases. This miracle implies a jump i the ivestmet rate, as Tobi s q i the south is more tha 1, ad rapid idustrializatio. Also icomes betwee the south ad the orth coverge. Figure 9 describes the effect of a icrease i λ o the model s stability properties i a diagram with λ ad s o the axes. λ (extet of regioal kowledge spillovers) 1 Symmetric stable, CP ustable Itegratio Path #: Trade itegratio with pro-spillover policies Oly asymmetric iterior equilibra stable Iitial poit Itegratio Path #1: Trade itegratio oly 0 1 CP stable, symmetric ustable φ (freeess of trade) Figure 9: Stability Map for LS Model: Stabilizig ad Destabilizig Itegratio 4.4. The learig-liked circular causality Aother way to characterize the essetial iterplay betwee the cost of tradig goods ad ideas is to focus o the symmetric outcome rather tha the fully-agglomerated outcome. It is useful to poit out that the localizatio of learig i the I-sector creates its ow distict agglomeratio force. This ew force, which is very much aki to a cost-likage that operates i the I-sector, ca be called learig-lik circular causality. That is, if a regio gets a slightly large amout of kowledge, it becomes a more attractive (cheaper) place to produce more kowledge, all else equal. Sice a faster rate of kowledge creatio sustais ad deepes the regio s advatage, a iitial bit of kowledge shiftig leads to kowledge-creatio shiftig which i turs leads to kowledge shiftig. Give this logic, it should be clear that makig it easier to trade ideas (i.e. raisig λ) teds to stabilize the symmetric equilibrium. We see therefore that there ca be a tesio betwee the de-stabilizig tedecy that arises whe goods become cheaper to trade ad the stabilizig tedecy that arises whe ideas become easier to trade. 31

35 To ivestigate a sceario i which the cost of sharig ideas λ chages together with the cost of tradig goods φ, Figure 9 depicts what Baldwi ad Forslid (000) call a stability map. This shows how the model s stability properties vary with λ ad φ. The diagram plots the break ad sustai poits agaist the various possible values of λ ad φ. The dashed curve is the break poit ad the solid curve is the sustai poit. The curves partitio the map ito three regios. Whe trade is ot very free, ad/or kowledge spillovers are very free, the the symmetric outcome is stable ad the core-periphery outcomes does ot exist. This is the orthwest regio i the diagram. Whe trade is quite free ad/or kowledge flows are very restricted, oly the coreperiphery outcomes are stable. This is the southeast regio of the map. For a arrow rage of φ s, two asymmetric iterior equilibria are the oly stable equilibria ad this is show as the area betwee the two curves. The results also poit out to a stark differece betwee lowerig trade costs o goods ad lowerig trasactio costs o ideas. Lower trade costs o goods may foster divergece i icomes if it triggers a agglomeratio process. However, lowerig trasactio costs o ideas has the opposite effect as it ca make the core-periphery equilibrium ustable ad trigger a sudde idustrializatio i the south which leads to covergece. I our model, the distictio betwee trade costs o goods ad trasactio costs o ideas is a easy oe. However, i reality tradig goods ofte implies exchagig ideas i the process so that the processes that gover the evolutio of the two types of trasactio costs are certaily itertwied. 5. OTHER CONTRIBUTIONS A early attempt to lik growth ad geography models was Walz (1996) who itroduces edogeously expadig product variety i a model with vertical likages ad migratio. His assumptio of costless migratio leads to a bag-bag migratio behavior. Walz (1997) exteds the model to a three-regio settig. Black ad Hederso (1999) model the relatio betwee urbaizatio ad growth: there are localized kowledge spillovers so that urbaizatio affects the edogeous growth of the ecoomy. Growth itself affects the size of cities. However, the assumptio of a migratio process that is determied by a city developer seems rather restrictive. The models of growth ad geography fid their atecedets i models of edogeous growth ad trade i particular Grossma ad Helpma (1991). Some of the results o geography are already preset as these authors show that with free trade ad whe kowledge spillovers are localized, the icreasig returs activity cocetrates i oe locatio. Models of edogeous growth ad trade do ot however all imply that free trade leads to divergece if trade also ivolves capital goods as show by Goh ad Olivier (00). Fujita ad Thisse (00 chapter 11 ad 003) combie a rugma type core-periphery model ad a Grossma-Helpma growth type model with horizotally differetiated products. As i the previous sectio ad the earlier literature o growth ad agglomeratio, they use a set-up where the fixed cost of firms is a patet. They aalyze the two cases of tradability ad o tradability of the patets. The skilled workers who produce these patets are themselves mobile ad they show that this is destabilizig factor. I the case of tradable patets, whe trade costs are sufficietly low, a core-periphery patter emerges with all the R&D sector as well as most of the maufacturig sector cocetrated i oe regio. I this case, agglomeratio takes place because 3

36 of workers mobility ad ot because of growth but growth is iflueced positively by spatial cocetratio because of the presece of localized spillovers. With o-tradability of patets, a third destabilizig force is added (the first beig the mobility of skilled workers ad the secod beig the localized spillovers) so that the core-periphery becomes sustaiable at higher trade costs. Baldwi (1999) presets a eoclassical growth model combied with a ecoomic geography model. He shows that growth ca affect the locatio idustry sice chages i regioal capital stocks chage the relative size of regioal markets ad this, via the home market effect, alters that spatial allocatio of idustry. The key to this is the fact that forces that ecourage productio i oe regio also ted to ecourage capital accumulatio i that regio. To put it differetly, capital accumulatio is aother way i which expediture shiftig ca be tied to productio shiftig. Moreover, whe this demad-likage is eutralized by assumig that all capital earigs are repatriated, the likage is broke. Figure 10: Real Per Capita Icome Chages CP vs CC Models Per capita real icome Norther real icome, CP model Per capita real icome Norther real icome, CC model Souther real icome CP model Souther real icome CC model φ B 1 φ φ B 1 φ Whe capital is immobile, the paper illustrates a secod ovel feature geography ca affect regioal growth, at least i the medium-ru. I particular, the Perroux (1955) otio of growth poles ad growth siks appears very clearly. Cosider, for istace, iitially symmetric regios facig trade costs that are high eough to esure that the symmetric outcome is stable. Whe trade becomes free eough, symmetry becomes ustable. To be cocrete, assume a small shock puts the orth a little a bit ahead so the core will evetually ed up i the orth. The istability arises sice the reward to capital rises i the orth ad falls i the south. This i tur would iduce orther residets to raise their ivestmet rate above the rate ecessary to sustai the iitial capital stock. The cosequece might be called agglomeratio-iduced, ivestmet-led growth. The orth s ivestmet rate rises, boostig its capital-labor ratio, ad thus its per capita icome ad output. This expasio of market size further favors ivestmet i the regio. I short, the orth has become a growth pole. Circular causality has a iterestig iterpretatio i 33

37 this cotext. Ivestmet i the growig regio is favored precisely because expediture i the regio is growig ad expediture is growig due to the high ivestmet rate. The reverse process operates i the south. The lower rate of retur iduces souther cosumers/savers to stop ivestig, so depreciatio erodes the souther capital stock ad souther per capita icome ad output begi to drop. Give the particular depreciatio process assumed, foreig firms shut dow oe by oe. I the simple models we work with here, workers displaced by the dowsizig of the south s idustrial sector immediately fid ew jobs i the o-idustrial sector. However, if fidig a ew job or expadig the o-idustrial sector took time, the periphery's dowward spiral would be associated with above-ormal uemploymet; the same labor market features would imply 'labor shortages' i the growig regio. More colloquially, the decliig regio would resemble a 'rust belt' ad the ascedig regio would resemble a 'boom belt'. Allowig growth leads to aother feature ot commoly foud i ecoomic geography models that exclude cosideratios of growth. I the stadard core-periphery ecoomic geography model fallig trade cost ca produce asymmetries i iitially symmetric regios. At itermediate trade costs, the two regios also experiece divergece of their real per capita icomes, but evetually, free trade re-equalizes icomes. This is illustrated i the left pael of figure 10 with the heavy solid lies (CP model stads for core-periphery model). At the break poit, all idustry moves orth (for coveiece, the diagram assumes all H moves immediately) ad this raises orther per capita icome. I Baldwi (1999), which assumes capital is immobile, the core-periphery outcomes comes about as a result i a chage i the two regio s capital labor ratios, with the orth s risig ad the south s fallig. Thus eve at free trade, the per capita icomes of the orth are permaetly higher tha those of the south. This is show i the right pael of figure 10 with CC model stadig for costructed capital model. As a aside, we should also ote that Baldwi (1999) also added a ew elemet to the eoclassical growth literature. This literature typically predict covergece of regioal icome levels. I Baldwi (1999), however, progressive trade liberalizatio betwee symmetric atios evetually produces the core-periphery outcome. Thus, cotrary to the stadard assertio i the growth literature, i this eoclassical growth model, ecoomic itegratio produces divergece i real per-capita icome levels. 6. CONCLUDING REMARS Itroducig growth ito ecoomic geography models icreases the degree of complexity of models that are already quite complex. Is it worth it? What isights do we gai from the marriage of growth ad geography? Geography ad growth models display a umber of features that do ot appear i static ecoomic geography models. These features are iterestig sice they help us orgaize our thikig about importat real-world pheomeo ad policies. Specifically: 1. I these models growth affects geography by creatig what could be called growth-liked circular causality; forces that foster the locatio of idustry i a regio also foster the ivestmet, i.e. the accumulatio of huma, physical ad/or kowledge capital i that regio. Sice these ew 34

38 factors ear icomes ad sped part of these icomes locally, capital accumulatio alters relative market size.. The agglomeratio process i these models would look like the appearace of growth poles ad siks firms wat to be i the growig regio, people wat to ivest i that regio sice it is growig ad this ivestmet i tur makes the regio grow faster. The opposite spiral would appear to be operatig i the growth sik. 3. The simple geography models predict that everyoe should be idifferet to agglomeratio oce trade became really free. I growth ad geography models, regio capitallabor ratios edowmets are permaetly altered by agglomeratio. Thus regioal, real per capital icome differetials do ot disappear as trade gets perfectly free. 4. Ecoomic itegratio is a multi-faceted pheomeo i the real world, yet the stadard models focus almost exclusive i the cost of sellig goods at a distace. Ecoomic itegratio has a much richer meaig i geography ad growth models. Geography ad growth models show that the cost of movig capital across borders (capital mobility) ad the cost of movig ideas across borders (learig spillovers) are also importat aspects of ecoomic itegratio. I particular, these other policies ca mitigate or exteuate the de-stabilizig aspects of freer trade. 5. Perhaps the most importat ew feature of geography ad growth models is the way i which they allow us to crystallize our thikig about the iterplay betwee the locatio of ecoomic activity ad the growth rate of ecoomic activity. 6. Oe aspect of this iterplay is importat for policy aalysis. Takig the stadard ecoomic geography models at face value produces higher protectioist policy implicatios (see Baldwi et al 003, chapter 1) sice agglomeratio of idustry is always a wi-lose situatio. I the geography ad growth models, the result is ot so stark. The cotiual lowerig of trade costs does produce ueve spatial developmet real per-capita icome rises i the core regio ad falls i the peripheral oe. However, the emergece of regioal imbalaces is accompaied by faster growth i all regios. Of course, this is good also for the periphery ad creates a tesio betwee the static loss due to relocatio ad the dyamic gai due to faster growth. Thus, while the core is uambiguously better off, the take-off has ambiguous effects of peripheral welfare. A similar applicatio is to realize that regioal policies at the atioal level that seek to avoid geography cocetratio of idustry may cost the coutry as a whole i growth terms. The itroductio of growth i geography models thus adds a ew dimesio to the possible spatial equity-efficiecy tradeoff. 7. Perhaps the most sweepig applicatio of these models ad oe that is ot yet complete cocers what might be called the grad uified theory of globalizatio ad geography. Here are the stylized facts of globalizatio sice the mid 19th cetury that the uified theory would have to explai. The world has see two waves of globalizatio oe from roughly 1850 to 1914 ad oe from the 1960s to the preset. At a high level of abstractio the key facts are: Idustrializatio/De-idustrializatio. I the first wave, the North (Wester Europe ad the US) idustrialized while South (especially Idia ad Chia) de-idustrialized. I the secod wave, the South (East Asia) idustrializes while the North de-idustrializes. Divergece. The first wave sees North ad South icomes diverge massively, while the secod wave witesses a covergece, at least betwee the North ad the idustrializig South. 35

39 Trade. Iteratioal trade i goods ad factors (labor migratio ad log-term capital flows) exploded i the first wave. After beig shut dow by two world wars, a surge of protectioism ad the Great Depressio, the secod wave was marked by a retur of trade ad capital flows to levels that have recetly topped those see i Victoria Eglad. Mass iteratioal migratio, however, remais small by the stadards of the first wave. Growth Take-off. Sometime before the first globalizatio wave kicks i, the Idustrial Revolutio triggers moder growth i the North, but the South cotiues to stagat i per capita terms. Moder growth, defied as a self-sustaied growth process whereby output per hour worked rises steadily, begis i the U ad spreads to Wester Europe ad the US aroud the middle of the 19th cetury. Of course, this it ot idepedet of the icome divergece sice big differeces i icome levels come from sustaied differeces i growth rates ot from oe-time shifts of the locatio of idustry. Moreover, the limited icome covergece i the secod wave is liked to spectacular growth i the idustrializig South ad a moderate slowdow i the North. Urbaizatio. While some of the largest cities i the world were i the South prior to the 19th cetury, the first globalizatio wave is accompaied by a rapid ad historically uprecedeted urbaizatio i the North. Norther urbaizatio cotiued durig the secod wave but cities grew eve more rapidly i the South. The closest the o-growth geography models have come to this is rugma ad Veables (1995), a paper that was kow o the streets as history-of-the-world-part-i. This paper sews together the first three of the five facts as follows. I 1750 or so, the world s ecoomic geography was quite homogeeous, i.e. poor ad agraria. With domestic ad iteratioal trade costs early prohibitive, each village essetially had to make all its ow goods; this meat maufactured goods were dear ad the available rage of varieties limited. As trade costs fell, both iside ad betwee atios, specializatio became feasible ad this triggered a process of what Myrdal called cumulative causality. Modelig this circular-causality process is the heart of the NEG cotributio, so a aside is i order. Migratio of firms or workers dehomogeize the world, turig it ito ecoomically big ad small regios (markets). Whe idustries are imperfectly competitive ad trade is costly, rugma s home market effect favors the locatio of idustry i large regios, but sice idustries are marked by icreasig returs, gettig a disproportioate share of idustry meas a regio s labor is disproportioately productive ad this i tur results i higher real wages ad/or a higher retur to capital. The circle is closed by otig that capital ad labor are attracted to the regio with higher rewards ad their migratio makes the big regio bigger ad the small regio smaller. Accordig to rugma-veables, advaces i trasport techology i the early 19th cetury triggered this de-homogeizatio of the world s ecoomic geography, ad, as history would have it, the North wo at the South s expese. This sigle evet is the root cause of the first three facts: Norther idustrializatio ad Souther de-idustrializatio, the rapid expasio of iteratioal trade (Eglad becomes the world s workshop providig cheap ad varied maufactured goods i exchage for raw materials ad this specializatio both fosters trade ad is fostered by it), ad icome divergece (due to icreasig returs i idustry ad decreasig returs i other sectors, a high share of idustry i GDP meas high labor productivity ad thus high icomes). 36

40 Oe problem with this story is that the magitudes just do ot fit. Oe-time cocetratios of idustry just caot accout for the observed icome gaps. Here is the argumet. rugma- Veables igore edogeous techological progress, assumig that physical techology is idetical i the North ad South. Thus i the rugma-veables story, the differece i icomes betwee the U ad Idia must be due to the differece i idustry s share i the U ad Idia output mix ad the productivity gap betwee idustry ad traditioal sectors. If the U s per capita icome was 100 i 1850, Idia s was 3 accordig to Maddiso (1995, Tables C16 & D1), so the icome gap to be explaied is 77. Moreover, Crafts (1989) tells us that i 1840, 47% of the U workforce was i idustry, ad Bairoch (198, Table 9) tells us that Idia was oly 4.7% as idustrialized as the U i 1860, so (igorig the mismatch i dates) we ca coclude that the static allocatio of idustry ca oly accout for the icome differece if idustrial workers are 171 times i.e. 17,100% more productive tha workers i the traditioal sector. This just caot be right. Plaily, the real story must lie elsewhere ad growth is the obvious suspect. Ideed, sice the headlie story i the 19th cetury was the spread of moder growth, the rugma-veables story is a bit like Hamlet with the Price. Clearly, oe has to add edogeous growth to the rugma-veables story to accout for the facts o icome divergece/covergece as well as o growth take-offs. As show i this chapter, allowig for edogeous growth, localized spillovers ad some capital immobility, we ca get the fourth fact of globalizatio ito a uified framework. The oly facts left u-accouted for cocers urbaizatio. To get this ito the story, oe would have to allow iteral geography i the regios cosidered, but oce the techical difficulties were mastered, the ecoomics would be straightforward. I the first wave of globalizatio, ecoomic activity characterized by localized spillovers is cocetratig i the North. It would ot therefore be too surprisig that urbaizatio proceeded faster i the North tha i the South durig this era. Likewise, i the secod wave of globalizatio, the idustrializatio of the South (emergece of the Asia tigers, etc.) stregthes the forces that foster withi South cocetratio of ecoomic activity, i.e. urbaizatio, while the de-idustrializatio of the North does the opposite. REFERENCES Bairoch, P. (1989), Europea trade policy, , i P. Mathias ad S. Pllard (eds.) The Cambridge Ecoomic History of Europe (vol. 8). Cambridge. Cambridge Uiversity Press. Baldwi, R. ad R. Forslid (1997), Trade liberalizatio ad edogeous growth: A q-theory approach, Joural of Iteratioal Ecoomics 50, Baldwi, R.E. (1999), Agglomeratio ad edogeous capital, Europea Ecoomic Review, 43, Baldwi, R. ad R. Forslid (000), The Core-Periphery model ad edogeous growth: Stabilisig ad de-stabilisig itegratio, Ecoomica 67, Baldwi, R., R. Forslid, P. Marti, G. Ottaviao ad Robert-Nicoud, 003, Ecoomic Geography ad Public Policy, forthcomig, Priceto Uiversity Press. 37

41 Baldwi, R., P. Marti ad G. Ottaviao, 001, Global icome divergece, trade ad idustrializatio: The geography of growth take-off, Joural of Ecoomic Growth 6, Barro, R. ad X. Sala-I-Marti, 1995, Ecoomic Growth, New York Mc Graw Hill. Basevi, G. ad G. Ottaviao, 00, The district goes global: Export vs FDI, Joural of Regioal Sciece 4, Bottazzi, L Globalizatio ad local proximity i iovatio: a dyamic process, Europea Ecoomic Review 45: Black, D, ad V. Hederso, 1999, A theory of urba growth, Joural of Political Ecoomy 107, Ciccoe, A., 00, "Agglomeratio-effects i Europe", Europea Ecoomic Review, Volume 46, Ciccoe, A. ad R. Hall, 1996, Productivity ad the desity of ecoomic activity, America Ecoomic Review 87, Coe, D. ad E. Helpma,1995, Iteratioal R&D Spillovers, Europea Ecoomic Review 39, Coe, D., E. Helpma ad A. Hoffmaister, 1997, North-South R&D spillovers, The Ecoomic Joural, 107, Crafts, N., 1989, British idustrializatio i a iteratioal cotext, Joural of iterdiscipliary history, 19, Durato G. ad D. Puga (001), Nursery cities: Urba diversity, process iovatio ad the life cycle of products, America Ecoomic Review, vol 5, Fujita, M. ad J. Thisse, 003, Does geographical agglomeratio foster ecoomic growth? Ad who gais ad looses from it? Japaese Ecoomic Review, forthcomig , 00, Ecoomics of Agglomeratio, Cambride Uiversity Press. Grossma, G. ad E. Helpma, 1991, Iovatio ad growth i the world ecoomy (Cambridge MA: MIT Press). Goh, A. ad J. Olivier, 00, Learig by doig, trade i capital goods ad growth, Joural of Iteratioal Ecoomics, 56, Hoheberg P. ad L.H. Lees, 1985, The makig of urba Europe ( ), Cambridge (Mass.), Harvard Uiversity Press. Jacobs, J., 1969, The ecoomy of cities (New York: Vitage). Jaffe A., M. Trajteberg ad R. Hederso,1993, Geographic localizatio of kowledge spillovers as evideced by patet citatios, Quarterly Joural of Ecoomics. 108: eller W., 00, Geographic localizatio of iteratioal techology diffusio, America Ecoomic Review 9, rugma, P., 1991, Icreasig returs ad ecoomic geography, Joural of Political Ecoomy 99,

42 rugma P. R. ad A. J.Veables, 1995, Globalizatio ad the iequality of atios, Quarterly Joural of Ecoomics 60, Lucas, R.E. (1988) O the mechaics of ecoomic developmet, Joural of Moetary Ecoomics, 3-4. Mazocchi, S. ad G. Ottaviao, 001, Outsiders i ecoomic itegratio: The case of a trasitio ecoomy, Ecoomics of Trasitio 9, 9-49 Marti, P., 1999 "Public policies, regioal iequalities ad growth", Joural of Public Ecoomics, 73, Marti, P. ad G. Ottaviao, 1999, Growig locatios: Idustry locatio i a model of edogeous growth, Europea Ecoomic Review 43, Marti, P. ad G. Ottaviao, 001, Growth ad agglomeratio, Iteratioal Ecoomic Review 4, Marti, P. et C. A. Rogers, 1995, Idustrial locatio ad public ifrastructure, Joural of Iteratioal Ecoomics, 39, Ottaviao, G.I.P., 1996, The locatio effects of isolatio, Swiss Joural of Statistics ad Ecoomics 13, Ottaviao, G.I.P., T. Tabuchi ad J.-F. Thisse, 00, Agglomeratio ad trade revisited, Iteratioal Ecoomic Review 43, Perroux, F., 1955, Note sur la croissace, Ecoomie Appliquée 1-, Puga D., 1999, The rise ad fall of regioal iequalities, Europea Ecoomic Review, vol. 43, pp Quah, D., Regioal Cohesio from Local Isolated Actios: 1. Historical Outcomes. LSE, mimeo. Quah, D., 00, Spatial agglomeratio dyamics, CEPR DP 308. Romer, P., (1990) Edogeous techological chage, Joural of Political Ecoomy 98.5, part II, S71-S10. Urba, D. (00), Neoclassical growth, maufacturig agglomeratio ad terms of trade, mimeo LSE. Waltz, U. (1996) Trasport Costs, Itermediate Goods ad Localized Growth, Regioal Sciece ad Urba Ecoomics 6, Walz, U. (1997) Growth ad deeper regioal itegratio i a three-coutry model, Review of Iteratioal Ecoomics 5, Williamso, J.G. (1988), Migratio ad urbaizatio, i H. Cheery ad T.N. Sriivasa (eds.), Hadbook of Developmet Ecoomics, volume 1, Amsterdam: North Hollad, Yamamoto,. (00), Agglomeratio ad growth with iovatio i the itermediate goods Sector, mimeo, Graduate School of Ecoomics, yoto Uiversity, forthcomig, Regioal Sciece ad Urba Ecoomics. 39