The Evolution of Productivity Gaps and Specialization Patterns *

Transcription

1 The Evolution o Produtivity Gaps and peialization Patterns * Bart Los University o Groningen, Groningen Growth and Development Center/OM Researh hool, P.O. Box 800, L-9700 AV Groningen, The etherlands. b.los@eo.rug.nl Bart Verspagen Eindhoven University o Tehnology, ECI, P.O. Box 513, L-5600 MB Eindhoven, The etherlands, and University o Oslo, TIK Center. b.verspagen@tm.tue.nl ABTRACT: The literature on athing-up based growth has developed mainly in isolation o other theories on tehnology and eonomi growth. This paper presents an industry-level tehnology gap model in whih evolving speialization patterns are the endogenous result o innovation, international tehnology diusion, learning-by-doing and balane-o-payments restrited growth. Dierenes between setors with regard to their share in onsumption are shown to reinore or mitigate the eets o speialization on aggregate produtivity onvergene patterns, depending on other parameters. The impliations o the model are studied by means o simulation analyses or a wide range o parameter onigurations. * This paper originates rom the TEG researh projet jointly arried out by researhers at the universities o Eindhoven, Groningen and Maastriht (see The Duth Organization or ientii Researh WO is grateully aknowledged or inanial support. Partiipants at the trutural Change and Eonomi Dynamis Conerene on Growth, Tehnology and Trade (Eindhoven, Otober 1999), the Annual Conerene o the European Assoiation or Evolutionary Politial Eonomy (Prague, ovember 1999), the Thirteenth International Conerene on Input-Output Tehniques (Maerata, August 2000), the DRUID elson & Winter Conerene (Aalborg, June 2001) and an ECI-seminar (Eindhoven, eptember 2000) are thanked or onstrutive omments on earlier versions o this paper.

2 The Evolution o Produtivity Gaps and peialization Patterns 1. Introdution The produtivity growth perormane o ountries has always been o entral interest to eonomists. Over time, many theories about the soures o growth have been proposed, tested and reined. In most theories, tehnologial progress emerges as the engine o growth. These theories vary widely, however, with regard to the speii ways in whih tehnology aets eonomi growth. In general, three soures o tehnologial progress at the national level are diserned: innovation, athing-up and learning-by-doing. Most theoretial models ous on a single soure o growth, whih renders their outomes o limited relevane. The vast majority o empirial studies also provide analyses that relate dierenes in growth perormanes between ountries to dierenes in their opportunities to beneit rom one or at most two o these soures. Fagerberg reviews many o these studies and onludes, probably, the estimation o a single-equation model with GDP per apita and other variables inluded- is an ativity to whih there are now sharply diminishing returns (Fagerberg, 1994, p. 1171). This quote ould be read as a plea or more empirial work that takes simultaneous interations between important variables into aount. In our view, a similar argument applies to theoretial models. We think that a model that presents a more uniied ramework is asked or, beause many ompliations blur the omparability o the major lessons to be learnt rom more partial models. One o the ompliations is that outomes oten dier due to partiular hoies onerning the level o aggregation. This holds or both theoretial and empirial studies. For instane, studies or single setors mostly yield dierent outomes than studies that suppose that eonomies onsist o one ommodity market. Dierenes between setors with regard to their tehnologial progress rom whatever soure and hanges o the setoral struture an together have important eets on aggregate produtivity growth rates. Baumol s disease (Baumol, 1967) illustrates this issue quite onviningly. Further, results are likely to be aeted by the perspetive hosen with respet to international trade. Espeially the eets o learning-by-doing ould well be highly dependent on the export perormane o ountries. Moreover, the international ompetitiveness o a ountry s produts is generally thought to be aeted by this ountry s tehnologial standards vis-à-vis its rivals. Consequently, a proess o virtuous (or viious) irles emerges, whih also aets the setoral struture. Thus, studies in whih ountries are seen as parts o an international system o 1

3 interdependent ountries are likely to yield dierent outomes than studies that onsider ountries as autarki entities. In this paper, we propose a very general model. It desribes the evolution o a system o two trading eonomies that onsist o multiple setors. The produtivity growth rates o setors, as well as the speialization patterns o ountries, are the outome o the interplay between innovation, athing-up and learning-by-doing. We will present outomes o the model or a rather omprehensive set o parameter values that indiate the relative strength o these soures o tehnologial progress. This allows us to draw some broad onlusions about the harateristis (in terms o parameter values) o tehnologial progress or whih aggregate labor produtivity levels o ountries tend to be relatively equal and to desribe the orresponding speialization patterns. The paper is organized as ollows. In the next setion, we will disuss the soures o produtivity growth and their impat on the onvergene proess aording to several growth theories. peial attention will be devoted to the interations o these soures with hanges in the setoral struture and international trade. etions 3 and 4 deal with the model equations. In etion 5, we will analyze the behavior o the model, mainly by means o simulation analysis. etion 6 onludes. 2. Growth and tehnology: theoretial perspetives Most eonomists will agree that in the long run, tehnology is one o the main drivers o eonomi growth. The relationship between growth and tehnology, however, takes many dierent orms and an hardly be envisaged as a simple proess that is steady through time. Looking at the literature on growth and tehnology, one may distinguish our main ways in whih tehnology and innovation have their impat on growth. The irst, and perhaps simplest, way is ound in the traditional neo-lassial way o onsidering the growth proess. This views eonomi growth as a steady-state proess in whih GDP per apita grows at a ixed rate over time. This rate, whih is equal to the rate o tehnologial progress, may be exogenously determined, as it was in the irst version o the model (olow, 1956). In the more reent so-alled endogenous growth theory, (e.g. Romer, 1986, and Luas, 1988) the rate o produtivity growth is determined endogenously through, or example, researh and development eorts. Viewed rom this perspetive, the answer to the question why growth rates dier an take two orms. The irst answer argues about dierenes in the steady states between ountries. For the old (olow) model, this poses a logial diiulty, espeially in relation to the assumption that knowledge and tehnology are publi goods, whih are reely available or all ountries in the world. Under this assumption, dierenes in the steady state between ountries annot exist. The new growth models solve this logial diiulty by modeling the steady state growth rate itsel as a untion o eonomi variables, suh as, or example, the 2

4 amount o human apital available in a ountry. In this ase, individual ountries onverge to their own steady state, whih will generally dier rom that o other ountries. The neolassial approah oers a seond explanation o dierent produtivity growth rates. Countries may not be on their steady state growth path, but may instead be onverging to it. Thus, both below and above steady state growth rates are possible, depending on whih side o the steady state the ountry starts rom. Traditionally, the apital labor ratio has been taken as an indiation o this, where the natural path or a ountry is to start rom a relatively low apital labor ratio. This is assoiated to high growth rates through the mehanism o dereasing marginal returns. The speed o the onvergene proess towards the steady state has been the subjet o a reent debate, in whih the overall onlusion seems to be that this speed is rather low (e.g., Mankiw, Romer & Weil, 1992). Thus, on any pratial time sale (say, deades), onvergene may be a more dominant ator behind growth rate dierentials than dierenes in steady states. The idea o onvergene is also the ruial ator in the seond notion o tehnologial hange ound in the literature. This is the literature that builds on the arguments o Gershenkron (1962) and Abramovitz (1979), and to whih we will reer as the athing-up literature. The main idea is that tehnologial knowledge may diuse rom advaned ountries to less advaned ountries, i.e., that relatively bakward ountries may learn rom more advaned ountries. This view is inspired by the notion that knowledge is to a ertain degree a publi good. Imitating may be heaper than developing brand new knowledge. In this way, there is atually an advantage to being relatively bakward, beause rapid growth may be ahieved at lower osts. 1 The main line o argument in the athing-up literature is quite dierent rom the neolassial perspetive. The dierene lies in the degree to whih it is assumed that knowledge is atually a publi good. The argument in the athing-up literature is that in order to beneit rom a athup bonus, several onditions need to be ulilled. Abramovitz (1979) has labeled these onditions soial apability and tehnologial ongruene. oial apability reers to the notion that in order to apply knowledge developed in a more advaned ountry, the athing-up ountry needs ertain skills, equipment or institutions. oial apability is thus a broad onept that inludes widely diering ators suh as a stable inanial system, a suiient level o human apital, a suiient level o inrastruture (transport, power generation), and so on. Without suiient soial apability, alling behind may be a more realisti outome than athing-up. The seond prerequisite or athing-up identiied by Abramovitz is tehnologial ongruene. This reers to the notion that tehnologies developed in advaned ountries may not always be appropriate or less advaned ountries. An important ator in this is the setoral struture o the eonomy. For example, many less advaned eonomies depend to a large extent on agriulture, while tehnologies developed by advaned ountries may be aimed at other setors suh as high-teh manuaturing. Cathing-up then beomes more than just applying oreign 1 I the level o tehnologial knowledge is related somehow to the apital labor ratio (e.g., tehnologial knowledge is embodied in mahines, or through a tehnial progress untion as in Kaldor, 1957), the neolassial story o onvergene may be observationally equivalent to this athing-up eet. 3

5 tehnology, and issues like ross-setoral transer o resoures enter the piture. Again, the onlusion is that with a lak o tehnologial ongruene, alling behind is the realisti outome. The third soure o tehnologial hange that we will disuss an be haraterized as learningby-doing or umulative learning. This is an important topi both in the early literature (e.g., Verdoorn, 1949, Arrow, 1962) and some o the new growth models (e.g., Young, 1991). 2 Tehnologial hange is generated as a result o experiene in prodution or use. uh a mehanism generates positive eedbak, i.e., high rates o tehnologial progress result rom high ativity levels, or high growth o ativity levels. A variety o mehanisms an be used to explain this phenomenon at the miroeonomi level. Most o these explanations argue that ideas and proedures or small (inremental) innovations related to implementation may emerge as a result o using a tehnology. Although every single inremental innovation may be small, their joint umulative eet is oten large, as is or example shown in the historial studies o Habakkuk (1962). The onsequenes o umulative learning run against onvergene. I using a tehnology enhanes learning, the ones who are most suessul at this will also learn most. That is, suess breeds suess. This implies a tendeny or divergene o tehnology levels between ountries, rather than onvergene. Kaldor (1966) and Dixon & Thirlwall (1975) use this argument to make a point about persistene o growth rate dierentials between regions. In a similar ashion, Luas (1988) presents a model about persistene o growth rate dierentials between ountries. The inal view on the role o tehnology in eonomi growth is the strutural view. Here it is argued that there are important dierenes between setors in terms o tehnology. These dierenes may be diretly related to tehnology, through variables suh as tehnologial opportunity or age o the tehnology. But also more indiret variables, suh as inome elastiities may play a role here, although only in ombination with the more diret dierenes in tehnology between setors. I setors are haraterized by dierent rates o produtivity growth, or by dierent rates o demand growth (through, or example inome elastiities), eonomi struture beomes important or aggregate eonomi growth. This is a topi that is mostly explored in the post-keynesian literature, suh as Pasinetti (1981) and Thirlwall (1979). Whereas Pasinetti (1981) onsiders this topi mostly in the ontext o a losed eonomy, Thirlwall (1979) brings in oreign demand. In the latter approah, the omposition o exports and imports, and espeially their respetive inome elastiities determine the growth potential o nations through balane-opayments onstraints. Eah o these dierent ways o looking at eonomi growth and tehnology has its own internal logi, as well as empirial support. Between some o the approahes, there are obvious links, suh as, or example, the notion o tehnologial ongruene rom the ath-up literature and the strutural view o the growth proess, or between the neo-lassial argument about 2 Interestingly, umulative learning plays an important role in both neolassial-oriented growth models and in more heterodox ontributions, or example the Post-Keynesian literature on growth. 4

6 onvergene and the idea o athing-up. But still, it is air to say that major dierenes o insight remain. These dierenes relate to undamental questions like whether onvergene or divergene is the natural outome o the growth proess, or, more broadly, what is behind empirially observed growth rate dierentials. The model developed in this paper is able to unite all the dierent views on the tehnology eonomi growth relationship that were briely disussed in this setion. This model will be used to analyze how the mix o relative importane o the various mehanisms will aet the likelihood o onvergene or divergene between ountries in terms o their produtivity levels. Thus our model will take the orm o a generi skeleton that enompasses both the steady state view o eonomi growth and the strutural view on eonomi growth. On top o this skeleton, three dierent orms o tehnologial hange may be imposed: an (exogenous) steady state exponential growth rate o produtivity, international tehnology diusion between setors potentially leading to athing-up, and produtivity growth in the orm o umulative learning. 3. Model Desription: hort-run Equations In order to keep the model relatively simple, we abstrat rom any other prodution ator than labor and urther assume that ommodities are produed or onsumption purposes only. 3 The world eonomy onsists o two ountries, alled orth () and outh (). In this world, n ommodities are produed. Both ountries are assumed to be able to produe all ommodities, but nothing preludes a situation in whih some o the ommodities appear to be produed in just one ountry. The harateristis o a speii ommodity are assumed to be independent o its ountry o origin. Consumption demand an be met by domestially produed and/or by imported ommodities. In eah period, the output and employment levels or both ountries are the result o the interplay o a number o state variables, presented in Table 1: Table 1: tate variables. 1. l, l (i=1,...,n) labor requirements per unit o output i i z, z (i=1,...,n) shares o domestially produed onsumption goods in onsumption demand. b i, b (i=1,...,n; b i = 1, b i = 1) shares o ommodities in aggregate onsumption p, p (i=1,...,n) ommodity pries 2. i i 3. i 4. i i ote: indies and reer to orth and outh, respetively. The irst set o state variables represents the tehnologies in use. The variables indiate the physial amounts o labor required to produe physial units o output, in eah o the industries 3 ee Los & Verspagen (2000) or a more elaborate model with intermediate input strutures. In a qualitative sense, all onlusions are robust to the inlusion o input-output relations between setors. 5

7 in orth and outh. Labor is supposed to be homogeneous, in the sense that workers an immediately and reely move rom one industry to another. On the other hand, we assume that labor is immobile in a geographial sense, i.e. that workers do not migrate rom orth to outh or vie versa. The seond set o variables indiates the rations o domestially produed outputs in onsumption, or eah o the ommodities and or both ountries. The third set relets the preerenes o onsumers in both ountries. These variables are deined as the shares o total onsumption in a ountry devoted to a partiular good, measured in onstant pries. Finally, the ourth set o state variables indiates the pries o the goods, expressed in a ommon urreny. The balane o payments plays an important role in our model. Arbitrary onsumption vetors would only by hane yield a balane-o-payments (urrent aount) equilibrium. As MCombie & Thirlwall (1994) argue, nothing prevents a ountry rom being aught in a situation o urrent aount deiits or a short time. In the long run, however, suh a state o aairs is unsustainable unless apital inlows keep oming in ininitely and in steadily inreasing amounts. Moreover, ininitely umulating stoks o outhern (orthern) urreny would not improve orth s (outh s) welare. Following Thirlwall (1979) and Verspagen (2001), we assume that total onsumption levels in orth and outh must always orrespond to balane-o-payments equilibrium. As we onsider a losed system without exports and imports to and rom third ountries, we ould write orth s urrent aount surplus (or deiit) as the dierene between the value o the goods imported by outh and the value o goods imported by orth (see MCombie, 1993, or a similar approah). Hene, urrent aount equilibrium prevails i and only i the ollowing holds: n i = 1 p i ( z ) b = p ( 1 z ) i i n 1 b, (1) i = 1 i i i in whih and denote the total onsumption levels (in onstant pries) in orth and outh, respetively. This equation an be rewritten in a way that expresses the urrent aountequilibrium onsumption level in outh in some o the state variables in Table 1 and the level o onsumption in orth: = n i= 1 n i= 1 p p i i ( 1 z ) i ( 1 z ) i b b i i r r (2) Equation (2) shows that the solutions that represent urrent aount equilibrium together onstitute a line in the plane -. ine pries and onsumption shares are always positive and trade shares annot exeed 1, the slope o the line is positive. The interpretation o this result is 6

8 rather straightorward. Inreased onsumption in orth indues more imports rom outh, whih enables outh to import more rom orth. Given urrent aount equilibrium, these imports inrease outh s onsumption. The value o the slope depends on the relative pries (exporting a heap good does not earn muh money or outh to import expensive goods rom orth), the trade shares (outh does not gain muh in terms o onsumption rom inreased orthern onsumption i orth produes its own goods, or i outh imports virtually everything) and the onsumption shares (outh does not gain muh by exporting a good that is hardly demanded by orth). In order to determine a unique short-run solution or and, (i.e., to hoose a speii point on the urrent aount equilibrium line) we have to impose an additional equation. We assume that one o the ountries is onstrained by available labor resoures. In eah period, either employment in orth equals its labor supply ( l sup ) or employment in outh equals its labor supply ( l sup ), depending on whih ountry reahes its onstraint irst. Labor supply is exogenous in every period. ine trade implies that employment levels in orth do not only depend on orth s own onsumption but also on onsumption in outh (and vie versa), the ull employment assumptions yield another two relations between the two total onsumption levels and. Full employment prevails in orth i and only i l sup = n i = 1 l i ( z b + [ z ] b ) i i 1 (3) i i This expression an be rewritten as = n i = 1 l i l sup i = 1 n [ 1 z i ] bi l i [ 1 z i ] i = 1 n l i z i b i b i l λ sup λ λ (4) ine both the numerator and the denominator o the slope oeiient are positive, the line desribed by equation (4) is downward sloping. I the onsumption level in orth would be redued, the onsumption level in outh would have to inrease in order to keep the orthern labor previously employed in the prodution o domestially demanded output at work. The slope itsel is determined by produtivity oeiients, trade oeiients and onsumer preerenes. Analogously, we an ind a relation orresponding to ull employment in outh: = n i = 1 l i l sup [ 1 z i ] b i l i [ 1 z i ] n i = 1 n i = 1 l i z i b i b i l µ sup µ µ (5) 7

9 olving equations (2) and (4) yields the situation in whih orth s onsumption is both balaneo-payments-onstrained and resoure-onstrained, but outh is only balane o paymentsonstrained: = r l and ( ) sup r λ + r λ r = sup l r λ + rλ (6) O ourse, we an also ind the intersetion o the upward sloping balane-o-payments line (2) and the downward sloping line (5), whih orresponds to resoures and balane-o-payments onstraints on outh s onsumption and balane o payments-onstrained onsumption in orth: = r l and ( ) sup r µ + r µ r = sup l rµ + r µ (7) The short-run equilibrium point in the (, )-plane is now deined as the minimum o the points given by equations (6) and (7), sine one ountry would produe above its apaity in the other intersetion point. Given these onsumption levels and their omposition with regard to industries and ountries o origin, the output levels and its setoral ompositions in orth and outh an be determined or the period under onsideration: q i = z ib i + ( 1 z i ) bi and q i ( z i ) b i + z ibi = 1 (i=1,...,n) (8) Finally, ommodity-speii pries (expressed in a ommon urreny, assuming an exhange rate whih is known at the beginning o eah period) are assumed to relet labor osts: p = w l and i i p = xw l (i=1,...,n) (9) i i The symbols w and w denote the nominal wage rates (in orth and outh, expressed in the national urrenies), whih we assume to be given at the beginning o eah period. The exhange rate (also given at the beginning o eah period) is denoted by x. This implies that we adopt the rule to express both orthern and outhern pries in orthern urreny. The short-run model we introdued in this setion yields output and employment levels by industry and ountry, as well as onsumption levels or eah o the ommodities produed in orth and outh. These levels are ompletely determined by the prodution tehnologies, trade relations, onsumer preerenes, labor supply, pries, the exhange rate and the nominal wage rates prevailing during a period. ine we are primarily interested in the long-run dynamis o the 8

10 endogenous variables mentioned, we now turn to the speiiation o the equations that desribe the intertemporal behavior o the variables that we have assumed so ar to be ully exogenous. 4. Model Desription: Intertemporal Relations In this setion we present the intertemporal equations that allow us to study long-run issues like output growth, onvergene and strutural hange. Unlike the previous setion, this setion does not inlude the derivation o solutions. Due to the mathematial omplexity aused by our expliit ous on eonomies onsisting o multiple industries, analytial solutions are hard to derive. We will irst deal with the equations desribing tehnologial progress and subsequently disuss the relations we speiied with regard to trade share dynamis and exhange rate movements. 4.a Tehnology Dynamis Following our earlier intersetoral models o tehnologial hange (Los, 2001, and Verspagen, 2001), we model innovation as hanges o input oeiients. We deine the (industry-speii) rates o tehnologial progress as the proportional hanges o the inverses o the l oeiients, i.e. the ratios between output and labor input. We write the dynamis o labor inputs per unit o output as: l [ t + 1] = γ [ t 1] l [ t ] and l [ t + 1] = γ [ t 1] l [ t ] (10) i i + i i i + i We allow both or dierenes in produtivity growth rates between industries and between ountries. Following the athing-up literature disussed in etion 2, we model two regimes. In the irst regime, the industry under onsideration has lower labor requirements per unit o output than its oreign ompetitor. In this ase, we all the industry in this ountry the leader industry, and the orresponding industry in the other ountry the lagging industry. We assume that leader industries experiene tehnologial progress through two mehanisms. First, a onstant exogenous produtivity growth rate is assumed, whih relets the laborsaving eets o innovation. 4 This relets the (neo-lassial) idea o steady state growth at a ixed rate. eond, a mehanism that we label the Kaldor-Verdoorn mehanism represents umulative learning: i the output o an industry grows, it is assumed that learning-by-doing and opportunities or speialization o workers lead to inreased produtivity. In the lagging-behind regime, we assume that the Kaldor-Verdoorn mehanism is still untioning, but that the steady-state ixed rate o tehnologial progress is absent. In other words, we assume that this soure o tehnologial progress is generated only by the leading 4 For simpliity, we do not inlude stohasti arrivals o innovations, nor do we inorporate expliit searh or innovations (R&D) in the model. ee Los (2001) or an intersetoral model with R&D and stohasti innovation in a single-ountry ontext. 9

11 ountry, as would be onsistent with an endogenous growth model in whih R&D an only be perormed by the advaned irms. Instead, in the lagging ountry, the tehnologial gap to the leader industry is assumed to give opportunities or athing-up, or instane by imitation o the ompetitor s prodution tehnology. ummarizing, the redutions in labor oeiients under the two regimes an be represented by Leader regime: 1 γ i [ t + 1] = (11) 1 σi q i [ t ] q i [ t 1] 1 + κ i + ρi q i [ t 1] Lagging regime: γ i [ t + 1] = 1 + κ i 1 q i [ t ] q i [ t 1] q i [ t 1] 1 σi + α i l i [ t ] ln * l i [ t ] (12) * in whih κ (>0), σ (>1), ρ (>0) and α (0<α<1) are industry-speii parameters and l i indiates the unit labor requirements in the orresponding leader industry. κ and σ relate to the Kaldor- Verdoorn mehanism taken rom Verspagen (1993) and relet the rate o dynami learning. The mehanism brings a positive eedbak into the dynami model, sine high output growth leads to high produtivity growth (although at a dereasing marginal rate). ρ is the steady-state rate o tehnologial progress in the leading industry, α relets the athing-up mehanism in the lagging ountry. The larger the produtivity gap in terms o labor inputs per unit o gross output, the more the laggard industry will ath up. The value o α is assumed to relet soial apability, whih means this is taken as an exogenous ator. ote, however, that our multi-industry speiiation impliitly takes aount o the at that inompatibility o output strutures plays an important role, i.e., tehnologial ongruene is endogenous. For example, i outh would lag orth in one industry but produes only a very small part o its output in this industry, aggregate labor produtivity would not beneit muh rom this industry-speii tehnology gap. 4.b Trade share dynamis Trade share dynamis are assumed to be ruled by hanges in relative ompetitiveness. Aording to traditional theory, the ompetitiveness o ountries is determined by osts per unit o output. In suh a situation, the interplay o two developments would determine hanges in a ountry s ompetitiveness: redutions in the amounts o labor required per unit o output and hanges in the relative wage rates. 5 These ators are summarized by pries (equation 9), so that we assume 5 These unit labor osts are generally onverted to a ommon urreny. Hene, exhange rate hanges may alter the ompetitiveness struture as well. 10

12 that hanges in a ountry s shares on the world markets are dependent on prie dierentials (only). To determine the ommodity-speii trade shares, we use the onept o an inverted logisti urve, as illustrated in Figure 1. In mathematial terms, this relation between the prie ratio and the equilibrium market share o orth s industry i on its domesti market or onsumption goods is: z * i = 1 + e 1 pi i ln ε ϕi p / i and z * i = 1 + e 1 pi i ln ε ϕi p / i (13) The parameter ε an be interpreted as the value o the logarithm o the prie ratio or whih the market shares are equally divided. For peretly tradable goods this parameter will equal zero, but or most goods the prie ratio orresponding to equal market shares will have a positive value. In this ase, the market shares o domestially produed inputs will be larger than ity perent when pries are equal. The extent to whih the market share at the unit prie ratio diers rom ity perent is also dependent on the parameter ϕ(>0), whih represents the ommodity-speii sensitivity o trade shares to hanges in the prie ratio. The lower ϕ, the more sensitive the trade shares are. The parameters ϕ may be aeted by a number o things, suh as osts o transportation, geographial distane and non-tari trade barriers. Figure 1: Trade hares 1 z i * ln(p i /p i ) Trade shares are not assumed to adjust immediately to hanges in pries. We model an adjustment proess, in whih the gap between the atual trade shares z and the equilibrium trade shares z * vanish gradually in the absene o shoks: * ( z[ t ] z [ + 1] ) t z[ t + 1] = z[ t ] η t (14) with η t (0<η t <1) denoting the speed o adjustment. 11

13 4. Wage rates, the exhange rate and remaining variables The two ountry-speii nominal wage rates are assumed to be onstant, at least i expressed in national urrenies. When tehnologial progress redues the unit labor requirements, pries will onsequently be redued and the real wage rate will grow. One aveat applies, however. In a system o lexible exhange rates, the purhasing power o a given amount o orthern urreny relative to an idential amount o outhern urreny may hange. In the modeling o exhange rate dynamis we use a speiiation similar to that o trade shares. The exhange rate is a weighted average o the atual rate and an equilibrium rate based on purhasing power parity o the two urrenies: * ( x[ t ] x [ + 1] ) x x[ t + 1] = x[ t ] η t (15) The smaller determined aording to: η x (0 η x 1), the more a system o ixed exhange rates is approximated. x * is n i = 1 nat i ( q [ t ] + q [ t ]) nat p i [ t ] i i * i = 1 x [ t + 1] = (16) n p [ t ] ( q [ t ] + q [ t ]) i i The superindies nat indiate pries expressed in national urrenies. Finally, we assume that the onsumption shares o the setors are ixed in eah ountry. Moreover, we assume that these variables do not dier between ountries. Thus, onsumer preerenes are assumed to be idential Model Analysis As mentioned earlier, the long-run behavior o the two national eonomies in our model an best be studied by means o simulation analysis. Beore we turn to a disussion o some o the simulation results we obtained, we illustrate the basi eets o an innovation by a diagram that depits some highly simpliied omparative statis. In Figure 2, the axes indiate the total onsumption levels or orth and outh. The solid upward sloping line (I) relets all pairs o onsumption levels or whih the balane o payments is in equilibrium in the initial situation, see equation (7). The downward sloping solid lines (II and II ) indiate all pairs o onsumption levels or whih ull employment initially prevails in orth and in outh, respetively, see equations (10) and (11). The slopes o these lines will generally dier, e.g. due to dierent ompositions o onsumption bundles with respet to 6 Los & Verspagen (2000) study the onsequenes o inome-speii onsumer preerenes or produtivity growth dierentials, by means o a model that resembles the one introdued here. 12

14 ountries o origin. In the situation depited, onsumption levels are given by the intersetion point F, in whih orth experienes ull employment and outh aes exess labor supply. Figure 2: Consumption eets o innovation. II I II I II I F F ow, suppose that orth generates a labor saving innovation. Consequently, the labor onstraint will be less tight, and or given onsumption levels in orth higher onsumption levels in outh are attainable, sine more eetive labor is available to produe exports. This is releted by the upward shit o the orthern ull employment line (see dashed line II ). In general, the slope will hange as well, but the sign o this hange depends on the interplay o many parameter values. evertheless, the irst order eet o tehnologial progress in the labor-onstrained ountry is an inrease in both orth s and outh s onsumption levels. The supposed innovation in orth also has some seond order eets. The net eets o these are ambiguous, as will beome lear ater studying the dashed lines I and I. The lines represent two important opposite eets. First, innovation yields a lower prie per unit o output or orth. This implies that or a given amount o exports, orth an buy ewer imports and must redue its onsumption, while outh an inrease its import volume at onstant osts (I ). This is a terms-o-trade eet. eond, orth s redued prie enhanes its ompetitiveness relative to outh, whih will ause higher market shares. Consequently, innovating orth requires ewer imports per unit o output, whih enables it to produe more onsumption goods. For outh the opposite holds and its attainable onsumption level will all. This eet is doumented by urve I. Whih o the two seond-order eets dominates depends on a number o parameters and variables, o whih the sensitivity o market shares to prie hanges is an important one. The bottom line o this simple omparative statis analysis is that it is impossible to tell in advane whih eet will dominate, and hene what the ultimate eet o an innovation on relative growth rates will be. 13

15 The interplay between the various orms o tehnologial progress in the model may also yield rather interesting eets. Espeially the ombination o the Kaldor-Verdoorn and athing-up eets is noteworthy. ine this mehanism, whih we dub as the athing-up-umulativelearning yle is rather ruial or the overall analysis o the model, we disuss it here in some detail. ote that the athing-up-umulative-learning yle is in some respets similar to the properties o the model proposed by Landesmann & tehrer (2000). Figure 3: The athing-up-umulative-learning yle Tehnology Gaps by Industry peialization Patterns by Produt A typial situation is depited in Figure 3. The vertial axis o the upper diagram indiates the soalled tehnology gap, whih is deined as the logarithm o the ratio between the labor requirements per unit o output in a orthern industry to suh requirements in its outhern ounterpart. Hene, a negative value points towards a tehnologial advantage o a orthern industry. In the lower panel, the shares o orth and outh in the world prodution o the two goods are indiated on the vertial axis (e.g., H-1 stands or the share o orth in the world prodution o good 1). The most prominent phenomenon emerging rom Figure 3 is that so-alled taking-over ours at the level o industries: initially eah ountry is leader in either one o the industries, but ater an interval o about 65 periods the leadership pattern is reversed. This taking-over happens almost simultaneously in both industries. peialization patterns also evolve in a ylial ashion. What drives these yles? 14

16 The ath-up part o the dynamis onsists o tehnologial imitation that drives the tehnology gap towards an equilibrium value. It is important to note that this equilibrium value an hange endogenously over the simulation, and this is exatly what happens when the tehnology gaps alternate between positive and negative attrators. Whether the equilibrium value is positive or negative depends on ρ and the Kaldor-Verdoorn eet. The irst o these two ators (ρ) always gives the leading ountry an advantage, sine ρ=0 in the lagging ountry. At the upper turning point o either one o the tehnology gaps in Figure 3, the lagging ountry has been experiening a all o its market share, beause the inreasing gap has led to a ompetitive disadvantage o the lagging ountry. The tehnology gap approahes a short-run equilibrium value, beause the ath-up bonus inreases, and thus osets the eet due to ρ and Kaldor-Verdoorn. Beause the tehnology gap now stops growing, the trend o a delining market share also stops. The laggard is now able to beneit rom the generally expanding world market and realize positive prodution growth. This sets in motion the Kaldor-Verdoorn learning eet. A slowdown o prodution growth in the leading ountry is indued beause the lagging ountry aptures more o the market. Through the Kaldor-Verdoorn eet, this indues a slowdown o the rate o produtivity growth in the leading ountry. This hanges the short-run equilibrium value o the tehnology gap, whih beomes smaller. The result is that the gap now starts to deline. When the gap beomes zero, the athing-up bonus disappears, but now the ountry beomes the leading ountry, and the eet due to a positive ρ sets in. The other (ormerly leading) ountry now loses the bonus due to ρ, but starts to experiene a ath-up bonus. In Figure 3, the parameter values have been hosen suh that the tehnology gap atually reverses sign, but with dierent parameter values, this does not need to happen. In partiular, or higher values o ρ, the leader ountry has suh a strong advantage that the gap does not reverse sign, and the lower turning point ours on the same side o the horizontal zero-level as the upper turning point. At the lower turning point, the same logi as or the upper turning point applies, hut now with the roles (leader or laggard) o the two ountries reversed. The dynamis are symmetri. In order to get insight into the behavior o the model beyond these simple omparative statis, we resort to simulation analysis. We onentrate on the set o parameters related to tehnologial progress, i.e. ρ, κ, σ and α. The number o setors is set to two in all simulations. To keep the analysis as tratable as possible, we hoose our basi parameter oniguration in a way that both goods and both ountries are (initially) as similar as possible. Exat parameter values are doumented in an appendix, whih shows that the prodution proesses o both goods in orth and outh are initially the same, exept or a very small dierene in labor requirements to indue dierenes between the two ountries in terms o the regimes o tehnologial progress. Eah ountry is assumed to be the tehnologial leader in one industry. Initial trade shares are all equal. The only dierene between setors lies in the onsumption shares: good 1 is onsumed our 15

17 times as muh as good 2. With respet to the other parameters that govern the dynami proesses, the two goods are peretly idential. The main variable that we are interested in is the aggregate level o inequality between ountries, whih we measure as the absolute value o the logarithm o the ratio between the maroeonomi labor produtivity levels in orth and outh, averaged over the simulation period o a single run. All results are based on 250 periods, o whih the irst 100 were not used beause they show traes o the hoie o initial onditions. To illustrate some o the general tendenies o the model, we show in Figure 4 the results or a range o values o ρ, while simultaneously swithing on or o the other orms o tehnologial progress. In the igure, the inequality indiator is depited on the vertial axis (higher values indiate more inequality). Values on the horizontal axis denote the value o ρ. The values or σ and α are 6.0 and 0.2, respetively. We pik the value o κ suh that the Kaldor-Verdoorn mehanism yields a 1% growth rate o labor produtivity or a growth rate o prodution equal to 1%. Figure 4: Eets o innovation rates on produtivity gaps none ala KV ala+kv The igure ontains our lines. The irst one is denoted by none, whih indiates that both the ath-up parameters and the growth rate implied by the Kaldor-Verdoorn mehanism (umulative learning) are set equal to zero. We see that this urve rises steeply in the segment o very low rates o tehnologial progress in the leading industries, reahes a maximum average aggregate tehnology gap or ρ=0.001 and approahes zero or larger values o ρ. This tendeny towards zero is perhaps easiest to grasp. outh is the leader in industry 1 and will thus also innovate in this industry. orth is the leader and innovator in industry 2. Without any other ways 16

18 o produtivity inrease, there is no way or the ollower to ath-up to the leader, and the prie gap between the two ountries or eah good will grow. Complete speialization is the result. ine both the rates o tehnologial progress and the initial labor produtivity levels are equal or both industries in this set o simulations, this will lead to equal maroeonomi levels o labor produtivity. 7 However, at low rates o innovation, we see the level o disparity between the ountries rising with ρ. The reason or this is that speialization is less pronouned in this ase, and both ountries remain ative in the industry in whih they have a ompetitive disadvantage. This most heavily aets orth, sine it attrats the same share o the world prodution o good 1 as outh attrats o the world prodution o good 2, but the market or good 1 is muh larger. Consequently, more labor is alloated to low-produtivity ativities in orth. This eet is obviously absent or ρ=0, but inreases or small positive values o ρ. This is releted in the rising trend o disparity. When omplete speialization starts to emerge, the urve peaks and starts to all towards zero in the way already desribed. Introdution o the Kaldor-Verdoorn umulative ausation mehanism (line KV ) leaves these dynamis essentially unhanged, but inreases the intensity. peialization in an industry auses output growth, whih in turn leads to produtivity growth and even more speialization. I the annual long-run growth rate implied by the Kaldor-Verdoorn mehanism is set at 0.01, very low levels o ρ (in the order o magnitude o 0.001) are already suiient to reah almost ull speialization beore period 100. Hene the KV line jumps up immediately ater ρ=0, but alls diretly ater that. With only tehnologial imitation o leaders by laggards being present, the nature o the dynamis is again similar (the ala -line). A positive rate o innovation or leaders and a positive rate o ath-up or laggards imply onvergene towards a onstant tehnology gap, and thereore a onstant degree o speialization. The higher ρ or the given value o α, the stronger is the long-run degree o speialization. Hene, or high values o ρ, speialization is almost omplete and both ountries perorm equally well aording to the maroeonomi labor produtivity yardstik. For low ρ, we observe the same kind o dynamis as was seen or the none line. ow, however, labor produtivity levels o both industries in a ountry deviate muh less, beause o the tendeny to onverge to a ixed gap. Hene inomplete speialization is relatively harmless in terms o aggregate tehnology gaps. This is why the upward-sloping part o the urve overs a wider span o ρ. The by ar most dramati eets o hanges in the rate o innovation in the leading industries are ound i Kaldor-Verdoorn eets and abilities to ath-up are simultaneously taken into aount (line ala+kv ). In this ase, the type o dynamis that was desribed in the disussion o Figure 3 start to play a role. In partiular, the steep rise and deline o labor produtivity 7 It should be noted that this does not lead to equal GDP levels: the unequal onsumption shares ause unemployment in the ountry that produes the good that is relatively unpopular with the onsumers. 17

19 dierentials in the range o ρs ater the value ρ=0.009 deserves speial attention. It turns out that this sudden hange o behavior o the aggregate produtivity gap is due to a qualitative hange in the athing-up-umulative-learning yle. To the let o the point ρ=0.009, the athing-up-umulative-learning yle unolds as in Figure 3, i.e., leadership periodially swithes between the ountries and the sign o the tehnology gaps reverses. The amplitude o the tehnology gap yles is relatively small, i.e., the upper and lower turner points our at relatively small (absolute) values o the gaps. peialization patterns o-evolve with the tehnology gaps, and this yields inequality as desribed in the disussion o Figure 3. To the right o the biuration point at ρ=0.009, the tehnology gaps no longer hange signs, and tehnologial leadership always remains with one ountry. This is due to the at that the bonus or the tehnologial leader (ρ) is now so high that it prevents taking-over. As a result, trade speialization does not hange sign over time, and this leads to a higher aggregate produtivity gap beause it is now always just one o the ountries beneiting rom the larger market or good 1. In at, at values o ρ just slightly larger than 0.009, the tehnology gaps onverge to an equilibrium value that orresponds to a ixed trade speialization pattern. The sharp drop in the ala+kv line at ρ=0.011 orresponds to a situation in whih outh is the tehnologial leader in both setors. The tehnology gap or orth is equal in the two setors, and hene no speialization ours: the share o orth (outh) in both setors is equal to eah other. peialization does not indue inequality in this ase. To the right o the point ρ=0.011, the behavior o the model does not hange in a qualitative sense. peialization beomes more pronouned, however, and hene inequality grows. Around the point ρ=0.022, speialization beomes almost omplete in both setors. The tendeny or the equilibrium tehnology gaps to grow does not stop, due to the inreasing ρ. Consequently, pries between the two ountries keep diverging. Beause o the omplete speialization, the trade shares o both ountries or the goods in whih they are speialized annot grow urther, and the only eet o the prie dierentials is on the terms o trade. In terms o the disussion o Figure 2 above, this means that one o the two seond-order eets (assoiated to a shit o the balane-o-payments-restrition line in Figure 2) disappears. This auses more equality, whih is releted the huge drop o the ala+kv -urve in Figure 4 or innovation rate values that exeed ρ= For very high values o ρ, the ala+kv -urve and the ala -urve oinide, whih relets that the strong eets o exogenous innovations dominate the Kaldor-Verdoorn eet. The point o the model is not so muh to explain speii igures like Figure 4. Ater all, by hoosing dierent values o the parameters, or even by plotting values o a dierent parameter on the horizontal axis, it would be possible to generate quite dierent igures. Thus, Figure 4 should only be onsidered as an illustration o the type o mehanisms that exist in the model, 18

20 and the way they interat. In order to paint a broader piture o the range o possible outomes, we proeed to vary the tehnologial hange parameters in a systemati way against eah other. In Figure 5, we plot the maroeonomi produtivity gap indiator that eatured in Figure 5 against two tehnology-related parameters, the innovation parameter ρ and the ath-up parameter α. The Kaldor-Verdoorn parameter σ is held onstant at 3.0. Dark (light) regions indiate parameter onigurations or whih the inequality indiator is high (low). The piture looks rather haoti or some ranges o parameter values, but some tendenies emerge immediately. For very low values o ρ and very high values o α, the gaps are small. This is due to the well-known logi rom tehnology-gap theories o growth that equilibrium gaps are low or suh parameter onigurations. The maroeonomi gap is thus small in both setors. Figure 5: Joint eets o innovation and ath-up on produtivity gaps At irst sight, the inding that the gaps are small or the opposite oniguration, in whih exogenous innovation is high and athing-up is virtually absent, may appear less straightorward. In this ase, omplete speialization prevails. Further, the terms-o-trade eet disussed with respet to the right-hand-side range o ρ-values in Figure 4 applies. The diagonally oriented ombinations o ρ and α values that produe large produtivity gaps orrespond to the situation in whih setoral gaps are large but speialization is not yet omplete. The steep deline to the 19

21 southeast also orresponds to the steep deline ound in Figure 4. Finally, no lear-ut pattern an be deteted or the range haraterized by low values o ρ and low to medium values o α. This is partly due to the presene o situations in whih one ountry beomes the produtivity leader in both setors and speialization hardly ours (note in partiular the narrow valley or ρs approximately equal to 0.02 and αs higher than about 0.15). The relationship between the aggregate produtivity gap on the one hand and the innovation rate ρ and umulative learning mehanism σ on the other is depited in Figure 6. The value o the athing-up parameter α is held onstant at 0.2. Figure 6: Joint eets o innovation and learning-by-doing on produtivity gaps For very low values o σ, the aggregate produtivity gap is huge (note the dierene in the indiator values assoiated with a given level o darkness, relative to the Figure 6). This is due to the at that a modest growth o output leads to a substantial inrease in produtivity in this range o σ values. Consequently, the yles rom Figure 3 have muh higher amplitudes (setorspeii gaps will be large) and the requeny o the yles is muh higher. peialization patterns hange quikly, but ull speialization ours oten. Hene, aggregate produtivity gaps hange sign quite oten, but are large in the majority o time periods. This eet is reinored i ρ takes on relatively high values, as is evidened by the border between the lightest and lightest but one shade. 20

22 For higher values o σ (exeeding 2.5), another interesting phenomenon emerges rom the igure. Both low and high values o ρ yield small gaps on average, whereas intermediate values yield larger gaps. Again, this resembles the hump-shape observed in Figure 4. For low values, gaps and speialization patterns behave ylially and or high values speialization is omplete. Due to negative terms o trade eets, inequality delines or higher ρ values. The inverse relation between ρ and σ that haraterizes this ridge o divergene is due to the strong Kaldor-Verdoorn eet, whih promotes ylial behavior. Thus, or a low value o σ, whih indiates strong umulative learning eets, a high exogenous innovation parameter value ρ is required to oset this tendeny and obtain ull speialization. Figure 7: Joint eets o athing-up and learning-by-doing on produtivity gaps Finally, Figure 7 gives an impression o the model s behavior or ombinations o varying athing-up parameter α and the learning-by-doing parameter σ. The exogenous innovation rate is held onstant at Like in Figure 6, the produtivity inequality is huge or low values o σ. Again, this is due to large produtivity gaps at the setoral level and ast reversals o speialization patterns. It should be noted, however, that a relatively modest strength o the umulative learning mehanism suies to generate suh patterns or low values o α. This is due to the at that weak apabilities to ath-up yield large short-run equilibrium gaps or a given innovation rate. Consequently, leader industries an beneit to a signiiant extent rom learning-by-doing. 21