Foreign Direct Investment, Local Talent, and

Backward Linkages∗

PRELIMINARY AND INCOMPLETE - PLEASE DO NOT QUOTE

Juan Carluccio† Thibault Fally‡

Abstract

This paper provides a theoretical investigation on the impact of inwardFDI on host country industrial development through backward linkageswith local suppliers. We contribute to the existing literature by incor-porating ”selection effects”: MNEs often source from the most qualifiedsuppliers, as evidence suggests. For this we assume that entrepreneurs inlocal upstream industries are heterogeneous, and that there are specificfixed costs associated with serving multinationals. These two featuresgenerate separating equilibria with a proportion of local firms servingonly multinationals. We show that this mechanism might endogenouslyamplify initial productivity differences between multinational and domes-tic firms or among suppliers. We then study how the dispersion of localsuppliers’ productivity affects selection and linkages effects and thus theimpact of FDI in the development of inter-linked industries.

∗We are indebted to Thierry Verdier for helpful comments and suggestions. We also thankJerome Pouyet for helpful discussions on earlier drafts of the paper and the seminar partici-pants at the Paris School of Economics. We are responsible for any remaining errors.

†Paris School of Economics. Corresponding author: juan.carluccio@ens.fr‡Paris School of Economics.

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1 Introduction

The host country effects of Foreign Direct Investment (FDI) constitute a tra-ditional concern in development economics. One of the consequences of theimpressive surge in FDI flows witnessed in last decades was to bring this debateback into the fore. The view about multinationals during present times is op-timistic, and there is a general feeling that, in many circumstances, FDI mayenhance the economic development of its destinations. A manifestation of thisfeeling is given by the inclusion of FDI attraction policies as a central elementin wider development policy packages by governments all over the developingworld. Moreover, FDI attraction seems to be also a high priority in the policyagenda of organisms such as the World Bank, the IMF and the OECD.

Given this enthusiasm, the question of whether attracting FDI constitutes alegitimate goal in itself arises naturally. Is it always the case that the arrival of anFDI project into a small developing economy will be welfare enhancing? Whatare the benefits and costs involved, and what determines the strengths of these?The economic literature, both theoretical and empirical, has identified a range ofchannels though which multinational firms (MNEs) affect local industry. Theseinclude the transfer of technology (explicitly or implicitly through spillovers ordemonstration effects), the introduction of tougher competition in concentratedoligopolistic markets and the presence of forward and backward linkages withlocal firms.

In this paper we attempt to contribute to our understanding of the lastchannel: the impact through linkages with local suppliers. We then contributeto a small (though growing) literature analyzing the host country effects of FDIthrough the backward linkage channel, pioneered by Rodriguez-Clare (1996) ina more aggregate setting, and extended to an analysis at the industry level byMarkusen and Venables (1999) -henceforth MV. The former work is the closestto our model, and can be considered as our main theoretical building block. Intheir setting of a two sector economy, MV show how the arrival of an FDI projectinto a final goods market may end up creating benefits for firms in the sameindustry by boosting the local upstream industry through backward linkageswhich turn into forward linkages, reducing the cost of intermediates and thusrasing downstream profitability and firm entry. The forward linkage in turnprompts a backward linkage, thus starting a process of cumulative causation.Depending on the magnitude of certain parameters, in particular the degree ofMNEs cost advantage and the intensity with which they use local inputs, theeffects of FDI might be the launch of a cumulative process that benefits bothdomestic intermediate and final goods producers. Moreover, they show that insome situations the arrival of an FDI project can cause a cumulative processthat ends up displacing the arriving foreign firms.

Most of this backward-forward linkage mechanism relies in the fact that,in their model, the arrival of multinationals creates opportunities for all lo-cal suppliers, who see a new ”market” for their products. This induces entryupstream and since all suppliers serve all downstream firms, this ends up ben-efiting domestic firms. This is somewhat unsatisfactory, since there is available

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evidence suggesting that the reality is different and that only a portion of localentrepreneurs are able to qualify and enter the supply chain for foreign sub-sidiaries. There is another work, by Lin and Saggi (2007) , that it is also closeto the esprit of our paper. In a two-tier Cournot oligopoly, they introduce an”exclusivity” aspect. Multinational firms are allowed to write contracts withtheir suppliers that prevent these to sell their production to the MNEs localrivals. They conclude that exclusivity might reduce welfare and backward link-ages as compared to autarky due to lessened competition among local suppliers.

The notion that the arrival of multinational firms may create opportunitiesfor only a portion of local entrepreneurs is a central point in the UNCTAD WorldInvestment Report 2001, based on case-study analysis about multinational firms(MNEs) and local suppliers. The following paragraph is illustrative: ”Affiliatessuch as in automotive and electronic industries source large numbers of com-ponents, sub-assemblies and services locally, with major opportunities for firmsthat qualify as suppliers.(MNEs) tend to reduce the number of first-tier sup-pliers and enter into closer relationships with those that remain. These coresuppliers are expected to have a capability to manufacture and supply –on aglobal basis – complex systems, to have independent design capacity and tosolve problems jointly with the assembler. Such requirements make it more dif-ficult for domestic supplier in host countries to enter the supply chain (Suzuki’saffiliate in Hungary, for example, only negotiates with potential suppliers thatare already ISO9000 and QS9000 certified)”.

The two main concepts suggested by the above lines that are relevant toour purposes are the following. First, multinational firms in some sectors in-creasingly rely on local suppliers for an important number of their activities,including both productive as well as administrative tasks. Second, that thisincreasing degree of local outsourcing by incoming foreign firms is rather selec-tive: multinationals subcontract only to certain suppliers that, because of theirproductive abilities, meet their stringent requirements. These two facts put to-gether suggest that MNEs can be a new source of industrial development andemployment creation, only when the local industry is able to ”receive” them.When supplier quality is low, foreign firms will chose either to produce thosecomponents or services within their boundaries, or either to import them fromtheir home (or a third) country. In such cases, only a small portion of localfirms will qualify and benefit from foreign presence.

In order to incorporate this notion of selectivity in vertical relationshipsbetween foreign affiliates and indigenous suppliers, we develop a simple theo-retical partial equilibrium model composed of two monopolistically competitivesectors, linked together by means of an output-input structure, in the spirit ofMV. As in that work, we assume that foreign presence can only occur in thedownstream market. We propose, nonetheless, two major departures. First, weadapt the basic model of monopolistic competition by introducing some degreeof heterogeneity among upstream firms, following the fast-developing work infirm heterogeneity in international trade started by Melitz (2003). Second, welet multinational firms the choice of bringing with them their methods of pro-duction, that have been developed in the north and are not locally available

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otherwise. As these methods are new for the host economy, local firms supply-ing foreign subsidiaries are assumed to be not ex ante ”prepared” to deliver theright kind of input, in terms of its compatibility with such methods. Our crucialassumption is that any local supplier willing to serve foreign firms is faced withextra costs required to adapt they inputs to the needs of the new technology.This appears to be a relevant fact in the real world, but that has not been, tothe best of our knowledge, into a model like this one.1

By adding these separation effects with origin in the technological differ-ences between domestic and multinational firms, our model generates multipleequilibria. We prove the existence of two alternative regimes, depending onthe technological requirements of multinational firms (which we consider as en-dogenous). The first type is a ”pooling” equilibrium where multinational firmsadapt to local technology, and all upstream firms may supply both multina-tional and domestic downstream firms using an homogeneous technology. Thisis the benchmark case. The second type of equilibrium that this model delivershas been labeled a ”separating” equilibrium where multinational firms requirespecific inputs, and upstream firms have to choose dichotomously between sup-plying multinational firms or domestic firms due to the required adaptation oftheir intermediate goods.

We show that a ”separating” equilibrium is possible when the upstream pro-ductivity dispersion is skewed enough (in which case the separating equilibriumis compatible with MNEs incentives) and when the share of multinational firmsis high enough (in term of suppliers incentives). In case of a separating equi-librium, we show that only best upstream firms choose to supply multinationalfirms: this screening effect comes from the fact that most productive formscan more easily recover the fixed cost of adaptation. This effect might createan endogenous productivity differential between downstream firms in favor ofMNEs. Since separating equilibria are more likely to occur when the technologyof multinational firms is more efficient than the local technology used by do-mestic firms, the later effect amplifies the advantage of multinational firms. Bythis, we suggest that the ex ante characteristics of local inter-linked industrieshas an impact on the strategies by multinational firms regarding the type ofentry into a market.

In terms of local development, we show that the equilibrium number ofupstream firms is lower in a separating equilibrium than in a pooling equilibriumwhen the cost of technology upgrading or the cost of imported inputs is high. Inthat case, the consumer price index is always higher in separating equilibriumthan in pooling equilibrium, which means that separation between suppliers hasa negative impact on consumers’ welfare. We also consider endogenous entryupstream. When multinational have higher fixed cost that domestic firms, then

1Some work incorporating contract incompleteness into the analysis assume the existenceof an investment that is specific to the supplier-buyer partnership, which is shared by thetwo parties according to their bargaining weights (see for example Grossman and Helpman(2003)). The way we model fixed costs is nonetheless different, since we are assuming thatthe effort is rather ”multinational-specific” than partnership-specific, and thus the identity ofthe parties is irrelevant in our case.

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domestic firms may evict multinational firms at later stages of development incase of pooling equilibrium, but multinational firms may dominate in case of aseparating equilibrium.

The paper is organized as follows. Second 2 describes the set up of the model.Section 3 provides a derivation of the conditions for separating equilibria to arise,taking into account optimal decision by both multinationals and local suppliers.In Section 4 we solve the game by imposing a free entry condition for upstreamfirms. In Section 5 we propose an alternative configuration of the model inwhich we lift the heterogeneous composition of the supplying industry. Section6 a brief discussion of related topics and extensions of the model is provided.Section 7 concludes.

2 Model

Downstream industry

Consumers preferences are assumed to be represented by an utility function ofthe Dixit-Stiglitz form

Y =

(∫ N

0

Yη−1

η

j

) ηη−1

where η > 1 is the elasticity of substitution of any two varieties of the genericconsumption good Y . The larger this elasticity, the less differentiated thesevarieties are in the eyes of consumers, and thus the lower is the market powerenjoyed by a single producer. N represents the total number of downstreamvarieties2. The downstream industry price index is described by the followingintegral

P =

(∫ N

0

P 1−ηj

) 11−η

where Pj is the price of variety j. If we denote by E the exogenous incomespent in the Y industry, the producer of a given variety j will face a demandcurve of the form

Yj =(

Pj

P

)−ηE

P.

Given the structure of preferences and the assumption that new varietiesare costlessly designed in equilibrium no variety is produced by two firms atthe same time; conversely, each firm is associated with one variety in which itenjoys a monopoly situation.

Production in the downstream industry requires unskilled labor and interme-diate goods. Final goods’ producers operate under a technology with increasing

2For simplicity in exposition, we shall henceforth denote all variables pertaining to thedownstream industry with capitals, as opposed to lowercase for those for the upstream indus-try.

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returns to scale, described by a cost function with constant marginal costs Cj interms of intermediate goods and labor, and fixed overhead costs Fj in terms oflabor. Henceforth, we shall assume that the two industries we study are part ofa larger economic system in which there exists a large competitive sector wherethe wage rate for the economy, w is determined. We shall then, without loss ofgenerality, set it equal to unity.

Under the ”large group assumption”, for a sufficiently large number of firms,each neglects the impact of its actions on the rest of producers, and perceiveη as the price elasticity of their good. In this case, profit maximization in thedownstream industry results in the usual mark-up pricing formula,

Pj =η

η − 1Cj .

Technology

We assume that the final goods industry is populated by two types of firms:domestic, whose total number is denoted ND, and multinational, NM , withN = ND + NM .

Firms are assumed to be identical at the interior of each category, but weallow for structural technological differences across groups. Domestic firms useintermediate goods produced by local suppliers according to the existing techno-logical standards of the country. We label these intermediate as of the ”D-type”.Domestic firms’ marginal cost of production is simply the price of these:

CD = pD

Multinational firms are assumed to be different than local firms in the fol-lowing sense. We suppose that they have access to a different technology ofproduction that have been developed in the north, and it is consequently notavailable to local downstream producers. An important feature of this lies inthe fact that, in order to make this ”northern” production methods operational,the use of compatible intermediate inputs is a requisite. We denote inputs thathave been produced for use in this technology as belonging to the ”M-type”.On the other hand, we allow for the possibility that the use of this differenttechnology results in enhanced productivity for firms adopting it. We capturethe higher efficiency of the northern technology by introducing an efficiencyparameter indexing the decrease in costs.

Upon arrival, multinationals decide whether to build their production facil-ities to be compatible with local technologies, or else they might replicate theirplants in the north. Nonetheless, we do not allow for a complete assimilationbetween foreign-owned and domestic plants, even in the case where multination-als decide not to import their northern technology and rely on local methods.We account for this by assuming that in the case where the local technology isadopted, multinationals still need to import a proportion of intermediates fromthe home country.

Therefore, in our model, subsidiaries’ marginal costs of production can beeither one of two types, according to whether they rely mainly in local techniques

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or whether they choose to import northern methods. In the first case, the typicalmultinational uses a combination of D-type inputs and imported inputs followinga Cobb-Douglas function3. We suppose that marginal costs write as:

CM = (pD)1−µ(p∗)µ

where p∗ is the price of imported inputs. On the other hand, in the case wherethe northern technology is implemented locally, the marginal cost of multina-tionals is the price of local ”M-type” inputs factorized by a factor 0 < λ ≤ 1indexing the increase in the productivity of inputs,

CM = λpM

In other words, a multinational firm does not need to import inputs when theM-technology is implemented locally.

The demand for locally produced intermediates derived from downstreamequilibrium will thus be conditional on the choice of technology by multination-als operating in the country. If multinational firms choose the M-technology, thedemand for D-type inputs corresponds to the demand from domestic firms onlyand the demand for M-type inputs will correspond to the demand from multi-national firms. If multinational firms choose the D-technology, the demand forM-type inputs is zero whereas the demand for D-type inputs equals the demandfrom local firms plus the demand in local inputs from the multinational firms.

In the following sections, we note XD the aggregate demand for D-typeinputs and XM the aggregate demand for M-type inputs.

Upstream industry

Locally produced intermediate goods enter the production process via a CEScomposite. For each type T ∈ {D,M} we have:

XT =(∫ nT

0

x1−σi

) 11−σ

,

where σ > 1 is the elasticity of substitution between any pair of intermediatevarieties and nT their number. We further assume that σ > η. This typeof production technology has the property of displaying ”love for variety” ininputs: efficiency is increasing in the number of available intermediates. If piT

denotes the price of input i of type T, then the cost function that is dual to theCES production function is

pT =(∫ nT

0

p1−σiT di

)1/(1−σ)

, T ∈ {D,M},

which is a price index of available T-type inputs. From this we can obtain thedemand for each variety of a given type

3A Leontief production function gives qualitatively the same results, but at the expense ofproducing less analytically tractable expression

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xiT =(

piT

pT

)−σ

XT

The upstream industry is represented by a continuum of firms (henceforth”suppliers”) of mass n. Each supplier is associated with a differentiated interme-diate variety, with nT representing the number of suppliers producing varietiesof type T , and n = nD + nM . Suppliers of each group perceive σ as the priceelasticity for their variety whenever nT is sufficiently large. In a symmetric equi-librium for each type, maximal profits are attained choosing a pricing formulaof the form

pi =σ

σ − 1ci

where ci is the marginal cost.

Technology and type of production

We assume that, upon entry, all local entrepreneurs are ready for the produc-tion of intermediate varieties of the local D-type. The adaption of their methodsto make their inputs to be compatible with the foreign technology is nonethe-less costly. These additional costs are fixed and independent of the volume ofproduction, and we model them as overhead costs of size fq in terms of ournumeraire.

Entry of firms and productivity differences

A fundamental feature distinguishing our upstream industry is the assumptionthat prospective entrants face a fundamental ex ante uncertainty regarding theirpost entry productivity. We justify this by assuming that entry into productiveactivities unearths characteristics and abilities which are otherwise unknown tothe agent himself. In analytical words, identical ex ante entrepreneurs becomeheterogeneous ex post, once their true parameters are revealed to themselvesand to the rest of the agents.

This mechanism is similar as that developed in the works of Hopenhayn(1993) and Melitz (2003); however here we choose to work under a simpler defi-nition of heterogeneity. We assume that there may exist two types of upstreamproducers; ”good” firms, whose superior abilities are materialized in lower unitlabor requirements, and ”bad” firms, in which a higher quantity of labor is re-quired to produce one unit of the intermediate input. In terms of the genericcost function above, this specification implies that the parameter indexing unitlabor requirements cu can take either of two values {cL, cH} depending on whichtype of entrepreneur owns the firm, with cL < cH

Entry into entrepreneurial activities requires the payment of an irreversiblefee that takes the form of a (sunk) fixed cost fe

4 The process through which costs

4We may then understand that entering the input market is equivalent to ”buying a lottery”which fee costs fe and whose expected value are profits associated with each type, weightedby the probability of each draw.

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- or conversely ”abilities” - are allocated is assumed to proceed in a completerandom fashion, and to be independent of any ex ante action by local would-beentrepreneurs. We assume that each individual faces an ex ante probability q ofreceiving the best draw cL, and the complementary probability 1−q of receivingthe less desirable one, cH . With a large pool of entrants, for a total number ofn firms, the Law of Large Numbers (LLN) ensures that ex post there will be nqfirms with cost parameter cL and the remaining n(1− q) requiring cH units oflabor to produce one unit of the intermediate good.

3 Pooling and separating equilibria

We now proceed to the solution of the model. From our discussion above, itis clear that two cases might arrive according to the decision of multinationalfirms regarding their production technology. When foreign subsidiaries decideto produce according to locally available methods, they use a mix of D-typeand imported inputs. In terms of the upstream industry equilibrium (to bederived soon), we will label this situation as a ”pooling” regime, where activesuppliers will specialize in the same technology. When, on the other hand, (atleast some) multinationals firms decide to import their methods of productionfrom the north, the possibility of equilibria in which some upstream firms decideto adapt to this technology and some others do not opens. Therefore, in thosecases we would see two distinct groups of suppliers; one serving only local firms,and the other serving only multinationals. We will refer to these situationsunder the name of ”separating” equilibria.

It is apparent that the existence of each type of equilibria will come as aresult of choices made by firms at both ends of the market. Downstream, thedecision of multinationals of operating under the M technology will be influencedby the choices they expect suppliers will make in terms of technology. Upstream,suppliers will choose technology by taking into account the gains associated tobeing attached to each type of downstream firm. In what follows, we study theoptimal decisions by firms in both industries, and derive stability conditions forboth types of equilibria.

Choice upstream

We start by studying the decisions taken by local entrepreneurs in the upstreamsector. Recall that the industry is populated by a continuum of firms, which areatomistic in the sense that they perceive their actions as having no industry-wideeffects. Taking this into account, we proceed as follows. We first hypothesizethe existence of a separating equilibrium and calculate profits for the typicalfirm in such a situation. We then construct the decision rule of the marginalsupplier regarding whether to move out of the status quo (i.e. the incentives todeviate), taking the actions of the rest of suppliers are given. Finally, we derivethe conditions in which a deviation is not profitable.

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Note that the game played by local upstream entrepreneurs may be sum-marized by a two-stage sequence. In a first stage, potential suppliers take theirdraw and find out about their true cost parameter. The structure of the secondstage takes place with suppliers having full knowledge of their productivity andthat of the rest of the agents5. Nonetheless, the decision by upstream firmsis conditional on the prevailing strategy by multinationals. In the case wherethe latter decide to operate under the local technology, no further decisionsare required, and stage two is simply production of the intermediate;6 all sup-pliers produce inputs according to local technological standards. However, incases when multinationals decide to set up their facilities in order to producelocally under northern methods, the choice in this second stage is dichotomic.Entrepreneurs must decide whether they will produce D-type inputs and servedomestic producers, or instead serve multinationals by becoming M-type sup-pliers; this last option carrying extra efforts in the form of overhead costs.

Therefore, the attractiveness of supplying MNEs over domestic firms willbe given by a comparison of the profit differential associated with entering thesupply chain of foreign subsidiaries against its costs in terms of fixed costs. Fora single upstream firm, this profit differential will be affected, on the one hand,by what it is happening in the downstream industry in terms of competitionbetween multinationals and domestic firms and, on the other, by the decisionsmade by the rest of suppliers. Intuitively, a higher number of suppliers special-izing in (say) D-type inputs lowers the costs of domestic firms due to love forvariety, therefore increasing their market share and boosting overall demand forD-type inputs. However, at the same time, the higher the number of suppliersbelonging to one group, the stronger business stealing effects are at the interiorof the group, thereby reducing individual profits.

It should then be clear that it is at this stage where costs differences acrossupstream firms will play a relevant role. Else equal, low cost suppliers makestrictly higher profits for any given level of intermediate demand7. Then, theyneed a lower demand differential coming from multinationals in order to findit profitable to pay the extra fixed costs required to adapt their varieties tothe M technology. High cost ones require a higher advantage of multinationalsin downstream markets in order to find the specialization in the M technologyoptimal. Thus, different configurations in the downstream sector will gener-ate different configurations upstream regarding the number and type of localentrepreneurs self-selecting into the supply chain of multinationals.

If we think of the separating equilibria in terms of the number of low andhigh costs suppliers self-selecting into domestic and multinational firms, it isclear that several configurations are possible. For simplicity in exposition, and

5We assume that there is no ex post uncertainty or asymmetry of information of any kind;both the value of the two cost parameters and their distribution is common knowledge.

6We could have also assumed that production needs the payment of overhead costs. Insuch case, the decision for suppliers would be whether to produce or exit according to the levelof profits. Note though that for high enough levels of the size of the downstream industry E,no exit would occur. Then, assuming zero fixed costs of production is equivalent to assumethat the ratio of E to these is sufficiently large.

7Note that cL < cH implies pL < pH , and thus all else equal πL > πH .

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in order to highlight the workings of our model, we will here develop the casewhere all low cost entrepreneurs self-select as MNE suppliers while all high costones decide to cater to domestic producers. In such a situation, the number ofM-type varieties, nM , is equal to the number of low cost suppliers, as given byqn, whereas the number of D-type suppliers, nD, equals that of high costs firms,(1− q)n.

In the case of a ”pure” separating equilibrium where all low cost suppliersproduce M-type inputs and all high cost ones produce those of the D-type, theno deviation condition for low cost entrepreneurs writes as

pMXM

nq− pDXD

n(1− q)

(cL

cH

)1−σ

> fq

The first term in the LHS are variable profits for a typical low cost firmswhen all suppliers of its own type produce M-type inputs. The second term isthe level of profits that such a supplier would obtain in case it decided to produceunder the local technology. By symmetry among low cost entrepreneurs, if thiscondition holds for one firm, then it holds for all of them, resulting in that noproducer will want to deviate from the equilibrium.

We can also write, in a similar fashion, the condition for high cost suppliersto stick to the production of D-type intermediates

pMXM

nq

(cH

cL

)1−σ

− pDXD

n(1− q)< fq

with analogous interpretation. In a ”pure” separating equilibrium, bothconditions need to hold at the same time. This requires,

fq <pMXM

nq− pDXD

n(1− q)

(cL

cH

)1−σ

< fq

(cL

cH

)1−σ

(1)

Note that it is clear that no supplier will switch to the M-technology if thedemand XM for M-type equals zero: it means a pooling equilibrium where thereis no demand for M-type inputs is always compatible with suppliers’ incentives.

In order to get a more subtle intuition regarding the stability condition (1)above, we may re-write it by incorporating the formulae for the price indicespM and pD, and for the demand for each type of input XM and XD, to derivea condition on the relative number of multinational firms:

NM

ND>

1

λ1−ηα1−η1−σ

[α + nqfq

E

1− nqfq

E

](2)

Note that unless nqfq

E < 1 then a separating equilibrium will never arise,no matter the number of multinational firms. However, later (section 4) weshow that this condition will always hold in the case when n is endogenouslydetermined by the free entry condition.

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The parameter α is defined by the following expression, that reflects theskewness of the productivity distribution:

α =q

1− q

(cL

cH

)1−σ

Then, the above condition states that, on the upper side of the market,a pure separating equilibrium requires the ratio of multinationals to domesticfirms to be higher than something that depends on the shape of the distributionof upstream productivity. Note that the LHS of (2) will be increasing in αwhenever σ > η, which means that intermediate inputs are better substitutes toeach other than final goods are. Hence, business stealing effects are stronger inthe former. Under this condition, the higher the proportion of good suppliers q,or the higher their productivity advantage -both increase α-, the higher is thegain derived from a move towards the D technology, making it difficult for a pureseparating equilibrium to be sustainable. Then, a more skewed productivitydistribution will require a larger share of multinational firms in order to have aseparating equilibrium, in order for gains in the form of higher total volume todominate losses from tougher competition.

On the other hand, the size of the supplying industry, as given by n alsomakes the condition more stringent: tougher competition makes reduces indi-vidual profits, making more more difficult to recover the fixed cost of switchingtechnologies.

We can also re-express the stability condition of pure separation for highcosts suppliers

NM

ND<

1

λ1−ηα1−η1−σ

α + nqfq

E

(cL

cH

)1−σ

1− nqfq

E

(cL

cH

)1−σ

. (3)

Which is similar to the one above, with the extra term making it harder toverify for a given ratio of foreign to domestic firms. Furthermore, if

nqfq

E

(cL

cH

)1−σ

> 1

then bad suppliers will never switch to the M-technology, no matter themarket share of multinational firms. Later, when the endogenous value of n isexplicitly incorporated, we show that this condition is verified for large enoughvalues of fq and of the productivity parameter α.

Choice of multinational firms

We now turn to the discussion of the conditions under which a pure separat-ing equilibrium will be validated in the downstream sector by optimal choicesby multinational firms. Variable profits for a typical multinational firm writegenerically as

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Π =1

η − 1C1−η

M

P 1−ηE

Under a pure separating regime upstream, type-specific price indices aregiven by: pM = cL(qn)1/(1−σ) and pD = cH ((1− q)n)1/(1−σ). Then the aboveexpression is is equal to:

Π =1

η − 1

[λcL(nq)

11−σ

]1−η E

P 1−η

Following the same reasoning we did in the previous subsection, we now lookat the conditions under which no multinational firm will want to deviate froman equilibrium where all of them decide to produce under the M technology.The level of profits a multinational would obtain if decided to switch to the Dtechnology are given by

1η − 1

[(cL(1− q)

11−σ n

11−σ )1−µ(p∗)µ

]1−η E

P 1−η

Combining the two we obtain the profit differential determining the conditionof stability:

λ1−σα >

((p∗)1−σ

c1−σH (1− q)En

)µ

Note that this equilibrium condition does not depend on the ratio of multi-national to domestic firms. It is though, positively affected by α. A largerdispersion in the upstream industry makes the separation more attractive tomultinationals, since it acts as a stronger foreclosure strategy on local firms,whose base of suppliers is relatively less competitive. Furthermore, the largeris the number of firms upstream n, the lower is the price index of local inputscompared to imported inputs and therefore the stronger are incentives to stayin a separating equilibrium. Note also that a pooling equilibrium will be alwaysstable. The reason is that no supplier will opt to switch to the M-technology ina pooling equilibrium, the price index for M-type inputs would be infinite.

4 Free entry into the upstream industry

We now turn to the determination of our industry equilibrium by analyzing entrydecisions in the upstream industry. Recall that for the moment we are takingthe number of downstream firms as given, later we provide intuitions are to howour results would be affected by allowing free entry in the downstream sector.In this section we proceed as follows. We first set the number of multinationalsto zero, and analyze the equilibrium in an ”autarky” situation. Then, we solvethe model with multinationals, analyzing the cases of pooling first, and thenthat of separating equilibrium.

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Due to productivity uncertainty, local suppliers take their entry decisionsbased on their expectations of profits, as given by the probabilities associatedwith each draw. The free entry condition for upstream firms thus writes as

πe = qπL + (1− q)πH = fe

whenever this holds, any potential entrepreneur will ex ante be indifferentbetween entering the market or not.

Equilibrium without multinational firms

When there are no multinationals operating in the country, given the CESdemand for inputs, expected profits for upstream entrants are given by

πe =pDXD

σn

Downstream, final goods are also subject to a CES demand structure, whichimplies that the above is re-written

πe =η − 1η σ

E

n

Solving for the number of n that makes this expression to equal the entryfee we get the equilibrium number of upstream varieties as

na =η − 1η σ

E

fe

where superscript ”a” indicates an autarky situation with no foreign firmsin the country.

The expression for the number of equilibrium varieties reveals to be quitesimple: it equals the size of the downstream industry divided by the fixed costof entry, multiplied by a constant depending on both markets elasticities. Thissimplicity is due on the one hand to the double CES demand structure, asexplained above, and by our assumption that the income spent in the industryis constant: the price elasticity of good Y being equal to unity, the elasticityof expenditures is null. Therefore, the number of upstream varieties, and itsconsequent negative effect on upstream prices has no effect on the ”size” of thedownstream market8.

Profits and entry in pooling equilibrium

Let us now analyze the case of a pooling equilibrium, as described in previoussections. In this case, profits expected by a potential entrant are still genericallyexpressed by

8Subsection (6.1) discusses what would be the implications of allowing for a higher thanunity industry elasticity downstream

14

πe =pDXD

σn

However, with the presence of multinationals, the revenues obtained fromthe production of D-type varieties are now the sum of sells to multinationalsand sells to domestic firms.

Taking this into account we obtain that ex ante profits in a pooling equilib-rium, net of the entry fee, write as

E

n

1− µ1

1 + ND

NM

(pp∗

)µ(1−η)

− fe

Where we note first that, when NM = 0, the expression into brackets equals1, and profits are thus the same as in the previous section. When the numberof multinational firms operating in the country is positive, NM > 0, the levelof profits a supplier expects after entry need to be recalculated, by subtractingthe loss in input demand due to the fact that foreign subsidiaries source bothlocally and from abroad. The size of this loss is given by the product betweenthe market share retained by multinationals and the share of their costs spentin imported inputs. Due to this, profits of upstream firms are decreasing in µand, provided that µ is nonzero, on the proportion of multinational firms. As inthe Markusen and Venables model, this results comes from the fact that multi-national firms in pooling equilibrium source less intensively from local suppliersthan domestic firms.

In the general case where the downstream market is populated both bydomestic and foreign-owned firms, the sharing of the market is determined en-dogenously by the equilibrium number of upstream firms. This effect is, again,due to the difference in their sourcing needs: by relying solely in indigenousinputs, domestic firms benefit relatively more from a wider availability of them,thereby their market share is increasing in n.

From an analytical point of view, this is somehow unfortunate since it impliesthat we are unable to obtain a clean solution for the number of upstream firms,contrary to the previous case where NM = 0. However, we can show (seeappendix) that the condition σ > η ensures that expected profits upstreamare (due to business stealing effects) a decreasing function of n for all possiblevalues, which ensure the uniqueness of the solution. Under this conditions, wemay write expected profits in the pooling equilibrium as a decreasing functionof both n and NM

ND:

πe ≡ πepool

(n,

NM

ND

)The equilibrium number of firms upstream is the solution of the equation

πepool

(npool, NM

ND

)= fe. This solution is decreasing with the share of multi-

national firms for positive values of the Cobb-Douglas parameter µ; the higher

15

their proportion, the lower the demand for local inputs. Therefore, npool ismaximal for µ > 0 and decreases with NM from :

η − 1η σ

E

fe

(same number of varieties as the case with no multinationals) to:

η − 1η σ

(1− µ)Efe

when there the downstream market is only populated by foreign subsidiaries.This last expression clearly illustrates how the lower intensity of multinationalsimpact on firm entry.

Profits and entry in separating equilibrium

In situations in which local suppliers decide on their entry decisions by antici-pating the arising of separating equilibrium with multinationals bringing in theM technology, expected profits are the weighted average of profits that low costsuppliers obtain from sourcing multinationals and of profits that high cost onesget from serving local firms, and the weights are given by the probability of eachdraw. In this case, it is possible to obtain the unique solution, which is givenby

nsep =η − 1η σ

E

fe + qfq

where it is evident that, ceteris paribus, the fixed costs associated with theadoption of the northern technology impact negatively on entry incentives.

Given that in this case we are able to obtain a clean expression for the equi-librium, we can readily compare the outcome in terms of equilibrium varietiesof a pooling vis a vis a separating equilibrium.

Ifµ <

η − 1η σ

qfq

fe + qfq

the number of upstream firms will always be smaller in a separating equilibriumthan pooling equilibrium. Otherwise, the number of upstream firms may besmaller in a pooling equilibrium when the proportion of multinational firms islarge. Since we cannot solve for the number of upstream firms in a poolingequilibrium there are both domestic and multinational firms downstream, wecannot directly compare n in both cases. However, we can derive an exactcondition. Because profits in the pooling equilibrium are decreasing in n, therewill be a larger upstream industry with the separating equilibrium if and onlyif:

πpool(

nsep,NM

ND

)< 0

16

which is equivalent to:

ND

NM<

[µ

(η − 1η σ

fe + qfq

qfq

)− 1][

p∗(fe + qfq)1

1−σ

cE1

1−σ

]µ(1−η)

since the right hand side is decreasing in fq and E and increasing in fe andc (average cost of producer), this condition will be harder to satisfy when fq

and E are large or when fe and c are low.

4.1 Conditions for separation with free entry upstream

Previously, we have shown that n the number of upstream firms affects thestability of the separating equilibrium. In the upstream industry, a higher nmakes the switch to the M-technology less attractive since it implies toughercompetition that makes it tougher to recover the fixed costs of technologicaladaptation. In the downstream industry, a higher n, reduces the price of localinputs compared to imported inputs, therefore tipping in favor of their usage.

Thanks to the fact that the number of upstream firms at the separatingequilibrium is determined by a simple expression, we can express the conditionfor the existence of such an equilibrium taking into account the endogeneity ofn. We start by doing so in the case of the upstream industry.

Before, we had derived a condition under which the minimal share of multi-national for the existence of the separating equilibrium is finite, which we nowrewrite using nsep

nqfq

E< 1 ⇔ η − 1

η σ

qfq

fe + qfq< 1

Note that the number of upstream firms that satisfies the free entry conditionwith equality is by uniqueness of the solution the maximal value that n mayattain (provided we are in a pure separation regime). Using this fact we are ableto show that a separating equilibrium will always exists (in term of upstreamfirms incentives) when the share of multinational firms is large enough. Moreprecisely, the condition for stability upstream is now:

NM

ND>

1

λ1−ηα1−η1−σ

[α + (1 + α)

qfq

fe

]On the contrary, if we suppose that

η − 1η σ

qfq

fe + qfq>

(cH

cL

)1−σ

then high-cost suppliers will never switch to the M-technology if there is free-entry upstream, whatever the number of multinational firms downstream. Sim-ilarly, we can also rewrite the condition for the stability of the separating equi-librium in term of MNEs incentives:

λ1−σα >

(p∗

cH

)µ(1−σ)(fe + qfq

(1− q)E

)µ

17

5 Separating equilibrium with homogenous sup-pliers

We have thus far focused on a case where exogenous productivity differencesmaps separation among suppliers. In this subsection we discuss a case wheresuppliers are homogeneous, thus cL = cH = c. The proportion of suppliersswitching to the M-type technology is denoted by q and derive endogenouslyabove, where we show that a separating equilibrium is still possible even ifupstream firms are homogenous.

In term of suppliers’ incentives, the break-even condition becomes:

pMXM

nq− pMXM

n(1− q)= fq

Given that pMXM and pMXM are functions of n and q, we can obtain thefollowing equation: (

q

1− q

)σ−ησ−1 1 + (1− q)nfq

E

1− qnfq

E

=NM

NDλ1−η

The left-hand side is increasing with q which means that there is a uniquesolution for q which is increasing with the fraction of multinational firms NM

ND

and the productivity gains λ1−η coming from the fact that multinational usethe M-technology.

There are however two caveats: there is no analytical solution q, as a functionof n and other parameters, and n is actually endogenous and depends on q:

n =η − 1η σ

E

fe + qfq

Fortunately, when the endogenous value of n is considered, it permits to obtainan analytical solution for q in term of exogenous parameters. At equilibriumwith free entry, q is now determined by:

q

1− q=(

NM

NDλ1−η fe

fe + fq

) σ−1σ−η

As expected, the proportion of suppliers switching to the M-technology isincreasing with the proportion of multinational firms, with the efficiency gainsto use the M-technology, and decreasing with the cost of switching (comparedto the cost of entry).

This example is illustrative since it permits to highlight one of the two mech-anisms that make separation attractive for foreign firms in this model. Byintroducing their alternative technologies and generating the segmentation ofthe local upstream industry, multinational firms in this model are able to de-velop a competitive advantage in the downstream industry. To illustrate this

18

last point, we recall that the ratio of multinational costs to domestic costs in ahomogeneous equilibrium is given by

cM

cD= λ

(q

1− q

) 11−σ

Replacing by the equilibrium conditions derived above this becomes

cM

cD= λ1+ σ−1

σ−η

(NM

ND

η − 1η σ

fe

fe + fq

) 1η−σ

This condition expresses the fact that, thanks to the fact that multinationalshave an ex ante productivity advantage given by the parameter λ, they are ableto attract a higher number of upstream firms, and this wider base of suppliersamplifies initial productivity differences. This is quite graphically indicated bynoting that, once the equilibrium value of q is taken into account, the exponenton λ increases9. This is one of the main properties of our model. The secondone is the fact that, given the existence of the fixed costs fq, when there is exante heterogeneity in the local upstream industry, a self-selection of high pro-ductivity suppliers into M takes place, adding another source of cost advantagefor multinationals.

We now derive the stability conditions for a separating equilibrium on thedownstream market. Since this itself depends on the number of switching sup-pliers, we need to discuss the choice of multinationals as a function of exogenousparameters. With free entry upstream, this writes:

λ1−σ

(q

1− q

)>

(p∗

cH

)µ(1−σ)(η σ

η − 1fe + qfq

(1− q)E

)µ

The left hand side is increasing in q and the left hand side in decreasing inq. Since q is itself increasing with the proportion of multinational firms, we con-clude that a separating equilibrium is possible when the number of multinationalfirms is large enough. As previously, incentives to stay in a separating equilib-rium are also stronger the higher are the gains from using the M-technology(λ1−σ).This is due to the fact that, the higher their ex ante advantage, thehigher the incentives to hurt domestic costs’ costs by generating a separationupstream.

Unlike a separating equilibrium between low-cost and high-cost suppliers, inthis case we obtain that a separation upstream is always possible in term of sup-pliers incentive. In term of multinational firms incentive, it depends now on therelative number of multinational firms compared to domestic firms (as it impactson the relative number of upstream firms switching to the M-technology).

9Recall that 0 < λ ≤ 1.

19

6 Impact on price indices and consumers wel-fare

After having characterized our alternative equilibrium configurations, it is timeto ask how they perform in terms of welfare. We then analyze the price indexin each regime

Price index under pooling equilibrium:

Ppool = (npool)1

1−σ (NM + ND)1

1−η[c1−σL q + c1−σ

H (1− q)] 1

1−σ

Price index under separating equilibrium:

P sep = (nsep)1

1−σ

[NMλ1−ηc1−η

L q1−η1−σ + NDc1−η

H (1− q)1−η1−σ

] 11−η

Suppose that µ ≤ η−1η σ

qfq

fe+qfq(such that nsep ≤ npool) and λ1−σ ≤ 1+ 1

α , thenthe price index under separating equilibrium will be always higher in separatingequilibrium than in pooling equilibrium:

Ppool < P sep

which means that consumers’ welfare will be higher in the pooling equilib-rium. Those are sufficient conditions but not necessary conditions. In order tohave a lower price index in the separating equilibrium, the number of upstreamfirms needs to be high enough. If the number of upstream firms is lower inthe separating equilibrium, the price index under separating equilibrium will belower only if:

• the number of firms in the upstream industry under pooling equilibriumis low enough

• the efficiency gains from using the M-technology are large enough (i.e. λis low enough).

• the proportion of multinational firms is high enough.

• the elasticity of substitution is high enough (the price index is decreasingwith the elasticity of substitution)

6.1 Endogenous market size

Throughout the paper, we have worked under the assumption that E = EP 1−ε

with ε ≥ 1 thus representing the elasticity of substitution between the basket offinal goods from this industry and the goods from another industry (until now,we focused on ε = 1).

This assumption was convenient as it allowed us to obtain simpler expres-sions for the equilibrium number of upstream varieties, which were independentof the number of downstream firms. In order to generalize our results a bit

20

further, we now comment briefly on the implications of lifting it, by allowing tobe substitution between our generic good Y and other goods. The first directimplication is that n now depends on the number of firms downstream, in bothcases of pooling and separating equilibria. The reason is that a higher number ofdownstream varieties implies a lower price index, and therefore a higher incomespent in the Y industry when the elasticity is positive.

Incorporating this feature, we obtain multiple equilibria in the case of pooledsuppliers. However, it is possible to show (not done here) that only one, thatwith the highest number of upstream varieties, is stable 10.

The conditions for stability of a separating in term of suppliers incentivesremain invariant to this alternative configuration (the effects of the price indexon the market size drop with the impact on the number of firms upstream n)with either heterogeneous or homogenous suppliers.

However, conditions for separating in term of multinational choice depend onthe market size: they now depend on the price index which depends itself on thenumber of downstream firms. The higher is the number of downstream firms,the larger is the market size, the larger is the number of upstream firms, thesmaller is the advantage of importing inputs over domestic firms, and throughthis mechanism, the stronger are incentives to stay in a separating equilibrium.

7 Free entry into the downstream industry

Long term equilibria

So far, we have considered the number of domestic and multinational firms asexogenous. This was a convenient assumption that helped us make our pointabout the possibility of separating equilibria and its impact on the developmentof inter-linked industries. Nonetheless, in order to have comprehensive resultswe need to take into account entry decisions by domestic and multinational firmsdownstream. Therefore, in this section we discuss the implications of allowingfor free entry downstream, in an intuitive way.

Suppose that multinationals face a fixed cost FM , and domestic firms a fixedcost FD. In the long term equilibrium with free entry, profits of surviving firmsmust equal fixed costs.

Unfortunately, our model does not allow for the possibility of mixed equi-librium in the long term. The reason for this is that firms at the interior ofeach group are strategic complements, but, the two groups of firms are strategicsubstitutes to each other. To appreciate this point, imagine that we are in apooling equilibrium, and we let the number of domestic firms to increase. Giventheir higher sourcing coefficient, this an increase in the share of domestic firmstends to raise the number of local suppliers which, in turn, decreases the relativecost of domestic firms, thereby providing incentives for more domestic entry andlowering multinational profits. On the other hand, starting from a separatingequilibrium, raising the fraction of multinational firms attracts good suppliers

10More specifically, three equilibria might arise

21

towards the M-technology, thereby reinforcing foreign subsidiaries’ cost advan-tage further and making entry for them more attractive.

Once this mechanism is understood, it is possible to show that, for some pa-rameter configurations, pooling equilibria will lead domestic firms to prevail andseparating equilibria will lead to the opposite situation in which multinationalfirms are the only survivors. More precisely, imagine a pooling equilibrium withonly multinational firms. If the number of upstream firms in such a situationis high enough is high enough such that the cost of multinational firms is notlower than the cost of domestic firms (equal to or higher than η−1

η σ(1−µ)E

fe), or

alternatively that fixed costs for multinational firms are larger than for domesticfirms (this is a natural assumption), then this situation will not se stable, andin the long run domestic firms may prevail in pooling equilibrium. Conversely,if the distribution of supplier productivity is ”skewed” enough (parameter α) orif the efficiency gains from using the M-technology are large enough (parameterλ−1), then multinational firms then when the separating equilibrium arises, thelong run industry equilibrium is going to be populated only by multinationalfirms.11

Thus, the relevant message of above brief digression is that for the deter-mination of the long run equilibrium situation, ”history matters” and initialconditions play an important role in determining final outcomes.

Initial conditions matter

We now briefly discuss with examples the above conclusion of the relevance ofinitial conditions. Imagine that some domestic firms first enter the market. Iftheir number if large enough, a new multinational firm will choose to imple-ment the D-technology because it won’t be able to attract enough suppliers andthe input price index would be too high with the M-technology. Since poolingequilibrium is stable (if all downstream firms use the M-technology, no firmwill switch to the M-technology for the same reason), the only long-term equi-librium is the pooling equilibrium where domestic firms may eventually evictmultinational firms.

Suppose now that multinational firms enter first. As we showed, good sup-pliers switch to the M-technology if the share of multinational firms with theM-technology is high enough. Why would multinational firms choose the M-technology? If the number of upstream firms increases slowly, then multina-tional firms may have a strong advantage by exporting and may not switchto the D-technology. In that case, the long term equilibrium is the poolingequilibrium. Oppositely, if the number of upstream firms reacts quickly to theentry of multinational firms, then these will choose the M-technology. In thatcase multinational firms may eventually evict all domestic firms entering in thedownstream industry.

Alternatively, we might also suppose that multinational firms may not adapt11Note that both sets of conditions are compatible: the first is a restriction on µ and FM

whereas the second set restricts α and λ.

22

to the D-technology if there is no domestic firms downstream (they have nodownstream firms to imitate). Therefore, the multinational that enter in a mar-ket where there is no domestic firms will automatically choose the M-technology,which could lead to a separating equilibrium in the long-term even if some do-mestic firms entered the market.

8 Conclusions

To be completed.

References

[1] Grossman, G. and Helpman, E. (2003) “Outsourcing versus FDI in In-dustry Equilibrium”. Journal of the European Economic Association 1317-327.

[2] Hopenhayn, H. (1992) “Entry, Exit, and firm Dynamics in the Long- Run”.Econometrica 6 (5) 11271150.

[3] Markusen, J. and Venables, A. (1999) “Foreign Direct Investment as aCatalyst for Industrial Development”. European Economic Review 43 335-356.

[4] Melitz, M. (2003) “The Impact of Trade on Intra-Industry Rellocationsand Aggregate Industry Productivity”. Econometrica 71 (6) 1695-1725.

[5] Ping, L. and Saggi, K. (2007) “Multinational firms, Exclusivity, and Back-ward Linkages”. Journal of International Economics 71 206-220.

[6] Rodriguez-Clare, A. (1996) “Multinationals, Linkages, and Economic De-velopment”. American Economic Review 86 852-873.

[7] UNCTAD (2001) “World Investment Report: Promoting Linkages”. UnitedNations, New York and Geneva.

23

Appendix

Proof of uniqueness of n in pooling equilibrium.We need to show that

π =E

n

[1− µτp∗

CM

NMC1−ηM

P 1−η

]− fe

is decreasing in n.We can rewrite:

π =E

n[1−A(n)B(n)]− fe

where A(n) is the fraction of costs of multinationals related to imported inputsand B(n) is the market share of multinational firms. Note that A(n) ≤ 1 isincreasing with n and B(n) ≤ 1 is increasing with n.

dπ

dn= −E

n[A′(n)B(n) + A(n)B′(n)]− E

n2[1−A(n)B(n)]

Hence:

dπ

dn< 0 ⇔ 1−A(n)B(n) + nA′(n)B(n) + nA(n)B′(n) > 0

Since A′(n) > 0 and A(n) ≤ 1, a sufficient condition is that

B(n)− nB′(n) < 1.

Let us rewrite B(n) as:

B(n) =1

1 + ND

NMG(n)

where G(n) =(1− µ + µτp∗c−1n

1σ−1

)η−1

. Note that the elasticity of G ac-

cording to n is less than 1 because nG′(n)G(n) ≤ η−1

σ−1 ≤ 1.We can now show that the condition on B is verified:

B(n)− nB′(n) =1

1 + ND

NMG(n)

[1 +

ND

NMnG′(n)

1 + ND

NMG(n)

]

≤ 11 + ND

NMG(n)

[1 +

ND

NMG(n)

1 + ND

NMG(n)

]<

11 + ND

NMG(n)

[1 +

ND

NMG(n)

]= 1

24