Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
FUNDACAO GETULIO VARGAS
ESCOLA DE POS-GRADUACAO EM ECONOMIA
PEDRO LUIS ACCIOLI NOBRE BRETAN
ESSAYS ON INDUSTRIAL ORGANIZATION
Rio de Janeiro
2010
PEDRO LUIS ACCIOLI NOBRE BRETAN
ESSAYS ON INDUSTRIAL ORGANIZATION
Tese submetida a Escola de Pos-Graduacao em Economia
da Fundacao Getulio Vargas como requisito para obtencao do
Tıtulo de Doutor em Economia
Orientadora: Maria Cristina Terra
Area de concentracao: Economia Industrial
Rio de Janeiro
2010
PEDRO LUIS ACCIOLI NOBRE BRETAN
ESSAYS ON INDUSTRIAL ORGANIZATION
Tese submetida a Escola de Pos-Graduacao em Economia
da Fundacao Getulio Vargas como requisito para obtencao do
Tıtulo de Doutor em Economia
Aprovado em 23/12/2010
pela comissao organizadora
Maria Cristina Terra (Orientadora - EPGE/FGV)
Humberto Moreira (EPGE/FGV)
German Pupato (EPGE/FGV)
Adriana Hernandez-Perez (ITAU-UNIBANCO)
Maurıcio Canedo (IBRE)
Rio de Janeiro
2010
Agradeco,
Aos meus pais e minha irma, pelo amor e apoio incondicional;
A minha orientadora, Maria Cristina Terra, por acreditar no meu projeto e guiar me em
seu seu desenvolvimento;
Aos amigos da EPGE e da FEA, que me apoiaram e me ”aguentaram” por todos esses anos.
A Gabi, pelo apoio incrıvel que me impulsionou no momento mais difıcil desta jornada.
Resumo
Esta tese compoe-se de tres ensaios que versam sobre o formato, em termos de estrutura de
governanca, das industrias e como a estrutura interna das mesmas influenciam esses formatos
e seus produtos. O primeiro capıtulo apresenta um modelo de como a qualidade institucional,
confianca e incompleteza contratual afetam as decisioes das firmas sobre a melhor forma de se
organizarem internacionalmente. O segundo capıtulo vai na mesma direcao de explicar a orga-
nizacao das industrias, mas com foco no efeito da transmissao de informacao entre as unidades
constituintes das organizacoes sobre o formato otimo das mesmas. Ambos trabalhos usam
modelos dinamicos. O terceiro capıtulo se utiliza da modelagem de organizacao industrial para
mostrar como a estrutura interna de uma industria influencia no risco de credito consignado.
Palavras-chave: integracao, terceirizacao, organizacao industrial, risco, credito consignado, in-
formacao, confianca, qualidade institucional.
Abstract
This thesis is comprised of three essays with a common goal: expand the theories about what
drives the shape of an industry and its consequences. All three are theoretical and applied,
in the sense of being detailed studies about the inner workings of industries and their impact
on the shape of the latter. In the first chapter I model how the interplay among institutional
quality, trust and contract incompleteness affects firms’ decisions about their international mode
of organization. Second second chapter also concerns industries’ ownership choices, but in a
complete different perspective, focusing in information transmission between the different parts
that constitute a supply chain. Finally, third chapter uses industrial organization modeling to
show how the internal structure of an industry influence the risk of payroll-backed loans.
Keywords: integration, outsourcing, industrial organization, risk, payroll-backed credit, infor-
mation, trust, institutional quality.
Sumario
Introducao - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1
Capıtulo 1: Trust, Institutions and the choice between out-
sourcing and FDI - - - - - - - - - - - - - - - - - - - - - - - - - - 2
Capıtulo 2: Information and Ownership Choice - - - - - - - - 36
Capıtulo 3: An economic model of the risk of payroll-backed
loans - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -71
Trust, Institutions and the
choice between Outsourcing and FDI
Abstract
I model how the interplay among institutional quality, trust and contract incompleteness
affects firms’ decisions about their international mode of organization. A producer wants
to form a partnership with a foreign distributor, through either Outsourcing (O) or Foreign
Direct Investment (FDI), but is uncertain over his commitment. A non-committed partner
will try to engage in illicit activities: for FDI, he can steal business plans, blueprints, etc; for
Outsourcing, the distributor collects the revenue and may default on his payments.
In a dynamic model with Bayesian learning, one-sided incomplete information and non-
observable investments, I show that reputation-building may induce a change in the long
run from FDI to Outsourcing. In accordance with the empirical literature, I show that for
weak institutions, entry happens via FDI when uncertainty over the commitment is high
and via Outsourcing when it is low. Conversely, with sound institutions entry is always via
Outsourcing. If entry took place via FDI, I show that after some time Outsourcing may
become preferable to FDI. The level of trust at which this change happens is decreasing in
the institutional quality.
Finally, I study how institutional reforms affect producers’ expectations about the evo-
lution of the partnership to FDI. Results indicate an institutional trap where the lower the
institutional framework, the smaller the impact from the reforms over expectations.
3
1 Introduction
Trust between business associates is an important element in successful and lasting partner-
ships1. Although in our times legal contracts are the primary way to establish the terms of an
agreement to trade, trust interplays with them in a two-way manner such that one attempts
to fill the gaps the other, for whatever reasons, is not capable to perform.2 For instance, when
institutions are not good enough to enforce contracts, a business partnership built on trust may
be capable to thrive. This is the first way. The other is the standard: in the absence of trust,
well-written contracts are necessary to make sure the trade obligations will be honored.
A big problem with the latter, though, is that it relies on the existence of well developed
institutions capable of enforcing the contracts. Therefore, if there is no trust between partners
and enforcement is poor, the possibilities of trade developing are dim. The former is not free
of its problems either: although, intuitively, trust can substitute for inadequate enforcement,
in general trust develops through a slow process of confidence building that in its course will
provide the society with an inefficient provision of the good or service in question.
Enforcement difficulties are particularly acute in the area of international relations: if one of
the parties reneges on a contract, the other must look for assistance in the courts and, depending
on the specifics of the market in question, the judicial system may be incapable of enforcing the
agreed contract. Poor enforcement is more likely in an international business relationship since
the costs for one of the parties to sue the other increase due to differences in the law system
and country-specific judicial procedures, besides the costs related to the distance per se. These
increased costs, in turn, make it easier for the courts to stand by their fellow citizens.
These problems inspired work by Araujo and Ornelas (2008). In their model, the interplay
between trust and enforcement is analyzed in a setting where an exporter needs a distributor
in a foreign country but cannot differentiate between the two types available there: myopic
and patients. The latter is interested in building a long-term partnership with the exporter,
whereas the former is shortsighted and thus is going to default on the contract whenever is
possible. Trust is defined as the value the exporter assigns to the probability that his distributor
is myopic. Enforcement shows up through an exogenous probability that a myopic distributor
has in finding a corrupt legal officer to back him in his unlawful plans. They show that for a given
enforcement level the incomplete information about the type of the distributor depresses trade
flows, but trade increases with the passage of time as the producer learns about the distributor
type. Improvement in enforcement also increases trade flows.
The present work builds on their model but, whereas they were concerned with the effects
of the interplay of trust and enforcement in trade flows, the focus here is on the effects of these
1My use of trust for business partnerships follows the definition of Mayer et al. (1995). They define it as: ”thewillingness of a party to be vulnerable to the actions of another party based on the expectations that the otherwill perform a particular action important to the trustor, irrespective of the ability to monitor or control thatother party”.
2See Egan and Mody (1990, p. 327).For example, at page 326-327, they state that ”Trust implies a moralcontract and long-term commitment which ”reflects a condition of mutual dependency where both client andsubcontractor are in a position to influence the other by their behavior”.
4
variables on the decision of multinational firms about the best way to structure their divisions
internationally. In accordance with the discussion in the second paragraph, the lack of good
enforcement disrupts business plans and distorts the optimal organization of production. This
paper shows that the above-mentioned “first way” of the trust-contract interaction may lead in
the long-run to the optimal organization, through a trust-building process. On the other hand,
as was mentioned in the second paragraph, this process is a long-run enterprise and does not
eliminate the distortions caused by bad institutions in the meantime.
I find that, broadly, the better the institutions, the more likely the foreign firm will enter
the market via Outsourcing; however, if she enters via FDI, with some probability a change to
Outsourcing may happen in the future. Finally, I determine the effects of institutional reforms
over the expectations of producers of a future change to FDI, with some interesting results.
Although the interplay of trust, institutions and ownership choice is widely discussed in
the management and economics literature, there are no theoretical models that study the joint
dynamics of them, and very few empirical papers, specially considering international aspects of
alliances. Among these few, Gulati (1995) studies 2400 alliances in various industrial sectors,
finding that equity sharing in a partnership is negatively related the duration of a repeated
relationship. Moreover, he finds that that international alliances are more likely to be equity
based than domestic alliances. From this, he concludes that trust affects the structure of interfirm
partnerships. Also, the franchising literature presents us cases that go in the direction of this
paper’s findings: for instance, Ko (2008) shows that both Mcdonalds and KFC decided to enter
the Chinese market via FDI given the unexistence of adequate laws at that time. In 2007, 17
years after entry, Mcdonalds still used mostly integrated structures to do business in China
(just 1 franchised outlet), although in the rest of the world non-integrated operational modes
accounted for 70% of its outlets.
Other authors also have studied the relationship between trust and ownership forms:
Brouthers and Brouthers (2003) find that industrial firms’ propensity to entry via integrated
FDI has a negative correlation with trust levels. The first study of forward integration into
distribution, by John and Weitz (1988), found that both environmental uncertainty and behav-
ioral uncertainty (related to trust) increase the probability of integration. Johnson et al. (2002),
studying post-communist countries, find first that courts are more important when relationships
are weaker, mostly in market-based transactions. Second, that in an established relationship,
after the development of trust, is the relationship itself which determines the cooperation, re-
gardless of the efficiency of the enforcement system. Another paper in the literature that studies
the effects of trust and ownership structure is Bottazzi et al. (2008): he finds that the lack of
trust undermines the use of sophisticated contracts.
This paper is also related to the literature on relational contracts and the theory of the
firm, specially the papers by Baker et al. (2002a,b). They examine relational contracts and
ownership structure in a very broad way. While these author link the relational aspect of
interfirm partnerships to the possibility of non-enforceable promises between the partners, here
I abstract from this element and focus on a different aspect: the learning process associated with
5
a relationship and the effect of institutional changes over it.
Thus, based on these evidences, I setup a two-country model where a producer wants to form
a partnership with a distributor in the other country to sell her goods, and faces two alternative
operational modes to establish this enterprise: she may start through Outsourcing or through a
Foreign Direct Investment.
In this paper trust between business partners is captured via the uncertainty the producers
have about the distributors, similar to Araujo and Ornelas (2008)’s. That is because distributors
can be of two types, one commited to the joint enterprise and another opportunist, and the
producer does not possess enough information to tell one apart from the other. Together with
the degree of institutional quality of the country, they are responsible for the potentials pitfalls
facing the producer as she makes business in Foreign. If she enters via Foreign Direct Investment,
the local distributor is part of the integrated firm. At this position, he has greater access to
classified information that is valuable to competitors and, depending on his type, he will obtain
and sell them, bringing harm to his former employer in terms of smaller future profits. Foreign
Direct Investment is also subject to a fixed cost related to all the hurdles and expenses that
come with integration.
On the other hand, if the entry choice was Outsourcing, the pitfall is of another nature:
now the proceeds of the sale are collected by the distributor and, depending on his type, he
may decide to run away with them. In both cases, Outsourcing or FDI, in order to complete
the unlawful action the distributor must find a corrupt legal agent, which is not certain. The
uncertainty revolving around the distributor’s possibilities to find this agent is this paper’s
measure of institutional quality: the better the enforcement, the more difficult is to evade the
law.
This story is modeled as repeated-game where a distributor and a producer meet period after
period to reassess their partnership. This way, in both operational modes one agent discovers
more about the other with the passage of time: as trade happens and if there is no record of
misbehavior by the part of the distributor, the producer slowly learns his partner’s true type,
through Bayes Rule.
The above-mentioned learning, when coupled with incomplete contracts, are responsible for a
relevant distinction between Outsourcing and FDI in this model: in the latter, the compensation
for the distributor is fixed, whereas in the former it may vary with time. At every period the
partners trade, there is some non-contractible investment to be done by the distributor in behalf
of the partnership, and after this work is finished the goods are produced, shipped and a bargain
takes place to split the surplus from the trade. In the case of FDI the splitting share is assumed
to be fixed, while in the case of Outsourcing it is subject to the uncertainty regarding the
type of the distributor. Therefore, in case this incomplete information were severe, the bargain
power shifts to the producer, who will get more of the surplus in exchange for the risk. The
downside of this, of course, are diminished incentives for the distributor to promote the good in
the country. At the end, the incomplete information causes the total profit from the operation
via Outsourcing to decrease, in comparison to FDI. Learning changes, over time, the severity of
6
the uncertainty over the distributor’s type, increasing the ex-post share of the distributor and
his investments, improving the outlook of Outsourcing via-ı¿12 -vis FDI.
This approach to reflect the risk of an arm’s-length operation is novel and describes well
how foreign investors react facing an uncertainty. Better institutions can mitigate the impact
of the incomplete information through enforcement, diminishing the risk and improving the
surplus sharing between the agents. Even if there is near-certainty over the opportunism of the
distributor, which would prompt almost total bargain power to the producer as an insurance
against this enormous risk, there is some critical level of enforcement such that beyond it the
bargain power of the producer starts to diminish. Intuitively, if the police are perfect, the
honesty of your business partner is almost irrelevant: legal deterrence at its best.
Before describing the results concerning optimal entry under incomplete information, a
benchmark is needed in order to jump from analytical results to any policy recommendation.
In this work, under complete information the preferred mode of operation would be Outsourc-
ing, given that in it producer and distributor share equally the ex-post surplus from trade and
investments are greater than in the case of FDI. This benchmark, of course, depends on the
assumption that just the distributor invests on the partnership. I decided to take this approach,
and not one with both investing or just the producer, due to three facts: first, to explore a
neglected side of the literature, which mostly focuses on investments upstream; second, because
the emphasis in the distributor’s investment allows me to focus on the effects of uncertainty
over the results of the partnership in the foreign country; third, and the most important, when
entering a new final-good market usually a good deal of the work that is necessary for the success
of the enterprise is done overseas, periodically. The emphasis is important: although one-shot
investments in production and distribution are relevant, here the focus are on the recurrent
investments necessary to maintain the correct course of a business enterprise.
In a environment with incomplete information, I show how institutional quality influence the
decision of the producer between entry via Foreign Direct Investment or Outsourcing: for lower
levels of enforcement, entry takes place via Foreign Direct Investment when the prior probability
that the distributor is an opportunist is high and via Outsourcing when it is low. However,
for some high enough enforcement level entry happens directly via Foreign Direct Investment,
regardless of the probability that the distributor is committed to the firm. Conditional on
entering via FDI, I also show that there is a unique critical trust level such that at it a change
of operational mode takes place.
The linking of compensation to trust directly through the bargaining process gives novel
results for the dynamics of outsourcing that are absent in Araujo and Ornelas’ work. There the
exporter is passive in his negotiations with the distributor, whatever his beliefs about the latter’s
type. Therefore, in case the exporter had near-certainty that his partner was myopic, the authors
assume that profits would be negative, regardless of the enforcement level. Here this is not the
case: near-perfect enforcement brings maximum profits for the producer, since in this case the
reputation of the distributor will not be relevant to the business. Another difference is that
in their model the increase in profits with the passage of time is due to increased trade flows.
7
Here I use revenue functions, and profits increase due to greater investments that happen as
the compensation of the distributor augments, but they do not come necessarily from increased
sales, although they could be interpreted this way.
Moreover, notice that there is effectively two kinds of contract incompleteness here: the
unobservable-investment one and the incompleteness brought by the imperfect enforcement.
Both contribute to underinvestment, and the latter affects directly the former: the weaker the
enforcement, the greater the hold-up problem since it affects directly the share of the trade
surplus that the distributor obtains.
Finally, a relevant policy question is how institutional improvements affect producers’ expec-
tations about doing business in the foreign country via FDI. I find that there is an institutional
trap effect, such that expectations improve if trust and institutional levels are already high, and
decrease otherwise.
1.1 Other related literature
Besides the empirical and theoretical works cited in the beginning of the section, this paper
is related to a large economics literature on Foreign Direct Investment and institutional quality,
most of it empirical. Studying expropriation, a risk not considered here, Eaton and Gersovitz
(1984) analyzed the relation between the type of FDI and political risk, coming with the idea
that the ownership of intangible assets diminishes the incentives to expropriation. However,
their model considered just FDI.
Yet Albuquerque (2003), in a setting with imperfect enforcement, allows for different types
of investment. He concludes, first, that the higher the political risk of the host country, the
greater is its share of FDI; second, that FDI is a more stable type of investment compared to
other types.
In a similar vein, Hausmann et al. (2000), in a empirical study over the types of flows coming
into Latin America, concludes that
“the share of FDI in total flows tends to be larger in countries that are riskier, more
distant, resource rich, financially underdeveloped, institutionally weak and suffering
from original sin.”
Thus, one of the conclusions of this paper in in line with these empirical findings of Hausmann,
that is, that institutional quality is inversely related to relative FDI flows.
Finally, Schnitzer (2002) analyzes the trade-off between FDI and debt finds that FDI is more
likely to be chosen the riskier the project, the greater the efficiency of the foreign investor and
the better its outside option.
None of these papers, though, consider how the interplay of trust, reputation and institutions
affect organizational choices in the international arena.
The effects of learning in the choice between operational modes were also analyzed by Kotseva
and Vettas (2005). However, in their model the learning is over levels of demand, given that the
agents are uncertain about the its true level.
8
Probably the work that more closely resembles this is from Straub (2008). He analyzes
the trade-off between FDI and debt in a model with incomplete contracts due to institutional
constraints in the host countries, such as problems of commitment and corruption. Two modes
of corruption are studied: petty bureaucratic corruption and high-level political corruption. In
line with the findings of this paper, his model predicts that multinational firms prefer FDI the
weaker the commitment of the host country, while both types of corruption favor more flexible
operational modes. To reach these conclusions, he models an environment with incomplete
information and assumes the parties split the gains from trade through a bargaining process.
The incomplete information, however, is over variables different from the ones in this work; thus,
is not directly comparable. In addition, the model is static and does not consider learning or
the possibility of a change from one mode to another due to institutional advances.
The paper proceeds as follows. Section 2 describes the economic background. Section 3
presents the learning environment. Sections 4 and 5 present the economic environment and
solve the producer’s problem of a choice between outsourcing and FDI. Section 6 solves the
distributor’s problem. At Section 7 I show that the producer and distributor’s strategies and
beliefs obtained in the previous sections constitute an equilibrium. Section 8 shows the effect
of changes in enforcement over, among other things, the time necessary to move from FDI to
Outsourcing and over the probability that this event will be attained. Section 9 concludes.
2 Background
Consider a world economy with two countries, Home and Foreign. There is a continuum
of identical producers and differentiated goods in Home and Foreign, with one producer per
good, and aggregate demand of any differentiated product, every period, is equal to one in both
nations. Producers sell their goods at Home and can access the Foreign market through one
of two possible operational modes: Outsourcing (O) or Foreign Direct Investment (I), which
generate revenue equal to Ri, i ∈ {O, I}. Whichever mode of entry is chosen, the producer
needs a distributor in Foreign to handle the whole sales operation: in the case of Outsourcing,
the distributor is contracted arm’s length; in the case of Foreign Direct Investment (henceforth
FDI), he is vertically merged in the organization, that is, the distribution business is a division
of a larger firm. Producers discount time at a rate β and I assume that the good is manufactured
with a bulk investment equal to k, thus the marginal cost is zero. Hereafter I will use female
pronouns when referring to the producer and male ones to the distributor.
What is the role of the distributor in the partnership? I say he has superior knowledge of
local conditions and thus is important for the enterprise to be successful. Indeed, he is the one
in charge of the recurrent investments that allow the product to be known and accessible to the
public, marketing for example.
There are two types of distributors in Foreign: either they can be opportunists (P ) or com-
mitted (and honest) (C), and each one knows his own type, which is his private information.
The producer, thus, is uncertain over the type of any distributor, but has enough information
9
to form a subjective belief concerning the type’s distribution, that is, she thinks they are op-
portunists with probability θ or committed with probability 1 − θ. Opportunistic distributors
discount the future at a rate equal to zero and thus are interested only in short-term gains from
a partnership, whereas committed ones desire to be part on a long-time business relationship
with the producer.3
Whichever operational mode the producer chooses, I assume she always offers a short-term
contract to the distributor. I will use the uppercase letter T when referring to one of this contract
periods (one year, for example), whereas the subperiods inside a generic T will be referred to
through lowercase letters, t.
In the case of FDI, the distributor is part of the integrated firm and his correct rank in
this context would be middle manager, that is, an agent in charge of a relevant division inside
the organization; thus, he has access to deep levels of information. Because of this, if he is
an opportunist just before the end of the period he searches for a corrupt legal officer; with
probability (1 − λ) he finds it and betrays his parent firm stealing, at a cost l, classified infor-
mation to be sold to competing firms. In this case I assume the producer loses forever a fraction
1 − ρ ∈ (0, 1) of future profits. The classified information can be anything from designs and
blueprints to distribution contacts and marketing actions that may be valuable to competitors.
Operation via FDI is also subject to a specific liability: a fixed setup cost f must be paid at en-
try, representing the various legal hurdles, expanded management operations and other specific
foreign-investment-related expenses.
When the operational mode is Outsourcing, the illicit opportunities for the distributor are of
another nature. Now, as the head of an independent firm, he is directly in charge of the proceeds
of the sale and, if an opportunist, may just run away with them before making his payments
to the producer. If this indeed happens, I assume that next period, T + 1, the producer stops
outsourcing for Foreign. Again, in order to do that he must find a corrupt legal office, which
happens with probability (1 − λ). Behind this story of default lies an important assumption,
namely, that the contracting parties use trade credit in their relationship. This means that all
monetary payments are done some time after the sales occurred. This gap, in turn, gives the
distributor the precious opportunity to run away with the sales revenue 4 .
Finally, the contract that binds the two firms is incomplete, that is, investments and product
quality are not observed by a third party, although the contracting parties do observe them.
Relationship-specific investments coupled with incomplete contracts means both parties bargain
over the division of the ex-post gains from trade, with the clearing happening at the end of each
contract period.
In case no unlawful action was taken by the distributor, in both operational modes the pro-
ducer updates his belief θ about the distributor and a new one-period partnership is contracted
for period T + 1. Before renewing, though, the producer checks which of the two operational
3This assumption is explained further in section 6.24I restrict each operational mode to those illicit opportunities since they are the more possible in each case.
However, in reality either mode could suffer from either type of illicit act.
10
modes is more profitable for him for the future: that is what I call the Producer’s Problem.
After the choice, the story repeats itself as described.
What about the Distributor’s Problem? It is exactly to take an unlawful action at the
end of each period (the opportunistic ones, of course). Next I present the exact timeline of each
contract period T .
Timelines under a generic contract period T
At t = 0 of T , the producer solves his problem, that is, whether to enter the market via
Outsourcing or Foreign Direct Investment and, after this choice, she makes a business offer to
the distributor, who may accept or reject it. If accepted, next period the distributor makes
investments E in the enterprise. These investments (marketing, retail, establishing distribution
centers, etc) have a positive effect on demand. At t = 2 goods are manufactured.
From t = 2 onwards the timeline for FDI is slightly different from the one for Outsourcing.
In the latter, at t = 3 uncertainty is resolved and distributor and producer bargain over the
price and, in the case of an agreement, the product is shipped. At t = 4 goods are sold. At
t = 5 the distributor decides his problem, that is, whether to steal the revenue; if not, at t = 6,
payment is done. Figure 1 below presents the timeline
Figure 1: Outsourcing - timing of events in a generic contract period T.
When the operational mode is FDI, at t = 3 uncertainty is resolved, distributor and producer
bargain over the price and, if there is an agreement, goods are shipped. Sales and payment
happen at t = 4. At t = 5 the distributor decides his problem, that is, whether to steal classified
information. The timeline is presented below in Figure 2.
Figure 2: FDI - Timing of events in a generic contract period T.
11
3 The learning mechanism
This section starts with the learning mechanism that will be used to connect producer and
distributor’s decisions across periods; it is based on the structure defined by Araujo and Ornelas.
Consider an ongoing partnership between a producer and a distributor at date T . As this
relationship evolves, the producer updates his belief with respect to the type of the distributor
through his experience. If the distributor defaulted (in the case of Outsourcing) or betrayed (in
the case of FDI) the producer last period, she forms a posterior equal to 1, that is, concludes the
distributor is an opportunist, and the partnership ends. Otherwise, if the distributor played by
the rules and did not default or betray, the producer updates his belief about his type according
to the Bayes rule:
θT+1 ≡ Pr(opportunist|no default ∩ θT ) =λθT
λθT + 1− θT< θT . (1)
Therefore, each period that the distributor did not behave unlawfully causes the producer
to decrease his belief that he is an opportunist.
In order to construct the dynamic strategies, let 0 and 1 indicate respectively a record of
good behavior and one of misbehavior in a given experience. Then, define θT (Y ) as the belief
that the distributor is an opportunist given an experience yT with size T and cardinality Y ,
where Y =∑T
i=1 yi, yi ∈ {0, 1}. Therefore, if there is no record of misbehavior, the producer
belief is given by the Bayes formula above; if misbehavior happened anytime, she updates her
beliefs to 1. Formally,
θT (Y ) =
λT θ0λT θ0+1−θ0 if Y = 0
1 if Y 6= 0(2)
It is clear that if the distributor is period after period committed to the partnership, in the
long-run the producer eventually becomes convinced (almost surely) that he is committed.
4 Producer’s Problem: Environment
In this section I show the economic structure that will support the producer’s problem of
choosing between FDI and Outsourcing, to be addressed in the subsequent section.
Assume throughout this subsection that the producer has two beliefs about the distributors:
1. that opportunistic distributors default or betray whether they find a corrupt legal officer,
and committed ones do not.
2. That both opportunistic and committed distributors make the same investment decisions
in a partnership with the producer, for each operational mode.
Section 6 will show that these beliefs are sequentially rational since they are dominant strate-
gies for the distributors.
12
4.1 Foreign Direct Investment
Consider the problems facing a producer when the operational mode in effect is Foreign
Direct Investment. In this operational mode the producer, as the sole owner of the firm, has
some residual rights over its assets. I start with the bargain.
The Bargain
At t = 3, producer and distributor bargain over the gains from trade. Bargain is over
incomplete information since the producer does not know the type of her partner; however,
remember that the distributor’s unlawfull actions in FDI do not affect current period profits.
Thus, incomplete information regarding the type of the distributor is innocuous here.
Therefore, I will model the bargain as the standard Nash one. If there is an accord, producer’s
gains from trade are equal to S = RI − pI where pI is the pric of the good in this operational
mode; if the bargain breaks down, she can always fire the distributor and still obtain a share
of RI , so her ex-post utility is a proportion γ ∈ (1/2, 1) of RI . Therefore, there is always some
potential loss when the distributor is fired before the end of a contract period.
Investments
At t = 1 the producer expects the distributor (whichever type, see beginning of this section)
to make investments EI that affect demand positively, that is:
EI = arg maxE
(1− γ)RI(E)− E, (3)
where RI(·) is increasing and concave.
Assuming that RI(E) = A√E, then the distributor’s profit is given by5
πDI =A2
4
(1− γ
)2.
Accordingly, producer’s profit is
πPI =A2
2γ(1− γ)− k + TI ,
where TI is the ex-ante transfer which is equal to the distributor’s ex-post profit. Finally, profit
for the integrated firm (and thus ex-ante profit for the producer) is:
ΠI =A2
4
(1− γ2
)− k. (4)
4.2 Outsourcing
Now, consider the case when the operational mode in effect is Outsourcing. Now, the use of
trade credit implies that there is an opportunity for him to literally run away with the proceeds
5The use of a specific functional form allows a clear presentation of the paper’s motivation and results.
13
of the sale before paying the producer. As done in the previous section for FDI, I start with the
bargain that happens at subperiod t = 3.
The Bargain
At t = 3, distributor and producer bargain over the gains from trade. Contrary to the
bargain in FDI, here the incomplete information about the type of the distributor has a profound
influence over producer’s decisions, since his misdeeds do affect current period profits. Incomplete
information basically changes the bargain powers between the two players; actually, the game
happens as if there were 3 players bargaining: the producer and both types of distributors. I
find Harsanyi and Selten’s (1972) approach, essentially a generalization of the Nash Bargain for
asymmetric bargaining powers, the most suitable for the problems in this paper. Observe that
the incomplete information affects the bargaining position insofar as the possibility of a default
directly affects current period profits.
Given that investment costs are bygones at the time of the bargain, the ex-post expected
utility of the producer (U) is pO (1− θ(1−λ)) (pO is the price of the good to be cleared through
the bargain), the expected price to be received for the sale of one unit of the good, and her
outside option is zero. An opportunistic distributor has utility Up = λ(RO − pO) + (1 − λ)RO
from the relationship and outside option equal to Uoutp = 0. A committed distributor has utility
UC = RO − pO and outside option UoutC = 0.
At the bargain, I assume that the producer and distributor call for an arbitrator to decide
their dispute. This arbitrator will receive all the necessary information from both players and
will choose an allocation that shares the gains from trade between the partners. For example, he
would receive from the producer her information about the potential types of the distributor and
her beliefs about them, θ; also, the arbitrator knows that in order to default on the payments
the distributor needs to find an officer, which happens with probability 1 − λ. With these
informations, the arbitrator makes a take-or-leave-it offer to both agents, which they both accept,
by construction.
Thus, the arbitrator chooses an offer, a price pO for the good, obtained from the maximization
of the following Generalized Nash Product (NP ):
pO = arg maxp
(p (1− θ(1− λ))
)(RO − p
)1−θ(λ(RO − p) + (1− λ)RO
)θs.t.
RO − p ≥ 0
λ(RO − p) + (1− λ)RO ≥ 0
(5)
I obtain that pO = Ψ(λ, θ)RO. See the Appendix A for the exact formula for pO. Then,
UC = (1−Ψ((λ, θ))R and UP = (1− λΨ(λ, θ))RO. The function Ψ(λ, θ) gives the ex-post share
of each partner over the revenue from the sale of the goods. It is the Outsourcing’s twin for
FDI’s γ parameter ; however, here the impact of the incomplete information makes the sharing
14
an interesting multivariate function.
There is a point worth mentioning about the choice of the above mechanism for the bargain.
There is no reason to expect any kind of separating equilibrium here because in no way the
distributor would reveal his own type, if an opportunist, since I am assuming that he would go
to jail in this case and would prefer not to reveal. Consequently, the arbitrator does not ask
the distributor for his type. The Nash Problem of the arbitrator is trying to balance out the
wishes of the partners taking into account the uncertainty from the uninformed side and the
institutional elements of the country, which are known to all agents. Mathematically, that is a
price that distributes the gain from trade between the parties through the maximization of a
subjective risk weighted welfare function.
Comparative statics over the bargain price derived from (5) reveal that
∂pO∂θ
> 0;∂pO∂λ≤ 0. (6)
See Appendix A for the proofs. These results are intuitive: the producer price increases
when her beliefs about the distributor being an opportunist are greater, and decreases with
improvements in law-enforcement. That is, when faced with increased uncertainty, if the bargain
is successful the resulting price insures the producer accordingly, since she is the one bearing
all the default risk. For a given uncertainty over the distributor’s type, increased enforcement
allows the bargain price to decrease, that is, the business is less risky for the producer and thus
she gives up more of the surplus to the distributor. Also,
limθ→0
Ψ(θ, λ) = 1/2 , lim(θ,λ)→(0,0)
Ψ(θ, λ) = 1/2 , lim(θ,λ)→(0,1)
Ψ(θ, λ) = 1/2, (7)
lim(θ,λ)→(1,1)
Ψ(θ, λ) = 1/2 and lim(θ,λ)→(1,0)
Ψ(θ, λ) = 1.
That is, when the producer is near-certain the distributor is committed, the resulting price
is the traditional Nash result with an equal split of the surplus, regardless of the enforcement
level; when there is perfect enforcement, Nash result is obtained again since there is no risk that
the distributor will default. Finally, when the producer is near-certain that the distributor is an
opportunist and enforcement is very poor, the price share goes to 1, representing the enormous
risk facing her.
There are two different graphics with these results. First, take a look at Figure B.1, in
the appendix, showing in a 3D setting the graph of Ψ(θ, λ). Observe that for a given θ, Ψ is
non-increasing in λ, and for a given λ, Ψ is increasing in θ. Figure 3, plotted below, shows the
same results in a composite two-dimensional graphic.
The limit of Ψ(θ, λ) when θ → 1 for arbitrary levels of λ can be seen graphically in Figure
3. The graphic shows an interesting property of the Ψ function: observe that for λ = 0.3,
Ψ(1, 0.3) = 1, whereas Ψ(1, 0.6) < 1. Therefore, for a sufficient level of enforcement the producer
share in the bargain is below 1, even if the producer beliefs about the distributor being an
opportunist are almost sure. In this case, enough enforcement causes the producer to let go
15
Figure 3: Relation between Ψ, θ and λ.
some of the insurance in favor of the distributor. Therefore, when θ = 1 the function Ψ is kinked
at a λ = 1/2:6
Ψ(1, λ) =
1, if λ ≤ λ1
2λ , if λ > λ.(8)
Appendix A shows this kinked function in detail; it is also visible in Figure B.1. This result
is important considering that it will force me to split each forgoing analysis among several λ
intervals, as will be clear afterward. Now, continuing backwards, I will detail the producer’s
expected profit.
Investments
As before, at t = 1 the producer expects the distributor to make investments EO such that
EO = arg maxE
(1−Ψ(θ, λ))RO(E)− E, (9)
where RO(·) is increasing and concave.
For RO(E) = A√E, the distributor’s ex-ante profits are thus given by
πDO =A2
4
(1−Ψ(θ, λ)
)2. (10)
6In another version of the paper, I considered the possibility of an exogenous cost of corruption, that is, theopportunistic distributor would have to pay a bribe to the corrupt legal officer in order to obtain his help in thecourts. In this case, λ would be negatively correlated with the bribe, reflecting the fact that if corruption is toocostly, the real amount of enforcement is higher. Consequently, λ diminishes since it is possible to share some ofthe surplus to the distributor at lower levels of enforcement.
16
Accordingly, Producer’s profit is
ΠPO = (1− θ + θλ)
[A2
2Ψ(θ, λ)
(1−Ψ(θ, λ)
)+ TO
]− k,
where TO are the ex-ante transfers which are equal to the distributor expected ex-ante profits.
Observe that these transfers are determined at the beginning of the contract period, but in the
case of Outsourcing they are paid at t = 5, together with the payment for the goods.7 Therefore,
joint (and producer) expected profits are:
ΠO(θ, λ) ≡ ΠO(θ, λ) = (1− θ + θλ)
[A2
4
(1−Ψ(θ, λ)2
)]− k. (11)
Notice that ∂ΠO(θ,λ)∂θ ≤ 0 and ∂ΠO(θ,λ)
∂λ ≥ 0.
5 Producer’s Problem: choosing between Outsourcing and FDI
This section deals with the determination of the producer choice between Outsourcing ver-
sus FDI. In order to that, the producer must compare the expected future profits from either
operational mode. I start showing the value function from the point of view of Outsourcing.
5.1 Outsourcing
At the beginning of a period of contract (t = 0 in the timeline from figure 1), if the distributor
did not default the producer must decide whether to continue working with him. Again, there
is just one variable connecting the current period with later ones, the distributor’s reputation θ,
and I can write the producer’s expected aggregate future profits in terms of a value function as
follows
VO(θT+1) = max{0, ΠO(θT ) + β Pr(0|θT )VO(θT+1(0)}, (12)
where Pr(0|θ) = 1 − θT + λθT is the probability of no default, given that the distributor is
perceived as an opportunist with probability θT . This notation follows the one introduced at
section 3. The reason I am not considering the option to change from Outsourcing to FDI will
be clear later. Therefore, when starting an arm’s-length partnership at date T = 0 the producer
expected present-valued profit is
VO(θ0) = ΠO(θ0) + β Pr(0|θ0)VO(θ1(0)). (13)
7If the transfer were equal to the distributor expected profit including his illicit possibilities, them only oppor-tunistic distributors would show up to be contacted. Knowing that, the producer would automatically update hisprior to 1 and would be out. A better strategy is to charge ex-ante from anybody the value given by (10): withprobability 1 − θ + θλ the producer earns exactly this amount, and with probability θ(1 − λ) the producer earnsnothing.
17
Substituting back VO(θ1(0)) in (13) and subsequently, I obtain that
VO(θ0) = ΠO(θ0) +∞∑j=1
βjΠO(θj)
(j−1∏i=0
(1− θi(0) + λθi(0))
). (14)
Notice that VO(θ0) is decreasing in θ0, since both 1−θi(0)+λθi(0) and ΠO(θj) are decreasing
in θ, which is increasing in θ0 by (2).
5.2 Foreign Direct Investment
Now, consider the problem facing a producer when the partnership is via FDI. At t = 0, if
the distributor did not betray the producer, she must decide whether to continue working with
him via Outsourcing, via FDI or to quit the foreign market. If he betrayed, then I assume the
producer continue to operate forever with imported managerial labor 8. Again, the distributor’s
reputation θ is the unique variable connecting the current period with later ones. So, I can write
the producer expected future profits in terms of a value function as this
VI(θ) = ΠI
(1 +
βρ(1− Pr(0|θ))1− β
)+ Pr(0|θ)β ×max
{0, VI(θ|0, θ), VO(θ|0, θ)
}, (15)
where the first element in the right-hand side is the expected discounted producer’s future profit
in case the distributor betrayed in the former period, and Pr(0|θ) = 1− θ+ θλ is the probability
of no betrayal by the distributor. The producer proposes a partnership to the distributor if
VI(θ0) ≥ 0, where
VI(θ0) = ΠI
(1 +
βρ(1− Pr(0|θ0))
1− β
)+ Pr(0|θ0)β ×max
{0, VI(θ1(0)), VO(θ1(0))
}− f (16)
Building on the structure defined until here, next I presents two important results: first, I
show that in case there was no record of betray from the distributor, a change from FDI to
Outsourcing may take place, depending on the institutional quality of the economy. Obviously,
for this change to occur entry via FDI must have happened, so the second result are the factors
that determine the initial choice between FDI or Outsourcing.
Before, though, some assumptions to keep the problem framed and interesting.
5.3 Assumptions
Assumption 2a: A is high enough and k low enough such that when Ψ = 1/2, ΠO(·) > 0.
Using the results from (7) and Assumption 2a, I obtain the asymptotic behavior of ΠO(θ, λ):
8This begs the question of why foreign labor is not used since the beginning. Foreign labor is more expensiveand does not have the local knowledge. Thus, it is used just as the last resource.
18
limθ→0
ΠO(θ, λ) > 0, lim(θ,λ)→(0,0)
ΠO(θ, λ) > 0, lim(θ,λ)→(0,1)
ΠO(θ, λ) > 0, (17)
lim(θ,λ)→(1,1)
ΠO(θ, λ) > 0 and lim(θ,λ)→(1,0)
ΠO(θ, λ) < 0.
As was the case in (7), there is a limit missing from the above list, the one when θ → 1 for
an arbitrary λ. In order to determine it, it is necessary to use the results given by condition (8).
It allows me to define a unique critical value λ such that9
limθ→1
ΠO(θ, λ) = 0. (18)
Thus,
limθ→1
ΠO(θ, λ)
≥ 0 if λ ≥ λ,
< 0 otherwise.(19)
Figure B.2 in the Appendix B shows the graphic of ΠO when A = 1 and k = 0.05. A line
indicates the plane where ΠO(θ, λ) = 0 and the value of λ is also displayed in the figure.
Assumption 2b: A is high enough and k low enough such that when γ = 1/2,ΠI(1/2) > 0.
Assumption 3: f < f = limγ→1/2
(1−β(1−ρ))1−β ΠI .
This last assumption says that when incentives are at the maximum (and thus profits), even
if the distributor betrayed the producer immediately after entry it is still worthwhile to enter
via FDI, that is, expected discounted profits net of the fixed cost f are positive.
Remember that ∂ΠI∂γ < 0 and lim
γ→1ΠI < 0. Together with Assumption 2b, these imply that
there exists a value γ such that
f =(1− β(1− ρ))
1− βΠI(γ). (20)
In order to keep the model interesting such that a choice between FDI and Outsourcing could
be considered, I will assume that it is always profitable to enter via FDI, given a fixed costs f
satisfying Assumption 3. This lead us to
Assumption 4: γ ∈ (1/2, γ).
5.4 A Change from FDI to Outsourcing
Assuming entry took place via FDI, why and when a change of operational mode may
happen? Remember that the mechanism of learning produces decreases in the belief parameter
θ with the passage of time, which in turn increases the value of current period’s expected
9Notice that when Ψ equal one, profit is negative (see equation 11); according to hyphotesis 2a, profit is positivewhen Ψ equals 0.5. Equation (8) guarantees that there is an intermediate λ such that profit is zero.
19
outsourcing profits. After enough time, future prospects from Outsourcing may look better than
the ones from FDI and a change of operational mode takes place. The next Lemma formalizes
this idea.
Lemma 1. Suppose the producer entered the market in Foreign via Foreign Direct Investment.
Then, for λ ∈ [0, λc], λc > 1/2, there is a unique value θ∗ such that at this value the producer
decides to switch the operational mode. Additionally, θ∗ is increasing in λ.
Proof: Appendix A.
This Lemma assures the existence of a unique threshold such that, after some time learning
about the distributor’s type, the producer decides to change the operational mode. The condition
is valid just for λ ∈ [0, λc], since in according with the discussion in Section 4.2, for values above
this the enforcement is good enough and the bargain price is low enough such that for any θ
the per-period expected profit obtained from Outsourcing is always greater than that obtained
from FDI, and therefore there is no change to be decided since there is no way FDI would ever
be chosen from the beginning.
5.5 Producer’s problem: Mode of entry
The results presented in Lemma 1 rested on the assumption that entry had already taken
place via FDI, but this may not be the case. A relevant question to ask, though, is whether is
more profitable for the producer to enter via FDI, with a possible change later to Outsourcing,
or directly via the latter. Next proposition answers this:
Proposition 1. Suppose the producer is considering entering the market in Foreign, and that
whichever operational mode he chooses, the distributor enters the partnership if invited to. Then,
entry occurs according to the following pattern:
1. For λ ∈ (0, λ), there is a unique θ∗0 ∈ (θ∗, θ0], such that at it the producer is indifferent
between entry via FDI or Outsourcing. For θ0 > θ∗0, entry is via FDI; otherwise, is via
Outsourcing.
2. For λ ∈ [λ, λ), there is a unique θ∗0 ∈ (θ∗, 1], such that at it the producer is indifferent
between entry via FDI or Outsourcing. For θ0 > θ∗0, entry is via FDI; otherwise, is via
Outsourcing.
3. For λ ∈ [λ, 1), entry is always via Outsourcing.
Proof: See Appendix A. λ, λ are defined, respectively, in equations (A.13) and (A.14).
Therefore, a producer who entered with great uncertainty (a high θ0) over the commitment
of her business partner chooses a mode of entry which gives her greater control. Eventually, with
experience, she might become convinced of the true type of the distributor, and in this process
at some point she will change from one operational mode to the other.
20
However, this story depends on the institutional quality λ, as Proposition 1 shows. If en-
forcement is good enough, the producer enters directly via Outsourcing, since the probability
of default is low enough (due to the good institutions) to make her give up some rent in the
bargain and therefore the incentives to invest are greater than the case of FDI. If it is low, entry
happens via FDI as an insurance against the risk and the change only occurs if the partnership
lasts enough to bring θ close to θ∗.
6 Distributor’s Behavior
This section deals with the determination of the opportunistic distributor’s problem of
whether to steal the classified information, in the case of FDI, or the revenue, in the case
of outsourcing.
6.1 Foreign Direct Investment
I now solve the distributor’s problem when the operational mode is FDI. Consider first the
problem faced by an opportunistic distributor. By definition, he does not care much about the
future, thus is less interested in building a good reputation. Also, he does not betray unless
he is able to find a corrupt legal agent, since otherwise he would be forced by the courts to
compensate the producer and pay a penalty fee Z > 0. When the distributor does find a corrupt
agent, he must spend an effort l to discover the producer’s plans. If the distributor does not
betray, he simply receives a fraction 1− γ of the revenue.
Thus, upon finding a corrupt agent, the distributor chooses to betray as long as
α(1− ρ)ΠI
1− β− l ≥ 0, (21)
=⇒ ΠI ≥l(1− β)
α(1− ρ). (22)
The right hand side of (21) gives the payoff from selling the confidential information to
another producer: is equal to the losses to be incurred by the producer, brought to the present
by the producers’ discount factor β, multiplied by the share to be appropriated by the distributor,
α.10 I assume henceforth that this inequality is always satisfied, that is, l and ρ are small enough
and α and β high enough such that (22) is valid.
6.2 Outsourcing
In the case of Outsourcing, obviously he always accepts the producer’s offer since he never
loses from doing it. If he is committed, he does not default.11 If he is an opportunist, first he
10I assume there is a bargain between the distributor and a potential local producer.11Instead, suppose the committed distributor is not intrinsically honest as I assumed. Then, if his profits from
the operation were some positive value (due to search costs for example), there exists some discount factor suchthat for values above it, a distributor prefers not to default, as show Araujo and Ornelas in their model. In orderto simplify the model, I assumed perfect competition in the distributor market, preventing them from obtaining
21
must decide whether to default at the end of the period. In order to do this, he must find a
corrupt legal officer. So, upon finding this agent, he defaults only if he finds profitable to do so:
A2
2
(1−Ψ(θ, λ)
)>A2
2
(1−Ψ(θ, λ)
)2m
Ψ(θ, λ) > 0.
(23)
Therefore, if a corrupt agent is found, an opportunistic distributor always defaults, for any
revenue. Given this behavior, the distributor, either type, invest EO in the partnership, given
by (9). Notice that if the investments were different the distributor type would be revealed
and, case he were an opportunist, he knows the producer would immediately update his prior
to θ = 1 and the bargain would break-down, leaving him with nothing. Therefore, either type
of distributor invests the amount indicated.
7 Equilibrium
Now I solve for the equilibrium strategies and beliefs of the game played by the producer
and the distributor. In order to do that, I show that the distributor’s strategy described in this
section, together with the producer strategies described in Proposition 1, are part of an squential
equilibrium12
Proposition 2. There is a sequential equilibrium where a Producer with a initial belief θ0 enters
according to Proposition 1. The distributor always accepts a partnership offer and, if an oppor-
tunist, always defaults; if committed, never does. If entry was via Foreign Direct Investment,
then with probabilityT ∗0−1∏j=0
1− θj(θ0) + λθj(θ0)
there is a change of operational mode to Outsourcing, at belief θ∗ and time T ∗0 .
Proof. Proposition 1 gives the producer’s entry strategies, contingent on the distributor default-
ing or betraying if an opportunist (and if a corrupt officer is found). But defaulting/betraying
is a dominant strategy for the opportunistic distributor, therefore the producer strategy is a
best-reply to the distributor’s one. These strategies are also sequentially rational, since both
agents are optimizing over their choice space. Given these strategies, the sequence of beliefs
{θi}∞i=1 given by equation 2 is consistent, since are formed by the Bayes Rule. T ∗0 is given by
(A.20) .
some profit.12See Kreps and Wilson (1982) and Araujo and Ornelas (2008).
22
8 Institutional Reforms, Expectations and the Attraction of FDI
As I show now, this model gives interesting results about the effects of institutional improve-
ments in the Foreign country over producers’ expectations over the evolution of the partnership
to the point of a change to FDI. The focus on FDI is due to the importance of this measure to
developing countries, with the consequence that these nations compete fiercely to attract this
kind of investment, implementing policies aimed directly at them.
In short, an institutional change affects two core variables related to producers’ expectations:
first, the probability that the partnership will last until change a from FDI to outsourcing; second,
the time span until the attainment, by the partnership, of this point of change, conditional on
it being reached. Basically, I identify an ”institutional trap” where improvements augment
expectations in”developed” areas and diminish them in ”underdeveloped” ones. An in-depth
analysis follows.
8.1 The time span until the change of operational mode
Consider an ongoing relationship between a producer and his distributor. Suppose the change
of operational mode, if possible, happens at some θ∗ < θj , with due time T ∗j , where j represents
their current trust level (from some initial θ0). What would be the effect of the unexpected
change of λ on the time span between today and the change of operational mode, conditional on
it being attained? Section 5.4’s Lemma says that θ∗ increases with λ, reducing the time span.
However, the improvement also reduces the future reputation of the distributor, that is, not just
θ∗ is affected but also all the future values of θ that must be attained before they reach the value
θ∗; for a given θ∗, this increases the time span.
The impact of the change over the time span is given by
∂T ∗j∂λ0
=
∂θ∗
∂λ0log λ0
(1−θ∗)θ∗ −log
((1−θj)θ
∗
θj(1−θ∗)
)λ0
(log λ0)2. (24)
Therefore, an improvement in the enforcement of contracts in Foreign causes a decrease in
the time span between entry via FDI and the change to Outsourcing if and only if
∂T ∗j∂λ
< 0⇐⇒ ∂θ∗
∂λ>T ∗jλθ∗(1− θ∗). (25)
Rewriting the inequality in terms of elasticities,
∂T ∗j∂λ
< 0⇐⇒ η(θ∗, λ) > T ∗j (1− θ∗), (26)
where η(θ∗, λ) is the elasticity of θ∗ with respect to λ.
Therefore, given that T ∗j is equal or greater than one, the impact of an institutional improve-
ment in θ∗ must be high enough to overcome the “bad” effect in the reputation. This is more
23
likely to happen when enforcement already attained some respectable level. In order to show
this, first I parametrize the model with reasonable values: β = 0.8, ρ = 0.75, A = 1, γ = 0.75
and (to simplify) j = 0.13 For these values, λ = 0.879655, that is, above this level entry is
direct via Outsourcing, thus with no room for a change of the operational mode. Given these
parameters, it is possible to obtain a (rather complicated) function of θ∗ depending on λ.
Figure B.3, in the Appendix B, shows the graph of T as a function of λ and θj . It was
constructed based on equation (A.20), substituting θ∗ for the function obtained from (A.6) and
taking into account that, for a given λ < λ, the θjs suitable for the analysis are those such that
θ∗0(λ) < θj(λ); for the other values of θj , T was set to Null, corresponding to the empty areas in
the figure.
Notice that the partial derivative of T with respect to λ is increasing for low values of λ
and becomes negative for higher values. Therefore, consider the case of a country with poor
institutions (low λ) and suppose that the prior belief of the producer, θ0, reflects this fact, for
instance θ0 > 0.5. In this case, an institutional improvement increases the time span necessary to
reach the trust level related to the change from FDI to Outsourcing, that is, the loss in learning
capabilities more than offset the increase in θ∗ that would allow the change to happen earlier.
Summarizing, for the given parameters an institutional improvement diminishes the time
necessary to attain the trust level related to the change of operational modes only if the country
already has a high level of enforcement. When enforcement is already high, any additional
tightening of it has a greater impact on θ∗ than on reputations, since the latter role is limited
if institutions are already good. There is a kind of institutional trap in this result, since the
improvements make more difficult for the agents to proceed towards the more efficient mode of
operation.
8.2 Probability of survival
The preceding analysis was made considering the effect of an institutional improvement over
the time span until the change from fdi to outsourcing, conditional on it being reached. But
the institutional improvement also effects the chance of survival of the partnership, that is, the
probability of that attaining θ∗. Therefore, starting from point θj , j ≥ 0, the probability that
the partnership will last until the attainment of θ∗ is
Pr(partnership lasts T ∗j periods) =
T ∗j −1∏i=j
(1− θi(θj) + λθi(θj)
). (27)
Changes in λ affect this probability through two channels: via the chance of not having a
betrayal or default in each of the preceding periods, and via the number of periods necessary to
reach the target event, that is, it affects T , the number of terms inside the productory. Figure
B.4 at the appendix, based on the same parameter values of the previous figure, shows the
13Calculations and figure were constructed with the software Mathematica 6.0.
24
graph of equation (27), in terms of the enforcement level λ and initial trust level θj ,with θ∗ as
the reference event in the future.
Notice that for a given θj , the probability is flat or increasing for the smaller values of λ, but
increases much faster for the larger ones. This pattern is caused by the two channels discussed
just above. The first one causes an small increase in the probability, given that every period
the chance of betrayal diminishes. Notice also some ripples in the figure: these are produced by
the second effect, the one of λ over T ∗j . Previous section showed that in general T ∗j is increasing
in λ for its lower values (due to the lock-in effect) and decreasing in it for the higher ones.
Therefore, starting from a given θj , j ≥ 0, as one moves along the lambda axis there will be
discrete changes in T ∗j , since in the calculation of (27) the time must be considered exactly as
in equation (A.20), that is, non-negative integers. For lower enforcement levels, the increase in
time adds another term to the product, counterbalancing the positive effect from the decrease
in each period’s probability of default it; the opposite happens when the time decreases with
higher enforcement levels, causing a huge increase in the probability.
9 Conclusion
The interplay between trust and contracts and their effects on the international organization
of production were analyzed here in a model with some novel features.
In a dynamic setting, I show that for lower levels of enforcement entry happens via Foreign
Direct Investment when the prior probability that the distributor is an opportunist is high and
via Outsourcing when it is low. However, for some high enough enforcement level entry is directly
via Outsourcing, regardless of the belief about the distributor. Conditional on entering via FDI,
I also show that there is a unique critical trust level such that at it a change of operational mode
takes place.
Finally, I study how institutional reforms affect producers’ expectations about doing busi-
ness in the foreign country via FDI. Results indicate an institutional trap where the lower the
institutional framework, the smaller the impact from the reforms over expectations.
The model generates some testable predictions: first, whether institutions (from trade fairs
to government promoted international business missions) that facilitate the exchange of infor-
mation across business partners promote the entry of multinational firms with a more flexible
organizational structure. Second, if different levels in the quality of enforcement of contracts
change the preferred way to enter a foreign country. Third, the effects of reputation-building on
the way multinational corporations organize their production internationally. That is, to test
whether after some time making business in a country with poor institutions (usually a devel-
oping one) the multinational decides to change from Foreign Direct Investment to Outsourcing
or some less rigid organizational structure due to improved confidence in the local partners.
25
References
Albuquerque, R., “The composition of international capital flows: risk sharing through foreign
direct investment,” Journal of International Economics, 2003, 61 (2), 353–383.
Araujo, L. and E. Ornelas, “Trust-Based Trade,” Working Paper, 2008.
Baker, G., R. Gibbons, and K.J. Murphy, “Relational Contracts and the Theory of the
Firm*,” Quarterly Journal of Economics, 2002, 117 (1), 39–84.
, , and , “Relational Contracts in Strategic Alliances,” 2002. mimeo.
Bottazzi, Laura, Marco Da Rin, and Thomas F. Hellmann, “The Importance of Trust
for Investment: Evidence from Venture Capital,” SSRN eLibrary, 2008.
Brouthers, K.D. and L.E. Brouthers, “Why Service and Manufacturing Entry Mode
Choices Differ: The Influence of Transaction Cost Factors, Risk and Trust*,” Journal of
Management Studies, 2003, 40 (5), 1179–1204.
Egan, M.L. and A. Mody, Buyer-seller Links in Export Development., Industry Development
Division, Industry and Energy Dept., Policy, Research, and External Affairs, 1990.
Gulati, R., “Does Familiarity Breed Trust? The Implications of Repeated Ties for Contractual
Choice in Alliances,” Academy of Management Journal, 1995, 38, 85–85.
Harsanyi, J.C. and R. Selten, “A Generalized Nash Solution for Two-Person Bargaining
Games with Incomplete Information,” Management Science, 1972, 18 (5), 80–106.
Hausmann, R., Research Dept, and Inter-American Development Bank, Foreign Di-
rect Investment: Good Cholesterol?, Inter-American Development Bank, 2000.
John, G. and B.A. Weitz, “Forward Integration into Distribution: An Empirical Test of
Transaction Cost Analysis,” Journal of Law, Economics, and Organization, 1988, 4 (2), 337–
355.
Johnson, S., J. McMillan, and C. Woodruff, “Courts and Relational Contracts,” The
Journal of Law, Economics, & Organization, 2002, 18 (1), 221–277.
Ko, S., “McDonald’s: Is China Lovin’ It?,” Case study, Asia Case Research Centre 2008.
http://hbr.org/product/mcdonald-s-is-china-lovin-it/an/HKU802-PDF-ENG.
Kotseva, R. and N. Vettas, “Foreign Direct Investment and Exports Dynamics with Learning
about Demand,” Working Paper, 2005.
Kreps, D.M. and R. Wilson, “Sequential equilibria,” Econometrica: Journal of the Econo-
metric Society, 1982, pp. 863–894.
26
Mayer, R.C., J.H. Davis, and F.D. Schoorman, “An integrative model of organizational
trust,” The Academy of Management Review, 1995, 20 (3), 709–734.
Schnitzer, M., “Debt v. Foreign Direct Investment: The Impact of Sovereign Risk on the
Structure of International Capital Flows,” Economica, 2002, 69 (273), 41–67.
Straub, Stephane, “Opportunism, corruption and the multinational firm’s mode of entry,”
Journal of International Economics, 2008, 74 (2), 245–263.
27
Appendix A
Formula for the bargain price
From equation (5), I obtain
pO =RO.Ψ(θ, λ, b)
= RO ·
(2− θ + λ(1 + θ)−
√(2− θ + λ(1 + θ))2 − 8λ
4λ
)(A.1)
Partial derivatives of the bargain price
From (A.1), define s(θ, λ) = 2 + λ+ θ(λ− 1). First, some results I will use later:
s(θ, λ) > 0
s(θ, λ) ≥ λ+ 2
s(θ, λ)2 − 8λ > 0
The last is less obvious: s(θ, λ)2 = ((1 + 2λ) + (1− θ)(1− λ))2 > (1 + 2λ)2 > 8λ.
Thus,∂pO∂θ
= (1− λ)(s(θ, λ)−
√s(θ, λ)2 − 8λ
)> 0 (A.2)
∂pO∂λ
= (2− θ)(s(θ, λ)−
√s(θ, λ)2 − 8λ
)− 4λ (A.3)
Notice that(s(θ, λ)−
√s(θ, λ)2 − 8λ
)− 2λ = (s(θ, λ)− 2λ)−
√s(θ, λ)2 − 8λ
= (s(θ, λ)− 2λ)−√
(s(θ, λ)− 2λ)2 + 4λs(θ, λ)− 4λ(λ+ 2)
= (s(θ, λ)− 2λ)−√
(s(θ, λ)− 2λ)2 + 4λ (s(θ, λ)− (λ+ 2)) ≤ 0,
(A.4)
since it is equal to zero for some values of λ when θ = 1. Therefore, ∂pO∂λ ≤ 0.
Derivation of the critical value λ
When evaluated at θ = 1, pO from (A.1) becomes
pO =RO.Ψ(1, λ)
=R ·(
1 + 2λ− |1− 2λ|4λ
) (A.5)
28
Notice that Ψ(1, λ, b) equals 1 whenever what is inside the absolute is positive. Therefore,
the critical value λ is the λ such that |1− 2λ| = 0, =⇒ λ = 12 .
Proof of Lemma.
Suppose that there was entry via FDI and the distributor did not betray the producer. Thus,
it is possible that after some time a operational mode change takes place. At this point, which is
related to a trust level θ∗, the producer would be indifferent between making FDI for one more
period and outsourcing from there on or starting outsourcing right at that moment:
ΠI
(1 +
βρ(1− Pr(0|θ∗))1− β
)+ Pr(0|θ∗)βVO(θ1(θ∗(0))) = VO(θ∗)
ΠI
(1 +
βρ(1− Pr(0|θ∗))1− β
)= VO(θ∗)− Pr(0|θ∗)βVO(θ1(0))
= ΠO(θ∗)
(A.6)
The right-hand side is decreasing in θ, whereas the left-hand side is increasing. Call RHS
the right hand side of (A.6), and LHS the left hand side. Then, using (7) and Assumption 4,
limθ→0
LHS < limθ0→0
RHS (A.7)
The limits approaching 1 are again more difficult. But it is possible to show that there exists
a unique λc such that
limθ→1
LHS = limθ0→1
RHS (A.8)
⇒ ΠI
(1 +
βρ(1− λc)1− β
)= ΠO(1;λc) (A.9)
Notice that λc ≥ λ = 1/2. This cutoff exists: first,the right hand side of (A.6) is increasing
in λ for any θ whereas the left hand side is non-increasing and linear. Second, from (7) and
Assumption 4,
lim(θ,λ)→(1,1)
LHS = Π(γ) < lim(θ,λ)→(1,1)
RHS = ΠO(1; 1)
lim(θ,λ)→(1,0)
LHS = Π(γ)
(1 +
βρ
1− β
)> 0 > lim
(θ,λ)→(1,0)RHS = ΠO(1; 0)
Thus, for λ ∈ (0, λc], limθ→1
LHS > limθ0→1
RHS and θ∗ is unique. Finally, given that both
ΠO(θ∗, λ) and Pr(0|θ∗) are decreasing in θ and increasing in λ, θ∗ is increasing in λ.
Proof of Proposition 1.
29
The proof follows the following procedure: first I define a hypothetical indifference condi-
tion (between FDI and Outsourcing), followed by convexity and asymptotic properties of this
condition
Consider the value functions from entry via Outsourcing and from entry via FDI, presented
respectively in sections 4.2 and 4.1. Notice that
limθ0→0
VO(θ0) =ΠO(0;λ)
1− β, (A.10)
and
limθ0→0
VI(θ0) = ΠI + limθ0→0
(Pr(0|θ0)×max
{βVI(θ1(0)), βVO(θ1(0))
})− f
≤ ΠI +βΠO(0;λ)
1− β− f
<ΠO(0;λ)
1− β,
(A.11)
since the maximum expected value possible for future profits is βΠO(0;λ)1−β , and ΠI < ΠO(0;λ),
by Assumption 4 and equation (7). Therefore, for prior beliefs close to 0, that is, when the
producer is near-certain that the distributor is committed, entry will be via Outsourcing.
Now, the limits when θ0 approaches 1. First, see that
limθ0→1
VI(θ0) = ΠI
(1 +
βρ(1− λ)
1− β
)+ limθ0→1
λmax{βv(θ1(0)), βVO(θ1(0))
}− f > 0, (A.12)
by Assumption 4.
In order to calculate the limit of VO(θ;λ) when θ approaches 1, I am forced to split the
analysis among some cases. In order to do that two cutoffs must be defined. Based on (8) and
(17) I define a cutoff λ such that
VO(1; λ) =ΠO(1; λ)
1− λβ= 0. (A.13)
For the second, define λ such that when θ = 1 the producer is indifferent between outsourcing
or FDI:
ΠI
(1− β + βρ(1− λ)
(1− β)(1− λβ)
)− f = VO(1; λ). (A.14)
This cutoff exists, since the right hand side is non-decreasing in λ (equation (8)), the left
hand side is increasing in λ, lim(θ,λ)→(1,1) ΠO(θ, λ) > ΠI and lim(θ,λ)→(1,0) ΠO(θ, λ) < 0 <
ΠI
(1 + βρ
1−β
)− f (equation (7) and Assumption 4). Notice that λ < λc.
With these cutoffs, the limit of VO(θ0;λ) when θ0 approaches 1 is immediately split among
three cases:
30
Case 1: λ ∈ (0, λ).
limθ0→1
VO(θ0;λ) =ΠO(1;λ)
1− λβ< 0. (A.15)
Case 2: λ ∈ [λ, λ).
0 ≤ limθ0→1
VO(θ0;λ) < ΠI
(1− β + βρ(1− λ)
(1− β)(1− λβ)
)− f. (A.16)
Case 3: λ ∈ [λ, 1).
limθ0→1
VO(θ0;λ) ≥ ΠI
(1− β + βρ(1− λ)
(1− β)(1− λβ)
)− f. (A.17)
Now, notice that when there is ex-ante certainty that the distributor is committed, entry via
Outsourcing is preferable, since by equation (6),
ΠI
1− β− f < ΠO(0)
1− β(A.18)
Besides this special case, the choice between FDI and Outsourcing rests on the values of the
parameter θ0, that is, on the initial reputation of the distributor.
From (A.10) and (A.11), it is clear that for prior beliefs close to 0, that is, when the producer
is near-certain that the distributor is committed, entry will be via Outsourcing, regardless of
the λ value, confirming (A.18). But as (A.12), (A.15),(A.16) and (A.17) show, the result is not
so straight for θ close to 1. Therefore, it is instructive to analyze the entry decision in some
separate cases, which in turn are determined exactly by the λ intervals defined in equations
(A.15)-(A.17).
Case 1: λ ∈ (0, λ)
For λ in this range, there is a value θ0 such that, for θ0 > θ0, VO(θ0) < 0; otherwise, is equal
or greater than zero. First, note that
limθ0→0
VO(θ0;λ) =ΠO(0;λ)
1− β> 0 >
ΠO(1;λ)
1− λβ= lim
θ0→1VO(θ0;λ).
Also, remember that ΠO is increasing in λ and VO(θ0) decreasing in θ0. Applying these
results to (A.13), the result follows.
Therefore, for θ0 > θ0, entry is via FDI. From (A.10), (A.11) and (A.12), for θ0 close to 0,
entry happens via Outsourcing. Thus, there may be a threshold θ∗0 such that at it the producer
is indifferent between entering via FDI or via Outsourcing:
VI(θ∗0) = VO(θ∗0)
31
Π(γ)z0 + x0z1βΠ(γ) + x0x1z2β2Π(γ) + · · ·+
(T−1∏i=0
x(θi)
)βTVO(θ∗T (0))− f =
ΠO(θ0)+βx(θ0)ΠO(θ1) + · · ·+ βT
(T−1∏i=0
x(θi)
)VO(θ∗T (0))
(A.19)
where xi = 1− θi +λθi and zi = (1 + βρ(1−Pr(θi|0))1−β ). Notice that θ∗T is the one obtained in (A.6),
where the producer is indifferent between the two operational modes, and T is the size of the
history preceding this event. T is endogenous for θ ∈ [θ∗, 1], and can be represented as:
T ∗0 ≡ T (θ0|θ∗) =
⌈ln (1− θ0)θ∗ − ln(1− θ∗)θ0
lnλ
⌉(A.20)
Therefore, (A.19) actually represents the equality of two finite series:
B︷ ︸︸ ︷Π(γ;A)
z(θ0) +
T ∗0−1∑j=1
βjzj
(j−1∏i=0
x(θi)
)− f =
C︷ ︸︸ ︷ΠO(θ0) +
T ∗0−1∑j=1
βjΠO(θj)
(j−1∏i=0
x(θi)
)
⇓(1 +
βρ
1− β
)Π(γ;A)
1 +
T ∗0−1∑j=1
βj
(j−1∏i=0
x(θi)
)︸ ︷︷ ︸
D
−f = ΠO(θ0) +
T ∗0−1∑j=1
βjΠO(θj)
(j−1∏i=0
x(θi)
)︸ ︷︷ ︸
E
+
βρ
1− βΠ(γ;A)
T ∗0−1∑j=1
βjx(θj)
(j−1∏i=0
x(θi)
)+βρΠ(γ;A)
1− βx(θ0)︸ ︷︷ ︸
F
(A.21)
Both D, E and F are decreasing in θ0, since ΠO(θk) and x(θk) are decreasing in θk, for any
k, and θ(k) in turn is increasing in θ0 (see equation (2)). Finally, whereas the second derivative
of E and F is not clear, D is linear, since the productory is linear in θ0. Notice that if f were
zero, for θ ∈ [θ∗, 1] entry is via FDI, otherwise is via Outsourcing ; that is, θ∗ from Lemma is
also a threshold for entry choice.
Also,
limθ0→θ∗+
B < limθ0→θ∗+
C (A.22)
m(1 +
βρ(1− x(θ∗))
1− β
)ΠI − f < ΠO(θ∗) (A.23)
32
which is true from (A.6), and
limθ0→θ−0
B > limθ0→θ−0
C (A.24)
m
Π(γ;A)
z(θ0) +
T ∗0−1∑j=1
βjzj(θj)
(j−1∏i=0
x(θi)
)− f > ΠO(θ0) +
T ∗0−1∑j=1
βjΠX(θj)
(j−1∏i=0
x(θi)
)(A.25)
Rearranging,
f < Π(γ;A)
z(θ0) +
T ∗0−1∑j=1
βjzj(θj)
(j−1∏i=0
x(θi)
)−ΠO(θ0)−T ∗0−1∑j=1
βjΠX(θj)
(j−1∏i=0
x(θi)
)
= Π(γ;A)
z(θ0) +
T ∗0−1∑j=1
βjzj(θj)
(j−1∏i=0
x(θi)
)−ΠO(θ0)−T ∗0−1∑j=1
βjΠX(θj)
(j−1∏i=0
x(θi)
)
+ βT
(T−1∏i=0
x(θi)
)VO(θ∗T (0))− βT
(T−1∏i=0
x(θi)
)VO(θ∗T (0))
= VI(θ0)− VO(θ0) = VI(θ0)
(A.26)
since VO(θ∗0) is equal to zero at θ0. By Assumption 3, the above inequality is valid. Therefore,
in this λ interval, there is a unique θ∗0 ∈ (θ∗, θ0], such that the producer is indifferent between
entry via FDI or Outsourcing. For θ0 > θ∗0, entry is via FDI; otherwise, is via Outsourcing.
Case 2: λ ∈ [λ, λ)
In this case, the only difference from the previous case are the limits approaching 1:
limθ0→θ∗+
B < limθ0→θ∗+
C (A.27)
m(1 +
βρ(1− x(θ∗)
1− β
)ΠI − f < ΠO(θ∗) (A.28)
which is true again from (A.6), and
limθ0→1
C = ΠI
(1− β + βρ(1− λ)
(1− β)(1− βλ)
)− f (A.29)
limθ0→1
C =ΠO(1;λ)
1− βλ≥ 0 (A.30)
where limθ0→1
T ∗0 = ∞. Both B and C are positive, with B > C: from (A.15) and (A.16), when
33
λ→ λ+, B > C; when λ→ λ−, B > C.
Case 3: λ ∈ [λ, 1)
limθ0→θ∗+
B < limθ0→θ∗+
C (A.31)
m(1 +
βρ(1− x(θ∗)
1− β
)ΠI − f < ΠO(θ∗) (A.32)
which is true again from (A.6), and
limθ0→1
A < limθ0→1
B (A.33)
m (A.34)
ΠI
(1− β + βρ(1− λ)
(1− β)(1− βλ)
)− f < ΠO(1;λ)
1− βλ(A.35)
which is true by definition (see (A.17)).
Appendix B
Figure B.1: Relation between Ψ, θ and λ.
34
Figure B.2: ΠO(θ, λ), showing λ. The red line indicates the grid line corresponding to ΠO(θ, λ) =0.
Figure B.3: Relation between T ∗k , θ0 and λ.
Information and ownership choice
Abstract
This paper shows that a transaction-costs model embedded with interfirm information
exchange and learning provide new results about the optimal vertical organizational form in
a supply chain.
The model is applied to study the effects of shocks over the organizational decisions of
firms, with a new type of vertical fdi described, without reference to factor costs: shocks
prompts an input supplier to acquire his buyer and quit the former business. I exemplify this
effect with documented actions and characteristics of two leading Brazilian meat-exporting
firms.
37
1 Introduction
The literature in optimal vertical organizational form in Industrial Organization has ad-
vanced remarkably since Williamson (1971, 1975, 1979, 1985) and Grossman and Hart (1986)’s
seminal works. In the present decade there was a renewed interest in this topic insofar the incom-
plete contract theory gave an useful foundation to explain much of the changes that happened
internationally with the globalization process1.
At the same time, an emerging literature in Organization Theory2 studies several different
aspects of the organization of the firm, both in terms of the separate units that constitute an
integrated firm and inside these units. This literature aims to explain the determinants and
consequences of Delegation, Centralization, Hierarchies, and other different kinds of governance
structures that exist. An important message of these works is the relevance of understanding the
appropriate ways communication flows between productive units in a economy, be these units
simple agents or larger structures, and how these flows contributes to give the firm a shape.
This paper intends to bring these two literatures a little closer, investigating the consequences
of information flows and knowledge exchange for the choice of optimal vertical organizational
form among productive units in a multi-layered supply chain. In other words, how information
and knowledge affect the decision each owner of a productive unit in a supply chain must
take: the best way to maximize profits in a supply chain is integrate or outsource with the
business partners? This is done through a transaction costs dynamic model that departs from
the traditional setup: there are no investment-related incentives and the productive process is
shaped by several persistent economic structures.
In a nutshell, I obtain that the decision of two units to integrate or outsource will depend on
the interplay among some factors: first, there are governance fixed costs related to integration;
second, integration may provide interfirm externalities that improve the joint profit of the two
units, vis-A -vis outsourcing; third, all firms in the supply chain are subject to random shocks
that prompt them to exchange information with their business partners. This exchange implies
that the firms learn about each other business and develop some kind of partnership-specific
knowledge capital. Fourth, both the strength of the externalities and of the governance costs
depend on the size of this knowledge capital. Fifth, in turn, the process of building the knowledge
capital depends on three key characteristics of the firms: their quality, a proxy for the dexterity
of the firm’s labor force in handling information knowledge; their size (number of inputs); the
degree of relationship between the firms in the supply chain, what I call connectivity.
An important message of this model is that the interconnected nature of supply chains
matters to explain their shape. Specially, the study of interfirm knowledge sharing is relevant,
since vertical decisions are not just about minimizing factor costs but also about appropriating
1For example, Grossman and Helpman (2003, 2005), Antras and Helpman (2004), Helpman (2006), amongothers.
2See Bolton and Dewatripont (1994), Puga and Trefler (2002), Dessein and Santos (2006), Cremer et al.(2007), Hart and Moore (2005), Rajan and Zingales (2001), Radner (1992), Radner (1993), Harris and Raviv(2002), Garicano (2000).
38
knowledge, as Antras and Rossi-Hansberg (2008) stress when discussing future directions for the
literature. In their landmark work, Ethier and Markusen (1996) recognized the importance of
knowledge-based capital for the optimal structure of an organization. However, their focus was
on specific technologies, embodied in products. Here, I focus on partnership-specific knowledge,
obtained only with the passage of time.
This model ends with some advantages compared to the workhorse of the literature, the
Property Right Theory (PRT, henceforth). First, is based on Transaction Costs Theory (TC
henceforth), which as stressed by Lafontaine and Slade (2007)’s survey, has a much better
empirical record than PRT. Second, it provides linkages with the Theory of Organization without
sacrificing the study of the supply chain, as in usual analysis of bilateral relationships.
Third, the local and economy-wide nature of the two empirical studies cited above make
models based on PRT poor fitted to offer an explanation for them. One reason is the dependence
of PRT on investment-related hold-ups which, as stressed by Hart and Holmstrom (2008), are
still ill-defined concepts; thus, the power of PRT to explain the shape of the supply chain is
more useful with static problems related to the initial establishment of innovative industrial
firms, specially concerning R&D issues, than to explain the broad structural elements behind
the development of a generic supply chain, which is a dynamic problem. Moreover, PRT is
more useful to explain settings in which large differences in factor costs between locations allow
an optimal arrangement of the spatial distribution of firms in a supply chain, to maximize the
return of their different types of investments. This is the success story of PRT in explaining
the globalization process, through the papers cited in the first paragraph. However, is not clear
why these elements would play such an important role into national economies, which are more
homogeneous in factor costs.
I use a novel term, connectivity, to measure the degree of a relationship between inputs
used in productive units. Connectivity is a measure of the number of channels for exchange of
information that exists between participants in some productive process.
Next, I show in detail the main elements of the model, followed also by a detailed description
of the results.
Characteristics of the model
First, I embed interfirm learning dynamics into the buyer-supplier relationships in supply
chains: units are subject period after period to shocks that prompt them to adapt their products
and managerial practices. In order to do that, these units exchange information with their buyer
and suppliers, given that these must also make changes in their own units. Also, given that the
buyers and suppliers participate in the readaptation effort, their own buyers and suppliers are
also called on: any shock reverberates upwards and downwards through all the production chain,
and at any time any unit may receive information not just from its suppliers but also from its
buyer, developing a knowledge stock about each of them.
Second, based on information theory, I show the information one unit absorbs with relation
39
to the another at any point in time depends on two elements: reception and comprehension of
the informational flow, which are functions of the units’ dexterity in handling information flows.
Third, units may be associate through one of two possible operational modes: outsourcing or
integration. The latter internalizes the externalities between the units, decreasing ordinary costs
relative to Outsourcing, but is subject to governance costs. These governance costs represent
costs that are absent only in a partnership that lasts for some time, like the other unit’s manage-
rial culture, knowledge of and relationship with the partner’s buyers and suppliers, preferential
agreements, detailed information about the partner’s production process, and so on.
Fourth, the exchange of information between units with the passage of time augments the
knowledge capital of one with relation to another. Consequently, it diminishes the governance
costs of integration and improves the strength of externalities in integration; Thus, this effect
sheds light on the findings of Kellogg (2008), the unique empirical paper in my knowledge
on interfirm relationship dynamics. This author shows that there are considerable productivity
gains from interfirm relationships, specially on non-technical dimensions. Acemoglu et al. (2004)
also shows that integration is correlated with the age of the firms, which hints at the importance
of dynamic considerations in the vertical decisions of the them.
Main results of the model
Based on this whole structure, I analyze the choice betweens Integration versus Outsourcing
in two different times: in a static environment with instantaneous information sharing, and in a
dynamic one where learning happens with time.
Under the static, instantaneous information model, I obtain the following results:
• first, the unit of the highest quality (dexterity in handling information flows) has just lower-
quality integrated supplier units to itself, no outsourced ones. In turn, these integrated
units may have some integrated units to themselves, and some outsourced, depending on
this: the lower the difference in quality of the parent unit relative to the supplier unit,
and the lower the quality of the parent unit, the greater the chance that this supplier unit
will be outsourced. Therefore, from the highest level of the supply chain to the lowest,
firms have increasingly more outsourced units and less integrated ones. This fits well with
the stylized fact that the most important managerial units are not outsourced or kept in
a separated entity, as discussed by Hortacsu and Syverson (2009). Integration is always
downward;
• low-quality units are small and numerous, whereas top-quality units are large and inte-
grated and the medium-quality units have intermediate configurations;
• based on the above results, this model sheds light on two conflicting empirical results, be-
tween Hortacsu and Syverson (2009)’s results of a positive relationship between integration
and suppliers productivity and Acemoglu et al. (2004)’s results on a inverse relationship
between supplier’s R&D and downward integration.
40
Under the dynamic model, I show that downward integration is more likely, among other
determinants, the higher is the the buyer’s quality, the lower the supplier’s quality relative to
the buyer’s one. However, the higher the difference in quality, the slower the learning process
for the partner and thus integration takes more time to come, although this is a second order
effect.
Contrary to the static model, here forward integration is viable, and also is more likely the
higher is the the buyer’s quality, the lower the supplier’s quality relative to the buyer’s one
and, as a first-order effect, the higher the connectivity of the supplier. However, the larger
the difference in quality, the more time it takes to reach it, here as first-order effect. Thus,
integration comes sooner for top quality firms close but not equal in quality, and the higher the
connectivity of the supplier. Either case, the position of the firms in the chain influences the
gathering of information and the probability of the merger.
These results hint to some reasons forward integration is less likely, as shown in data: first,
due to the learning advantages of buyers relative to suppliers; second, due to the first-order effect
of the difference in quality for forward information gathering, related to the second-order in the
case of downward.
Finally, the dynamic model is applied to study the effects of regulatory shocks over the
organizational decisions of units, with a new vertical foreign-direct investment effect described:
shocks prompts an input supplier to acquires his buyer and quit the former business. The model’s
prediction about the production chain characteristics that enhance the likelihood of this effect is
confirmed with documented actions and characteristics of two leading Brazilian meat-exporting
firms.
Findings with relation to the Literature
This paper is related to two strands of the literature. First, there is a vast number of papers
that study the design of internal organizations, that is, from inside the firm. The literature is
huge, for instance: Williamson (1967) studied hierarchical structures from the side of produc-
tivity enhancement and span of control, Rosen (1982), Harris and Raviv (2002) and Garicano
(2000) from the view of task assignment and coordination, Radner (1992, 1993) from the view
of information processing, Aghion and Tirole (1997), Baker et al. (1999), Rajan and Zingales
(2001) and Hart and Moore (2005) from the view of authority, developing the concept of delega-
tion. Second, there are those papers that look through the external view of the firm, like Antras
and Helpman (2004), Hart and Holmstrom (2002) and Acemoglu et al. (2004).
What is the difference between this paper and these others? This is the first paper to consider
the effect of an heterogeneous supply chain with two-way communication between firms in the
organizational mode. Albeit the results of this paper may look similar to Antras and Helpman
(2004) and Acemoglu et al. (2004) results, here I do not use property-rights theory, actually
incentives do not play any role3; I also endogenize the size of each unit, their informational
3Contrary also to the works by Acemoglu et al. (2007) and Hart and Holmstrom (2002).
41
channels and show with details the possibilities on which not just downward but also forward
integration happens, which is absent in the literature and allowed me to explain and describe
the occurrence of an new type of FDI.
Second, the dynamics of learning bring new results to the effect of the decision to integrate
versus outsourcing: contrary to Hart and Holmstrom (2002), outsourcing does not comes from
a deliberate behavior of agents in ignoring externalities, but is the result of a difficult process of
learning that takes time to develop.
The paper proceeds as follows. Section 2 describes the economic environment. Section 3
determines the fundamental, building blocks of the model. Section 4 defines the informational
environment and at Section 5 the learning mechanism, based on the informational environment,
is explained. Section 6 integrates all elements to build the economic components of the model:
revenue and costs functions. Section 7 uses the whole previous structure to analyze the choice
between integration versus outsourcing at the static, instantaneous information model. Section
8 discusses a puzzle in the literature and shows how the model helps understanding it. Section
9 shows the dynamics of integration versus outsourcing. Section 10 applies the dynamic model
to the behavior of two large Brazilian units facing regulatory shocks, showing a different kind of
vertical foreign-direct investment. Section 11 concludes.
2 Background
Suppose there is a final good in the economy that must be produced: thus, a supply chain
must be structured, but what is a supply chain?
A supply chain represents the production process behind the final good. Different from the
traditional view of a production function, it gives attention to the specifics behind the relationship
between all the elements that make part in the various processes that constitute the final good;
thus, it presents the various underlying production processes of the production function.
The aim of this paper is evaluate how specific characteristics of an arbitrary supply chain
affect the decision of firms in a economy to integrate or outsource. In order to start, this section
introduces the background economic environment related to the structure of this arbitrary supply
chain.
The economy where the supply chain exists is a discrete-time one. In this economy, units
are the standard types of structure in the productive process and I assume the whole economy
is composed of a infinitely large number of them. Thus, supply chains are made of units.
Definition 1 (Units).
A unit is an element of the productive process, such that:
• There are some individuals in the economy that own it;
• There is an homogeneous output produced at it;
42
• At least one individual works at it.
Definition 2 (Inputs).
Each unit in the supply chain makes one unit of a output each period. This output is produced
from a combination of some intermediate inputs or labor. Intermediate inputs are the outputs
from other units; labor inputs are those from workers inside each unit.
The economy is populated by many supply chains, each made of different number of units.
It is not necessary for this paper to take some specific supply chain as reference. Thus, when I
refer to the supply chain, I am referring to an arbitrary one with at least 2 units belonging to it
(otherwise there is no chain).
In this supply chain, each supplier sells just to one buyer, but each buyer can have multiple
suppliers. All buyer-supplier unit pairs in this supply chain have a business partnership that
lasts indefinitely.
Consider a long-term relationship between two units of this supply chain: an forward unit
(supplier) and a downward one (buyer). The governance structure of this partnership is of two
possible forms: the units can be either Integrated, or Outsourced with relation to each other. As I
show later, at Integrated units information flows between units is faster compared to outsourced
units; however, there are governance costs of integration. This decision is evaluated at the
beginning of each period t of their partnership.
At any period t, following the definition of the ownership structure of the units, there is the
realization of a shock over some units in the supply chain. This temporary shock prompts some
units to change their outputs or internal environments. After a unit receives the call to change,
she arranges a meeting with her suppliers and her buyer to address the necessary changes the
partners must also accomplish. Summarizing, any shock reverberates not just upward in the
production chain but also downwards, and a output related to several different inputs expects to
be subject to a greater number of shocks with the passage of time, directly or indirectly. After
the shock, the units that received it make the necessary adjustments.
Thus, following the realization of the adaptations, the buyer-supplier pairs exchange proto-
types and based on this they meet to discuss the terms of trade, that is, the prices.
After that, the first unit in the supply chain produces its output and sends it to its buying
unit, who receives it along other inputs, and produces its own output, and so on, until the final
output is made. Figure 1 next page summarizes this story.
43
Figure 1: Timeline.
Figure 2 below presents an example tree of a four stage supply chain. This example will
also be used next in this section and in others to facilitate the understanding of the model. The
vertical dimension of the supply chain in the example is 4. In turn, each stage is made of 1 to 3
inputs.
Figure 2: Example of a Supply Chain Tree.
As the figure shows, supply chains are complex. However, I will use a simple notation when
referring to units in the chain: I am going to consider one buyer unit (i) and her forward
suppliers, called indistinctly by (k). Figure 3 next page shows this easier notation.
Next section I explain in detail exactly the properties associate with units that constitute
the supply chain (and the economy). After that, sections 4 and 5 explain the shocks and
informational flows along the supply chain, and the mechanism used by units to learn from each
other.
44
Figure 3: Notation to be used throughout the paper.
3 Structure of the Units
This section presents the structural properties endowed to the units in the supply chain; as
I show along the paper, these properties have a great impact on the way units relate to each
other.
3.1 Characteristics
Each unit in the economy is born with three characteristics associated with. The three char-
acteristics are: quality, related to the dexterity of the unit’s workers in handling informational
flows from other units.; size, related to the number of intermediate inputs necessary to the pro-
duction of the output of the unit; and connectivity, a measure of the way the inputs of some unit
are related to each other. At birth, each characteristic is drawn from appropriate distributions.
Notice that the model’s findings are dependent neither on any particular combination of these
characteristics.
Next, I define these three in detail and explain their role in the paper.
Definition 3 (Size). Size refers to the number of intermediate inputs some unit uses in the
production of its output. Formally:
Each unit (i) in the supply chain makes one unit of a output each period from the combination
of some inputs. There are two types of inputs: intermediate inputs, and one labor input. Define
• |Mi| = mi as the number of intermediate inputs that are used by unit (i);
As I show in section 5, the greater the size of the business partners of some unit, the greater
the expected amount of information this unit is going to receive and learn from these other units.
This effect is important for choice between integration versus outsourcing in a dynamic model,
at section 9.
The definition of connectivity is made through the development of two concepts, presented
in sequence.
Concept 1 (Messages). Consider two inputs k, k′of unit (i) (either labor or intermediate).
Communication between them is done through a message Mk,k′, which is a informative content,
45
an information for short, about k that reaches k′. If the message Mk,k′ is totally absorbed by k′,
then k′ is capable to reproduce it; consequently, is able to reproduce part of k.
Concept 2 (Connections). A connection between two inputs is the existence of a channel for
transmission of information between them. Formally:
A connection between inputs k and k′ is a directed and oriented graph4, that is it, an
ordered pair (Vk,k′ , Ak,k′), where Vk,k′ = {k, k′} is a set of vertexes and Ak,k′ an oriented ordered
pair (k, k′) (called an arrow), such that
• k is the the sending vertex;
• k′ is the the receiving vertex;
• Unlimited messages Mk,k′ are allowed to flow between k and k′.
Figure 4 presents a directed and oriented graph:
Figure 4: A connection between inputs k and k’: a direct oriented graph.
In terms of the example at figure 3, there are two conections: from i to k and vice-versa.
Definition 4 (Connectivity). Connectivity is a measure of the interaction of some input with
respect to all the necessary parts that the output is made of. Formally:
Let Gi be a set containing the connections, in the sense of Concept 2, among all its in-
puts that participate into the production process of the output of unit (i). Formally, Gi =
{(Vk,k′ , Ak,k′) ∀ k, k′ ∈Mi}. This set has the following properties:
• Each element in Gi is a connection as defined in Concepts 1 and 2;
• Gi(k) ⊂ Gi, k ∈ Mi, is the set of connections where input k is present as a sender or as
a receiver;
• The connectivity of an input k ∈Mi is si(k) = |Gi(k)||Gi| ∈ [0, 1];
In terms of figure 3, set Gi has dimension equal to 1 (there is just one input overall), and
the connectivity of input k is equal to 1 since i is made entirely from k.
As I show in sections 4 and 5, ceteris paribus a supplier with greater connectivity to his
buyer will learn more from it, but does not affect the buyer learning from the supplier. This is
important when I analyze the difference between downward and forward integration in a dynamic
setting, at section 9.
4Graphic demonstration here: http://mathworld.wolfram.com/OrientedGraph.html
46
Definition 5 (Quality).
Quality of some unit (i), represented by qi ∈ [0, 1], is a measure of this unit’s labor dexterity
in handling informational flows from other units. The greater the quality, the greater the units
capacity to receive, comprehend and execute information transmitted from other units. Thus, it
is a measure of productivity in dealing with information flows.
The effect of quality is as follows: If some message is transmitted to some unit (k), it receives
just the fraction qk of it, comprehends a fraction qk of the information available at the received
message and, depending on the ownership mode, executes it with dexterity determined by its
quality. The next three sections are dedicated to explain those effects in greater detail.
4 Shocks and information flows
This section is concerned with the definition of the way information affects and flows between
units in the supply chain. I start with the concept of a shock.
4.1 The Shock
Units are always tweaking their internal elements to address a variety of demands. Regu-
latory norms, preference changes, cost-cutting necessities, innovations, all present a unit with
the necessity to change its way of producing and internal structure. Therefore, every begin of
a period t there is the possibility of a temporary shock that prompts some unit to modify its
product or internal environment. This shock is placed on some final or intermediate input, thus
in some unit itself.
After some unit (i) received a call to change, she arranges a meeting with her suppliers and
her buyer to address the necessary changes the partners must also accomplish. That is, the unit
that received the shock sends messages, as defined in Concept 1, to the buyer and suppliers.
These messages contain informative elements about the changes that the suppliers must do in
their outputs. However, the content of the message includes informative elements about the
other inputs that make part in (i)’s output.
In terms of the example from figure 3, if unit (i) receives the shock, she talks with unit (k)
about possible changes. If the shock were over (k), she would talk with (i).
Summarizing, any shock reverberates not just upward in the production chain but also down-
wards, and a product made of several different units expects to be subject to a greater number
of shocks with the passage of time, directly or indirectly.
It is important to be able to pinpoint the unit that will do the initial studies concerning the
necessary modifications. For example, suppose the original shock was placed on the final good
producing unit. However, actually the shock was entirely reflected in one specific input of this
final product. Then, this input unit is the one who has actually received the shock first.
Definition 6. The unit responsible for the initial redesign is the first one, from the top of the
47
supply chain to the bottom, that had more than one of its suppliers affected (since, in this case,
this firm must lead the redesign in order to manage the simultaneous changes in all its suppliers).
Timing of a Shock
The signal that shows which units will be affected by a shock at any instant of time comes
from a Poisson Process. Thus, the probability of receiving a signal u periods from today is
independent from the last time the unit got it, and is given by γe−γu.
Target and Size of a Shock
After unit (i) received the shock, she compiles a list of her direct intermediate inputs (from
Mi) that must be adapted. Let Λti be the set of (i)′s intermediate inputs that were affect by the
shock.
4.2 The Propagation of the Information
After unit (i) received the shock and evaluated the necessary changes, it will contact her
partners to discuss the necessary changes they must also accomplish. In order to do so, she must
send messages to the other units, downward and upward. How are the messages distributed with
the suppliers, and what is their content?
4.2.1 Downwards
An useful proxy is that the share of each input in the redevelopment process is a function of
its connectivity. Thus, if (i) is hit by a shock, the messages sent to supplier k areMti,k = si(k)Λti.
But suppose this input supplier also had 2 external inputs. Call one of them k. Thus, ks share
will be sk(k)si(k)× Λti, and so on as long as there are suppliers.
Therefore, in the sense of Concept 1, the messages allow the receptor to replicate the content,
thus to learn part of the business of the unit that sent the message.
4.2.2 Upwards
Now, if unit (k) was hit by a shock, his buyer, some other unit (i), will too be called to
make changes in his productive process due to the supplier’s modifications. Moreover, the buyer
will share the information received from this supplier with his other suppliers, according to the
following share: each of the other k′ input suppliers of (k)’s will receive messages
Mtk,k′ = si(k
′)× si(k)× Λtk.
However, the buyer receives the whole information from her supplier, that is, Mtk,i = Λtk
. Next figure shows the flow of raw information between partners in the same supply chain
48
considered in figure 2. Notice that unit on which the shock was placed does not learn about her
partners.
Figure 5: Distribution of the information through a supply chain tree.
49
5 Absorptive capacity and the Learning Mechanism
As explained last section, after the shock the flow of information is bidirectional, from the
one who received it to the suppliers and buyers. But how this information is absorbed by the
units? In other words, how do they receive and comprehend this information so that it can be
used? This section proposes a structure to model this question.
Reception of information
In order to model the reception of information, I propose an structure inspired by the work
of Claude Shannon, on Information Theory(Shannon, 1984). Shannon derived a concept called
Information Capacity, which is the maximum amount of information that can pass through
a channel without error, for a given amount of noise in the system5. Another definition of
Information Capacity is a measure of the units’ mutual information, that is, the information
the units share with each other. Thus, the greater the noise in the communication between two
units, the lower is their expected mutual information and channel capacity.
I model reception of information inspired on this concept, with some differences accounting
to the economic environment.
First, I define noise as the difficult in transmitting some given amount of information in a
language such that it can be understood by both receiver and sender. For example, consider
two people from different divisions in a company discussing a mutual problem. Since they have
different environments and internal languages, there may be some noise in their communication.
However, noise is asymmetric: the unit with greater ability to handle informational flows is
able to receive proportionally more of the messages transmitted from other unit. Thus, I model
this asymmetric noise considering that there is noise just when the receiver is of less quality than
the sender.
Thus, based on the reasoning explained above, the formula to model the reception of infor-
mation by unit (k) from unit (i) is (1
1 + max{qi, qk} − qk
), (1)
The denominator is a function of the distance between two units, when the sender is of greater
quality than the receiver (the max operator).
Comprehension of the information
Besides problems related to the transmission of information, there are also some problems
related to the comprehension of the information during an exchange. That is, even if information
is error-free and fully transmitted, the information transmitted must be understood6. In the
simplest way, I model the comprehension threshold of a unit as its own quality.
5See Sims (2003)6See Boisot and Canals (2004) for a discussion over the distinction between knowledge and information in
economics. Also, see the introduction in Shannon (1948).
50
Absorptive Capacity
Thus, bringing both together, the absorptive capacity of information by some unit (i)
from other unbit (k) is: (qi
1 + max{qi, qk} − qk
)(2)
The informational stock
Finally, I present the formula that represents the way the informational stock of one unit
about other is formed.
Let Hti (k) represent the set of information of unit (i) with respect to her supplier. Thus,
unit (i) learns according to this function:
Hti (k) = Ht−1
i (k) ∪(
qi1 + max{qi, qk} − qi
)×Mt
k,i \Ht−1i (k), (3)
where H0i (k) = ∅. Its algebraic analog, hti(k), is given by equation (A.5).
What is the intuition behind this formula? First, learning is incremental, thus it starts at the
previous period’s learning stock, Ht−1i (k). Second, each new shock brings messagens that contain
new information, which changes the knowledge base only if adds something to it, represented by
the termMtk,i \H
t−1i (k). Third, the term inside parenthesis is the absorptive capacity explained
just before.
Accordingly, (k)’s learning as a supplier to (i) is
Htk(i) = Ht−1
k (i) ∪(
qk1 + max{qk, qi} − qk
)×Mt
i,k \Ht−1k (i), (4)
with analogous properties to (3) and algebraic version htk(i) given by (A.4).
The following proposition summarizes the results from these learning equations.
Proposition 1. Based on the learning structure defined above, I can say that the expected
accumulated information to be received by some unit (k) from her buyer (i) at some period t is
greater:
1. The smaller the noise through their communication, that is, their distance in quality.
2. The better the unit’s own quality, a proxy for her capacity to ”understand” the received
information;
3. The larger the unit’s connectivity, since there are more channels of information between
the units.
4. The greater is the size of her buyer’s other partners since this means more shocks and more
information shared.
51
Proof: Appendix.
Accordingly,
Proposition 2. Based on the learning structure defined before, I can say that the accumulated
information received by some unit (i) from one of her suppliers, (k), at some period t is greater:
1. The better the unit’s own quality, a proxy for her capacity to ‘”understand” the received
information;
2. The greater is the size of her supplier’s other partners, since this means more shocks and
more information shared;
Proof: Appendix.
6 Revenue and Costs
This section uses the building blocks from the previous sections to build the units’ funda-
mental decision variables: revenue and costs function. Specifically, I show how the way the
information stock of one unit about others affect their main variables. I start with the determi-
nation of revenue. Since the units produce one unit of output per period, revenue of any unit is
given by its price.
6.1 Revenue
In the case of two vertically integrated units (i) and (k), input price pk is given by a measure
vk related to the market assessment of the value of the output.
That is just not the case if the units are outsourced in relation to each other. They determine
their trade price through a bargain process. As shown in figure 1, at t = 4 all parties meet to
put through their positions in the bargain.
If the bargain breaks down, unit k has outside option equal to vk − c where c is the cost
to bring the good to the market and vk the revenue from selling to the market ; otherwise, her
utility is Uk = pk. The buyer, unit (i), has utility Ui = pi−pk−P−ki if the bargain is successful,
and Uoi = pi− vk−P−ki if it is not, where P−ki is the price of the other intermediate inputs from
(i), excluding unit (k).
The bargain revenue, given by the Nash result, is given by pk = vk − 12 (c).
6.2 Costs
6.2.1 Adaptation Costs
A unit with quality qk called by external events to modify its product faces adaptation costs
that, as I show later, have a great impact over the choice of organizational form.
Adaptation costs are related to the redesign of the unit’s input and its delivery to the buyer;
in this case, adaptation by (k) to deliver to (i). In particular, there is the possibility that (k)
52
takes to too much time to research the adaptation. Since the shock comes in the beginning
of a period t, the unit must complete the research in adaptations until the half of this period
so that products sold in t + 1 already incorporate the necessary changes. With probability ρ
the unit completes the adaptation work in time; otherwise, sales happen normally without the
modification but there is a penalty cost K > 0.
There is a difference, though, between integration and outsourcing. For the latter, the greater
proximity of the units implies that their mutual stock of knowledge decreases the possibility
of delays, since there are few barriers between buyer and supplier. Hurdles are greater for
outsourcing, since the units are separate. There are several transaction costs that are diminished
in integration, usually those related to informational flows between adjacent units: a common
business culture, common regulations, same physical space make decisions faster, besides that
fact that there is no contract binding all actions. Thus, making adjustments is easier when
integrated.
Thus, the difference in ρ between integration and outsourcing is a measure of the dexterity
of the execution of the new information assimilated. I capture this effect in a simple way:
Let htk,i =htk(i)+h
ti(k)
2 the average bilateral stock of information; then I define the probability
of receiving a penalty cost K as:
ρk(i) = qihtk,i + qk(1− htk,i) if integration,
ρk(i) = qk if outsourcing.(5)
Thus, the bilateral stock of information of one unit with relation to another makes procedures
between these two units faster when their are integrated, compared to the case of outsourcing. I
use the bilateral stock since it reflects the bilateral exchange of information between units. The
greater the bilateral stock, the faster is communication in integration vis-a-vis outsourcing.
Consequently, for each mode of ownership, variable costs are given by
• Vertical Integration
Since is the forward firm that pays the price for the delays, its costs are given by
K(1− qihtk,i − qk(1− htk,i)
). (6)
• Outsourcing
Again, costs of the forward firm are given by
K(1− qk). (7)
53
6.2.2 Fixed Costs of integration
Finally, I define the fixed governance costs related to integration: they are given by
F (htk(i)) for forward integration,
F (hti(k)) for downward integration.(8)
with F ′(·) < 0, F ′′(·) > 0, (htk(i) is the information stock of the supplier with relation to the
buyer, (hti(k) the information stock of the buyer with relation to the supplier.
Contrary to adaptation costs, governance costs are related to the unilateral stock of infor-
mation of the buying firm with respect to the acquired one. This is so because the acquirer, as
the new owner of the combined firm, must set the new governance structure and the more he
knows about the other unit, the better he is able to do it. Since the choices are prerrogative of
the owner, his information is the one more relevant.
7 Static, Instantaneous Information Model
In this section I present a model where information is readily observed by all firms at the
begin of times and is instantaneously shared. Thus, everything happens as if there was an
instantaneous shock of size 1 in all units in the economy.
The reason behind this radical assumption is to separate general properties of the model from
those specific for the dynamic model, present in Section 8. Also, this model presents results that
are not usual in the literature.
Since I assume information is readily observed by all firms, for a relationship between a buyer
and a supplier, their proportional information stock is given only by the absorptive capacity of
one with relation to the other.
With this background, I proceed to the steps necessary to deliver the problem of choosing
between integration and outsourcing.
7.1 Joint Profit of a Partnership
From the title, notice that I am defining the joint profit of a relationship, not the aggregate
one for the two partners. The latter includes the costs for both the forward and downward units
with relation to their respective buyer and suppliers, besides an explicit account of their profits
with these other relationships: the whole supply chain.
For the case of Integration, the joint profit of the partnership between units (i) and (k) at
period t is given by
pi −[K(1− qihtk,i − qk(1− htk,i)
)]− P−ki − Pk − ωk − ωi − F (·) (9)
where the form of F (·) depends whether integration is forward or downward (see (8)), Pk is the
sum of prices from the suppliers to unit (k) and both ωk and ωi are the wage of the respective
54
units. For the case of Outsourcing, aggregate profit between unit (k) and (i) is given by
pi − [K(1− qk)]− P−ki − Pk − ωk − ωi. (10)
7.2 Ranking of qualitites
Equilibrium properties of this model starts with a rank of the qualities from all units of the
supply chain. Notice that, regardless of the ownership structure, for any conceivable pair of units
that may participate in any stage of the production process, the quality of the unit downward
must be higher than that of the unit forward. Suppose this was not true and consider two units
qi, qk, k downward to i with qi > qk. If qi > qk, then by either (9) or (10) aggregate profits could
be increased if the firms switched position in the chain. In the case of outsourcing, at equation
(10) is clear cost are increasing in the quality of the supplier.
Results are not so straightforward with respect to integrated firms. However, notice that
costs again would decrease if the firms switched place, for the following reasons:
1. Governance fixed costs are decreasing in quality;
2. Adaptation costs are decreasing in quality since:
• From (9), cost is increasing in ρ. Notice that if both firms switched place, the average
informational stock would go up, because absoptive capacitites would increase:
qi +qk
1 + max{qi, qk} − qk− qk −
qi1 + max{qi, qk} − qi
> 0 (11)
• A greater average informational bilateral informational stock makes ρ smaller if the
downward quality is greater than the forward one, see (5).
Therefore, the following proposition summarizes the assortment property of the static model:
Proposition 3. Regardless of their owership structure, downward units are of greater quality
than forward ones in the static model.
7.3 Choice of Outsourcing versus Integration
When all information is expected to be readily shared between the units in the industries,
what drives the division of some activities between integrated units and outsourced ones?
It is fair to say that the reason lies entirely in the differences of quality. Explaining: for a
given quality, the greater the connectivity, the greater is the supplier’s accumulated information
about the parent unit. Therefore, the decision about downward integration versus outsourcing
is based on whether (9) is greater than (10), that is, whether the numerator is greater than the
denominator in the following ratio:
Θ(qi, qk) =pi −
[K(
1− qihtk,i − qk(1− htk,i))]− P−ki − Pk − ωk − ωi − F (·)
pi − [K(1− qk)]− P−ki − Pk − ωk − ωi(12)
55
where the form of F (·) depends whether integration is forward or downward (see (8). Based on
Θ(qi, qk), next proposition follows.
Proposition 4. Consider the ratio Θ(qi, qk) in (12) above. Based on it, I can say that
1. For a given supplier quality, qk, there is a threshold qi such that for values of qi above it,
integration between units qi and qk happens. Notice that
∂Θ(qi, qk)
∂qi> 0, (13)
and,∂qi(qk)
∂qk> 0.
Therefore, the unit of the highest quality has all his supplier units integrated to itself,
no outsourced ones. In turn, these integrated units may have some integrated units to
themselves, and some outsourced: the smaller the difference in quality of the parent unit
relative to the supplier unit, and the lower the quality of the buying unit, the greater the
chance that this supplier will be outsourced. Hence, from the highest level of the supply
chain to the lowest, firms have increasingly more outsourced units and less integrated ones.
2. There is never forward integration in this static model.
Proof at Appendix.
The intuition behind this results follows: the greater the difference in quality, the more
integration adds value to the partnership, since information flows are greater. Also, the greater
the quality of the downward unit, the lower are the governance fixed costs.
The fact that forward integrations are not possible in this static model is due to the static
nature of it, that gives the higher quality firm (the buyer) all the advantage since their learning,
instantaneous in this case, is always greater.
Notice that both size and connectivity do not play great roles here. This is because their
influence appears only in a dynamic setting. At Section 9 I show that in a dynamic model
connectivity and size have a great role in the ownership choice, and that forward integration is
possible.
8 Relation to findings of the literature
I show now how the model developed here sheds some light on the findings of Acemoglu et
al. (2004)’s empirical findings of an inversed relationship between integration and supplier R&D
intensity and Hortacsu and Syverson (2009)’s findings on an increasing relationship between
integration and supplier plant productivity.
Notice that the theory developed until here implies that
56
1. Units are more likely to be integrated the greater the distance in quality between them
and the buyer, the greater the quality of the buyer and the higher the connectivity of the
supplier.
2. Integrated structures are more productive than outsourced ones of the same industry, due
to the externalities.
This model speaks in terms of labor quality in an informational sense. If one assume that
labor quality is necessary for intense if R&D expenditures, the model gives that high-tech
units (those with higher R&D expenditures) must be of high-quality, which in turn are more
productive. However, but for a given buyer quality integration is decreasing in the quality of
the supplier, and for a given supplier quality, is increasing in the quality of the buyer. Thus,
the model shows Property Rights Theory is not necessary to explain Acemoglu et al.’s empirical
findings, but also these finds do not contradict Hortacsu and Syverson’s findings as well. Of
course, a new round of econometric evaluation is necessary, since the three models are very
different.
9 The Dynamic model
Previous section results were done over the assumption that information between firms is
instantaneously shared. Following the environment developed in section 6, now I consider the
dynamics of integration versus outsourcing, starting from moment zero, when there is no infor-
mation shared. In contrast with the previous section’s model, now the decision to integrate or
outsource must take into account the production shocks and the learning process that follows
from it, with very different results from the static model.
9.1 Outsourcing versus Integration with Learning
Consider the case of a supplying unit (k) and her buyer (i): their joint value functions in
each organizational mode in some specific period t are:
V V,tk,i = pi −K
(1− qihtk,i − qk(1− htk,i)
)− P−k
i − Pk − ωk − ωi + Et+1
(βV V,t+1
k,i
); (14)
V O,tk,i = pi −K (1− qk)− P−k
i − Pk − ωk − ωi + Et+1βmax {V V,t+1k,i − F t(·), V O,t+1
k,i }. (15)
where O index the outsourcing value function, and V the integration one. The form of F (·)depends whether integration is forward or downward (see (8)).
Notice that the above equations represent the functional form of the present-value joint profit
functions, not the solved value function with the solution for the trajectories. The existence of
a solution for each period is given just ahead in section 9.2 .
57
9.2 Ranking of qualities
Ranking in the dynamic model is no different than that of section 7.2: at each time t,
regardless of the ownership structure, for any conceivable pair of units that may participate in
any stage of the production process of the supply chain, the quality of the unit downward must
be higher than that of the unit forward.
The proof follows that from section 7.2 since, by (14) or (15), the only difference between
the static and the dynamic model is the dynamic movement of the value stock of information.
First, notice that if that some pair of firms kept their ownership structure intact for the
future, then the dynamic model is just a repetition of the static one and the same proof from
7.2 applies. This is always true, thus, for integrated units at birth.
However, for outsourced units, does the possibility of a change to integration make it possible
that the quality of a downward unit be smaller than the quality of a forward unit? Not likely,
since from 7.2 costs decrease when units switch places in both ownership modes.
Proposition 5. In the dynamic model, downward units are of greater quality than forward ones,
regardless of their ownership mode.
9.3 The choice between Integration and Outsourcing
Next series of propositions consider the interplay between interfirm learning dynamics and
supply chain characteristics over the choice between Integration and Outsourcing.
Lemma. Sufficient conditions for the existence of an knowledge threshold for integration are
high enough fixed costs and the buyer’s quality being sufficiently greater than the supplier’s.
Proposition 6. Consider the decision between two vertically adjacent units in a supply chain, (i)
and (k), of whether or not to integrate. Provided the conditions on Lemma 9.3 are met, the units
start their partnership via Outsourcing and change latter to Integration, at some information
threshold h.
Corollary 1. Assume the sufficient condition specified in lemma 9.3 is valid. Then, about
downward mergers, one can say that
1. Considering the value of the threshold necessary for a transition from outsourcing to inte-
gration:
it is decreasing in the quality of the buyer:
∂hi(k)
∂qi< 0, (16)
58
and is increasing with reference to the quality of the supplier:
(17)
∂hi(k)
∂qk> 0. (18)
2. Considering the accumulation of knowledge capital, downward mergers happen faster:
(a) the greater is the the buyer’s quality,
(b) The greater is the size of the supplier’s (and of his suppliers, and so on...), since this
means more shocks and more information shared;
Proof at Appendix.
The above proposition address two elements of importance when considering integration
versus outsourcing in a dynamic setting: first, it says that for a given supplier quality, a buyer
of greater quality need attain an information threshold smaller since the extra value obtained
from the integration is greater. Accordingly, for a given buyer, the smaller the quality of the
supplier, the lower the necessary threshold since, again, the extra value obtained from integration
is greater.
Second, at item 2, proposition says which elements make it faster the coming of the inte-
gration threshold. The greater quality of the buyer is due to increased learning from shocks.
Learning also is greater the larger the dimension supplier’s own supply chain, since there are
more shocks that may hit the supplier and prompt information sharing.
Now, let me show results concerning the existence of forward integration.
Corollary 2. Assume the sufficient condition specified in Corollary 9.3 is valid. Then, about
forward mergers, I can say that
1. Considering the value of the threshold necessary for a transition from outsourcing to inte-
gration:
it is decreasing in the quality of the buyer and is increasing in the quality of the supplier:
∂hk(i)
∂qk> 0, (19)
∂hk(i)
∂qi< 0. (20)
2. Considering the accumulation of knowledge capital, forward mergers happen faster:
(a) The smaller the noise through their communication, that is, their distance in quality,
a proxy for her capacity to receive the information;
(b) The better the unit’s own quality, a proxy for her capacity to ‘”understand” the infor-
mation;
59
(c) The larger the unit’s connectivity;
(d) The greater is the size of the buyer (and of the other partners of the buyer, and so
on...), since this means more shocks and more information shared.
3. Summarizing: two elements affect the time until the change of ownership mode. First,
there is the target level itself, which as shown in the last item, is increasing in the buyer’s
quality and decreasing in the supplier’s one. Second, the expect time to reach this level
depends on the elements described in item 2. Therefore, although with a larger difference
in quality the target level is smaller, the time necessary to reach it augments, since this
difference diminishes the accumulation of information.
Summing Up
• From the point of view of maximizing value, the higher the buyer’s quality in the supply
chain, the more likely is both types of integration.
– forward integration happens sooner between firms not too much apart in quality,
where the connectivity of the supplier is high and the firms are located at the top of the
supply chain. In this setup, an increased difference in quality increases the creation
of value but diminishes learning; location is also important: forward information
gathering increases with the distance from the top of the chain, since the frequency of
shocks is higher, but also decreases with it, since the size of shocks are more diluted.
The contrary happens to downward integration.
– downward integration happens sooner between firms apart in quality: an increased
difference in quality augments the creation of value; location is also important: down-
ward information gathering decreases with the distance from the top of the chain, since
the frequency of shocks is lower, but also augments with it, since the size of shocks
are more diluted.
• At any time, both downward and forward integration may happen, contrary to the model
from Section 7. Yet, from Proposition 6, Corollaries 1 and 2, is clear that if buyers are of
greater quality than suppliers, downward mergers are more likely than forward mergers,
since buyers in average absorb more information per unit of time. Also, as shown in the
items above, the difference in quality between units hinders the supplier’s gathering of
information, worsening the prospects of forward integration vis-ı¿12 -vis the downward one.
10 Case study
In this section I show some interesting application of the above theory, related to a real
case that happened with two Brazilian companies, namely, Sadia and Friboi. Brazil is one the
60
world’s greatest raw meat exporter, being the first in beef, the second in poultry, specially chicken
and the fourth in pork, as of 2008. Several meat packers export these products to all around
the globe. Besides raw inputs, some of the most successful Brazilian companies also produce
processed meat; among these, two are reference: Sadia7 and JBS-Friboi8, the latter being the
largest exporting and beef-processing unit in the world.
In the last few years, there were several outbreaks of foot-and-mouth disease in Brazil that
severely hampered Brazilian exports of raw and processed beef products. Although this disease
does not poses harm to consumers, it is used by importer countries and competitors as excuses
to lobby in order to displace Brazilian producers off the meat market.
This type of restriction also affected the poultry export market, which is Sadia’s main one:
twice in 2007 Russia, Brazil’s larger buyer, halted imports alleging sanitary concerns.
In the last four years, these two Brazilian units adopted similar strategies: internationaliza-
tion. Friboi bought in 2007 the American Swift Foods Company to access the American and
Argentinian markets; Sadia opened in 2008 its first foreign industrial plant, in Russia.
According to JBS-Friboi’s executive director of business, in an interview to one of Brazil’s
most prestigious business newspapers (Gazeta Mercantil, 2006a) at the time of the first foreign
acquisition (translation by the author):
”We are looking for diversification in foreign markets and also a ’sanitary hedge’.”
In the same vein, commenting for the same newspaper (Gazeta Mercantil, 2006b) the decision
to build a plant in Russia, Sadia’s CEO at that time said that:
“Nowadays, sanitary quality is our greatest problem in Brazil.”
Both companies exported raw and semi-processed products to these markets for at least 10
years, and after the devaluation of Brazil’s currency, the Real, in 1999, their exports increased
remarkably. The quotes above indicate that the sequence of regulatory shocks of the last 5 years
was one of the reasons that prompted them to build stronger positions in their main exporting
markets, in order to defend themselves.
These two stories fit within the model developed in the preceding sections. First, notice that
these companies were exporters for a long time and had already gained considerable information
about their foreign partners and market structure, after a series of small shocks into the daily
operation of their units. Second, they confronted large shocks in the last few years that, if not
addressed, could halt completely their exports and harm their relations with the buyers. These
shocks represented large costs, as in equation (7), thatif not addressedwould lead to great losses.
Thus, these companies perceived that with some great probability their presence in the foreign
market, built for so many time, would be lost. The alternative? Some merger or acquisition
that allowed the continuation of their business, from the perspective of the buyer.
7http://www.sadia.com/en/home/index.asp8http://www.jbs.com.br/defaultEn.aspx?PagId=FLGCORVM
61
Consider the model developed at Section 9, with a supply chain made up of just a supplier
indexed 1 and a buyer indexed 0, at some generic time t, and assume that a strong regulatory
shock happened. If the supplier does not make the costly adaptations C, he is out of the export
business. Yet, even making the adaptations, with probability 1−z they are useless in preventing
an outbreak of disease and the cost is even bigger, J . Than, the supplier-buyer pairs must
choose between three options: nothing, outsourcing with exports, outsourcing with domestic
production.
max
{0, z(V O − C) + (1− z)(V O − J), OV − F
}. (21)
The novelty is the third option, where the supplier acquires the buyer, does not invests in
sanitary measures and continue buying from another supplier.
Before moving to explain the decision of the Brazilian companies, one has to explain why
prior to the shock the units were operating in outsourcing mode. According to the model, that
would be the case if both had medium and close qualities such that integration externalities
would be negligible but interfirm learning would be medium for both.
The meatpacking business has characteristics that satisfy these descriptions: first, these firms
probably have close qualities since the skill requirements are similar in all countries9; Also, given
the commodity-related nature of good, the average quality of the labor in the meatpacking is
probably not high and and the small degree of specificity of this business diminishes the incentives
to integration.
The next proposition follows, a straightforward application of the theory developed through
this paper:
Proposition 7. Consider two firms operating via outsourcing, each in a different country, H
and F , where H ′s firm (supplier) exports to F ′s (buyer). After a regulatory shock, the supplier
will decide to quit its local operations, buy its downward buyer and outsource from F according
to the following:
• the greater the size of those buyer-related units;
• the lower the difference in quality between the two units;
• the larger the supplier’s connectivity;
• the greater the amount of time of their relationship.
Proof. Equation (21) and Corollary 2.
This definition applies very well to the Brazilian units quoted before:
9I am still short on data about the costs of these units and plants, but given the comparative advantagesof Brazil in labor and natural resources, probably Brazilian costs are smaller: public data on the non-profitresearch institute Agri Benchmark shows that Brazil has one of the lowest livestock prices of the world. Seehttp://www.agribenchmark.org/.
62
• Both produce inputs, almost-final good products or processed meat, that demand great
interconnection with the buyers, that is, their inputs’ connectivity is high. For two reasons:
technical, since the meat are the most important intermediate inputs that enters in the final
product, and constitute the larger fraction of it; quality concerns, that demand constant
interconnection;
• The supply chain’s dimensional is smaller in the vertical dimension relative to most other
industries (since the meat comes directly from livestock farms to those units), but the
horizontal dimension of the chain related to the buyer is large since it involves, downward,
several interconnected wholesale, distribution, marketing and retail operations.
• Some knowledge of operating in foreign countries and companies can be learned indepen-
dently of the market, since they are common to all of them:
– Sadia exports to 65 different markets and is the leading producer of processed poultry
in Brazil.
– JBS-FRiboi is the second largest exporter of meat in the world, the largest of processed
meat. Has 500 clients in 110 countries.
• The companies had at least 10 years of experience exporting to these markets.
• Due to the low-tech nature of the industry, the quality of the Brazilian firms probably is
close or superior to those of the acquired foreign firms, facilitating the interfirm learning.
Although the horizontal dimension forward is also large (numerous producers), nowadays the
shocks coming from these are usually small by the simple nature of their tasks and because there
is already considerable integration forward. The fact that forward integration came sooner in
Brazil is not difficult to understand: in the last decades the considerable disruption in the live-
stock production and slaughtering business caused many problems for an efficient management
of the supply chain. Product quality was specially important (Lawrence et al., 2001; Hayenga
et al., 2000). downward, however, the competitive aspect of the retailing market, the lack of
stringent technical and food safety regulations and simpler consumer preferences in terms of va-
rieties (due to smaller market sizes) all contributed to low product complexity and slow interfirm
learning from the downward side of the chain.
However, this changed in the last decade: increased consumption of meat by the emerging
markets, increased number of product varieties due to more diversified consumer preferences,
increased horizontal concentration in the retailing sector, non-food technical regulations, export-
ing market barriers, all pose great pressure in the units in the middle of the chain. Shocks come
specially from the retail segment, since in several countries there is extreme concentration of
power with few units (Taylor, 2006; Netland et al., 2008). Schulze et al. (2006) discuss these
new developments and the implication in line of transaction costs.
63
11 Conclusion
This paper shows that a transaction-costs model together embedded with interfirm infor-
mation exchange and learning provides an unified explanation to several recent unexplained
empirical findings about the optimal vertical organizational form in a diverse supply chain.
Each period firms in a multi-layered supply chain must reevaluate their organizational form.
Also, they may receive a shock, which induces changes in the firm’s output, compelling it to
exchange information with its partners, which learn about it in turn. The shock disseminates
through all the chain, according to each firm’s quality, size (number of intermediate inputs) and
connectivity (measure of the informational channels between inputs). The knowledge capital one
firm has about its partners diminish the size of the governance costs of integration and improves
interfirm externalities of integration.
First, in a static model, I show that from the highest level of the supply chain to the lowest,
integration is more likely the higher the quality of the buyer, and the difference in quality between
firms. Thus, firms from top to bottom firms have increasingly more outsourced units and less
integrated ones. Also, just downward integration happens. These results shed lights on two
apparently contradictory empirical results of the literature.
Second, in a dynamic model, I show the determinants of interfirm downward and forward
learning, the characteristics that causes forward and downward integration and why the latter is
more likely, as shown in data. Contrary to the static model, now forward integration happens.
Finally, the dynamic model is applied to study the effects of regulatory shocks over the
organizational decisions of firms, with a new type of vertical foreign-direct investment explained.
I exemplify this effect with documented actions and characteristics of two leading Brazilian meat-
exporting firms.
64
References
Acemoglu, D., P. Aghion, C. Lelarge, J. Van Reenen, and F. Zilibotti, “Technology,
Information, and the Decentralization of the Firm*,” Quarterly Journal of Economics, 2007,
122 (4), 1759–1799.
, , R. Griffith, and F. Zilibotti, “Vertical Integration and Technology: Theory and
Evidence,” Working Paper 10997, National Bureau of Economic Research December 2004.
Aghion, P. and J. Tirole, “Formal and Real Authority in Organizations,” The Journal of
Political Economy, 1997, 105 (1), 1–29.
Antras, P. and E. Helpman, “Global Sourcing,” Journal of Political Economy, 2004, 112 (3),
552–580.
Antras, Pol and Esteban A. Rossi-Hansberg, “Organizations and Trade,” SSRN eLibrary,
2008.
Baker, G., R. Gibbons, and KJ Murphy, “Informal authority in organizations,” Journal of
Law, Economics, and Organization, 1999, 15 (1), 56–73.
Boisot, M. and A. Canals, “Data, information and knowledge: have we got it right?,” Journal
of Evolutionary Economics, 2004, 14 (1), 43–67.
Bolton, P. and M. Dewatripont, “The firm as a communication network,” The Quarterly
Journal of Economics, 1994, pp. 809–839.
Cremer, J., L. Garicano, and A. Prat, “Language and the Theory of the Firm,” The
Quarterly Journal of Economics, 2007, 122 (1), 373–407.
Dessein, W. and T. Santos, “Adaptive organizations,” Journal of Political Economy, 2006,
114 (5), 956–995.
Ethier, W.J. and J.R. Markusen, “Multinational firms, technology diffusion and trade,”
Journal of International Economics, 1996, 41 (1-2), 1–28.
Garicano, L., “Hierarchies and the Organization of Knowledge in Production,” Journal of
Political Economy, 2000, 108 (5), 874–904.
Gazeta Mercantil, “Frigorıficos investem no Mercosul,” Newspaper article, November 10, 2006.
, “Industrias de aves e suınos tambem querem se internacionalizar,” Newspaper article, De-
cember 14, 2006.
Grossman, G.M. and E. Helpman, “Outsourcing Versus FDI in Industry Equilibrium,”
Journal of the European Economic Association, 2003, 1 (2-3), 317–327.
65
and , “Outsourcing in a Global Economy,” Review of Economic Studies, 2005, 72 (1),
135–159.
Grossman, S.J. and O.D. Hart, “The Costs and Benefits of Ownership: A Theory of Vertical
and Lateral Integration,” The Journal of Political Economy, 1986, 94 (4), 691.
Harris, M. and A. Raviv, “Organizational Design,” Management Science, 2002, 48 (7), 852–
865.
Hart, O. and J. Moore, “On the Design of Hierarchies: Coordination versus Specialization,”
Journal of Political Economy, 2005, 113 (4), 675–702.
Hart, Oliver and Bengt Holmstrom, “A Theory of Firm Scope,” Working Paper 14613,
National Bureau of Economic Research December 2008.
Hart, Oliver D. and Bengt R. Holmstrom, “A Theory of Firm Scope,” SSRN eLibrary,
2002.
Hayenga, M., T. Schroeder, J. Lawrence, D. Hayes, T. Vukina, C. Ward, and
W. Purcell, “Meat Packer Vertical Integration and Contract Linkages in the Beef and Pork
Industries: An Economic Perspective,” Report for the American Meat Institute, 2000.
Helpman, E., “Trade, FDI, and the Organization of Firms,” Journal of Economic Literature,
2006, 44, 589–630.
Hortacsu, A. and C. Syverson, “Why Do Firms Own Production Chains,” University of
Chicago, mimeo, 2009.
Kellogg, Ryan, “Learning by Drilling: Inter-Firm Learning and Relationship Persistence in
the Texas Oilpatch ,” Department of Economics, University of Michigan, mimeo, 2008.
Lafontaine, F. and M. Slade, “Vertical Integration and Firm Boundaries: The Evidence,”
Journal of Economic Literature, 2007, 45 (3), 629–685.
Lawrence, J.D., T.C. Schroeder, and M.L. Hayenga, “Evolving Producer-Packer-
Customer Linkages in the Beef and Pork Industries,” Review of Agricultural Economics, 2001,
23 (2), 370–385.
Netland, T.H., E. Alfnes, I. Heskestad, and BA Nortura, “Integrated manufacturing
planning in agri-food supply chains: Towards end-to-end integration in a Norwegian meat
company,” 2008. mimeo.
Puga, Diego and Daniel Trefler, “Knowledge Creation and Control in Organizations,” SSRN
eLibrary, 2002.
Radner, R., “Hierarchy: The Economics of Management,” Journal of Economic Literature,
1992, 30 (3), 1382–1415.
66
, “The Organization of Decentralized Information Processing,” Econometrica, 1993, 61 (5),
1109–1146.
Rajan, R.G. and L. Zingales, “The Firm as a Dedicated Hierarchy: A Theory of the Origins
and Growth of Firms*,” Quarterly Journal of Economics, 2001, 116 (3), 805–851.
Rosen, S., “Authority, Control, and the Distribution of Earnings,” Bell Journal of Economics,
1982, 13 (2), 311–323.
Schulze, B., P. der Goettinger Sieben, A. Spiller, and L. Theuvsen, “Vertical Coordina-
tion in German Pork Production: Towards more Integration?,” in “16th Annual World Forum
and Symposium “Agribusiness, Food, Health, and Nutrition”, IAMA Conference, June” 2006,
pp. 10–13.
Shannon, C.E., “A mathematical theory of communication,” Bell System Technical Journal,
1948, 27, 379–423, 623–656.
, “Communication in the presence of noise,” Proceedings of the IEEE, 1984, 72 (9), 1192–1201.
Sims, Christopher A., “Implications of rational inattention,” Journal of Monetary Economics,
2003, 50 (3), 665 – 690.
Taylor, D.H., “Strategic considerations in the development of lean agri-food supply chains: a
case study of the UK pork sector,” Supply Chain Management: An International Journal,
2006, 11 (3), 271–280.
Williamson, O.E., “Hierarchical Control and Optimum Firm Size,” The Journal of Political
Economy, 1967, 75 (2), 123.
, “The Vertical Integration of Production: Market Failure Considerations,” The American
Economic Review, 1971, 61 (2), 112–123.
, Markets and hierarchies-analysis and antitrust implications, Free Pr., 1975.
, “Transaction-Cost Economics: The Governance of Contractual Relations,” The Journal of
Law and Economics, 1979, 22 (2), 233.
, The economic institutions of capitalism, Free Press New York, 1985.
67
Appendix
Proof of Propositions 1 and 2:
Remember that the buyer must share information with his other suppliers, so the shock prompts some level of
information sharing across all the units in the industry. Therefore, which is the accumulated information one unit
has from her buyer and supplier in some period t?
Notice that the learning from the suppliers comes from shocks happening just in the “tree” that starts with
the unit itself and goes through the suppliers own ramifications. Learning from the buyer side comes from shocks
originated in the rest of the tree.
Therefore, the accumulated information unit (k) obtains from her buyer i at time t, from time t− 1, is
Htk(i) = Ht−1
k (i) ∪(
qk1 + max{qk, qi} − qk
)×
((At
i × si(k)
)\Ht−1
k (i)
), (A.1)
where Ati =⋃
Λti are all the messages sent from (i)’s10.
Accordingly, the accumulated information unit (i) obtains from her supplier k at time t, from time t− 1, is
Hti (k) = Ht−1
i (k) ∪(
qi1 + max{qi, qk} − qi
)×(At
k \Ht−1i (k)
), (A.2)
where analogously Atk =⋃
Λtk are all the messages sent from (k)’s.
It is going to be useful later to translate into some algebraic measure the information in the form of partitions
of both the shocks received from other units, Λ, as the accumulated information Ht one unit has about another.
Define the algebraic size of the shock, αti,as the proportion of inputs from Mi that must be adapted at time t:
αti =|Λti|mi
. (A.3)
Thus, the algebraic analogs of (A.1) and (A.2) are:
htk(i) = ht−1k (i) +
(qk
1 + max{qk, qi} − qk
)(ati × si(k)− ht−1
k (i))+, (A.4)
.
Accordingly,
hti(k) = ht−1i (k) +
(qi
1 + max{qi, qk} − qi
)(atk − ht−1
i (k))+. (A.5)
.
Proof of Proposition 4:
1. I start the proof considering a downward integration, that is, F (·) is F (qi).
First, check that limqi→1 Θ(qi, qk) > 1 ∀qk; limqi→0 Θ(qi, qk) < 1∀qk < qi; limqk→1 Θ(qi, qk) > 1∀qi > qk;
Now, the derivatives. Θ(·) is increasing in qi, since its sign rests on:
∂Θ(qi, qk)
∂qi=
(−F ′(qi) +K
∂ρk(i)
∂qi
)> 0, (A.6)
10To facilitate the notation, I hereafter will define the shocks affecting some unit (i) but that originated inanother unit as Λi(k), with k ∈ Zi; the same to their interval analog, αi.
68
considering that∂ρk(i)
∂qi= (qi − qk)
(((1 + qi − qk)2)− si(k)qk
2(1 + qi − qk)2
)+ h
ti,k > 0. (A.7)
Therefore, there exists a qi such that
− F (qi) +Kρk(i) = Kqk (A.8)
Notice that
∂qi∂qk
=K(∂ρk(i)∂qk
− 1)
−K ∂ρk(i)∂qi
+ F ′(qi)> 0, (A.9)
given that the denominator is negative from F (·) decreasing. The next figure shows the value of the
numerator (referred to by Φ) for arbitrary qi and qk, notice it is always negative:
Figure 6: Numerator of (A.9)
Now, consider the possibility of forward integration. Since there is an instantaneous shock, the information
received by the dowstream unit about the forward partner is always greater than the one received by the forward
about the downward partner. This happens because the downward unit has greater quality (see section 7.2) and
information received by the forward unit is proportional to the connectivity of this unit, which is smaller or equal
to 1. Thus, there is never forward integration.
Proof of Lemma and Proposition 6:
A threshold exists when there is an equilibrium with integration starting today (14) (LHS) equals outsourcing
today and integration tomorrow (15) (RHS). It is different whether integration is downward or forward. A
threshold exists if...
in the case of downward integration versus outsourcing:
69
• limhi(k)→0 LHS < limhi(k)→0 RHS
Valid for a high F (0) and qi close to qk;
• limhi(k)→1 LHS > limhk(i)→1 RHS.
Always valid.
Now, for forward integration versus outsourcing, conditions are the same (limits, in this case, are for hk(i)).
• ∂V Vk,i
∂hi(k)≥ 0, since the continuation payoff is never smaller - information accumulated does not depreciate.
Also, fixed costs get smaller.
• F (·) decreases with more information.
• ∆VO
∆hi(k)≥ 0. To see this, notice that next period’s value function is not smaller than current one, given that
the information does not depreciates, and the unit has the option to choose the best alternative.
Therefore, there is at one level of information that, if reached, prompts a change from outsourcing to integra-
tion. This level is hi(k) (for downward Integration), or hk(i) (forward integration).
Considering downward integration, the threshold is such that
Kqk − β EF(hi(k)
)= Kρ(hk(i))− F (hi(k)). (A.10)
For forward integration,
Kqk − β EF(hk(i)
)= Kρ(hk(i))− F (hk(i)). (A.11)
Proof of Corollary 1:
See that
∂hi(k)
∂qi=
−K ∂ρk(i)∂qi
k ∂ρ(hi(k))
∂hi(k)− F ′(hi(k)) + β EF ′
(hi(k)
) < 0, (A.12)
since the derivative in the numerator is negative as shown in (A.6) and the denominator is positive given that
F (·) is decreasing and convex and from (5).
Finally,
∂hi(k)
∂qk=
K(
1− ∂ρk(i)∂qk
)k ∂ρk(i)
∂hi(k)− F ′(hi(k)) + β EF ′ (hi(k))
> 0. (A.13)
The sign depends on the value of the numerator, which is determined by the following terms:(qi,
si(k)qk1 + qi − qk
, t,si(k)(1 + qi)(qi − qk)
(1 + qi − qk)2
). (A.14)
It turns out that the behavior of the numerator follows the inverse of the function showed in figure 6, thus it
is always positive.
Proof of Corollary 2:
∂hk(i)
∂qi=
−K ∂ρk(i)∂qi
k ∂ρk(i)
∂hk(i)− F ′(hk(i)) + β EF ′
(hk(i)
) < 0, (A.15)
since the derivative in the numerator is positive.
Finally,
∂hk(i)
∂qk=
K(
1− ∂ρk(i)∂qk
)k ∂ρk(i)
∂hk(i)− F ′(hk(i)) + β EF ′
(hk(i)
) > 0. (A.16)
An economic model of the risk of payroll-backed loans
Abstract
This work presents a theoretical evaluation of the main characteristics that drive the risk
of credit losses on a portfolio of consumer payroll-backed loans. Consumer credit through
payroll-backed loans is one of the fastest growing credit lines in Brazil. Under reasonable
assumptions, I construct a microeconomic-based model of an industry whose workers are
borrowers of payroll-backed loans. Then, I build a formula for the probability of default
and expected losses for both an individual loan and a portfolio of loans from the industry’s
workers. Finally, variables of the formula are subject to a sensibility analysis to determine
their influence on the risk of payroll-backed loans.
72
1 Introduction
Models for credit risk assessment were introduced by Merton (1974). In his approach the
stochastic behavior of the value of a firm’s assets is modeled and if the value becomes lower
than a threshold, the company is considered to be in default. This model is seminal and was
chosen as the foundation for the capital allocation formula proposed by the Bank of International
Settlements, the Basel II Accord; Merton’s model gave the base not just for corporate risk models
but also to modeling risk on consumer loans, as stressed by Thomas (2009).
However, due to the very different nature of the underlying economic structure behind cor-
porate and consumer credit, there is considerable skepticism about the applicability of Merton’s
framework to measure consumer credit risk, as highlighted by Thomas et al. (2005). Notwith-
standing, the Basel propose has highlighted that although there are a number of well established
credit risk models for portfolios of corporate loans which are widely used by financial organi-
zations, there are no such established consumer credit risk models for portfolios of consumer
loans. Work towards establishing this benchmark has begun with, among others, de Andrade
and Thomas (2007) and Thomas (2009). These two papers construct Merton-style option-based
models, substituting the concept of a consumer’s call option value on the value of its reputation
for the assumption, present in corporate models, of a call option on the assets of the firms.
In this paper, I intend on contributing to the literature on consumer credit risk models
through a microeconomic study disentangling the risk properties of a popular and important
kind of consumer credit that is thriving in Brazil: consumer payroll-backed loans. Payroll-
backed loans are a fast-growing business in Brazil and is one the credit products responsible for
the explosion on borrowing in recent years.
I build a microeconomic model of a industrial sector, whose workers take payroll-backed
loans. Then, this model is used to construct a formula for the probability of default and expected
losses on both an individual loan and on a portfolio of payroll-backed loans. This theoretical
risk formula is very tractable and allows me to study the effects of changes in variables on the
risk of this credit product, and thus on its supply by the financial institutions.
There are three variables responsible for the bulk of the behavior of the above-mentioned
equation for the probability of default: the quality of the industry’s labor, the size of the in-
dustry’s labor force and the exposure of the industrial sector to shocks at its prices. Those
three variables, in turn, are related to the main driver of default in payroll-backed loans: unem-
ployment. Therefore, at subsection 1.1 next I explain a little about the risk characteristics of
this credit product, with a focus on unemployment. Following, at subsection 1.2, I explain the
modeling strategy and its findings.
1.1 Unemployment and risk in payroll-backed loans
Basically, payroll-backed loans are contracts among workers from some industry, their union
and a financial institution. The union negotiate a rate with the latter and the workers can borrow
at this rate until a fixed proportion of their payroll income, now 20%. Since the loan’s payments
73
are automatically deduced each month from the borrowers payroll, credit risk is minimal for
those employed. That is why the biggest market for payroll-backed loans in Brazil are workers
of the public sector, that have job stability.
However, there is also a considerable market for payroll-backed loans to private sector work-
ers. Credit risk in this case is also usually thought to be small, but is that true?
As the recent world economic crisis has shown us, that is not always the case. The main
driver for risk in payroll-backed loans is unemployment. As stressed in several newspapers, some
banks in Brazil had considerable losses from loans linked to sectors affected with more severity
by the world crisis. For instance, because of the crisis, one of the leading banks in Brazil for
this type of credit, BMG, decided to stop operating payroll-backed loans with private firms; say
Ricardo Guimaraes, president of BMG (Estado de Minas, 2010):
”(...) we decided, in 2009, that payroll-backed loans to the private sector were not
our focus anymore. Risk and default rates are greater than those from public sector
workers and recipients of public pension funds.”
De facto, default rates for workers from the private sector are much greater than those from
the public sector. In a recent interview to the Brazilian business journal Brasil Economico
Pirelli, a director of Bradesco, Brazil’s third largest financial institution, said that at that time,
09/24/2010, default rates for private-sector workers were almost 4%, against 1.8% of public-
sector workers (Brasil Economico, 2010). However, in the same interview the bank’s president,
Luis Trabuco, reckons that the biggest growth in the future will come from the private sector.
Thus, payroll-backed loans are very sensitive to aggregate risk, that cause mass unemploy-
ment. Besides, the aggregate risk is sector-based: in this sense, it feels like a corporate-risk
model since the industrial sector must be modeled in order to extrapolate its characteristics to
the loans its workers have taken. Credit risk of payroll-backed loans is also linked to idiosyncratic
unemployment risk: workers’ mistakes that cause their layoff.
The importance of understanding workers’ behavior (related to idiosyncratic risk) and indus-
try performance (related to aggregate risk) to assess default risk in portfolios of payroll-backed
loans is already reckoned in the consumer credit industry. For instance, Both Itau Unibanco
and Santander, Brazil’s second and fourth largest banks respectively, offer insurance together
with the payroll-backed credit to assure the payment of part of the credit in case of default.1
They also demand some minimum employment time (six months at Itau Unibanco) to minimize
idiosyncratic unemployment risk.
In short, two elements make payroll-backed loans apart from other types of consumer loans:
1. Large and direct risk from aggregate unemployment shocks;
2. It is a consumer product with a considerable industry-based risk;
1See http://ww2.itau.com.br/creditoconsignado/func_servpub.htm.
74
Thus, although all consumer credit has its risk linked to unemployment in some way, in the
case of payroll-backed loans risk is directly linked to the performance of the sector; this allows
one to focus the study of credit risk on the sector’s behavior, besides workers’ behavior.
1.2 About the model and its results
In order to model both the industrial sectors’ macro behavior, related to the aggregate risk,
and the workers’ behavior, related to the idiosyncratic risk, this paper uses a simple and flexible
two-period model based on the work of Kremer (1993).
Kremer’s model allows one to simulate the characteristics of labor inside an industry with
a focus on the ”quality” of labor, that is, the chance each worker has in making a critical
mistake on the production. Thus, KLremer’s model allows me to link the risk from idiosyncratic
unemployment to the probability of a worker making a mistake and being fired.
Considering the modeling of aggregate risk, Kremer’s model also poses no hurdles. This risk
is realized through an ad hoc aggregate shock that happens every period and affects with random
severity the industry’s prices, at each one of them. Since the industry chooses the size of its
labor force each period, after the first one it must either hire new workers if the shock happened
and was positive (in the sense of allowing hiring) or dismiss some workers if happened and was
negative (in the sense of causing unemployment).
Analysis of default is made with reference to the second period. Thus, if a negative shock
happens and some workers are fired, there is the possibility of default. Otherwise, default is
possible due to idiosyncratic risk. Thus, I obtain a formula for the probability of default and
expected losses for both a single loan and the portfolio of payroll-backed loans. The formula is
tractable and allows me to perform a sensibility analysis of its core variables: the quality of the
workers, that is, their probability of doing some critical mistake (idiosyncratic risk); the initial
size of the labor force; and the exposure of the industrial sector to an aggregate shock.
I find that the greater the idiosyncratic risk, the higher the probability of default, everything
else constant. Also, the effect of the size of the labor force over the probability of default
is complex, because any change on this variable causes two opposing effects: an increase on it
raises revenue for a given total productivity, but also decreases productivity; however, I find that
the lower are both the labor force and the idiosyncratic risk, the more likely that an increase in
labor force will lead to an increase in the overall probability of default for an individual loan.
The exposure of the industry to aggregate shocks is studied via a mean-preserving spread of
the distribution of severity of the shock, which causes an overall increase in the probability of
default, everything else constant.
The structure of the paper is as follows: section 2 summarizes the institutional framework
governing payroll-backed loans in Brazil; section 3 presents the microeconomic model that gives
the foundation for the development of the risk formula; section 4 incorporates the preceding
model in a model of default risk and expected losses; section 5 presents the portfolio view of the
previous analysis. Section 6 presents a sensitivity analysis of the risk formula with respect to
75
important variables. Section 7 concludes.
2 The Brazilian laws regulating payroll-backed loans
In 2003, the Brazilian Congress passed a law (number 10820/2003) regulating the so called
emprestimo consignado, namely, payroll-backed loans. This law represented a watershed moment
for credit in Brazil: it gave both consumers and financial institutions the necessary tools to make
credit more affordable and less risky.
As stated in the introduction, according to the law a payroll-backed loan is a contract among
workers, firms, unions and banks. Firms must make the necessary arrangements to share all
necessary information about the workers to the financial institutions, and make the monthly
deductions of the loan parcels from the payroll. Financial institutions negotiate with the unions
on the available rates and maturities for the loans, which the worker/borrower may accept or not.
Finally, although the firm may itself arrange special terms with banks, these must be approved
by the labor union in behalf of the employees.
These special allowances to the unions gives them lots of leverage to negotiate the terms
of these loans with the financial institutions, especially when representing employees with poor
credit history which would have great difficult in getting good terms, or any credit at all. Thus,
payroll-backed loans gave cheaper credit for borrowers with good credit history, and gave those
with poor credit score an instrument to borrow again.
The picture next show the explosive growth for payroll-backed loans since the approval of
the law:
Figure 1: Payroll-backed Loans - Balance in Million R$.
76
3 The Microeconomic model
3.1 Background
The economy is composed of several industries, indexed by ω. Time is discrete, restricted to
two periods, 1 and 2. Workers from these industries are indexed by i and each one produces one
unit of output each period.
At each one of these two periods, the industrial sector is subject to aggregate risk, that
materializes via an industry-specific shock. This shock comes right at the beginning of each
period, and affects the industry’s price. It can either increase or decrease it.
Following the shock, the industry’s labor force is determine in period 1; accordingly, at period
2 after the same shock labor force is reevaluated. Thus this second shock, if smaller then the one
at the previous period, can cause unemployment; otherwise, the hiring of new workers. These
shocks are independent and identically disributed over time, happens in any of the two periods
and affects the industry’s price P (zt) with intensity zt, which is given by a distribution F (zt), t
indexing the period 1 or 2. Assume P ′(zt) > 0 and .
Unemployment is also caused by worker-specific, idiosyncratic risks, that materializes
via shocks that affect the workers directly. This shock I describe through the variable v ∈ [0, 1],
with the following meaning: with probability v any worker makes a mistake that hampers
production at his industry and he is fired. Thus, it is a proxy for the quality of the industry’s
labor force. Thus, the worker-specific shock happens with probability v and may happen once
per worker during each period 1 and 2.
This shock can be anything from the entrance of a new competitor, a global crisis, etc.
Figure below shows the timeline associate with one period:
Figure 2: Timeline of the model.
In the following section I solve for both periods’ optimal labor level. I start with a brief recall
of what happens in each period, following figure 2.
• Consider the economy at period 1. At first there is the realization of shock z1, z∗1 . Following,
labor n1 ≡ n1(z∗1) is hired.
• Consider period 2. At the beginning, shock z∗2 is realized; subsequently, labor n2 ≡ n2(z∗2)
is defined; thus, there is the hiring or laying-off of some workers from previous period.
77
3.2 Problem of the industry
Consider some industry ω. Recall that each worker of this industry has probability v of
making an critical error that hampers production; thus, with probability
(1− v)nt ,
no worker does any critical, unemployment-inducing error and each one produces one unit of
output, resulting in nt of output sold at price P (zt). Finally, each worker is paid the nominal
wage W .
Following the timeline presented above, to solve the problem of the industry, the problem of
the industry in each period, 1 and 2, is to choose its labor force nt. First period is the initial
hiring stage, whereas at the second one there is a reevaluation of the mature project.
Thus, in each period t, for a given realization of the respective shock zt, the problem of the
industry is to choose the respective labor force nt:
maxnt
P (zt)nt(1− v)nt − ntW. (1)
First-order condition at both periods is given by2:
(1− v)nt + nt(1− v)nt log(1− v) =W
P (z∗t ). (2)
Now, notice that I am interested not just in the value of the labor forces, but specifically
whether there are hires or layoffs at period 2 relative to period 1.
Thus, given that some labor n1 was chosen at period 1, for which values of shock z2 is there
dismissal of workers in period 2 relative to period 1?
Let me define a critical value of z2, z2, separating a second-period where more labor is hired
(relative to n1) from a second-period with layoffs. This critical value is the realized second-period
shock such that the second period’s market price makes the industry choose the same number
of workers chosen at period 1; therefore, z2 = z∗1 .
Therefore, at the second period if z∗2 > z2, it is optimal to hire people n2 ≡ n(z∗2) > n1;
hereafter I will call shocks that follow this inequality positive shocks.
Otherwise, if z∗2 < z2 then it is optimal to dismiss workers until labor force n2 ≡ n(z∗2);
accordingly, hereafter I will call shocks that follow this inequality negative shocks.
Notice that first period labor has no effect into the second period profit, since there are no
upfront cost associated with hiring or dismissing labor. Now that first and second period labor
forces were determined, the modeling of the risk of default of payroll-backed loans can start.
2Since marginal cost is positivem there is a solution just if marginal revenue is positive, which happens all{v, nt} such that 1 + nt log(1− v) ≥ 0.
78
4 Modeling the risk of payroll-backed loans
At this section, I use the microeconomic model developed to determine the probability of
default and expected losses at period 2 of an individual payroll-backed loan that some worker
hired by the industrial sector took at period 1. Therefore, is an assessment of the future expected
losses at period 2, from the perspective of period 1, after first-period labor force were determined.
As explained before, in order to model the risk of losses from the default of some worker’s
payroll-backed loan, first one must determine the chance of this particular worker being un-
employed. Unemployment is caused by 2 independent events: the worker’s industry received a
negative shock and he is laid-off; second, he does some individual layoff-inducing mistake.
However, being unemployed is neither necessary nor sufficient for a default: the dismissed
worker must also be short on collateral, liquid assets such that he is not able to bear the loan
payments.
In order to model the situations described above, first a description of the dynamics of
workers’ assets flows is necessary. Let Ai be the end-of-period value of the i-th borrower assets,
described by the processes
Ai2 = Ai1 + IisiW (3)
Ai1 = Ai0 + siW (4)
where si is the worker’s saving share of the income and Iit an indicator function equal to one
if the worker was not dismissed at the beginning of period 2, zero otherwise. Ai0 is the initial
asset status of each worker that was hired at period 1, before joining the industry.
First equation, (3), gives second period’s end-of-period asset stock, formed by first period’s
asset stock plus savings from the salaries received during the second period, conditional on this
worker being employed. Accordingly, second equation, (4), gives first period’s end-of-period
asset stock, formed by the workers’ initial asset stock plus savings from the salaries received
during the first period.
Notice that although I continue the assumption that the workers are identical in terms of
their probability v of making a layoff-inducing error, I do not assume that their initial assets Ai0
are the same.
A consumer defaults over his payroll-backed loan if the value Ai of his assets at period 2 falls
below the contractual present value Bi of its payments:
Pr[worker defaults in period 2] ≡ Pr[Ai2 < Bi
2] (5)
In order to solve the above equation, I begin with the following assumption
Assumption: if assets from borrower i at period 1 are greater than his liabilities, expected
79
loss is zero. Thus, I assume full expected recovery of assets in the event of a default. Formally,
Pr[loss|Ai1 ≥ Bi
2] = 0.
This assumption allows me to focus on the loans for which losses are certain if there is
unemployment.
Therefore, for those loans that do not match the above criteria, expected losses depend on
the default probability which, in turn, is a function of the probability of unemployment by
idiosyncratic and aggregate shocks. There are three cases to be considered here3:
a) If z∗2 < z, then a negative shock happened and default might come for those workers chosen
to be laid-off.
b) If z∗2 < z,negative shock happened but the worker is not chosen to be laid-off; then, default
may happens due to idiosyncratic risk events, that is, workers’ mistakes.
c) If z∗2 > z, positive shock happened; then, default may happens due to idiosyncratic risk
events.
Thus, the probability of default on an individual loan is:
F (z2)
[EG
(n1 − n2(z2)
n1
)︸ ︷︷ ︸
Case a)
+
(1− EG
(n1 − n2(z2)
n1
))v︸ ︷︷ ︸
Case b)
]+ (1− F (z2)) v︸ ︷︷ ︸
Case c)
,(6)
where distribution G is F (z2|z2 < z2).
First brace represents Case a) above, that is, it is the expected probability of being fired
given an unemployment-inducing aggregate shock. It is based on the idea that the probability
of being fired, for any worker, is the number of dismissals (that is, n1 minus n2) over the total
number of workers from period 1. The expectation is over the possible realizations of the number
of dismissals.
Second brace represents Case b) above, that is, shock happened but was not unemployment-
inducing for this worker. Default comes from the probability of idiosyncratic unemployment,
v.
Third brace represents the case of a positive shock. Again, default comes from the probability
of idiosyncratic unemployment, v.Now is possible to have a complete assessment of the probability of default:
Pr[Ai2 < Bi
2] =
0 if Ai
1 ≥ Bi2;
F (z2)
[EG
(n1 − n2(z2)
n1
)+
(1− EG
(n1 − n2(z2)
n1
))v
]+ (1− F (z2)) v,
if Ai1 < Bi
2.
(7)
3I do not address the case where the consumer is not fired but his income drops such that he is not able to paythe loan because in Brazil employers are not allowed to decrease payroll of the employees.
80
5 Portfolio Risk
The previous analysis considered credit risk on individual loans. Now, I will use the reasoning
developed there to determine the expected losses on a portfolio of payroll-backed loans.
Consider a portfolio consisting of k ≤ n1 payroll-backed loans in equal value amounts, with
the same term T . Assume one loan for worker, thus I am dealing with loans from k workers.
Let Li be the gross loss (before recoveries) on the i-th loan, so that Li = 1 if the i-th worker
defaults and Li = 0 otherwise. Let L be the portfolio percentage gross loss, that is,
L =1
k
k∑i=1
Li. (8)
Considering just the k∗ workers that have Ai1 < Bi
24,
L∗ =1
k∗
k∗∑i=1
L∗i . (9)
I am interested in the portfolio’s default. Thus, I must consider losses from the workers
affected by an aggregate shock and from those that were affect by idiosyncratic shocks.
Notice that all events are mutually exclusive, you can’t be unemployed more than once. Also,
the probability of a worker being chosen for dismissal is, ex-ante, independent of another worker.Thus, the probability of a default up to r% of the portfolio means up to k∗r
100 workers default
in their loans. Therefore, k∗×m100 workers either got the aggregate negative shock:
PDN = Pr[negative shock and some worker defaults]
= F (z2)
[EG
(n1 − n2(z2)
n1
)+
(1− EG
(n1 − n2(z2)
n1
))v
](10)
or a positive one
Pr[positive shock and some worker defaults]
= (1− F (z2)) v.(11)
Thus, folows the paper’s first proposition:
Proposition 1. Consider a portfolio of k payroll-backed loans in equal value amounts, with the
same term T . The expected loss of the portfolio is given as follows:
• Consider those borrowers/workers i such that Ai1 ≥ Bi
2; then, Expected Loss is zero.
4I will use the asterisk (*) to mark any function defined over the subset of workers satisfying this inequality.
81
• Otherwise, the Probability of a Portfolio Loss less or equal to a share r is given by
Pr[L∗ ≤ r] = Pr[ k∗r or less workers default ]
= F (z2)B
(k∗r; k∗,
PDN
F (z2)
)+ (1− F (z2))B
(k∗r; k∗,
v
(1− F (z2))
) (12)
where PDN is given respectively by (10) and (11). B(k∗r; k∗, PDN
F (z2)
)is the cumulative
distribution function at position k∗r of a Binomial distribution with parameters k∗ andPDNF (z2)
; accordingly, B(k∗r; k∗, v
(1−F (z2)
)is the cumulative distribution function at position
k∗r of a Binomial distribution with parameters k∗ and v(1−F (z2)
:
B(k∗r; k∗, PDN) =k∗r∑i=0
(k∗
i
)(PDN
F (z2)
)i(1− PDN
F (z2)
)k∗−i(13)
B(k∗r; k∗, v) =
k∗r∑i=0
(k∗
i
)(v
1− F (z2)
)i(1− v
1− F (z2)
)k∗−i. (14)
In both binomials in (12) the number of trials is represented by the size of the portfolio and
”success” by the probability of default.
The use of a binomial distribution is due to way I chose to analyze default here: probability
of default in a percentage of the portfolio. Thus I must consider, for instance, out of k∗ workers,
the probability of one worker fired because of idiosyncratic unemployment and k∗ − 1 not fired,
or two workers fired and k∗ − 2 not, and so on until k∗r workers.
6 Comparative Statics
Previous sections showed formulas giving the riskiness of individual loans and of a portfolio
made up from payroll-backed loans. Here, I go further to analyze the sensitivity of the underlying
forces that drive default. Unless otherwise noticed, I will base the analysis on the formula for
an individual loan, equation (7), since the individual view is enough to assess the effects of the
main drivers of risk.
Default probabilities are driven by three variables: v, n1 and F (z). I describe their effects in
this sequence.
Proposition 2. The effects over the default risk from changes in the variables v, n1, everything
else constant (for each one) are:
(a) An increase in the idiosyncratic probability of unemployment, v, everything else constant,
increases the probability of default;
(b) An increase in first-period labor, n1, has ambiguous results. However, the lower are both n1
and the idiosyncratic probability of default, the more likely that an increase in labor force
will lead to an increase in the overall probability of default for an individual loan.
82
(c) A mean-preserving spread increases the probability of default from an aggregate negative
shock, everything else constant.
Proof: Appendix.
The variable whose effect is more difficult to describe is the labor force at the initial period,
n1. This is due to two opposing effects caused by any change in the labor force: first, any rise in
n1 increases output for a given productivity; however, it diminishes productivity, but this effect
is smaller the lower is v.
To capture the impact of this effect, consider a specific economic scenario: how the risk of
an individual payroll-backed loan changes during some period of downturn in the sector.
In terms of the model, the equivalent question is this:
Under which conditions the ocurrence of a negative shock in period 1 decreases the
probability of default at period 2?
Based on the effects described in Proposition 2, given that the shock at period one lowers
this period’s labor force, according to equation (A.1) the lower is v the more likely that this
decrease in n1 will lead to a decrease in z2, in turn lowering the probability of a second negative
shock.
Intuition is this:
1. First, there is the direct effect from the fall in n1 over z2 and over F (z2):
i. a fall in n1 decreases output but increases total productivity (because if there are fewer
workers, there are less things that can go wrong, see (1)) for a given output;
ii. the lower is v, the lower the impact of the decrease in n1 over total productivity and
thus the less likely that the increase in productivity compensates the other effect,
resulting in lower overall revenue;
iii. However, the lower are v and n1 after the shock, the higher the marginal revenue;
iv. Therefore, at second period, the equivalent marginal cost to induce the same choice of
labor from the first-period is higher than in the same cenario with a higher v;
v. Finally, for the given nominal salary, this implies a lower price, and thus a lower
threshold z2 (P ′ > 0).
2. Finally, the lower n1 decreases the probability of any remaining worker being chosen for
layoff at second-period, if another negative shock happens.
Next proposition summarizes this discussion:
Proposition 3. Consider a scenario where a negative aggregate shock happens at period one.
Then, the lower is the idiosincratic probability of default and the labor force at period one, the
smaller is the total probability of default at period 2.
83
7 Conclusion
This work presents a theoretical evaluation of the main characteristics that drive the risk of
credit losses on a portfolio of consumer payroll-backed loans. Consumer credit through payroll-
backed loans is one of the fastest growing credit lines in Brazil. Under reasonable assumptions, I
construct a microeconomic-based model of an industry whose workers are borrowers of payroll-
backed loans. Then, I derive a formula for the probability of default and expected losses for
both an individual loan and a portfolio of loans from the industry’s workers. Finally, the core
variables of the formula are subject to a sensibility analysis to determine their influence on the
risk of payroll-backed loans.
84
References
Brasil Economico, “Bradesco quer participacao maior do
consignado privado,” http://www.brasileconomico.com.br/noticias/
bradesco-quer-participacao-maior-do-consignado-privado_91701.html. Septem-
ber 24, 2010.
de Andrade, F.W.M. and L. Thomas, “Structural models in consumer credit,” European
Journal of Operational Research, 2007, 183 (3), 1569–1581.
Estado de Minas, “Credito consignado garante lucro recorde ao BMG,” http:
//www.em.com.br/app/noticia/economia/2010/01/26/internas_economia,145230/
credito-consignado-garante-lucro-recorde-ao-bmg.shtml. January 26, 2010.
Kremer, M., “The O-ring theory of economic development,” The Quarterly Journal of Eco-
nomics, 1993, 108 (3), 551–575.
Merton, R.C., “On the pricing of corporate debt: The risk structure of interest rates,” Journal
of finance, 1974, pp. 449–470.
Thomas, L.C., “Modelling the Credit Risk for Portfolios of Consumer Loans: Analogies with
corporate loan models,” Mathematics and Computers in Simulation, 2009, 79 (8), 2525–2534.
Thomas, LC, RW Oliver, and DJ Hand, “A survey of the issues in consumer credit mod-
elling research,” Journal of the Operational Research Society, 2005, 56 (9), 1006–1015.
85
Appendix
Proof of Proposition 2:
Item (a): See (7).
Item (b):
The proof follows by showing the effect of a change in one variable over the default equation,
everything else constant.
I start with the effects an increase in n1 has over the individual elements of the default
equation. After that, I given an example to integrate the whole effect.
• From (7), EG
(n1−n2(z2)
n1
)increases with an increase in n1, everything else constant.
• The threshold z2 is affected by n1, that is, the threshold probability of a negative shock
given an aggregate shoc, everything else constant. I obtain that
∂z2∂n1
T 0⇐⇒ 2 + n1 log (1− v) T 0 (A.1)
• Finally, if the threshold z2 is affected, so are both F (z2) and expectations over the truncated
distribution function G(z) (G = F (z|z < z2). I obtain the following effects:
– An increase in z2 increases the cumulative probability given by F (z2);
– An increase in z2 increases EG(z).
Now, an example to make all these effects more clear.
For instance, suppose both n1 and v are large, such that 2 + n1 log (1− v) < 0; then, an
increase in n1...
• increases the default probability via the following channels:
– the chance of a particular worker being chosen for layoff increases, because EG
(n1−n2(z2)
n1
)increases for a given n2 and a given distribution G;
• decreases the default probability via the following channels:
– the probability of an idiosyncratic shock (F (z2)), since z2 decreases;
– the expectation of n2(z2) decreases due to the changes in the truncated distribution
G(z2), caused by the decrease in z2
Item (c): In order to assess the effect of changes in the distribution of severity, F (zt), let me
examine the effect of a mean-preserving spread on F (z2). Call the new distribution F ′(z2). A
mean-preserving spread makes tails fatter; therefore, E(G′(z)) decreases, that is, the expected
negative shock increases because distribution G is distribution F truncated below: since there is
more mass in the left tail, the mean decreases.