The Pennsylvania State University
The Graduate School
ESSAYS IN INTERNATIONAL TRADE AND DEVELOPMENT
A Dissertation in
Economics
by
Yelena Sheveleva
© 2014 Yelena Sheveleva
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
August 2014
The dissertation of Yelena Sheveleva was reviewed and approved∗ by the following:
Kala Krishna
Professor of Economics and NBER and CES-IFO Research Associate
Dissertation Adviser
Chair of Committee
James Tybout
Professor of Economics
Stephen Ross Yeaple
Professor of Economics
Edward Jaenicke
Associate Professor of Agricultural Economics
Robert Marshall
Distinguished Professor of Economics
Head, Department of Economics
∗
Signatures are on file in the Graduate School.
ii
Abstract
This dissertation consists of three essays spanning the fields of international trade
and economic development. In the first essay, we ask why developing countries fail
to specialize in products in which they (at least potentially) have a comparative advantage? For example, farmers in land-poor developing countries overwhelmingly
produce staples rather than exotic fruits that command high prices. We propose
a simple model of trade and intermediation that shows how holdup resulting from
poor contracting environment can produce such an outcome. We use the model
to examine which polices can help ameliorate the problem, even when its cause
cannot be eliminated.
In the second and the third essays, we study how exporters introduce new
products into the export market. In the second essay, using information on the
universe of Chinese exporters to the US, we document a number of empirircal
facts that discipline economists’ undrstanding of dynamic aspects of multiproduct
exporters. In the third essay, we estimate a structural dynamic model of multiproduct exporting.
In Chapter 1, “Wheat or Strawberries? Intermediated Trade with
Limited Contracting,” we develop the model that provides a new explanation
as to why developing countries have agricultural productivity orders of magnitude
smaller than in the developing countries. We propose that due to contracting
frictions agricultural producers often specialize in staples in which they have a
comparative disadvantage, instead of specializing in fruits and vegetables which
they can grow efficiently and which command higher prices in the export markets.
While farmers can subsits on staples, farmers require services of the intermediaries
to deliver cash crops to the export market. When markets are thin intermediaries
hold the bulk of the bargaining power and offer a small price to the farmer for his
produce. Foreseeing the hold up farmers choose to specialize in the staples.
In the model, farmers can produce two types of goods: wheat and strawberries.
iii
Wheat is suitable for subsistence but farmers are inefficient in producing it. Farmers are efficient in making strawberries, but cannot subsist on it, and have to sell
them to an intermediary who makes profits by selling it at the world price. In a
frictionless world farmers would specialize in strawberries. Central to the model is
the inability of farmers and traders to contract ex-ante on a price. The absence of
enforceable contracts sets the stage for the classic hold up problem and precludes
negotiating the terms of trade prior to entry into production. We use a two period
model with a continuum of traders and farmers. In the first period, farmers decide whether to produce wheat or strawberries and intermediaries decide whether
to enter the business of intermediation. In the second period, farmers and traders
meet randomly and trade. Since meetings are random and traders do not know the
number of local competitors but do know how thick the market is, they can infer
the distribution of potential rivals and offer a price based on this information. In
other words, traders compete for the output of farmers in the first price auction.
As a result, some farmers fetch a high price for their strawberries; others fetch
a low price, or even fail to meet an intermediary. Farmers make the production
decision based on the expected price.
We solve the model and characterize all the possible equilibria as a function
of the primitive parameters. Of particular interest is the region in the parameter
space that yields multiple equilibria. In the good equilibrium, specialization occurs
according to comparative advantage and there is intermediation, while in the bad
equilibrium, there is no intermediation and the staple is produced. Our work
suggests that there may be some simple measures to ensure intermediation and
specialization according to comparative advantage even if the government is not
able to resolve the core issue, the underlying lack of enforceable contracts. A
temporary production subsidy or a marketing board that ensures a sufficiently
high minimum price to the farmer can help an economy remove the bad equilibrium
without intermediation.
This paper is closely related to the work of Antras and Costinot (2011). In
their paper they focus on the implications of intermediation for globalization in a
model that assumes that contracts between traders and producers are enforceable.
In contrast we study the implications of contractual failure on production choices
in a model of trade with intermediation.
In Chapter 2, “Multiproduct Exporters: Empirical Regularities,” we
use information on Chinese exporters to the US to document a number of empirical regularities regarding dynamic multiproduct exporter behaviour. First, we
confirm that scope and firm scale are positively associated. This suggests that
more productive firms select to produce more products. Furthermore we find empirical regularities that are consistent with firms facing uncertainty in the export
market. We explore the conjecture that firms learn about their potential in new
iv
export products trough exporting similar products. We find only tentative support
for this conjecture.
In chapter 3, “Multiproduct Exporters: Learning versus Knowing,”
we develop and estimate a structural model of multiproduct exporters based on
three empirical regularities documented using data on Chinese exporters. These
regularities are as follows: (1) multi-product exporters introduce their best-selling
products early; (2) more than 40% of the new products introduced by incumbent
exporters are dropped due to low sales within the first year; (3) for a firm, the
probability of introducing a new product is positively related to the survival and
success of the earlier products.
The first regularity is consistent with unobserved firm-product specific heterogeneity. The second suggests that both incumbents and new exporters face
uncertainty when they introduce new products. The third is consistent with firms
learning about their potential in an export market, i.e., their brand effect, as they
introduce new products. We develop a model which incorporates all of these features, and we estimate it structurally using data on Chinese exporters to the U.S.
in the plastics industry.
First, we find that known demand shocks play an important role in whether
producers enter the exporting market or not. Second, we find that it is important
to account for large attrition among new exporters including uncertainty about
the brand effect. When we let firms know their brand effect precisely, only those
with sufficiently high brand effects enter, and then the model cannot replicate
disproportionately large attrition of new products among new exporters. Third,
we find that while firms act consistently with learning about their brand effect, the
uncertainty that firms face in conjunction with introducing new products looms
large, and limits the extent to which learning affects incentives of firms to add
new products. Our counterfactuals show that the distribution of products among
the high brand effect firms only marginally first order stochastically dominates the
distribution for low brand effect firms.
Using our model we revisit the question of trade policy in the multiproduct
firm setting. We simulate a decrease in the cost of introducing new products for
firms. Our simulations suggest that in the presence of economies of scope and even
moderate learning effects, decreasing costs of introducing subsequent products can
make a significant contribution to increasing trade flows.
v
Contents
List of Figures
ix
List of Tables
xi
Acknowledgments
xiii
Chapter 1
Wheat or Strawberries? Intermediated Trade with Limited
Contracting (co-authored with Kala Krishna)
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Motivating The Modelling Assumptions . . . . . . . . . . . .
1.1.2 Relation To Existing Work . . . . . . . . . . . . . . . . . . .
1.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 The Meeting Process . . . . . . . . . . . . . . . . . . . . . .
1.2.2 The Trader’s problem . . . . . . . . . . . . . . . . . . . . . .
1.2.3 The Farmer’s Problem . . . . . . . . . . . . . . . . . . . . .
1.2.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Comparative Statics: Price And Intermediation As κ, R, α, P w Change
1.3.1 E(p) & κ . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 E(p) & α . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.3 E(p) & R . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.4 E(p) & P w . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Policy Implications . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Eliminating The Bad Equilibrium . . . . . . . . . . . . . . .
1.4.1.1 A Production Subsidy . . . . . . . . . . . . . . . .
1.4.1.2 An Export Board . . . . . . . . . . . . . . . . . . .
vi
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Reducing entry costs
board . . . . . . . .
1.5 Conclusion . . . . . . . . . . . . . . .
Bibliography . . . . . . . . . . . . . . . .
in the presence of an
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Appendix
1.A Appendix 1: The Expected Price . . . . . . . . . . . . . .
1.B Appendix 2: Risk Averse Farmers . . . . . . . . . . . . . .
1.B.0.4 Production Subsidy . . . . . . . . . . . .
1.B.0.4.1 Export Board: Reservation price
export
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Chapter 2
Multiproduct Exporters: Empirical Regularities (co-authored
with Kala Krishna and Hong Ma)
2.A Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.A.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . .
2.B Empirical Patterns . . . . . . . . . . . . . . . . . . . . . . . . . .
2.B.1 Data Description . . . . . . . . . . . . . . . . . . . . . . .
2.B.2 Growth Decomposition . . . . . . . . . . . . . . . . . . . .
2.B.2.1 Firm-Level Productivity . . . . . . . . . . . . . .
2.B.3 Dynamic Aspects: First-Year Effect For The New Products
2.B.4 Expansion Decisions . . . . . . . . . . . . . . . . . . . . .
2.C Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Chapter 3
Multiproduct Exporters: Learning versus Knowing (co-authored
with Kala Krishna)
73
3.A Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.A.1 Relation To The Literature . . . . . . . . . . . . . . . . . . 77
3.B Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.C Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.C.1 Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.C.2 Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.C.3 Timing & Information Set . . . . . . . . . . . . . . . . . . . 87
3.C.4 Decision To Continue Exporting Or Terminate A Product
Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.C.5 Introduction Of New Products . . . . . . . . . . . . . . . . . 90
3.D Estimation And Identification . . . . . . . . . . . . . . . . . . . . . 91
3.D.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
vii
3.D.2 Estimation Routine . . . . . . . . . . . . . . . . . . . . . .
3.D.3 Identification . . . . . . . . . . . . . . . . . . . . . . . . .
3.E Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.E.1 Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.E.2 Uncertainty, Experimentation, Selection Into Products, And
Their Consequences . . . . . . . . . . . . . . . . . . . . . .
3.E.2.1 Baseline Case . . . . . . . . . . . . . . . . . . . .
3.E.2.2 No Learning Case . . . . . . . . . . . . . . . . .
3.E.2.3 Full Information . . . . . . . . . . . . . . . . . .
3.E.2.4 No “Known” Demand Shocks . . . . . . . . . . .
3.E.2.5 Aggregate Magnitudes . . . . . . . . . . . . . . .
3.E.3 Costs Of Introducing New Products . . . . . . . . . . . . .
3.F Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix
3.A Tables . . . . . . . . . .
3.B Figures . . . . . . . . . .
3.C Empirical Regularities In
3.D Standard Errors . . . . .
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The Plastics Industry
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viii
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List of Figures
1.1 Types of equilibria. . . . . . . . . . . . . . . .
1.2 Equilibrium Types In The Parameter Space (κ
1.B.1Output response to a subsidy. . . . . . . . .
1.B.2Intermediation and the subsidy. . . . . . . .
1.B.3Utility as a function of the subsidy. . . . . .
1.B.4Response of output to R. . . . . . . . . . . .
1.B.5Response of intermediation to R. . . . . . . .
1.B.6Response of farmer’s utility to R. . . . . . . .
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23
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2.C.1Within firm sales distribution . . . . . . . . . . . . . . . . . . . . .
2.C.2Mean exporter scope and mean exporter scale . . . . . . . . . . . .
71
72
3.B.1Median monthly product sales vs. order of introduction . . . . . .
3.B.2Median monthly product sales vs. order of introduction conditional
on the number of months the product has been exported . . . . .
3.B.3Evolution of the variance of the firm’s beliefs about its brand effect
as a function of the number of products introduced . . . . . . . .
3.B.4Distribution of firms over the number of products conditional on
the brand effect. Baseline. (ψ = 0.2). Cohort of firms that entered
exporting in the same year, i.e., in year 1. . . . . . . . . . . . . .
3.B.5Distribution of firms over the number of products conditional on
the brand effect. Baseline. case (ψ = 0.89). Cohort of firms that
entered exporting in the same year, i.e., in year 1. . . . . . . . . .
3.B.6Distribution of firms over the number of products conditional on
the brand effect. No learning (ψ = 0.89). Cohort of firms that
entered exporting in the same year, i.e., in year 1. . . . . . . . . .
3.B.7Distribution of firms over the number of products conditional on
the brand effect. Full information (ψ = 0.89). Cohort of firms that
entered exporting in the same year, i.e., in year 1. . . . . . . . . .
3.B.8Share of products dropped relative to the total number of products
in the four scenarios. . . . . . . . . . . . . . . . . . . . . . . . . .
ix
. 113
. 114
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. 120
3.B.9No “known” demand shocks vs. baseline case. Distribution of firms
over the number of products. Cohort of firms that entered exporting
in the same year, i.e., in year 1. . . . . . . . . . . . . . . . . . . .
3.B.10 Aggregate sales of the cohort . . . . . . . . . . . . . . . . . . .
3.B.11 No learning vs. baseline scenarios (ψ = 0.89). Distribution of
firms over the number of products. Cohort of firms that entered
exporting in the same year. . . . . . . . . . . . . . . . . . . . . .
3.B.12 Quadrisemestre aggregate sales. Decreasing the cost of introducing new products. . . . . . . . . . . . . . . . . . . . . . . . . . .
x
. 121
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List of Tables
2.B.1Pairwise decomposition of the Chinese exports growth to the US
into contributions of entrants, exiters and continuing exporters .
2.B.2Pairwise decomposition of the continuing firms’ contribution to the
exports growth into contributions of new products, discontinued
products and growth of xisting products
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2.B.3Evolution of the number of products introduced in 2001 by continuing exporters . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.B.4Evolution of the average sales per product for products introduced
in 2001 by continuing exporters . . . . . . . . . . . . . . . . . . .
2.B.5Sample exit probabilities for new products conditional on the decile
of product’s initial sales and tenure . . . . . . . . . . . . . . . . .
2.B.6Sample probabilities of expansion in the same two digit HS group
conditional on the quintile of firm’s average sales per product . . .
2.B.7Sample probabilities for new products introduced by firms with
experience exporting other products in the same two digit HS group
and products intrduced by firms that have never exported products
in the same two digit HS group. . . . . . . . . . . . . . . . . . . .
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3.A.1Product monthly prices and its order of introduction for the plastics
industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.A.2Product monthly sales and its order of introduction (all firms excluding textiles) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.A.3Evolution of the number of products introduced in 2001 . . . . . . . 108
3.A.4Average monthly sales per product. Cohort of products introduced
in 2001. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.A.5Logit, FE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.A.6Data vs. simulated moments (Q.p (.) stands for pth percentile of variable (.)) 110
3.A.7Data vs. Simulated Moments (Continued) . . . . . . . . . . . . . . 111
3.A.8Learning and Demand Parameters. . . . . . . . . . . . . . . . . . . 111
3.A.9Cost of production. . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
xi
3.A.10....Estimates of parameters governing introduction of new products:
Economies of Scope. . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.C.1Product monthly sales and its order of introduction. Plastics industry. 125
3.C.2Evolution of the number of products introduced in 2002 by firms
that started exporting in 2001. Sample includes only firms that
operated in the plastics industry in 2001-2004. HS 4-digit category. 126
3.C.3Average monthly sales per product among products introduced in
2002 by firms that have started exporting in 2001. Sample includes
only firms that operated in the plastics industry in 2001-2004. HS
4-digit category. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
3.C.4Evolution of the number of products introduced in the first half of
2002 by firms that started exporting in the first half of 2001. The
sample includes only firms that operated in the plastics industry in
2001-2004. HS-4 digit category. . . . . . . . . . . . . . . . . . . . . 127
3.C.5Logit, FE. Plastics industry. . . . . . . . . . . . . . . . . . . . . . . 128
xii
Acknowledgments
I would not have been able to successfully complete this dissertation without the
help of countless individuals. And at the risk of missing many persons who played
a part, directly or indirectly, I will say thanks to a few persons here. Obviously,
this list is by no means exhaustive.
I would like to extend my sincere appreciation to Professor Kala Krishna, Professor Stephen Yeaple and Professor James Tybout, who provided invaluable support, direction, and advise during my PhD. Thanks to Professor Neil Wallace,
Professor Ruilin Zhou for their assistance of all types. Thanks to my family,
friends and fellow PhD students for their support and encouragement.
xiii
Chapter
1
Wheat or Strawberries?
Intermediated Trade with Limited
Contracting (co-authored with Kala
Krishna)
1.1
Introduction
There is a large literature that documents that labour productivity in developing
countries is orders of magnitude smaller than in developed ones, and that this is
more so in agriculture than in manufacturing. For example, Caselli (2005) shows
that aggregate productivity at the 90th percentile of income relative to the 10th
percentile is 22, while this ratio for agriculture is 45. Despite this, most developing
countries tend to be predominantly agricultural economies.
These differences in agricultural productivity could arise from differences in
efficiencies conditional on the set of products made and/or composition effects.
In other words, farmers in developing countries could be allocating the bulk of
their labor to the production of capital intensive staples, and shun away from
labor intensive exotic fruits and vegetables. Capital intensive staples are produced
efficiently on large swathes of land using machinery, while labor intensive fruits and
vegetables could be efficiently produced in the developing countries and exported.
2
Lagakos and Waugh, 2013 show that for maize, rice, and wheat the ratio of output
per worker in the top and bottom 10% of countries is 146, 90, and 83 respectively.
The analogous ratio for agricultural sector as a whole is just 45. Yet, farmers in
developing countries persist in producing staples like wheat, corn or maize, rather
than exotic produce, e.g. strawberries, that are highly valued in urban areas or
export markets.
To explain this situation we develop a model of agricultural trade with intermediation where contracts on price cannot be enforced, as often is the case in the
developing countries. In our set up, farmers in the developing world have the technology to produce both staples and exotic produce. Farmers choose to produce
staples because they can survive on their wheat if the need arises, while they cannot survive on strawberries. Not only are strawberries nutritionally inadequate,
but they are perishable, and have to be sold quickly. This gives intermediaries
bargaining power when markets are thin, and makes farmers reluctant to grow
strawberries. This in turn makes intermediaries reluctant to enter, resulting in the
expected thin markets materializing.
The environment in a developing country is very different from that in a developed one. A number of factors limit a farmer’s ability to transport his strawberries to an urban or export location himself: roads are poor, trucks are expensive,
and credit markets are poorly developed. Hence a farmer must rely on intermediaries (traders) to deliver his produce.1 At the same time, traders are scarce,
irregular in their arrivals, and unreliable, as contracts are poorly enforced.
Central to our story is the inability of farmers and traders to contract ex ante
on price. The absence of enforceable contracts precludes negotiating the terms of
trade prior to production and sets the stage for the classic hold up problem. If
contracts were enforceable, traders and farmers could search for matches in the
beginning of the period and then make production decisions after bargaining over
the surplus from the match. The price of the good would be determined by the
1
There is considerable evidence that intermediaries play a critical role in connecting the farmer
to formal markets as we assume. A number of papers have documented that farmers tend to sell
through intermediaries at the farm gate unless they are very close to the market. See Fafchamp
and Vargas Hill (2005). Their interactions with such intermediaries are often not repeated. See
Fafchamp and Vargas Hill (2008) for evidence on Ghanian coffee growers and buyers. They
document that most farmers sell at the farm gate to itinerant traders, known as ddebe boys, who
are usually not known to them.
3
farmers outside option: producing the staple good.
Here we consider an environment where such contracts cannot be made as the
trader has an incentive to defect from such arrangements ex post. This environment produces the central coordination failure we study: farmers would choose to
produce strawberries if they could count on a buyer and buyers would put up the
sunk costs of entry if there were farmers making strawberries. However, depending
on what agents believe, we may have the opposite happen in equilibrium.2
In other words, if the product is produced by many agents and there are many
intermediaries, the market functions well and the developing country can specialize
according to comparative advantage. Though improvements in the contracting
environment can alleviate the holdup problem, the required judicial and political
reforms to do this are hard and time consuming to implement. We therefore take
as given the problematic contracting environment in the less developed countries.
In the following section we develop a simple model that captures essential features of the environment in which agricultural producers (and producers more
generally) operate in the less developed countries. Our model is designed to evaluate the effects of the various policy options that might be open to a government
or an NGO.
In our model farmers can produce two goods that differ along three dimensions:
the farmer’s ability to consume them, the farmer’s efficiency in producing them,
and the kind of market in which they are traded. The first good is what we have
been calling wheat, is a staple that has a local market. Farmer can subsist on
wheat alone though they are relatively inefficient at making it, and with perfect
markets, would not choose to do so. The second good, that we have been calling
strawberries, is a non staple and farmers cannot subsist on strawberries. In addition, strawberries are perishable so the farmer cannot just store them and wait for
a trader to show up.
In the developing world, the perishability of goods is accentuated by poor
storage conditions that farmers face, as well as the lack of access to credit. Even
2
Other reasons why agricultural exports from developing countries are problematic have to do
with phyto-sanitary requirements. For example, Indian mangoes can not be exported to the US
without being irradiated, which was infeasible prior to the nuclear deal struck during the Bush
Administration. In the same vein, Australia and New Zealand, with their strict phytosanitary
requirements, are difficult export markets to crack, especially for developing countries. These
laws can also be abused. See Engel, 2001 for some illustrations.
4
goods that are potentially storable can deteriorate rapidly in the presence of vermin
and the absence of refrigeration.3 Moreover, as agents in developing countries live
from hand to mouth, they do not have the luxury of waiting for a better offer,
even if one is likely. Interest rates from informal sources are very high, rates of
20% a month are not uncommon, and formal credit is very hard to obtain. All of
this heightens the “perishability” of the non staple good.
Traders, unlike farmers, have access to a Walrasian market and can sell the
good at the given world price. Traders incur a sunk cost of entry, which captures
their transportation and opportunity costs. Farmers and traders cannot contract
on price ex-ante. They meet randomly and there is free entry of intermediaries.
When a farmer and a trader meet, the trader offers the farmer a price and the
farmer accepts or rejects it. When the trader makes the offer he does not know
the number of rival traders who have visited a given farmer or the prices they have
offered. However, a trader does know how likely each outcome is and makes the
decisions based on the probability distribution over competitors’ price offers. The
trader who offers the highest price to the farmer gets the good. Of course, there
may be no traders at a farmer’s doorstep, in which case the farmer exercises his
outside option, which may be zero.
We solve the model and characterize all the possible equilibria as a function of
the four primitive parameters: productivity in the export good, price of the export
good in the world and the local markets, and the sunk cost of intermediation. Of
particular interest is the region in parameter space with multiple equilibria. In the
“good” equilibrium farmers specialize in strawberries, which they produce more
efficiently than the staple, and there is intermediation. In the “bad” equilibrium,
there is no intermediation and the staple is produced.
When the price the farmer can get in the local market for the export good
(his outside option) is low, beliefs about the level of intermediation determine
the equilibrium output of each commodity. Economies with low cost of entry
for traders can successfully overcome the matching frictions and specialize in the
export good regardless of the farmer’s outside option. The outside option plays a
relatively more important role when entry costs for traders are high.
3
Estimates suggest that as much as 22% of wheat production is lost to vermin in India. For
fresh fruit and vegetables, the loss may be over 50%. See for example, “Farmers Plagued by Post
Harvest Food Losses”, August 31, 2011, The Gleaner, Kingston, Jamaica.
5
Our work suggests that there are simple policies to ensure intermediation and
specialization according to comparative advantage even if the government is not
able to resolve the core issue: the underlying lack of enforceable contracts. When
primitive parameters are such that there are multiple equilibria: a temporary production subsidy, or a marketing board that ensures a sufficiently high minimum
price to the farmer can remove the bad equilibrium without intermediation.
4
A
number of policies improve social welfare of an economy in a “good” equilibrium,
when intermediation and specialization already present. For example, our work
suggests a new reason for promoting extension programs that aim to improve agricultural productivity. Not only do they directly raise farmers output and income,
but by encouraging intermediation, they increase competition among traders so
that farmers obtain a higher expected price for their produce. Our results also
have implications for the efficient operation of a marketing board. We show that
when intermediaries are more efficient when the marketing board, social welfare
is maximized when a marketing board that makes zero profits. When marketing board is more efficient than the intermediaries, a marketing board that is the
sole buyer that pays the producer price high enough to drive out the intermediaries yields the highest level of welfare. Thus we make a case for having marketing
boards who set the farmer’s price as high as possible on the basis of overall welfare,
not distributional concerns.
Our work also has a number of results that shed new light on some classic
questions. We provide an alternative explanation as to why increases in world
prices may not feed back fully into prices obtained by farmers5 , especially in the
short term.
Finally, our results suggest that the lack of a local market for strawberries is
particularly important in economies with high entry costs for traders, i.e. communities with poor road conditions or landlocked economies. In the economies
with easy access to farmers, the value of the outside option for farmers plays a
small role as competition among traders is sufficient to sustain a high expected
producer price.
4
In the presence of risk aversion, as shown in the Appendix, these policies have an extra bang
as there are additional production effects that amplify their effects.
5
This has been noted for coffee farmers by Fafchamps and Hill, 2008.
6
1.1.1
Motivating The Modelling Assumptions
In the model we make a number of assumptions that drive our results. In particular
we assume that intermediaries play an essential role in delivering strawberries from
the farmer to the world market. Furthermore we also assume away the possibility
of enforcing contracts through repeated interactions. In this section we provide
some evidence in support of these assumtions.
Fafchamps, Gabre-Madhin and Minten, 2005 provide some support for our
model structure. They document that market liberalization in poor countries has
resulted in multiple layers of intermediaries. There are a large number of small
market participants and a few large ones. Large traders specialize in wholesaling
and rarely sell retail. They rarely buy directly from producers, buying instead
from many small itinerant traders who specialize in buying from producers and
selling to wholesale traders or organized markets. These small itinerant traders
who mediate between the organized market and small producers are what we call
intermediaries in our model. They are large in total number, but small in terms
of their presence in any particular neighborhood.
Fafchamps and Hill, 2005 document that farmers face a decision whether to
sell at the farm gate or to travel to the nearest centralized market to sell the good.
Farmers are less likely to travel to the local market and more likely to sell to the
local trader when the nearest market is far or the cost of transportation is high.
Similarly Osborne, 2005 finds that in poorer and more remote areas, traders have
more market power than in markets that are close to big trading centers. In our
model we allow the presence of a local market for the export good in the form of
an “outside option” for the farmer in his interactions with the trader. In other
words, the farmer will find it worthwhile to sell at his door only if the trader offers
a price at least as good as the price he can obtain in the local market, which may
be zero if such a market does not exist.
A historical example of the holdup problem that we focus on in the paper, and
one solution to it, can be found in Kranton and Swamy, 2008. They argue that the
Opium Agency, initiated by the East India Company (EIC) in India, had a similar
problem and recognized it. As the agency was the sole procurer of opium it had
monopsony power. In order to prevent the agents of the EIC from behaving opportunistically with respect to the farmers, which would have reduced the incentives
7
to produce opium on their part, the Opium Agency expended significant resources
monitoring their own agents. Kranton and Swamy, 2008 also assume there are no
relational contracts possible and for similar reasons.
The historical role of dairy cooperatives in India, e.g., Amul, is another anecdote
that supports our model. In India prior to Operation Flood, milk was hard to come
by in urban areas. Farmers were reluctant to produce milk because of the risk of
spoilage and the lack of distribution channels for their milk. Urban consumers
would buy milk from small scale “milkmen” who transported their milk doorto-door on bicycles without refrigeration or quality control. The addition of (not
very clean) water to the milk was a common practice. Milk had to be boiled before
being safe for consumption and was not homogenized and processed as in developed
countries. Dairy cooperatives that took hold in India during the Operation Flood
shared rents with the farmers by giving them a “fair” price for their milk. They
provided the refrigeration, quality control and marketing services for milk and
milk products, like yogurt and cheese, needed to serve urban consumers, as well
as extension-services to improve productivity. Their success produced a flood of
milk and was a key part of the “white revolution” in India. India went from being
a milk deficient nation in the 1970s to being the worlds largest milk producer in
2011.6
An important feature of our work is that we do not allow for the possibility of repeated interaction between farmers and traders. There is considerable uncertainty
in developing countries: weather variability, political uncertainty and disease, all
of which make people focus on the short term so that the future is highly discounted. Such considerations call for the use of static models that exclude repeated
interactions and relational contracting.
The long term relations and reputation have received a lot of attention in recent years they been shown to play an important role in terms of the contractual
arrangements in established markets. Banerjee and Duflo, 2000 focus on the role
played by repeated interactions in the software industry in India, Macchiavello
and Morjaria, 2012 consider this in the context of rose exports from Kenya, while
McMillan and Woodruff, 1999 look at credit relations between firms in Vietman.
6
See Delgado, Narrod and Tiongco, 2003 for more on how the white revolution occurred in
India.
8
Antras and Foley, 2011 show that prepayment for orders is more common when
relational capital is low, i.e., at the start of a relationship. Greif, 2005 uses historical examples to study how contractual problems were resolved among Magrabi
traders. All these are established markets. However, the operation of established
markets is not the focus of our work. Rather, we ask why certain markets do not
come into being when there is no repeated interaction.
1.1.2
Relation To Existing Work
Although this paper is cast as a model of agricultural trade, it relates to a number
of other areas in development.
The big push types of stories as in Nurkse, 1966 and Rosenstein-Rodan, 1943
and more recently Murphy, Shleifer and Vishny, 1989 emphasize that a firm’s
decision whether to industrialize or not depends on its expectation of what other
firms will do. In particular, they emphasize the role of demand externalities. While
industrializing for any one firm is unprofitable, if all firms industrialized simultaneously increased profits of the firms would generate greater aggregate demand
making industrialization profitable for each individual firm.
In contrast to the “big push” idea is the unbalanced growth literature. This
suggests that producing some goods is more growth enhancing than producing others and that coordination failures may result in a sub optimal outcome. Hirschman,
1988, suggests that sectors with greater linkages (both backward and forward) are
likely to be more growth enhancing, and that there may be a role for government
to intervene. This literature tends to focus on complementarities that result in
coordination failure that may create a role for government intervention. Instead,
we focus on the contracting imperfections that result in the coordination failures
that make farmers choose to produce low priced staples.
Hausmann and Rodrik, 2003 and Hausmann, Hwang and Rodrik, 2007 portray
development as a process of self discovery. In their framework entrepreneurs do
not know which products a country can produce efficiently until someone tries it.
Trials involve uncertainty and are costly. Moreover, successful products can be
replicated so a successful innovator will soon face tight competition so that the
cost is private while the benefit is public. As a result, too little discovery occurs.
9
Our model does not rely on such informational frictions to explain the lack of
investment in non traditional products. With contractual frictions farmers know
about their options but choose not to avail of them because non traditional product
markets are thin and holdup is likely.
Our work is also related to Antras and Costinot, 1993 which introduces intermediation into a two-good two-country Ricardian framework. Their focus is
on the implications of globalization in the presence of intermediation.
They
find that integration of the commodity markets produces gains for both countries,
while integration of matching markets (markets where intermediaries and producers/farmers meet) leads to welfare losses if in the country where intermediaries
are less efficient and have smaller bargaining power. In their model producers and
intermediaries form matches and bargain over the surplus with exogenously given
bargaining power and an endogenous outside option.
In contrast in our model,
the terms of exchange between farmers and traders is endogenously determined:
traders who show up at the farm gate participate in a first price auction. If the
market is thick, there is more competition in this auction. Our focus is on the
implications of search frictions and lack of enforceable contracts on specialization
patterns with a view to policy. For example, our results suggest that extension programs that improve productivity of the intermediated good will result in farmers
gaining both because they are more productive, and because greater productivity
improves intermediation so that they also get more for what they make when their
productivity rises.
Our paper is also related to a small literature focusing on the price transmission
mechanism in agricultural trade from retail market to the producer price and more
broadly on the gap between producer and consumer prices. Fafchamps and Hill,
2008 analyze transmission of the export coffee price to the Uganda farmer who
sells at the farm gate. Their analysis is based on original data collected by the
authors on all coffee exporters as well as on random samples of coffee traders and
producers in Uganda. They find that when the international price rises, domestic
prices follow suit, except for the price paid to producers, which rises by far less than
the international price. They argue that the cause of this incomplete pass through
is the lack of information about world price movements on the part of the farmer.
World price increases attract more traders into the market which dissipates the
10
rents, and due to farmers’ ignorance of the world price, there is little or no benefit
to them. There is no direct test of the information friction hypotheses in their
model. It is important to understand why farmer prices are low: if they are low
because of trade frictions, then providing information to farmers, say by posting
the world price in a public place, would not help raise the price they obtain or affect
the extent of pass through. This is exactly what is found in Mitra, Mookherjee,
Torero and Visaria, 2012. However, this is not to say that greater cell phone usage,
if it reduced the cost to a trader of visiting a farmer, and so led to a flood of trader
entry, would not raise the price offered to farmers.
We proceed as follows. Section 1 lays out the model. Section 2 constructs the
equilibrium when farmers are risk neutral. Section 3 looks at the efficacy of various
policy options. Three kinds of policies are considered: decreasing the cost of entry
for traders, a production subsidy to farmers, and raising the outside option for the
farmers closer to the world price. Section 4 concludes. Extensions to risk averse
farmers and details of proofs are in the Appendix.
1.2
The Model
The modelling framework builds on Burdett and Mortensen, 1998 and Galenianos
and Kircher, 2008. The economy consists of a continuum of farmers of measure
one and a continuum of traders whose measure is determined endogenously in
equilibrium. Farmers can produce the staple or the perishable good. It takes one
unit of labor to produce one unit of the staple while each unit of labor produces
α units of the perishable good. Each farmer is endowed with one unit of labor.
All farmers are ex-ante identical and of measure zero so that their actions do not
affect the equilibrium outcome. We begin by assuming that farmers and traders
are risk neutral. This causes farmers to (generically) specialize in either the export
or the staple good. Adding risk aversion on the side of the farmers, as we do in
the Appendix, moves us away from this bang-bang solution as farmers diversify
their output. This makes the supply of the export and staple good a continuous
function of the model’s parameters.
Farmers can consume the staple themselves or sell it at a fixed price which
is normalized to unity. The perishable good has to be exchanged for the staple
11
in a Walrasian market (i.e. the world market which has a single market clearing
price) to which farmers have no direct access. To exchange the perishable good
farmers have to meet with a trader. The role of the trader in this model is to
deliver the good from the farmer to the Walrasian market. The objective of the
trader is to maximize his expected profit. There is an infinite number of potential
traders who can become actual traders by paying a sunk entry cost κ. Each trader
who paid the sunk cost randomly meets a single farmer. It is possible that the
farmer is approached by more than one trader. The trader at the time he makes
the offer does not observe how many traders he is competing with. However, he
knows the ratio of traders to farmers in the market and so can infer the probability
distribution over the number of potential competitors. The good is then allocated
to a trader through the first price auction mechanism: in other words, the trader
with the highest bid gets the product.
The model is static. Farmers and traders simultaneously choose their strategies.
The strategies are played and the outcomes are revealed. The farmer chooses the
labor, l ∈ [0, 1], that he allocates to the production of the export good (1 − l is
allocated to the production of the subsistence good). The strategy of a potential
trader consists of a binary decision to enter or not, and the price distribution to
offer conditional on entry. All agents take the strategies of all other traders and
farmers as given.
Traders meet farmers in a random manner. A trader can approach only one
farmer. If the farmer is producing the perishable good, the trader offers a price
for the output and if his price is the highest offered to the farmer, he obtains the
output at the price bid. If the farmer is producing the staple the trader goes away
empty handed. Each trader neither observes the bid of any of the other trader nor
observes the number of competing traders present. Hence every trader makes the
decision about the price based on the expected number of rivals and their bidding
strategies.
1.2.1
The Meeting Process
We assume that farmers and traders meet randomly according to a Poisson Process.
This process arises naturally when traders arbitrarily meet one out of N farmers
12
producing for export and is convenient in modelling coordination frictions that
result when there are many small market participants.
Let Pk be the probability that a trader who randomly arrives at the gate of
one of the farmers in the continuum meets k rivals, where λ =
1
N
is the probability
that a given trader visits this farmer:
Pk =
T −1 k
λ (1 − λ)T −1−k .
k
Denote the ratio of traders to farmers by θ =
T
.
N
Rewriting Pk in terms of θ
and λ yields
Pk
T −1 1 k
1
=
( ) (1 − )T −1−k
k
N
N
θ
θ
(T − 1)!
( )k (1 − )T −1−k
=
(T − 1 − k)!k! T
T
=
θ T
(T − 1)!
θ −(1+k)
(θ) k
(1
−
)
(1
−
)
(T − 1 − k)!T k k!
T
T
Now let T and N go to infinity keeping θ constant. Then λ =
1
N
goes to zero
while θ is a finite number.
Thus,
lim Pk
T,N →∞
−(1+k)
θk
(T − 1)!
θ T
θ
= lim
(1 − )
(1 − )
T,N →∞ k! (T − 1 − k)!T k
T
T
k
θ −θ
=
e .
k!
This follows from
(T − 1)(T − 2).....(T − k)
1
k
(T − 1)!
= lim
= lim (1− )...(1− ) = 1
k
k
T →∞ (T − 1 − k)!T
T →∞
T →∞
T
T
T
lim
and
−(1+k)
θ
lim (1 − )
= 1.
T →∞
T
Also, by definition, e = lim (1 + T1 )T so that
T →∞
13
θ T
lim (1 − ) = e−θ .
T →∞
T
Thus, for a sufficiently large number of market participants the probability that
a trader meets k rivals, or Pk , is given by
1.2.2
θk −θ
e .
k!
The Trader’s problem
The trader’s problem consists of two parts. For a given level of market intermediation, that is, for the given number of traders and producers, a potential trader
needs to decide whether to enter the intermediation market or not. Second, given
that he has entered, he has to decide what price to post. As usual, we need to
solve this backwards. First, consider the problem of optimally choosing the price
to post, given the number of traders in the market.
As all traders are ex-ante identical, we limit ourselves to considering only symmetric equilibria. The trader knows the probability that a given p is the highest
posted price in a meeting with k rivals is given by [F (p)]k . Thus, if he meets k
rivals and offers p, he will be the highest bidder with probability [F (p)]k . As discussed earlier, for large T and N, the number of rivals in a meeting is given by the
Poisson process. Hence the probability that a trader offering price p is the highest
bidder involves summing over the number of rivals the trader could potentially
meet:
∞
X
k
Pk [F (p)]
=
k=0
∞
X
e−θ
θk
[F (p)]k
k!
e−θ
[θF (p)]k
.
k!
k=0
=
∞
X
k=0
−θ θF (p)
= e e
= e−θ(1−F (p))
If a trader offering p wins, he makes (pw − p) αl∗ where l∗ is the labor devoted to
making the export good by a farmer. Thus, the expected profits of a trader offering
price p, conditional on the farmer making the export good, is the product of the
margin from obtaining αl∗ units of the specialized good at price p is (P w − p)αl∗
14
and the probability of actually being the highest bidder in the meeting e−θ(1−F (p)) .7
π(p) = (P w − p) αl∗ e−θ(1−F (p)) .
For traders to choose to mix over prices in equilibrium any price in the support
of F (p) must be the same. Thus, π(p) = π, for each p in the support.
Let R be the price which a farmer can obtain if he does not meet a trader. This
may be the price offered, for example, by the local canning factory. It may even
be zero. This defines the farmer’s outside option regardless of how many traders
he meets. It can also be interpreted as the price net of costs obtained by a farmer
travelling to the local market. The value of R puts a lower bound on the price
that the farmer will accept for his output.
Proposition 1. In the symmetric mixed strategy equilibrium, traders mix over the
interval (R, pmax ) according to F (p) where
F (p) = 0 f or p < R
1
Pw − R
=
ln( w
) f or R ≤ p ≤ pmax ,
θ
P −p
and expected equilibrium profits equal (P w − R)αl∗ e−θ .
Proof. First, we show that the support starts at R, has no gaps and the distribution
function is continuous, i.e., the density function has no mass points. Since no
farmer will accept a price below R, the support of F (·) cannot include any such
points. Suppose the support of F (·) starts at p > R. Then a trader who bids a
price in the interval R, p will only win if there are no other traders, i.e., with
probability P0 = e−θ . His expected profit if he wins is
π(p) = (P w − p)αl∗ e−θ ,
which is decreasing in p. Thus, the trader would be better off charging R, or any
price in R, p than offering p which contradicts the assumption that p is in the
support of the mixed strategy equilibrium.
7
Note that if there is a per unit cost of transport, c, that has to be paid in addition to any
sunk costs of visiting the market, we can do so by replacing P w by P w − c in what follows.
15
Next, we establish that there are no gaps in the support of the distribution.
Nor are there any atoms anywhere in the interior or at the lower bound of the
support of the distribution. There may be a mass point at the top of the support.
Let us first rule out gaps in the support of the distribution. Suppose there is
a gap in the support of F (·): no one bids in the interval (p0 , p00 ). If there is no
mass point at p00 , then a trader who posts a price p∗ ∈ (p0 , p00 ) will be better off
00
than bidding p , as the probability of winning does not decrease, but the profit
margin rises. Hence, there are no gaps in the support unless there is a mass point
at p00 . Such a mass point would cause a jump down in profits at prices just below
p00 , and validate the hole in the price distribution posited. Can we rule out such
atoms at p00 ? Yes, we can. If there is an atom at p00 , then bidding p00 + ε causes
a discrete jump in trader’s profits as he increases the offer price only marginally,
but this increases his probability of winning discretely.
The same argument rules out atoms at any pb in the interior of the support of
the distribution or at R: bidding p = pb+ε causes a discrete jump in trader’s profits
as he increases the offer price only marginally, but this increases his probability
of winning discretely. In equilibrium all prices in the support must yield the same
profits, hence such mass points cannot occur. They cannot even occur at the upper
end of the support. As will be confirmed later, the upper end of the distribution
support is given by pmax < P w . If there were a mass point at pmax , raising p slightly
above pmax must raise profits which rules out a mass point at pmax .
Next we can use the property of the equality of payoffs at every point of the
support to obtain the explicit expression for the cumulative distribution of bids,
F (p). Equating the expected profits at an arbitrary price p and expected profits
at the lower end of the support R , i.e., setting π(p) = π(R), we can solve for the
bidding function of the trader as a function of world price (P w ), market thickness
(θ), and R, the farmer’s outside option.
(P w − p)e−θ(1−F (p)) = (P w − R)e−θ
(P w − R)
e θF (p) =
(P w − p)
1
Pw − R
F (p) =
ln( w
)
θ
P −p
16
Setting the obtained expression for the probability distribution to equal unity
at p = pmax gives
F (pmax ) = 1 =
1
Pw − R
ln( w
).
θ
P − pmax
(1.2.1)
Solving for pmax from equation (1.2.1) we obtain
eθ = (
Pw − R
)
P w − pmax
and
pmax = P w (1 − e−θ ) + e−θ R.
Note that eθ = 1 + θ +
θ2
2!
+
θ3
...
3!
> 1 for any θ > 0. Thus, 0 < e−θ < 1. The
upper bound of the support is thus a convex combination of the world price and the
outside option of the farmer which is his reservation price. The higher θ, the level
of intermediation the closer pmax is to P w . The lower bound of the support is fixed
by the farmer’s reservation price, while the upper bound is increasing in the world
price of the specialized good, but lies strictly below it. pmax is increasing in the
prevalent level of intermediation (θ), and the farmers’ outside option. Expected
profits of the trader (which are equal to profits at p = R) in equilibrium are
π(p) = (P w − R)αl∗ e−θ .
These expected profits are clearly increasing in P w , and decreasing in R and θ.
Now that we can evaluate traders’ expected profits prior to entry ( given P w ,
R and θ) we can consider the decision regarding whether or not to enter.
Proposition 2. The free entry level of intermediation is
θ = 0 if l∗ < lmin
(P w − R)αl∗
θ = ln(
) if l∗ ≥ lmin .
κ
Proof. There are an infinite number of potential traders who can enter if the expected traders profits from entry exceed the sunk cost of entry. Entry of traders
17
will continue until the benefits from entry exactly equal the costs:
π(p) = κ.
Since profits are the same at every point in the support, without loss of generality
we can solve for the level of intermediation by equating profits at the lower end of
the support to the cost of entry.:
(P w − R)αl∗ e−θ = κ.
Solving for θ gives
θ = ln(
(P w − R)αl∗
).
κ
Thus, the equilibrium level of intermediation is increasing in the world price and
the output of the export good. It is decreasing in the sunk cost and the farmer’s
outside option. Note that θ > 0 if and only if
ln(
(P w − R)αl∗
) > 0,
κ
or
l∗ > lmin =
κ
.
− R)
α(P w
Proposition 2 says that positive levels of intermediation prevail when the output
of the export good αl∗ is higher than the minimum level denoted by αlmin =
κ
(P w −R)
which ensures that the profits made from trading the good exceed the fixed cost of
doing so. Equilibrium intensity of intermediation is higher when the world price
is higher, the farmers’ reservation price is lower, or the fixed cost of entry into
intermediation is lower.
1.2.3
The Farmer’s Problem
Having characterized the traders’ problem, we now describe the problem of a risk
neutral farmer and consider the implications of the model for policy in this setting.
With risk neutrality, farmers choose to produce the crop that gives them higher
18
expected profits. Only when the two crops give the same level of expected profits
are they willing to diversify. However, this case is inherently unstable: should
farmers make more of the non staple, more traders would enter and farmers would
be strictly better off making the non staple. Thus, looking forward, when we
consider the market equilibrium, taking into consideration the behavior of both
traders and farmers there will be only two possible levels of output of the export
good α or 0. This implies that the level of intermediation can take on only two
values as well.8
(P w − R)α
) if (P w − R)α ≥ κ with l∗ = 1
κ
θ = 0 if (P w − R)α < κ with l∗ = 0
θ = ln(
(1.2.2)
Let Gk (p) = [F (p)]k be the cumulative density function of the highest price
offered when the farmer meets k traders. Each farmer has a linear utility function
defined over the units of the numeraire (staple good). If the farmer puts l units of
labor into the non staple good and gets price p, with 1 − l units going to produce
the staple good, he makes
π(l, p) = αlp + (1 − l)
= (αp − 1) l + 1.
The farmer maximizes the expected value of his profits as he is risk neutral. As
the farmer consumes only the numeraire good, his indirect utility is the same as
his income.
Let E(p) be the price farmers expect to fetch for the export good. Note that
if αE(p) − 1 > 0, the farmer will produce only the non staple.
Lemma 1. As the number of traders and farmer goes to ∞, the probability that a
farmer meets k traders, or Qk , is also given by
θk −θ
e .
k!
Proof. With a finite number of traders (denoted by T ) in the market the probability of the farmer having k traders arrive at his door is the probability that exactly
8
The assumption that farmer’s are risk neutral is relaxed in appendix 1.B.
19
k out of T agents arrive at his door which is given by
T k
Qk =
λ (1 − λ)T −k .
k
Denote the ratio of traders to farmers by θ =
T
.
N
Rewriting Qk in terms of θ and
λ yields
Qk
T
1
1
=
( )k (1 − )T −k
k N
N
(T )!
θ
θ
=
( )k (1 − )T −k
(T − k)!k! T
T
θ
θ
(T )!
(θ) k
(1 − )T (1 − )−(k) .
=
k
(T − k)!T k!
T
T
Thus
lim Qk
T,N →∞
−(k)
θk
(T )!
θ T
θ
= lim
(1 − )
(1 − )
T,N →∞ k! (T − k)!T k
T
T
k
θ −θ
=
e .
k!
Farmers take the level of intermediation (θ), the pricing strategy of the traders
F (·), and the meeting process {Qk }∞
k=0 as given.
Lemma 2. Given the level of intermediation, θ, the expected price is given by
E(p) =
∞
X
k=0
w
pZmax
Qk
pdGk (p)
R
−θ
= P − e (P w − R)(1 + θ)
= P w 1 − e−θ (1 + θ) + Re−θ (1 + θ)
(1.2.3)
As 0 < e−θ (1 + θ) < 1, 9 the expected price is a convex combination of the world
price and R.
Proof. As this proof involves some calculations, it is placed in the Appendix.
9 θ
e > 1 + θ so
1
1+θ
> e−θ or 1 > e−θ (1 + θ) .
20
The expected producer price increases with the world price (P w ), level of intermediation θ, and the producer reservation price (R).
Note that
∂E(p)
= 1 − e−θ (1 + θ) > 0 for θ > 0,
∂P w
which follows from e−θ (1 + θ) < 1, which is the same as eθ > 1 + θ. This in turn
holds as by definition, eθ = 1 +
θ
1!
+
θ2
2!
+ ... > 1 + θ for any θ > 0. Also,
∂E(p)
= e−θ (1 + θ) > 0.
∂R
Finally,
∂E(p)
= (P w − R)e−θ θ > 0.
∂θ
Hence, there is partial pass through of the world price and R into the price the
farmers obtain on average. The extent of this pass through depends on the thickness of market as both e−θ (1 + θ) and e−θ are decreasing in θ.
1.2.4
Equilibrium
In the Nash equilibrium, each farmer chooses what to produce so as to maximize
his profits, each active trader is choosing what price (or distribution of prices) to
offer, all potential traders are indifferent between becoming active or not, and the
decisions of these agents are mutually consistent.
An equilibrium consists of three objects (θ, F (p), l(θ)). θ is the level of intermediation, the equilibrium ratio of traders to farmers. F (p), is the distribution of
prices for the non staple good that the profit maximizing trader offers in equilibrium; and l(θ) is the profit maximizing output of the export good for the farmer.
So far, we have shown that the following properties of the equilibrium objects hold:
1. Output of the Non-Staple Good Per Farmer:
l(E(p)) = 1 if αE(p) ≥ 1
= 0 if αE(p) < 1
21
where
E(p) = P w (1 − e−θ (1 + θ)) + Re−θ (1 + θ).
(1.2.4)
An increase in θ raises the expected price as it reduces the weight on R. As θ
rises and E(p) exceeds
1
,
α
farmers specialize in the production of the expor good
and l(.) = 1. Let l(E(p|θ))) ≡ l(θ). Then, we can write the farmers’ best response
function above as:
l(θ) = 1 f or θ ≥ θmin .
l(θ) = 0 f or θ < θmin
(1.2.5)
where θmin is the solution to E(p|θ) = α1 . It is easy to see that θmin is unaffected
by κ and decreases as α rises.
2. Equilibrium level of intermediation:
(P w − R)αl(.) κ
θ = ln
> 0 if l(.) > lmin =
w
κ
α(P − R)
θ = 0 if l(.) < lmin
(1.2.6)
θ(l) is zero for l < lmin . If farmers produce less than lmin the expected profits
from intermediating a trade in the non-staple fall short of covering the sunk cost
of entry. For values of l greater than lmin θ(.) rises with l10 . Note that lmin depends
on the primitive parameters κ, R, α, P w . lmin moves together with κ and R and
in the opposite direction to α, P w .
3. Distribution of Price Offers:
The distribution of prices in equilibrium is:
F (p) =
1
Pw − R
ln( w
) for p ∈ [R, pmax ]
θ
P −p
where pmax = P w (1 − e−θ ) + e−θ R . As θ rises, there are more traders relative to
farmers, and the upper end of the distribution rises. The price distribution with
10
We already know that l(.) is going to be either zero or unity. If no farmer makes the
specialized good, then no traders will enter and θ = 0. Given no traders will enter, no farmers
will make the specialized good. Thus, this is always an equilibrium.
22
higher values of θ first order stochastically dominates distributions with the lower
ones. This makes intuitive sense as more competition to buy from the farmers will
raise prices.
Equations (1.2.5) and (1.2.6) above give us the equilibrium. There are four possible
equilibria, all depicted in Figure 1.1. Figures 1.1a and 1.1b show the equilibrium
outcomes when R < 1/α and farmers specialize in the staple unless there is enough
intermediation. In Figures 1.1c and 1.1d, R > 1/α, so that farmers will produce
even if there is no intermediation.
In Figure 1.1a there is a unique equilibrium with complete specialization in the
staple good: l(.) and θ(.) have only one intersection at the origin. Here θmin > θ(1),
and
l(.) and θ(.) have only one intersection at the origin. This outcome occurs
when it is not optimal to produce the export good because P w is low, α is low
(agriculture is inefficient) and κ, the cost of entry for traders, is high. As a result,
the level of intermediation implied by the amount of export good produced by
farmers falls short of the level of intermediation necessary to induce farmers to
produce the corresponding amount of the output.
Multiple equilibria, depicted in Figure 1.1b, arise when θmin < θ(1) and R < α1 .
In Figure 1.1b the farmers best response function, l(θ), and traders’ free entry
condition, θ(l), intersect three times implying three equilibria. Two of these are
stable.
If no farmer makes the export good, then no traders will enter and θ = 0.
Given no traders will enter, no farmers will make the export good. This is always
a stable equilibrium. The other stable equilibrium is where farmers produce only
the export good,
23
l
l
6
6
1
1
l(θ)
θ(l)
θ(l)
l(θ)
lmin
lmin
θmin
0
θ
-
(a) Unique Equilibrium (N)
θmin
0
-
θ
(b) Unique Equilibrium (M)
l
l
lmin6
1
l(θ)
l(θ)
6
1
θ(l)
θ(l)
lmin
-
0
θ
(c) Unique Equilibrium (P-NI)
0
-
θ
(d) Unique Equilibrium (P-I)
Figure 1.1: Types of equilibria.
l(.) = 1, and given this, the number of intermediaries who enter is enough for
the farmers to choose to produce only the export good.
The equilibrium where farmers produce both goods is not stable. Farmers do
not care how much of each good they produce as they are indifferent between
them. Just enough traders enter to make them indifferent, and given indifference,
farmers produce just enough to keep entry at this indifference level. But this is
a fragile equilibrium: small perturbations will move the equilibrium to one of the
two stable equilibria.
When R >
1
,
α
it is profitable to make the specialized good even if there are
no intermediaries. Figures 1.1c and 1.1d show configurations of equilibria with
complete specialization in the export good with and without intermediation. Thus,
24
l(θ) = 1 for all θ ≥ 0, and the unique equilibrium is thus at θ(l = 1). If lmin < 1,
then θ(l = 1) > 0 and the unique equilibrium is such that intermediation occurs
and the export good is made by all farmers as in Figure 1.1c. If lmin > 1, then
θ(l = 1) equals zero and in equilibrium, θ = 0 and l = 1 as in Figure 1.1c. lmin > 1
if R and/or κ is high, i.e., if
(P w
κ
> 1.
− R)α
Figure 1.2 depicts the possible equilibrium outcomes for different values taken
by the primitive parameters R (the outside option) and κ (cost of entry), given
values for the world price (P w ) and productivity in the export good (α).
When R <
1
α
and κ is relatively low, whether or not farmers produce the export
good depends on their beliefs about the prevailing level of intermediation. In region
M multiplicity of equilibria in the sense of Figure 1.1b is endemic. When κ becomes
so high that farmers find it unprofitable to enter in the unique equilibrium none of
the export good will be made. This is the semicircular region in Figure 1.2 labelled
N for no production. This situation corresponds to Figure 1.1a. The boundary
between region M and N is defined by θ(1) = θmin .11
When R is above the cutoff level of α1 , the farmer’s outside option for the export
good is high enough so that the equilibrium with no production of the export good
is eliminated. However, when R > P w − ακ , the expected profits of intermediaries
fall short of the entry cost: no traders enter and the export good is sold to the
canning factory which pays R. This corresponds to the region which in Figure 1.2 is
labelled P −N I for Production and No Intermediation. Only in the triangular area,
labelled P − I for Production and Intermediation, is there a unique equilibrium
where the specialized good is produced and intermediaries connect farmers to the
world market. This case is depicted in Figure 1.1c.12
11
Recall that θmin is defined implicitly by E(p/θmin ) =
1
α
and that θ(1) = ln
(P w −R)α
κ
. Using
the expression for E(P ) from equation (1.2.4) gives this boundary as the R and κ such that:
w
w
κ
(P − R)α
κ
(P − R)α
1
P w (1 −
)(1
+
ln
))
+
R
(1
+
ln
)= .
(P w − R)α
κ
(P w − R)α
κ
α
12
We assume P w is exogenously given as the home country is small. However, if the home
country is large, its entry into production would reduce the world price which in turn would make
production and intermediation less likely as the regions in Figure 5 are conditional on the world
price.
25
R
6
P-NI
P-I
'
1/α
M
N
-
0
κ
Figure 1.2: Equilibrium Types In The Parameter Space (κ & R)
The moral here is that too much of a good thing may be bad. Raising R, up
to a point, helps as it removes the bad equilibrium where none of the export good
is made. But raising it beyond a point destroys intermediation. Having some idea
now of when intermediation can connect farmers to the world market, we proceed
to consider the effects of various parameter changes on the outcomes.
1.3
Comparative Statics: Price And Intermediation As κ, R, α, P w Change
We have shown that depending on the values of the primitive parameters there may
be multiple or unique equilibria. How small changes in the primitive parameters
impact the equilibrium outcomes, i.e. level of intermediation and producer price,
depends on what region these parameters belong to and what equilibrium we are
in. Since there is no production in region N, and there is no intermediation in
region P-NI, the comparative statics we consider are relevant only in regions P-I
and M. We will then build on these results to better understand how policy could
help overcome the coordination failure that leads to sub optimal outcomes.
As might be expected, an increase in the world price (P w ), productivity (α),
and the reservation price (R) as well as a decrease in the entry cost (κ) lead to an
26
increase in the expected producer price in equilibrium. An increase in the world
price, for example, raises the expected producer price directly (as the expected
price is a convex combination of the world and reservation price with the weight
on the world price increasing in the level of intermediation) and also raises the
weight put on the world price as intermediation also rises. A fall in κ raises entry
and improves intermediation, thereby increasing the weight on P w and raising the
expected price. In our setting, an improvement in agricultural productivity (α),
not only raises farmers incomes directly, but also encourages more intermediation
and via this effect raises the expected price farmers obtain. The direct effect of the
increase in R on the producer price dominates the indirect effect of discouraging
intermediation.
1.3.1
E(p) & κ
Consider, for example, the effect of a decrease in the cost of entry for intermediaries,
κ. For a given mass of traders, expected profits will turn positive as κ falls, which
will induce entry. This in turn will raise the competition at the farmers gate and
raise the expected price paid by intermediaries. Entry will occur until the rise in
this expected price just compensates for the lower κ. Thus, a fall in the entry costs
raises the level of intermediation in equilibrium as well as the equilibrium expected
producer price.
This can be seen in Figures 1.1a and 1.1b, where a lower κ will shift the
θ(l) function to the right so that the equilibrium level of intermediation increases
θ(l = 1). Then using the expression for expected price from equation (1.2.3)
E(p) = P w (1 − e−θ (1 + θ)) + Re−θ (1 + θ),
the higher θ will reduce e−θ (1 + θ), the weight on R, thereby raising the expected
price which is a convex combination of R and P w .
More formally,
w
d ln( (P −R)α
)
dθ(l = 1)
1
κ
=
=− <0
dκ
dκ
κ
dE(p|θ(l = 1))
dE(p) dθ
=
dκ
dθ dκ
(1.3.1)
27
1
= (P − R)e θ −
κ
θ
= − <0
α
−θ
w
as θ(1) = ln( (P
1.3.2
w −R)αl(.)
κ
) so that e−θ =
κ
(P w −R)α
(1.3.2)
in the intermediation equilibrium.
E(p) & α
What about the effect of an increase in the productivity of the export good? At
the existing level of intermediation with an increase in α each trader will make
positive expected profits making entry for new intermediaries profitable, which in
turn will raise the expected price and bring profits back in line with entry costs.
13
In Figures 1.1a and 1.1b the l(θ) curve will shift to the left as farmers will be
willing to make the export good at a lower level of intermediation, θ(l) will move
to the right. In an equilibrium where risk-neutral farmers specialize in the export
good only the shift in θ(l) affects the equilibrium outcomes: θ rises, raising E(p).
In our model of agricultural trade with intermediation, productivity and producer price move in the same direction. Much of the literature focuses on the adverse
price effects of a productivity increase in competitive markets where the fear would
be that greater productivity would raise supply and depress the equilibrium price.
In our model, the world price is fixed so that this is not an issue. Farmers thus
gain when productivity improves, not only because they are more productive but
because increased competition among intermediaries raises the producer expected
price.
Remark 1. Note, this implies that extension programs that aim to improve agricultural productivity not only will directly raise farmers output and income, but
by encouraging intermediation they will let them obtain a higher expected price for
their produce.
More formally,
dE(p|θ(l = 1))
=
dα
13
κ ln
α(P w −R)
κ
α2
> 0 for θ > 0.
It will also affect the definitions of the regions in Figure 3.
(1.3.3)
28
1.3.3
E(p) & R
In Figures 1.1a and 1.1b, an increase in the local price of the export good, R will
shift the l(θ) curve to the left as farmers will be willing to make the export good
at a lower level of intermediation. However, θ(l) will also move to the left. Only
the latter affects the equilibrium where l = 1, and thus the equilibrium θ falls.
While the rise in R raises E(p) directly, the fall in θ reduces competition among
intermediaries and reduces E(p).
The following expresses the producer price in terms of the model primitives
(using θ(1) = ln( (P
w −R)αl(.)
κ
), l(.) = 1, and equation (1.2.3)).
E(p) = P w − (P w − R) e−θ (1 + θ)
w
κ
(P − R)α
w
= P −
1 + ln
.
α
κ
(1.3.4)
Differentiating E(p) with respect to R :
κ
1
dE(p)
=
= e−θ > 0.
w
dR
α (P − R)
There are two effects of an increase in R on E(P ) : directly via R and indirectly via
the effect of R on θ. The direct effect raises E(p), while the indirect one reduces
it14 . According to equation 1.3.4 the former dominates the latter, and the expected
price goes up together with R.
Remark 2. Note that this suggests that policies which provide a sure market for
farmers could be a double edged sword: while they increase the reservation price,
they discourage direct intermediation.
Also note that
d2 E(p)
dRdκ
is positive. This is noteworthy. Raising R and reducing
κ both raise E(p). However, marginal effect of an increase in R is larger when κ
is large. This suggests that reducing κ and raising R are substitutes: using one
policy instrument makes the other weaker. Also noteworthy is the fact that changes
in the outside option have little effect on the expected price when entry cost for
traders is relatively low. This suggests that the lack of a local market for the
14
A higher R reduces θ, which raises the chance of not being matched, and lowers expected
price.
29
good is important in economies with high entry costs for traders, i.e. communities
with poor road conditions or landlocked economies. In the economies with easy
access to farmers, the value of the outside option or the local market for the export
good plays a small role as competition among traders is sufficient to sustain a high
expected producer price.
1.3.4
E(p) & P w
In Figures 1.1a and 1.1b, an increase in P w will shift the θ(l) to the right, raising the
equilibrium θ. A rise in P w raises E(p) directly, and a higher θ further reinforces
the direct effect. Doing the comparative statics more formally,
dE(p|θ(l = 1))
=
dP w
h
d Pw −
κ
α
1 + ln
(P w −R)α
κ
i
dP w
κ
1
α
= 1− w
α (P −R)α κ
κ
κ
= 1− w
(P − R)α
= 1 − e−θ
(1.3.5)
> 0 for θ > 0,
as (P w − R)α = κeθ from the intermediary free entry condition.
The effect of changes in the world price deserves special attention as it connects
the model to observable the outcomes. Empirical studies (i.e. Fafchamps and Hill,
2008) find that the pass through of the changes in world commodity price to the
producer prices is only partial, because when world price goes up new traders enter
and dissipate the profits increasing the search cost. Our model on the contrary
predicts that entry of new intermediaries in response to changes in world price
of the export good is needed to ensure price transmission. We find that in the
long run when the measure of traders adjusts to the change in the world price the
elasticity of expected producer price with respect to world price is greater than 1.
In the short run the elasticity may be less than unity if the farmer’s outside option
is positive. When R is high, intermediation is low, and a small change in the world
30
price has little effect on the price obtained by farmers.
Proposition 3. (i) In the long run, the elasticity of the expected price farmers
obtain with respect to the world price is more than that in the short run. (ii) The
short run elasticity is less than unity for R > 0, and equals unity for R = 0. As the
long run elasticity exceeds the short run one, the long run elasticity exceeds unity
for low enough values of R. (iii) A unit increase in the world price never fully
passes through into the expected price. In the long run dE(p)
= 1 − e−θ < 1, and
dP w
in the short run
∂E(p)
∂P w
= (1 − e−θ (1 + θ)) < 1 so that the extent of pass through in
both the long and the short run are positively related to the level of intermediation.
Proof. The long run elasticity is given by
dE(p) P w
=
dP w E(p)
w
∂e−θ (1 + θ) ∂θ
P
(1 − e (1 + θ)) − (P − R)
w
∂θ
∂P
E(p)
w
P
−θ
w
−θ
−θ ∂θ
(1 − e (1 + θ)) − (P − R) (−e (1 + θ) + e ) w
∂P
E(p)
w
P
(1 − e−θ (1 + θ)) − (−e−θ θ)
E(p)
w
−θ
1−e
P
.
E(p)
=
=
=
=
w
∂E(p) ∂E(p) ∂θ
P
+
w
w
∂P
∂θ ∂P
E(p)
−θ
w
The short run elasticity is given by
∂E(p) P w
Pw
−θ
=
(1
−
e
(1
+
θ))
∂P w E(p)
E(p)
(1 − e−θ (1 + θ))P w
=
P w (1 − e−θ (1 + θ)) + Re−θ (1 + θ)
,
which is unity when R = 0. It is less than unity when R is positive.
The long run elasticity is more than the short run one as
∂E(p) ∂θ
∂θ ∂P w
> 0. When
the world price rises, intermediaries enter and this drives up the price obtained by
farmers.
31
1.4
Policy Implications
In our model the interaction of several market frictions can prevent the efficient
allocation of resources. In fact, the economy can end up specializing in the commodity in which it has a comparative disadvantage. In what follows, we take the
existence of these frictions as given and look at the efficacy of alternative policy
instruments and their welfare implications. We consider a production subsidy,
policies reducing intermediation costs, lump sum taxes and transfers, and the creation of a cooperative that guarantees to purchase from a farmer at a fixed price,
i.e. R.
Here we focus on policies that are applicable when primitive parameters are
such that multiple equilibria are endemic, i.e. region M in Figure 1.1. We ask how
one can move economy from the bad equilibrium, where farmers sub-optimally
specialize in the staple good, to the good equilibrium, where strawberries are produced for export. Both a production subsidy and a marketing board that buys
strawberries eliminate multiplicity of equilibria by making specialization in the
export good the dominant strategy for the farmers. However, as we show below,
they have different implications for the level of intermediation, producer prices and
welfare.
1.4.1
Eliminating The Bad Equilibrium
If we can ensure that it is a dominant strategy for the farmer to produce the export
good, then the bad equilibrium is eliminated. We could raise the farmer’s pay-offs
from making the export good by offering a production subsidy or a price support
in the form of an export board willing to pay a sufficiently high fixed price for the
export good.
1.4.1.1
A Production Subsidy
Consider a production subsidy per unit of output of the export good. As domestic
agents consume only the staple, welfare is the income of farmers (from production
and the production subsidy) plus that of traders and net government revenue,
NGR.
W = αE(p)l∗ + αsl∗ + (1 − l∗ ) + (π(p) − κ) + N GR
32
Traders make zero expected profits so that their contribution to welfare, π(p)−κ, is
zero. NGR equals expenditure on the subsidy or −αsl∗ . The subsidy is a transfer
between farmers and the government so that it washes out in welfare in terms of
its direct effect. Thus, welfare boils down to the earnings of farmers, net of the
production subsidy.
W = αE(p)l∗ + (1 − l∗ )
where p denotes the price obtained by the farmer.
Suppose the government offers a per unit subsidy slightly above s =
1
α
1
,
α
say
+ . Then farmers will specialize in the export good as even with no traders,
farmers’ expected income from making the export good exceeds that from making
the staple: α( α1 + ) > 1. Knowing that farmers will produce the export good,
traders will enter. Farmers who are approached by traders sell to the highest
bidder, while farmers who meet no traders receive for their output R ≥ 0.
It is easy to see that in Figure 1.1b, which depicts the type of equilibrium
that arises in region with multiple equilibria (M ) in Figure 1.2 withR < α1 , such
a subsidy will create a unique equilibrium with all farmers producing the export
good.
When such a subsidy induces a move from the bad equilibrium to good
equilibrium welfare increases as αE(p) > 1.
What about the other regions? In region N, farmers have a comparative advantage in the staple and specialize in it. Hence subsidizing production of strawberries
reduces overall welfare. If the economy is in P − I or P − N I farmers always
specialize in the strawberries and the production subsidy will just create a transfer
between the government and the farmers with no real effects as the production
subsidy has no effect on intermediation in our model due to inelastic supply of
labor and risk neutrality.
Proposition 4. A per unit production subsidy greater than or equal to 1/α can
move the equilibrium to the one with intermediation and raise welfare if the economy is in region M. It will lower welfare if the economy is in region N , and have
no effect otherwise.
33
1.4.1.2
An Export Board
What would be the effect of an export board that commits to purchase the output
of the export good from the farmer at a fixed price in the economy where multiple
equilibria persist? If the board offers a price less than α1 , multiplicity remains. The
board will have no effect when the expport good is not produced. When farmers
produce the export good and sell it to the intermediaries, introduction of an export
board will lower the level of intermediation but still raise the expected producer
price. An export board that pays a price R ≥
1
α
per unit of the export good
ensures that farmers specialize in the export good and eliminates the multiplicity
of equilibria.15
With an export board in place, the social welfare function becomes
(
W =
αE(p) + α(P g − R)e−θ if α(P w − R) > κ, i.e. θ > 0
αP g if α(P w − R) ≤ κ, i.e. θ = 0.
(1.4.1)
When intermediation is profitable, i.e. α(P w − R) > κ, the social welfare is the
sum of the expected earnings of a farmer through meeting a trader or selling to the
board, αE(p) and the board’s profits when the farmer sells to it, α(P g − R)e−θ .16
When intermediation is not profitable, i.e. α(P w − R) ≤ κ, social welfare is
determined by revenues of the export board and is constant at αP g . Welfare
increases in R as long as the equilibrium level of intermediation is positive. This
can be seen by differentiating the welfare function with respect to R.
dW
dE(p)
−θ
g
−θ dθ
=α
− e − (P − R)e
.
dR
dR
dR
(1.4.2)
Substituting for
dE(p)
= e−θ
dR
in 1.4.2 gives
15
In contrast, recall that a production subsidy had no effect on intermediation.
Recall that a farmer only sells to the board if there is no match with a trader which occurs
with probability e−θ .
16
34
dW
dR
dθ
= α −(P − R)e
dR
g
(P − R) −θ
= α
e
(P w − R)
κ(P g − R)
=
> 0 if P g − R > 0
w
2
(P − R)
where we use the fact that e−θ =
−θ
g
(1.4.3)
κ
.
α(P w −R)
The optimal value of R depends whether the board or the intermediaries are
more efficient. We say that intermediaries are more efficient than the board when
α(P w −P g ) > κ, or the resources that are spent on intermediation are less than the
loss in revenue from selling the export good at P g rather than P w (at the country
level). If the export board is more efficient than the intermediaries, α(P w −P g ) > κ,
the optimal price at which the board should purchase from the farmer is R = P g . If
intermediaries are more efficient, α(P w − P g ) ≤ κ, then any R at or above P w − ακ
is optimal.
To see this, note that as R rises, the level of intermediation falls, while social
welfare increases. When R increases to the point that κ ≤ α(P w − R) intermediation becomes unprofitable and welfare is constant at αP g . If intermediation
remains positive at R = P g then according to 1.4.3 the optimal price for the export board to offer to the farmers is P g . If intermediation becomes unprofitable
before R reaches P g , i.e., α(P w − P g ) ≤ κ, then welfare is no longer affected by R,
so it is optimal to set R at or above P w −
κ
α
which eliminates intermediation and
implies welfare of αP g .
Proposition 5. If α (P w − P g ) > κ, it is optimal to set R = P g . If α (P w − P g ) ≤
κ, then any R at or above P w −
κ
α
is optimal.
What is the economic intuition behind this result? When α (P w − P g ) ≤ κ
intermediaries waste more resources than the board and hence it is socially optimal
for all farmers to sell their output to the board. When intermediaries are more
efficient than the board, α (P w − P g ) > κ, profits of intermediaries are dissipated
by entry, while the positive profits of the board when P g − R > 0 are included in
the social welfare. Hence we want to maximize the joint income of farmers and
35
the board. An increase in R raises the earnings of the farmer by e−θ and reduces
w
g
the profits of the board by e−θ PP w−P
. When R is less than P g the marginal cost
−R
to the board is smaller than the marginal increase in the producer price. When R
is exactly equal to P g , the marginal increase in the producer price is exactly equal
to the decrease in the revenues of the board. Hence it is optimal to set R equal to
P g as long as there is intermediation.
1.4.1.3
Reducing entry costs in the presence of an export board
While social welfare increases in R, the price the export board pays to the farmer,
we know that a higher value of R reduces entry of intermediaries which in turn
puts negative pressure on the producer price. In this section we consider the effect
of changing the cost of entry for intermediaries in the presense of the export board.
We ask if a reduction in the cost of entry for intermediaries, exogenous or facilitated
by the government improves welfare.
In equilibrium where the export good is produced, a reduction in the cost of
intermediation increases competition among traders and increases the producer
price. Reducing the cost of intermediation does not affect the decision of farmers
to produce, and therefore does not eliminate the no production equilibrium. When
no export good is produced, no intermediaries enter.
In the presence of an export board and s positive level of itemediation, welfare
for a unit mass of farmers is given by 1.4.1. Formally, for an exogenous change in
κ the change in welfare is given by:
dW
dκ
dE(p)
de−θ
= α
+ α(P g − R)
dκ
dκ
(P g − R)
= −θ + w
(P − R)
w
−θ(P − R) + (P g − R)
=
(P w − R)
Pg − R
= −θ + w
.
P −R
(1.4.4)
A reduction in the intermediary cost of entry, κ, has two effects on social welfare.
First, it increases the income of farmers. Second, the probability of not meeting a
trader and selling to the board, e−θ , falls together with κ. When P g − R > 0 this
36
reduces the profits of the board. In general, which of the two effects dominates
depends on the prevailing level of intermediation, as seen in 1.4.4. When R is set
optimally the effect of an exogenous decrease in κ is unequivocal. When the board
sets R optimally at P g profits of the export board are exactly zero and no longer
play a role in welfare. Then a decrease in κ is welfare improving.
If intermediation is not efficient, i.e., α(P w − P g ) > κ, then R is set so that
intermediation vanishes and θ is zero. In this case, κ does not affect welfare. This
is summarized in the next proposition.
Proposition 6 summarizes the discussion:
Proposition 6. If government is less efficient than intermediaries, and sets R
optimally, there will be intermediation, and an exogenous fall in entry costs raises
welfare. If government is more efficient than intermediaries, and sets R optimally,
there will be no intermediation and an exogenous fall in entry costs has no effect
on welfare.
If the entry cost is reduced by a government subsidy rather than being exogenous, then we need to add the cost of doing so to welfare:
(
W =
αE(p) + α(P g − R)e−θ − sθ if α(P w − R) > κ , i.e.θ > 0
αP g if α(P w − R) ≤ κ , i.e. θ = 0.
(1.4.5)
A decrease in the cost of intermediation, whether subsidized or exogenous, has
an ambigous effect on the joint income of the farmers and the export board. When
intermediaries are more efficient than the board and the value of R is set at P g ,
a decrease in the cost of intermediation improves the income of the farmers. The
expenditure on the subsidy always decrease the welfare. To deteermine if there
exists a welfare maximizing tax or subsidy scheme differentiate 1.4.5 with respect
to s.
Let κ = κ0 − s where κ0 is the initial cost of intermediation and s is the amount
of the subsidy. Then
dκ
ds
= −1 and
dθ dκ
d (sθ)
= θ+s
ds
ds
dκ
s
= θ+
.
κ
37
Thus, increasing the subsidy to entry costs reduces entry costs but raises expenditure on the subsidy. From the equation (1.4.5) and using equation (1.3.2) gives
dW
ds
dE(p) dκ
de−θ dθ dκ d(sθ)
+ α(P g − R)
−
dκ ds
dθ dκ ds
ds
dE(p)
dθ
s
α
(−1) + α(P g − R)(−e−θ ) (−1) − (θ + )
dκ
dκ
κ
−θ
e
s
θ
− (θ + )
−α(− ) − α(P g − R)
α
κ
κ
−θ
e
s
−α(P g − R)
−
κ
κ
Pg − R
s
− .
− w
P −R κ
= α
=
=
=
=
(1.4.6)
A subsidy cannot raise welfare as long as (P g − R) > 0.
At the optimum,
dW
ds
= 0. Setting κ = κ0 − s, and solving for the optimal s
from equation (1.4.7) the optimal level of the subsidy, s∗ is given by 1.4.7.
s∗ = −
κ0 (P g − R)
.
[P w − P g ]
(1.4.7)
When intemediaries are more efficient than the board, and R is set optimally at
P g it is optimal to neither subsidize or tax the entry of intermediaries, s∗ = 0.
When R is not chosen optimally and the board makes positive profits, it is optimal
to tax the entry of intermediaires. In this case intermediaries do not internalize
the effect of their entry on the profits of the board, and the tax on intermediaries
corrects the externality. Proposition 7 summarizes the results.
Proposition 7. If R is not set optimally, then it is optimal to tax entry when
intermediairies are more efficient than the board because there is excessive entry.
If R is set optimally, there is no case for an entry tax or subsidy.
1.5
Conclusion
Our model is related to the literature that attributes the low incomes of the developing countries to specializing in the wrong goods (i.e. Hausmann and Rodrik,
2003. However it is different from this strand of literature in that the root cause of
38
the problem is not that producers are ignorant about the profitability of the goods
they have no experience in. Rather, the root cause is the lack of enforceable contracts that hamper intermediation. Our model provides an alternative rationale as
to why developing countries specialize in the traditional goods despite the presence
of more lucrative options. In our model we present how, even if farmers are more
efficient in producing an export good, they may not specialize in it. The lack of
enforceable contracts between intermediaries and producers gives rise to multiple
equilibria. When a large number of people produce the intermediated good, markets function reasonably well. Otherwise the economy ends up specializing in the
staple good instead of the export good.
Our model reveals a number of novel results. First it suggests that there may
be some simple solutions to these problems even if the government is not able
to resolve the core issue (the lack of enforceable contracts) responsible for the
problem. A temporary production subsidy, or a marketing board that ensures a
minimum price to the farmer can help an economy remove the bad equilibrium
without intermediation.17 However, these intiatives need not raise welfare.
There are also polices that can raise welfare when intermediation occurs. Our
work also suggests a new reason for promoting agricultural extension programs that
aim to improve agricultural productivity. Not only do they directly raise farmers
output and income, but by encouraging intermediation they increase competition
among traders so that the farmer obtains a higher expected price for his produce.
The results we obtain also shed light on why increases in world prices may not feed
back fully into prices obtained by farmers (as has been noted for coffee), especially
in the short run. Finally, our results suggest that social welfare is maximized when
an export board offers the farmer the highest price it can, and thus this article
makes the case for having cooperatives or non profits in this role.
References
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17
In the presence of risk aversion, as shown in the Appendix, these policies are shown to have
an extra bang as there are additional production effects that amplify the effects of such policies.
39
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Appendix
1.A
Appendix 1: The Expected Price
Lemma 3. Given the level of intermediation, θ, the expected price is given by
E(p) =
∞
X
pZmax
Qk
k=0
pdGk (p)
R
= P w − e−θ (P w − R)(1 + θ)
= P w 1 − e−θ (1 + θ) + Re−θ (1 + θ).
(1.A.1)
As 0 < e−θ (1 + θ) < 1, 18 the expected price is also a convex combination of the
world price and R.
Proof. By definition, the expected value of the price the farmer gets is
E(p) =
∞
X
Qk Ek (p)
k=0
= Q0 R +
∞
X
Z
pgk (p)dp]
R
k=1
= Q0 R +
∞
X
Z
e > 1 + θ so
1
1+θ
pmax
Qk [
k=1
18 θ
pmax
Qk [
> e−θ or 1 > e−θ (1 + θ) .
R
pk[F (p)]k−1 f (p)dp].
42
Recall that
Qk =
θk −θ
e , Gk (p) = [F (p)]k , gk (p) = k[F (p)]k−1 f (p)
k!
pmax = P w (1 − e−θ ) + e−θ R
Pw − R
Pw − R
=
P w − pmax
P w − [P w (1 − e−θ ) + e−θ R]
= eθ
1
Pw − R
ln( w
) f or R ≤ p ≤ pmax
θ
P −p
w
1 Pw − p
P −R
(
)
f or R ≤ p ≤ pmax
θ P w − R (P w − p)2
1
1
f or R ≤ p ≤ pmax
w
θ (P − p)
1
θ
1 P w − (P w (1 − e−θ ) + e−θ R)
(
)
θ
Pw − R
e−θ
.
θ
F (p) =
f (p) =
=
f (R) =
f (pmax ) =
=
Now we are ready to show that
Q0 R +
∞
X
k=1
Z
Qk [
pmax
pk[F (p)]k−1 f (p)dp] = P w 1 − e−θ (1 + θ) + Re−θ (1 + θ).
R
First we obtain the expected price when k traders show up:
pmax
Z
Ek (p) =
pgk (p)dp
R
Z
pmax
= k
pf (p) [F (p)]k−1 dp
R
k
= k
θ
Z
pmax
[ln(
R
P w − R k−1 p
)]
dp for k ≥ 1
Pw − p
Pw − p
(1.A.2)
43
Then we take the expectation over all possible k.
We start by solving for the indefinite integral, a key part of Ek (p).
Z
[ln(
P w − R k−1 p
)]
dp.
Pw − p
Pw − p
(1.A.3)
w
To do so we change variables. Let x = ln( PP w−R
).
−p
ex
=⇒
Pw − R
Pw − p
P w − p = e−x (P w − R)
=⇒
p = P w − e−x (P w − R).
=
(1.A.4)
This gives p in terms of x.To change variables we note
dp = e−x (P w − R)dx.
(1.A.5)
Substituting for p from (1.A.4) we get
P w − e−x (P w − R)
p
=
Pw − p
e−x (P w − R)
Pw
= −x w
− 1.
e (P − R)
(1.A.6)
Using equations (1.A.4),(1.A.5), and (1.A.6) we can rewrite the integral in equation
(1.A.3) as
Pw
x
e
− 1 e−x (P w − R)dx =
w
(P − R)
Z
Z
w
k−1
w
x dx − (P − R) e−x xk−1 dx =
=P
Z
k
wx
w
k−1 −x
−x k−2
=P
− (P − R) x e (−1) − (k − 1) (−1)e x dx =
k
k−1
k
x
xk−2
wx
w
−x
=P
+ (P − R)e (k − 1)!
+
+ .. + 1 =
k
(k − 1)! (k − 2)!
" k−1 #
k
X xj
x
= P w + (P w − R)(k − 1)!e−x
k
j!
j=0
Z
k−1
x
(1.A.7)
44
Substituting back to obtain the expression above in terms of p
pZmax
P w − R k−1 p
[ln( w
)]
dp = (1) + (2)
P −p
Pw − p
R
P w − R k pmax
Pw
[ln( w
)] |R
k
P −p
Pw
Pw − R k Pw
Pw − R k
=
[ln( w
[ln(
)]
)]
−
k
P − pmax
k
Pw − R
Pw
=
[ln(eθ )]k − 0
k
Pw k
=
θ
k
(1) =
and
w
P −R j
k−1
P w − p X [ln( P w −p )] pmax
[
]|R
(2) = (P − R)(k − 1)! w
P − R j=0
j!
w
−θ
w
= (k − 1)!{(P − R)e [
k−1
X
[ln(eθ )]j
j!
j=0
w
] − (P − R)[1 −
j=0
|
= (k − 1)!(P w − R){e−θ [
k−1 j
X
θ
j=0
= (P w − R)(k − 1)!{e−θ
k−1
X
j=0
j!
w −R
k−1
X
[ln( PP w −R
)]j
{z
(P w −R)
j!
]}
}
] − 1}
θj
− 1)}
j!
where we use the fact that P w − pmax = e−θ (P w − R) . Next we find Ek (p) for
k > 1 for a given θ.
k
Ek≥1 (p|θ) = k
θ
pZmax
p
P w − R k−1
[ln(
)] dp
Pw − p
Pw − p
R
=
k
[(1) + (2)]
θk
45
k−1
X θj
k w θk
w
−θ
+
(P
−
R)(k
−
1)!{e
) − 1})
(P
θk
k
j!
j=0
=
k−1
X θj
(k)!
= P + (P − R) k {e−θ
− 1}
θ
j!
j=0
w
w
Hence the expected price conditional on at least one trader showing up is as
follows:
∞
X
Qk Ek (p) =
k=1
∞
X
θk
k=1
=
k!
∞
X
θk
k=1
k!
"
e−θ
−θ
#
k−1 j
X
k!
θ
P w + (P w − R) k (e−θ
− 1)
θ
j!
j=0
w
−θ
w
e P + (P − R)e
∞
X
(e
−θ
j=0
k=1
"
= e−θ P w (eθ − 1) + (P w − R)e−θ
k−1 j
X
θ
j!
− 1)
∞
k−1 j
X
X
θ
−θ
(e
− 1)
j!
j=0
k=1
#
= e−θ P w (eθ − 1) + (P w − R)e−θ [−θ]
where we use the fact that
∞
P
(e−θ
k−1
P
θj
j!
j=0
k=1
− 1) = −θ. This can be verified as
follows:
∞
X
k=1
(e
−θ
∞
∞
X
θj X θj
− 1) =
(e (
−
) − 1)
j!
j! j=k j!
j=0
k=1
k−1 j
X
θ
j=0
=
=
∞
X
−θ
∞
X
−θ
k=1
∞
X
θ
(e (e −
((1 − e−θ
k=1
= −e−θ
= −e
j=k
∞
X
j=k
∞ X
∞
X
k=1 j=k
−θ
∞
X
θj
j!
) − 1)
θj
) − 1)
j!
θj
j!
j
∞ X
X
θj
j=1 k=1
j!
The above change in summations can be verified by writing out terms in each one
and noting that the first term in the former corresponds to the last term in the
46
latter. Thus
∞
X
k=1
−θ
(e
k−1 j
X
θ
j=0
j!
j
∞
X
θj X
(
1)
j! k=1
j=1
− 1) = −e
−θ
= −e
−θ
∞
X
−θ
j=1
∞
X
θj
(j − 1)!
= −e θ
j=1
θj−1
(j − 1)!
= −θ.
Finally, the first moment of price is
E(p) = Q0 R +
∞
X
Qk Ek (p)
k=1
w −θ
= e−θ R + P e (eθ − 1) + e−θ (P w − R)(−θ)
= e−θ R + P w − P w e−θ − θe−θ (P w − R)
= −e−θ (P w − R) + P w − θe−θ (P w − R)
= P w − e−θ (P w − R)(1 + θ).
1.B
Appendix 2: Risk Averse Farmers
When farmers are risk neutral, they choose to produce the crop with the higher
expected payoff. When they are risk averse, they could choose to produce both
goods to help insure themselves. This is consistent with anecdotal evidence on
small agricultural households.
Risk aversion affects the farmers’ side of the model. A risk averse farmer
with a concave utility function U (·), defined over the units of the numeraire good,
maximizes his expected utility by allocating his labor endowment between the
47
production of the two goods given the distrbution of prices:
(
max
e−θ U (l, R) +
l∈[0,1]
Z
∞
X
e−θ θk
k=1
k!
)
pmax
U (l, p̃)dGk (p)
pmin
As in the risk neutral case, Gk = [F (p)]k denotes the CDF of the distribution of
the maximum price when a farmer meets k traders. If l∗ is the equilibrium output
of the exportn good by each o
farmer, then the level of intermediation is given by
w
∗
), 0 .
θ(l∗ ) = max ln( (P −R)αl
κ
Multiplicity of equilibria persists in this set up. When farmers believe that no
intermediaries will enter and the local price of the export good is low, they chose not
to produce the export good at all so that no intermediation occurs. Two properties
of the equilibrium when farmers are risk averse stand out relative to the case of risk
neutral farmers. First, farmer does not specialize in the production of the export
good as soon as the expected price exceeds the opportunity cost of specializing in
the staple. He requires a premium for taking the risk of receiving a low price for
the export good. Second, l∗ (θ) is no longer a step function as farmers choose to
diversify their output. As a consequence, policies can affect the allocation of labor
across crops so that they have real effects on output. Unfortunately, analytical
solutions with risk aversion are impossible and we rely on simulations for results.
Next we will use numerical examples to consider implications of a production
subsidy and export board in the set up where farmers are risk averse.
1.B.0.4
Production Subsidy
With risk aversion a production subsidy increases both the output of the export
good and the level of intermediation in the good equilibrium. The production
subsidy gives farmers a direct incentive to increase output. The increase in output,
in turn, has a positive effect on the level of intermediation which again increases
the expected producer price.
We simulate the equilibrium for different values of the parameters. The qualitative conclusions are similar across different sets of parameters so here we report
the simulation for the CRRA utility function with relative risk aversion of 1.5 for
the following parameter values: P w = 3, α = 2, R = 0, κ = 1. In this simulation we
48
5
Output of the Export Good
4.5
4
3.5
3
2.5
0
0.05
0.1
Subsidy
0.15
0.2
Figure 1.B.1: Output response to a subsidy.
solve for the equilibrium level of intermediation and output by each farmer for a
set of subsidy values from 0 to
1 19
.
α
Figures 1.B.1 and 1.B.2 show that the output
of the export good and the level of intermediation (on the y-axis) rise with the
amount of the subsidy (on the x-axis). Until the farmer completely specializes in
the export good, increases in the subsidy raise both the level of intermediation and
the output of the specialized good. It is worth pointing out that the subsidy has no
direct effect on the level of intermediation as it does not directly enter the expression for the level of intermediation 1.2.6. Increases in intermediation occur entirely
via the equilibrium effect of increased output. Figure 1.B.3 depicts the farmer’s
utility as the subsidy rises. Note that utility rises faster before complete specialization than after. Farmers choose to make both goods because poor intermediation
increases the risk of not being matched. A subsidy increases the production of the
export good, which in turn induces more intermediation, which reduces the risk
of making the export good and raises utility. There is also a direct effect of the
subsidy on utility. Once specialization occurs, only the latter operates.
1.B.0.4.1
Export Board: Reservation price Figures 1.B.4, 1.B.5, 1.B.6
show how output, level of intermediation and farmer utility change in response to
changes in the value of reservation price for the export good, respectively. Just
Although we compute allocations for subsidies ≤ α1 = .5, the figure only contains values until
.2. The rst of the outcomes were omitted because the specialization has occurred long before .5
is reached.
19
49
2.8
2.7
Level of Intermediation
2.6
2.5
2.4
2.3
2.2
2.1
2
0
0.05
0.1
Subsidy
0.15
0.2
Figure 1.B.2: Intermediation and the subsidy.
−0.45
−0.5
−0.55
−0.6
Utils
−0.65
−0.7
−0.75
−0.8
−0.85
−0.9
−0.95
0
0.05
0.1
Subsidy
0.15
0.2
Figure 1.B.3: Utility as a function of the subsidy.
as in the risk neutral case, when farmer is risk averse an increase in the farmer’s
reservation price has a direct effect of raising the expected price of the export
good while reducing it through its affect on intermediation. Unless the farmer has
already specialized in the export good, an increase in the expected price leads to
a reallocation of labor from the production of the staple good to the production of
the export good, which in turn increase the profit margin of traders and induces
more trader entry. The equilibrium expected price rises as the direct effect of
raising R dominates.
The simulations in figures 1.B.4, 1.B.5 show that until farmers specialize, labor
allocated to the export good and intermediation levels both increase with R. With
50
5
4.5
Output
4
3.5
3
2.5
2
0
0.05
0.1
0.15
0.2
R
0.25
0.3
0.35
0.4
Figure 1.B.4: Response of output to R.
2.4
2.3
2.2
Intermediation Level
2.1
2
1.9
1.8
1.7
1.6
1.5
1.4
0
0.05
0.1
R
0.15
0.2
Figure 1.B.5: Response of intermediation to R.
risk aversion, increase in R not only raises the expected price but also rises intermediation as long as the output of the export good is increasing. Once farmers
have specialized in the export good, only the effect via the outside option operates
and the level of intermediation starts falling. The farmer’s utility continues to
increase in R even after specialization has occurred, although at a slower rate than
before specialization.
20
20
The simulation reported here is done for the same parameters as in the exercise with the
subsidy.
51
−0.7
−0.8
−0.9
Utility
−1
−1.1
−1.2
−1.3
−1.4
−1.5
0
0.05
0.1
R
0.15
0.2
Figure 1.B.6: Response of farmer’s utility to R.
Chapter
2
Multiproduct Exporters: Empirical
Regularities (co-authored with Kala
Krishna and Hong Ma)
2.A
Introduction
In this paper we document data regularities that discipline economists’ understanding of how firms begin to export new product varieties, and facilitate development
of dynamic models.
Our data exercises suggest that firms deal with uncertainty when they make
a decision to introduce a new product to a market. The patterns of product introduction and discontinuation for multi-product firms also suggest that there is
a learning process through which firms learn about the demand for their products
over time. It is also plausible that learning to produce one product provides information to the firm about other related products.
We use firm-product level information on Chinese exports to the US. To motivate the study of the multi-product firms, we single out the contribution of the
new products by existing firms to the overall growth of sales from one year to the
next as well as over the sample period. We find that new products contribute from
20 to 30 percent to the total growth of exports on a year-to-year basis.
Next, we reproduce a few exercises done with various other data sets to see if
53
the patterns that earlier studies find hold for Chinese multi-product exporters. In
accord with earlier work, we find that the distribution of sales across products for
an exporter is highly skewed. Wider scope exporters also sell more of their top
selling products than narrow scope exporters. The skewed sales distribution of
products for a multi-product firm can be interpreted as evidence of firm-productspecific heterogeneity. That the sales in the top ranked products are higher for
wide scope exporters is interpreted as evidence for firm-level productivity that
is common across products within a firm. Such firm productivity allows multiproduct firms to have higher sales in their top-selling products while exporting a
wider range of products.
Earlier multi-product firm literature, descriptive or empirical, has been largely
concerned with static properties of the multi-product firm whereas the contribution
of our exercise is uncovering two sets of data regularities that discipline the dynamic
aspects of the analysis.
The first set of data facts pertains to the patterns of product introduction. We
find that a large number of products introduced by existing firms are terminated
within the first year. Products that do survive the first year are the ones that
have higher sales. Conditional on surviving the first year, initial sales have no
implications on the survival of a product line in later years. We interpret these
regularities as evidence for uncertainty about the demand that a firm faces prior
to launch of a product. When a firm introduces a new product, it draws a product
firm specific demand shock, but it does not observe it until it observes the sales.
The second set of facts is related to the observation that some products are
technologically similar to one another while others are not, and the conjecture that
the decision to expand in the product space is related to the current product mix
of a firm. To see what we mean by similarity, consider the following. Leather
shoes and plastic shoes (both belong to the same Harmonized System group at
the two digit level are similar products while leather shoes and ceramic statuettes
appear to be very different products both in terms of production technologies and
the demand that these firms face (different HS groups at the two digit level ).
We investigate the data and find some tentative support for this conjecture. In
particular we find that the higher the firm’s sales in a group of products are, the
more likely it is to introduce another product in the same group the following year.
54
Also, products that are introduced by a firm that has had experience producing a
similar product are more likely to survive the first year.
The empirical observations that we make in this paper motivate further research
about firm decision making. Do firms experiment with new products? When
do firms introduce products similar to their current product mix, and when do
they introduce different ones? Which are the firms that introduce products across
different HS groups at the two digit level ? Are these the highly productive firms
that push new frontiers because they have exhausted their possibilities of expansion
in the similar products. Or are these the firms looking for a better product niche
that venture into entirely new products?
2.A.1
Literature Review
Before we proceed to the data patterns in the Chinese exporters data set, we discuss
the approaches that have been taken towards understanding multiproduct firms in
the literature. Theoretical papers that unwrap firm heterogeneity at the product
level include Andrew B. Bernard, Redding and Schott, 2010, Eckel and Neary, 2010
and Nocke and Yeaple, 2006. What unites these papers is the ultimate purpose to
understand how the scope of the firm is endogenously determined. The modelling
approaches that these authors adopt are diverse. Andrew B. Bernard et al., 2010
model firm-product-specific competencies. Eckel and Neary, 2010, model firms as
having a core competency element. In Nocke and Yeaple, 2006 the firm’s products
are symmetric. In these papers the firm’s scop is determined by its productivity.
The productivity varies across firms but is common across products in a firm. In
a nutshell, the more productive firms are able to add more varieties.
Another strand of multiproduct firm literature headed by Feenstra and Ma,
2007 and Dhingra, 2013 explore the effect of cannibalization for varieties within a
firm.
De Loecker, 2011 and Levinsohn and M. Melitz, 2002 and Shen, 2012 look at
the link between the measured productivity of the firm and the introduction of
new products. Levinsohn and M. Melitz, 2002 provide theoretical insights into
estimating productivity of a multiproduct firm using the firm-level data on inputs.
De Loecker, 2011 builds on their insights to estimate productivity of the Dutch
55
textile firms and evaluates the impact of trade liberalization on productivity of
a multinational firm. Building on these two papers Shen, 2012 extends the idea
of Aw, Roberts and Xu, 2008 to a multiproduct firm. The focus of her paper is
on exporting and increasing the product range, both of which presumably make
productivity enhancing investments more profitable.
Since in this essay we look at the product mix decisions of the exporters, the
applications of the multiproduct firm models to exporting are most relevant. We
proceed by discussing the findings of these studies in greater detail. First, we
consider the data regularities that disciplined these models and then discuss their
economic results.
1. The distribution of product sales within a firm is highly skewed. Firms’ sales
are concentrated in few high selling products.
Andrew B. Bernard et al., 2010 document this for US plants and Arkolakis
and Muendler, 2010 for the Brazillian exporters.
2. Wide scope exporters have higher sales in their top ranked products and lower
sales in their least ranked products compared to the narrow scope exporters.
3. The distribution of exporter product sales is similar across markets for exporters.
Arkolakis and Muendler, 2010 document this for Brazillian exporters and
Mayer, Melitz and Ottaviano, 2011 document it for French exporters.
4. Product additions are associated with increases in productivity.
Andrew B. Bernard et al., 2010 use OLS regressions to study the relationship
between changes in the firm characteristics such as real output, employment,
output per worker and TFP and net decrease or increase in its product
scope over a five year interval. They find positive and significant association
between measures of productivity and net increase in the firm’s scope.
Now we discuss the economic findings of these applications.
Andrew B. Bernard et al., 2010 adopt the model in M. J. Melitz, 2003 to incorporate firm-product-specific competencies. Their model is based on two sources
56
of heterogeneity. First, firms have firm-specific productivity parameter, i.e., firmability, as in M. J. Melitz, 2003. Firm-ability is common across products within
a firm and determines the marginal cost of production. Second, firms draw firmproduct-specific attributes which ensure that firms have differential sales across
products. Firm-ability and firm-product-specific attributes are drawn from independent Pareto distributions. The assumption of the Pareto distribution delivers
the skewed distribution of sales within a firm. One of the main results of the model
is that the scope of the firm is an increasing log linear function of firm ability.
Andrew B Bernard, Redding and Schott, 2011 is the extension of Andrew B.
Bernard et al., 2010 where the closed economy model is extended to an open
multicountry framework. The model is used to explain the gravity relationship
for bilateral trade flows and do comparative statics with respect to variable trade
costs. They apply the model to the trade flows between US and Canada after
the Canada-US Free Trade Agreement in 1998. Using the difference-in-difference
estimator, they find that US firms that were under a greater protection under the
tariffs were more likely to shed products after the liberalization.
Mayer et al., 2011 using a linear demand model show how tougher competition
in an export market is associated with a downward shift in the distribution of
markups across all products sold in the market and induces firms to shift its export
activity towards its best performing products.
Andrew B. Bernard et al., 2010 built on Eckel and Neary, 2010 and assume that
within a firm product heterogeneity is deterministic: firms have a core competency
element for which their productivity is equal to the firm-level productivity. Product
specific productivity decreases deterministically for products further away from the
core competency element. More productive firms are able to add more products.
Their model includes the fixed cost of adding one more product and it can be either
an increasing or a decreasing function of scope. Hence the theoretical model allows
for diseconomies of scope on the cost side, and for economies of scope in terms
of entry costs. Which force prevails is the empirical question. Using Brazillian
customs data they find that diseconomies of scope dominate, and that the elasticity
of trade volume with respect to the sunk cost of introducing additional products
into a market is low.
57
2.B
2.B.1
Empirical Patterns
Data Description
We use records on the Chinese exporters to the US from the Chinese Customs data
set for the years 2000-2006. For each firm, these records have information on sales
of each product identified up to 8 digit HS category to each destination.
The sample that was used in the exercises excluded firms that contained the
word “intermediary” in their name, trade between affiliated parties, as well as
trade in agricultural products. In the data exercises we present below the results
are presented for US only.
2.B.2
Growth Decomposition
We want to understand how introduction of new products contributes to export
growth relative to entry of new firms. To this end we decompose export growth
of the Chinese exports into the contributions of the continuing, new, and exiting
exporters. Then we further decompose the growth in the exports of the continuing
firms into growth in the sales of existing products and introduction of new product
lines. In this manner we are able to evaluate the contribution of the new product
margin to the overall export growth.
To decompose the Chinese exports growth over time, we follow Eaton, Eslava,
Kugler and Tybout, 2008. We look at how growth in exports reflects contributions
of continuing, entering, and exiting firms using the following identity:
P
=
t−1
j∈CNn
Xn (t)−Xn (t−1)
[Xn (t)+Xn (t−1)]/2
 P
[xn (j,t−1)+xn (j,t)]/2 !
=
(2.B.1)
[xn (j,t−1)−xn (j,t)]/2

[xn (j,t−1)+xn (j,t)]/2
+
t−1
[Xn (t)+Xn (t−1)]/2
Γ1
 j∈CN
Pn
t−1
j∈CNn
Γ2
P
t−1
xn (t−1)
n
+ [XNnEN
+
(t)+Xn (t−1)]/2
Γ3
t−1,t
N EXn
xn (t−1)
− [X
−
n (t−1)+Xn (t)]/2
Γ5
[xn (j,t)−xn (t−1)]
t−1,t
j∈ENn
−
[Xn (t)+Xn (t−1)]/2
Γ4
P
[xn (j,t−1)−xn (t−1)]
t−1,t
j∈EXn
[Xn (t)+Xn (t−1)]/2
Γ6
.
58
Table 2.B.1: Pairwise decomposition of the Chinese exports growth to the US
into contributions of entrants, exiters and continuing exporters
∆t
2000-2001
2001-2002
2002-2003
2003-2004
2004-2005
2005-2006
2000-2004
2000-2005
2000-2006
2001-2006
∆ Exports
0.16
0.37
0.32
0.34
0.42
0.22
1.07
1.34
1.45
1.37
Γ1
0.90
0.89
0.91
0.90
0.88
0.89
0.44
0.31
0.26
0.35
Γ2
0.09
0.27
0.23
0.24
0.28
0.20
0.28
0.25
0.24
0.31
Γ1 Γ
0.08
0.24
0.21
0.22
0.25
018
0.63
0.79
0.93
0.89
Γ3
0.40
0.41
0.40
0.45
0.54
0.35
1.02
1.17
1.05
0.97
Γ4
(0.26)
(0.24)
(0.26)
(0.29)
(0.34)
(0.22)
(0.06)
0.06
0.30
0.21
Γ3 + Γ 4
0.14
0.17
0.14
0.16
0.21
0.13
0.96
1.23
1.35
1.18
Γ5
0.23
0.18
0.16
0.16
0.16
0.30
0.25
0.20
0.18
0.18
Γ6
(0.17)
(0.13)
(0.12)
(0.12)
(0.12)
(0.21)
(0.09)
(0.06)
(0.04)
(0.06)
−(Γ5 + Γ6 )
0.06
0.04
0.03
0.04
0.03
0.09
0.16
0.14
0.14
0.12
Here Xn (t) denotes total Chinese exports by non-intermediary firms to destination n in year t, and xn (j, t) represent exports by firm j to country n at time
t. The terms CNnt−1 , ENnt−1,t , EXnt−1,t denote the sets of firms that exported to
country n in both year t − 1 and t , the set of firms that did not export in t − 1
but started to export in t, and the set of firms that exported in t − 1 but ceased to
export in t, respectively. The terms N ENnt−1 and N EXnt−1 represent the number
of elements in sets ENnt−1,t and EXnt−1,t respectively.
The left hand side of the identity measures the export growth of the Chinese
firms between t − 1 and t. The product of the first two terms on the right hand
side of the equals sign, Γ1 Γ2 , yields the growth in the sales of the continuing firms.
The first multiplier, Γ1 , is the share of continuing firm exports in total exports
over the two years. The second multiplier, Γ2 , is the average growth of the sales
of continuing exporters.
The sum of the third and fourth terms, Γ3 + Γ4 , yields the contribution of new
exporters to the overall growth of exports to destination n. The first summant, Γ3 ,
represents counterfactual growth in exports implied by the increase in the number
of exporters if the new exporters were the size of the average exporter in the
previous year. The second summant, Γ4 , is the sum of the deviations of exports
by new firms from the exports of an average firm in t − 1. The sum of the last two
terms on the right hand side, Γ5 + Γ6 , represent the decline in exports due to firms
that exit. Analogously to the case of entrants, the first of the two terms, represents
the counterfactual decline in exports due to exit of firms if exiting exporters were
the size of the average exporter in the previous year. The second term, Γ6 , is the
59
deviation of the sales of the exiting exporters from the average size.
The Table 2.B.1 shows the decomposition of exports from China to the USA,
i,e, n = U SA. The first six lines of the table present the results of applying the
equation 2.B.1 to aggregate export growth from one year to another. The last
four lines show the application of the decomposition across several years with the
intervals indicated in the leftmost column.
Table 2.B.1 indicates that continuing firms are responsible for most of the year
to year changes in aggregate exports with the exception of 2001. Entry of new
firms in 2001 is responsible for 14% when total exports rose by 16%. Possibly,
large entry of firms into the export market can be explained by the beginning of
China’s ascension into the WTO. The overall pattern is that entering and exiting
firms are large in number but small in size. The export growth is driven by the
continuing firms not only because they are large in numbers but also because sales
of these exporters grow substantially from year to year. The average growth of the
sales of continuing exporters over a one year period constitutes on average 20%.
The decomposition across spans of several years in contrast shows that over longer
periods of time export growth is driven by entrants.
Next, we decompose growth of exports of the continuing firms into sales growth
of existing products, introduction of new products, and discontinuation of the
existing ones. We apply formula 2.B.3 which is the analogue of formula 2.B.1. In
formula 2.B.3, X CN (t) denotes exports of the firms that exported in both period t−
1 and in period t. Since we are only considering exports to the US, the destination
index n is omitted. xn (j, k, t) is the exports of firm j, of product k in period t to
the US. CP t−1,t , N P t−1,t and DP t−1,t denotes the set of products that are sold in
both year t − 1 and t, sold in year t + 1 for the first time, and products that have
been sold in t − 1 but were discontinued in t. N CP t−1,t ,N N P t−1,t , and N DP t−1,t
denote the number of observations in each set, respectively. x(t − 1) is the average
sales per product line for firms and products that were exported in t − 1. Similarly,
X CN (t)−X CN (t−1)
[X CN (t)+X CN (t−1)]/2
=
(2.B.2)
60
Table 2.B.2: Pairwise decomposition of the continuing firms’ contribution to
the exports growth into contributions of new products, discontinued products
and growth of xisting products
∆t
2000-2001
2001-2002
2002-2003
2003-2004
2004-2005
2005-2006
2000-2004
2000-2005
2000-2006
2001-2006
∆ Export
0.08
0.21
0.21
0.22
0.25
0.18
0.28
0.25
0.24
0.31
P
=
Θ1
0.83
0.86
0.86
0.85
0.82
0.84
0.35
0.24
0.20
0.28
Θ2
0.08
0.20
0.20
0.23
0.24
0.20
0.58
0.70
0.88
0.84
Θ1 Θ2
0.07
0.17
0.17
0.20
0.20
0.17
0.20
0.17
0.18
0.24
P
[x(j,k,t−1)+x(j,k,t)]/2
Θ4
(0.32)
(0.31)
(0.31)
(0.27)
(0.31)
(0.25)
(0.12)
(0.06)
(0.04)
(0.05)
Θ3 + Θ3
0.08
0.07
0.07
0.06
0.08
0.05
0.12
0.11
0.09
0.11
Θ5
0.34
0.31
0.31
0.30
0.28
0.31
0.15
0.09
0.07
0.09
Θ6
(0.27)
(0.27)
(0.27)
(0.26)
(0.24)
(0.27)
(0.10)
(0.06)
(0.04)
(0.06)
[x(j,k,t−1)−x(j,k,t)]/2
j∈CP t−1,t
j∈CP t−1
[X CN (t)+X CN (t−1)]/2
Θ1
Θ3
0.39
0.38
0.38
0.34
0.40
0.30
0.24
0.17
0.13
0.16
P
[x(j,k,t−1)+x(j,k,t)]/2
+
j∈CN P t−1,t
Θ2
P
t−1,t
x(t−1)
NNP
+
+ [X CN
(t)+X CN (t−1)]/2
j∈N P t−1,t
[X CN (t)+X CN (t−1)]/2
Θ3
t−1,t
Θ5
−
Θ4
P
N DP
x(t−1)
− [X CN
−
(t)+X CN (t−1)]/2
[x(j,k,t)−x(t−1)]
[x(j,k,t−1)−x(t−1)]
j∈DP t−1,t
[X CN (t)+X CN (t−1)]/2
Θ6
Table 2.B.2 shows the results of the decomposition. It indicates that year-toyear growth in the exports of the continuing firms is driven mostly by growth in
the sales of the existing products. Not only they constitute a large share exports
over the course of two years, but also products of individual firms on average by
20% from one year to the next. The contribution of new product lines to the
growth of sales of existing firms is not negligible, though. However, for the larger
spans of time contribution of new product lines does not increase as much as the
contribution of new firms with the passage of time.
2.B.2.1
Firm-Level Productivity
First, we document for the Chinese data the facts that Arkolakis and Muendler,
2010 document for Brazilian customs dataset. These facts support the conjecture
−(Θ5 + Θ6 )
0.06
0.04
0.04
0.04
0.04
0.04
0.05
0.03
0.03
0.03
61
that firms are endowed with a firm-specific characteristic that affects all products
within a firm. Substantial variation of sales across products within a firm suggests
that there is room for product heterogeneity within a firm.
The data facts are as follows:
a)a firm’s sales within a destination are concentrated in a few products;
b)wide scope exporters sell more of their top selling products than
the exporters with few products;
c)wide scope exporters sell their lowest selling products in small
amounts compared to the exporters with few products;
d)average sales per product are increasing with scope.
Figure 2.C.1 captures evidence in support of facts a), b), and c). Following
Arkolakis and Muendler, 2010, it depicts the distribution products sales within
the firm. We consider firms with the same number of products and rank the
products of each firm from the top selling (rank 1) to the lowest selling in the US
market. Then we take the average across firms with the same number of products
at a given product rank and plot the average sales at a product rank against the
rank on the log-log scale.1
Figure 2.C.1 shows this relationship for firms with 3,4, 8, 16, and 32 products
in 2003. Overall he pattern that wide scope exporters have higher product sales in
their top ranked products persists. The pattern is especially clear for firms with
4, 8, and 16 products, as the sales in equally ranked products for the wider scope
exporters lie strictly above those for the exporters with fewer product. Furthermore, the lower ranked products of large scope exporters sell in smaller amounts
than those of large scope exporters.
As Arkolakis and Muendler, 2010 point out the figure 2.C.1 may lead one to
conjecture that wide scope exporters have lower average sales per product because
wide scope exporters have a few products that sell in small amount. Figure 2.C.2
shows that the average sales per product do not fall (at least substantially) with
1
Throughout the document the results that pertain to the sales of the firms are related to
sales that have been deflated as follows. For each year we calculated average sales for each HS
4 digit level product category and divided the sales of each firm product observation by the
corresponding average.
62
the increase in the scope which confirms that wide scope exporters are on average
indeed more productive.
Figure 2.C.2 contains two cumulative plots: the logarithm of average sales per
product and the average number of products both plotted against the percentile
scale of firm sales. The averages are computed for groups of firms whose sales
are equal to or greater than the percentile marked on the horizontal axis. The
two plots are constructed as follows. We arrange firms in the increasing order
according to their firm level sales. We then take all the firms whose sales are equal
to or greater than 99th percentile and compute average sales per product for these
firms. We then plot the percentile, i.e. 99th percentile, on the horizontal axis and
the corresponding logarithm of average sales per product, and average number of
products across firms on the vertical axis. Next, we keep only the firms which
have sales above the 98th percentile, and compute the average sales per product
and average number of products for this group of firms. We continue in this manner
until we exhaust all observations in the sample.
Comparing the plot of the logarithm of average sales and the average number
of products, one can see that as one moves from left to right, the average sales
increase along with the number of products. Firms that sell more overall, sell a
greater number of products, and sell more of each product.
2.B.3
Dynamic Aspects: First-Year Effect For The New
Products
Introduction of new products is clearly a dynamic decision. The set of facts that we
present in this subsection pertains to the dynamic patterns of product introduction
and they suggest that firms face uncertainty about the potential success of their
new products in the market.
In the following data exercises, we follow the methodology that Eaton et al.,
2008 use to uncover the dynamic patterns of the firm entry and exit into exporting.
Eaton et al., 2008 look at the cohort of firms by the year of entry as they age. Here
we look at the cohort of product-firm pairs by their year of introduction.
In the tables that follow, the product lines introduced in association with the
firm entry are excluded from the sample. Sales of products are reported as relative
63
to the average sales of all firms producing the same product in a given year.2 We
define product varieties as the first four digits of the HS code. The results are
reported for the year 2001 only in order to conserve space as patterns are similar
for other years in the sample.
The unit of observation in Table 2.B.3 is a product-firm pair. We consider how
the number of products in the cohort of products introduced in 2001 evolves. The
first colum shows the year. The second column reports the number of products
exported to the US in a given year from those introduced in 2001. We separate the
products that are exported in a given year into those that continue to be exported in
the following year and products that are discontinued, either because the carrying
firm stops exporting to the US altogether or because products are discontinued
while the firm continues to export. So column three shows the number of products
that were sold in both year t and t + 1. Column four shows the number of products
that were sold in t but are no longer sold in t + 1 because the exporting firm has
exited the US market altogether. Column 5 shows the number of products that
were sold in t but were discontinued in t + 1, while the carrying firm continued to
export.
In the first year after introduction more than 45% of the products are discontinued in the same year by firms that continue to export to the same market.
Attrition in the subsequent years is about 25%.
Table 2.B.4 is a companion table of Table 2.B.3 and reports average sales for
each group of product lines in the 2001 cohort for years 2001-2005. It shows
that surviving products have sales that are higher than average among the new
products. Average sales grow as the cohort ages. The fastest growth occurs in
the first year after introduction across all cohorts. Also average sales across all
cohorts increase in year 2005. Large growth in 2005 can potentially be attributed
to a number of reforms undertaken in that year, including trade and bank sector
liberalizations that took place in China.
Table 2.B.5 relates product’s initial sales to the probability of its discontinuation. It shows the deciles of products’ initial sales and the sample probability of
2
If sik denotes the sales of product k by firm i then the sales deflated by the average of all
sikt
firms selling the same product is sg
ikt = P
I
sikt
i=1
64
Table 2.B.3: Evolution of the number of products introduced in 2001 by con-
tinuing exporters
t
# of
products
sold in t:
Sold in t &
t+1
Sold in t,
not t + 1 due
to firm exit
Sold in t,
not t + 1
discontinued
by an active
exporter
2001
9,440
4, 378
1, 008
4, 054
(46%)
(11%)
(43%)
2002
4,378
3, 174
295
909
(72%)
(7%)
(21%)
2003
3,174
2, 426
201
547
(76%)
(6%)
(17%)
2004
2,426
1, 861
121
444
(77%)
(5%)
(18%)
2005
1,861
1, 345
115
401
(72%)
(6%)
(22%)
Table 2.B.4: Evolution of the average sales per product for products introduced
in 2001 by continuing exporters
t
2001
2002
2003
2004
2005
Cont
0.56
0.82
0.95
1.05
1.72
2001
Firm EXT Prod Disc
0.24
0.24
0.51
0.38
0.40
0.43
0.55
0.31
0.32
0.41
exiting in year t conditional on surviving t − 1 years. For each decile of initial sales
the first column reports the probability that the product line is discontinued in
the first year. The second column reports the sample probability that a product
line exits in the second year conditional on survival in the first year.
Two patterns stand out in Table 2.B.5. First, the higher the sales are in the first
year the higher is the probability of surviving past the first year. Second pattern
is that conditional on surviving the first year the probability of dropping out in
the second year decreases compared to the first year. This decrease is especially
prominent for products that started in the lower sales deciles while the products
that started in higher deciles loose their advantage after the first year.
65
Table 2.B.5: Sample exit probabilities for new products conditional on the decile
of product’s initial sales and tenure
2001
1
2
3
4
5
6
7
8
9
10
1
0.69
0.59
0.58
0.58
0.58
0.51
0.48
0.47
0.44
0.33
Age at Exit
2
3
4
0.20 0.16 0.19
0.23 0.21 0.19
0.23 0.19 0.25
0.28 0.20 0.21
0.29 0.18 0.22
0.28 0.20 0.20
0.25 0.22 0.25
0.25 0.20 0.20
0.23 0.22 0.15
0.25 0.20 0.19
5+
0.31
0.21
0.25
0.27
0.30
0.21
0.22
0.20
0.20
0.18
To summarize, the dynamic facts that we uncover about the entry and selection
of new products by existing firms at a destination are:
a) new product lines are most likely to be discontinued within a
year after introduction;
b) after the first year attrition remains constant;
c) products that start with low sales are more likely to exit within
the first year;
d) as the cohort of products ages its average sales increase;
e) aurvival probability increases for products that survive the first
year and especially so for products with lower sales. Initial sales are
irrelevant for the survival in later years.
Table 2.B.3 provides support for the facts a and b. Table 2.B.4 points out
facts c and d, and Table 2.B.5 supports fact e. Together these facts are consistent
with exporters facing uncertainty when introducing new products into the expor
market.
2.B.4
Expansion Decisions
In the previous subsection, we have documented empirical regularities consistent
with firms gradually learning about the profitability of their products. In this
66
section, we consider how the current product mix of a firm affects its decision to
expand. We find preliminary evidence that not all products are symmetric from a
firm’s point view and that its decision to expand is related to the identity of goods
it already produces.
In the context of the data, products are defined as similar if they share the first
two digits of the HS code. We conjecture that experience with products in a given
two digit HS group may inform the firm about demand shock in that group, and
then affect its decision to expand in the same group or in a different one.
Each column in Table 2.B.6 reports the probability of expansion for a firm in
the two digit HS group in which it has already exported in a given year. For all of
the years except 20003 the probability of adding a new product in the same two
digit HS group increased with the quintile. Although increase in the number of
expansions is not monotone with each quintile, on average, product groups that
had higher sales in a given two digit HS group in the previous year are more likely
to expand in the same group. Year 2000 does not conform to the patterns observed
in later year. This at least in some part can be attributed to the unusually large
exit among firms and products triggered by anti-inflationary policies undertaken
in 2000.
To construct this table, we first calculated average sales across a firm’s products
in each of the two digit HS groups in which a firm produces. Next, we arranged
the average sales for each firm and each two digit HS group into quintiles. In
each quintile we select firms that introduce new products in the same two digit
HS group and use it to compute the sample probability of expantion in the same
two digit HS group for each firm and each two digit HS group. Note that the firm
and two digit HS group pairs that did not expand include firms that exited in the
following year and a firm can appear multiple times in the sample if it produced
in multiple two digit level HS groups.
In Table 2.B.7 we divide all products introduced by continuing firms into two
groups. In the first group,“New HS2” , are all products that were introduced in a
two digit HS group in which the firm already had experience. In the second group,
“Existing HS2”, are products that were introduced in a two digit HS group new for
3
In year 2000 the Chinese economy experience what is referred to as “soft landing”. That
year is not very representative because there is a lot of exit and little entry, both in terms of
firms and products.
67
Table 2.B.6: Sample probabilities of expansion in the same two digit HS group
conditional on the quintile of firm’s average sales per product
Quintiles of sales
1
2
3
4
5
2000 2001
0.50 0.30
0.53 0.33
0.57 0.37
0.56 0.38
0.50 0.40
2002
0.28
0.32
0.33
0.36
0.36
2003
0.24
0.28
0.29
0.33
0.35
2004
0.26
0.30
0.32
0.36
0.37
2005
0.17
0.19
0.22
0.25
0.25
a given firm. For each of the two groups we then compute the sample probability
that a product that was introduced in year in year t is sold in t + 1, the probability
that is discontinued in t + 1 becuase the exporting firm leaves the export market,
and the probability that it is sold in t but in t + 1 the product is discontinued while
the carrying firm continues to export other products. The numbers in brackets are
the number of obsrvations in each group.
In Table 2.B.7, products that in 2001 were introduced by firms that had other
products in the same two digit HS group are more likely to survive the first year
after introdction. In subsequent years, products that were introduced by firms
experienced in exporting similar prducts have a greater chance to be exported in
the following year. The only exception to this pattern is the year 2005. In 2005,
products that were introduced in firms with no prior expereince in the same two
digit group were less likely to be discontinued than products that were introduced in
firms with prior expereince in the same two digit HS group. This can be explained
by the disproportionally large exit of exporters and a large entry of new firms,
triggered by completing the Chinese ascention into the WTO.
Another pattern that stands out from Table 2.B.7 is that the number of product
lines that are introduced in a new for a firm HS2 group exceeds the number of
products introduced in existing ones in all years except 2004. As long as one
considers division of products into two digit HS groups to be a reasonable metric
for similarity then it suggests that a large number of firms find it profitable to
introduce products dissimilar to their current product mix. Firms may desire to
diversify its exports portfolio for a number of reasons. First, firms may find moving
to a new marginal revenue curve profitable even in the presence of uncertainty.
Another possibility is that the expected value of introducing products in new for
68
Table 2.B.7: Sample probabilities for new products introduced by firms with
experience exporting other products in the same two digit HS group and products
intrduced by firms that have never exported products in the same two digit HS
group.
Sample Probabilities
Year of introduction/t
2001
2002
2003
2004
2005
Sold in t &
t+1
Sold in t &
t+1
Sold in t &
t+1
New HS2
0.42
0.11
0.46
(2,268)
(614)
(2,472)
Existing HS2
0.52
0.10
0.39
(2,110)
(394)
(1,582)
New HS2
0.43
0.12
0.45
(2,704)
(722)
(2,803)
Existing HS2
0.49
0.09
0.42
(2,677)
(485)
(2,333)
New HS2
0.40
0.11
0.49
(3,098)
(890)
(3,820)
Existing HS2
0.47
0.09
0.44
(3,476)
(633)
3,215()
New HS2
0.43
0.04
0.54
(3,384)
(294)
(4,254)
Existing HS2
0.47
0.03
0.50
(3,793)
(261)
(4,074)
New HS2
0.26
0.25
0.49
(3,771)
(3,599)
7,113()
Existing HS2
0.33
0.16
0.51
(4,099)
(1,997)
(6,308)
The number in brackets denotes the number observations in each group of products.
a firm two digit HS group carries a value of learning about demand shocks in that
group.
Admittedly in both of the tables presented in this section the differences in the
sample probabilities among the groups are not large. Still the persistence of the
ranking over time in Table 2.B.6 suggests that introduction of a new product in an
existing HS2 group is systematically related to the prior success of a firm in that
two digit HS group. Similarly Table 2.B.7 suggests that the survival of a product
line past the first year is related to whether a firm has had experience producing
a product in the same group or not.
In summary, two facts appear to support the implications of the conjecture we
have outlined. First, firms that have higher than average sales in a given two digit
HS group are more likely to expand by introducing another product in the same HS
group than are firms with lower sales. Second, product lines that are introduced
69
by firms that have produced in the same two digit HS group are marginally more
likely to survive.
2.C
Conclusion
This paper focuses on exploring the data patterns that discipline the economists
understanding of dynamic aspects of multiroduct exporter pobelm. We find some
tentative evidence in support of the conjecture that large exporters face uncertainty
when they introduce new products to the market. We also find that uncertainty
is potentially correlated across products: hence firms can infer their potential in
new products from their success in the existing products. This is especially true
for relatively similar products.
References
Arkolakis, C. & Muendler, M.-A. (2010). The extensive margin of exporting products:
a firm-level analysis. National Bureau of Economic Research.
Aw, B. Y., Roberts, M. J. & Xu, D. Y. (2008). R&d investments, exporting, and
the evolution of firm productivity. The American Economic Review, 451–456.
Bernard, A. B. [Andrew B.], Redding, S. J. & Schott, P. K. (2010). Multipleproduct firms and product switching. American Economic Review, 100 (1),
70–97. doi:10.1257/aer.100.1.70
Bernard, A. B. [Andrew B], Redding, S. J. & Schott, P. K. (2011). Multiproduct
firms and trade liberalization. The Quarterly Journal of Economics, 126 (3),
1271–1318.
De Loecker, J. (2011). Product differentiation, multiproduct firms, and estimating the impact of trade liberalization on productivity. Econometrica, 79 (5),
1407–1451.
Dhingra, S. (2013). Trading away wide brands for cheap brands. The American
Economic Review, 103 (6), 2554–2584.
Eaton, J., Eslava, M., Kugler, M. & Tybout, J. (2008). The margins of entry into
export markets: evidence from colombia. The Organization of Firms in a
Global Economy, Cambridge, MA: Harvard University Press.
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Eckel, C. & Neary, J. P. (2010). Multi-product firms and flexible manufacturing in
the global economy. The Review of Economic Studies, 77 (1), 188–217.
Feenstra, R. & Ma, H. (2007). Optimal choice of product scope for multiproduct
firms under monopolistic competition. National Bureau of Economic Research.
Levinsohn, J. & Melitz, M. (2002). Productivity in a differentiated products market
equilibrium. Unpublished manuscript, 9, 12–25.
Mayer, T., Melitz, M. J. & Ottaviano, G. I. (2011). Market size, competition, and
the product mix of exporters. National Bureau of Economic Research.
Melitz, M. J. (2003). The impact of trade on intra-industry reallocations and aggregate industry productivity. Econometrica, 71 (6), 1695–1725.
Nocke, V. & Yeaple, S. (2006). Globalization and endogenous firm scope. National
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Shen, L. (2012). Product restructuring, exports, investment, and growth dynamics.
Mimeo.
71
Figure 2.C.1: Within firm sales distribution
Sales vs. Product Rank
2
10
3 product firms
4 product firms
8 product firms
16 product firms
32 product firms
1
Mean Sales at Rank
10
0
10
−1
10
−2
10
1
2
3
4
5
6 7 8
16
Within Firm Product Rank
32
72
Figure 2.C.2: Mean exporter scope and mean exporter scale
1
10
0
−1
10
2
−2
10
1
−3
99
75
60
45
Percentile
30
15
97531
10
log Sales
Number of Products
10
Chapter
3
Multiproduct Exporters: Learning
versus Knowing (co-authored with
Kala Krishna)
3.A
Introduction
In recent years trade economists have gained access to narrow classifications of
firms’ exports. This has spurred their interest in the role of multiproduct exporters.
It has been documented for a number of countries that multiproduct firms are
important players in international trade. While small in number they account for
a large share of domestic production and international trade. This preponderance
has led to the conjecture that the addition of products within firms might be a
significant margin of expansion for international trade. While the efficacy of trade
policies has been studied carefully in the single-product firm set up, we still lack a
good understanding of how trade policies affect multiproduct firms.
The response of multiproduct firms to trade policies has been studied in two
sets of frameworks: static models with unobserved firm-product heterogeneity (e.g.
Andrew B Bernard, Redding and Schott, 2011) and static models with core competence on the supply side (e.g. Arkolakis and Muendler, 2010). In these setups
falling entry costs induce entry of only marginally productive firms or the addition
of only marginally profitable products. As a result incumbent firms respond to a
74
reduction in trade costs with introduction of products that sell in minor quantities
and add little to aggregate trade flows.
In this paper we document three data regularities that static models of multiproduct exporters cannot explain. We develop a dynamic model of multiproduct
firms that accounts for these empirical regularities and use it to revisit the question
of trade policy.
Using information on Chinese multiproduct exporters we document the following regularities: (1) multiproduct exporters introduce their best-selling products
first, everything else constant; (2) more than 40% of the new products introduced
by incumbent exporters are dropped due to low sales within the first year1 ; (3)
the probability that a firm introduces a new product is positively related to the
survival and success of its earlier products.
The first empirical regularity is consistent with firms having prior knowledge
about the success of their future product lines, while the second points to uncertainty that incumbent exporters face when they introduce new products. The
third pattern is consistent with firms learning about their potential in an export
market as they introduce new products.
We develop a dynamic model that can fit all three of the above data regularities.
In our model, a firm that contemplates entry into the export market draws a vector
of demand shocks for each of its potential product lines. This set of demand shocks
is known to the firm, but is unobserved to the econometrician. We call these
“known” shocks. They capture the prior knowledge a firm has about the success
of each of its potential products. The fact that firms have prior knowledge about
the demand for each of their potential products makes firms introduce their best
products early on in their exporting experience.
To capture the uncertainty that firms face when they introduce new product
lines and to allow firms to learn about their potential in the export market, we
introduce a Bayesian learning mechanism into the model. Specifically, we assume
that firms are endowed with a firm-specific demand parameter, which we will call
a brand effect. A firm does not directly observe its brand effect, but the brand
effect influences demand for each of its products in a stochastic manner. For each
1
Javoric and Iacovone(2012) document a similar pattern for Mexican firms, except they do
not distinguish between new and incumbent exporters.
75
product that the firm introduces, it draws a second demand shock from a known
distribution with the mean given by the brand effect. These shocks are the sum of
the brand effect and a random component that represents uncertainty. (In the rest
of the paper we will refer to this shock as “uncertainty” shock.) Neither the firm,
nor the econometrician, observe this shock until the firm launches the product and
observes its sales. We call these shocks “s shocks” as they are the signal from which
the firm infers its brand effect. The presence of this uncertainty generates products
that sell poorly and are dropped shortly after launch. As the firm introduces
products into the export market it learns about its underlying brand effect, which
generates history dependence, i.e., firms that have been successful in the past are
more likely to expand.
The model also includes time-varying cost and demand shocks that are needed
to account for the intertemporal variation in the data. More importantly, we
allow the cost of introducing new products to vary with the product scope of the
firm. We do so to ensure that learning effects are not conflated with economies or
dis-economies of scope.
The empirical questions that we ask in this paper are twofold. First, we want
to understand how important each of the mechanisms that we have introduced in
the model is in the data (i.e. “known” demand shocks, uncertainty and learning
about the brand effect). Second, we want to understand what the implications
of these mechanisms for trade policy are. In our model “known” demand shocks,
uncertainty and learning about the brand effect have opposing implications for the
efficacy of trade policy and the overall result depends on which of the mechanisms
dominates in the data. “Known” demand shocks imply that returns to introducing
new products decrease with the scope of the firm. This suggests that a decrease in
the costs of introducing subsequent products will induce introduction of only less
profitable products. Uncertainty about demand in the export market implies that
products that firms expect to be best-selling may not turn out to be successful expost. Similarly, products that firms do not expect to be successful may generate
unexpectedly large sales. Learning about the brand effect further suggests that
there may be additional gains from reducing costs for introducing new products.
For example, lower tariffs or lower market entry costs will induce some foreign
firms to start exporting, i.e., introduce their first product into the export market.
76
As these new exporters learn about their ability to serve the foreign market though
their first product, some will find they are high ability firms and will continue to
enter new product markets more aggressively.2
To answer these questions we use data on Chinese exporters to the U.S. in the
plastics industry, estimate the model structurally, and use it to perform counterfactual experiments. First, we find that known demand shocks play an important
role in whether producers enter the export market or not. Without “known” demand shocks significantly fewer firms enter the export market. Second, we find
that including uncertainty about the brand effect is necessary to account for large
attrition among new exporters. When we let firms know their brand effect precisely, only those with sufficiently high brand effects enter. In that case, the model
cannot replicate disproportionately large attrition of products among new exporters. Third, we find that while firms’ actions are consistent with learning about
their brand effect, the uncertainty they face in conjunction with introducing new
products looms large and limits the impact of learning on firms’ incentives to add
new products. We find that the distribution of products among the high brand
effect firms only marginally first order stochastically dominates the distribution
for low brand effect firms. Furthermore, even when we preclude firms from updating their beliefs about the brand effect, we are still able to (largely) replicate
the distribution of firms over the number of products conditional on the brand
effect. Hence, we conclude that learning affects decisions of firms to introduce new
products only moderately.
Finally, we revisit the question of trade policy in the multiproduct firm setting.
We consider the effect of a decline in the market entry cost for new products
on aggregate exports. Specifically, we look at three scenarios: only the cost of
introducing the first product decreases, the costs of introducing all but the first
product decrease, and the costs of introducing all products decrease. Naturally
a decrease in the cost of introduction for all products has the biggest impact on
aggregate sales. What is interesting is that decreasing only the cost for the first
product has less effect on aggregate sales than decreasing the cost of introduction
for all but the first product. In the first case aggregate sales increase, on average, by
2
Albornoz, Calvo Pardo, Corcos and Ornelas, 2012 propose a similar argument with regard
to firms expansion in new geographic markets.
77
6% and in the second case they increase, on average, by 9% over the period of ten
years. This contrasts with the results of Arkolakis and Muendler, 2010 who find
that a large share of the simulated increase in trade and welfare is attributable
to the decline in the cost of introducing the first product. We find that more
than half of the increase in aggregate sales can be attributed to decreasing costs of
introducing subsequent products. Hence, in the presence of economies of scope and
uncertainty, decreasing costs of market entry for subsequent products can make a
significant contribution to increasing trade flows.
3.A.1
Relation To The Literature
Our paper is closely related to the work of Arkolakis and Muendler, 2010 on the
account of our first data regularity, namely, that sales of products are negatively
related to their order of introduction within a firm. Using information on Brazillian
exporters they document that wide-scope exporters have their sales concentrated in
few top selling products.3 ’4 They interpret this regularity as evidence of decreasing
product specific efficiency , i.e., core competence. Taken literally, their model
predicts that prices should rise as firms introduce products further away from
their core competence. Since firms would introduce products closest to their core
competence first, product prices should rise for products introduced introduced
later in firms’ exporting careers. Table 3.A.1 shows the regression of monthly
prices on the product’s order of introduction within a firm, number of products
attempted by a firm and the age of the product in months. Price and order of
introduction are negatively related suggesting that at least in our sample of firms
core competencies do not belong to the cost side. Our first data regularity is
consistent with the notion of core competence set up on the demand side, or what
3
This regularity is similar to the Andrew B. Bernard, Redding and Schott, 2010 stylized fact
that within firm sales of multiproduct exporters follow a Pareto distribution.
4
It is worth pointing out that this regularity could come about purely as an artifact of
order statistics, rather than as a consequence of core competence. Suppose that firms were
heterogeneous in productivities and drew from a distribution of demand shocks. More productive
firms would take on more risk and attempt to introduce more products. Some of their products
will be successful; others will not be. The maximum (minimum) sales of a firm with many
products would of course be higher (lower) than the maximum (minimum) sales of a firm with
fewer products. This would result in the same pattern as they document. One could tell whether
this patter is just an artifact of order statistics by looking at the order of introduction of a
product and its sales, as we do.
78
we call “known” demand shocks.
Our model is similar in spirit to that of Timoshenko (2013) in that we also
explore the dynamics of firms learning about their brand effect through exporting
new product lines. The novelty of our approach is that we introduce heterogeneity in the prior beliefs of firm managers about firm-product specific success ,i.e.,
“known” shocks. Our strategy to separate the effects of “known” demand shocks
from “uncertainty” relies on the data regularity that firms introduce their bestselling products early on. The relative magnitudes of variances of the “known”
shocks and “uncertainty” shocks determine the extent to which the effects of selection (i.e., firms introduce products that they expect to be best first) are manifested
in the data. If the variance of the “uncertainty” shocks is large, the importance
of the selection mechanism is mitigated: even if firms introduce their best selling
products first, unexpected realizations of “uncertainty” shocks that are not observed until the first sale has been made, will determine which products end up as
best-selling in the data.
Our paper is also indirectly related to the literature that has focused on the
relationship between scope and productivity in order to explain why multiproduct
firms are few in number. Nocke and Yeaple, 2006 focus on the “span of control
approach” (as in Lucas Jr, 1978), and model costs of firms rising for all products
as the firm’s scope increases. Eckel and Neary, 2010 introduce the idea of core
competence: as firms introduce products further away from the core competence,
the marginal cost of each new product increases. Timoshenko, 2013 and Arkolakis
and Muendler, 2010 both embed a model of Eckel and Neary, 2010 into an open
economy setup. We chose not to do so because in our data we do not find evidence of a positive association between price and order of introduction as would be
implied by their assumption.5
The paper is organized as follows. In Section 2 we describe in detail the data
regularities on which we base our model. Section 3 lays out the model. Section 4
describes the estimation procedure and intuition behind identification. Section 5
presents the results and Section 6 concludes.
5
See Table 3.A.1
79
3.B
Empirical Evidence
In this section we discuss the data patterns that shape our modeling decisions.
We will use information on the universe of Chinese exporters supplying the US in
years 2001-2006. For each exporter we have monthly data on sales and prices for
each of their exported varieties at the 6 digit level. Unless stated otherwise before
we do any analysis we standardize sales (prices) for each firm-product pair relative
to the mean sales (prices) across firms for a given HS 6-digit category in a given
month.6
First, we document that a product’s median monthly sales and its order of
introduction within a firm are negatively related. Figure 1 depicts the log of
median monthly firm-product sales plotted against their order of introduction on
the horizontal axis for the cohort of firms that started exporting to the US in
2001.7 Specifically, we take all products that were introduced first, second, etc.,
by all the firms in the sample over the period of four years and compute the log of
median sales for each group. There is a clear decrease in the median monthly sales
as the order of introduction increases. If firms had some information about which
of their potential products were going to be successful in the export market, this
pattern is exactly what we would expect.
To make the case for firms knowing about the potential success of their products
in the market, we need to rule out that products introduced earlier have accumulated a bigger client base and so have larger sales. To address this concern we
regress the log of firm-product monthly sales on the the number of products that
the firm has, the product’s order of introduction, and its tenure in months. We
also incorporate year and industry fixed effects. Table 3.A.2 presents the results.
The coefficient on a product’s age in months is positive and significant indicating
that older products indeed have larger sales. Nevertheless, the effect of the order
of introduction remains negative and significant.
8
The coefficient on a number of
6
Before we use information on prices and sales in our analysis we standardize them as follows.
For each product introduced by a firm we calculate the ratio of sales per month to average sales
in that product category by all firms in that month. This scaling makes sales comparable across
products: a ratio of 1.4 means the product has 40% higher sales than the average for the product.
7
Here we are not excluding products with quotas on them. The pattern is unchanged if we
do.
8
As we are restricting attention to a cohort, we need not worry about composition effects due
to single product firms being young (and possibly more productive).
80
products a firm has is positive, suggesting that overall more productive firms, or
firms with a higher firm-level appeal introduce more products.9
Figure 3.B.2 shows the log of median monthly sales vs. the order of introduction
for product lines that have been exported for the same number of months (2-16
months). The figure corroborates that firms enter exporting with the products
they expect to be most successful.
Recent work by Albornoz et al., 2012, Eaton, Eslava, Krizan, Kugler and Tybout, 2009, and Freund and Pierola, 2010 documents that exit rates are high
among new exporters, and that exporters that survive the first year experience
rapid sales growth. This has been interpreted as evidence for exporters learning
about their appeal in the market. Firms with low appeal drop out of exporting,
while firms that remain grow rapidly. Below we show that the data suggests that
even firms that have previously exported to a market still face risk in conjunction
with introducing new products10 . Tables 3.A.3 and 3.A.4 provide information on
firm-product pairs that were introduced into the export market in 2001.11 Only
firms that have exported before 2001 are included in the sample so that patterns
that characterize first time exporters do not influence conclusions of the exercise.
In Table 3.A.3 we show how the number of firm-product pairs introduced
in 2001 evolves as the cohort ages. The second column of the table reports the
total number of products that are present in a given year out of the total number
of products that were introduced in 2001. For example, out of the 9,440 new
product lines introduced in 2001, 4,378 of them, or about 46%, are still sold in
2002, 3,174 in 2003 and so on. The product lines present in the beginning of the
year are divided into three groups depending on their situation in the beginning
of the following year. Column three reports the products that are still sold in the
following year. Column four shows the number of products that were discontinued
by firms that continued exporting. Column five reports the number of products
that exit because the carrying firm quits exporting. The number in brackets is the
9
One may expect that only the more productive firms introduce new products. Therefore, we
would expect products introduced earlier to have lower median sales than products introduced
later and this would should only strengthen the pattern we observe. If we sort firms by the total
number of products produced and repeat the above exercise, the same pattern emerges.
10
By new products we mean products new for a firm, not a country.
11
Industries with quotas on them include textiles, footwear and headgear. Here other forces
are at play.
81
percentage of products in the given group relative to the total number of products
that were sold in a given year. For example, of the 9,440 products introduced in
2001, we see that 4,054, or about 43%, of them are discontinued by firms that
continued to sell other products in 2002, while 1,008 products disappear from the
export market along with the firm that introduced the product.
A striking pattern is that more than 40% of the products that were introduced
in 2001 are discontinued in the same year by firms that continue to export to the
same market. Attrition in subsequent years drops to about 25%. We interpret
this pattern as evidence that firms face uncertainty about demand for their new
products. The fact that attrition stabilizes quickly after introduction also suggests
that the uncertainty about demand for a given product is resolved soon after
introduction.12
Table 3.A.413 shows the average monthly sales for the cohort of firm-product
pairs that were introduced into the export market in 2001, conditional on whether
the firm-product pair is still exported in the following year. Specifically, it shows
average sales among continuing products (products introduced in t and present in
t+1), products dropped despite the firm remaining in the export market (products
in t, which exit in t + 1 conditional on the firm staying in t + 1), and products
dropped due to firm exit from the export market (products in t, which exit in
t + 1 along with the mother firm). The average monthly sales among products
that are exported in the following period are higher than among products that are
discontinued, regardless of whether the carrying firm continues to export or not.
This is consistent with firms facing uncertainty about their demand shock before
they observe sales of their product.
Now we consider the possibility that firms are endowed with a brand effect that
is common across products, and as exporters introduce new products they learn
about their firm-specific potential in the export market. Such learning would imply
that firms that have introduced successful products in the past would perceive this
as evidence that their brand effect is high and would introduce new products
12
This pattern is consistently present in all cohorts.
Average monthly sales grow as cohort ages. The fastest growth occurs in the first year after
introduction across all cohorts. This pattern also suggests that learning about the demand shock
is fast. Also average sales across all cohorts increase in year 2005. Large growth in year 2005 can
potentially be attributed to a number of reforms undertaken in that year, including trade and
bank sector liberalizations.
13
82
more aggressively. By analogy, firms that introduced products that were dropped
shortly after introduction will perceive this as evidence of a low brand effect and
they would be less likely to introduce new products. To investigate the conjecture
that the past successes and failures inform the decision of the firm to expand its
scope, we estimate the binary logistic probability model of the firm introducing a
new product line:
Pr(yf t = 1|X) = G α + β1 F ratef (t−1) + β2 nf (t−1) + β3 Av.salesf (t−1) + β4 Agef t + β5 T ot expt
(3.B.1)
The dependent variable yf t is the indicator variable that takes value 1 if the firm
indexed by f introduces at least one new product in year t. The independent
regressor F ratef (t−1) denotes the failure rate for the firm f as of time t. It is
computed as the ratio of the number of products the firm has introduced and
abandoned by year t relative to the total number of products the firm (f ) has
introduced since entry into the export market. It is included to test the hypothesis that firms learn about their firm-specific brand appeal as they introduce
new products. If firms learn and take into account their histories, we expect the
probability of introducing a new product to be negatively related to the share of
a firm’s failed products.
nf t−1 is the number of products that the firm has introduced by year t. It
is included to account for the fact that the share of products dropped may have
a different effect on the probability of introducing new products depending on
the scope of the firm. The number of products that a firm has introduced also
may capture the fact that large scope exporters have exhausted their best selling
products and now have a lower probability of introducing a new product. Finally,
it is possible that the cost of entering the export market with each subsequent
product decreases(increases) with scope.
Av.salesf t stands for the average sales per product of a firm. We include
average sales per product for each firm as a measure of firm productivity to account
for the fact that firms that have experienced a rise in productivity will be more
likely to introduce a new product.
The age of exporter f in year t (Agef t ) is simply the number of years we
14
G(.) is the pdf of the logistic distribution.
14
83
observe the firm exporting. Age of the firm is included to account for the fact that
incentives of firms to introduce new products may change with their experience in
the export market. For instance, young firms may experiment with new products
to learn about their brand appeal.
T ot expt is the total exports of the Chinese firms in year t. Annual aggregate
sales are included to account for the changes that affect all exporters over time.
To control for the firm-specific time invariant effects (productivity, industry, etc.)
we use a within estimator for panel data.
In Table 3.A.5 we present the results of the regression for firms that started
exporting between 2001 and 2004 for firms operating in quota-free industries. The
proxy for the history of failures has a negative sign suggesting that firms indeed
take into account their history. Average sales per product and number of products
per firm are marginally significant. Average sales per product has a positive sign
as expected. The number of products has a negative sign consistent with the
hypothesis that firms introduce their best products first. Age has negative sign
suggesting the value of experimentation for the young firms. Total exports that
are included to capture time effects are all near zero and insignificant.
To summarize, we document that (1) multi-product exporters introduce their
best-selling products early; (2) more than 40% of the new products by incumbent
exporters are dropped due to low sales within the first year; (3) for a firm the
probability of introducing a new product is positively related to the survival and
success of its earlier products.
In the following section we describe the model that accommodates each of these
three empirical regularities.
3.C
Model
We develop a partial equilibrium model of multiproduct exporter behavior consistent with the data patterns we have described in the previous section. Launching
new products into the export market is costly and the success of these new products
is uncertain. Firms choose to introduce the kinds of products they believe will be
successful in based on their individual experience.
Our model is cast in continuous time and is based on the modeling techniques of
84
Klette and Kortum, 2004, Eaton et al., 2009, and Arcidiacono, Bayer, Blevins and
Ellickson, 2012. With time being continuous, instead of assuming that events and
decisions are made at fixed intervals of time (i.e. yearly or monthly), we assume
that decisions are made at stochastic intervals of time. For instance, we have
data on monthly sales of the firm, so we could say that firms have to make a sale
every month. Instead, we say that firms make sales on average every x months,
and let the data determine the value of x. Allowing the data determine how
frequently adjustments happen has a few advantages over fixing the times when
firms draw shocks and make decisions. The payoff to introducing new products
changes depending on the history of the firm. A continuous time framework allows
firms to revise their behavior after every event. It also simplifies the computational
burden: in continuous time a firm faces a decision to introduce one more product,
rather than deciding how many products to introduce over a fixed interval of
time as in a discrete time model. For instance, Timoshenko, 2013 allows firms to
experience a change in demand and introduce a new product only once a year. If in
reality the bulk of firms make decisions and draw demand shocks more frequently
than once a year, then the magnitude of the estimated parameters would have to
compensate for the unrealistic rigidity of the model. Choosing a small but fixed
interval of time would not bias estimates, but increases the computational burden
greatly as the number of times the firm’s problem needs to be solved grows rapidly.
We explicitly model a small open economy in a partial equilibrium framework
because we do not have enough data to confidently estimate a general equilibrium
model. We also focus on the US export market only. Previous research suggests
that firms face different entry costs in different markets and may even face different demand structures. Meaningfully incorporating learning across products and
geographic markets would be a computationally daunting task.
Henceforth: f indexes firms, n products and their order of introduction, and t
time. We start with the exposition of the cost side of the firm.
3.C.1
Cost
To incorporate heterogeneity arising from the production side we model the marginal cost of an nth product of a firm f as:
85
cf nt = exp(−$f + uf nt )wfγw kfγr
(3.C.1)
where ($f ) is the firm-specific productivity shifter and (wf ) and (kf ) are the
firm-specific wage rate and capital stock, respectively. The capital stock is included
as a size shifter, i.e., firms with different capital stocks presumably face different
rates of return on capital. The effects of the wage and capital stock on the cost
of the firm are measured by γw and γr . The productivity shock($f ) is constant
over time for each firm and is drawn from a normal distribution with mean m$f
and variance κ$f . uf nt is firm-product specific time variant cost shock. The
distributional assumptions about the firm-product idiosyncratic shock (uf nt ) will
be relayed later. At this point, we will just say that it changes with intensity
(Poisson rate parameter) λeu .
The monopolistic competition assumption yields the price rule for each product
that the firm makes:
pf nt =
3.C.2
σ
cf nt
σ−1
σ ∈ (1, ∞)
(3.C.2)
Demand
A representative consumer at the export destination has CES preferences. There is
a mass of firms supplying multiple products to the foreign consumer. Some of these
firms are Chinese in origin. These are the firms we are studying here. In particular,
there are K products in the universe of exported products. A firm can produce
multiple products indexed by n, but is associated with a unique variety in each
product f . The number of products is finite and in the empirical implementation
will correspond to the four digit international product codes (HS 4-digit). The
number of varieties, or firms, that produce each product can be infinite.
With CES preferences and the assumption that the elasticity of substitution
between products and varieties is the same, demand for a product n made by firm
f at time t is given by:
qf nt = (pf nt )−σ Φ exp(zf nt ).
(3.C.3)
86
σ is the elasticity of substitution between products and varieties and zf nt is the
demand shock for firm f , product n at time t. Since in the empirical implementation we standardize data on products, Φ is the market demand shifter common to
all products.
From now on the subscript n stands for the order of introduction of the product
within a firm, rather than a product category.
The demand shock zf nt is a composite of the firm-product specific permanent
shocks µf n (“known” shock), sf n (s shock), and time variant idiosyncratic firmproduct specific demand shock εf nt :
zf nt = sf n + µf n + εf nt
(3.C.4)
We assume that each firm can make any product from a fixed set of products. For
each of these products a firm draws a permanent product specific demand shock
µf n prior to entry into the export market from a normal distribution N (0, κ2 ). The
realizations of the product specific shocks µf n are known to the firm throughout
its existence. This shock captures the amount of product-specific information that
a firm has about the demand it is going to face in the export market.
The firm-product permanent demand shock sf n is drawn from the normal distribution with mean ηf and variance ψ 2 . More precisely, sf n = ηf + xf n , where ηf
is unobserved to the firm and xf n is normally distributed with mean 0 and variance
ψ. The value of ψ is a common knowledge across all exporters. The firm-specific
parameter, the brand effect ηf , in turn is drawn from a normal distribution with
mean zero and variance τ 2 :
ηf ∼ N (0, τ 2 )
(3.C.5)
The firm does not observe the value of ηf , but knows the distribution from
which it has been drawn. The beliefs of the firm about the value of ηf evolve over
time with the introduction of new products into the export market.
εf nt is drawn together with uf nt from a joint normal distribution N (0, Σ). The
two are potentially correlated. The two shocks change simultaneously according
to the homogeneous Poisson process with rate λeu .
We introduce correlation between the time-variant cost and demand shocks to
relax the consequences of the monopolistic competition assumption. The monopol-
87
istic competition assumption rules out the possibility that profit maximizing firms
with higher demand shocks can charge a higher price for their products. Allowing
the time variant firm-product specific cost shock uf nt to be correlated with the time
variant firm-product specific demand shock εf nt permits us to model the demand
that the firm faces as monopolistic competition without violating the data.
3.C.3
Timing & Information Set
Before we proceed to describe the problem of the firm in detail we lay out a brief
preview of the model and describe the timing assumptions we make. In our set up a
domestic firm that contemplates entry into the export market is described by four
elements: (1) its firm level productivity draw $f , (2) belief about its firm-specific
brand effect ηf n , (3) the set of “known” permanent firm-product specific demand
→ = {µ }N , (4)
shocks for each of its potential products in the export market, −
µ
f
f n n=1
the distribution over possible realizations of the time variant shocks, uf nt and εf nt .
At any instant of time a firm chooses an intensity with which it introduces a new
product into the export market, and wether to continue exporting each product in
its current export portfolio.
→, beThe firm observes the permanent firm-product specific demand shocks, −
µ
f
fore it starts exporting. These shocks are meant to capture the idea that potential
exporters have had domestic experience in selling their products and must have
learned with which products they are most likely to succeed in the export market.
Even exporters that have not sold domestically or exported to other destinations
would have better knowledge about the potential of the firm in a set of products
it can start exporting than would an econometrician. This is the notion of the
demand shock typically employed in heterogeneous demand models where the demand shock is known to the firm but is unobserved to the econometrician.
By construction, expected profits from a product line are directly proportional
to the realization of the firm-product specific shock µf n . It is therefore optimal for
the firm to start exporting with the highest µf n product. To choose how much to
invest into introducing a product into the export market, the firm compares the
payoff to introducing the product with the cost of choosing the intensity with which
this happens. The payoff depends on the expected discounted stream of profits
88
from the product line plus the information value from learning about the firmspecific brand effect. A firm that chooses a hazard rate of introducing a product, λr ,
will be ready do so after a period of time determined by the exponential distribution
with rate parameter λr .
Just before starting production of a product with a given “known” demand
shock µf n , the firm observes the product specific cost and demand shocks (εf nt , uf nt ).
Upon observing these two shocks the firm will decide whether to proceed with the
introduction of the product or not. Variation in the firm-product specific demand
and cost shocks is meant to capture changes in the buyer specific relationships or
physical conditions at the firm’s production facilities that would result in temporary changes in cost or demand. Since conditions at the production facilities are
changing over time, it is reasonable to assume that firms take into account only
the distribution over the possible realizations of εf nt and uf nt when they contemplate entry into new markets. Should we not make this assumption, the number of
state variables that the firm has to track when it introduces a new product would
increase dramatically,15 making the problem intractable.
A firm that decides to start production of its first product after observing the
time variant firm-product specific cost and demand shocks will make its first sale
at the exogenous Poisson rate λs . After making the first shipment of the product
the firm learns the permanent firm product specific shock sf n = ηf + xf n that has
been unknown to it until sale, and updates beliefs about its firm level effect ηf in
a Bayesian manner to (ηf 1 , (τ1 )2 ). To be concise, we omit the firm-specific index
on ηf , ηf n sf n , and xf n from now on.
The updating rule is given by the following sequential update where
sn = η +
(xn
ηn ψ 2 +sn τn2
ψ 2 +τn2
ηn+1 =
ηn otherwise
(
2
τn+1
=
if the firm has introduced a new product and observed sn
τn2 ψ 2
τn2 +ψ 2
if the firm has introduced a new product and observed sn
τn otherwise
So far, we have considered a number of strict timing assumptions about the
sequence of shocks realizations and timing of firms’ actions. These assumptions
15
A firm would have to keep track of the evolution of the firm-product specific shocks $f nt
and uf nt for each product that it can start exporting.
89
considerably simplify the estimation procedure. One such assumption that deserves
particular justification is that it is enough for the firm to observe one sale of a
product to learn about its permanent firm-product specific demand component.
While this assumption clearly oversimplifies the process through which firms learn
about the demand they face for their new product we believe that it does not bias
our results. Table 3.A.3 shows the attrition rates for new products are high in the
first year and stabilize from the second year on. This suggests that learning about
the potential of a product in the market happens quickly.
3.C.4
Decision To Continue Exporting Or Terminate A
Product Line
Before we move on to consider the firm’s problem of introducing a new product
line into the export market we look at the decision of the firm to keep or terminate
an existing product. The present discounted value of a product that the firm is
currently selling can be described by the Bellman equation:
V (ε, u; sn , µn , $) =
max
(3.C.6)
−F + λs [π(ε, u; sn , µn , $) + V (ε, u; sn , µn , $)] + λε,u Eε0 ,u0 V (ε0 , u0 ; sn , µn , $))
,0
ρ + λs + λε,u
The present discounted stream of profits is denoted as V (ε, u; sn , µn , $) where
we omit firm-product specific indices on εf nt and uf nt for brevity. It depends on
the firm-specific productivity $, the two firm-product specific permanent demand
shocks: µn and sn , and the firm product specific time variant cost and demand
shocks: ε, u. A forward looking firm that discounts future at rate ρ and contemplates whether to keep or terminate the product anticipates that it will make a
sale at rate λs and collect profits in the amount π(ε, u; sn , µn , $). It also takes into
consideration the evolution of the product specific cost and demand shocks (ε, u),
which change with exogenously given intensity λeu . The firm pays the fixed cost of
exporting a product F and can terminate the product at any instant of time if the
expected value of profits fails to compensate for the expenditures on fixed cost.
90
3.C.5
Introduction Of New Products
Now we characterize how firms introduce new products. At each instant of time the
firm chooses the intensity with which it introduces a new product to the market,
λr . It choses a value of λr by comparing the expected benefit from adding a
product line to the flow cost of maintaining a given value of λr , cn (λr ). The cost of
choosing an intensity of starting to export a new product, cn (λr ), depends on the
number of products the firm has attempted to export so far. Let v(sn , µn+1 , $)
denote the expected present value of profits from a product before the values of
the time-variant firm-product specific shocks (ε, u) are observed. We obtain it by
integrating the present discounted value of a product line, V (ε, u; sn+1 , µn+1 , $),
over all possible realizations of ε and u:
Z
v(sn+1 , µn+1 , $) =
V (ε, u; sn+1 , µn+1 , $)dN (ε, u; 0, Σ)
(3.C.7)
ε×u
The present value of introducing the (n+1)th product for a firm with n products
depends on the updated distribution of beliefs about the brand effect (ηn , τn2 ),
→:
productivity $, and a set of product specific shocks −
µ
f
→) =
W ((ηn , τn2 ); $, −
µ
f
( −c
= max
λr
n (λr )+λr
R
sn+1
2
);$,−
µ→
[v(sn+1 ,µn+1 ,$)+W ((ηn+1 (sn+1 ),τn+1
f )]dN (sn+1 ;ηn
(3.C.8)
)
,τ 2 +ψ 2 )
n
ρ+λr
where N (sn+1 ; ηn , τn2 +ψ 2 ) represents the normal distribution with mean ηn and
variance τn2 + ψ 2 . The optimal value of λr depends on the expected payoff from
introducing a product: the expected stream of profits plus the value of learning
about its brand effect relative to the cost of choosing the intensity.
To solve the model we assume that the cost attaining a particular hazard
rate,λr , takes the following functional form:
1− c1
c2n (1 − (1 − λr )
cn (λr ) =
1 − c11
1
)
(3.C.9)
We borrow this cost function from Arkolakis and Muendler, 2010 as it has a
number of attractive properties. First, it does not satisfy the Inada condition as
91
λr goes to 0, which allows us to replicate the empirical fact that a large fraction
of firms choose to introduce just one or two products. Second, it lends itself to an
analytical solution. Parameter c1 determines the curvature of the cost function,
while c2n is the scale parameter. c2n varies with the number of products that a
firm has attempted to introduce in order to allow for (dis-)economies of scope. In
the empirical implementation we assume that c2n may be different for products for
the first seven products and remain constant for more products.
16
Solving the first order condition yields a closed form solution for the rate of
introducing new products:
λr = 1−
 R
sn+1

(3.C.10)
→) −c1
→] dN (s ; η n+1 , τ 2 + ψ 2 ) − W (η ; $, −
µ
[v(sn+1 ; µn+1 , $) + W (ηn+1 (sn+1 ); $, −
µ
n
f
f
n+1 n
n

 .
c2(n+1)
The intensity of introducing a new product has the upper limit of one17 and
is increasing in the difference between the expected value of introducing another
product line and the value of maintain the current scope.
Our empirical model consists of key structural equations: the demand equation( 3.C.3), price rule ( 3.C.2) and marginal cost function( 3.C.1) , product introduction equation( 3.C.8), and market participation decision for each product( 3.C.6).
In the following section we will proceed to describe the estimation routine.
3.D
3.D.1
Estimation And Identification
Data
In our structural estimation exercise we focus on firms that operated in the plastics
industry. We chose the plastics industry because it was free from quotas and
16
The reason we assume that the cost of introducing seven or more products is constant is that
we have few firms that have more than seven products, which makes estimating c2n for large n
difficult. An alternative would have been to impose a structure on c2n as a function of n. Our
estimates however suggest that the costs of introducing a new product do not systematically vary
with scope, introducing a functional form could lead to misleading results.
17
The upper limit of one is never binding
92
tariff restrictions during the sample period. We limit ourselves to information
about exporters in 2001-2004, because our model is not equipped to handle the
implications of a number of reforms that took effect in 2005, e.g., banking sector
reform. In Appendix 3 we verify that the patterns we have documented for the
universe of Chinese exporters persist in this subsample of firms that we use for the
structural estimation.
We prepare the sample of firms for the estimation as follows. Using the firm survey dataset we obtain information on the wage rate, capital stock, firm registration
date and start date of exporting for each firm. For firms that export directly18 , we
add to the firm level information data on monthly sales and prices of products at
the 4-digit level from the universe of customs transactions. After excluding firms
that exited and reentered the sample we are left with 5,860 potential exporters
of different ages, of which 645 enter into exporting in 2001. We track these firms
from the moment of their entry to the end of 2004.
3.D.2
Estimation Routine
We estimate all of the parameters in the described model except for the elasticity
of substitution between the products, which set to values to values established in
the literature. We use σ = 8 based on estimates in Das, Roberts and Tybout,
2007, and the instantaneous discount factor, ρ = 0.02, which corresponds to the
annual discount factor of 0.98, as in Arcidiacono et al., 2012. In order to identify
the remaining 22 parameters we will use the indirect inference approach. Using
−−−−−→
actual data we create a vector of moments to match, βd (θtrue ). Given an initial
guess for the set of parameter estimates, θ0 , we generate continuous time data
using the model and then aggregate it to the same level as the observed data.
Using the aggregated data we construct a counterpart of the targeted moments
−−−→
vector, βs (θ0 ). Then using a global search genetic algorithm we numerically solve
for the value of θ̂ such that it minimizes the objective function given by:
−−−→ −−−−−→
−−−→ −−−−−→
(βs (θ̂) − βd (θtrue ))0 W (βs (θ̂) − βd (θtrue ))
18
i.e., those firms that have a match in the customs data
(3.D.1)
93
where W is a weighting matrix. We use a diagonal weighting matrix, whose ele−−−−−→
−−−−−→
ments are given by V ar−1 (βd (θtrue )). We compute each element of V ar−1 (βd (θtrue ))
using the bootstrap.
For each firm in the firm-level survey we observe its first year of operation,
annual wages, capital stocks, and exporting status. For exporters we have data
on sales and prices for each of the exported products at the 4-digit level. In the
simulation routine for each firm in the firm level survey we draw a productivity
2
), and firmshock ($f ) from the distribution of firm productivities N (m$f , κ$
f
specific brand effect, ηf , from the distribution of the brand effects N (0, τ 2 ), and a
vector of time-invariant firm-product shocks for each of the 25 products that the
=25
firm can potentially make {µf n }N
n=1 . Given the draws of primitive shocks, we solve
the firm’s problem to obtain the policy function: the intensity of introducing a new
product. Given the intensity of introducing a product, λr , we draw the time when
the firm starts production from the exponential distribution with the intensity
λr . Next, we draw the time of the first sale from the exponential distribution
with intensity λs , common to all firms and products. After the first sale the firm
observes the demand shock signal sn = ηf + xf n and updates its beliefs about
the distribution of the demand shocks it is facing for its subsequent product, and
chooses a level of intensity of introducing a new product.
For each product the firm introduces, we draw a vector of transitory cost and
demand shocks, as well as the times of their change. Using the policy function of
the firm, we determine which products are going to be sold and which are going
to be dropped. The products with positive present values remain and we simulate
sales of these products.
Eventually for each firm we will have an array of simulated prices, revenues
and times of sale. We use this information to construct analogues of the annual
and monthly datasets that we observe in the data.
3.D.3
Identification
Discussion of identification is informal. The mechanisms presented in the model
are relatively complex and the primitive parameters are jointly responsible for
generating the distribution of sales, prices, and products. To achieve identific-
94
ation we choose moments that are sensitive to changes in some parameters but
not to changes in other parameters. The values of the data and their simulated
counterparts are shown in tables 3.A.6 and 3.A.7 in the order they are discussed
here.
First of all, we face the problem of separately identifying variance of the brand
effects from the variance of the productivity shocks. τ 2 denotes the variance of the
distribution of the brand effects (ηf ). m$f and κ$f are the mean and variance
of the normal distribution from which firm specific productivity shocks, $f , are
drawn. In the model, differences in productivities across firms influence the distribution of prices, while firms’ innate brand effects influence sales conditional on
prices. To pin down the parameters that govern the distribution of firm-specific
productivities we target the {0.25,0.5,0.75,0.98} percentiles of the distribution of
the firm level price indices (average price across all products of the firm and across
time).
In order to identify the variance of the distribution of brand effects, τ 2 , we need
to disentangle the price effect on firm sales from the brand effect. To do so we
use information on prices and sales along with the model to derive an empirical
measure of brand effects. In the model, the composite demand shock is given
by zf nt =
sf nt
p1−σ
f nt Φ
and Φ is constant across products, firms, and time. The ratio
s
f nt
of sales to prices to the power of 1-σ ( p1−σ
∝ zf nt ) is informative about firms’
f nt
demand shocks net of productivity effects. Now, we construct a statistic that is
informative about firm-specific brand effects. We will refer to it as ηf -proxy. First,
we compute a proxy of a product specific demand shock zf n -proxy, by averaging
across monthly values of
sf nt
.
p1−σ
f nt
Then, we compute ηf -proxy as an average across
zf n - proxies. For example, if a given firm f has introduced nf products by the end
of our sample ηf -proxy =
P nf
n=1 zf n −proxy
nf
. We then match the {0.25,0.5,0.75,0.98}
percentiles of the distribution of the brand effect proxies (ηf -proxy).
Another pair of parameters whose identification is tricky are the variances of
the distribution of the unobserved demand shock xf n and “known” demand shock
µf n . The former, xf n , is drawn from N (0, ψ 2 ) and the latter (µf n ) from N (0, κ2 ).
Both of these shocks determine quantities of products sold in the market, as well
as the probability of introducing a new product. A crucial distinction between
the two is that µf n is known by the firm throughout its existence. As for the
95
xf n , the firm only observes the composite sf n = xf n + ηf after the product has
been produced and exported. Intuitively the distribution of xf n pins down the
share of products that are dropped by the firm after introduction due to low sales.
Uncertainty about the realization of xf n , and consequently sf n , is the only source
of uncertainty in the model and explains why firms introduce products that are
quickly dropped due to low sales, as we observe in the data.
The presence of prior knowledge about the success of new products, or the
“known” demand shocks µf n , implies that on average firms will select into their
best-selling products early in their exporting career. The relative magnitudes of
ψ and κ, the variances of xf n and µf n respectively, determine the extent to which
the effects of selection are manifested in the data. If ψ is large the importance
of the selection mechanism is mitigated. Even if firms introduce their best selling
products first, unexpected realizations of xf n , and hence sf n , will determine which
products end up as best selling in the data.
To identify κ, we use information on the relationship between the product’s
demand shocks and it’s order of introduction within a firm. The value of zf n proxy is informative about the underlying µf n + xf n . We regress the obtained
value of zf n -proxy of a permanent firm-product specific demand shock on its order
of introduction within a firm and the number of products the firm has attempted
over the sample period. We include the number of products attempted to account
for the fact that more productive firms would export more products.
Parameters that determine how costly introduction of new products is (c1 and
c21 , c22 , c23 , c24 , c25 , c26 , c27 ) influence the distribution of firms over the number of
products. c1 determines how much firms adjust the intensity of introducing a
new product in response to changes in the expected profits from introducing new
products. Hence c1 not only determines how much firms adjust their intensities
in response to learning more about their brand effect, but also how much intensities differ across firms with different productivities and different sets of “known”
demand shocks. For lower values of c1 we expect to have less dispersion in the
number of products per firm than when c1 is large. To this end, we match the
number of firms that have from one to ten products.
In our model both the learning mechanism and the economies(dis-economies)
of scope imply that firms’ incentives to expand are influenced by the products
96
they have introduced in the past. The implications of the two mechanisms differ
as follows. Learning makes firms that have introduced successful products in the
past more likely to expand, and firms that have introduced products that sold
poorly less likely to expand. If costs of introducing new products are increasing
(decreasing) with scope it affects all firms that have introduced a certain number
of products, regardless of how well these products sold.
To help identify the scope parameters separately from the effect of learning we
match the coefficients of a Poisson regression where the dependent variable is the
number of products introduced in year y and the independent variables describe
the state of the firm in the previous year y − 1. The first independent variable is
the proxy of a firm’s beliefs about its brand effect after introducing nf products by
the end of year y. We denote it as ηf ny -proxy. We first need to compute a statistic
that is informative about the firm-specific demand shock. For each product the
firm has introduced by the end of year y − 1 we will compute an average of
sf nm
p1−σ
f nm
over the number of months a product has been sold since introduction until the
end of the year y −1. Finally, we approximate the belief of the firm about its brand
effect, ηf ny -proxy, as the average value of
sf nm
p1−σ
f nm
over the number of products the
firm has introduced by the end of the year y − 1. We also include the number of
products the firm has introduced and the number of products a firm has dropped
by the end of the previous year.
The ηf ny -proxy and the number of dropped products help to capture how much
a firm responds to changes in their beliefs about its underlying brand effect. They
help pin down the values of c1 , ψ, and τ . The number of products a firm has
attempted so far is informative about the effect of scope parameters, i.e., c21 , c22 ,
c23 , c24 , c25 , c26 , c27 . If costs of introducing new products are decreasing with the
number of products, we expect large scope firms to introduce products more intensively, despite the fact that incentives to introduce new products decrease as
firms run out of their “best-selling” products. Similarly, if costs of introducing new
products are increasing with the number of products we expect that the intensity
with which firms introduce new products will decrease with scope beyond what
is implied by the value of κ, which governs the extent to which firms appear to
introduce their best products first in the data.
The age of firms at the time when they start exporting to the US helps us
97
identify the mean and variance of the firm-specific productivity distribution and
cost of introducing the first product into the export market. Our model implies
that firms that took longer to start exporting since registering are less productive
relative to firms that start earlier.
Even though we have information on the registration date of all firms, we treat
firms that were registered before 1999 as if they did so in 1999 to avoid dealing with
long term dynamics. Firms that have been producing domestically before 1999 (as
early as 1916) may have experienced a change in productivity, ownership, etc. over
such a long period of time. Our model rules that out and would misinterpret firms
that took a long time to start exporting as unproductive.
The fixed cost of exporting a product is pinned down by the mean sales among
the products that are dropped. The intensity of making a sale λs is identified by
matching the average number of shipments per year.
In order to identify the variance-covariance matrix of the distribution of the
time variant cost and demand shocks, Σ, and the hazard rate of a change in these
two shocks,λeu , we target moments of monthly price and sales distributions. We
match the four quantiles {0.25,0.5,0.75,0.98} of monthly prices and backed out
demand shock distributions. We also target correlation between prices and sales.
The correlation between prices and wages, and the correlation between prices
and firms’ capital stocks pin down the effect of wage rates and capital stocks on
the marginal cost of the firm.
3.E
Results
In this section, we present the estimates of the parameters, as well as the counterfactual experiments.
3.E.1
Estimates
Table 3.A.8 shows the estimates of the demand side parameters. The first parameter in the table, τ , is the standard deviation of the firm-specific brand effects.
The second parameter, ψ, determines the degree of uncertainty that firms face
in the export market when they introduce new products. These two parameters
98
govern how long it takes a firm to learn about its brand effect. The larger ψ and
τ are, the harder it is for a firm to extract information about its brand effect
from the signal it receives when it makes a sale. The value of ψ determines the
residual uncertainty that persists even when the brand effect is fully known by
the exporter. Figure 3.B.3 shows the evolution of the variance of the exporter’s
beliefs about its underlying brand effect as it introduces new product lines. The
variance of the perceived brand effect shocks falls by 20% after the introduction
of the first product. After the introduction of the second product, the variance
falls by another 13%. The incremental effects of subsequent new signals decrease
monotonically, so that most of the learning happens with the introduction of the
first few products.
The third row of the table shows the estimate of κ, the standard deviation
of the “known” shocks. Even though it is small in magnitude our counterfactuals
suggest that it plays an important role in determining entry of firms into exporting.
The value of λs we estimate translates into a product being shipped to the
export market at an average rate of 5 times per year, or approximately every 2.5
months. This is consistent with the data sample average. All of the learning and
demand estimates are significant.
Table 3.A.9 shows the estimates of the supply side parameters. The first two
parameters are the mean and standard deviation of the firm-level productivity
distribution. Comparing the standard deviation of the productivity shocks and
the standard deviation of the firm-specific brand effects suggests that the bulk of
firm heterogeneity lies on the demand side. The wage coefficient βw is positive
and significant as would be expected. The coefficient on capital stock, a measure
of firm’s size, has a positive sign, and is insignificant. This is consistent with the
absence of size effects.
The value of λeu , the hazard rate of transient costs and demand shocks changing, translates into such changes occurring on average twice a year. Σ11 = .283
and Σ22 = .973 point to large variation in prices and quantities over time for each
product. The variance of the transient cost shocks is particularly large. This suggests that firm-specific productivity is not sufficient to account for variation in
costs. The correlation between the cost and demand is small but still positive.
The first row of Table 3.A.10 gives the estimate of the instantaneous fixed cost
99
of exporting a product. It translates into the fixed cost of exporting a product being
about 39% of the average profits from a product line across all firms and products.
The scope parameters c21 , c22 , c23 , c24 ,c25 , c26 and c27 are roughly decreasing with
the number of products attempted, consistent with limited economies of scope.
3.E.2
Uncertainty, Experimentation, Selection Into Products,
And Their Consequences
Next we use our estimates to assess the importance of “uncertainty” shocks, learning about the brand effect, and the “known” demand shocks in generating the
histories of firms observed in the data.
We will consider several scenarios. In the full-information scenario we generate
the data under the assumption that firms know their brand effect exactly. We
continue to have firms draw their brand effects from the population distribution,
N (0, τ 2 ), but assume these are known to the firm. To consider the “no learning”
scenario we preclude firms from updating their beliefs about their brand effect
draw. To understand the role that the “known” demand shocks play in determining
the behavior of firms we simulate the model setting the variance of the “known”
shocks to zero.19
In each scenario we simulate a pool of producers that contemplate entry into
exporting. We allow entry of new firms for three quadrimestres (or one year) and
then restrict entry of new firms into exporting and track this cohort of firms for
another nine quadrimestres (three years).
3.E.2.1
Baseline Case
Our model predicts that firms learn about their underlying brand effect through
introducing new products. Firms that have a high brand effect or firms that
come to believe they have a high brand effect, will add products more intensively.
Conversely, firms that come to believe they have a low brand effect stop expanding.
This has implications for the distribution of the number of products per firm for a
cohort of exporters. We expect that as the cohort matures, the distribution of the
19
We might have just made the known demand shock unknown, i.e., added it to the unknown
demand shock instead. We chose not to do this as this would raise the noise in the model and
change the extent to which firms could learn about their brand effect.
100
number of products per exporter for firms with a high brand effect will first order
stochastically dominate the distribution for those with lower brand effects. This is
more so when the variation in the “uncertainty” shocks is low and learning happens
quickly. Figure 3.B.4 illustrates the case when we set the standard deviation of
the “uncertainty” shocks at ψ = 0.2 instead of the estimated ψ = 0.9. It shows
the distribution of firms over the number of products for a cohort of exporters
that started exporting this year conditional on their brand effect. We consider
two groups of exporters: those with a brand effect higher than 0.1 and those with
brand effect below -0.1.
The first panel of the figure 3.B.4 shows the high brand effect exporters and
low brand effect exporters in their first year with ψ = 0.2. There are 41 high brand
firms and 49 low brand ones entering the export market during one year. In the
first year the two groups of exporters exhibit similar distributions of firms over
the number of products. This is natural since prior to entry exporters don’t know
about their brand effect. As the cohort ages, high brand effect firms add a larger
number of products, so that their distribution moves to the right and grows taller.
This pattern becomes clearer as the cohort ages in the third and fourth panels of
the Figure 3.B.4.
Now consider figure 3.B.5. This figure is analogous to Figure 3.B.4 except that
we have used the estimated variance of the “uncertainty” shocks of .9. In this
scenario, the uncertainty that exporters face is much larger than in the previous
scenario. This means learning is more difficult now and firms need to introduce
more products to learn about their brand effect. Thus, the difference in the number
of products that high and low brand effect firms introduce over time is smaller.
Comparing figures 3.B.4 and 3.B.5 we can also see that when uncertainty is
reduced fewer firms enter, and fewer new products are introduced. This is expected
because forecasted profits increase in ψ: when uncertainty is large even firms with
a low productivity and a low brand effect stand a chance to launch a profitable
product with a high unobserved firm-specific demand shock.
3.E.2.2
No Learning Case
When we eliminate the learning mechanism we continue to have firms draw brand
effects from the population distribution, but preclude firms from updating their
101
beliefs. Firms perceive that the unobserved demand shock sn is drawn from the
normal distribution with mean zero and variance given by τ 2 + ψ 2 at all times.
Here we use the estimated value of ψ = 0.89.
Without learning firms’ incentives to introduce new products are independent
of their brand effects and their histories. Figure 3.B.6 shows the distribution of
firms over the number of products for a cohort of exporters conditional on the
brand effect. As in the previous counterfactual we consider firms that draw a
brand effect less than -0.1 (113 entrants ) and those with a brand effect greater
than 0.1 (107 entrants). Note that the distributions for low and high brand effect
firms still differ, but this is just because of selection. High brand effect firms drop
products less often even though they never learn about their brand effect.
Comparing the distributions of firms over the number of products conditional
on the brand effect in the baseline scenario and the analogous distribution of firms
in the no learning scenario in Figures 3.B.5 and 3.B.6 respectively, one can see
that the distributions in the two cases are similar. This reiterates the observation
that just a moderate amount of learning is sufficient to rationalize the product
introducing behavior of exporters in the data.
3.E.2.3
Full Information
Now we consider the full information counterfactual where firms observe their
brand effect draw, ηf , but still face uncertainty about the firm-product specific
demand shocks.
Figure 3.B.7 shows the distribution of firms over the number of products for a
cohort of exporters by brand effect. We consider firms with a brand effect less than
-0.1 and greater than 0.1. The pattern that comes across is the disproportionately
large entry of high brand exporters. 167 exporters with high brand and 48 with
low brand effect enter exporting. The low brand effect exporters that enter are
the highly productive exporters that introduce new products intensively, and so
we see a few large scope low brand effect firms in panels 3-4 that show matured
exporters.
Comparing Figure 3.B.7 to its baseline scenario analogue Figure 3.B.5 suggests that uncertainty about the brand effect is needed to account for the share
of low brand effect firms entering exporting and generating attrition among new
102
exporters.
3.E.2.4
No “Known” Demand Shocks
When we set the variance of the “known” demand shocks to zero, firms no longer
select their best products to introduce first and their incentive to introduce new
products will not decrease over time. This also means that now firms are identically
uncertain about the overall demand for their new products. One would expect that
fewer firms will introduce their first product, or enter exporting.
Figure 3.B.9 shows the distribution of firms over the number of products for a
cohort of exporters under the baseline and no “known” demand shocks assumption.
As expected the number of products in the no “known” demand shocks scenario
falls relative to the baseline. From the first panel in Figure 3.B.9 we can see that
fewer firms enter in the no “known” demand shocks than in the baseline scenario.
3.E.2.5
Aggregate Magnitudes
Now that we have a better understanding how each of the mechanisms is reflected
in the data, we are interested in their implications for aggregate trade flows. Here
we consider the implications of the learning mechanism, uncertainty about the
brand effect and the “known” demand shocks on aggregate sales.
Figure 3.B.10 shows aggregate sales in each of the four counterfactual scenarios
we have considered so far. Implications of the full information and no “known”
shocks scenarios are clear. In the first case, high brand effect firms will introduce
new products more intensely and drive aggregate sales up. In the no “known”
shocks case fewer firms enter exporting and as a result aggregate sales will be
lower than in the baseline case. Aggregate sales in the no learning and baseline
cases are very similar.
To understand why, consider Figure 3.B.11 ,which compares the distribution
of the number of products resulting in the no learning and the baseline cases. One
can see that the number of new exporters is in fact higher in the no learning case
than in the learning one. This means that expected present value of entry is in
fact higher when firms are not learning. This happens because expected profits
are increasing in both τ and ψ. The number of small scope firms is larger in the
103
no learning scenario because firms that fail in the first few products do not cease
to attempt to introduce new products as they do when learning takes place. There
are a few large scope exporters in the baseline scenario. A higher number of the
small scope exporters in the no learning case compensates for the sales generated
by the large scope exporters when firms learn.
To summarize, our counterfactual experiments have identified the channels
through which the mechanisms incorporated in our model (uncertainty, “known”
demand shocks, and learning about brand effect) operate. First, “known” shocks
influence firms’ decisions of whether to start exporting or not. In other words,
firms cope with uncertainty that they face in the export market by introducing
products that they expect to be successful first, i.e., products that have sold well
domestically. This resonates with the empirical regularity that firms usually start
exporting with products that they have sold domestically.20 Second, we find that
uncertainty is large. Even though firms update their beliefs in a Bayesian manner,
the learning is so noisy that their behavior is similar to firms that do not update
their beliefs.
In the following section we reduce costs of introducing new products and evaluate the quantitative implications of the policy.
3.E.3
Costs Of Introducing New Products
In our model the cost of introducing the first product is included in the cost of
starting to export for a firm as it does so with the first product. Here we consider
the effect of a decline in the cost of introducing new products into the export
market on aggregate exports. Specifically, we consider three scenarios. First, we
consider a 25% drop in the cost of introducing the first product (25% drop in
c21 ). Second, we decrease the cost of introducing all of products for a firm (25%
drop in c21 ,c22 ,c23 ,c24 ,c25 ,c26 ,c27 ). Finally, we consider a 25% decrease in the cost
of introducing all but the first product (25% drop in c22 ,c23 ,c24 ,c25 ,c26 ,c27 ).
We simulate a cohort of potential exporters that start production at the beginning of time (i.e., 2001) and gradually enter exporting. We follow their activities in
20
Javoric and Iacovone document this pattern for Mexican firms.
104
the export market for thirty quadrimesters21 . Figure 3.B.12 shows the result. Naturally a decrease in costs for all products has the biggest impact on sales. What is
interesting is that decreasing only the cost for the first product has less of an effect
on aggregate sales compared to decreasing the cost of introduction for subsequent
products, but not the first product. In the first case aggregate sales increase by an
average of 6% and in the second case they increase by an average of 9% . Decreasing the costs of introducing all but the first product disproportionately affects the
more productive exporters, and those exporters who had high s shocks draws and
believe that they have a high brand effect.
The finding that decreasing the cost of introducing subsequent products has at
least as much effect on aggregate sales as does decreasing the cost of introducing the
first product relates to the two experiments with entry costs performed in Arkolakis
and Muendler, 2010. In the first scenario they lower the cost of introducing only
for the first product. In the second, they reduce the cost of introduction into the
export market for all products. They find that the results from the two experiments
are similar to each other, and conclude that the simulated increase in welfare
is attributable to a decline in the firm’s entry cost for the first product. Their
explanation is that product efficiency decreases fast along with costs of introducing
new products. As a result only wide scope exporters find it profitable to introduce
new products, but these products sell in minor amounts and matter little for
bilateral trade.
It is fair to say that, since our model is a partial equilibrium one and is estimated
for just a single industry we could not derive implications for multi-country trade
flows to make it directly comparable to the results of Arkolakis and Muendler,
2010. Nevertheless, our counterfactual suggests that in the presence of uncertainty
and even moderate learning effects, decreasing the costs of introducing subsequent
products can make a significant contribution to increasing trade flows.
3.F
Conclusion
In this paper we quantify the importance of the three mechanisms in determining
observed firm outcomes. The three mechanisms are: uncertainty firms face about
21
In this counterfactual we consider firms entering throughout the simulation time.
105
demand when introducing new products (1), firms learning about their brand effects (2), and firms’ prior knowledge about their potential in each of their products
prior to product introduction (3). To do so we develop a dynamic model of multiproduct exporters with heterogeneity both on the demand and supply side. We
estimate it using information on firms in the Chinese plastics industry and detailed
information on their exports to the US.
We find that the incorporating “known” demand shocks and “uncertainty”
into the model is empirically important in order to account for firms’ product
introducing behavior. We find that “known” shocks play a significant role in
determining new exporter behavior and that “uncertainty” in the export market
is high, making learning noisy.
Next, we revisit the question of trade policy in multi-product setting. We simulate a decrease in the cost of introducing new products for firms. Our simulations
suggest that in the presence of economies of scope and even moderate learning
effects, decreasing costs of introducing subsequent products can make a significant
contribution to increasing trade flows.
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Appendix
3.A
Tables
Table 3.A.1: Product monthly prices and its order of introduction for the
plastics industry
Age in months
Dependent variable: log of monthly product prices
0.0008
(0.0007)
Order of introduction
# of products
N
r2
Standard errors in parentheses.
∗
p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
Includes year fixed effects.
-0.0281∗∗∗
(0.0013)
-0.0215
(0.0358)
34549
0.3667
108
Table 3.A.2: Product monthly sales and its order of introduction (all firms
excluding textiles)
Dependent variable: Monthly product sales
REG1
REG2
∗∗∗
# of products
0.0064
0.0038∗∗∗
(0.0004)
(0.0004)
Order of introduction
-0.0943∗∗∗
(0.0014)
-0.0194∗∗∗
(0.0019)
738,239
0.0070
0.0199∗∗∗
(0.0003)
738,239
0.0118
Age in months
N
r2
Standard errors in parentheses.
∗
p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
Includes year and industry fixed effects.
Table 3.A.3: Evolution of the number of products introduced in 2001
Number
of Sold in t and t + 1 Sold in t only, Sold in t only, carproducts
intro- (% of total).
carrying firm is rying firm exits in
duced in 2001
present in t+1 (% t + 1 (% of total).
and sold in t.
of total).
2001 9,440
4,378 (46%)
4,054 (43%)
1,008 (11%)
2002 4,378
3,174 (72%)
909 (21%)
295 (7%)
2003 3,174
2,426 (76%)
547 (17%)
201 (6%)
2004 2,426
1,861 (77%)
444 (18%)
121 (5%)
2005 1,861
1,345 (72%)
401 (22%)
115 (6%)
Sample includes all firms that started exporting before 2001, excluding those that export textiles, footw
t
109
Table 3.A.4: Average monthly sales per product. Cohort of products introduced
in 2001.
t
2001
2002
2003
2004
2005
Mean sales for products
introduced in 2001 and
sold in t.
0.56
0.82
0.95
1.05
1.72
Mean sales for products
in t, which exit in t +
1 conditional on firm
staying.
0.24
0.38
0.43
0.31
0.41
Mean sales for products
in t, which exit in t + 1
along with the firm.
0.24
0.51
0.40
0.55
0.32
Table 3.A.5: Logit, FE
Dep.var. takes value 1 if a firm has introduce
at least one new product in a year, 0 otherwise.
Share of products dropped after one year in
total number of products (F ratef (t−1) )
-0.9518∗∗∗
Number of products (nf (t−1) )
-0.2822∗∗
Av. sales per product (Av.salesf (t−1) )
0.0416∗∗
Age
Total exports
Obs.
Standard errors in parentheses.
∗
p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
−0.1205∗∗∗
0
4,198
110
Table 3.A.6: Data vs. simulated moments
(Q.p (.) stands for pth percentile of variable (.))
Moment
Data
Simulated
2
N (m$f , κ$
).
f
Firms’ productivity distribution
Firm level price, quantiles
Q.25 (pf )
-1.200
-1.016
Q.5 (pf )
-0.786
-0.455
Q.75 (pf )
-0.248
-0.191
Q.98 (pf )
2.567
0.4
2
Firms’ brand effects distribution N (0, τ ).
Firm brand effect (ηf − proxy)
Q.25 (ηˆf )
-9.319
-4.721
Q.5 (ηˆf )
-4.0249
-4.033
Q.75 (ηˆf )
0.377
-3.3026
Q.98 (ηˆf )
33.956
0.139
2
Distribution of “uncertainty”(xf n ) shocks N (0, ψ ).
Share of products dropped
0.213
0.213
2
Distribution of “known”(µf n ) shocks N (0, κ ).
zf n − proxy = α + β1 nf + β2 max(nf )
α (se)
-4.856(0.269)
-4.464(0.147)
β1 (se)
-0.127(0.044)
-0.093 (0.044)
β2 (se)
0.0497(0.0291)
0.107(0.0341)
7
Cost of introducing new products (c1 , {c2n }n=1 ).
Share of firms that have introduced N products
N=1,2
0.325, 0.187
0.283,0.233
N=3,4
0.142, 0.076
0.183, 0.067
N=5,6
0.0526, 0.0371
0.066, 0.0333
N=7,8
0.023, 0.0263
0.050,0.033
N=9,10
0.0263, 0.020
0.050,0.002
7
Cost of introducing new products (c1 , {c2n }n=1 ). Learning effects, i.e. ψ.
#new products in year y=α + β1 ηf ny−1
ˆ + β2 # products dropped (y-1) +β3 nf y−1 + β4 year
α
112.183 (92.159)
126.75 (72.691)
β1
0.048 (0.01)
0.028 (0.052)
β2
-0.002 (0.0231)
-0.044(0.097)
β3
0.095(0.006)
0.063(0.012)
β4
-0.056(0.046)
-0.063(0.036)
2
Firms’ productivity distribution N (m$f , κ$
) & c1 .
f
Share of firms born in 1998 started exporting in
2001
0.124
0.08
1999
0.065
0.005
2000
0.0534
0.0231
Fixed cost of exporting a product F .
Mean sales among dropped products
-2.620
-2.144
Frequency of shipments, λs .
Average number of shipments per year 5.664
6.82
111
Table 3.A.7: Data vs. Simulated Moments (Continued)
Moment
Data
Simulated
Distribution of transitory cost (uf nt ) and demand shocks (εf nt ). Σ. λeu .
Firm-product price, quantiles
Q.25 (pf ny )
-1.244
-0.981
Q.5 (pf ny )
-0.610
-0.457
Q.75 (pf ny )
-0.131
-0.215
Q.98 (pf ny )
5.470
0.482
Firm-product sales, quantiles
Q.25 (sf ny )
-2.134
-2.247
Q.5 (sf ny )
-0.615
-0.718
Q.75 (sf ny )
0.6803
1.035
Q.98 (sf ny )
4.815
5.589
Covariance between prices and capital stocks 0.1122
0.0014
Unit cost of production.
Covariance between prices and sales
0.105
-0.919
Covariance between prices and wages
0.0323
-0.0211
Table 3.A.8: Learning and Demand Parameters.
Parameter
τ
ψ
κ
Φ
λs
Point estimate(st.error)
St.dev. of brand effects
St.dev. of unobserved demand shocks
St.dev. of known demand shocks
Demand shifter
Hazard rate of making a sale
0.4486
0.8854
0.1316
0.0107
0.1938
(0.068)
(0.011)
(0.012)
(0.034)
(0.277)
Table 3.A.9: Cost of production.
Parameter
m$f
κ$f
βk
βw
λeu
Σ11
Σ12
Σ22
Mean of productivity shocks distribution
St.dev. of productivity shocks distribution
Elasticity of marginal cost wrt. to capital stock
Elasticity of marginal cost wrt. to wage
Hazard rate of a change of transient cost and demand shocks
St.dev of the transient demand shocks
Covariance of the transient cost and demand shocks
St.dev. of the transient cost shocks
Point estimate(st.error)
-0.2266(0.01)
0.1706 (0.0018)
0.0015 (0.0014)
0.0255 (0.0076)
0.0365 (0.036)
0.2831 (0.0006)
0.0073 (0.0036)
0.973 (0.0386)
112
....Estimates of parameters governing introduction of new
products: Economies of Scope.
Table 3.A.10:
Parameter
F
c1
c21
c22
c23
c24
c25
c26
c27
Point estimate(st.error)
Fixed cost of exporting a product
Cost of introducing a new product
Curvature
Cost shifter for the 1st product
Cost shifter for the 2nd product
Cost shifter for the 3rd product
Cost shifter for the 4th product
Cost shifter for the 5th product
Cost shifter for the 6th
Cost shifter for the 7th and higher products
0.0375 (0.003)
0.0114 (0.01)
0.5447 (0.0011)
0.4307 (0.0019)
0.2495 (0.027)
0.3630 (0.0065)
0.4940 (0.0396)
0.1121 (0.0032)
0.065 (0.0462)
113
3.B
Figures
−1
Figure 3.B.1: Median monthly product sales vs. order of introduction
−2
−1.5
21577
11915
7530
3502
−2.5
5294
2433 1654
654
365
197
20
−3.5
−3
1060
78
0
5
10
order_int
log_monthly_sales
Fitted values
15
114
Figure 3.B.2: Median monthly product sales vs. order of introduction condi-
tional on the number of months the product has been exported
−1.5 −1 −.5 0
2
3
2382
362261 138
1262
188 85
818512
−1.5 −1 −.5 0
7
100
115
196
76
49
12
13
644358
250169 58
105 53
42
63
58
11
132
73 58
225
664
176
398
14
1395
100
682393
259150 96
37
15
99
1246
128
800473
293196 92 68
10
1364
1365
659 238
111 55 44
412
188 87
1385
1516
105
680
76
405239
190
6
1558
837517347207134
118
63
94
9
1460
730
56
385254181
111 74
90
696430323
5
1726
911554364
79
266172112
101
8
1471
−1.5 −1 −.5 0
4
1909
2071
412
1139
678 312
16310071
225
49
52
16
1146
1281
595355237159
523 199121
313
539343191 90
134 63 38 40
72 42 27
91
68
44
52
42
0
−1.5 −1 −.5 0
17
18
498
109
169 73
271
43
506283 102
186
18
5
73 49 32
10
0
34
1063
34
0
19
1009
1124
5
5
480
263174 75
59
102
25
27
10
0
5
10
order_int
log_monthly_sales
Graphs by age_in_month
Fitted values
10
0
5
10
115
Figure 3.B.3: Evolution of the variance of the firm’s beliefs about its brand
effect as a function of the number of products introduced
0.25
0.2
τ2(n)
0.15
0.1
0.05
0
0
5
10
15
20
25
Number of products
30
35
40
116
Figure 3.B.4: Distribution of firms over the number of products conditional on
the brand effect. Baseline. (ψ = 0.2). Cohort of firms that entered exporting in
the same year, i.e., in year 1.
Year 1
60
η>0.1; 41 entrants
η<−0.1; 49 entrants
40
20
0
1
2
3
4
5
6
7
8
9
10
Year 2
15
η>0.1
η<−0.1
10
5
0
1
2
3
4
5
6
7
8
9
10
Year 3
10
η>0.1
η<−0.1
5
0
1
2
3
4
5
6
7
8
9
10
Year 4
10
η>0.1
η<−0.1
5
0
1
2
3
4
5
6
7
8
9
10
117
Figure 3.B.5: Distribution of firms over the number of products conditional
on the brand effect. Baseline. case (ψ = 0.89). Cohort of firms that entered
exporting in the same year, i.e., in year 1.
Year 1
100
η>0.1; 105 entrants
η<−0.1; 111 entrants
50
0
1
2
3
4
5
6
7
8
9
10
Year 2
40
η>0.1
η<−0.1
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Year 3
30
η>0.1
η<−0.1
20
10
0
1
2
3
4
5
6
7
8
9
10
Year 4
30
η>0.1
η<−0.1
20
10
0
1
2
3
4
5
6
7
8
9
10
118
Figure 3.B.6: Distribution of firms over the number of products conditional on
the brand effect. No learning (ψ = 0.89). Cohort of firms that entered exporting
in the same year, i.e., in year 1.
Year 1
100
η>0.1; 107 entrants
η<−0.1; 113 entrants
50
0
1
2
3
4
5
6
7
8
9
10
Year 2
40
η>0.1
η<−0.1
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Year 3
40
η>0.1
η<−0.1
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Year 4
30
η>0.1
η<−0.1
20
10
0
1
2
3
4
5
6
7
8
9
10
119
Figure 3.B.7: Distribution of firms over the number of products conditional
on the brand effect. Full information (ψ = 0.89). Cohort of firms that entered
exporting in the same year, i.e., in year 1.
Year 1
150
η>0.1; 167 entrants
η<−0.1; 48 entrants
100
50
0
1
2
3
4
5
6
7
8
9
10
Year 2
60
η>0.1
η<−0.1
40
20
0
1
2
3
4
5
6
7
8
9
10
Year 3
40
η>0.1
η<−0.1
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Year 4
40
η>0.1
η<−0.1
30
20
10
0
1
2
3
4
5
6
7
8
9
10
120
Figure 3.B.8: Share of products dropped relative to the total number of products
in the four scenarios.
0.55
baseline−case
full−information−case
no learning
no heterogeneity in product−specific known demand shocks
0.5
0.45
0.4
Share
0.35
0.3
0.25
0.2
0.15
0.1
0.05
1
2
3
4
5
6
Quaters
7
8
9
10
11
121
Figure 3.B.9: No “known” demand shocks vs. baseline case. Distribution of
firms over the number of products. Cohort of firms that entered exporting in the
same year, i.e., in year 1.
Year 1
200
baseline, 262 entrants
no "known" shocks, 191 entrants
150
100
50
0
1
2
3
4
5
6
7
8
9
10
Year 2
100
baseline
no "known" shocks
50
0
1
2
3
4
5
6
7
8
9
10
Year 3
100
baseline
no "known" shocks
50
0
1
2
3
4
5
6
7
8
9
10
Year 4
60
baseline
no "known" shocks
40
20
0
1
2
3
4
5
6
7
8
9
10
122
Aggregate sales of the cohort
Figure 3.B.10:
8.5
8
Log Aggregate Sales
7.5
7
6.5
6
base case
full−information−case
no learning
no heterogeneity in product−spacific known demand shocks
5.5
5
0
2
4
6
8
Time (Quadrimesters)
10
12
123
No learning vs. baseline scenarios (ψ = 0.89). Distribution
of firms over the number of products. Cohort of firms that entered exporting in
the same year.
Figure 3.B.11:
Year 1
200
baseline, 262 entrant
no learning, 269 entrant
150
100
50
0
1
2
3
4
5
6
7
8
9
10
Year 2
100
baseline
no learning
50
0
1
2
3
4
5
6
7
8
9
10
Year 3
100
baseline
no learning
50
0
1
2
3
4
5
6
7
8
9
10
Year 4
100
baseline
no learning
50
0
1
2
3
4
5
6
7
8
9
10
124
Quadrisemestre aggregate sales. Decreasing the cost of introducing new products.
Figure 3.B.12:
7000
6000
Aggregate Sales
5000
4000
3000
2000
base case
25% drop in c1,c2,c3,c4,c5,c6
25% rop in c1
25% drop in c2,c3,c4,c5,c6
1000
0
0
5
10
15
20
Time (Quadrisemestres)
25
30
125
3.C
Empirical Regularities In The Plastics Industry
In this appendix we verify the data patterns that we have demonstrated in Section
2 for the subsample of exporters operating in the plastics industry between 2001
and 2004. Here we use the HS 4-digit definition of a product.
First, we consider the relationship between the product’s order of introduction
and its sales. We regress the log of firm-product monthly sales on the the number
of products that the firm has, the product’s order of introduction, and its tenure
in months. We also incorporate year fixed effects. Table 3.C.1 presents the results.
As in Table 3.A.2, the effect of a product’s order of introduction on it’s sales is
negative and significant. Similarly, the coefficient on a product’s age is positive
and significant. The coefficient on a number of products a firm retains its positive
sign.
Table 3.C.1: Product monthly sales and its order of introduction. Plastics
industry.
Dependent variable: Monthly product sales
REG1
REG2
∗∗∗
# of products
.058
0.047∗∗∗
(.003)
(0.003)
Order of introduction
-.223∗∗∗
( .007)
-0.161∗∗∗
(0.009)
34521
0.026
0.047∗∗∗
(0.004)
34521
0.03
Age in months
N
r2
Standard errors in parentheses.
∗
p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
Includes year fixed effects.
Next we verify for the plastics industry that a large share of new products are
discontinued shortly after their introduction due to low sales. Table 3.C.2 is the
analogue of Table 3.A.3. It shows how the number of products in a cohort of
products introduced in 2002 by firms that started exporting in 2001 evolves over
126
the years for the subset of firms in the plastics industry. The second column shows
that 40% of products introduced in 2002 are dropped by firms that continue to
export in 2003. In the following year attrition drops to 30%. Table 3.C.3 shows
average monthly product sales as the cohort ages. Sales among products dropped
by firms that continue exporting are lower than for products that are still exported
in the following year.
Table 3.C.2: Evolution of the number of products introduced in 2002 by firms
that started exporting in 2001. Sample includes only firms that operated in the
plastics industry in 2001-2004. HS 4-digit category.
t
2002
2003
Number
of
products
introduced in 2002
and sold in t.
450
245
Sold in t and t + 1
(% of the total).
245(54%)
147(60%)
Sold in t only, the
carrying firm is
present in t+1 (%
of the total).
181(40%)
74(30%)
Sold in t only, carrying firm exits in
t (% of the total).
24(5%)
24(9.8%)
Table 3.C.3: Average monthly sales per product among products introduced in
2002 by firms that have started exporting in 2001. Sample includes only firms
that operated in the plastics industry in 2001-2004. HS 4-digit category.
t
2002
2003
Mean sales for products
introduced in 2002 and
sold in t
0.56
0.87
Mean sales for products
in t, which exit in t +
1 conditional on firm
staying.
0.27
0.21
Mean sales for products
in t, which exit in t + 1
along with the firm
0.46
0.44
In Table 3.C.4 we verify the pattern again by looking at the evolution of the
number of products at the half year intervals. Here we consider the cohort of
products introduced in the first half of 2002 by firms that started exporting in the
first half of 2001 in the plastics industry. A similar pattern emerges.
Finally, we consider wether firms that have introduced successful products in
the past are more likely to expand further. To this end we estimate the binary
logistic probability model of the firm introducing a new product line as we did
in Section 2. Here we omit the total exports variable since it was not significant
in the full sample of the universe of Chinese exporters. Table 3.C.5 presents the
127
Table 3.C.4: Evolution of the number of products introduced in the first half
of 2002 by firms that started exporting in the first half of 2001. The sample
includes only firms that operated in the plastics industry in 2001-2004. HS-4
digit category.
t
2002,1-6
2002,7-12
2003,1-6
2003,7-12
2004,1-6
Number
of
products
introduced in 2002,
1-6 and sold in t.
182
104
73
56
48
Sold in t and t + 1
(% from total).
104(57%)
73(70%)
56(77%)
48(86%)
40(83%)
Sold in t only,
carrying firm is
present in t+1 (%
from total).
75(41%)
24(23%)
16(22%)
7(13%)
5(10%)
Sold in t only, carrying firm exits in
t (% from total).
3(2%)
7(7%)
1(1%)
1(2%)
3(6%)
results. The coefficient on the proxy for the history of failures has a negative sign
confirming that firms indeed take into account their history. The standard error
for the coefficient is higher than what we saw when we considered the universe
of Chinese exporters in Table 3.A.5. This is not surprising since in the plastics
industry we only have 645 observations and the panel is shorter.
Interestingly the coefficient on the number of products a firm has attempted
is larger and more significant compared to the Table 3.A.5. The coefficient on
the age of a firm has a positive sign. The variable age in this regression cannot
be directly compared to the age variable in the analogous regression in Section 2
because there we have considered multiple cohorts of firms, while here we have
only firms that started exporting in 2001.
Overall, we conclude that the patterns we have documented for the universe
of Chinese exporters are present in the subsample of exporters operating in the
plastics industry.
128
Table 3.C.5: Logit, FE. Plastics industry.
Dep.var. takes value 1 if a firm has introduce
at least one new product in a year, 0 otherwise.
Share of products dropped after one year in
total number of products (F ratef (t−1) )
−1.146∗∗
Number of products (nf (t−1) )
−2.116∗∗∗
Av. sales per product (Av.salesf (t−1) )
−.007
Age
Obs.
1.061
645
Standard errors in parentheses.
∗
p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
∗∗∗
129
3.D
Standard Errors
We compute standard errors numerically according to the formula:
0
V ar(θ̂) =
∂m(θ̂) ∂m(θ̂)
W
∂θ
∂θ
!−1
0
∂m(θ̂)
∂m(θ̂)
W [m(θ̂)m(θ̂)0 ]W
∂θ
∂θ
−−−→ −−−−−→
−−−−−→
where m(θ̂) = βs (θ̂) − βd (θtrue ), and W=V ar−1 (βd (θtrue ))
0
∂m(θ̂) ∂m(θ̂)
W
∂θ
∂θ
(3.D.1)
!−1
Lena Sheveleva
Vairo 300 F, State College, PA
[email protected]
(814) 852-9114
EDUCATION
PhD in Economics, Pennsylvania State University, August 2014 (expected).
BA in Economics and Mathematics, American University in Bulgaria (Magna
Cum Laude), 2004-2007.
PhD. THESIS
Essays in Development and International Trade.
Thesis Advisor: Kala Krishna.
FIELDS
Primary: International Trade, Development.
Secondary: Industrial Organization, Macroeconomics.
WORKING PAPERS
Multiproduct Exporters: Learning vs. Prior Knowledge. (job market paper
with Kala Krishna)
Wheat or Strawberries? Intermediated Trade with Limited Contracting. (job
market paper with Kala Krishna)
WORK IN PROGRESS
Multiproduct Exporters. Productivity Differences or Order Statistics. (with
Kala Krishna and Hong Ma)
FELLOWSHIPS
Open Society Institute Fellowship, 2004-2007.
RESEARCH EXPERIENCE
Research Assistant to Kala Krishna, summer 2010-2013.
TEACHING ASSISTANT
ECON 471 International Development (1 semester);
ECON 434 International Finance and Open Economy Macroeconomics (5
semesters);
ECON 304 Intermediate Macroeconomic Analysis (2 semesters);
ECON 104 Introductory Macroeconomic Analysis and Policy (2 semesters).