Product Quality, Market Size and Welfare: Theory and
Evidence from French Exporters⇤
Job Market Paper
Silja Baller
University of Oxford
November 17, 2013
Abstract
This paper presents novel theoretical and empirical insights on the effect of market
size on welfare when product quality is an important dimension of competition. The
setting is a heterogeneous firms trade model with competition effects. I show that the
level of “competitive toughness” in a market is an ambiguous concept in the qualityaugmented model and hence not an informative welfare indicator. Instead, I rely on a
decomposition of the indirect utility function for the subsequent welfare analysis. Although
overall gains from trade are positive, an increase in market size can have conflicting effects
on welfare through different channels. The most robust welfare mechanism associated with
an increase in market-size is an increase in market share for high quality firms. Using
French firm-level export data and a direct measure of firm quality, I provide evidence that
this quality-competition effect is indeed important.
⇤
Acknowledgments: I would like to thank Peter Neary and Beata Javorcik for their continued guidance
and support. I am also grateful to the CEPII in Paris for hosting me as a visiting researcher, Patrice Dumont at
French Customs for helping to obtain data access, and Matthieu Crozet for sharing code. Furthermore, I would
like to thank Richard Baldwin, Paula Bustos, Arnaud Costinot, Matthieu Crozet, Banu Demir, Carsten Eckel,
Lionel Fontagné, Gino Gancia, Thierry Mayer, Gianmarco Ottaviano, Mathieu Parenti and Tony Venables,
as well as seminar participants at the CEPII, LMU Munich, LSE, Oxford, PSE, and participants of ETSG
2013, the 2013 RIEF Doctoral Meetings at Paris I Panthéon-Sorbonne, the 2013 GEP Postgraduate Conference
Nottingham (especially Frank Pisch for acting as a discussant), the 2012 Maynooth INFER Workshop, the
2012 Brixen Workshop on International Trade and Finance, ETSG 2012, the CESifo Conference on Global
Economy 2012, and the 2012 RES Annual Conference for insightful comments, pointers and discussions. I am
grateful to Konrad-Adenauer-Stiftung, Germany for financial support.
1
1
Introduction
Product quality is an important dimension of international competition. The recent trade
literature has provided strong empirical evidence1 of this and several theoretical papers have
formalized the mechanisms.2 This paper adds to the literature by analysing the quality implications for gains from trade and by providing the first empirical evidence for a mechanism
that emerges as very robust from the welfare analysis: a larger market is associated with a
greater market share for high quality firms.
To guide the welfare analysis, I build a quality-augmented heterogeneous firms model with
variable elasticity of substitution (VES) preferences and hence market size effects. The model
combines several mechanisms for gains from trade: quality-adjusted prices and the mass of
varieties are affected by changes on the extensive and intensive margin as well as by firms’
responses in terms of quality choice. Quality affects welfare both directly and indirectly
through the various welfare channels implied by the model.
In the traditional heterogeneous firms models, welfare is directly related to the level of
competitive toughness in a market, which can in turn be summarized by the cost cut-off (the
level of marginal cost that implies break-even in equilibrium). This paper adds to the literature
by showing that in the quality-augmented model, these relationships no longer hold due to
an additional quality channel. An alternative welfare analysis is required. The indirect utility
function is hence derived to provide a complete picture of welfare. Guided by the structure of
the indirect utility function, I analyse each welfare channel in turn and show that an increase
in market size can have conflicting effects on the individual channels. Overall gains from trade
are nevertheless positive.
When it comes to market size effects, I argue that it is necessary to distinguish between two
quality cost structures: when quality is achieved via fixed cost investment only, the optimal
level of quality chosen by high quality firms is increasing in market size. In addition, average
quality increases due to tougher selection and larger market shares for the high quality firms.
When quality production incurs only variable cost, on the other hand, a larger market has no
effect on firm quality choice, such that only the extensive and intensive margin effects remain.
Furthermore, the theoretical welfare impact of the extensive margin depends on assumptions
1
Schott, 2004; Hummels and Klenow, 2005; Hallak, 2006; Iacovone and Javorcik, 2007; Verhoogen, 2008;
Eckel, Iacovone, Javorcik and Neary 2010; Khandelwal, 2010; Baldwin and Harrigan, 2011; Kugler and Verhoogen, 2012; Crozet, Head and Mayer, 2012.
2
Antoniades, 2008; Eckel, Iacovone, Javorcik and Neary, 2010; Baldwin and Harrigan, 2011; Johnson, 2011;
Demir, 2011; Fajgelbaum, Grossman and Helpman, 2011; Fieler, 2011; Crozet, Head and Mayer, 2012.
2
about fixed costs of production and exporting: while the marginal firm has a strictly positive
mass and therefore a positive welfare weight in Melitz (2003)-type models (entrants have to
cover fixed costs of entry, requiring a strictly postive level of output), entrants in models with
a choke price and no fixed costs - as the one presented here - are of zero mass. I therefore do
not emphasize welfare effects with respect to the extensive margin.
The most important welfare prediction for the fixed and variable quality cost models considered here, is that of pro-competitive quality effects on the intensive margin: the assumed
quadratic preference structure implies that a larger market is associated with higher market
shares for high quality firms. Using French firm-level export data and a direct measure of firm
quality, I show that these quality-competition effects are indeed important. I use a dataset
constructed by Crozet, Head and Mayer (2012), which combines French customs data at the
firm-product-destination level (8 digits) for champagne exports with firm quality ratings from
Juhlin’s (2008) champagne guide. The dataset is unique in providing this direct measure of
firm quality. The key idea behind the emprirical implementation is that a larger export market should be associated with a larger increase in a firm’s export sales, the higher its quality
rating. My empirical strategy relies on exogenous variation in market size in the cross-section
of French export destinations as in Mayer, Melitz and Ottaviano (forthcoming). I identify
parameters based on within-firm variation in export sales across these markets. Since the
champagne trade matrix contains only 7% positive trade flows, controlling for selection into
exporting is important. I follow Crozet, Head and Mayer (2012) in using a Tobit model for
this purpose. I find evidence which is consistent with the prediction that high quality firms
increase their export sales disproportionately in a larger market. These findings are robust to
different measures of market size and different definitions of the quality indicator.
This paper was inspired by a rapidly growing empirical literature pointing to an important
role for product quality in international competition. Schott’s (2004) initial observation that
product quality is an important factor in explaining trade patterns has been substantiated by
a wave of recent evidence. In line with the rest of the empirical trade literature over the last
decade, contributions have moved from showing a quality-trade relationship at the country
level to more disaggregated analyses at the product- and firm-level. This paper is the first to
consider the role of quality-related market size effects in the literature.
My contribution builds on Melitz and Ottaviano’s (2008) model of heterogeneous firms
with endogenous mark-ups. I draw elements from two recent quality-augmented models with
VES preferences: the preference structure is adapted from Eckel, Iacovone, Javorcik and Neary
(2010), who assume quality-augmented quadratic preferences in a multi-product firms context.
3
Their formulation with only one quality-related parameter allows for a convenient isolation of
the quality dimension, as opposed to a direct quality-augmentation of Meliz-Ottaviano (2008)
preferences. The assumption, in the baseline model, that quality upgrading requires a fixed
cost follows Antoniades (2008). My paper goes beyond the existing literature by considering
the implications of product quality for gains from trade, checking for robustness of results
across fixed and variable quality cost structures. To the best of my knowledge, this is the first
paper to consider the welfare impact of product quality in a heterogeneous firms context.
Importantly, the VES demand specification allows me to capture the effect of market size
on firm behaviour. Since changes in market size affect the elasticity of demand and hence
mark-ups, a larger market entails a pro-competitive effect. Other recent quality-augmented
theories rely on Melitz (2003) who assumes CES preferences, and therefore do not address
market size effects (Baldwin and Harrigan, 2011; Johnson, 2011; Crozet, Head and Mayer,
2012). Several recent contributions have shown that the assumption of endogenous markups is empirically highly relevant: findings of Syverson (2004) and Campbell and Hopenhayn
(2005), based on data on US states, are consistent with theoretical predictions regarding the
effect of market size on firm selection. Mayer, Melitz and Ottaviano (forthcoming) find that
the size of the destination market is an important determinant of the export behaviour of
multi-product firms in terms of product range and product mix; in particular, they find strong
evidence that in markets with tougher competition, multi-product firms skew their exports
towards their best performing products. My paper adds to this literature by providing some
first empirical evidence on the importance of procompetitive quality effects in a trade context.
The paper fits broadly into the current debate around new trade models and gains from
trade sparked by Arkolakis, Costinot and Rodriguez-Clare’s (2012) contribution. The authors
show that in a large class of trade models ranging from Krugman (1980) to Melitz (2003),
welfare can be summarized by the share of expenditure on domestic goods and a gravityestimator for the elasticity of imports with respect to variable trade costs. Arkolakis, Costinot,
Donaldson and Rodriguez-Clare (2012) show that a variation of this result also applies to a
class of VES models which includes Melitz and Ottaviano (2008). The calibration approach
by ACR (2012) and ACDR (2012), which holds behavioural responses to liberalization fixed,
is, however, not directly comparable to the approach taken here.
The remainder of the paper is organized as follows: the next section presents the theoretical
framework underlying the welfare analysis. Section 3 considers the impact of product quality
on product market competition. Section 4 analyzes the effect of product quality on individual
mechanisms for gains from trade. Section 5 presents the open economy version of the model
4
necessary for the empirical analysis in Section 6. Section 7 concludes.
2
Setup
2.1
Consumers
There are L consumers in the economy, who each supply one unit of labour, and consume
e of a differentiated product; ⌦ will denote the endogenous subset
varieties i from a set ⌦
which is actually consumed. Consumers in this model have identical tastes. Adapting the
specification in Eckel, Iacovone, Javorcik and Neary (2010), I assume quasi-linear preferences,
which are quadratic in the differentiated varieties, and exhibit love of variety and a preference
for quality:
(1)
U = q 0 + u 1 + u2 ,
where
u1 = ↵Q
u2 = b (1

Z
1
b (1 e)
qi2 di + eQ2
2
e
i✏⌦
Z
e)
qi zi di.
e
i✏⌦
Here, q0 denotes the outside good, qi the quantity consumed of variety i, and Q ⌘
The level of product quality embedded in variety i is zi . The parameter
R
e qi di.
i✏⌦
can be interpreted as
capturing the strength of consumers’ quality valuation. The introduction of an explicit quality
parameter as opposed to a more direct quality-augmentation of Melitz and Ottaviano’s (2008)
preferences makes the model highly tractable: setting
= 0 collapses the model to the no-
quality benchmark. The parameter e denotes the degree of horizontal differentiation which
is defined to lie in the range 0 < e < 1; as e ! 1 varieties become perfect substitutes.
Furthermore, note that quality enters utility linearly, as opposed to Antoniades (2008), where
it enters quadratically. I show below that results for the equilibrium mass of varieties and
related welfare results are sensitive to the way in which quality preferences are formulated.
R
Consumers maximise utility subject to the budget constraint q0 + i✏⌦e pi qi di = I. Individual
inverse linear demand functions can then be aggregrated over all consumers to give inverse
market demand faced by firms for each variety. Given market clearing, xi = Lqi , we have:
pi = a i
eb [(1
5
e) xi + eX] ,
(2)
where eb ⌘
b
L
and X ⌘
R
i✏⌦ xi di.
The intercept is ai = ↵ + b (1
e) zi , with product quality
entering as a demand shifter.
The specification of quadratic preferences yields a linear expression for demand for goods
from the differentiated sector. From equation (2), we can write direct demand for variety i as:
xi =
↵
✏eb
1
eb (1
e)
pi +
eN
✏eb (1
e)
beN
z,
✏eb
p + Lzi
(3)
where ✏ = 1 e+eN and where N is the mass of firms in the market (equivalently, the measure
of varieties), p is the average price and z is the average industry quality level. Since demand
is linear, there is a maximum bound to the price pi that firms can charge and face positive
demand. This choke price pmax occurs where demand xi = 0. From equation (3), firms face
positive demand as long as
pi < pmax ⌘
↵ (1 e) eN
+
p + b (1
✏
✏
e) zi
b (1
e) eN
✏
z.
(4)
I show below that zi = 0 if xi = 0, and so the choke price pmax
is the same for all varieties. The
i
fact that selection happens through a choke price rather than due to a fixed cost as in Melitz
(2003), has important welfare implications. In particular, it means that the marginal firm in
this model has zero mass, and hence entry and exit are irrelevant from the point of view of
welfare (Arkolakis, Costinot, Donaldson and Rodriguez-Clare, 2012; Mayer, Melitz, Ottaviano
forthcoming). For completeness, I include analytical results for the extensive margin below,
but do not emphasize them in the empirical analysis.
2.2
Firms
The model economy consists of two sectors, one producing a homogeneous outside good under
perfect competition and constant returns to scale and the other made up of a continuum of
monopolistically competitive firms producing differentiated varieties indexed by i. Labour is
the only factor of production in the model and its supply is perfectly inelastic. The labour
market is assumed to be perfectly competitive and wage is unity.
Firms in the model have rational expectations. In the monopolistically competitive sector,
a continuum of ex ante identical firms initially faces Melitz-type uncertainty about their productivity; the latter is represented by the inverse of their unit cost ci . Paying a sunk cost f
allows firms to draw their cost from a known distribution. Only those firms whose productivity
6
draw is favourable enough to at least break even will stay in the market and produce. All
other firms exit immediately.
All firms that stay in the market in equilibrium also invest in quality. Quality investment
in the differentiated sector is not strategic, rather firms are aggregrate-quality-takers, just like
they are price-index takers. In reality, product quality can be achieved by fixed cost outlays
or additional per unit costs. Here, I consider first the case where product quality incurs
a fixed cost only. Product quality can be interpreted as perceived or real quality and can
therefore be achieved via marketing expenditure or actual product innovation which requires
fixed cost outlays in the form of R&D. I use the cost formulation by Antoniades (2008), where
the level of the fixed cost depends on the level of quality optimally chosen by firms, and is
hence endogenous. Cost is increasing in quality and there are diminishing returns to quality
investment. In Section 4.2, I check for robustness of the fixed cost results for a variable quality
cost structure. The total cost function of a firm consists of two components, a firm-specific
variable cost and an endogenous fixed cost component associated with quality investment:
1
T Ci = ci xi + ✓zi 2 .
2
(5)
The marginal cost of quality also depends on a technology parameter ✓, which is country
specific.
The sequencing of the model is as follows: firms pay the sunk entry cost f which gives
them the right to draw their unit cost ci . Firms whose productivity draw is too low to cover
fixed costs withdraw. The remaining firms simultaneously choose the optimal level of quality
and output, zi and xi . A firm’s profit maximising price and output must satisfy:
pi = eb (1
e) xi + ci ,
(6)
and, its profit maximising level of quality is given by the first-order condition:
zi =
b (1
e) xi
✓
.
(7)
From equation (7), there will be no quality investment by any firm if the cost of quality
upgrading is prohibitive (✓ ! 1), or if consumers do not value quality ( = 0). Importantly,
from equation (7), the optimal level of quality investment is increasing in firm scale xi .
In the class of heterogeneous firms models with monopolistic competition and VES preferences, all equilibrium expressions can be written in terms of a firm’s relative efficiency,
7
ci ) (Arkolakis, Costinot, Donaldson, Rodriguez-Clare, 2012). Optimal quality zi⇤ is here
(cD
given by:
zi⇤ =
where
=
L
2✓
2 b(1
e)L
.
(cD
(8)
ci ) ,
can be interpreted as a market-level indicator of the degree of quality
competition - the greater is , the faster is optimal quality increasing in firm productivity.
is
increasing in market size, a country’s technological capabilities, and preference for quality and
decreasing in the degree of product differentiation. Note that it is positive by second-order
conditions, implying a negative monotonic relationship between optimal quality and a firm’s
cost draw. This insight is important for the empirical implementation below.
At this stage, we can drop the i subscripts since a cost draw c uniquely identifies a product/firm.
2.3
Equilibrium
The model can be solved in the standard way, using the free entry condition (expected profits
have to be zero in equilibrium in the differentiated sector) and parametrizing the cost distribution using Pareto (Melitz-Ottaviano, 2008; Antoniades, 2008). In particular, I assume firms
draw their costs from
G(c) =
✓
c
cM
◆n
, c 2 [0, cM ] ,
where n is the dispersion parameter of the distribution, and a higher n implies a more unequal
distribution of resources among firms (many small firms, very few very large firms). The
explicit solution for the equilibrium cost-cut off is given by:

b (1 e)
cD =
(1 + B) L
where I define
⌘ 2(n + 1)(n + 2)(cM )n f and B ⌘
1
n+2
(9)
,
b (1
e). B can be interpreted as a
demand side summary statistic which is increasing in the scope for quality differentiation.
The cut-off is an indicator of the strength of selection, and affects all firm level and aggregate
indicators of interest – in particular mark-ups, quality levels and the mass of firms.
The mass of active firms in the differentiated sector is given by:
N=
2 (n + 1) (1 e) (↵ cD )
.
e (1 + B)
cD
8
(10)
In the no-quality case, a tougher cut-off is associated with a higher mass of firms. The presence
of product quality adds two effects: (i) from equation (9), we know that quality competition
toughens selection, implying a lower cD and therefore a higher mass of firms. There is, however,
also (ii) a direct effect of quality which works in the opposite direction, implying a lower mass
of firms for higher levels of quality competition. The overall effect of quality on the mass of
firms depends on parameter values.3 I consider the behaviour of the mass of varieties in more
detail below.
The above expressions can be simplified by defining:
" ⌘
" is the elasticity of
@ L
2✓
=
= 1 + B.
@L
2✓
BL
(11)
with respect to market size and can be interpreted as an indicator for a
market’s scope for quality differentiation. It shows how quickly quality competition toughens
as market size increases. Using this definition, all variables of interest can be written in terms
of " and relative efficiency:
p(cD , c) = µ(cD , c) + c =
x(cD , c) =
z(cD , c) =
⇡(cD , c) =
N (cD , c) =
"
(cD
2
c) + c,
" L
(cD c) ,
2b(1 e)
(cD c)
" L
(cD c)2 ,
4b (1 e)
1 2 (n + 1) (1 e) (↵ cD )
.
"
e
cD
(12)
(13)
(14)
(15)
(16)
Note that where quality does not play a role, " = 1 and all expressions reduce to those found
in Melitz and Ottaviano (2008).
3
Antoniades (2008) is an intermediate case, where quality affects the mass of firms only via the cut-off:
the fact that the utility function in Antoniades (2008) is quadratic in quality means firms get an additional
kick in willingness to pay from any given quality investment such that the market can support more firms in
equilibrium. This resonates with Zhelobodko, Kokovin, Parenti and Thisse‘s (2011) observation that "what
looks like an anti-competitive outcome" [here a lower mass of firms in equilibrium for the linear case] "need
not be driven by defence or collusive strategies: it may result from the nature of preferences with well-behaved
utility functions". In the appendix, I present preferences that nest both the specification in this paper and
Antoniades (2008) and derive the associated generalized demand and equilibrium mass of varieties.
9
3
Quality and Product Market Competition
In Melitz (2003) as well as Melitz and Ottaviano (2008), the productivity- or cost cut-off can
be used as short-hand for the level of competition in a market and is therefore informative
for welfare: a lower cut-off implies more stringent selection, greater product variety and lower
prices on average due to higher average productivity of firms and lower mark-ups. Here, I
demonstrate that “competitive toughness” is an ambiguous concept in the quality-augmented
model. Using two standard indicators for the level of competition - the cost cut-off (cD ,
selection) and average mark-ups (µ̄, market power) - I show divergence between the two as the
scope for quality differentiation increases. I illustrate this point by considering divergence of
the two indicators across degrees of product differentiation; the same type of divergence can
also be shown across markets of different size. I hence derive the indirect utility function to
give a more complete picture of welfare and use its structure to guide the analysis of gains
from trade in Section 4.
3.1
Divergence of Competition Measures
In this model, the scope for quality upgrading is increasing in the degree of horizontal differentiation, (1
e). The theoretical link between horizontal and vertical differentiation is
consistent with empirical evidence which suggests that quality investment plays a larger role
in more differentiated sectors (for example Eckel, Iacovone, Javorcik and Neary, 2010; Mandel, 2010; Kugler and Verhoogen, 2012). In particular, we can show that the average level of
quality in an industry is increasing monotonically with the degree of product differentiation
(see appendix). The more differentiated are varieties, the higher are incentives for quality
investment for the most productive firms.
3.1.1
Selection
In Melitz and Ottaviano (2008), the relationship between the degree of product differentiation
and the cost cut-off is monotonic: the more substitutable are products, the tougher is the level
of competition in the market and the tougher is selection. The introduction of quality adds a
countervailing effect. Recalling from equation (9) the expression for the cut-off,
cD =

b (1 e)
" L
10
1
(n+2)
cD#
e=0#
e=1#
e#
Figure 1: Cost cut-off for different degrees of product differentiation (light line: MO benchmark)
the following result obtains:
Lemma 1. The relationship between the cost cut-off and the degree of product differentiation
has an inverted U-shape. Selection is most stringent at the extremes of the differentiation
spectrum, namely where varieties are closely substitutable and where demands are highly independent.
Proof. See Appendix A2.
The result is illustrated in Figure 1, with the monotonic relationship in Melitz and Ottaviano (2008) given as a benchmark case. For values of e which are associated with a high
degree of substitutability (i.e. as e ! 1), the competition effect outweighs the quality effect,
and the relationship hence resembles the no quality-benchmark. As product differentiation
increases, incentives of highly productive firms to invest in quality increase. This is reflected
in a cost cut-off that is falling in product differentiation towards the high differentiation end
of the spectrum. Low productivity firms find it harder to compete, the higher the degree of
differentiation. Note that the location of the turning point in the cD $ e relationship depends
on ✓, the cost of quality innovation, , consumers’ preference for quality and market size L.
The lower the cost of innovation, the higher consumers’ preference for quality, and the larger
the market, the stronger will be the quality effect.
11
3.1.2
Market Power
Mark-ups are another important indicator of the level of competition in a market. Indeed,
the Lerner Index, which is a widely used measure of competition in the industrial organization literature, uses firms’ mark-ups to capture their market power. The model predicts the
following for the average mark-up across different degrees of product differentiation:
Lemma 2. Average mark-ups are monotonically increasing in the degree of product differentiation. Hence, for a high degree of product differentiation, while firms need a higher productivity
to produce [Lemma 1], competition conditional on successful entry is lax.
Proof. See Appendix A3.
In the case of mark-ups, the competition and quality effects are reinforcing each other: as
varieties become more highly differentiated and firms are more protected from their competition, mark-ups are rising. At the same time, the highest productivity firms are investing in
more quality, which increases consumers’ willingness to pay and hence allows those firms to
charge a higher mark-up.
3.1.3
Competitive Toughness
In Melitz and Ottaviano (2008), cD and µ move in the same direction, such that a market
which has tough selection also has low mark-ups; “competitive toughness” is high. In the
quality-augmented model, the idea of “competititve toughness” becomes ambiguous. We can
find two markets at opposite ends of the differentiation spectrum which are characterised by
the same cut-off; however, average mark-ups in the more differentiated market are higher than
in the less differentiated market. Analogous results hold for average quality and conversely,
for the mass of firms (the highly differentiated market has a relatively low mass of firms).
Proposition 3. From Lemmas 2 and 3, the domestic cost cut-off does not fully characterise
the competitive environment. Markets with equally tough selection can have different levels of
average mark-ups, average quality and mass of firms.
In a model where quality investments are important, it is hence necessary to distinguish
between two types of “competitive toughness”: (i) how difficult it is to enter the market as
summarized by the cost cut-off cD ; and (ii) the degree of market power of the average firm,
which is reflected in the average mark-up, µ.
12
More importantly, given the question of market size effects, similar results can be shown
to hold for markets of different size. A larger market always leads to more stringent selection,
but can imply higher average mark-ups for large enough values of
4
(see appendix).
Welfare
In order to avoid the ambiguity associated with the idea of competitive toughness in this
model, I derive the indirect utility function as a more complete indicator for welfare. The
latter takes the following form:
U = Ic +
N
(↵
2✏b
p + Bz)2 +
⇥
N
2b (1 e)
2
p
+ B2
2
z
⇤
.
(17)
Here, I c is the consumer’s income, p2 the variance of prices, and z2 is the variance of quality
R
levels. I assume I c > i✏⌦e pi qi di = pQ b(1N e) p2 , such that the consumption of the numeraire
good is strictly positive. As in Melitz and Ottaviano (2008), the welfare expression displays
love of variety: utility increases in product variety N . Furthermore, welfare is higher, ceteris
paribus, the lower the average price p, the higher the average level of quality z, and the greater
the variance of both prices and quality levels.
4.1
Gains from Trade
When considering the gains from trade in this model, I focus entirely on the market size effects
arising from trade integration. In doing so, I follow the thought experiment in Krugman (1979).
For now, I assume free trade. In Section 5, I consider the open economy version with ice-berg
trade costs for the purpose of the empirical implementation.
13
The relevant expressions for the respective gains from trade mechanisms are given by:
N
=
p =
z =
2
p
=
2
z
=
1 2 (n + 1) (1
"
e
2n + "
cD
2 (n + 1)
e) (↵
cD
(18)
(19)
cD
n+1
1 n ("
2)2
c2
4 (n + 2) (n + 1)2 D
n 2
c2D .
(n + 2) (n + 1)2
Note that where consumers do not value quality, (
cD )
(20)
(21)
(22)
= 0), or where quality investment is
infinitely expensive (✓ ! 1), the above expressions reduce to the expressions in Melitz and
Ottaviano (2008).
4.1.1
Quality
I first consider the implications of trade integration for product quality. Importantly, in the
fixed quality cost case, changes in market size have an effect on quality at the firm level in
addition to the industry composition effect that is characteristic of heterogeneous firms trade
models. Industry composition in turn changes due to responses on the intensive and extensive
margin. I examine all three effects in turn.
Industry Composition: Intensive & Extensive Margin The assumption of VES preferences implies that changes in market size have an effect on firm size (as opposed to CES
preferences, where firm size is fixed and adjustment happens only via the extensive margin).
Combined with the assumption of heterogeneous firms and a profit function which is submodular in market size and firms’ cost draws, an increase in market size has asymmetric effects
across the distribution of firms. We observe what Mrazova and Neary (2011) call the “Matthew
Effect”: to those who have, more shall be given - trade integration magnifies competitive advantages. In our concrete case, it means that an increase in market size will disproportionately
benefit the highest quality firms.
The redistribution of market share to the high quality firms is one mechanism which
contributes to an increase in average quality and hence to an increase in welfare. We can show
14
the result formally for sales:
@r2
@c@L
@r2
@c@L

✓
"2
B
n+1
=
cD
2b(1 e) L n + 2
n+1
< 0 for c <
cD .
n+2
◆
c + B (cD
c) + c
(23)
Firm-level sales are falling in a firm’s marginal cost draw, and these gaps become even larger as
the market gets bigger. From equation (23), note that a higher scope for quality differentiation
increases the skewness of the effect.
Proposition 4. The optimized profit function is submodular in c and L for all cost draws with
c<
n+1
n+2 cD :
an increase in market size implies a disproportionate expansion in sales for high
quality firms. This effect is greater, the greater the scope for quality differentiation.
This result carries over to the degree of quality differentiation, as the gap in quality investment between highly productive firms and lower productivity firms increases as a consequence
of integration:
@z 2
=
@c@L
@
< 0.
@L
On the extensive margin, selection is unambiguously getting tougher in market size, as the
effects of the competition channel are reinforced by the quality channel:
@cD
=
@L
" cD
< 0.
L(n + 2)
As market size gets bigger, only the relatively high quality firms survive. The contribution of
the extensive margin therefore goes in the same direction as the intensive margin in terms of
increasing average quality.
Firm Quality Choice Consider now the effect of an increase in market size across firms
with different cost draws. Figure 2 provides an illustration. As in Antoniades (2008), the
overall pivot of the curve in Figure 2 can be decomposed into a (hypothetical) pivot out to the
right around cD and a (hypothetical) parallel shift in to the new cut-off: the former reflects
the proportional increase in sales which allows a higher level of quality investment for all firms
(i.e. a scale effect); the latter reflects a tightening of selection via a decrease in cD and pushes
the least productive firms out of the market. As a consequence firms fall into one of three
15
z*
cD
upgrade
quality
downgrade
quality
c
exit
Figure 2: Trade Integration and Quality
categories: the best firms optimally choose a higher level of quality. Firms with intermediate
capabilities offer a lower quality product; the lowest quality firms to the right of the new cut-off
do not produce. Intuitively, for the most productive firms, incentives to invest in quality are
higher in markets which are characterised by a higher scope for quality differentiation, making
their varieties even more attractive for consumers. This in turn makes it increasingly difficult
for the least productive firms to enter.
4.1.2
Quality-adjusted Prices
What matters in terms of welfare (Equation 17), are average price and quality levels - or
ultimately, average quality-adjusted prices. For quality, the decomposition into intensive and
extensive margin and firm quality choice effects above shows that all effects are contributing
to an increase in average quality. Prices are affected along the same three margins. Due
to conflicting competition and quality effects, however, average prices can be increasing or
decreasing in market size. If
is high, for example, the quality effect can outweigh the
competition effect, such that average prices increase. We can show formally, however, that the
combined welfare effect is positive.
Proposition 5. Trade integration induces an increase in average quality and can also lead to
an increase in the average price if consumers’ preference for quality is strong. However, the
combined effect on welfare is unambiguously positive.
Proof. See Appendix A5.
16
plot of N for b=1 e=0.5 etc
250
200
B=0
B=1
B=2
N
150
100
50
0
0
1
2
3
4
5
L
6
7
8
9
10
Figure 3: Variety and Market Size
4.1.3
Mass of Varieties
Krugman (1979) first captured the idea of gains from trade through more available product
variety. This result carries over to Melitz and Ottaviano (2008) and also to Antoniades (2008).
However, in the model presented here, for high values of , consumers are trading off higher
quality for variety, such that variety can also be falling in market size.
Proposition 6. In the presence of quality investment, the effect of integration on product
variety is ambiguous; it is negative for large enough values of .
Proof. See Appendix A4.
Where quality differentiation does not play a role ( = 0), the impact of trade integration
on the mass of varieties available is unambiguously positive: a larger market implies a bigger
mass of firms as aggregate demand increases and more firms can be accomodated. However, the
possibility of quality differentiation here dampens this effect, and can reverse it for large enough
. Where consumers have a strong preference for quality, the mass of firms is lower in a larger
market as the most productive firms expand market share and push out disproportionately
many small, low-quality firms.
The result is reminiscent of and adds granularity to Shaked and Sutton’s (1983) finding
that industries in which quality is important, do not see complete fragmentation as market
size gets large.
Note that the result of the quality-variety trade-off relies on two assumptions: (i) consumers’ preferences are linear in quality, i.e. consumers value all quality upgrades equally. In
Antoniades (2008), where preferences are quadratic in quality, a larger market means both
17
Effect of " L on
Mass of firms
Quality-adjusted price
2
p
2
z
for low
"
#
#
"
for high
#
#
"
"
Table 1: Channels for gains from trade
higher average quality and more variety, i.e. consumers in this set-up value quality improvements more at higher levels of quality (in reverse, a downgrade in quality for less productive
firms means only a small loss in willingness to pay); (ii) the assumption of firm heterogeneity is
also necessary (see Baller 2013 for the symmetric firms case, which implies gains from variety
for all parameter values).
4.1.4
Summary & Overall Welfare Impact
Table 1 summarizes the effects of trade integration on the different elements of the welfare
function for environments with high and low scope of quality differentiation (see appendix for
variance results). From this, the overall impact of symmetric trade integration on welfare is
ambiguous. Two predictions stand out: (i) in this model, consumers will benefit from trade
liberalization via higher quality products, with quality-adjusted prices now lower; however
(ii) the higher the scope for quality upgrading, the lower are the gains from variety; industry
concentration may even increase post trade-liberalization, as consumers trade away variety
for higher quality.
By substituting the expressions from equations (18)-(22), we can write welfare in terms of
the endogenous cost-cut off and subsequently obtain a result for overall gains from trade:
1
U =1+
(↵
2eb
⇢
cD ) ↵

✓
n+1
"
1
2n
cD +
1+
1
n+2
n+2
n+1
2
"
◆
cD .
We can show formally:
Proposition 7. Symmetric trade integration has a strictly positive effect on welfare.
Proof. See Appendix A7.
18
(24)
4.2
Variable Cost of Quality
I have so far considered welfare implications of trade integration when quality incurs only
fixed costs. Much empirical evidence however points to the importance of variable quality
cost. Crozet, Head, Mayer (2012) in their paper on quality sorting of champagne exporters
argue that higher quality Champagne incurs higher variable cost due to variation in production
methods and input quality: the variable cost of quality is increasing in the quality of the land
on which the grapes are grown, in the ratio of land to grapes, the time the grapes stay on
the lees, and the cost of the liquids which are added to the champagne at later production
stages. Kugler and Verhoogen (2012) present evidence from Colombian firm-level data showing
that high quality firms systematically use higher quality inputs.4 In what follows, I check for
robustness of results obtained under the fixed cost structure in the case, where quality is
achieved via higher variable cost outlays only.
The set-up is as before with the exception of the firms’ total cost functions. Firm i’s cost
ci is determined as before via a random draw from a known distribution. Total cost is now:
1
xi ci zi' .
'
T Ci =
(25)
In order to ensure an interior solution, I restrict ' > 1, i.e. total cost is convex in quality. Importantly for the empirical implementation, this restriction again implies that the relationship
between firms’ cost draws and optimal quality is monotonic. Firms optimally choose output
and quality according to the following first-order conditions:
and
pi = eb (1
zi =
e) xi +
✓
B
ci
✓
B
ci
◆
1 '
ci z
' i
(26)
.
(27)
1
' 1
Equilibrium quality for firm i is thus simply given by
zi⇤
=
◆
1
' 1
.
Importantly, the optimal level of quality is independent of the cost cut-off. It is determined
4
Baldwin and Harrigan (2011) and Johnson (2011) also assume variable cost of quality.
19
solely by a firm’s cost draw, demand side parameters and the curvature of the MC function.
This is in contrast to the fixed cost case. Intuitively, an increase in scale should not affect
firms’ quality decisions in the absence of fixed costs.
When quality incurs only variable cost, the quality upgrading channel is thus shut down.
Average quality is still increasing in market size, however, this time only due to intensive and
extensive margin effects. The welfare argument for the extensive margin applies as above. I
therefore concentrate my empirical application on identifying intensive margin effects only.
5
Open Economy
Since the empirical specification in Section 6 relies on bilateral export data, I subsequently
derive the main testable prediction of the model for the open economy. Consider now a world
economy with two countries H and F (with l = H, F ), a continuum of differentiated goods
i 2 ⌦, an outside good q0 in each country which is non-tradeable, and iceberg trade costs,
⌧ lh . There is one factor of production L, which is mobile across sectors but immobile across
countries. The consumption side is as above and the production side follows Antoniades (2008).
5.1
Firms
The basic set-up for the production sector is as described for the closed economy above. In
addition, firms now face variable trade costs for their exports. If a firm in l exports to h, its
delivered cost is ⌧ lh c, where ⌧ lh are iceberg trade costs. Note that I assume ⌧ hl = ⌧ lh > 1 for
l 6= h and that I normalize ⌧ ll = 1. Markets are segmented, so firms independently maximise
profits for each market. The optimal level of quality z ⇤ for the domestic and export market
respectively, is here given by:
where
l
D
=
(l) Ll
2✓ (l)
(l)2 b(1
e)Ll
⇣
l⇤
zD
(c) =
l
D
l⇤
zX
(c) =
l lh
X⌧
and
l
X
=
clD
⇣
c
clX
⌘
c
⌘
(h) Lh
2✓ (l)
(h)2 b(1
e)Lh
. Note that the optimal level of
quality depends on the market size of the destination market. It also depends on
which for
simplicity is assumed to be equal in the two countries. As for the domestic variables above,
export prices and quantities for firms in country l exporting to country h can be written as
20
functions of firms’ relative efficiencies, chD
⌧ lh c :
⌘
"lh ⇣ h
cD ⌧ lh c + ⌧ lh c
2
⌘
Lh "lh ⇣ h
cD ⌧ lh c
2b (1 e)
⇣
⌘2
"lh Lh
2
⌧ lh clX c ,
4b (1 e)
plX (c) =
xlX (c) =
l
⇡X
(c) =
where
"lh = 1 + B
is the elasticity of
l
X
lh
=1+B
(h) Lh
2✓(l)
(h)2 b (1
e) Lh
with respect to destination country market size Lh . It gives an indication
of the scope for quality upgrading for l-country firms in export market h.
As before, I assume that productivity draws come from a Pareto distribution. The equilibrium cost cut-off in the open economy can then be shown to be:
2
b (1
6
clD = 4 ⇣
1
where ⇢lh = ⌧ lh
k
e)
⇣
1
"lh hl
⇢
"hh
"lh "hl hl lh
⇢ ⇢
"hh "ll
⌘
1
⌘ 3 n+2
"ll Ll
7
5
. The export cut-off is given by:
clX =
2
chD
1 6 b (1
=
4⇣
⌧ lh
⌧ lh
1
e)
⇣
"hl lh
⇢
"ll
1
"lh "hl hl lh
⇢ ⇢
"hh "ll
⌘
1
⌘ 3 n+2
"hh Lh
7
5
.
If countries have the same quality taste and trade costs are symmetric, the expressions for the
domestic and export cut-off reduce to:
clD
clX
where "h = 1 + B 2✓
Lh
2 b(1
e)Lh
=
=

1
n+2
b (1 e)
(1 + ⇢) "l Ll

1
b (1 e)
⌧ lh (1 + ⇢) "h Lh
1
n+2
,
and analogously for "l . From this, we can see that tougher
21
quality competition in the export market due to larger market size will reduce clX , and therefore
make it harder for l-country firms to export.
Export sales by a firm in l with cost draw c are given by:
l
rX
L h "h ⇣ h
(c) =
c
2b (1 e) D
lh
⌧ c
⌘  "h ⇣
2
chD
⌘
⌧ lh c + ⌧ lh c .
Equivalent to the closed economy case, we can write:
@r2
@c@L
@r2
@c@L

✓
("h )2
B h n+1 h
=
c
2b(1 e) Lh
n+2 D
n+1 h
< 0 for ⌧ lh c <
c .
n+2 D
lh
◆
⌧ c +B
h
(chD
⌧ lh c) + ⌧ lh c
As the size of the export market increases, it is again the high quality firms who benefit
disproportionately in terms of their export sales.
6
Empirical Analysis
I now estimate the importance of the intensive margin effect which emerged as the most robust
mechanism from the theoretical analysis: the model predicts that a larger market is associated
with larger market shares for the firms at the upper end of the quality distribution.
In the model, the impact of market size on firm performance measures such as sales and
product quality depends on a firm’s productivity draw. In both the fixed and variable cost case,
optimal quality is monotonically increasing in productivity, such that a firm’s productivity
draw can also be thought of as their ability to produce quality (or a quality draw in reduced
form).
I rely on exogenous variation in market size across French export destinations. This identification strategy is also used by Mayer, Melitz and Ottaviano (forthcoming), who estimate the
impact of market size on within-firm allocation of resources across products. An alternative
strategy would be to consider liberalization episodes, using variation in market size over time.
However, France has not had liberalization episodes recently which are suitable to capture
exogenous changes in market size.
I rely on within-firm variation in export sales to estimate the quality composition effects.
22
6.1
Data
I use a dataset constructed by Crozet, Head and Mayer (2012), which matches confidential
French firm-product-destination level data of champagne exports with firm-level quality ratings. I consider a cross-section for the year 2005. The champagne producer ratings are from
Juhlin (2008), the most comprehensive existing Champagne guide. The export data comes
from declarations made by French exporters to French Customs. Information about export
flows is collected annually at the 8-digit level. Conveniently, champagne receives its own 8-digit
product code (22041011).
As Crozet, Head and Mayer (2012) argue, Champagne is a fitting product for this analysis
for many reasons: (i) it is one of very few products for which a comprehensive producer quality
rating exists. Juhlin’s (2008) guide provides producer ratings of 1 to 5 stars which can be used
to capture the “real” (as opposed to perceived/marketing) part of product quality. His ratings
cover producers which together cover approximately 90% of all champagne shipments domestically and abroad. Juhlin gives one star to “producers whose wines have aroused my interest”;
just under half the rated firms fall into this category. Five stars are given to the “perfect”
Champagne. There is a high correlation between Juhlin’s ratings and other, less comprehensive, guidebooks. Furthermore, it is common for Champagne producers to blend vintages in
order to guarantee a stable quality such that these ratings remain valid over time; (ii) the industry structure closely resembles the monopolistically competitive structure assumed in the
model: the Champagne industry consists of many small producers (Herfindahl index of 0.033),
who produce differentiated varieties; (iii) 80% of Champagne is exported by firms classified
either as grape-growers or wine-makers, and only 13% is exported by wholesalers; (iv) of those
direct exports, 94% in 2005 came from firms which can be matched to Juhlin ratings. Much
more detail can be found in Crozet, Head and Mayer (2012).
Of the Juhlin-rated firms, in 2005, 284 can be matched with exporting firms which export
to 157 countries, yielding a sample of 44,586 observations once two outliers are removed.5
Of these, 3205 correspond to positive export flows. A full dataset with all relevant gravity
controls is available for 38,574 observations of which 2882 are non-zero export flows.
5
The champagne exporters which were not rated by Juhlin, are currently not included in the sample. They
account for approximately 6% of exports.
23
6.2
Estimation Strategy
The key idea underlying the empirical strategy is that the impact of market size varies with
firms’ quality draw as captured by Juhlin’s producer star ratings. More specifically, we expect
the coefficient on the interaction between market size and firm ratings to be increasing in a
firm’s rating.
The champagne trade matrix contains many zeroes. Of the 38,574 observations in the
dataset, approximately 7.5% correspond to positive export flows. This makes selection into
export markets an important issue. Monte Carlo simulations by Crozet, Head and Mayer
(2012) demonstrate that coefficients are biased in OLS estimations. I control for selection
by estimating the export value equation using a Tobit specification, following Crozet, Head
and Mayer (2012). The authors show that the Tobit estimator performs well in the Monte
Carlo simulations. My model implies a censoring point of zero, since the marginal exporter
here has a zero mass due to the absence of fixed export costs. Since fixed export costs are,
however, important in reality, my preferred specification follows Eaton and Kortum (2001)
and Crozet, Head and Mayer (2012) with regards to the censoring point. Eaton and Kortum
(2001) show that the value of minimum destination exports is a maximum likelihood estimator
of the censoring point in a model with fixed export costs: exports are only observed once a
firm has high enough sales to cover the fixed costs of entry to a market.
Variables I consider two types of quality interaction: (i) a high-low quality dummy where
the high quality dummy is 1 when Juhlin assigns either two, three, four or five stars and 0 if
Juhlin assigns only one star (approximately 40% of firms fall into the one-star category); (ii)
a dummy for each quality level from two to five stars, using the one star group as the base
category.
I also use different measures to capture market size. The first specification simply uses log
GDP as is common in the literature (Hummels and Klenow, 2005; Kneller and Yu, 2008; Harrigan et al, 2012; Mayer, Melitz, Ottaviano, forthcoming;); secondly, I proxy market size with the
log of product-specific absorption (= gross production + imports - exports) as used by Eaton,
Kortum and Kramarz (2004). Since Champagne is produced only in France, Champagne absorption in a destination market consists only of France’s total exports to that destination.
While variation in log GDP is arguably more exogenous, log Champagne absorption seems a
better proxy for market size. To check robustness, I also estimate a specification using market
share as the dependent variable.
24
We have evidence that destination market income, i.e. GDP per capita also matters
for quality trade patterns - Hallak (2006), for example presents evidence that high income
countries tend to import more from countries that produce high-quality varieties. However,
the assumption of quasi-linear preferences in my model abstracts from income effects.
I control for destination market characteristics, using standard gravity variables provided
by the CEPII. In this case, it is possible to identify the destination market size effect for the
base category. Alternatively, I estimate specifications with destination fixed effects, in which
case only the quality-market size interaction is identified.
All specifications contain firm fixed effects. The inclusion of fixed effects in a Tobit model
raises ancillary parameter issues. However, here, the number of fixed effects is small compared
to the number of observations, which reduces these issues significantly (cf Monte Carlo simulations by Crozet, Head and Mayer, 2012). Furthermore, standard errors are clustered at the
country level in all specifications.
Export Value Specification I estimate the following export value relationship for firm f
with producer rating s exporting to destination d:
ln xFf dOB = Zf ⇤ ln Ld + ln Ld + Xd + FFE + "fd ,
or alternatively with firm and destination fixed effects as
ln xFf dOB = Zf ⇤ ln Ld + FFE + DFE + "fd .
With individual star dummies as quality indicators, this specification becomes:
ln xFf dOB = ⌃
s
Zf ⇤ ln Ld + ln Ld + Xd + FFE + "fd
or
ln xFf dOB = ⌃
s
Zf ⇤ ln Ld + FFE + DFE + "fd .
Here, ln xFf dOB is the log export value (using free on board prices),
or
s
are the coefficients
of interest, Zf is an indicator for the star rating, ln Ld is the log of market size, and Xd are
standard gravity controls (since France is always the exporter, they are effectively reduced to
being destination characteristics rather than being dyadic). F F E denote firm fixed effects
and DF E are destination fixed effects.
25
Market Share Specification To check for robustness of results, I also estimate a specification with market share as the dependent variable. Here, the market share of firm f with
producer rating s in destination market d is given by:
msf d =
s s
I ⇤ ln Ld + F F E + "f d ,
where F F E are firm fixed effects. Gravity variables cancel out in the market share specification, only the interaction terms remain.
6.3
Results
While magnitudes of market size effects vary across specifications, they are present and strong
in all of them. Table 2 shows results for the specification with a minimum export value
censoring point and a high/low dummy as a quality indicator (standard errors are given in
parentheses). Columns 1 and 2 include firm fixed effects, while columns 3 and 4 have both firm
and destination fixed effects. In columns 1 and 2, both GDP and Champagne absorption have
a positive and significant effect on their own. More importantly, their interaction with the
quality dummy is also positive and highly significant. This is consistent with the theoretical
prediction that high quality firms increase sales disproportionately relative to low quality
firms as market size gets bigger. Controlling for destination characteristics by means of a
set of gravity controls may not be sufficient to control fully for the competitive environment
in the destination markets. I therefore include destination fixed effects in columns 3 and 4.
The magnitude and significance of the interaction terms are very similar in the specifications
with and without country fixed effects. Note that results are qualitatively the same when
observations are censored at zero rather than the Eaton and Kortum (2001) way (see appendix,
Table 3).
The next specification separates out the interaction effect for each star rating. Table 4
shows the results: columns 1 ane 2 again contain only firm fixed effects and control for destination characteristics using gravity variables; columns 3 and 4 have both firm and destination
fixed effects and identify only coefficients on the interaction terms. Coefficients on all star
ratings are significantly bigger than the 1-star base category in all four specifications. From
column 1, where I control for destination market characteristics explicitly and which uses GDP
as a measure of market size, producers with intermediate star ratings seem to experience the
largest boost from an increase in market size. Effects are more even across high quality producers in column 2, where market size is proxied by the value of champagne absorption in the
26
destination market. When the estimations contain both firm and country fixed effects, rankings as predicted by the theory come through more strongly. In fact, the ranking is perfectly
monotonic in the specification with Champagne absorption interactions.
To check for robustness, I also run specifications with market share as the dependent
variable. These estimations again suggest that the high quality firms are gaining market share
at the expense of the low quality firms as markets get bigger. Table 5 shows results for the
market size interactions with the high quality dummy.
7
Conclusion
The recent literature has presented rich evidence on the importance of product quality in
international trade. This paper provides novel insights on the relationship between product
quality, market size and welfare. The analysis is conducted using the structure of a heterogeneous firms trade model with competition effects. I show theoretically that product quality
has important repercussions on traditional mechanisms for gains from trade and provide empirical evidence for the most robust quality-related welfare channel that emerges from the
analysis. In the quality-augmented model, the idea of the level of “competitive toughness”
in a market is ambiguous, and the cost cut-off is hence no longer an informative summary
statistic for industry aggregates. In order to obtain a complete picture of welfare, I therefore
derive the indirect utility function and use its structure to guide my analysis of market size
effects. I show that an increase in market size can have conflicting effects on the two principal welfare channels in the model: while the quality-adjusted price index falls, variety may
also be reduced if consumers place a high weight on product quality. Nevertheless, overall
gains from trade are positive in all cases. Changes in industry aggregates come about through
changes on the intensive and extensive margin, and in the case of fixed quality costs, there
is also a quality-upgrading margin. I argue that the intensive margin adjustment is the most
robust welfare mechanism in the model, and subsequently provide empirical evidence on its
importance. Using confidential French firm-level data, which is linked to a direct measure of
firm quality, I show that in a larger market, market share is redistributed to the high quality
firms, which raises overall quality in the market. The underlying mechanism to this result is
a complementarity which allows higher quality firms to benefit disproportionately more from
increases in market size.
27
References
[1] Antoniades, Alexis (2008), "Heterogeneous Firms, Quality and Trade", Columbia University, mimeo
[2] Arkolakis, Costas, Arnaud Costinot and Andres Rodriguez-Clare (2012), “New Trade
Models, Same Old Gains?” American Economic Review, 102(1), 94-130.
[3] Arkolakis, Costas, Arnaud Costinot, Dave Donaldson and Andres Rodriguez-Clare (2012),
“The Elusive Pro-Competitive Effects of Trade”, mimeo.
[4] Baldwin, Richard and James Harrigan (2011), "Zeroes, Quality and Space: Trade Theory
and Trade Evidence", American Economic Journal: Microeconomics, 3(2): 60–88
[5] Baller, Silja (2013), DPhil chapter, University of Oxford, mimeo
[6] Berry, Steven and Joel Waldfogel (2004), “Product Quality and Market Size”, Yale Working Papers on Economic Applications and Policy, Discussion Paper No.1
[7] Campbell, Jeffrey R. and Hugo Hopenhayn (2005), "Market Size Matters," Journal of
Industrial Economics, vol. 53(1), 1-25
[8] Crozet, Matthieu, Keith Head and Thierry Mayer (2012), "Quality-Sorting and Trade:
Firm-level Evidence for French Wine", Review of Economic Studies 79(2), 609-644
[9] Demir, F. Banu (2011), "Trading Tasks and Quality," Economics Series Working Papers
582, University of Oxford, Department of Economics.
[10] Eaton, Jonathan and Samuel Kortum (2001), “Trade in Capital Goods”, European Economic Review, 45, 1195–1235.
[11] Eaton, Jonathan, Samuel Kortum and Francis Kramarz (2004), “Dissecting Trade: Firms,
Industries and Export Destinations”, American Economic Review, Vol. 94(2), pp. 150-154
[12] Eckel, Carsten, Leonardo Iacovone, Beata S.Javorcik and J.Peter Neary (2010), "MultiProduct Firms at Home and Away" University of Oxford, mimeo.
[13] Fajgelbaum, Pablo, Gene M. Grossman, Elhanan Helpman (2011), "Income Distribution,
Product Quality, and International Trade", Journal of Political Economy, Vol. 119, No.
4, pp. 721-765
28
[14] Fieler, Ana Cecilia (2011), "Nonhomotheticity and Bilateral Trade: Evidence and a Quantitative Explanation", Econometrica, Vol.79, No.4, pp.1069-1101
[15] Hallak, Juan Carlos (2006), "Product Quality and the Direction of Trade", Journal of
International Economics 68, 238-265
[16] Harrigan, James, Xiangjun Ma, Victor Shlychkov, “Export Prices of US firms”, mimeo
[17] Hummels David and Peter J. Klenow (2005), "The Variety and Quality of a Nation’s
Exports", American Economic Review, 95(3), 704-723
[18] Iacovone, Leonardo and Beata S. Javorcik (2007), "Shipping The Good Tequila Out: Investment, Domestic Unit Values and Entry of Multi-Product Plants into Export Markets",
University of Oxford, mimeo
[19] Johnson, Robert C. (2011), "Trade and Prices with Heterogeneous Firms", Journal of
International Economics, Volume 86(1), 43-56
[20] Juhlin, Richard, Champagne Guide (Richard Juhlin Publishing AB)
[21] Khandelwal, Amit (2010), “The Long and Short (of) Quality Ladders”, Review of Economic Studies, 77, 1450–1476
[22] Kneller, Richard and Zhihong Yu (2008), “Quality Selection, Chinese Exports and Theories of Heterogeneous Firm Trade”, research paper 2008/44, University of Nottingham
[23] Krugman, Paul (1979), "Increasing Returns, Monopolistic Competition and Trade", Journal of International Economics, November 1979, 9, 469-479
[24] Krugman, Paul (1980), “Scale Economies, Product Differentiation, and the Pattern of
Trade”, The American Economic Review 70(5):950-959
[25] Kugler, Maurice and Eric Verhoogen (2012), "Prices, Plant Size, and Product Quality",
Review of Economic Studies, Volume 79(1), 307-339
[26] Mandel, Benjamin (2010), "Heterogeneous Firms and Import Quality: Evidence from
Transaction-Level Prices", Federal Reserve Board International Finance Discussion Paper
No.991
29
[27] Manova, Kalina and Zhiwei Zhang (2012), "Export Prices Across Firms and Destinations", The Quarterly Journal of Economics, Volume 127 (1), 379-436
[28] Mayer, Thierry, Marc Melitz and Gianmarco Ottaviano (forthcoming), "Market Size,
Competition, and the Product Mix of Exporters", American Economic Review
[29] Melitz, Marc J. (2003), "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity", Econometrica, Vol.71(6), 1695-1725
[30] Melitz, Marc and Gianmarco Ottaviano (2008), "Market Size, Trade and Productivity",
Review of Economic Studies 75, 295-316
[31] Meyer, Margaret and Bruno Strulovici (2011), "The Supermodular Stochastic Ordering",
University of Oxford, mimeo
[32] Mrazova, Monika and J.Peter Neary (2011), "Selection Effects with Heterogeneous
Firms", University of Oxford, Discussion Paper Series No.588
[33] Ottaviano, Gianmarco I.P., Takatoshi Tabuchi and Jacques-Francois Thisse (2002), "Agglomeration and Trade Revisited", International Economic Review, 43, 409-436
[34] Shaked, Avner and John Sutton (1983), "Natural Oligopolies", Econometrica, Vol.51 (5),
1469-1483
[35] Schott, Peter K. (2004), "Across-Product vs Within-Product Specialization in International Trade", Quarterly Journal of Economics, Vol.119(2), 647-687
[36] Sutton, John (1991), Sunk Costs and Market Structure, Cambridge, MA: MIT Press.
[37] Syverson, Chad (2004), "Market Structure and Productivity: A Concrete Example",
Journal of Political Economy, 112, 1181-1222
[38] Verhoogen, Eric A. (2008), “Trade, Quality Upgrading and Wage Inequality in the Mexican Manufacturing Sector”, Quarterly Journal of Economics, vol. 123, no. 2, 489-530
[39] Zhelobodko, Evgeny, Sergey Kokovin, Mathieu Parenti, Jacques-Francois Thisse (2011),
"Monopolistic competition in general equilibrium: Beyond the CES," PSE Working Papers halshs-00566431
30
A
Appendix
A.1
Alternative preference specification nesting both Antoniades (2008)
and this paper:
A general preference specification which nests both Antoniades (2008) and the model presented
in this paper is the following:
U
1
b (1
2
= q0 + ↵Q + ↵⇠Z
Z
+ b (1 e) qi zi di.
e)
Z
1
⇠b (1
2
qi2 di
e)
Z
⇢Z ✓
zi2 di
1
be
2
Z
qi zi di
qi
◆
1
⇠zi di
2
2
Letting
⇠ = 1;
= 1;
b(1
be=⌘,
b
e)=
b ; and
the preference specification reduces to Antoniades (2008):
U
= q0 + ↵
Z
qi di + ↵
= q0 + ↵Q + ↵Z
Z
1
2
1
2
zi di
Z
qi2 di
Z
1
2
1
2
qi2 di
Z
zi2 di +
Z
Z
zi2 di +
qi zi di
⇢
1
⌘ Q2
2
1
⌘
2
⇢Z ✓
1
QZ + Z 2
4
Letting
⇠ = 0; and
✓
0 <
<
2✓
Lb(1 e)
◆1
2
we revert to the utility function assumed in equation (1) of this paper:
U = q0 + ↵Q
1
b (1
2
e)
Z
qi2 di
31
1
beQ2 + b (1
2
e)
Z
qi
qi zi di
2
◆
1
zi di
2
2
Similarly, the general demand specification is:
pi = ↵ + b (1
e) zi
b (1
e) qi
be
Z ✓
be
Z ✓
qi
◆
1
⇠zi di.
2
while for the special cases we have - Antoniades:
pi = ↵ + b (1
e) zi
b (1
e) qi
qi
and for this paper:
pi = ↵ + b (1
e) zi
b (1
e) qi
be
Z
◆
1
zi di
2
qi di.
The expression for direct demand derived from the general indirect demand expression above
is:
xi =
A.2
↵
eb✏
1
eb (1
e)
pi +
eN
p + Lzi
eb (1 e)
(2
⇠)
Derivation of a general expression for N:
cD =
1

1
↵ (1
e + eN
N
e) + eN
2n + 1 + B
cD
2 (n + 1)
=
2 (n + 1) (1 e)(↵ cD )
.
B + (2
⇠) b(1 e))ecD
(1
This reduces to
(2
N=
2 (n + 1) (1 e)(↵
ecD
cD )
N=
2 (n + 1) (1 e)(↵
" ecD
cD )
in Antoniades (2008); and to
in this paper.
32
⇠) b(1
beN
z.
2eb✏
e)eN
2 (n + 1)
cD
A.3
Product Differentiation and Average Quality
cD
n+1 
cD 1 + B (n + 1)
=
n + 1 (n + 2) (1 e)
< 0
z =
@z
@e
A.4
Proof of Lemma 1
@cD
@e
B
1
cD
(n + 2) (1 e)
✓
= 0 if e = 1
.
2 bL
=
The limiting cases are:
lim cD
= 0
lim cD

e!1
e!0
A.5
=
b
✓
1
L
2b
2✓
◆
.
Proof of Lemma 2
" cD
2 (n + 1)
" [1 + B (n + 1)]
=
cD
2 (n + 1) (n + 2) (1 e)
< 0.
µ =
@µ
@e
A.6
1
n+2
“Competitive Toughness” and Market Size
A larger market always leads to more stringent selection:
@cD
=
@L
" cD
< 0,
L(n + 2)
33
but can imply higher average mark-ups for large enough values of :
@µ
@L
A.7

" cD
B (n + 1) 1
=
2 (n + 1)
(n + 2) L
1

2
1
2✓
> 0 for
<
n + 2 Lb(1 e)

2✓
<
Lb(1 e)
1
2
.
Proof of Proposition 5
@p
@L
or if
2n + " @cD
1
@"
+
cD
2 (n + 1) @L
2 (n + 1) @L

" cD
B (n + 1) 2n 1
=
2 (n + 1)
(n + 2) L
> 0 if B (n + 1) > 2n + 1
1

2
(2n + 1)
2✓
>
(3n + 2) b(1 e)L
(28)
=
@z
@L
=
(29)
(30)
(31)
"
cD > 0
(n + 2) L
(32)
From equation (17), welfare rises as long as:
@p
@L
B
@z
< 0.
@L
From equations (29) and (32)
@p
@L
A.8
@z
B
=
@L

" cD
n
" +
< 0.
2 (n + 2) L
n+1
Proof of Proposition 6

✓
cn+1
@N
↵
D
=
+ cD
@L
eb (n + 2) f cm n + 2
34
◆
n+1
↵ B
n+2
7 0.
(33)
A.9
Price and Quality Variance
@ p2
@L
=
2 0
1
1 ncD (B
1) 4 @ @cD
@ A
B
+ cD
+ @L
2 (n + 2) (n + 1)2
@L
+
+
|
{z
+
> 0 if B > 1
< 0 if 0  B < 1
3
@cD 5
@L
}
The quality variance on the other hand can be shown to be unambiguously increasing in
market size:
A.10
@ z2
2n cD
=
@L
(n + 2) (n + 1)2
✓
@cD
@
+ cD
@L
@L
◆
>0
Proof of Proposition 7
We have that
U
1
= 1+
(↵
2eb
1
= 1+
(↵
2eb
⇢
n+1
cD +
n+2
n+1
cD +
n+2
cD ) ↵
⇢
cD ) ↵

✓
◆
"
1
2n
2
1+
1
cD
n+2
n+1
"

B
2n (B
1)
cD 1 +
n+2
(n + 1) (1 + B )
We know that in the benchmark case without quality upgrading, symmetric trade integration
unambiguously implies welfare gains:
@U
=
@L
since a > cD and
@cD
@L
1
2eb
✓
2n + 3
↵
n+2
2n + 2
cD
n+2
◆
@cD
> 0,
@L
< 0. This result carries over directly from Melitz and Ottaviano (2008).
For " > 1, it can be shown that the additional term in equation (24) is increasing in L,
such that the above welfare result of positive gains from trade remains:
@ ( cD )
> 0.
@L
Further
@
⇣
B 1
1+B
@L
⌘
=
2B
@
2 @L > 0.
(1 + B )
35
It is hence the case that
A.11
@U
@L
> 0.
Empirics
Table 2: Export Values (Tobit EK censored)
(1)
(2)
(3)
firm FE
yes
yes
yes
destination FE
no
no
yes
ln GDP dest
0.879⇤⇤⇤
(0.199)
ln GDP*quality
0.396⇤⇤⇤
(0.0880)
0.449⇤⇤⇤
(0.0601)
ln ch-absorption
0.983⇤⇤⇤
(0.0889)
ln ch-absorption*quality
0.305⇤⇤⇤
(0.0748)
41462
0.401
Observations
Pseudo R2
38622
0.356
Standard errors in parentheses
⇤
p < 0.05,
⇤⇤
p < 0.01,
⇤⇤⇤
p < 0.001
Note: se clustered at country level
36
(4)
yes
yes
39190
0.424
0.310⇤⇤⇤
(0.0676)
44586
0.418
Table 3: Export Values (Tobit zero censored)
(1)
(2)
(3)
firm FE
yes
yes
yes
destination FE
no
no
yes
ln GDP dest
2.776⇤⇤⇤
(0.478)
ln GDP*quality
0.823⇤⇤
(0.262)
0.924⇤⇤⇤
(0.193)
ln ch-absorption
3.068⇤⇤⇤
(0.192)
ln ch-absorption*quality
0.589⇤⇤
(0.194)
41462
0.320
Observations
Pseudo R2
38622
0.288
Standard errors in parentheses
⇤
p < 0.05,
⇤⇤
p < 0.01,
⇤⇤⇤
p < 0.001
Note: se clustered at country level
37
(4)
yes
yes
39190
0.338
0.553⇤⇤
(0.177)
44586
0.333
Table 4: Export Values
(1)
firm FE
yes
destination FE
no
ln GDP dest
0.884⇤⇤⇤
(0.199)
(Tobit EK censored)
(2)
(3)
(4)
yes
yes
yes
no
yes
yes
ln GDP*2star
0.514⇤⇤⇤
(0.108)
0.356⇤⇤⇤
(0.0616)
ln GDP*3star
0.550⇤⇤⇤
(0.0996)
0.451⇤⇤⇤
(0.0629)
ln GDP*4star
0.297⇤
(0.117)
0.501⇤⇤⇤
(0.0697)
ln GDP*5star
0.222
(0.136)
0.480⇤⇤⇤
(0.0866)
ln ch-absorption
0.985⇤⇤⇤
(0.0917)
ln ch-abs*2star
0.311⇤⇤⇤
(0.0748)
0.243⇤⇤⇤
(0.0543)
ln ch-abs*3star
0.324⇤⇤⇤
(0.0830)
0.266⇤⇤⇤
(0.0643)
ln ch-abs*4star
0.277⇤⇤
(0.0945)
0.386⇤⇤⇤
(0.0869)
ln ch-abs*5star
0.324⇤⇤
(0.109)
41462
0.401
0.426⇤⇤⇤
(0.0960)
44586
0.419
Observations
Pseudo R2
38622
0.357
Standard errors in parentheses
⇤
p < 0.05,
⇤⇤
p < 0.01,
⇤⇤⇤
p < 0.001
Note: s.e. clustered at country level
38
39190
0.424
Table 5: Market Share
(1)
firm FE
yes
ln GDP*quality
0.0341⇤⇤⇤
(0.000967)
ln ch-absorption*quality
Observations
Pseudo R2
39190
0.693
Standard errors in parentheses
⇤
p < 0.05,
⇤⇤
p < 0.01,
⇤⇤⇤
p < 0.001
39
(2)
yes
0.0359⇤⇤⇤
(0.000890)
44586
0.753