### CESIS

### Electronic Working Paper Series

**Paper No. 43 **

**International Trade and Product Variety ** **- a firm level study**

^{1}**Martin Andersson **

### (JIBS)

### Oct 2005

1* Status of the paper: Will be presented at the conference on Globalization and Economic Growth: *

*The Role of Openness, Innovation and Human Capital- Evidence from Micro Data, Shanghai, *
November 4-6, 2005** **** **

**International Trade and Product Variety **

*a firm-level study *

### Martin Andersson

^{Ψ}

*martin.andersson@jibs.hj.se*

*October 2005 *

**Abstract **

This paper adds to the knowledge of the relationship between international trade and product variety by analyzing the relationship between variety in export supply and exports at the firm-level. Using highly detailed firm-level export data in 2003, the paper finds clear empirical evidence for gains from variety in export supply at the level of individual firms. By applying a decomposition methodology related to Hummels & Klenow (2004), it is shown that these gains can be attributed to a larger amount of markets served and larger export sales per market, roughly on a 50-50 basis. The paper also examines how the export variety of firms varies with distance and GDP across markets. The variety of a firm’s export flows to a market increases with the market’s GDP but decreases with distance. The paper estimates that 15 % of the larger export sales to a market with larger GDP can be attributed to a larger number of products exported to the market. Moreover, the paper finds empirical support for quality differentiation on the behalf of individual firms among markets with different GDP. About one third of the effect of GDP on the total value of the export flows to a market can be ascribed to higher average prices per kilogram of the export products. Products shipped over longer distances tend also to have higher average prices per kilogram.

**Keywords: exports, product variety, international trade, multi-product firms **
**JEL codes:** F12, D21, O40

Ψ* JIBS (Jönköping International Business School, Jönköping) and CESIS (Centre for Science and *
*Innovation Studies, Royal Institute of Technology, Stockholm). *

*Contact details: JIBS, P.O Box 1026, SE-551 11, Jönköping Sweden. Phone +46 (0)36 15 75 89, Fax *
+46 (0)36 12 18 32

**1. INTRODUCTION **

Recent contributions to the theory of international trade emphasize the role of product variety. In this approach, gains from trade arise because consumers’

preferences are assumed to be characterized by ‘love-for-variety’ and imports expand the set of product varieties available for consumption. Scale economies in the production of each variety and limited domestic resources prevent a single country from producing all possible varieties. One of several merits of this type of framework is that it offers an explanation for intra-industry (or two-way) trade.

With reference to the new trade theory, a growing literature tries to quantify
the relationships between product variety, trade and welfare. For instance,
Hummels & Klenow (2004) investigates whether larger economies export more
by exporting more of a common set of goods (the intensive margin) or by
exporting a larger set of goods to more markets (the extensive margin). They find
that about 60 % of the bigger exports of larger countries are accounted for by the
extensive margin^{2}. A study by Broda & Weinstein (2004) suggests that
increasing global varieties has a positive impact on world welfare. Moreover, in
a series of papers Funke & Ruhwedel (2001, 2002) have examined the link
between export variety and export performance in East Asian and OECD
countries respectively. Their findings suggest that production of differentiated
export products allows for export market penetration and growth. These results
point towards a positive relationship between product differentiation and
comparative advantage.

The existing literature on the role of variety for exports is, almost without
exceptions, focused on the national level. However, product differentiation also
applies to the export supply of individual firms in the sense that most firms
*supply a product line, i.e. a set of related products (c.f Brander & Eaton, 1984; *

Katz, 1984). In fact, modern manufacturing firms are often ‘multi-variety’ firms.

### 1.1 Product variety in modern manufacturing firms

Milgrom & Roberts (1990) and Milgrom, Qian & Roberts (1991) remark that a
characteristic feature of ‘modern manufacturing’ firms is broad product lines
coupled with frequent updates of the product lines. According to the authors, this
is a response to the development of flexible machine tools and programmable
multitask production equipment in the late 20^{th} century. These technical
innovations lowered the cost of realizing the demand advantages of having
broader product lines, by implying a higher extent of economies of scope.

*Moreover, in the acclaimed book on The Modern Firm, Roberts (2004) *
*emphasizes that there is complementarity between flexibility and variety in *
supply at the level of the individual firm in the sense that “…it will be
worthwhile to bear the costs of flexibility only if the desired variety is high, and
a high level of variety will be worthwhile only if the production system is
flexible”, (ibid, p.38).

Many firms do indeed supply a set of related products. Firms such as Nikon and Pentax, for instance, supply a wide range of different cameras with associated accessories. Similarly, the product lines of firms in the mobile-phone industry, such as Ericsson, Nokia, Motorola, etc., typically consist of a number of differentiated mobile-phones. The same principle obviously applies to the

2 In addition, Schott (2004) finds that richer economies export to the U.S at higher unit prices within narrow product categories.

majority of car manufacturers around the globe. In fact, limited competitiveness
of firms is often partly explained by limited variety in supply^{3}.

### 1.2 Purpose and outline of the paper

Against the background above, this paper analyzes the relationship between the
variety in export supply and exports at the level of the individual firm. To the
author’s knowledge, the existing literature scrutinizing trade at the firm level has
yet not considered this perspective^{4}. The paper estimates an overall elasticity of
firms’ total export value with respect to the variety in their export supply. Then,
the total export value of each firm is decomposed into different components,
such that the relative contribution of each component to the estimated elasticity
can be revealed. The paper also examines how the variety in export supply of an
individual firm to a given market varies with the size of the market’s potential
demand (GDP) and its distance from the country in which the exporting firm is
located. In this respect the paper adheres to the literature on trade that focuses on
the distribution and direction of trade flows.

To assess the relationship between the variety in the export supply of an individual firm and its exports, the paper investigates highly detailed firm-level export data. These data include all Swedish exporting firms during the period.

For each firm, product category and export destination (country) these data
provide information on export value (SEK) and export volume (kilogram). The
product categories are the finest possible according to the CN^{5} classification
system, which is common for EU-member countries. For instance, Swedish firms
exported well over 9 000 different product categories in 2003 according to this
classification system. Moreover, the structure of these data makes it possible to
measure a firm’s export variety along two dimensions: 1) export product
categories and 2) export destinations.

The rest of the paper is organized in the following fashion: Section 2 starts by presenting the typical results as regards export variety and export performance in Krugman (1980), which motivates an overall positive relationship between export variety and the size of exports. Then, the paper uses a model set-up by Johansson (2005) to show how multi-product firms – i.e. firms that produce more than one variety – can be incorporated in the basic framework by Krugman (1980). Section 3 presents the data and reports some stylized facts about export variety at the firm level as regards Swedish firm-level export data. The empirical analysis is presented in the same section. Conclusions of the paper are given in Section 4.

**2. PRODUCT VARIETY AND EXPORT PERFORMANCE **

By using the model of monopolistic competition developed by Dixit & Stiglitz (1977), Krugman (1980) showed how the combination of scale economies, product differentiation and imperfect competition can explain trade between countries with identical factor endowments. Krugman’s analysis also provided a simple illustration of the relationship between the size of a country’s exports and the number of differentiated goods (varities) produced within that country.

3 See for instance Roberts (2004) for a discussion of Ford versus Toyota as regards flexibility, variety and performance.

4 See Tybout (2003) for a survey of this literature.

5 CN = combined nomenclature.

### 2.1 The basic Krugman (1980) result

Consider a case in which consumers derive utility *among a set of K={1,…,n} *

*different product groups. Each product group k can be thought of as the selection *
of differentiated products belonging to a distinct industry. Every consumer shares
the same Cobb-Douglas preferences for the different product groups:

### ∏

∈### =

*k*

*K*

*C*

*k*

^{k}*U* ^{β}

### ∑

*k*

*∈K*

### β

*k*

### = 1

(2.1)where

### β

_{k}*denotes the constant budget share of goods in product group k, 0<*β

*k*

<1∀*k*∈*K. Since each product group k consists of a number of products, each *
*C** _{k }*represents a composite index of the consumption of products in product group

*k. Thus, C*

*k*

*is a sub-utility function defined over the set N*

^{k }*={1,…,n} of products*

*belonging to product group k. C*

*k*is assumed to be a CES-aggregator over the

*varieties available in product group k and takes the following form:*

*C**k*

^{=} ( _{∑}

_{j}_{∈}

_{N}

^{k}*x*

^{θ}

*j*

## )

^{θ}

^{1}∀

*k*∈

*K*(2.2)

*which implies ‘love-for-variety’ for the products within every product group k,*

*since 0< θ <1. A consumer is better off the larger the set of products available for*consumption in each product group.

*Let us now focus on product group k. The specification in (2.2) implies that *
*the demand for a variety in product group k is given by: *

* ^{x}*

*j*=

^{p}^{−}

*j*

^{ε}

### (

^{P}*k*

^{1}

^{−}

^{ε}

### β

*k*

^{Y}### )

*P*

*k*

^{≡} ( _{∑}

_{j}_{∈}

_{N}

^{k}*p*

^{1}

*j*

^{−}

^{ε}

## )

^{1}

^{−}

^{1}

^{ε}

### ∀

*j*

### ∈

*N*

*(2.3)*

^{k}where

### ε ≡ ( 1 − θ )

^{−}

^{1}

*denotes the price elasticity of demand, Y is the consumer*

*income, p*

*j*

*is the price of variety j and P*

*k*denotes the price index of the varieties

*in product group k.*

*Every variety in product group k is produced according to the following cost *
function:

*j*

*j* *x*

*x*

*c*

### ( ) = λ + µ ∀

*j*

### ∈

*N*

*(2.4)*

^{k}where *c*

### (

*x*

_{j}### )

*denotes the total cost of producing x*

*. Equation (2.4) clearly implies (internal) scale economies in production and each variety will thus be produced by a single firm.*

_{j}Given (2.3) and (2.4) each firm will obey the following pricing rule:

### ε µ ε ⎟

### ⎠

### ⎜ ⎞

### ⎝

### ⎛

### = −

*j*

### 1

*p* (2.5)

Since each variety enters in the utility function in (2.2) in a symmetric fashion,
*we have that x**j**=x and p**j**=p for all* *j*∈*N** ^{k}*. This means that the equilibrium

*number of products available for consumption in product group k, n*

_{k}*, can be*expressed as:

### λε β

*Y*

*n** _{k}* =

*∀*

^{k}*k*∈

*K*(2.6)

where

### β

_{k}*Ydenotes the total expenditure on varieties product group k and λ*denotes the fixed costs in production.

Consider now a foreign country denoted by (*), which is identical as regards
consumer preferences and production technology. Assuming that the two
*countries trade in product group k, the total amount of products in this product *
*group available for consumption becomes (n*_{k}* + n*_{k}**). The home country’s share *
*of world exports in product group k can then be formulated as in Equation (2.7): *

^{*} ( _{k}_{k}^{*})

*k*
*k*

*k*
*k*

*n*
*n*

*Y*
*n*

*n*
*n*

= +

+

### λ

### ε

### β

∀*k*∈

*M*(2.7)

*This equation states that if the home country’s expenditure on product group k *
increases relative to foreign, then the home country will increase its share of
world exports in the same product group simply because it increases the number
of products produced in that product group. According to this framework then,
the size of the total export in a specific product group and the number of products
produced in the same product group are inseparable phenomena.

### 2.2 Allowing for multi-product firms

In the former model each variety is produced by single firm. However, as stated in the introduction many firms can be characterized as ‘multi-product’ firms in the sense that they produce a range of products, often within a specific product group. Here a model set-up by Johansson (2005) will be used to illustrate how economies of scope – and hence multi-product (or multi-variety) firms – can be incorporated in the basic Krugman (1980) structure.

Formally, economies of scope obtains when the following condition is satisfied, (Bailey & Friedlander, 1982):

) , 0 ( ) 0 , ( ) ,

(*x*_{1} *x*_{2} *c* *x*_{1} *c* *x*_{2}

*c* < + (2.8)

*i.e. when the joint production of x*_{1 }*and x** _{2 }*results in lower total costs than separate
production. A cost function which contains an input common for a set of
products (or varieties) satisfies the criteria in (2.8), (Panzar & Willig, 1981).

In order to allow for multi-product firms in the former setting, we follow
*Johansson (2005) and rewrite the cost function for a typical firm h in product *
*group k (2.4) to read: *

*j*
*j*
*j*
*j*

*h* *x* *x*

*c*

### ( ) = α + λ + µ

(2.9)*where α denotes firm-specific fixed costs. For each firm h it is assumed that α *
can be shared among a sub-set *n*^{h}

### ⊂

*n*of the total amount of varieties.

### λ

_{j}denotes product-specific fixed costs whereas

### µ

*remains the marginal cost of production. Both*

_{j}### λ

*and*

_{j}### µ

*are assumed to be the same for all varieties.*

_{j}Equation (2.9) obviously satisfies the condition in Equation (2.8). There are
*several types of investments that give rise to a fixed cost such as α, e.g. flexible *
production technologies and distribution centers, etc. However, the most general

common input is certainly knowledge and information, (Carlton & Perloff,
1994). Knowledge and information gained by producing and selling one product
is usually applicable for a set of related products^{6}.

*If firm h produces n**h **varieties and each variety j*∈*n** ^{h}*, then the total cost of

*firm h of producing those varieties is given by Equation (2.10):*

*j*
*h*
*j*
*h*
*h*

*h* *n* *n* *n* *x*

*c* ( )=

### α

+### λ

+### µ

(2.10)*Now, assuming that Equation (2.1)-(2.3) still applies and that firm h maximizes *
its profit on each of the varieties it supplies, the optimal pricing rule for each
variety remains at:

*j*

*p**j*

### µ

### ε ε ⎟

### ⎠

### ⎜ ⎞

### ⎝

### ⎛

### = −

### 1

^{(2.11) }

which means that it is the varieties that compete with each other and that all firms lack market power even when they supply more than one variety, (Johansson, 2005). Hence, when a firm chooses the price of a variety it takes the prices of all other varieties (including its own) as given. This prevents strategic behavior, such as cross-subsidizing.

How can the equilibrium solution be described when (2.9) applies to all
firms? The model approaches equilibrium as new varieties are introduced on the
market. If the actual number of varieties on the market is less than the
*equilibrium number varieties, n<n** ^{e}*, then there are incentives for variety
introduction because of profit opportunities, i.e. gross profits > fixed costs.

Following Johansson (2005), it is assumed that the introduction of an
additional variety requires a variety idea. In present context, this requirement
translates into an entry barrier. If such variety ideas arrive to established and
potential firms in a random process, an equilibrium in which there are both
multi-variety firms and one-variety firms can be established. This happens when
*a firm h receives at least two variety ideas i,j*

### ∈

*n*

*, i.e. ideas for varieties that*

^{h}*jointly can rely on α, whereas some firms are left with only one variety when*equilibrium is reached.

An equilibrium of the type described above is illustrated in Figure 2.1, which
shows the relationship between the operating profits (profits gross over fixed
costs) of a variety and the number of products on the market. In the figure, the
*operating profits of variety j, *

### π

*, is expressed as a function of the number of varieties on the market. As shown in the figure, it is the size of the fixed cost of the firms that remain small and produce only one variety that determines the equilibrium number of products on the market*

_{j}^{7}. This is a manifestation of the

*condition in (2.11). All varieties have the same price, p*

*, and are produced in*

_{0}6 With respect to knowledge being a common input, it should be noted that Teece (1980, 1982) forcefully argued that economies of scope does not imply that it is more efficient to produce two goods by one firm unless the market for the common input is imperfect. The market for knowledge and information tend certainly to be imperfect, (c.f. Arrow, 1962).

7 If all firms in equilibrium would be multi-variety firms and produce an equal amount of varieties
each, then _{n}* ^{e}*=(ελ

*+εα*

_{i}*)*

_{n}^{−}

^{1}β

_{Y}*, where n is the number of varities produced per firm and βY denotes*the income devoted to consumption of such varieties. Under these circumstances each firm makes zero profits.

*equal amount, x**0**8**. This means that the following condition holds at n** ^{e}* for a firm
that only produces one variety:

0 0

) (

1 *x*

*p* _{j}

### α λ

^{j}### ε µ

### ε

_{=}

^{+}

⎟⎠

⎜ ⎞

⎝

⎛

= − * (2.12) *

*which implies that one-variety firms make zero profits. However, for a firm h *
that has received ideas for varieties that jointly can rely on the firm’s fixed cost
*α, the following holds at n*^{e}*, where n*^{h}* denotes the number of varieties produced *
by the firm:

0

0

### 1

*x*

*p* _{j}

### α

*n*

^{h}### λ

^{j}### ε µ

### ε _{>} ^{+}

### ⎟ ⎠

### ⎜ ⎞

### ⎝

### ⎛

### = −

*, iff n*

*>1 (2.13)*

^{h}Hence, if there are some small one-variety firms in the market equilibrium, each
multi-product (or multi-variety) firm will make positive profits. The reason is
*that such firms are able to spread the fixed cost α over a larger amount of *
varieties. Note that since (2.9) applies to all firms, it means that all firms have a
*potential to realize the demand advantages of having broader product lines, i.e. a *
larger amount of varieties. In the present framework, whether or not this
*potential is exploited for a given firm h depends on whether or not it receives *
multiple ideas for varieties that belongs to the set of varieties that jointly can rely
*on α, n .*^{h}

**Figure 2.1. The relationship between the number of products and the operating profit ***per variety on the market. *

The framework above suggests that a multi-variety exporting firm will have
larger export sales. It also suggests that, in equilibrium, the elastictity of the total
export value with respect to the number of export varieties will equal one. A firm
which supplies twice as many export varieties will have twice the export value,
*since x*_{0}* and p** _{0}* are the same for all varieties on the market. This is of course due
that the varieties are symmetric and consumers are homogenous.

Observe that the gains from producing a number of varieties in the model
*above arise because all consumers buy a limited amount of each variety. An *
alternative approach to product variety is to assume that the benefit of product

8 Recall that both

### λ

*and*

_{j}### µ

*are assumed to be the same for all varieties.*

_{j})

*j**(n*

### π

*n*

*e*

*0* *n*^{e}

λ*j*

α +

)

*j**(n*
π
)

*j**(n*

### π

*n*

*e*

*0* *n*^{e}

λ*j*

α +

)

*j**(n*
π

variety arise from the presence of heterogeneous consumers. Lancaster (1990:

p.189) points out that “… demand for variety may arise from a taste for diversity
*in individual consumption and/or from diversity in tastes even when each *
consumer chooses a single variant”. The formulation in (2.2) is an example of the
former, i.e. taste for diversity in individual consumption. If there is diversity in
tastes when each consumer buys a single variety, returns from supplying a set of
varieties arise from heterogeneous preferences among consumers. In this case,
multi-variety firms would be a reflection of that firms can discriminate between
consumers with different preferences and develop a product line accordingly.

Such type of product differentiation can be illustrated with the ‘characteristic-
*approach’ developed in Lancaster (1966a,b). Figure 2.2 illustrates the principle. *

**Figure 2.2. Perfect product differentiation in Lancaster’s ‘characteristics approach’. **

*In the figure, consumers are assumed to derive utility from two characteristics, Z*_{1 }*and Z** _{2}*. There are three varieties available on the market with different densities

*of the two characteristics. This give rise to three variety vectors a, b and c. The*straight and negatively sloped line that joins these variety vectors is the characteristics frontier, which is the same for all consumers. Consumers choose a point on the characteristics frontier according their preferences. There are three groups of consumers (I, II, III) with different preferences over the two characteristics. The figure describes ‘perfect’ product differentiation as each group of customer would consume a single variety and there is a perfect match between the preferences of the consumers and the density in terms of the

*characteristics of the varieties.*

In the subsequent section, the paper provides an empirical assessment of the returns to variety in export supply at the firm-level. The section also describes the data and presents an overall picture of the extent of variety in product supply among exporting firms.

**3. EXPORT VARIETY AT THE LEVEL OF THE INDIVIDUAL FIRM **
**- what the Swedish data tell **

### 3.1 Presentation of data

The data used in the paper consist of highly detailed firm-level export data.

These data include all Swedish exporting firms. In 2003, the total number of Swedish firms with registered exports amounted to about 37 500. For each firm,

I

II

III I

II

III
*a*

*b*

*c*
* Z**1 *

* Z**2 *

product category and export destination (country) these data provide information
on (i) export value (SEK) and (ii) export volume (kilogram). The product
categories are the finest possible according to the CN^{9} classification system,
which is common for EU-member countries. In 2003, Swedish firms exported
well over 9 000 different product categories according to this classification.

Since each firm may produce a number of products that each are exported to a set of destinations the database is very large. For example, for the year 2003 there are over 640 000 entries in the database. The structure of these data makes it possible to measure a firm’s export variety along two dimensions: 1) export product categories and 2) export destinations.

The exports of each firm are recorded into export categories according to the
8-digit CN classification scheme. In this paper, each such 8-digit category is
referred to as an export product^{10}. Variety in the export supply of a firm then
manifests itself in that a firm exports a set of such export categories (products).

This means that a higher number of export categories is interpreted as a higher variety in export supply. Moreover, a destination (country) will be referred to as a market.

Table 3.1 presents descriptive statistics over the extent of export variety
among Swedish exporting firms in 2003. All firms were categorized into six
classes according the number of export products^{11}. For each class, the table
presents (i) the mean number of export products per firm, (ii) the mean number of
markets penetrated by the firms, (ii) the number of firms belonging to the class,
(iv) each class’ share of the total number of export firms and (v) each class’ share
of Sweden’s total export value.

**Table 3.1. Descriptive statistics for six categories of firms in 2003 (Categories ***constructed based on the number of export products). *

Class Mean no.

products Mean no.

of markets Number of firms

Share of firms

(%)

Share of Sweden’s total

export value (%)

1 1.0

(0.0) 1.1

(0.8) 16 159 43.1 1.4

2 2.0

(0.0) 1.9

(2.1) 5 413 14.4 1.1

3 3.4

(0.5) 3.1

(3.7) 5 239 14.0 2.5

4 5.4

(2.2) 4.5

(5.2) 2 770 7.4 3.4

5 9.6

(2.2) 7.7

(8.5) 4 261 11.4 9.0

6 44.7

(98.1) 17.6

(17.9) 3 634 9.7 82.6

*) Standard deviations are presented within brackets.

The table shows that most firms export a very limited number of products to a
very limited number of markets. In fact, the typical export firm exports one
product to one market. However, these firms (41 %) only constitute 1.4 % of
Sweden’s total export value. In the 6^{th} category we find the firms with the highest
variety in their exports. On average, these firms export about 45 products to a

9 CN = combined nomenclature.

10 A similar definition of products can be found in Schott (2004), though referring to imports into the U.S.

11 The observations in each category correspond to a 1/6-percentile.

total of about 18 markets and constitute over 80 % of Sweden’s total export^{12}.
That 10 % of the exporting firms account for over 80 % of the exports illustrates
strong concentration to a few firms. Of course, this is a reflection of Sweden’s
dependence on a limited number of large multinational firms, such as Volvo and
Ericsson.

Figure 3.1 and 3.2 provide an illustration of the frequency by which Swedish
exporting firms export different number of products and serve different number
of markets, respectively. The horizontal axis measures number products and
number of markets. In each figure the vertical axis measures number of firms. An
observation then shows the number of firms which exports to a given number of
products (markets). Figure 3.3 is constructed in exactly the same fashion as
Figure 3.1 and 3.2, but reports the number of products that are exported to
different number of markets. The relationships in each figure are summarized by
*the corresponding equations, where f denotes number of firms, p number of *
*products and m number of markets. t-values of the parameters in the equations *
are written underneath the parameter estimates.

0 2 4 6 8 10

0 1 2 3 4 5 6 7 8 9

**Figure 3.1. Frequency by which Swedish exporting firms exports different number ***products (logarithmic scales) *

### ε +

### −

### =

−*p*

*f*

### 9 . 14 1 . 60 ln

### ln

46.13 38.96 (3.1)Figure 3.1 and 3.2 show that the frequency by which more export products are supplied and more markets are penetrated declines smoothly with the number of firms until a few firms export a large amount of products and have penetrated a large amount of markets, respectively. Equation (3.1) shows that the number of firms falls off with the number of export products, i.e. the extent of export variety, with an elasticity of 1.6. The corresponding elasticity for the number of markets amounts to 2.2, (see Equation 3.2). The latter elasticity is remarkably consistent with the one reported in Eaton, Kortum & Kramarz (2004) who estimate an identical elasticity of 2.5 on French firm-level export data. Moreover, Figure 3.3 shows how the number of export products falls of with the number of markets. Evidently, most products are exported to a limited number of markets.

The corresponding elasticity reported in Equation (3.3) amounts to 1.7.

12 However, the standard deviations reveal that there is a large dispersion within the category.

*No. of products *
*No. of firms *

0 2 4 6 8 10 12

0 1 2 3 4 5

**Figure 3.2. Frequency by which Swedish exporting firms serves different number of ***markets (logarithmic scales) *

### ε +

### −

### =

−*m*

*f*

### 11 . 02 2 . 23 ln

### ln

57.26 44.46 (3.2)0 1 2 3 4 5 6 7 8

0 1 2 3 4 5 6

**Figure 3.3. Frequency by which export products are exported to different number of ***markets (logarithmic scales) *

### ε +

### −

### =

−*m*

*p*

### 9 . 55 1 . 70 ln

### ln

35.62 25.87 (3.3)In summary, the data shows firstly that firms’ export variety in terms of the number of export products is limited. Over 50 % of the firms export only one or two products. But, firms with a large export variety account for over 80 % of the total exports. Secondly, firms usually export to a limited set of markets, but firms with higher export variety tend to serve more markets. Thirdly, just as firms serve a limited number of markets, most products are exported to a limited number of markets.

### 3.2 An empirical assessment of the returns to export variety

The theoretical framework in Section 2 implies that firms with larger export variety should have larger export sales and, hence, that there are returns to export variety at the level of the individual firm. This section aims at quantifying these returns and examining what factors accounts for the estimated returns. The latter

*No. of markets *

*No. of markets *
*No. of products *

*No. of firms *

is achieved by decomposing a firm’s total export value into different components, (c.f Hummels & Klenow, 2004).

Gains from export variety for individual firms are estimated by regressing the
*total export value of firm i, x** _{i}*, on the number of export products of the same

*firm, p*

*:*

_{i}### ε γ

### β

### φ + + ∑

=### +

### =

^{96}

### ln

1### ln

*x*

*i*

*p*

*i*

*j*

*j*

*D*

*j*(3.4)

which yields an estimated elasticity of the export value with respect to the extent
of export variety. Equation (3.8) also contains industry dummies to control for
*heterogeneity among industries. D*_{j }*is 1 if firm i belongs to industry j. An *
industry is defined as a 2-digit CN-classification code.

*The decomposition of the total exports of each firm i, x** _{i}*, starts from the

*observation that x*

_{i}*can be expressed as:*

### ∑ ∑

∈ ∈### =

*r*

*m*

*i*

*s*

*n*

*i*

*i*

*sr*

*i*

*sr*

*i* *p* *q*

*x* _{,} _{,} (3.5)

*where m*^{i }*denotes the set of markets firm i exports to and n** ^{i }*denotes the set of
products that the firm is exporting,

*p*

_{i}_{,}

_{sr}*the price of product s in market r and*

*sr*

*q**i*_{,} * the volume (kilogram) exported of product s to market r. Equation (3.5) can *
be rewritten to read:

### ∑

∈### =

*r*

*m*

*i*

*i*

*r*

*i*

*r*

*i* *P* *Q*

*x* _{,} _{,} *P**i*_{,}*r**Q**i*_{,}*r* ≡

### ∑

*s*∈

*n*

*i*

*p*

*i*

_{,}

*sr*

*q*

*i*

_{,}

*sr*(3.6)

*which simply states that the total export of firm i is the sum of the total export *
value to each market. The right-hand-side in (3.6) can now be decomposed into:

### (

*^{*},

### )

,*r* *i**r*
*i*
*i*

*i* *M* *P* *Q*

*x* =

^{≡} ( )

*i*

^{−}

_{∑}

_{r}_{∈}

_{m}

^{i}*i*

*r*

*i*

*r*

*r*

*i*
*r*

*i* *Q* *M* *P* *Q*

*P*^{*}_{,} ^{*}_{,} ^{1} _{,} _{,} (3.7)

*where M*^{i }*denotes the number of markets firm i has entered and P*_{i}^{*}_{,}_{r}*Q*_{i}^{*}_{,}* _{r}* denotes
the average value of the shipments to a market. In Hummel’s & Klenow’s (2004)

*terminology, M*

*can be interpreted as the ‘extensive’-margin whereas*

^{i}*P*

_{i}^{*}

_{,}

_{r}*Q*

_{i}^{*}

_{,}

*can be interpreted as the ‘intensive’-margin. Equation (3.7) implies that:*

_{r}) ln(

ln

ln*x** _{i}* =

*M*

*+*

^{i}*P*

_{i}^{*}

_{,}

_{r}*Q*

_{i}^{*}

_{,}

*(3.8)*

_{r}Of course, a decomposition of *P*_{i}^{*}_{,}_{r}*Q*_{i}^{*}_{,}* _{r}* can be made by distinguishing between
average prices per kilogram and average volumes (kilogram):

(3.9)

which means that:

* ,

*

* ,

*

,

### ) ln ˆ ln ˆ

### ln(

*P*

_{i}

_{r}*Q*

_{i}

_{r}### =

*P*

_{i}### +

*Q*

_{i}*. (3.10)*

_{r}* , , *

, ,

,

* , ,

*

,

### ˆ ˆ

*r*
*i*
*i* *i*

*m*

*r* *i**r* *i**r*

*m*

*r* *i**r*

*m*

*r* *i**r* *i**r*

*r*
*i*
*r*

*i* *P* *Q*

*M*
*Q*
*P*
*Q*

*Q*
*Q* *P*

*P* ^{i}

*i*

*i*

### =

### = ∑

### ∑ ∑

∈∈

∈

The described decomposition methodology implies that the question whether a
larger export value of a firm is primarily associated with larger export sales per
*market (the intensive-margin) or that the firm exports to a larger number of *
markets (the extensive-margin) can be assessed. It also allows for an assessment
of whether the effect of the intensive margin is primarily due to (average) prices
or (average) quantities.

In order to achieve this, Equation (3.4) is firstly estimated by means of OLS.

This gives an estimate of the

### β

-parameter in Equation (3.4), i.e. an estimated elasticity of the export value of firms with respect to the variety in export supply.Then each of the components described in Equation (3.8) and (3.10) is regressed separately on the variables on the right-hand-side in Equation (3.4). Since OLS is a linear operator, the estimated coefficients of these components sum to the original estimated

### β

-parameter obtained from the OLS estimation of (3.4). This means in turn that the contribution of each component to the estimated### β

-*parameter in Equation (3.4) can be revealed.*

The results of the procedure described above are presented in Table 3.2. In these estimations, only firms with an aggregate export value above 50 000 SEK (approx. 5 000 €) are included, which means that the total sample consists of 21 191 exporting firms. The estimations are based on data in 2003.

**Table 3.2. The relationship between export variety and the size of export sales **

*p**i*

### ln

Share of estimated*β*in

Equation (3.4) *R*^{2 }

*x**i*

### ln

^{1.23* }**(116.56)** **- 0.42 **

*M**i*

### ln

_{(128.87) }^{0.64* }

^{52 % }

^{0.48 })

ln(*P*_{i}^{*}_{,}_{r}*Q*_{i}^{*}_{,}_{r}^{0.59* }

**(67.92) ** **48 % ** **0.24 **

ˆ*

ln*P*_{i}^{-0.05* }

**(-5.81) ** **- 4 % ** **0.44 **

*

### ˆ

,### ln

*Q*

_{i}

_{r}

^{0.65* }**(48.44) ** **52 % ** **0.40 **

**) t-values presented within brackets. *

**) * denotes significance at the 0.01-level.

The estimated

### β

-parameter in Equation (3.8) amounts 1.23 and is statistically significant at the 0.01-level. This suggests that a firm with 10 % higher export variety in general have 12,3 % larger export value, which is a clear indication of that there are gains from export variety. Indeed, it implies increasing returns to export variety at the level of the individual firm. This is clearly larger than motivated by the equilibrium solution in the monopolistic competition model with multi-product firms presented in the former section.It is also evident that about 52 % of the extra exports associated with higher export variety are due to the ‘extensive’-margin, namely that the firms serve more markets. This result indicates that variety in export supply allows for the penetration of a larger amount of international markets. Naturally, 48 % can be attributed to the ‘intensive’-margin, i.e. larger export sales per market. Moreover, the results show that within the ‘intensive’-margin, the positive effect is solely

due to larger export volumes per market. The contribution from the price-
component is negative. This means that firms with higher variety in export-
supply tend to have lower average prices per kilogram which has a negative
effect on the firms’ total export value and, hence, the estimated elasticity. Of the
estimated elasticity of export value with respect to variety in export supply, - 4 %
can be attributed to higher average prices whereas 52 % can be attributed to
larger volume of sales per market^{13}.

### 3.3 The direction of export flows and export variety

The preceding section showed that there are clear gains from variety in export supply at the firm-level. It also showed that these gains could be attributed to the fact that a firm with larger export variety serves more markets and has larger export sales per market, roughly on a 50-50 basis. This section analyzes how firms’ export sales to a market vary with the size of that market and its distance from the country in which the exporting firm is located. Special attention is paid to how large part of the variation in export sales to different markets that can be explained by the variation in export variety to those markets.

The use of market size (GDP) and distance to analyze the direction of trade
flows has its roots in the gravity model. In essence, this model states that the
export flow from one country (origin) to another (destination) is proportional to
the market size in the other country (destination), but inversely proportional to
the distance between the two countries, (see e.g. Rauch, 1999). Empirical studies
using gravity specifications generally conclude that the size of mutual trade (i)
increases with market-size and (ii) decreases with the distance between the origin
and the destination^{14}. In these models, distance does not only relate to
transportation costs, but also transaction costs. A large literature on the direction
of trade flows, for instance, typically adopts a network approach to trade, in
which the total exports of an individual firm is specified as a function of the
number of economic links the firm has established and the size of the flows on
each link. Formation of such economic links implies investments in durable
interaction capacity, (Johansson & Westin, 1994) and involves several activities
that are highly contact intensive and, hence, are facilitated by proximity and
common languages.

Although the effect of GDP and distance on aggregate trade flows is well documented, less is known how the variety in export supply at the level of the individual firm is affected by these factors. In general, it can be expected that the variety in supply is increasing in the size of the destination market. For instance, the probable number of separable customer groups is certainly increasing in the number of (potential) consumers, (see Figure 2.2). Due to the distance-effects described above, export variety is expected to be negatively associated with distance as well. Actually, a set of studies states that differentiated products in general are more distance-sensitive than standardized (non-differentiated) products, (see e.g. Johansson & Westin 1994 and Rauch 1999). Differentiation implies that price comparisons alone are not sufficient for making a purchase decision since there are no reference prices. Because of this, international transactions of differentiated goods are maintained to be associated with extensive search on the behalf of buyers and sellers and that such search activities are distance sensitive. This also suggests that the variety in the export

13 Observe that these two percentages sum to the share of the total ‘intensive’-margin, i.e. 48 %.

14 Several studies also show that common languages and similar cultures stimulate trade.

flows of individual firms to a market would decreases with the distance to the
market^{15}.

Table 3.3 and 3.4 provides – in descending order – the 10 markets (countries) which imports from the largest number of Swedish firms and which imported the largest number of products in total from Swedish firms, respectively in 2003.

The tables also reports each market’s GDP 2003 in relation to the U.S and each market’s share of Sweden’s total exports. All markets’ GDP are compared with that of the U.S because the U.S is the largest market (in terms of GDP) in the world. These tables serve as gross illustrations of distance-effects and give some insights into the underlying structure of the data analyzed in the sequel.

**Table 3.3. The 10 markets which imports from the largest number of Swedish firms **
in 2003.

Market GDP 2003 in

relation to U.S (%)

Number of firms

Share of Sweden’s total export value 2003 (%)

Norway 1.9 15 197 8.49

Finland 1.8 6 202 5.52

U.S 100.0 6 009 11.63

Denmark 2.3 5 560 6.20

Germany 28.6 4 723 10.01

Switzerland 3.6 4 424 1.12

Poland 1.9 4 164 1.67

U.K 14.7 3 986 7.72

Estonia 0.1 3 878 0.68

Netherlands 5.3 3 375 4.92

*) Only firms with an aggregate export value > 50 000 SEK (approx. 5 000 €).

***) GDP data from World Development Indicators (2004) in current prices. *

The tables indicate a clear ‘Nordic bias’ among Swedish exporting firms.

Although the market in Norway in terms of GDP is less than 2 % of the U.S market, more than twice as many firms export to Norway compared to the U.S.

**Table 3.4. The 10 markets which import the largest number of products from **
Swedish firms in 2003.

Market GDP 2003 in relation to U.S

(%)

Number of

products Share of Sweden’s total export value 2003 (%)

Norway 1.9 7 419 8.49

Finland 1.8 6 455 5.52

Denmark 2.3 6 264 6.20

Germany 28.6 5 052 10.01

Estonia 0.1 4 410 0.68

U.K 14.7 4 408 7.72

Poland 1.9 4 071 1.67

U.S 100.0 4 020 11.63

France 19.4 3 858 4.86

Netherlands 5.3 3 819 4.92

*) Only firms with an aggregate export value > 50 000 SEK (approx. 5 000 €).

***) GDP data from World Development Indicators (2004) in current prices. *

Moreover, the U.K ends up on 7^{th} place after e.g. Norway, Denmark, Finland and
Poland in spite of the fact that the market in the U.K is about 7 times larger than
the markets in these countries. It is also evident that that there is no clear-cut

15Rauch (1999, p.10) writes that “…proximity and common language/colonial ties should have the greatest effects on matching international buyers and sellers of differentiated products, and search costs should act as the greatest barrier to trade for differentiated products”.

relationship between the size of a market and the number of products export to the market. Also here, the Nordic countries are ranked high. However, the picture changes of course when looking at the markets’ share of Sweden’s total exports and their respective GDP.

In order to analyze the general relationships between market-size, distance and export flows of the firms in the sample, this section applies a similar procedure as in the former section. The basic equation to be estimated takes the following form:

### ε γ

### λ δ

### φ + + + ∑

=### +

### =

_{,}

^{96}

_{1}

,

### ln ln

### ln

*x*

_{i}

_{r}*Y*

_{r}*d*

_{i}

_{r}

_{j}

_{j}*D*

*(3.11)*

_{j}where *x*_{i}_{,}_{r}* denotes the value of the total export flows of firm i to market *
*(country) r, Y*_{r}* the GDP in market r and d*_{i}_{,}* _{r}* the distance from Sweden to

*country r. As in Equation (3.4), the model above includes industry dummies to*control for differences across industries.

As in the preceding section, a decomposition methodology is applied to assess the contribution of different components of the total export value.

*Specifically, the total export value of a firm i to a market r is now decomposed *
such that:

) ln(

ln

ln*x*_{i}_{,}* _{r}* =

*N*

_{r}*+*

^{i}*P*

_{i}^{*}

_{,}

_{r}*Q*

_{i}^{*}

_{,}

*(3.12)*

_{r}where *N*_{r}^{i}* denotes the number of export products firm i exports to market r and *
)

(*P*_{i}^{*}_{,}_{r}*Q*_{i}^{*}_{,}_{r}* denotes the average export value per product of firm i to the same *
market. This decomposition implies that the contribution of variety in export
*supply to the estimated parameters (δ and λ) in Equation (3.11) can be calculated. *

Furthermore, (*P*_{i}^{*}_{,}_{r}*Q*_{i}^{*}_{,}* _{r}*) is decomposed into average prices per kilogram and
average volumes such that:

* ,

* ,

* ,

*

,

### ) ln ˆ ln ˆ

### ln(

*P*

_{i}

_{r}*Q*

_{i}

_{r}### =

*P*

_{i}

_{r}### +

*Q*

_{i}*(3.13)*

_{r}where

### ˆ

^{*}

_{,}

*r*

*P**i* * denotes the average price per kilogram of the products that firm I *
*exports to market r and *

### ˆ

^{*}

_{,}

*r*

*Q**i* denotes the average volume per product to the
same market.

As in the former analysis, Equation (3.11) is first estimated and then each of
the components of *x*_{i}_{,}* _{r}* is regressed on the variables on the right-hand-side in
(3.11). This procedure allows for a calculation of the contribution of each of the
components in (3.12) and (3.13) to the estimated parameters in (3.11).

The results of the methodology are presented in Table 3.5. Data on GDP and
distance could be obtained for 113 markets. The GDP data is extracted from
*World Development Indicators (2004) and is measured in U.S $ (current prices). *

Since many firms export to multiple markets, there are over 122 000 observations in the sample. All figures are from 2003 and the sample consists only of firms with an aggregate export value above 50 000 SEK (approx. 5 000

€).

About 10 % of the variation in firms’ export sales across markets can be explained by GDP and distance. As expected, the export sales of a firm to a market increase with the GDP in the market and decreases with the distance to

the market. The average elasticity of the export value to a market with respect to the GDP in the market amounts to 0.26. The number of products a firm exports to a market tends to increase with the GDP in the market, but the effect is small.

The estimated elasticity amounts to 0.04. Only 15 % of the larger export sales to a market with larger GDP can be attributed to a larger number of products exported to the market. This means that 85 % can be ascribed to larger export sales per products. Thus, the main explanation for the positive relationship between GDP and the size of the aggregate export flows of firms is larger export sales per product. Moreover, both the number of products and the average export sales per product to a market decrease with the distance to the market. However, the average export sales per product account for the largest share of the negative effect of distance, (69 %).

**Table 3.5. The effect of GDP and distance on export flows. **

*Y**r*

ln *estimated δ in *^{Share of }

Equation (3.9) ^{i}^{r}

*d*_{,}

### ln

*estimated λ in*

^{Share of }Equation (3.9)

*R*

^{2}*r*

*x**i*_{,}

### ln

^{0.26* }**(60.69) ** **- ** **-0.49* **

**(-71.55) ** **- 0.10 **

*i*

*N**r*

### ln

^{0.04* }**(27.71) ** **15 % ** **-0.15* **

**(-61.52) ** **31 % ** **0.07 **

)

ln(*P*_{i}^{*}_{,}_{r}*Q*_{i}^{*}_{,}_{r}^{0.22* }

**(58.43) ** **85 % ** **-0.34* **

**(-57.35) ** **69 % ** **0.11 **

*

### ˆ

,### ln

*P*

_{i}

_{r}

^{0.08* }**(30.76) ** **31 % ** **0.09* **

**(19.53) ** **-18 % ** **0.40 **

*

### ˆ

,### ln

*Q*

_{i}

_{r}

^{0.14* }**(29.84) ** **54 % ** **-0.43* **

**(-58.03) ** **87 % ** **0.29 **

**) t-values presented within brackets. *

**) * denotes significance at the 0.01-level.

Even though the distinction between number of products and average export sales per product shows a limited effect of GDP on the number of products, additional insights are provided by the decomposition of average export sales per product into average prices per kilogram and average volumes.

Table results show that as much as 31 % of the estimated elasticity of the export value with respect to GDP is accounted for by that fact that the average prices per kilogram of the export products supplied by a firm tend to be increase with the GDP in the export market. This indicates quality differentiation across markets and can be due to either that (i) the prices of the same export products differ between markets with different GDP or that (ii) the additional products exported to markets with higher GDP have substantial higher prices or (iii) both.

Hence, there might be additional variety that is not picked up by the use of export categories. It is also evident that products shipped over longer distances tend to have higher prices. The coefficient estimate of distance for the average price component is positive and significant. This indicates clearly that products with higher prices per kilogram can be shipped over longer distances because the transport costs’ share will be lower for each given distance, which is a classic result in the Weber (1909) location model, (see e.g. McCann, 2002).

About 54 % of the estimated elasticity of total export value with respect to GDP is due to larger export volumes per product. Of course, average export

volumes per product accounts for the largest share of the negative effect of distance

**4. CONCLUSIONS **

New trade theory suggests an important link between product variety and international trade and a growing literature is devoted to empirical assessments of the relationships involved. This paper has contributed to this literature by analyzing the relationship between variety in export supply and exports at the firm-level.

Using highly disaggregated Swedish firm-level export data for 2003 it is shown that most firms supply a limited amount of export products to a limited amount of markets. Although firms with a large variety in export supply are relatively few in numbers, they constitute a substantial share of the Sweden’s total export. This calls for models in which firms may supply a set of export products, i.e. multi-product exporting firms. The low frequency by which firms serve a large number of markets lends support for models in which market penetration is associated with sunk costs.

The paper finds clear evidence of gains from variety in export supply at the firm-level. By estimating an elasticity of the total export value with respect to the number of export products, it is shown that there are increasing returns from variety in export supply at the firm-level. A decomposition methodology related to Hummels & Klenow (2004) shows that about 52 % of the effect of variety in export supply on the total export value is due to that firms with a high variety in export supply exports to a larger set of markets. 48 % is due to larger average export value per market.

The paper has also examined how the export variety of firms varies with distance and GDP across markets. This part of the analysis shows that the variety in export flows to a market increases with the market’s GDP but decreases with distance. 15 % of the larger export sales to a market with larger GDP can be attributed to a larger number of products exported to the market. Moreover, the paper finds empirical support for quality differentiation on the behalf of individual firms among markets with different GDP. About one third of the effect of GDP on the total value of the export flows to a market can be ascribed to higher average prices per kilogram of the export products. In addition, products shipped over longer distances tend to have higher average prices per kilogram.

.

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