Trade Liberalization, Intermediate Inputs andFirm Competitiveness:

Direct versus Indirect Modes of Import

Michele Imbruno�

August 7, 2011

Abstract

This paper is aimed at studying the impact of input trade liberalization on nal goodrms competitiveness, aggregate productivity and welfare, by developing a theoreticalframework à la Melitz (2003), which incorporates: a) trade in nal goods/intermediateinputs between similar countries, b) rms decisions to import intermediate inputs andto export nal output.

This model shows di¤erent e¤ects from reducing input tari¤s, according to if all in-termediates are assumed to be imported directly by nal good rms through incurringadditional xed cost or indirectly through an e¢ cient wholesale system, withoutmaking any further xed investment. If all foreign intermediates are indirectly im-ported, all nal good rms uniformly gain in competitiveness from trade liberalizationin intermediates, since they are able to substitute the worst domestic inputs with thebest foreign ones (gains from input switching). These uniform competitiveness gainswill translate entirely into an increase in consumerswelfare without any particularrm dynamics within nal good sector. Whereas, if all foreign intermediates are di-rectly imported, only the more productive rms (importers) will be able to use foreigninputs, and therefore enjoy some competitiveness gains from input trade liberalization.Conversely, the other rms (non-importers) will su¤er some competitiveness losses,mainly due to a decrease in domestic input varieties available. That would force theleast productive rms to exit the domestic market and the least productive exportersto leave international market, causing some business reallocation towards the moreproductive rms (import-export rms), and consequently some aggregate productivitygains and some nal variety losses. Nevertheless, consumers welfare seems to increaseagain by considering altogether these e¤ects.

JEL: F12, F13Keywords: Firm heterogeneity, Trade liberalization, Intermediate inputs, Produc-

tivity, Import-Export behaviour

�GEP University of Nottingham. E-mail address: lexmi7@nottingham.ac.uk. The author would liketo thank Fabrice Defever and Richard Kneller for their helpful comments and suggestions. All remainingerrors remain his own.

1

1 Introduction

In the last few years, international trade literature has emphasized the important role played

by rm heterogeneity in productivity in order to explain the microeconomic relationship be-

tween trade openness and economic growth. Most of these studies focus on export behaviour

and trade liberalization in nal goods1 , without paying any attention about import behav-

iour and trade liberalization in intermediate inputs.

Amiti and Konings (2007) rst investigated empirically the impact of reducing input

tari¤s on rms, by isolating importers from other rms. They found that all rms en-

joy productivity gains from trade liberalization in intermediate inputs, although importers

would benet relatively more than nonimporters, by arguing that this larger e¤ect for im-

porting rms might be linked to several channels as the theory predicts such as access

to more input varieties, access to higher quality inputs, and learning e¤ects (Ethier 1982;

Markusen 1989; Grossman and Helpman 1991)2 . However, they did not attempt to disentan-

gle any single channel and to mention any peculiar reason why nonimportersperformance

also enhances3 .1The majority of empirical studies (from Bernard and Jensen (1995) for US) focus on the export-

productivity linkage and show that exporters are actually more productive than non-exporters, becauseof self-selection mechanism, rather than some post-entry e¤ects see Wagner (2007) and Greenaway andKneller (2007) for a survey as well as productivity gains from trade might arise from resources or marketshares reallocation across rms within industry from the least productive which exit the domestic market(Aw et al. (2000)(Aw, Chung, and Roberts 2000)) and the most productive which also serve internationalmarket (Bernard and Jensen (1999)). In light of these facts, Melitz (2003) develops a general equilibriumtrade model à la Krugman i.e. assuming monopolistic competition and increasing returns to scale with heterogeneous rms, incorporating both self-selection and business reallocation mechanisms, abovedescribed.

2All these theoretical frameworks are based on rm homogeneity assumption. However recently, someempirical evidences have analyzed the import-productivity linkage at a rm-level, arguing importers are onaverage more productive than non-importers, thanks to some positive post-import e¤ects within rm. Inparticular, Kasahara and Rodrigue (2008) nd importing intermediate goods improves Chilean plant-levelproductivity, and Halpern et al. (2005) show theoretically and empirically by using rm-level data fromHungary as imports raise aggregate productivity, because of an increase in importer-level productivity,as well as some reallocation e¤ects towards importers. Similarly, Gibson and Graciano (2009) develop atrade model à la Melitz by focusing on the import side. They assume there are two di¤erent technologies:the rst uses only the domestic inputs, and the second one uses both domestic and foreign inputs. Inparticular, the latter is associated with higher xed cost compared to the former. Thus, rms would self-select to import inputs, and trade liberalization (or terms of trade improvement) would cause resourcesreallocation from the least productive rms (exiters) to the best ones (importers) determining an increasein aggregate productivity (welfare). Halpern, Koren and Szeidl (2009) show more specically through atheoretical model and using data from Hungarian rms during 1992-2003 period that imported inputsgenerate productivity gains linked to two channels: quality (foreign inputs are better than domestic ones)and complementarity mechanism (gains from intermediates combination are larger than the sum of theparts). In particular, they highlight how complementary mechanism governs the quality elasticity of importdemand: if intermediates are perfect substitutes, even a small quality improvement would determine a largeincrease in imports in intermediates; however, if intermediatescomplementarity is strong, import demandwould change a little despite a substantial improvement in quality.

3An increase in nonimportersproductivity has been attributed to some spillover e¤ects, i.e. importerscan transfer their benets to other rms along the vertical production chain through the sale of their goods,

2

The main purpose of this paper is to study the impact of trade liberalization in inter-

mediate inputs on nal good rms competitiveness, aggregate productivity and welfare, by

developing a theoretical framework à la Melitz (2003), which incorporates: a) trade in nal

goods/intermediate inputs between similar countries, b) rms decisions to import interme-

diate inputs and to export nal output. In particular, this paper aimed at addressing i)

whether a further channel through which importers improve their competitiveness exists; as

well as ii) why and whether nonimporters always benet from input tari¤ cutting.

To address the rst research question (i), we have to consider that Ethier (1982) demon-

strated that trade openness can increase rmscompetitiveness, because rms can access

to more di¤erentiated intermediate varieties (gains from input varieties). Thus, by con-

sidering that rmscompetitiveness is inversely related to the price index of intermediate

inputs, which in turn is decreasing in both number and average productivity of input sup-

pliers, he showed that trade liberalization would basically entail an improvement in rm

competitiveness thanks to a higher number of input suppliers (or input varieties) available,

while the related average productivity remains constant, given that all input suppliers have

been assumed to be homogeneous in productivity. Now, through assuming that intermedi-

ate good rms are actually heterogeneous in productivity, following Melitz (2003), we can

show that trade in intermediates can also determine an increase in average productivity of

input suppliers, due to the exit of the least productive domestic rms and the entry of the

most productive foreign ones within the intermediate sector, entailing a further increase in

nal good rmscompetitiveness. In other words, nal good rms can replace the worst

domestic intermediates with the best ones from abroad, becoming more competitive (gains

from input switching).

As concerns the second research question (ii), a reason why nonimporters also increase

their performance, might be that some of them are invisible importers. Firms can have

access to some foreign inputs only through directly importing them, by incurring an ad-

ditional xed cost (o¢ cial or direct importers). However, rms can also use some foreign

inputs by indirectly importing them, i.e. through very e¢ cient wholesalers, without making

any further xed investment (invisible or indirect importers). Thus, some rms can actually

or alternatively, domestic producers of intermediates can be induced to become more competitive, entailingsome indirect benets for the users of such domestic intermediates.

3

use foreign inputs and enjoy competitiveness gains, although they look like non-importers

in the data. This argumentation is coherent with some recent empirical evidences (Bernard,

Grazzi and Tomasi (2010), Bernard, Jensen, Redding and Schott (2010)) and theoretical

models (Ahn et al. (2010), Akerman (2010), Blum et al. (2011)) stressing the role of trade

intermediaries from export point of view: in particular, all these studies show theoretically

and/or empirically that the least productive rms serve only the domestic market, the most

productive ones serve also the foreign market through direct exports, whereas the remain-

ing rms export indirectly through wholesalers by assuming that the direct channel is

associated with higher xed cost and lower marginal cost compared to the indirect channel.

In our framework, we assume to have two similar countries, where any heterogeneous

rm enters the home market by paying a xed cost of entry, with the purpose to produce

either a di¤erentiated intermediate good through using only labour or a di¤erentiated

nal good by combining also all di¤erentiated intermediates available under increasing

returns to scale. In particular, the intermediate inputs enter under CES form within nal

good rms production function, implying that the marginal cost is decreasing in the number

of intermediate varieties used and in average productivity of input suppliers as in Ethier

(1982). Then, two scenarios have been allowed for: 1) indirect imports scenario (i.e. zero

xed cost of importing) and 2) direct imports scenario (i.e. high xed cost of importing).

Under the rst scenario, any rm within both nal good and intermediate good sectors

can choose to serve the whole foreign market, by paying additional xed costs of exporting

and facing per-unit iceberg trade costs. Thus, as in Melitzs model, all nal good exporters

match with all foreign nal consumers, and similarly, all intermediate good exporters match

with all nal good rms abroad (indirect importers), i.e. all nal good rms within a coun-

try would have an easy access to foreign intermediates arising from the best input suppliers

abroad, through a very e¢ cient wholesale system. In this environment, trade liberalization

in intermediates would imply an increase in average productivity of intermediate good rms

through some reallocation e¤ects from the least productive rms (which quit the market)

to more productive rms (which export), entailing an uniform increase in nal good rms

competitiveness, and consequently, an increase in consumerswelfare, without any particu-

lar entry-exit dynamics within nal good sector. Therefore, a new source of competitiveness

gains from input trade liberalization can be highlighted: all nal good rms would become

4

more competitive since they can replace the worst domestic intermediates with the best

ones from abroad (gains from input switching) regardless of the change in total number

of input varieties available (gains form input variety à la Ethier).

However, under the second scenario (direct imports scenario) only some nal good rms

can actually import some additional intermediates by paying some xed costs of import-

ing (which are assumed to be larger than xed costs of exporting, coherently with several

empirical evidences4), and consequently, intermediate good rms are assumed to be able to

serve only a portion of foreign nal good rms, by incurring a variable selling cost increas-

ing in the fraction of foreign importers, as in Arkolakis (2008), rather than a xed cost of

exporting. Hence, all nal good exporters match with all foreign nal consumers again as in

Melitz (2003), whereas, all intermediate good exporters match only with more productive

nal good rms abroad (direct importers), i.e. solely the best nal good rms within a

country can have an access to intermediates arising from the best input suppliers abroad,

through paying a huge xed cost of importing. Therefore, following input tari¤ reducing,

only importers would enjoy some competitiveness gains from input switching, as described

above. Conversely, nonimporters would su¤er some competitiveness losses, due mainly to

a decrease in domestic input varieties available, causing some reallocation e¤ects towards

the more productive rms (import-export rms), at the expenses of the least productive

rms (quitters) and the least productive exporters (which leave the international market).

As a consequence, consumerswelfare improvement occurs thanks to aggregate productiv-

ity gains from reallocation e¤ects within nal good sector, in addition to heterogeneous

competitiveness gains and despite some losses in nal varieties.

Our theoretical framework is closely related to Kasahara and Lapham (2008) and Bas

(2009) studies. Kasahara and Lapham (2008) have also extended the Melitzs model in order

to account for both import and export decisions simultaneously. However, by assuming that

rms are homogeneous within intermediate input sector, they focus only on nal good sector

4By using Belgian rm-level dataset, Muuls and Pisu (2009) stress that two-way traders outperformimporters, who in turn exhibit a higher performance respect to exporters, reaching the conclusion thatself-selection would take place in both international activities. The same ndings have been achieved byCastellani, Serti and Tomasi (2010), through using Italian rmsdata: in particular, they certicate moreaccurately the self-selection hypothesis in import (export) markets, recognizing the existence of an ex-anteproductivity premium i.e. a productivity di¤erential between future importers (future exporters) andpermanent pure domestic rms. Altomonte and Bekes (2009) nd similar results in Hungary; however,following a deeper exploration about self-selection mechanism across international rms, they realize itactually takes place via importing, rather than via exporting (maybe because the choice of importing wouldrequire a more complex organization of production, compared to the choice of exporting).

5

where rms are assumed to be heterogeneous in productivity. In addition to Melitzs export

story, they show that trade liberalization in intermediates would determine an increase in

aggregate productivity and welfare, because of both rm-level improvement in importers

productivity (due to the use of a higher number of intermediates, i.e. the additional use of

foreign intermediates which is allowed only to rms able to pay some xed costs of importing)

and some reallocation e¤ects from pure domestic rms (exiters) to import-export rms.

Unlike their model, our framework pays more attention about the intermediate sector, where

rms are assumed to be heterogeneous and consequently the price index of intermediates

is assumed to be endogenous (i.e. decreasing in the number of input varieties used and

in the average productivity of input suppliers) and di¤erent between importers and non-

importers. In terms of predictions, our framework is able to show that some gains from

input trade liberalization are due to some input switching e¤ects, rather than a simple

increase in input varieties available, and that these gains can concern all rms, regardless

of their import status, or only some of them (importers), given that the low productive

rms can actually su¤er some competitiveness losses. Bas (2009)s study is an extension

of Melitz-Ottaviano (2008) framework aimed at analyzing the impact of a fall in input

trade barriers (i.e. relative factor price movements) in addition to trade liberalization in

nal goods (i.e. import competition e¤ect) on rmsproduction and exports decisions.

More specically, by examining solely the nal good sector and the rms export behaviour,

she argues that a removal of input import barriers (or simply an increase in input import

intensity) within industry would cause an increase in consumers demand, as well as a

proportional enhancement in competitiveness of all domestic rms such that both intensive

(export volume) and extensive (number of new exporters) margins of exports would rise.

Thus, unlike her model, we consider both import and export decisions at nal good rm level,

by assuming rm heterogeneity within both intermediate and nal good sectors, through

which we are able to demonstrate that the change in competitiveness is di¤erent across nal

good rms (i.e. between importers and non-importers) and the total number of exporters

(thus, the total number of nal good varieties) can also decrease following a fall in trade

costs of intermediates.

The rest of the paper is organized as follows. Section 2 introduces the model in both

Closed and Open Economy. Section 3 explores the impact of trade liberalization in inter-

6

mediate inputs on the economy. Section 4 concludes. All details about proofs are provided

in Appendix.

2 Set-up of the model

2.1 Closed Economy

The basic framework can be considered an extension of Melitz (2003)s monopolistic com-

petition model, since an intermediate good (m) sector has been added to the nal good

(y) sector, and all rms within each sector turn out to be heterogeneous in productivity

and produce di¤erentiated varieties under increasing returns to scale. A country has been

assumed to be endowed with Lm units of m-specic labour and Ly units of y-specic labour,

which are inelastically supplied at the common wage rate w, where w has been normalized

to one, and the total number of workers (nal consumers) is L = Lm + Ly.

2.1.1 Intermediate good sector

All nal good rms (y-rms) have the same CES preferences in available di¤erentiated

intermediates, therefore, the industry aggregate demand of intermediates takes the following

functional form: Qm =

"MR0

q�mdm

# 1�

, where qm is the demand for each intermediate variety

m, and M is number of intermediate varieties available (i.e. the number of incumbent

intermediate good rms). The intermediates are substitutes, implying 0 < � < 1 and an

elasticity of substitution between any two intermediate varieties is � = 11�� > 1. The related

industry aggregate price which corresponds to the price index of intermediates for each

nal good rm, since all rms within nal good sector are assumed to use all intermediates

available within country is Pm =

"MR0

p1��m dm

# 11��

, where pm is the price of individual

intermediate variety.

The production technology within intermediate good sector assumes there is a continuum

of rms producing a di¤erentiated variety, by using a single factor lm (m-specic labour),

through the cost function5 cm =�wf + w qm'm

�= w

�f + qm'm

�, where the xed cost f is

common, and the productivity level 'm is constant but di¤erent across rms. It becomes

5Both xed and variable costs are assumed to use labour.

7

cm =�f + qm'm

�since the common wage has been normalized to one. Intermediate good

rms enter the market by paying a xed cost of entry fe to draw their productivity 'm

from the Pareto cumulative distribution G('m) = 1 � '�km , where k > 1, and then decide

whether to exit the market or to stay.

Each intermediate rm faces a residual demand curve with constant elasticity �, i.e. it

chooses the same prot maximizing mark-up ���1 =1� . Consequently, the pricing rule is

pm ('m) =w�'m

, while the output, the revenues and the prots are respectively: qm ('m) =

RmP��1m (�'m)

�, rm ('m) = Rm (Pm�'m)��1, and �m ('m) =

rm('m)� � f . The latter

function is represented by the Figure 1, which shows that only rms whose productivity is

high enough to make non-negative prot ('m > '�m ) will survive in the market.

Moreover, the price index of intermediates can be written as follows:

Pm =

24 MZ0

[pm ('m)]1��

d'm

351

1��

=M1

1�� pm

��'m

�=M

11��

��'m

(1)

where�'m ('

�m) =

"1

1�Gm('�m)

1R'�m

'��1m g ('m) d'm

# 11��

is the weighted average produc-

tivity of intermediate good rms and '�m is the related survival productivity cuto¤, i.e. the

minimum level of productivity required to survive in the intermediate good market6 .

2.1.2 Final good sector

Consumers have identical love for varietypreferences for di¤erentiated nal goods, there-

fore, the related aggregated demand is assumed to take a CES functional form Qy ="NR0

q�ydy

# 1�

, whose the aggregate price Py =

"NR0

p1��y dy

# 11��

is where qy and py are re-

spectively the demand and the price of each nal variety, N is the number of nal varieties

available (i.e. the mass of incumbent nal good rms) and � = 11�� > 1 is the constant

elasticity of substitution across them.

The production technology in the nal good sector assumes a continuum of rms produc-

ing a di¤erentiated variety, by combining the y-specic labour ly with intermediate inputs

m arising from all rms within intermediate sector. In particular, the related cost function

6 In aggregate terms, the output is Qm = M1� qm

��'m

�, the revenues are Rm = PmQm = Mrm

��'m

�and the prots are �m =M�m

��'m

�.

8

takes the following form7 cy =�wf + Pm

qy'y

�, where the xed cost f is common, and the

productivity level 'y is constant but di¤erent across rms, as in the intermediate sector.

It becomes cy =�f + Pm

qy'y

�since the common wage has been normalized to one. No-

tice that Pm = M1

1��

��'m

is the aggregate price of intermediates used, which is decreasing in

both number and average productivity of all input suppliers (corresponding to the mass of

intermediate good rms).

Like the intermediate sector, nal good rms enter the market by paying a xed cost

of entry fe to draw their productivity 'y from the Pareto cumulative distribution G('y) =

1�'�ky , where k > 1, and then decide whether to leave the market or to produce. According

to all assumptions above, the nal good rm will charge the price py�'y�= Pm�'y

, and

the rm level output, revenues and prots will respectively be qy�'y�= RyP

��1y

��'yPm

��,

ry�'y�= Ry

�Py�'yPm

���1, and �y

�'y�=

ry('y)� � f . The prot function is represented by

the Figure 1, which displays that only rms whose productivity is high enough to make

non-negative prot ('y > '�y ) will decide to stay in the market. It is worth noting that an

increase in intermediate rmsaverage productivity as well as an increase in intermediate

varieties can a¤ect positively nal good rmsoutput, revenues and prots.

Finally, the price index of nal good will be

Py =

24 NZ0

�py�'y��1��

d'y

351

1��

= N1

1�� py

��'y

�= N

11��

Pm

��'y

=(NM)

11��

�2�'y

�'m

(2)

where�'y�'�y�=

"1

1�Gy('�y)

1R'�y

'��1y g�'y�d'y

# 11��

is the weighted average productivity

of nal good rms and '�y is the related survival productivity threshold, i.e. the minimum

level of productivity required to survive in the nal good market8 . By considering that it is

inversely related to the consumerswelfare, we can see that the latter is increasing in both

number and average productivity of input suppliers, in addition to be positively related to

both number and average productivity of nal good rms as in Melitz (2003).

7Fixed costs are assumed to use labour, whereas variable costs are assumed to use intermediates inputs.8 In aggregate terms, the output is Qy = N

1� qy

��'y

�, the revenue is Ry = PyQy = Mry

��'y

�and the

prot is �y =M�y��'y

�.

9

2.1.3 Equilibrium

Any rm will stay in the market till its prot is positive (�j�'j�> 0; for j = m; y ).

Thus, we can dene the zero prot cuto¤ '�j such that �j�'�j�= 0 (Zero Prot Condition).

Furthermore, it will take into consideration the possibility to enter the market only if the

net value of entry is positive (vej�'j�> 0 ) i.e. only if the present value of expected prots

1R'�j

�j�'j�dG�'j�=

1�G('j)�

_�j is higher than the sunk xed cost of entry fe. Consequently,

the free entry cuto¤ '�j is such that vej

�'j�= 0, 1�G('j)�

_�j = fe (Free entry condition).

By allowing for both conditions above, we can highlight the uniqueness of equilibrium in

both sectors ('�j and_�jfor j = m; y)9 .

The steady state equilibrium requires that the aggregate variables are constant over time,

whereas the market clearing conditions entail that nal good rmsaggregate revenues (Ry)

must equal the sum of the total payments to y-specic workers (wLy = Ly) and intermediate

good rms aggregate revenues (Rm ), while the latter must be equivalent to the total

payment to m-specic workers (wLm = Lm ):

Ry = Ly +Rm = Ly + Lm (3)

From the respective average prots levels (_�mand

_�y) and survival productivity thresh-

olds ('�m and '�y), the mass of rms in both sectors (M and N) can be derived, which in

turn can be used to determine the equilibrium price indexes (Pm and Py):

M =Rm_rm

=Lm

��_�m + f

� =) Pm = M 11����'m ('

�m)

(4)

N =Ry_ry=

Ly + Lm

��_�y + f

� =) Py = N 11��Pm��'y�'�y� (5)

2.2 Open Economy

This section considers two symmetric countries (i.e. countries with same endowments, wage

rate and all the other aggregates) involved in international trade. In particular, the rst

subsection is related to the scenario of Indirect Imports, where any rm within both nal

9See the Appendix A.

10

good and intermediate good sectors can choose to serve the whole foreign market, by paying

additional xed costs of exporting (common across sectors) and facing per-unit iceberg trade

costs (di¤erent across sectors). Thus, as in Melitzs model, all nal good exporters match

with all foreign nal consumers, and similarly, all intermediate good exporters match with

all nal good rms abroad (indirect importers), i.e. all nal good rms within a country

can easily access to foreign intermediates arising from the best input suppliers abroad,

without any particular e¤ort through a very e¢ cient wholesale system. Whereas, the second

subsection concerns the Direct Imports scenario, where only some nal good rms can

actually import some additional intermediates by paying some xed costs of importing

(which are assumed to be larger than xed costs of exporting, coherently with several

empirical evidences), and consequently, intermediate good rms are assumed to be able

to serve only a portion of foreign nal good rms, by incurring a variable selling cost

increasing in the fraction of foreign importers, as in Arkolakis (2008), rather than a xed

cost of exporting. Hence, all nal good exporters match with all foreign nal consumers

again (as in Melitz (2003)), whereas all intermediate good exporters match only with more

productive nal good rms abroad (direct importers), i.e. solely the best nal good rms

within a country can have an access to intermediates arising from the best input suppliers

abroad, through incurring additional searching e¤ort and investment in an own distribution

network.

2.2.1 Indirect imports scenario

Intermediate good sector An intermediate good rm within each economy can serve

all foreign nal good producers, by paying additional xed costs fx > f and facing per-unit

iceberg intermediate trade costs �m > 1. For this reason, the rm will set a higher export

price pXm ('m) =�m�'m

= �mpDm ('m), and will obtain lower revenues r

Xm ('m) = �

1��m r

Dm ('m)

and prots �Xm ('m) =rXm('m)

� �fX from the international market, compared to the domestic

one. Therefore, exporters total prot will be �D+Xm ('m) =�1 + �1��m

� rDm('m)� � (f + fX).

Now, the aggregate price index of intermediates (PTm ) is decreasing in both number

(MT =M +MX =�1 + Xm

�M)10 and average productivity (

�'T

m) of all intermediate good

10MX = XmM is the mass of intermediate good exporters, where

Xm represents the fraction of exporters

or the probability of exporting within intermediate good sector.

11

rms competing within a country: PTm =M1

1��T pm

��'T

m

�=

(M+MX)1

1��

��'T

m

:

Final good sector Similarly, a nal good rm can choose to export by paying additional

xed costs fx > f and facing per-unit iceberg output trade costs �y > 1. Therefore, it will

charge a higher export price pXy�'y�=

�yPTm

�'y= �yp

Dy

�'y�11 , and obtain lower revenue

rXy�'y�= �1��y r

Dy

�'y�and prot �Xy

�'y�=

rXy ('y)� � fX from foreign market, respect

to home one. In particular, the nal good exporters total prot will be �D+Xy�'y�=�

1 + �1��y� rDy ('y)

� �(f + fX). Notice that the price index of intermediates (PTm ) is common

across all nal good rms, as in the closed economy model, therefore, any change in it will

reect uniformly upon all rms within nal good sector.

Here, the aggregate price index of nal goods (PTy ) is decreasing in the price index

of intermediates, in addition to be negatively related to both number (NT = N + NX =�1 + Xy

�N )12 and average productivity (

�'T

y ) of all nal good rms competing within a

country as in Melitz (2003): PTy = N1

1��T py

��'T

y

�=

(N+NX)1

1�� PTm

��'T

y

:

Equilibrium As in the closed economy model, a rm will stay in the home market till its

prot is positive (�Dj�'Dj�> 0; for j = m; y ). Thus, the survival productivity threshold

is 'Dj such that �Dj

�'Dj�= 0 (Zero Domestic Prot Condition). Moreover, a rm will

serve the foreign market only if the export prot is positive (�Xj�'Xj�> 0; for j = m; y).

Therefore, the export productivity threshold 'Xj is such that �Xj

�'Xj�= 0 (Zero Export

Prot Condition). The free entry condition in the open economy scenario is vej�'j�= 0,

1�G('Dj )�

_�j = fe for j = m; y, where

_�j = �

Dj

��'j

�+ Xj �

Xj

��'X

j

�.

From all conditions above, the uniqueness of equilibrium ('Dj , 'Xj and

_�jfor j = m; y)

can be highlighted in both nal good and intermediate good sectors13 , and the export

threshold 'Xj can be written as function of survival threshold 'Dj : '

Xj = '

Dj � j

�fXf

� 1��1

.

Thus, 'Xj > 'Dj if trade costs are su¢ ciently higher than xed production cost (fX�

��1j > f

).

From the Figure 2, we can see as a country opens to trade, the least productive good11Notice that the price of intermediates is still the same amongst all nal good rms (i.e. both exporters

and non-exporters) PTm, but lower compared to the closed economy scenario Pm.12NX =

Xy N is the mass of intermediate good exporters, where

Xy represents the fraction of exporters

or the probability of exporting within nal good sector.13See the Appendix B.

12

rms will exit the market (i.e. all rms whose productivity 'j is such that '�j < 'j < '

Dj ),

the best ones will also serve the whole market abroad (i.e. all rms whose productivity

'j is such that 'j > 'Xj ), and the remaining rms will continue to produce only for the

home market (i.e. all rms whose productivity 'j is such that 'Dj < 'j < '

Xj ) in both

sectors. Therefore, some reallocation e¤ects occur across rms within each sector, implying

an increase in aggregate productivity. Notice that the aggregate productivity gains within

intermediate sector due to reallocation e¤ects entails some uniform competitiveness gains

within nal good sector due to input switching e¤ects: i.e. all nal good rms are basically

able to replace the worst domestic intermediate inputs with the best ones from abroad,

becoming more competitive.

From the average prot levels and productivity thresholds, the mass of both intermediate

rms and nal good rms (M and N) can be derived, which in turn can be used to determine

the equilibrium price indexes (PTmand PTy )

14 . In particular, within intermediate sector,

rmsaverage prot is_�m ('m) =

_rm('m)

� ��f + XmfX

�; the mass of home rms is M =

Rm_rm

= Lm�(

_�m+f+ XmfX)

; whereas, the mass of rms competing within a country is MT =

M +MX =�1 + Xm

�M , which equals the number of intermediate varieties available for

nal good rms; and the related price index is PTm =M

11��T

��'T

m

, which can be simply written

as function of survival cuto¤ 'Dm: PTm =

�Lm�f

� 11�� 1

�'Dm. Whereas, within nal good sector,

rmsaverage prot is_�y�'y�=

_ry('y)� �

�f + Xy fX

�; the mass of domestic rms is N =

Ry_ry=

Lm+Ly

�(_�y+f+ Xy fX)

; the mass of rms competing within a country is the NT = N +NX =�1 + Xy

�N , which is in turn equivalent to the number of nal good varieties available

for all consumers, whose the price index is PTy = N1

1��T py

��'y

�=

N1

1��T Pm

��'y

. The latter

can be easily expressed as function of survival cuto¤ and the price index of intermediates:

PTy =�Lm+Ly�f

� 11�� PTm

�'Dy.

2.2.2 Direct imports scenario

Intermediate good sector Unlike the former scenario, an intermediate good rm is

assumed to be able to serve solely a fraction of foreign nal good producers ( MXy ) i.e.

exclusively those nal good rms which are productive enough to cover some xed costs

14See the Appendix C for more details.

13

of importing (direct importers) by making additional investments proportional to the

share of foreign customers ( MXy fx)15 and facing as before per-unit iceberg intermediate

trade costs �m > 1. Therefore, an intermediate exporter will charge the same export price

pXm ('m) =�m�'m

= �mpDm ('m) as in Indirect exports scenarioand yield however relatively

lower export revenues MXy rXm ('m) =

MXy �

1��m r

Dm ('m) and export prot

MXy �

Xm ('m) =

MXy rXm('m)

� � MXy fX since they are proportional to fraction of foreign customers served

entailing that exporters total prot will be �D+Xm ('m) =�1 + �1��m

MXy

�rDm('m)

� ��f + MXy fX

�. The price index of intermediates used by all nal good rms located within

a country is on average PTm =M1

1��T pm

��'T

m

�=

M1

1��T

��'T

m

, which is decreasing in both number

(MT = M + MXy MX =

�1 + MXy

Xm

�M )16 and average productivity (

�'T

m ) of input

suppliers competing within country. However, the portion of nal good importers also plays

a relevant role now to determine the current price index: an increase in the fraction of

importers within nal good sector entails a fall in the price index of intermediates, since a

relatively higher number of nal good rms can access to better foreign inputs.

Final good sector A nal good rm can still choose to serve the whole foreign market

as in Melitz (2003), and not only a share of it, by paying additional xed costs fx > 1 and

facing per-unit iceberg output trade costs �y > 1.

Furthermore, some nal good rms can also import directly foreign intermediates

arising from the most productive foreign intermediate rms (i.e. foreign m-exporters)

in order to yield higher variable prots. Indeed, within-importer aggregate price of inter-

mediates PMm =M

11��M

��'T

m

=(M+MX)

11��

��'T

m

turns out to be lower than within-nonimporter one

PDm =M

11��

��'m

(i.e. PDm = �PMm where � =

�1 + ��km

�fXf

���k�1��1

� 1��1

> 1) 17 .

However, rms have to pay some xed costs of importing fM , which have been assumed

15The foreign market entry costs are assumed to be increasing in relative foreign market size as in themodels of Arkolakis (2008) and Akerman and Forslid (2009)): they argue that marketing costs of establishinga new brand would be relatively higher in markets with a higher share of potential buyers. It is worth notingthat if all nal good rms are able to import directly by paying the xed cost of importing (i.e. if MXy = 1)implies that intermediated good exporters can serve the whole market abroad, by paying the xed cost ofexporting fX as in the former scenario.16MX =

XmM is the mass of intermediate good exporters,

Xm and

MXy represent the fraction of

exporters within intermediate good sector and the fraction of import-export rms within nal good sector,respectively.17M and

�'m(MM =M +MX and

�'M

m ) are respectively the number and the trade-cost-adjusted averageproductivity of intermediate good rms supplying i.e. of intermediate varieties available for nal goodnonimporters (nal good importers). See the Appendix C for more details.

14

to be larger than costs of exporting fX . As a consequence, within nal good sector, im-

porters charge lower domestic price and are associated with larger revenues and prots from

home market respect to nonimporters on the one hand, and import-export rms set lower

export prices and exhibit larger revenues and prots from foreign market, compared to

only-exporters on the other hand:

Firm-level variables Nonimporters Importers

Domestic price pDy�'y�=

PDm�'y

pMy�'y�=

PMm�'y

=��1PDm�'y

= ��1pDy�'y�

Domestic revenue rDy�'y�= Ry

�Py�'y

PDm

���1rMy

�'y�= Ry

�Py�'y

PMm

���1= ���1rDy

�'y�

Domestic prot �Dy�'y�=

rDy ('y)� � f �

My

�'y�=

rMy ('y)� � (f + fM )

Export price pXy�'y�=

�yPDm

�'y= �yp

Dy

�'y�

pMXy�'y�=

�yPMm

�'y= �yp

My

�'y�= �y�

�1pMDy�'y�

Export revenue rXy�'y�= �1��y r

Dy

�'y�

rMXy�'y�= �1��y r

My

�'y�

Export prot �Xy�'y�=

rXy ('y)� � fX �

MXy

�'y�=

rMXy ('y)� � fX

Exporters total prot �D+Xy�'y�=�1 + �1��y

� rDy ('y)� � (f + fX) �

M+MXy

�'y�=�1 + �1��y

�rnMy ('y)

� � (f + fX + fM )

Equilibrium Under the current scenario, intermediate good rms still make two decisions:

whether producing for the home market and whether serving also a portion of a foreign

market. Therefore, by allowing for the zero domestic prot condition (�Dm�'Dm�= 0 ),

zero export prot condition ( MXy �Xm

�'Xm�> 0 ) and the free entry condition (vem ('m) =

0 , 1�G('Dm)

�

_�m = fe where

_�m = �

Dm

��'m

�+ Xm

MXy �

Xm

��'X

m

�)18 , the uniqueness of

equilibrium within sector can be highlighted i.e. both survival and export productivity

thresholds as well as the average prot ('Dm, 'Xm and

_�m) and 'Xm can be written again

as a function of 'Dm: 'Xm = '

Dm�m

�fXf

� 1��1entailing that 'Xm > '

Dm only if export costs

are high enough respect to xed cost of production (fX���1m > f ). Consequently, trade

openness leads the least productive intermediate good rms to exit the market (i.e. rms

whose productivity 'm is such that '�m < 'm < '

Dm), the most productive ones to serve

also a fraction of foreign nal good producers (i.e. rms whose productivity 'm is such that

'm > 'Xm), and the remaining rms to supply only all domestic nal good producers (i.e.

rms whose productivity 'm is such that 'Dm < 'm < '

Xm): some reallocation e¤ects occur

again within intermediate good sector, implying an increase in aggregate productivity (see

the Figure 3).

Whereas, nal good rms make three decisions now: whether producing for the home

18 Xm is rmsprobability of exporting (or fraction of exporters) within intermediate sector, and MXy

is rmsprobability of two-way trading (or fraction of import-export rms) within nal good sector, whichequals rmsprobability of importing (or fraction of importers) in our model.

15

market, whether exporting the nal output and whether directly importing intermediate

inputs. Since fM > fX , all nal good importers are assumed to be able to serve interna-

tional markets, whereas some nal good exporters cannot import additional intermediates.

A rm will decide to buy intermediates from abroad, only if the related extra-prot is pos-

itive (�M+MXy�'MXy

�> �D+Xy

�'MXy

�). Thus, the import-export productivity threshold

'MXy is such that �M+MXy

�'MXy

�� �D+Xy

�'MXy

�= 0 (Zero Import-Export Prot Condi-

tion). By considering the latter condition with zero domestic prot condition (�Dy�'Dy�= 0

), zero export prot condition (�Xy�'Xy�= 0 ) and the free entry condition (vey

�'y�=

0 , 1�G('Dy )

�

_�y = fe , where

_�y =

Dy �

Dy

��'D

y

�+ Xy �

Xy

��'X

y

�+ MXy �

M+MXy

��'MX

y

�),

the uniqueness of equilibrium within sector can be found i.e. survival, export, and

import-export productivity thresholds, as well as the average prot ('Dy , 'Xy , '

MXy and

_�y)19 and import-export cuto¤ 'MXy can be written as function of export cuto¤ '

Xy

('MXy =�

fMf(1+���1y )(���1�1)

� 1��1 �

fXf �

��1y

�� 1��1'Xy ), which in turn can be expressed as

function of survival threshold 'Dy ('Xy = '

Dy �y

�fXf

� 1��1

). Notice that 'Dy < 'Xy < '

MXy

if and only if xed cost of importing is su¢ ciently higher than the xed cost of exporting (

fM > fX���1y

�1 + ���1y

� ����1 � 1

�), which in turn is high enough respect to xed cost of

production (fX > f�1��y ).

The Figure 4 shows as trade openness induces the worst rms to leave the market

(rms whose productivity 'y is such that '�y < 'y < '

Dy ) and the best ones to import

from the best foreign input suppliers and serve all foreign consumers at the same time (i.e.

all rms whose productivity 'y is such that 'y > 'MXy ). While the remaining rms can

be distinguished in two groups: the less productive rms which are able to serve only the

domestic market (i.e. all rms whose productivity 'y is such that 'Dy < 'y < '

Xy ) and the

more productive rms which are also able to export without importing (i.e. all rms whose

productivity 'y is such that 'Xy < 'y < '

MXy ). Therefore, some reallocation e¤ects occur

again within nal good sector, implying an increase in aggregate productivity. However, it is

worth noting that now only direct importers (import-export rms in our model) can actually

enjoy some competitiveness gains from input switching mechanism, whereas the remaining

rms (pure domestic rms and only-exporters) basically would su¤er some competitiveness

19 Dy = 1 � MXy is rmsprobability of non-importing (or fraction of non-importers) and Xy is rmsprobability of only-exporting (or fraction of only-exporters) within nal good sector.

16

losses, due mainly to a decrease in domestic intermediate varieties available. In other words,

productivity-enhancing reallocation e¤ects within nal good sector linked to trade in nal

goods (as in Melitz (2003)) are further boosted through these heterogeneous competitiveness

e¤ects arising from trade in intermediate inputs.

From the average prot levels and productivity thresholds in both sectors, the mass of

both intermediate good rms and nal good rms (M and N) can be derived, which in turn

are needed to determine the equilibrium price indexes (PTm and PTy )

20 .

In particular, in the intermediate good sector, the average prot is_�m ('m) =

_rm('m)

� ��f + Xm

MXy fX

�; the mass of home rms is M = Rm_

rm= Lm

�(_�m+f+ Xm

MXy fX)

, which equals

the number of intermediate varieties available for nal good nonimporters; whereas, the num-

ber of input varieties available for nal good importers is MM =M +MX =�1 + Xm

�M .

Thus, the number of intermediate varieties available for all nal good rms within a coun-

try is on average MT = M + MXy MX =

�1 + MXy

Xm

�M , and the related price index is

PTm =M

11��T

��'T

m

. It is worth noting that the price index of intermediates within a country is

now also decreasing in the fraction of importers: a change in relative number of nal good

rms able to import matters as a change in either number or average productivity of inter-

mediate rms competing within a country, to understand the dynamics of the price index

of intermediates. However, it can be again expressed as a function of survival threshold

PTm =�Lm�f

� 11�� 1

�'Dm.

Similarly, in the nal good sector, nal good rmsaverage prot is_�y�'y�=

_ry('y)� ��

f + X+MXy fX + MXy fM

�; the mass of domestic rms isN = Ry_

ry=

Lm+Ly

�(_�y+f+ X+MXy fX+

MXy fM)

;

whereas, the mass of rms competing within a country is the NT = N + NX+MX =�1 + X+MXy

�N , which in turn equals the number of nal good varieties available for

all consumers, whose the price index is PTy = N1

1��T py

��'T

y

�=

N1

1��T P

TTm

��'T

y

. Notice that PTTm

is the price index of intermediates used by all rms competing within a country, whereas

PTm is the price index of intermediates used by all rms located within a country (see the

Appendix C for more details). Therefore, a decrease in the former price index of interme-

diates in addition to an increase in average productivity of nal good rms and a possible

higher number of available nal goods would imply a fall in average price of nal goods (i.e.

20See the Appendix C for more details.

17

an increase in consumerswelfare). However, the latter variable can be expressed as a func-

tion of survival threshold and the price index of intermediates used by all rms competing

within an economy: PTy =�Lm+Ly�f

� 11�� PTTm

�'Dy.

3 Impact of trade liberalization in intermediate goods

This section aims at studying the impact of trade liberalization in intermediate goods on

rm behaviour within both intermediate and nal good sectors, as well as on welfares

consumers, in both scenarios described in the previous section.

3.1 Indirect imports scenario

3.1.1 Intermediate good sector

As we can see from the Appendix D, following a fall in trade cost of intermediates goods

the survival productivity cuto¤ increases @'Dm

@�m< 0, which is conrmed by a decrease in

the fraction of surviving rms (or rms probability of surviving) @ inm

@�m> 0. Whereas, the

export productivity cuto¤ decreases @'Xm

@�m> 0, indeed, the fraction of exporters (or rms

probability of exporting) increases as well @ Xm

@�m< 0 . Therefore, as in Melitz (2003), the

least productive rms are forced to exit the home market, but now more rms can also

start exporting, implying an increase in aggregate productivity within sector, due to such

reallocation e¤ects towards the more productive rms (see the Figure 5). This aggregate

productivity enhancement would entail on average a fall in the price index of intermediates

(@PTm

@�m> 0 ), although the change in the total number of intermediates available seems to be

ambiguous (@MT@�m =? ).

3.1.2 Final good sector

As concerns the e¤ects of trade liberalization in intermediates on nal good sector, we can

notice that only a fall in price of nal goods takes place@PTy@�m

> 0. In other words, all

nal good rms uniformly enhance their competitiveness following trade liberalization in

intermediates since they can replace the worst domestic intermediated inputs with better

foreign ones (gains from input switching) which would reect as whole on consumers

welfare, without any particular dynamics within nal good sector.

18

3.2 Direct imports scenario

3.2.1 Intermediate good sector

Trade liberalization in intermediate inputs implies similar e¤ects as in the former scenario:

productivity gains from reallocation e¤ects seem to prevail on possible losses in varieties

within intermediate goods sector21 (see the Figure 6). Therefore, nal good rmscompet-

itiveness seems to increase on average, although heterogeneously as we will see later.

3.2.2 Final good sector

As concerns the e¤ects of trade liberalization in intermediates on nal good sector, we can

notice that both survival and export cuto¤s increase@'Dy@�m

< 0,@'Xy@�m

< 0; whereas the import-

export cuto¤ decreases@'MXy@�m

> 0. Thus, we have two kinds of e¤ect linked to the more

intense import activity: the worst nal good rms exit completely the market on the one

hand, and the least productive exporters also leave the international market and decide to

focus exclusively on the home market again on the other hand (see the Figure 7). Indeed,

we can see clearly that both fractions of survivors and only-exporters (i.e. both probabilities

of surviving and of only-exporting) decrease@ iny@�m

> 0,@ Xy@�m

> 0, whereas the fraction of

import-export rms (i.e. the probability of two-way trading) increases@ MXy@�m

< 022 . There-

fore, some reallocations e¤ects also take place within nal good sector from less productive

rms (nonimporters) to more productive ones (import-export ms), implying an aggregate

productivity improvement, mainly due to some heterogeneous competitiveness gains from

input trade liberalization. In particular, we can see an overall fall in price index of interme-

diates (@PTm

@�m> 0) is associated with an increase in input price di¤erential between importers

and nonimporters within nal good sector ( @�@�m < 0). More specically, we can notice that

21 It is worth noting that the change in the export productivity cuto¤ is not so straightforward @'Xm

@�m=?,

since we have an increase in both export variable prot opportunities due to a fall in trade costs andan increase in the portion of y-importers and xed cost of exporting which is positively related tothe increasing fraction of y-importers. However, the fraction of m-exporters (or m-rms probability of

exporting) undoubtedly increases @ Xm

@�m< 0: this might mean that the number of m-exporters decreases

less than the number of m-surviving rms or even increases. In a few words, we have a certain domesticselection e¤ ect and an ambiguous export selection e¤ ect across m-rms following trade liberalization inintermediates (see the Figure 6).22However, the fraction of all exporters (i.e. the probability of exporting) seems to be not a¤ected

@ X+MXy@�m

= 0, since both number of surviving rms and number of all exporters decrease proportionally(or simply because the probability of exporting nal goods is marginally a¤ected by trade liberalization inintermediate inputs).

19

the price of intermediates for nonimporters actually increases (@PDm

@�m< 0). Therefore, we can

reach the conclusion that: following input tari¤ cutting, rm competitiveness on average en-

hances within nal good sector, although actually, only some rms (import-export rms)23

would enjoy competitiveness gains from input switching mechanism, whereas the remain-

ing rms would su¤er some competitiveness losses, due mainly to a fall in input varieties

available24 .

4 Conclusion

This paper attempts to study the impact of trade liberalization in intermediate inputs

within a general equilibrium framework à la Melitz (2003), where all rms are assumed

to be heterogeneous in productivity and can produce either intermediate goods or nal

goods under monopolistic competition. In particular, our model shows di¤erent e¤ects from

reducing input tari¤s, according to if all intermediates are assumed to be imported directly by

nal good rms through incurring additional xed cost or indirectly through an e¢ cient

wholesale system, without making any further xed investment. If all foreign intermediates

are indirectly imported, all nal good rms gain uniformly in competitiveness from trade

liberalization in intermediates, since they are able to substitute the worst domestic inputs

with the best foreign ones (gains from input switching). These uniform competitiveness

gains will translate entirely into an increase in consumerswelfare without any particular

rm dynamics within nal good sector. Whereas, if all foreign intermediates are directly

imported, only the more productive rms (importers) will be able to use foreign inputs,

and therefore enjoy some competitiveness gains from input trade liberalization. Conversely,

the other rms (non-importers) will su¤er some competitiveness losses, mainly due to a

23 In spite of the change in price of intermediates for importers is not so straightforward ( @PMm

@�m=?), we

can highlight that this price falls, since we have shown that the price of intermediates for all nal good

rms within a country decreases ( @PTm

@�m> 0), although the price of intermediates for nonimporters rises

( @PDm

@�m< 0).

24 In other words, if nal good rms performance incorporates the e¤ects arising from intermediate sectorthrough the related price Pm (which is endogenous) in addition to the technology component 'y (which

is constant at rm level), we would have an improvement in importers productivity (�My ='yPMm

) and a

worsening in nonimportersproductivity (�Dy ='yPDm

) within nal good sector, following trade liberalization

in intermediates. That could contribute to explain why several empirical studies nd insignicant learning-by-exporting e¤ects, given that some exporters (only-exporters) will lose and some others (import-exportrms) will gain in performance terms from trade liberalization policies.

20

decrease in domestic input varieties available. That would force the least productive rms

to exit the domestic market and the least productive exporters to leave international market,

causing some market shares reallocation towards the more productive rms (import-export

rms), and consequently some aggregate productivity gains and some nal variety losses.

Nevertheless, consumers welfare seems to increase again by considering altogether these

positive and negative e¤ects. An empirical investigation on main predictions of the current

theoretical model is left for future research.

21

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Figure 1: Closed Economy Intermediate good (m) and Final good (y) sectors (j = m,y)

DOMs

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Figure 2: Open Economy Indirect Imports Intermediate good (m) and Final good (y)sectors (j = m,y)

Exiters DOMs EXPs

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Figure 3: Open Economy Direct Imports Intermediate good (m) sector

m-Exiters m-DOMs m-EXPs

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Figure 4: Open Economy Direct Imports Final good (y) sector

y-exiters y-DOMs y-EXPs y-IMPEXPs

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Figure 5: Trade liberalization in intermediate goods Indirect Imports Intermediate good(m) sector

Exiters DOMs newEXPs EXPs

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Figure 6: Trade liberalization in intermediate goods Direct Imports Intermediate good(m) sector

Exiters DOMs newEXPs EXPs

[ Exiters DOMs EXPexiters EXPs ]

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Figure 7: Trade liberalization in intermediate goods Direct Imports Final good (y) sector

DOMexiters EXPexiters newIMPEXPsDOMs EXPs IMPEXPs

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