Study Reports on Firm Dynamics, Endogenous Growth and International Trade

Description
Study Reports on Firm Dynamics, Endogenous Growth and International Trade:- International trade is the exchange of capital, goods, and services across international borders or territories.[1] In most countries, such trade represents a significant share of gross domestic product (GDP). While international trade has been present throughout much of history

Study Reports on Firm Dynamics, Endogenous
Growth and International Trade
Abstract



Recent empirical firm level studies reveal the structural heterogeneity of firms in process
and product innovation, as well as the central role of product quality in determining world trade
patterns and intensities. This calls for a better understanding of the link between firm
heterogeneity and the innovation and export decisions of firms which are at the base of
productivity growth and, hence, economic growth and development.

My dissertation contributes to this debate focusing on the supply side. I propose a
novel way to model the production technology of firms by introducing two attributes of firm
heterogeneity: cost efciency and product quality. The goal of the first thesis chapter is to study
the efects of process and product innovation on firm dynamics, productivity and endogenous
long run growth. In the second chapter an open econ- omy framework with trade between
symmetric countries is analyzed. Here the focus is on quantifying the impact of trade as well as
trade liberalization on firm innovation dynamics and productivity- and aggregate growth. The
third chapter abstracts from endogenous growth and examines the role of the two attributes of
firm heterogeneity in shaping the trade patterns and intensities within and across developed and
developing countries.

















Contents




Acknowledgements i


Abstract ii


List of Figures vi

List of Tables vii



I Introduction ix


II Chapters 1

1 Product and Process Innovation in a Growth Model of
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Related Literature . . . . . . . . . . . . . . . . .
1.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Consumer Problem . . . . . . . . . . . . . . . . . 1.2.2 Firms .
. . . . . . . . . . . . . . . . . . . . . . .
1.2.2.1 Production Decision . . . . . . . . . . . 1.2.2.2
Innovation Decision . . . . . . . . . . . 1.2.2.3 Firm
Value Function . . . . . . . . . . . 1.2.2.4 The Exit
Decision . . . . . . . . . . . . 1.2.2.5 Firms Entry . . . . . .
. . . . . . . . .
1.2.3 Cross Sectional Distribution and Aggregates . . . 1.2.4
Equilibrium Definition . . . . . . . . . . . . . . .
1.3 Endogenous Growth . . . . . . . . . . . . . . . . . . . .
1.3.1 Balanced Growth Path . . . . . . . . . . . . . . . 1.3.2
Growth Rate Determinants . . . . . . . . . . . . 1.3.3 Growth
Rate Decomposition . . . . . . . . . . .
1.4 Numerical Analysis . . . . . . . . . . . . . . . . . . . . .
1.4.1 Calibration . . . . . . . . . . . . . . . . . . . . . 1.4.2 The Role
of Innovation . . . . . . . . . . . . . . 1.4.3 Firms Partition and
Cutof Functions . . . . . . 1.4.4 Firms Distribution . . . . . . . . .
. . . . . . . .


iii

Firm Selection
..........
.......... ..........
.......... ..........
.......... ..........
.......... ..........
.......... ..........
.......... ..........
.......... ..........
.......... ..........
.......... ..........
.......... ..........

2
2
5
8
8
9
10
12
13
15
15
16
17
18
18
20
21
23
23
27
28
30




Contents iv


1.5 Comparative Statics . . . . . . . . . ...... . . . . . . . . . . . . . . . 32
1.6 Final Remarks . . . . . . . . . . . . ...... . . . . . . . . . . . . . . . 35
References . . . . . . . . . . . . . . . . . . ...... . . . . . . . . . . . . . . . 36
Appendix . . . . . . . . . . . . . . . . . . ...... . . . . . . . . . . . . . . . 39
A Partitions and Innovation Cutof Functions . . . . . . . . . . . . . . . 39
B Aggregate Variables . . . . . . . ...... . . . . . . . . . . . . . . . 39
C Growth Rate Disaggregation . . ...... . . . . . . . . . . . . . . . 40
D Algorithm . . . . . . . . . . . . ...... . . . . . . . . . . . . . . . 40
E Conditional Probabilities . . . . ...... . . . . . . . . . . . . . . . 41

2 Trade and Growth: Selection versus Process and Product Innovation
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Open Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Production and Innovation . . . . . . . . . . . . . . . . . . . . . .
2.2.1.1 Firm Dynamic Optimization . . . . . . . . . . . . . . . . 2.2.2 Exit,
Entry, and the Cutof Functions . . . . . . . . . . . . . . . . 2.2.3 Firm Distribution . . .
. . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Equilibrium and Balanced Growth Path . . .
. . . . . . . . . . . .
2.3 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Closed and
Open Economy . . . . . . . . . . . . . . . . . . . . . .
2.3.2.1 Firms Partition and Distributions . . . . . . . . . . . . .
2.3.3 Trade Liberalization . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Final Remarks
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Innovation Cutof Functions . . . . . . . . . . . . . . . . . . . . . . . B Value Function
in the Closed Economy . . . . . . . . . . . . . . . . . C Value Function in the Open
Economy . . . . . . . . . . . . . . . . . . D Algorithm . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . E Closed vs. Open Economy and Trade Liberalization . . . . . . . . . .

43
43
46
47
47
48
49
50
50
50
54
55
56
59
60
63
63
63
64
65
66

3 World Trade Patterns and Prices: The Role of Cost and Quality Het-
erogeneity 68
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2 The Model Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.2.1 Consumers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.2.2 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2.2.1 Production Decision . . . . . . . . . . . . . . . . . . . . . 73
3.2.2.2 The Exit Decision . . . . . . . . . . . . . . . . . . . . . . 74
3.2.2.3 Firms Entry . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.2.3 Cross Sectional Distribution and Aggregates . . . . . . . . . . . . . 76
3.2.4 Steady-State Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 76
3.3 Equilibrium in the Open Economy . . . . . . . . . . . . . . . . . . . . . . 77
3.3.1 Symmetric Countries . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.3.1.1 Cross Sectional Distribution and Aggregates . . . . . . . 79
3.3.2 Asymmetric Countries . . . . . . . . . . . . . . . . . . . . . . . . . 80






Contents v


3.3.2.1 Firms Entry . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.3.3 Four Countries, Open Economy Model . . . . . . . . . . . . . . . . 81
3.3.3.1 Production and Export . . . . . . . . . . . . . . . . . . . 81
3.3.3.2 Cross Sectional Distribution and Aggregates . . . . . . . 83
3.3.3.3 Steady-State Equilibrium . . . . . . . . . . . . . . . . . . 84
3.3.4 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.4 Four-Country Scenario Results . . . . . . . . . . . . . . . . . . . . . . . . 86
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
A Conditions on Fixed Costs and Technological Lag . . . . . . . . . . . . 94
B Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
C Size Distribution and Average Productivities . . . . . . . . . . . . . . 95















































List of Figures



1.1 Firms Partition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.2 Bivariate and Univariate Firms Distribution . . . . . . . . . . . . . . . . . 30
1.3 Conditional Firms Size Distributions . . . . . . . . . . . . . . . . . . . . . 31
1.4 Comparative statics for diferent c
a
and c
q
. . . . . . . . . . . . . . . . . . 33
1.5 g for diferent c
a
and c
q
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.6 Comparative Statics for diferent c
e
. . . . . . . . . . . . . . . . . . . . . . 34
1.7 g for diferent c
e
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.1 Firms Partition, Closed (Left) vs. Open (Right) . . . . . . . . ...... . 55
2.2 Bivariate Firms Distribution, Closed (Left) vs. Open (Right) ...... . 56
2.3 Firms Distribution, Closed vs. Open (Left), Non Exporters vs. Exporters
(Right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... . 56
2.4 Growth Diferential for diferentt . . . . . . . . . . . . . . . ...... . 57
2.5 Growth Diferential for diferent c
ex
. . . . . . . . . . . . . . ...... . 58
2.6 Trade Liberalization -t . . . . . . . . . . . . . . . . . . . . . ...... . 66
2.7 Trade Liberalization - c
ex
. . . . . . . . . . . . . . . . . . . . ...... . 67

3.1 Incumbents Distribution over Productivity and Quality . . . . . . . . . . 86
3.2 Firms Partition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.3 Distribution of Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.4 Expenditure Shares Distribution over Quality . . . . . . . . . . . . . . . . 89
3.5 Total Trade Values Within and Across Regions . . . . . . . . . . . . . . . 90
3.6 Conditional Labor Distribution over Technology . . . . . . . . . . . . . . 96




















vi



List of Tables



1.1 Heterogeneity in Innovation Strategies . . . . . . . . . . . . . . . . . . . .
31.2 Calibration . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 25 1.3
Empirical Targets and Model Statistics . . . . . . . . . . . . . . . . . . . . 26
1.4 Conditional Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.5 Descriptive Statistics of Firms Distributions . . . . . . . . . . . . . . . . . 32

2.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.2 Empirical Targets and Model Statistics . . . . . . . . . . . . . . . . . . . . 52
2.3 Growth Rates in the Open Economy . . . . . . . . . . . . . . . . . . . . . 54
2.4 Growth Rates in the Closed and Open Economy . . . . . . . . . . . . . . 54
2.5 Model Statistics in the Closed and Open Economy . . . . . . . . . . . . . 66

3.1 Average Import Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.2 Targets and
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.3 Weighted Average
Technology Across Firm Partition . . . . . . . . . . . . 95






























vii



Dedicato a mia mamma Antonella per una promessa mantenuta


e a mio pap` Silvio per la sua continua presenza a

































viii



Part I




Introduction































ix



Introduction x


In the last decades a growing availability of data at the firm level covering production,
innovation investments, financial systems, and exports has challenged both empirical and
theoretical researchers in answering new questions. A key and common issue has become the
understanding of the efects of firm decisions on the mechanism of resource reallocation from
exiting and contracting firms to new and expanding ones and how this translates into persistent
firm level heterogeneity and growth. This thesis collocates within this research area emphasizing
the diferent role played by heterogeneity in firm efciency and product quality in shaping firms'
innovation and export decisions and their impact on firm size, pricing, productivity- and
aggregate growth, and direction of trade. I believe that this is an important research area as
innovation and international trade are among the main factors leading a country growth. Hence,
contributing in understanding their causes and consequences could help to explain diferences in
the growth rate of industries and hence countries and to design policies aimed at promoting
growth and development.

The first chapter is directly motivated by this recent empirical evidence concerning firms
innovation investments. In particular, it is shown that firms are heterogeneous also in their
innovation activities and that process and product innovations have diferent efects on firms
productivity levels, productivity- and aggregate growth. To explain this evidence, this chapter
develops an endogenous growth model with two sources of firm heterogeneity: production
efciency and product quality. Both attributes evolve endogenously through firms' innovation
choices and permanent idiosyncratic shocks. Growth is driven by innovation and self-selection of
unsuccessful firms and sustained by entrants who imitate successful incumbent firms. Calibrating
the economy to match the Spanish manufacturing sector, the model enables to quantify the
diferent efects of selection, innovation, and imitation as well as product and process innovation on
growth. Moreover, it provides a complete characterization of firms' innovation choices explaining
the partition of firms along diferent innovation strategies and generating consistent firm size
distributions.

In the second chapter this model is applied to study how symmetric trade afects the
decisions of firms to invest in process and product innovation and how this generates firm level-
and aggregate growth. In particular, costly trade impacts on the growth mechanism through a
tougher selection of unsuccessful firms, a selection of the marginal innovators, and a higher
innovation intensity. The quantitative analysis shows that the combination of these factors has a
positive efect on the growth rate. Hence, exposure to trade increases unambiguously growth. This
comes together with a more concentrated industry and a higher share of product innovators than
in the closed economy. Con- cerning the debate on trade liberalization, the model yields
interesting predictions. A reduction of the variable cost of trade unambiguously promotes growth
and fosters the





Introduction xi


difusion of higher product quality. Instead a too strong reduction of the fixed export
cost is detrimental for growth and it is accompanied by a reduction of product quality in favor of
cheaper varieties.

The third chapter is a joint work with Teodora Borota. We abandon endogenous growth
and analyze the role of production efciency and product quality in shaping the trade patterns and
trade intensities within and across two groups of countries, the developed and richer North and
the developing South. Taking prices as a proxy for quality, recent empirical literature identifies a
positive relation between income per capita and both export and import prices, suggesting that
rich countries trade goods of relatively higher quality. The novelty of this model is that instead
of relying on specific demand side mechanisms such as non-homothetic preferences for
explaining these findings, it focuses on the supply side and North-South diferences in technology
as the key determinants of trade specialization over quality. We employ a four country North-
South trade model with two dimensions of firm heterogeneity. Diferences in firms product
qualities and cost efciencies result in a price distribution which, when the fixed cost of trade is
applied, generate diferent consumption bundles and the predicted export and import prices
across income levels. Furthermore, the resulting total expenditure allocation across quality
shows that the North (South) spends a larger share of its income on high (low) quality even with
the same homothetic preferences across regions.






































Part II




Chapters
































1



Chapter 1




Product and Process Innovation
in a Growth Model of Firm
Selection




1.1 Introduction


Globalization and the rise of new technologies have challenged firms' abilities in develop-
ing innovation strategies to face increasing market competition. Innovation has become a
fundamental source of firm survival and growth.
1
The literature has widely analyzed the
relationship between innovation and economic growth.
2
However, little attention has been paid to
the relationship between firm heterogeneity and innovation activities and even less to the
relationship between firm heterogeneity and diferent innovation strate- gies as well as to their
impact on firms' competitiveness and productivity growth. The channel between firm growth and
aggregate growth is still comparatively unexplored. Understanding the determinants of firms'
innovation strategies and the mechanism of resource reallocation through which they impact on
aggregate growth is therefore cru- cial and can also contribute to enhance the efectiveness of
policies aimed at fostering economic growth and welfare.

1
For instance, on a panel of Dutch firms Cefis and Marsili (2005) find that the expected longevity of innovative
firms is 11% higher than non-innovative firms while Doraszelski and Jaumandreu (2008) using a Spanish panel
estimate that the sole contribution of firms that perform R&D explains between 45% and 85% of productivity growth
in the industry with intermediate or high innovation activity. Moreover, Bartelsman and Doms (2000) report evidence of
a self-reinforcing mechanism between productivity and innovation. Profitable firms have a higher propensity to
innovate and innovation is positively related with productivity and productivity growth.
2
Few examples are Aghion and Howitt (1992), Grossman and Helpman (1991) and Romer (1990).




2



Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 3


This need comes together with an increasing availability of data at the firm-level which
distinguish between process and product innovation.
3
These data have stimulated a series of
empirical studies which highlight three main pieces of evidence: innovations are heterogeneous,
asymmetric, and complementary.

Firstly, innovation are heterogeneous in the sense that some firms do not innovate, some
firms specialize in process innovation, others in product innovation and some in both types of
innovations. Thus, firms have diferent incentives to invest either in product or process
innovation. Table 1 shows the share of firms across the diferent innovation strategies for four
European countries.
4
Huergo and Jaumandreu (2004) finds in a sample of Spanish firms in the
manufacturing sector that half of the firms never innovate, 30% undertake either process or
product innovation and 20% of the firms undergo both types of innovations. Similar statistics are
also available for Germany and Great Britain (Harrison et. al. (2008)) and the Netherlands (Cefis
and Marsili (2005)).

Table 1.1: Heterogeneity in Innovation Strategies


Country Share of Innovative Firms
No Innovation Process Product Process and Product
Spain 55.4% 12.2% 12.4% 20%
Germany 41% 10.2% 21% 27.4%
Great Britain 60.5% 11% 14.2% 14.3%
Netherlands 36.6% 5.8% 18.8% 42.7%


Secondly, the innovation strategies are asymmetric. Parisi et. al. (2006) estimate on an
Italian panel that process innovation increases productivity by 14% and product innova- tion by
4% over a three year period. As expected, innovating firms are characterized by a productivity
distribution that stochastically dominates the productivity distribution of non-innovators. But in
the case of product innovation the distribution becomes more skewed to the right. Huergo and
Jaumandreu (2004) show similar results for Spain and highlight a relation betwen firm size and
type of innovation. Small firms are more likely

3
The

European Commission has developed a program aimed at studying the innovation systems of
the States member of the European Union with the scope of promoting innovation and growth. The core of the
program is based on firm-level surveys (Community Innovation Surveys) which ask detailed questions about the
innovation investments of firms distinguishing between process and product innova- tions. In particular, process
innovation occurs when firms introduce some significant modification of the productive process as the introduction of
new machines or the introduction of new methods of organi- zation, while product innovation occurs when firms report
a new or improved good. This information is then merged with structural and macroeconomic data drawn from OECD
surveys. Additionally, some European Countries carry out nation-specific surveys. For instance, in Spain there is the
Encuestas So- bre Estrategias Empresariales that is issued every three years. The same analysis becomes more difcult with
American data where innovation is measured as patents and therefore the two innovations cannot be distinguished.
However, for a concise summary Klette and Kortum (2004) report a list of stylized facts concerning firm R&D,
innovation, and productivity.
4
It should be noticed that the data sets are not homogeneous. Hence table 1 does not allow compar- isons across
countries but only the ability to observe the stated heterogeneity in the innovation choices.





Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 4


to undertake product innovation while large firms are more likely to undertake process
innovation.

Thirdly, innovations are complements. Process innovation is more frequent than product
innovation, while the probability of introducing a product innovation is higher for firms that also
introduce a process innovation in the same period. However process innova- tion does not
necessarily imply product innovation.
5
Firms innovate on their existing products, aiming at
increasing product diferentiation and hence prices, in the hope of exploiting consumers'
willingness to pay for a higher quality good. Instead process inno- vation increases the firms'
production efciency. This leads to higher firm productivity, lower prices and a larger scale of
production.
6
Complementarity between process and product innovation then arises: product
innovation allows new product designs but these new designs become profitable only when they
are afordable for the consumers.

Entry and exit play an important role in explaining the reallocation of resources from
less productive firms to more productive firms and therefore growth.
7
In addition, Huergo and
Jaumadreu (2004) show that exit is associated with a lower level of pre-exit innovations, while
entrants present a high probability of innovation.

Existing growth literature cannot explain all these pieces of evidence as it treats quality
upgradings and cost reduction innovations as interchangeable. Moreover, the literature on
heterogeneous firms is usually based only on one factor of heterogeneity, either cost efciency or
the ability of producing quality. In these models a single attribute mono- tonically predicts firms'
revenue, competitiveness, and innovation. This characteristic then implies a threshold firm size
above which all firms innovate and below none do and hence predictions not in line with the
empirical results.

Hence, motivated by the discrepancy between the existing theoretical literature and the
empirical evidence, this paper proposes a new framework able to explain and quan- titatively
replicate the empirical regularities discussed. It analyzes the efects of cost reduction (process)
and quality improving (product) innovations on firm dynamics, productivity- and aggregate
growth, highlighting the importance of product quality in the growth process. For this purpose, I
develop a general equilibrium model with endoge- nous process and product innovation. The
industry dynamics are taken from Hopenhayn (1992) using monopolistic competition as in Melitz
(2003). Firms produce diferentiated

5
See

Miravate and Pernias (2004) on data for the ceramic tile industry in Spain, Martinez-Ros (1999)
for Spanish manufacturing firms and Parisi et. al. (2006) for Italy.
6
See Smolny (1998) for an empirical study on the efects of process and product innovation on the prices charged
by German firms.
7
Foster et. al. (2001) on data from the US manufacturing sector find that more than 25% of the growth between
1997 and 1998 was due to net entry. However, Bartelsman et. al. (2004) find that in Europe the contribution of net
entry is comparatively low than in US.







Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 5


goods and are heterogeneous in their production efciency and in their product qual-
ity. The evolution of both efciency and quality is given by an idiosyncratic permanent component
and by an endogenous component proportional to the optimal investment decision taken by the
firm. Product innovation increases firms product quality while process innovation increases firm
production efciency. In each period non profitable incumbents exit the industry, and are replaced
by new firms. Entrants imitate the av- erage incumbent as in Gabler and Licandro (2005) and
Luttmer (2007) and on average they are more productive than exiting firms increasing the
average productivity of the industry. Hence, growth arises due to firms' innovation and firms'
self-selection and is sustained endogenously by entrants' imitation.

The model is calibrated to match the Spanish manufacturing sector for which there is
a large availability of firm-level data and related empirical studies on both firm dynam- ics and
innovation dimensions. Besides matching closely the data, the model generates moments and a
firm size distribution consistent with the empirical evidence. The in- terplay between the two
sources of firm heterogeneity and costly innovation results in a non-monotonic relation between
firm size and innovation strategies. Small firms un- dertake product innovation, medium firms
both process and product innovation while large firms specialize mainly in process innovation.
Moreover, it emphasizes the impor- tance of the reallocation of resources among incumbents and
innovators as the main source of growth. In fact, firms' turnover explains only 8.13% of
aggregate growth and when innovation is banned output growth declines by 3.1 percentage
points. Another interesting prediction that can be empirically tested is the contribution of the
growth in production efciency and product quality in explaining productivity growth. The model
predicts that efciency growth plays the major role explaining 69.8% of output growth.
Additionally, this model contributes to the literature that tries to understand why firm
heterogenity is persistent endogenizing the evolution of firm technology.

In this model the relationship between firm size and innovative strategies is more artic-
ulate in explaining why diferent firms choose optimally diferent innovation strategies.
Additionally, comparing industries that difer for innovation costs or for entry barriers allows for a
better understanding of the growth rate composition and how it is afected by changes in the
industry structure. Hence this model provide a suitable framework for the analysis of policy
implications aimed at fostering growth.



1.1.1 Related Literature


This paper attempts to link the literature on firm dynamics and endogenous growth
theory by explicitly modeling diferent types of firm-level innovations. As in the seminal






Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 6


models of Romer (1990), Grossman and Helpman (1991) and Aghion and Howitt (1992),
innovation is firm-specific and it is motivated by the appropriation of revenues associated with a
successful R&D investment. In Romer (1990) growth is driven by two elements. The first one is
the invention of new inputs which make the production of the final good sector more efcient. In
this sense and from the point of view of the final good firm it can be seen as process innovation.
The second one is knowledge spillovers from past R&D: the higher the stock of knowledge, the
easier the invention of new varieties. In this paper there is a similar spillover, which is the
imperfect imitation of incumbent firms by entrants. Grossman and Helpman (1991) introduce
growth through quality improving innovation of existing products. However, in their model,
diferent qualities are perceived as perfect substitutes and hence the representative consumer buys
only the cheapest variety (adjusted by quality). Instead, in my model each variety is perceived as
diferent by the consumer and higher quality varieties give higher utility. In Aghion and Howitt
(1992) growth is based on the idea of Schumpeterian creative destruction in which new
innovations replace the previous ones driving the incumbent monopolist out of the industry. The
creative destruction mechanism is not far from the idea of firm selection. Successful firms grow
and drive out of the market unsuccessful ones. Based on these general features my work adds
firm heterogeneity, permanent idiosyncratic shocks that hit both production efciency and product
quality, and endogenous investment choices made by incumbent firms. These new elements
endogenously link aggregate growth with firm-specific growth and hence with the mechanism of
resource reallocation from non- innovators to innovators and from exiting to active firms. The
resulting distribution of firm size is consistent with the data.

The idea of firm selection was already present in Jovanovic (1982). He introduces the
first model with firm-specific stochastic productivities with unknown mean but known variance.
As time goes by firms learn their productivity and the inefcient firms exit. As firms learn their
productivity the efects of selection on firms evolution dies out and eventually the industry
converges to a stationary equilibrium without entry and exit. For this reason, this paper takes the
industry structure from Hopenhayn (1992), who develops a partial dynamics stochastic
heterogeneous firms' model which generates a stationary equilibrium with entry and exit that is
capable of studying the efects of structural changes in the industry on the distribution of firm size
and age. Hopenhayn and Rogerson (1993) analyze the general equilibrium of the Hopenhayn
model focusing on the process of labor reallocation. Both papers study the stationary
equilibrium in which each firm is hit by shocks characterized by a stationary AR(1) process.
However, both papers focus only on firm productivity growth between cohorts and disregard the
efects on aggregate growth.








Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 7


The link between the process of resource reallocation due to selection at the firm level
and economic growth is studied in Gabler and Licandro (2005) and in Luttmer (2007). In both
papers firm technology is hit by permanent shocks which together with firm selection and
entrant imitation generates endogenous growth. The resulting stationary distribution is a
consequence of the knowledge spillover that links the distribution of en- trants productivities to
the distribution of incumbents productivities. This assumption is necessary to generate
endogenous growth. In fact without imitation, as incumbent firms become more productive
through selection, the incentives to enter the industry diminish and eventually vanish. In the end
no new firms enter into the industry and the equilibrium is characterized by the absence of entry
and exit similarly as Jovanovic (1982). Gabler and Licandro (2005) model a competitive
equilibrium with heterogeneous firms using both labor and capital as inputs. When calibrating
their model on US data they show that selection and imitation account for a fifth of productivity
growth. This represents a lower bound. Luttmer (2007) instead considers a monopolistic
competition market in which each firm produces a diferent variety and it is subjected to shocks to
both productivity and demand. Calibrating his model to US data he finds that half of output
growth can be attributed to selection and imitation. This can be seen as an upper bound.

This paper attempts to extend Gabler and Licandro (2005) and Luttmer (2007) by
considering alongside their models the role of innovation in linking firm level growth to
aggregate growth. Modeling endogenously firm innovation investments in both firm efciency and
product quality can help to distinguish the difering contributions of selec- tion and imitation
versus innovation in process and product when explaining economic growth.

The other papers that shed light on the relationship between innovation, firm hetero-
geneity and the role of resource reallocation of the growth process are Klette and Kortum (2004)
and Lenz and Mortensen (2008). The former, building on Grossman and Helpman (1991),
introduces firms that exogenously difer in the profits earned by selling their own products.
Endogenous growth is then generated through innovation investments aimed at increasing the
number of goods produced by each firm and firms adjust the produc- tion lines in response to
their own and competitors' investment in R&D. However they posit permanent exogenous
diferences across firm profitability and hence across the size of the innovative step. This
simplification results in a distribution of innovative firms that have the same volatility as the
distribution of the firms that do not innovate. This model, defining innovation as an endogenous
drift into the stochastic evolution of firm productivity and quality, can account for the difering
variances of the distribution of innovators and non-innovators. Lenz and Mortensen (2008) relate
to Klette and Kor- tum (2004) introducing heterogeneity in the expected productivity of the new
variety





Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 8


produced. But as in both models the engine of growth is a mechanism of creative de-
struction on the numbers of goods existing in the economy at a given point in time, they can
analyze only one channel of innovation.

More recently, Atkeson and Burstein (2007) address the relation between the decision
of heterogeneous firms to innovate and engage in international trade by introducing two types of
stochastic innovation activities. Though their model abstracts from endogenous growth, they
define as process innovation the decision to increase the stock of firm- specific factors that then
translates in higher profits opportunities. This is analogous to process innovation defined in this
model. They define as product innovation the creation of a new firm and hence a new product.
This is the analogous to firm entry discussed in this model. In fact, this model defines diferently
from them as product innovation the decision of firms to improve the quality of an exiting
variety. Moreover, the jump in the efciency and/or quality scale are, in this paper, proportional to
the research intensity.

Finally two other papers of note, Melitz (2003) and Hallak and Sivadasan (2008). Melitz
(2003) proposes a static model with heterogeneous firms in which the exposure to inter- national
trade increases firm selection and generates a partition among firms such that the more
productive firms are the ones who gain access to foreign markets. Hallak and Sivadasan (2008),
building on Melitz (2003), introduce a partial and static equilibrium model in which firms difer in
two attributes: labor efciency and ability to produce high quality varieties. Under the assumption
of minimum quality requirements they study how openness afects firm distribution. In their
model as in Melitz (2003) the partition of firms between domestic producers and exporters is
generated by the presence of a fixed cost to enter the foreign market. Here the same mechanism
is used to generate the partition of firms among the diferent innovation strategies. However, the
firm partition and the efects on the size distribution of firms is not the result of a one-shot change
but it is the result of the combination of permanent shocks on both states and inter-temporal
innovation decisions.




1.2 The Model


This section develops a general equilibrium model in discrete time with infinite horizon.



1.2.1 Consumer Problem


The representative consumer maximizes his utility choosing consumption and supplying
labor inelastically at the wage rate w. Its lifetime utility is assumed to take the following






Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 9


form:




U=



·


t =0



|
t
ln(U
t
)




(1.1)
where|< 1 is the discount factor and t is the time index. In every period the con-
sumer faces the problem of maximizing his current consumption across a continuum of
diferentiated products indexed by i e I where I is a measure of the available varieties in the economy.
Specifically, the preferences are represented by an augmented Dixit- Stiglitz utility function with
constant elasticity of substitution between any two goods
o = 1/(1 ÷o)> 1 witho e (0, 1). Hence, the utility function at time t is:

1
o
U
t
= ( q
t
( i ) x
t
( i ) )
o
d i . (1.2)
ieI

where x(i) is the quantity of variety i e I and q(i) is the corresponding quality. This
utility function is augmented to account for quality variation across products and quality acts as
an utility shifter: for a given price the consumer prefers products with high quality rather than
products with low quality.


The per period budget constraint is E
t
=


ieI


p
t
(i)x
t
(i)di where E
t
is total expenditure
at time t and p
t
(i) is the price of variety i e I at time t. Solving the intra-temporal
consumer problem yields the demand for each variety i e I:


x
t
(i ) =


P
t
q
o
(i) t
p
t
( i )

1
1÷o


X
t
=


P
t
o
q
o
(i) t
p
t
( i )

1
1÷o


E
t


(1.3)

with:



P
t
=




ieI


p
t
( i )
q
t
( i )


o
o÷1



di


o÷1
o



and X
t
= U
t
.



(1.4)

P
t
is the price quality index at time t of all the bundle of varieties consumed and X
t
is
the aggregate set of varieties consumed.

Finally, the optimal inter-temporal allocation of consumption yields the standard Euler
equation:
X
t
+
1
=| ( 1 + r ) . t
X
t
(1.5)
where r
t
is the return on asset holding.



1.2.2 Firms


This section outlines a dynamic two factors heterogeneous firm model. The first source
of heterogeneity is production efciency, a(i) e R++, which increases the marginal
productivity of labor, as in the seminal paper of Hopenhayn (1992), and the second






Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 10


source is quality of the firm's variety, q(i) e R++ (0, 1), which decreases the marginal
productivity of labor. In this respect, a higher quality variety has a higher variable cost.
Firms are distributed over productivity and quality. µ(a, q) = µ(a, q)I is the measure of firm with
state (a, q) at time t, where I is the number of firms in the industry and µ(a, q) is a density
function. It is assumed that each firm produces only one variety so that the index i identifies both
the firm and the corresponding variety produced by that firm and I represents both the set of
varieties and the mass of incumbent firms active in the industry. The following definition are
used, A is the set of all production efciencies, Q is the set of all product qualities, and O ÷ A · Q is
the state space.



1.2.2.1 Production Decision


After paying a fixed operational cost, c
f
, expressed in terms of labor, active firms receive
their new technology level, (a, q). Firms produce and price their own products under
the assumption of monopolistic competition. As in Hallak and Sivadasan (2008), the production
function is assumed to be linear in labor, n, which is the unique input, increasing in firm
efciency, a, and decreasing in firm product quality, q. That is,
x
t
(i) = a
t
(i)q
t
(i)
÷
q
n
t
(i) withq e (0, 1). The parameterq introduces asymmetry between
firm efciency and product quality and measures the difculties in producing a higher
quality variety: the higherq, the more difcult and costly it becomes to produce a high quality product. This
particular functional form is justified by empirical evidence: it generates a price distribution
consistent with the estimates of Smolny (1998) and moreover complementarity between process
and product innovation is obtained.

The profit maximization problem, faced by each firm, is:


t
t
(a(i), q(i)) = max p
t
(i)x
t
(i) ÷ w
t
n
t
(i) ÷ w
t
c
f
(1.6)
p(i)

where w
t
is the wage rate at time t common to all firms. The first order condition with
respect to price yields the optimal pricing rule:

w
t
q
q
(i ) .
p
t
(a(i), q(i)) =oat(i) t
(1.7)

1/o is the constant mark-up associated with the CES demand function. In contrast
to the standard models with a single factor of firm heterogeneity, firms' prices depend on both
firms' efciency and quality. Consistent with both the theoretical predictions and the empirical
estimates, the price schedule is increasing in product quality and









Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 11


decreasing in efciency.
8
As in Melitz (2003) the nominal wage is normalized to one.
Using the monopolistic price to solve for the optimal demand for each variety yields:

1
x
t
(a (i ), q (i ) ) =
oa
t
(i)P
t
o
q
t
( i )
q
÷o
1÷o
E
t
. (1.8)

Firm output is an increasing function of both the aggregates and of the efciency level of
firms. The relationship between product quality and output is ambiguous and depends on the
comparison betweeno, related to consumer preferences, andq, coming from firm production function.
Ifq>o then firm output is decreasing in the product quality: high quality varieties are characterized by a
relatively lower market share. In this case, the positive efect of quality on consumer utility is
completely ofset by the related high market price. The opposite is true wheno>q.

The optimal labor demand is given by:

o
n
t
(a (i ), q (i ) ) = a
t
( i ) q
t
(i)
1
÷q
1÷o

oP
t
o
1
1÷o
E
t
. (1.9)


Labor input is an increasing function of both firms' state variables. Consequently, firms
with more advanced technology demand more labor input. Finally, the net per period
profit of firm i is given by:


t
t
(a(i), q(i)) = a
t
(i)q
t
(i)
1
÷
q
o

o
1÷o

o
(1 ÷o)P
t
1÷
o
E
t
÷ c
f
.


(1.10)


Although product quality has an ambiguous efect on the optimal output of firms, profits
are increasing in both labor efciency and product quality. This provides incentives for firms to
improve endogenously their position in the technology distribution via firms' innovation policies.
In this respect, the model predicts that a change in efciency impacts more a firm's profit than a
change in quality.

The diferent efects of firm efciency and quality on the monopolistic price, on the
output, and on the profits provide a suitable framework in which to study the inter- play among
diferent innovation choices taken by a firm and their efects on a firm's
competitiveness.
9

8
Smolny

(1998), studying a panel of West German firms in the manufacturing sector in the period
1980-1992, estimates that product innovation increases the probability and the frequency of positive net prices
increases by more than 18% while process innovation does not reveal a conclusive efect on firm pricing strategies.
However, he clearly estimates that process innovations increases the probability of employment and especially output
increases. Making increases in output and employment without a lower price is difcult. Hence the efects on output and
employment support the relevance of price efects and of the complementarity between the two forms of innovation.
9
An innovation in product, aimed at increasing product quality, results in a higher market price for the given
variety and, for appropriate parameters, in a contraction of the market quota. This then determines an incentive to
invest also in process innovation and hence to increase firm efciency. That in turn leads to a lower market price and to
an unambiguous larger market share.






Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 12


1.2.2.2 Innovation Decision


Firms receive idiosyncratic permanent shocks on both states. That is, firms' log efciency
and log quality follow a random walk. This is a way of capturing the role of firm- specific
characteristics and the persistence of firm productivity which is established in the empirical
literature.
10
Besides the exogenous random walks, firms can endogenously afect the evolution of
their states through private innovation activities. In line with the terminology used in the surveys
at the firm-level, this paper identify two diferent types of innovation: process innovation and product
innovation. Process innovation refers to the decision of firms to invest labor, with the aim of
lowering firm production costs, while product innovation refers to the decision of firms to direct
labor investment at increasing the quality of the varieties produced.

According to the theoretical growth literature, the benefits derived by firms' innovation
investments are proportional to the amount of resources spent. In particular, innovation
introduces an endogenous drift in the random walk processes which re?ects the amount of
variable labor that firms optimally invest in R&D. The innovation choice is history dependent as
today investment in process or product innovation results in tomorrow higher firm production
efciency and/or product quality. In addition, firms have to pay
also a fixed cost of innovation, c
a
and c
q
, for process and product innovation, respectively.
This is a way of capturing the costs necessary to set up an R&D department, to conduct
market analysis and technically it determines the partition of firms among diferent innovation
strategies. Depending on the firms' technology state, some firms decide to innovate either in
process or in product or in both types of innovation. In whichever form innovation comes, it
represents a first source of endogenous growth since it shifts the bivariate firms' distribution to
the right.

Specifically, log efciency is assumed to evolve according to:


log a
t
+c
a
+1

t
when z
t
= 0
log a
t
+1
log a
t
+ì
a
log z
t
(a, q) +c
a
+1 otherwise . z
t
(1.11)
Shocks are firm-specific and distributed asc
a
+1 ? N (0, o
2
),c
a
+1 ? N (0, o
2
z) whereo
2
is z
t a t a a
the variance of the random walk when innovation does not occur ando
2
z is the variance a
of the process when innovation takes place. z
t
(a, q)> 0 is the labor that a firm with
states (a, q) decide optimally to invest in process innovation.ì
a
> 0 is a parameter that,
together with the log form of the innovation drift, scales the efects of innovation. The log
functional form chosen for the innovation drift is important as together with firm

10
For

instance, the idiosyncratic shocks can capture factors as absorption techniques, managerial
ability, gain and losses due to the change in the labor composition and so on.






Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 13


selection assure a bounded growth and hence the existence of a stationary distribution.
Similarly log quality evolves as:


log q
t
+c
q
+1
t


when l
t
= 0
log q
t
+1
log q
t
+ì
q
log l
t
(a, q) +c
ql
+1 otherwise . t
(1.12)
Againc
q
+1 ? N (0, o
2
),c
ql
+1 ? N (0, o
2
l) whereo
2
ando
2
l are the two variances without
t q t q q q
and with innovation. l
t
(a, q) is the variable labor devoted to product innovation and
ì
q
> 0 is the related scale parameter. The means of the efciency and quality shocks
are normalized to zero eliminating exogenous sources of growth. In fact, abstracting from
innovation and firm selection, in expectation firms do not grow.

The random componentc is independent both across firms and over time. Moreover,
the two processes, efciency and quality, are independent.
11
Define the density function
of a
t
+1 conditional on a
t
as f(a
t
+1,a
t
), and the density functions of q
t
+1 conditional on q
t

as p(q
t
+1,q
t
). The transition of the two state variables depends on the firms' innovation
decisions and the idiosyncratic shocks. Considering jointly the two transition functions,
u : O ÷O can be defined as the joint transition function, which moves firms' quality and efciency states. The
corresponding transition probability function is defined as | : O ·O ÷ [0, 1], which gives the probability
of going from state (a, q) to state (a
?
, q
?
). The transition probability takes diferent forms depending on the
innovation decisions and on the exit decision defined below. If the two processes are
independent then |(-) = f(-)p(-).



1.2.2.3 Firm Value Function


Incumbent firms face a dynamic optimization problem of maximizing their expected
value. Once abstracted from the innovation decision this is a particularly simple prob- lem since
it is a sequence of static optimizations. With the innovation scheme, current investments in
innovation afect the transition probabilities and thus the value of future technology. This
generates a dynamic interplay between firm technology and the inno- vative position taken by the
firm. This is summarized by the following value function:


v(a, q) = max{v
P
(a, q), v
A
(a, q), v
AQ
(a, q), v
Q
(a, q)}. (1.13)


The max operator indicates that in each period firms face diferent discrete choices
which depend on the current level of production efciency and product quality. v
P
(a, q)

11
This

simplification does not afect qualitatively the model predictions, but it has the advantage
to narrow the set of parameters to calibrate since it is possible to ignore the covariances of the two processes.






Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 14


is the value when no innovation investments occurred, v
A
(a, q) when a firm produces and
innovates in process, v
AQ
(a, q) when both process and product innovation are undertaken and v
Q
(a,
q) when a firm specializes only in product innovation.

Using J = {P, A, Q, AQ} and defining with prime the next period variables, the Belman
equation for each choice is given by:


1
v
J
(a, q) = maxt
J
(a, q) + 1 + r max p

O
v(a
?
, q
?
)|(a
?
, q
?
,a, q)da
?
dq
?
, 0 . (1.14)


wheret
P
(a, q) is given by equation (11),t
A
(a, q) =t(a, q) ÷ z(a, q) ÷ c
a
,t
AQ
(a, q) =
t(a, q) ÷ (z(a, q) + l(a, q)) ÷ c
a
÷ c
q
, andt
Q
(a, q) =t(a, q) ÷ l(a, q) ÷ c
q
.

These value functions characterize a partition of firms among the diferent decisions
(only produce or produce and innovate, and in the latter case if process, or product or both at the
same time) which depends on the relation between the technological state of each firm and the
fixed costs. In fact, given the specific position of a firm inside the bivariate distribution of
technology, the fixed costs of innovation generate diferent firms decisions consistently with
equation (14). Two sources of firm heterogeneity implies that the thresholds, characterizing the
border among the diferent innovation strategies, are given by infinite combinations of (a,q)
couples. For this reason, it becomes convenient to express the reservation values in terms of
efciency as a function of quality, a(q) and to obtain cutof functions rather than cutof values as in
one factor heterogeneous firm models. For given q e Q it is possible to define the following cutof
functions:
a
A
(q) delimits the area in which process innovation is optimal, a
Q
(q) delimits the area
in which product innovation is optimal, and a
AQ
(q) delimits the area in which both
innovations are chosen by the firms.
12
Appendix A provides a formal definition of these
cutof functions.

The cutof functions are decreasing in q and hence also less efcient firms but charac-
terized by a product with high quality may innovate. Notice that firm profits,t(a, q), are increasing
in both efciency and quality generating the incentives to innovate which are slowed down by the
log form in which the innovation drift is modeled. Abstracting from the discontinuity in the value
function due to the fixed costs of innovation, the more advanced the firm technology, the higher
the innovation investment but the lower the benefit due to the diminishing returns of innovation.

12
It

is equivalent to express product quality as a function of efciency, q(a). Using a specific formulation
for the cutof function does not afect the implications of the model.











Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 15


1.2.2.4 The Exit Decision


Firms exit the industry after a bad technological draw such that the expected value of
continuing is lower than the exit value which has been normalized to zero.
13
Since firm value is
increasing in both states the exit reservation value is decreasing in both of them.
Again a cutof function a
x
(q) can be defined such that:


E[v(a
?
(q), q
?
),(a
x
(q), q)] = 0. (1.15)


For each quality level, there is a maximum efciency level such that below this maximum
firm value is negative and therefore firms find optimally to exit the industry. Interest-
ingly, the cutof function a
x
(q) is decreasing in quality: for given efciency firms with
a high quality product can survive longer in the market when hit by a bad efciency
shock.

Firms innovation decisions, exit and the law of motion of (a, q) define the transition
function u
xI
: A A
x
· Q ÷ (A
p
A
A
A
Q
A
AQ
A
x
) · Q where the support
of efciency is partitioned into the exit support, A
x
, the production support, A
P
, the process
innovation support, A
A
, the product innovation support, A
Q
, and the process and product
innovation support, A
AQ
. These partitions difer across diferent elements of Q.
14
The
corresponding transition probability of going from state (a, q) e (A
p
A
A
A
Q
A
AQ
) · Q to (a
?
, q
?
) e
(A
p
A
A
A
Q
A
AQ
A
x
) · Q is given by a function|
xI
(-).



1.2.2.5 Firms Entry


Every period there is a mass of potential entrants in the industry which are a priori
identical. To enter firms have to pay a sunk entry cost, c
e
, expressed in terms of labor.
This cost can be interpreted as an irreversible investment into setting up the production
facilities. After paying the initial cost, firms draw their initial a and q from a common bivariate
density function,¸(a, q). The associated distribution is denoted by I(a, q) and
has support in R
+
· R
+
. Define¸
e
the mean of the joint distribution ando
2
ando
2
ea eq
the variances of the entrants efciency and quality processes.
15
Moreover, as in Gabler
and Licandro (2005) and Luttmer (2007) I assume that entrants are on average less productive
than successful incumbent and that they imitate them. In particular, the

13
Notice

that exit is triggered by the assumption of fixed operational costs, c
f
, paid by active firms
in each period. Without fixed operational costs, firms hit by bad shocks instead of exiting the market could temporary
shut down their production and just wait for better periods when positive shocks hit their technology and then start
again producing.
14
Appendix A defines mathematically these supports.
15
The covariance is zero given the current assumption of independence between the evolution of the
two states.







Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 16


mean of the entrant distribution is a constant fraction¢
e
e (0, 1) of the mean of the joint
distribution of incumbents defined as µ. That is,¸
e
=¢
e
µ. This knowledge spillover,
that goes from incumbent firms to entrants, is the only externality of the model and
combined with firm selection and innovation generates endogenous growth.
16


In equilibrium the free entry condition holds: potential entrants enter until the expected
value of entry is equal to the entry cost:


v
e
(a , q ) = v(a, q)dI(a, q) = c
e
, (1.16)
Oe

M
t
is the mass of firms that enter in the industry at time t. At the stationary equilibrium
also a stability condition holds: the mass of new entrants exactly replaces the mass of
unsuccessful incumbents who are hit by a bad shock and exit the market. That is,
ax(q)
M
?
=



1.2.3
0
Q
I µ(a, q).


Cross Sectional Distribution and Aggregates


All firms' choices and the processes for the idiosyncratic shocks yield the low of motion
of firms distribution across efciencies and qualities, µ(a, q). That is:


I
?
µ
?
( a
?
, q
?
) = I µ(a, q)|(a
?
, q
?
,a, q)dqda + (1.17)
AP Q

µ(a, q)|(a
?
, q
?
,a, q, z)dqda + µ(a, q)|(a
?
, q
?
,a, q, z, l)dqda +
AA Q AAQ Q

µ(a, q)|(a
?
, q
?
,a, q, l)dqda + M
?
¸ (a
?
, q
?
)
AQ Q


Tomorrow density is given by the contribution of all surviving firms (the domain of the
integrals is restricted to surviving firms only) and of entrants. The contribution of new firms is
represented by the last term of (17). The first integral represents the share of surviving firms that
only produce and do not innovate, the second integral shows the contribution of the firms that
successfully produce and invest in process innovation. The third one instead represents the firms
that produce and undertake both types of innovation and finally the forth one highlights the share
of producers that specialize in
product innovation only.
17

16
Eeckhout

and Jovanovic (2002) used a wider mechanisms of knowledge spillover in which all firms
and not only entering firms, can imperfectly imitate the whole population of firms.
17
Since the industry is populated by a continuum of firms and only independent idiosyncratic shocks occur the
aggregate distribution evolves deterministically. As a consequence, though the identity of any firms i associated with a
couple (a, q) is not determined, their aggregate measure is deterministic. For the same reason the other aggregate
variables evolve deterministically.







Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 17


To summarize the information about the average firm efciency and product quality, a
weighted mean of firm technology can be introduced. That is:

1÷o
o
o
µ=
ax(q)

Q
aq
1
÷q
1÷o
µ(a, q)dqda . (1.18)

Notice that aq
1
÷
q
is an index of firm level technology that maps one to one to firms'
profits and size. Difering from Melitz (2003), this weighted mean not only depends on two states,
efciency and quality, but also the weights re?ect the relative quality adjusted output shares of
firms with diferent technology levels rather than the simple output shares. Moreover, the
weighted mean can be also seen as the aggregate technology incorporating all the information
contained in µ(a, q). In fact, it has the property that the aggregate variables can be expressed as
a function of only µ disregarding the
technology distribution, µ(a, q).
18



1.2.4 Equilibrium Definition


In equilibrium the representative consumer maximizes its utility, firms maximize their
discounted expected profit and markets clear. The stationary equilibrium of this econ-
omy is a sequences of prices {p
t
}· 0, {P
t
}· 0, real numbers {I
t
}· 0, {M
t
}· 0, {X
t
}· 0
t= t= t= t= t=
functions n(a, q; µ), z(a, q; µ), l(a, q; µ), v(a, q; µ), cutof functions a
x
(q), a
A
(q), a
AQ
(q),
and a
Q
(q) and a sequence of probability density function {µ
t
}· 0 such that: t=


• the representative consumer chooses asset holding and consumption optimally so
that to satisfy the Euler Equation (5),

• all active firms maximize their profits choosing a price that satisfies (7) and employ-
ment and innovation policies that satisfy n(a, q; µ), z(a, q; µ), and l(a, q; µ) yielding
the value function v(a, q) as specified by equation (13) and its components,

• innovation is optimal such that the cutof functions a
A
(q), a
AQ
(q), and a
Q
(q)
satisfy the previous conditions,

• exit is optimal such that a
x
(q) is given by equation (15) and firms exit if a(q)<
a
x
(q ) ,

• entry is optimal: firms enter until equation (16) and the aggregate stability con-
dition are satisfied,

18
See

Appendix B for more details.









Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 18


• the number of active firms I adjusts till the labor market clears: L
P
+ L
I
+ Ic
f
+
M
?
c
e
.
19


• the stationary distribution of firms evolves accordingly to (17) given µ
0
, I, M and
the cutof values,

ax(q)
• the stability condition, M
?
=
0
Q
I µ(a, q),
holds.


In equilibrium a
x
, a
A
, a
AQ
, a
Q
, I and M are such that the sequence of firms distribution
is consistent with the law of motion generated by the entry and exit rules.
20




1.3 Endogenous Growth


1.3.1 Balanced Growth Path


In general, on the Balanced Growth Path output, consumption, real wage, prices and the
aggregate technology grow at a constant rate, the bivariate distribution of efciency and quality
shifts to the right by constant steps, its shape is time invariant, and the interest rate, the aggregate
expenditure, the aggregate profit, the profit and the labor demand distributions, the number of
firms, the firm turnover rate, and the other characteristics of the firms' distribution are constant.

Define g as the average growth rate of firm productivity, µ. It is given by a combination
of the growth rate of the efciency state, denoted by g
a
, and of the growth rate of the
product quality state, indicated by g
q
. Intuitively, growth arises because in every period
the log of the joint aggregate technology shifts to the right by a factor g, meaning that
the average efciency and the average product quality of the industry grow. Defining
at+1
the growth factors of firm efciency and product quality by G
A
=
qt+1
at
= 1 + g
a
and
G
Q
= = 1 + g
q
, the Balanced Growth Path can be found as follows. From the labor qt
market clearing condition, given the assumption of a constant labor supply, N
s
, also the
number of incumbent firms, I, and the number of entrants, M , have to be constant as well
as the share of labor allocated to production and innovation.
21
Aggregate expenditure,
E, has to be equal to the aggregate labor income, N
s
, given the wage normalization.
This in turn implies that E is constant and hence also H has to be constant. The profit

19
Where

L
P
=
A
Q
n(a, q)Iµ(a, q)dqda is the production labor and L
I
=
A
Q
(l(a, q) +
z(a, q))Iµ(a, q)dqda + I
AA
Q
µ(a, q)c
a
dqda + I
AQ
Q
µ(a, q)c
r
dqda + I
A
AQ
Q
µ(a, q)(c
a
+ c
r
)dqda
is the innovation labor considering both the variable and fixed costs.
20
Hopenhayn (1992)'s paper proves the existence of equilibrium for similar economies.
21
If there was population growth then the number of varieties, and the number of entrant firms would
grow at the same rate as population grows.






Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 19


distribution, equation (10), shows thatt(a, q) has to be constant because of constant
fixed operational costs. Given a constant expenditure, profits are constant only if aq
1
÷
q
P is
constant. For positive growth rate of the technology, the previous condition holds if the price
index growth factor is inversely related to the average technology growth factor,
G
P
= (G
A
G
1
÷
q
)
÷
1
. In other words, as the industry grows and the average technology Q
advances, the price index diminishes. With the same reasoning also the distribution
of manufacturing labor, equation (9), is time invariant, which together with the labor market
clearing condition implies that also the distributions of the labor hired for the innovation
activities, z(a, q) and l(a, q), are constant. From the consumer problem E = P X, which holds
only if the aggregate consumption X grows at a constant factor
(G
A
G
1
÷
q
). This results in a constant interest rate as shown by the Euler equation, Q
G
q
r = (1 + g)| ÷ 1. The price distribution, p(a, q), decreases at a factor equal to
Q
Ga
which
is lower than the growth rate of the price index. This is a consequence of the fact that
the price index is adjusted to consider the growth in the product quality. Finally, x(a, q)
grows at a factor of

GA .
G
q
Q

A Balanced Growth Path equilibrium exists if there is a g
a
and a g
q
consistent with the
stationary equilibrium. To find these growth rates and to characterize the equilibrium
itself and the stationary firms' distribution it is necessary to transform the model such that all the
variables are constant along the Balanced Growth Path. Hence, all growing
variables need to be divided by the corresponding growth factor, s = s/G
ts
and the
stochastic processes in efciency and quality need to be de-trended by the respective
growth rates, log a
t
= log a
t
÷ g
a
t and log q
t
= log q
t
÷ g
q
t, where "?" denotes the
stationarized variables. In expected terms both average firm efciency and average
quality increase and thus in expectation in every period each firm falls back relative to the
distribution. This transformation afects also the transition functions and hence log
efciency and log quality, in the stationarized economy, which evolve according to:


log a
t
÷ g
a
+c
a
+1

log a
t
+1
t
log a
t
÷ g
a
+ì
a
log z
t
+c
a
+1 z
t
(1.19)
log q
t
÷ g
q
+c
q
+1

log q
t
+1
t
log q
t
÷ g
q
+ì
q
log l
t
+c
ql
+1. t
(1.20)
These negative trends together with decreasing return in innovation determine a finite
expected lifetime for any level of technology (a, q). Any successful firm which performs
innovation will not be an innovator forever but eventually it will exit the market, leading to a
finite expectation and to a finite variance of the incumbent firm distribution and
hence assuring the existence of a stationary distribution in the de-trended economy.







Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 20


The previous discussion leads to the following proposition:
Proposition 1: Given G
a
and G
q
growth factors of firms efciency and quality the
economy admits a Balanced Growth Path along which the mean of the joint distribution
of incumbent firms and of entrant firms and the aggregate consumption grow at a rate
G
a
G
1
÷
q
, the price index decreases at a rate G
a
G
1
÷
q
, the output distribution grows at a
q q
rate G
a
/G
q
, the price distribution grows at a rate G
q
/G
q
and the number of firms, the
q a
number of entrants, the aggregate expenditure, the aggregate profits, the profit distribu-
tion, and the labor distributions are constant.



1.3.2 Growth Rate Determinants


Firms' Selection and Innovation drive endogenous growth which is then sustained by
entrants' Imitation. Firm selection results from the assumption of a random walk process for both
the evolution of labor efciency and product quality together with firm exit. Considering only a
cohort of firms and abstracting from the endogenous drift introduced by innovations, in the
growing economy the random walk processes are characterized by constant expectations and by
variances of the distribution of those firms that increase over time. However, among the given
firms the ones with low efciency and low quality exit the industry truncating the joint
distribution from below. This implies that the distribution can spread only towards higher level
of efciency and quality resulting in a higher average productivity of the remaining firms in the
cohort.

Firms' innovation reinforces growth. For a given set of innovative firms also the produc-
tivity and quality expectations increase over time and they depend on the initial states and on the
sequences of innovation investments. In fact, after every successful innovation the average
technology shifts upwards due to the endogenous drifts generating growth. However, innovation
has decreasing returns through the log form in which the innovation drift is modeled. For this
reason the resource reallocation efect from non-innovators to innovators is controlled by the
selection efect and the result is that growth is reinforced but still bounded. As a result the average
productivity of innovators grows slower than the exit cutof. Consequently, as time goes by firms
keep exiting the industry and the distribution shrinks.

Hence, entrants' imitation is needed to sustain growth and assure the existence of a
stationary distribution with entry and exit. In equilibrium the mass of entrants has to be equal to
the mass of firms exiting the market. However entrants are on average more productive than
exiting firms otherwise they would not find optimal to enter the market. Since exiting firms are
replaced by entrants with on average better efciency and quality levels, the resulting firm
distribution moves every period upwards towards






Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 21


higher technological levels.
22
Notice that innovation afects growth also allowing for
better imitation.

When innovation occurs the efciency and quality processes have also higher variances
of the stochastic component. This increases the probability of a bad shock hitting the innovative
firms and the dispersion of the innovator distribution against the distribution of non-innovators
and exiting firms. On the one hand, selection results in a higher average technology for
innovators because relatively bad firms fall among the pool of non-innovators resulting in a
scenario where only relatively low cost and high quality firms keep innovating. On the other
hand, the pool of non-innovators becomes larger, implying a higher weight to the distribution of
non-innovators which has a lower average technology. The final efect of higher variances of the
innovation random walks on the mean of the joint distribution is ambiguous. However, calibrating
the model to match the Spanish data shows that the positive efect of innovation always outweighs
the negative efect.



1.3.3 Growth Rate Decomposition


On the Balanced Growth Path the growth rate of aggregate and average consumption is
the same and can be rewritten and approximated (the derivations are in the Appendix)
as:

1
g~
oX
o
¯
ˆ(a, q)
o
u
xI
µ(a, q) ÷ 1 ÷ M µ(a, q) + M ¸(a, q) ÷ µ(a, q) dqda , x
A Q
I I
(1.21)
where X is the average consumption, ˆ(a, q) = qx(a, q) is the firm's quality weighted
¯ x
output, u
xI
is the transition function with the exit and innovation rules and M/I is
the entry/exit equilibrium rate. The first diference into the squared bracket represents
the growth contribution of selection and innovation. That is, the diference between the quality-
output weighted average productivity of surviving firms (both innovators and non innovators)
and the one of the previous period incumbents. The more significant
the innovation investment is, the larger u
xI
µ and the tougher selection is, the smaller
(1 ÷ M/I)µ. Hence, both more innovation and tougher selection promotes growth. The
second diference instead represents the contribution of entrants' imitation. The easier or cheaper
the imitation mechanism (the smaller the distance between the entrants' and incumbents'
distributions) the larger the contribution of entrants to the aggregate growth. Adopting the
terminology introduced by Poschke (2008), µ can be divided into

22
Randomness

and innovation are important to emphasize the fundamental role of reallocation of
resources in the growth process. Growth could still be generated without selection and innovation assuming that the
joint mean of the entrants distribution shifts every period exogenously by g. However in this way growth would just
result from entry and exit.





Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 22


µ
con
, continuing firms, and µ
exit
, exiting firms. This allows for a further disaggregation
of the aggregate growth rate:


1
g~
oX
o
¯

A

Q
xˆ(a, q)
o
uµ
con
(a, q) ÷ µ
con
(a, q) dqda +


+



A



Q

xˆ(a, q)
o
M ¸(a, q) ÷ µ
exit
(a, q)
I


.


(1.22)


The first integral catches the share of growth due to firms' innovation activities and
due to the idiosyncratic shocks hitting surviving firms' level technology.
23
The second integral
instead represents the share of growth due to net entry. It is clear that the selection of inefcient
firms exiting the market and the imitation of new entrants generate positive growth only if
entrants are on average more productive than exiting firms. This condition holds in the stationary
equilibrium with positive entry. Furthermore, splitting
the density of continuing firms between the densities of firms that only produce, µ
p
, and
of firms that innovate and produce, µ
i
, the first integral in equation (22) can be further
disaggregated in:


xˆ(a, q)
o
uµ
con
(a, q) ÷ µ
con
(a, q) dqda =
A Q

xˆ(a, q)
o
(uµ
p
(a, q) ÷ µ
p
(a, q)) + (uµ
i
(a, q) ÷ µ
i
(a, q)) dqda. (1.23)
A Q

Among surviving firms it is now possible to calculate the share of growth that is due
to only firms' experimentation based on the random walk processes without drift and the share of
growth due to both experimentation and firms' innovation. The numerical analysis of the model
will then quantify the share of growth due to net entry, innovation together with experimentation,
and firms' experimentation.

The innovation investments of firms afect aggregate growth both directly and indirectly
through a better imitation. In fact, innovation results in a higher joint mean of the incumbents'
distribution and hence on entrants that can draw their initial technology from a distribution that
stochastically dominates the distribution of entrants in an econ-
omy without innovation. Given that ¯ is the key variable in the imitation process, the µ
contribution of innovation on a better imitation can be assessed rewriting ¯ as: µ

1÷o
o
¯=
µ

AP

Q
(aq
1
÷
q
)
o
1÷o µ
p
(a, q)dada +
AI

Q
(aq
1
÷
q
)
o
1÷o µ
i
(a, q)dqda (1.24)

23
Without

weighting the firm distribution by the share of quality weighted output the resulting ex-
pected growth rate of the average technology of continuing firms would be zero. However, given that the optimal
consumption is a convex function of the technology index aq
1
÷
q
, by Jensen inequality, the average growth rate of the output
weighted technology is positive.







Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 23


and using the following equation:


1=



¯
µ


1
o
1÷o



AP



Q


o
(aq
1
÷
q
)1÷
o
u
p
(a, q)dqda +



AI



Q


o
(aq
1
÷
q
)1÷
o
u
i
(a, q)dqda , (1.25)

where A
P
is the support of surviving firms that produce but do not innovate while
A
I
= A
A
A
Q
A
AQ
is the support of firms that produce and innovate. The second
integral captures the contribution of innovation in determining the joint mean of the
incumbent firms. It is clear that the larger this term is, the higher the indirect growth
contribution of innovation via a better imitation.




1.4 Numerical Analysis


The algorithm, used to solve the model in the stationary equilibrium, is explained in
Appendix D.



1.4.1 Calibration


Sixteen parameters, linked to firm dynamics characteristics, firms specific innovation
behavior and the general economic environment, need to be chosen. Since all of them interact
with each other to determine the stationary equilibrium only the discount factor,
|, the preference parameter,o, and the imitation parameter,¢
e
are chosen a priori.
The others are jointly calibrated to match the Spanish manufacturing sector.
24
In detail,
| is set equal to 0.95 to analyze a yearly time span. Accordingly to Ghironi and Melitz (2003),o is set equal to 0.73,
so that the price mark-up charged by the monopolistic firm
is of 36% over the marginal cost.
25
¢
e
, relating the mean of the entrants distribution
with the mean of the incumbents, is a key parameter in determining growth. For this
reason it is set individually to match its empirical counterpart. That is,¢
e
is chosen
such that the average size of entrants is 38% of the size of incumbent firms as estimated
by Gracia and Puente (2006).

24
The

Spanish economy has been empirically widely studied in both the dimensions object of this
paper: the new dimension related to firm innovation behavior and the traditional dimension related to firm dynamics.
Hence, from the Spanish data it is possible to obtain enough information to calibrate successfully the model. Similar
studies are available also for other European countries (Bartelsman et al. (2004), Bartelsman et al. (2003) for OECD
countries; Cefis and Marsili (2005) for the Netherlands, Smolny (2003) and Fritsch and Meschede (2001) for Germany).
25
This high mark-up could be seen at odds with the macro literature that delivers a standard mark- up of around
20% over the marginal/average cost. In this model, a higher mark-up is justified by the presence of the fixed costs. In
fact, given the free entry condition, firms on average break even. Hence on average, firms price at the average cost
leading to reasonaby high mark-ups over the average cost.







Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 24


Twelve parameters are calibrated using a genetic algorithm as described by Dorsey and
Mayer (1995).
26
These are: the ratio among the fixed costs, c
e
/c
f
, c
a
/c
f
, and c
q
/c
f
,
the quality parameterq, the four variances of the incumbent random walkso
a
,o
az
,o
q
,
ando
ql
, the two variances of the entrant random walks,o
ea
ando
eq
, and finally the
two parameters that scale the innovation drifts into the stochastic processes,ì
a
andì
q
.
These parameters jointly determine the shape, the truncation functions of the stationary
distribution of firms, and the partition of firms among the diferent innovation strategies. They are
calibrated, using as targets, static and dynamic empirical moments that are informative and
related to the main objective of the paper. It is possible to distinguish between two sets of targets.

Firstly, I use moments related to the literature on firm dynamics. These are firms'
survival rates after two and five years upon entry, firms' yearly turnover rate, the job creation rate
due to entry, the fraction of firms below average productivity, and the productivity spread,
which calibrate the six variances of the model and the size of entrants with respect to exiting
firms which gives information about the entry cost. Accordingly to Garcia and Puente (2006), the
two and five year survival rates for Spanish manufacturing firms are estimated to be 82% and
58%, respectively.
27
They report also a yearly firm turnover rate of 9% and a job creation rate
due to entry equal to 3%.
28
Garcia and Puente (2006), estimate that entrants firms are 23%
bigger than exiting firms in terms of employment. Bartelsman et al. (2004) estimate that the
fraction of Spanish firms below average productivity is equal to 83%, highlighting a right skewed
firm size distribution. The last moment is the productivity spread between the 85
th
and 15
th

percentile which is estimated to be between 3 and 4.

A second set of moments are instead taken from the empirical literature on firm innova-
tion. The targets used are the share of Spanish manufacturing firms performing process
innovation, product innovation and the share of firms that do not innovate and the in- tensity of
the innovation investments in process and product, respectively. In the scope of this paper these
are relevant moments that help to calibrate the fixed cost of process
and product innovation,q,ì
a
, andì
q
. Harrison et al. (2008) working on data derived
from the CIS report that 12.2% of Spanish firms in the manufacturing sector declared
process innovation between 1998 and 2000, while 12.4% declare product innovation and

26
The

object of the algorithm is to jointly calibrate the parameters in order to minimize the mean
relative squared deviation of twelve model moments with respect to the corresponding moments in the data. Since the
problem is highly non-linear, the minimization can be characterized by many local minima and the genetic algorithm
used has the nice feature to increase the probability of choosing the global minimum.
27
Those numbers are aligned to the one reported by other developed countries as UK, Germany and Nederland
(Bartelsman et al. (2003)).
28
Firms' turnover is computed as the sum of the number of entering and exiting firms over the total number of firms
while job creation rate is computed as the total amount of labor employed by entering firms in a year divided by the
total employment in the same year.






Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 25


more than half of the firms do not innovate in the time span considered. This numbers
are very close to the one published by the National Statistics Institute (www.ine.es) using the
ESEE. The innovation intensity, computed as the ratio between the aggregate investment in
innovation and the aggregate sales, in the 1998 is of 1.71%, process inno- vation intensity
accounts for 1.26% while product innovation intensity accounts for the
remaining 0.44%.
29


Finally, the last parameter to calibrate is the growth rate of the economy, g. In fact, the
aim of this paper is to provide a model able to disentangle the contribution of efciency and
quality improvements in explaining the economy growth rate and not to test the ability of the
model in matching the aggregate growth rate. For this reason g is set equal to 0.042 accordingly
to the European Innovation Scoreboard (2001) and represents the labor productivity growth
measured in terms of value added per worker as average over the nineties.
Table 1.2: Calibration


Parameter
Calibrated Parameters
c
e

c
f
c
a
c
q

q
o
a

o
az

o
q

o
q
lo
ea
o
eq
ì
a
ì
q

Parametrization
|
o
u


Value


142.28%
3.85%
31.96%
16.29%
0.74
0.15
0.9
0.32
1.2
0.40
0.48
0.083
0.025


0.95
0.73
0.38


Description


Entry cost, % of average firm size
Fixed cost, % of average firm size
Process innovation cost, % of average firm size
Product innovation cost, % of average firm size
Quality parameter
Variance of efciency shock
Variance of efciency shock with innovation
Variance of quality shock
Variance of quality shock with innovation
Variance of efciency distribution of entrants
Variance of quality distribution of entrants
Scale coefcient for process innovation Scale
coefcient for product innovation


Discount factor
Preference parameter
Relative entrant mean



Table 2 shows the values assigned to the parameters characterizing the economy. The
fixed costs are expressed in relation to the average employment devoted to production.

29
The

European Innovation Scoreboard 2001 reports an innovation intensity for the Spanish manu-
facturing sector in the 1998 of 2.4% of aggregate sales. This number has been computed on the basis of the CIS which
includes also external R&D investments. This can explain the diferent numbers between the Euroean Commission
survey and the INE statistics.





Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 26


Table 1.3: Empirical Targets and Model Statistics


Targets
Targets for Calibration
Share process innovation
Share no innovation
Share product innovation
Product innovation intensity
Process innovation intensity
2 year survival rate 5
year survival rate Firm
turnover rate
Firm below average productivity
Job creation due to entry
Size entrants wrt exiting firms
Productivity spread
Targets for Parametrization
Entrant size/incumbent size
Mark-up over marginal cost
Growth rate of labor productivity


Data


12.2%
55.4%
12.4%
0.44%
1.26%
0.8
0.58
0.09
0.83
0.03
1.23
[2, 3]


0.38
0.37
0.042


Model


13.4%
60.92%
11.1%
0.5%
1.29%
0.74 0.6
0.086
0.78 0.02
1.31 2.48


0.38
0.37
0.042



As expected the entry cost, which represents a sunk entry investment, is the highest.
Reasonable values are attributed to the fixed cost of both process and product innova- tion. The
parameter associated with the difculty to produce high quality,q, is just aboveo.
30
When new firms
enter the market there is high uncertainty on their prof- itability, and the probability of surviving the market
competition is low. However, the growth rate of surviving young firms is on average higher than
the growth rate of in- cumbents. This fragility is represented by a variance of the entrants
distribution that is higher than the variance of the random walk process associated with a and q
when firms only produce.
31
Innovation also increases uncertainty. This is re?ected by higher
vari- ances of the corresponding random walk processes. In particular, a very high variance
is associated with product innovation.
32


Table 3 reports the empirical targets used and the corresponding model moments. De-
spite the large number of parameters to calibrate, the model statistics match closely

30
Bils

and Klenov (2001) estimate quality Engel curves for 66 durable goods in US using data on
consumers expenditures. They find that the weighted average slope of the quality Engel curve is of 0.76. This number is
very closed to the calibratedq of this model.
31
For OECD countries the higher uncertainty faced by entering firms is documented by Bartelsman et. al. (2004).
32
The higher uncertainty of product innovation is, for instance, documented by Parisi et. al. (2006).






Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 27


the data in both sets of targets. Hence, the innovation choices of firms, the shape of
the distribution, its dynamic characteristics, and entrants' behavior seem to reproduce accurately
the Spanish manufacturing sector.



1.4.2 The Role of Innovation


After setting g equal to 4.2%, the model predicts an annual growth rate of firms'
production efciency, g
a
, of 2.93% and of product quality, g
q
, of 4.64%. Using that
g ~ g
a
+ (1 ÷q)g
q
, 69.8% of the aggregate growth is due to the growth in firms' level
efciency and that only 29.81% is due to the growth in product quality.
33
Though these
figures represents the growth in efciency and quality due to both innovation and ran- domness,
they confirm a higher impact of efceny in explaing growth accordingly the estimates reported by
Huergo and Jamandreu (2004).

Equations (22) and (23) are used to distinguish the efect of innovation and firm ex-
perimentation, selection, and imitation in determining the aggregate growth rate. The model
predicts that 8.63% of the growth is due to entry (10.61%) and exit (÷1.98%) and the remaining
91.37% is due to both experimentation and innovation of the firms that remain active in the
industry. Hence, incumbent firms represent the main source of growth in the Spanish
manufacturing sector.
34
Decomposing further the growth contri- bution of incumbents in the
contribution of non-innovators and innovators helps to asses the important role played by
innovative firms in determining the aggregate growth rate. In fact, the growth contribution of
non-innovators is negative (÷8.34% of the 91.37%). These firms are characterized by a low level of
technology and are destined to exit the market after a series of bad shocks. The high likelihood of
receiveing a bad shock and the firm's powerlesseness to escape exit explains their negative
contribution to growth. This negative efect is more than compensated by the growth contribution
of innovative firms that develops to be the leading force of aggregate growth. However, it should
be noticed that the growth derived by innovators is a combined efect of the within firm
growth, of the reallocation of resources between incumbents and of tougher selection.

33
In equilibrium (1 + g) = (1 + g )(1 + g )
(1
÷q
)
holds. Approximating it using a logarithmic transfor-
mation yields g ~ g
a
+ (1 ÷q)g
q
.
a q
34
Farina and Ruano (2004) estimate that the within firm growth accounts for 58% of the aggregate
Spanish productivity growth while net entry accounts between 5% and 10% and the remaining part is due to
reallocation of resources between contractiong and expanding incumbents. This numbers are in line with Bartelsman
et. al. (2004). Their general finding is that the role of entry and exit in explaining productivity growth is marginal
compared with US. Foster et. al. (2001) find that in the U.S. Census Manufactures, more than a quarter of the increase
in aggregate productivity between 1978 and 1997 was due to entry and exit. Moreover, Lenz and Mortensen (2008)
estimating their model on a panel of Danish firms find that entry and exit of firms can account for 20% of the aggregate
growth while within firm growth account for 55%.








Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 28


More insights on the importance of innovation can be obtained simulating an economy
with the same parameters values in which innovation is shut down and growth is gener- ated by
only selection and imitation. In this example the share of aggregate growth due
to g
a
is fixed to 69.8% given the previous results and the aggregate growth rate, g is now
determined endogenously. In the absence of innovation the growth rate is 1.1% falling
of 3.1 percentage points. This confirm the fundamental role of innovation in explaing
productivity growth in the Spanish manufacturing sector.
35


Additionally, innovative firms have a higher weighted mean of their technology index
than non-innovators. This implies that innovation increases the weighted mean of the technology
distribution of active firms, that is used as reference by the entering firms. Hence innovation also
means better imitation and therefore higher growth. Applying equation (25), it is possible to
conclude that 84.31% of the joint mean is due to the average technology level reached by the
innovative firms.



1.4.3 Firms Partition and Cutof Functions


Figure 1 displays how the two attributes of firm heterogeneity together with the fixed
operational and innovation costs determine the partition of firms between those exiting and
remaining, and among process innovators, product innovators, and both types of innovators or
non-innovators. Hence, it illustrates the equilibrium cutof functions and the combinations of
efciency (x-axis) and quality (y-axis) for which the diferent choices faced by firms are optimal.
The firm distribution over the two dimensions of technology (Figure 2, left) is right skewed in
both states as the largest mass of firms is concentrated in the bottom-left corner. This
information complements the partition of firms and strengthens the subsequent interpretation.

The first area on the left represents the firms with production efciency and product
quality lower than a
x
(q) which optimally exit the market. These area represent about
9% of the total mass of firms given by the sum of incumbents and of entrants. The exit
cutof function is the border between the exit region and the region where firms remain active and
only produce. Due to the trade-of between quality and efciency this cutof function is decreasing
in quality: relatively high cost firms can survive longer in the market when the quality of their
variety is high. In the second region, for slightly higher level of efciency and quality, firms are
sufciently profitable to stay in the market but not enough to innovate, v(a, q) = v
P
(a, q). These are
firms with relatively high level

35
The

growth reduction is accompanied by a lower turnover rate equal to only 1.57% showing how
innovation increases also market selection. Using equation (22) the growth contribution of net entry reaches 12.1%
confirming the importance of within firm growth.







Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 29


of cost but with all the possible levels of quality. In fact, product quality has a lower
impact on firm profitability than production efciency.


FirmPartition


Process&PRoductProductProcess
ProductionExit


÷Q(q)a


÷Q(q)
aA




÷a(q)A
÷x(q)a


Productivity


Figure 1.1: Firms Partition



Moving along the efciency dimension, for relatively small level of quality, it is optimal
for firms to pay c
a
and undertake process innovation while for relatively high level of
quality it is optimal to pay c
q
and undertake product innovation. This is the result
of the interplay between the fixed costs of innovation and the convexity of the profit
function in a. The higher the efciency level reached by the firm the higher the gain in terms of
profitability resulting from a marginal reduction of the production cost. This explains why it is
optimal for firms to innovate in process when their efciency has already reached a minimum
level. The same is true for the quality dimension, though the profit function is concave in q.
However this disadvantage is compensated by the lower fixed cost of product innovation. The
last region is represented by firms with high efciency and high quality that optimally innovate in
both process and product.

Table 1.4: Conditional Probabilities


Exit No Innovation Process Product Both
No Innovation 5.1% 87.84% 0.84% 5.6% 0.21%
Process 0 4.5% 75.9% 0.95% 18.65%
Product 0 34.65% 1.22% 51.84% 12.3%
Both 0 1.83% 33.26% 3.3% 61.61%


Table 4 shows the equilibrium conditional probabilities of switching actions after a one-
year period given the current decision of incumbent firms.
36
The first column lists the current
action of the firms and the rows give the transition probabilities of each

36
This

information is contained in the optimal transition function T
XI
and the derivations are in the
Appendix.





Q
u a l i t y
Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 30


future decision. Due to the persistence of the random walk process a high probability
is attached to the repetition of the current action.
37
Interestingly, consistent with the Spanish
empirical evidence shown by Huergo and Jaumandreu (2004), this persistence appears less strong
in the case of product innovators: 34% of product innovators today will not innovate tomorrow
while 15% will switch to process innovation, both alone andwith product innovation, and only
51% will repeat an innovation in product quality. The relative low persistence in quality
enhancing innovation is due to the high variance associated with this decision. A high variance
implies that the probability of receiving a bad shock is high as well as the probability of
switching to a difernt strategy. Empirical evidence emphasises that exit is associated with a low
level of pre-exit innovation (Huergo and Jamandreu (2004) for evidence on Spanish firms). This
model predicts that an incumbent firm exits the market with 5% of probabilty only if in the
current year no innovation has been introduced. This also implies that an innovative firm, before
exiting the market, has to receive a bad shock and become a non-innovator.



1.4.4 Firms Distribution


Firms Size Distribution BivariateFirms
Distribution
0.7

0.6

Firms Size Distribution
Log Normal
ExtremeValue
0.07

0.06
0.5
0.05

0.04
0.4

0.03
0.02 0.3

0.01
0.2025
2025
15 20 0.1

10

5


0


0

5

10
15

0
Productivity
Quality
0 1 2 3 4 5 6 7 8
Technology


Figure 1.2: Bivariate and Univariate Firms Distribution




The equilibrium distribution of firms is determined endogenously and it is shaped by
the static and dynamic decisions of incumbent firms together with entrants imitation. Figure 2,
left panel, shows the bivariate firms distribution over the two attributes of firm heterogeneity.
However, empirical studies are not able to distinguish these two dimensions and hence Figure 2,
right panel, displays the corresponding univariate firm size distribution over a technological
index that summarizes the information contained

37
This

can be read as persistent firms productivity which is documented by the empirical literature
in the case of Spain by Garcia et. al. (2008).






D
e
n
s
i t
y


Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 31


Conditional Distribution Producers Conditional Distribution Process Innovators

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

Cond Distrib Producers
Extreme Value Log Normal

0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

Cond Distr Process Innov
Log Normal
Extreme Value
0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7
8Technology Technology


1.4
1.2
1
0.8
0.6
0.4
0.2
0

Conditional Distribution Product Innovators
Cond Distr Product Innov Log Normal


0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

Conditional Distribution Process and Product Innovators
Cond Distr Both Innov
Log Normal
Extreme Value
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Technology Technology



Figure 1.3: Conditional Firms Size Distributions


in a and q. That is, aq
1
÷
q
. Notice that this is the equivalent of the employment
distribution of firms which is observed in the data. The univariate firm distribution looks right
skewed and hence with a right thick tail (the moments of the distribution are reported in Table
5).
38
In fact, a log-normal distribution fits the date well. However, empirically there is not much
information about the moments of the size distribution of the manufacturing firms in the Spanish
economy but in general it is possible to conclude
that it is right skewed.
39


The conditional distribution of firms that only produce and do not innovate is concen-
trated at lower levels of the technological index aq
1
÷
q
than the conditional distributions of innovators
(Figure 3 and Table 5). Consistently with the empirical evidence (see Doraszelski and
Jaumandreu (2007)) innovative firms have a higher labor productivity and are bigger than firms
that do not innovate. The comparison among innovators is more interestingly: on average small
firms do product innovation, medium and large firms do both product and process innovation
and large firms do process innovation.
40
Finally, the conditional distribution of product
innovators is more right skewed than the distribution of firms that do process innovation or do
not innovate. Also this last feature is confirmed by empirical estimations of the firm size
distribution in the Spanish manufacturing sector.


38
The


underlying distribution used to compute the skewness in Table 5 is a log-normal distribution.
39
See Doraszelski and Jaumandreu (2007) and Garcia and Puente (2006) for Spanish firms. Cabral and
Mata (2003) estimate that the distribution of Portuguese firms converge to a log-normal distribution.
40
Huergo and Jaumandreu (2004) find that innovation is systematically related to size: large firms have a higher
probability of innovating but this size advantage reduces in the case of product innovation.







D
e
n
s
i t
y


D
e
n
s
i t
y


D
e
n
s
i t
y


D
e
n
s
i t
y


Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 32


Table 1.5: Descriptive Statistics of Firms Distributions


Mean Variance Coef. of Variation Skewness
Size Distribution 2.41 3.05 0.72 0.95
Cond. on Process Innov. 5.9 1.26 0.19 0.89
Cond. on Product Innov. 2.08 0.24 0.23 2.32
Cond. on Both Innov. 4.63 0.98 0.21 1.1
Cond. on No innovation 1.67 3.05 0.44 0.95


1.5 Comparative Statics


This section analyzes how changes in the key parameters of the model, which characterize
the industry structure, afect the process of labor reallocation among firms and hence the
equilibrium growth rates of the economy. In particular, changes in the innovation costs,
c
a
and c
q
, as well as changes in the entry cost, c
e
, are analyzed. Both types of costs are
directly linked to growth: changes in c
a
and c
q
bring changes in the composition of the pool of
innovative firms and changes in c
e
afect the imitation process of entrants firms.
High entry cost are seen as barrier to enter the industry and they are often regarded as
a protection of incumbent firms and hence as a stimulus to innovation. On the other hand, high
innovation costs are seen as detrimental of innovation. Hence, it becomes important to
understand how the economy responds to changes in these key parameters in order to design
policy recommendations aimed at fostering growth.

Using the quantitative results of Section 4.3 let fix the fraction of growth explained by
the growth in efciency to 69.8% and determine edogenously the aggregate growth rate.

Figure 5, left panel, plots the equilibrium growth rate for diferent values of the fixed
costs of innovation: on the x-axis the cost of doing product innovation, c
q
, while on the
y-axis the cost of doing process innovation, c
a
. As both the innovation fixed costs decline
two opposite efects arise. On the one hand, innovation becomes cheaper and more firms
find it profitable. Hence the pool of innovative firms increases and this afects positively and
directly the growth rate of the economy (Figure 4). This positive efect is then reinforced by an
indirect efect. If the mass of innovators is larger, more firms will pay the fixed costs. This
sustains the demand of labor and hence the wage rate, thus assuring a strong selection. On the
other hand, if the innovation costs are reduced, less labor is demanded by the individual
innovative firm. Consequently, the demand of labor by an innovative firm declines and hence the
real wage declines to satisfy the labor market clearing condition. A lower wage translates into a
weaker selection and hence in a lower efect on the economy growth rate. The final response of
the growth rate to the changes in the innovation costs results from the combination of these two
efects. Generally,






Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 33



Exit Rate for Difefrent ca and cr Share of Growth due to Entry and Exit for Difefrent ca and cr Share of PRoduct Innovators for Difefrent ca and cr

0.05
0.04
0.03
0.02
0.01 30






20






30

0.1
0.08
0.06
0.04
0.02
030






20






30

0.4
0.3
0.2
0.1
030






20






30
20 20 20
10 10 10 10 10 10
ca 0 0 cr ca 0 0 cr ca 0 0 cr


Share of Process Innovators for Difefrent ca and cr Share of Process and Product Innovators for Difefrent ca and cr Share of No Innovators for Difefrent ca and cr

1
0.8
0.6
0.4
0.2
030






20






30

0.4
0.3
0.2
0.1
030






20






30

0.8
0.6
0.4
0.2
030






20






30
20 20 20
10 10 10 10 10 10
ca 0 0 cr ca 0 0 cr ca 0 0 cr



Figure 1.4: Comparative statics for diferent c
a
and c
q



Growth Rate for Different ca and cr Growth Rate Levels for Different ca and cr 2


0.046

0.045

0.044

0.043

1.8

1.6

1.4

1.2



0.04



1



5



0.042


0.041





0.042

0.042

0.041

0.04

0.039

1

0.8



00
.4



4
0.0425
0.043

0.0435




0.044


0.043

0.038
2


1.5



1


1.5


2
0.6

0.4

0.2
0.044 5
0.045
0.0455



0.04



56

0.0445

0.045
1 0.0455 0.5 0.5 0.045 0.045
0.0445 0.0445 0.044
ca 00 0 cr
0 0.5 1 1.5 2cr



Figure 1.5: g for diferent c
a
and c
q




the positive efect prevails. The lower the innovation costs, the higher the growth rate.
This holds true for all the values of the fixed cost of undertaking product innovation but only for
high and intermediate value of the fixed cost of doing process innovation. The
maximum growth rate is obtained for c
q
= 0 but small and positive c
a
, showing that
for very low levels of c
a
the negative efect ofsets the positive one. Additionally, the economy
growth rate is more sensitive to changes in c
a
than to changes in c
q
. Hence, a
policy aimed at promoting only growth would be more successful when used to address
an increase in process innovation.






0
.
0
4
1


c a


Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 34



0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0



ExitRate



0.35
0.3
0.25
0.2
0.15
0.1
0.05
0



ShareofGrowthduetoEntryandExit



0.15
0.14
0.13
0.12
0.11
0.1
0.09
0.08
0.07
0.06



ShareofProductInnovators
0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35
c
e
c
e
c
e

0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05

ShareofProcessInnovators

0.32
0.3
0.28
0.26
0.24
0.22
0.2
0.18
0.16
0.14

ShareofProcessandProductInnovators

0.7
0.65
0.6
0.55
0.5
0.45
0.4
0.35
0.3

ShareofnonInnovators
0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35
c
e
c
e
c
e


Figure 1.6: Comparative Statics for diferent c
e


GrowthRatefroDifrentc
e
e
0.044

0.043

0.042

0.041

0.04

0.039

0.038

0.037
0 5 10 15 20 25 30 35 40
c
e

Figure 1.7: g for diferent c
e




When entry cost are low, imitation is cheap (Figure 6), and many firms enter and exit
the market, which results in a high growth rate (Figure 7). As the entry cost increases firm
selection and imitation become weaker and the growth rate declines. However
higher c
e
leads to a higher expected value of entrants which in turn imply that the
discounted expected profits of incumbents need to be higher. Hence, progressively the
mass of innovative firms increases and this generates an inversion in the direction of the growth
rate. However, as the entry barrier increases further the industry becomes more and more
concentrated and the number of innovators slightly declines. Thought few firms enter the
industry they drain a lot of labor increasing the wage rate and hence







S
h
o
f G
r
o
w
t h

E
n
t r
y
&
E
x
i t

S
h
o
f
P
r
o
d
u
c
t I n
n
o
v
a
t o
r
s


E
x
i t R
a
t e


S
h
o
f
P
r
o
c
e
s
s
I n
n
o
a
v
t o
r
s


S
h
o
f
B
o
t h
I
n
n
o
a
v
t o
r
s


S
h
o
f N
o
n
I n
n
o
v
a
t o
r
s


G
r o w
t h R
a t e
Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 35


innovation becomes more costly.
41




1.6 Final Remarks


This paper proposes an endogenous growth model with heterogeneous firms where firms
difer in two dimensions: production efciency and product quality. Both dimensions are subject
to idiosyncratic permanent shocks but firms can afect endogenously their evolution through
process, product or both types of innovations. Growth arises due to incumbent firms' innovation
and selection and is sustained by entrants' imitation. Selection eliminates the inefcient firms from
the market, thereby increasing the average productivity of incumbents. Innovation amplifies this
not only increasing directly the average technology of firms but also increasing selection.
Entrants imitate the average incumbent and are, on average, more productive than exiting firms.
The result is that the firm distribution shifts upwards, generating growth.

The economy is calibrated to the Spanish manufacturing sector and closely matches
static and dynamic moments related to the firm distribution and new moments related to the
innovation behavior of firms. Hence, the model provides an accurate representa- tion of the
Spanish economy and an explanation of the heterogeneity in the innovation activities among
firms. Improvements in production efciency explain 69.8% of the out- put growth while quality
upgrading contributes only for the remaining 30.2%. Moreover, decomposing the aggregate
growth in the contribution of firm turnover and innovation and experimantation by incumbents
shows that net entry contributes only marginally. In fact, more than 90% of growth is due to
within and between firms growth and when in- novation is banned output growth declines of
almost 74%. Innovation is also necessary to survive market competion: only non-innovative
firms exit the industry. An unan- swered question is to identify which type of innovation,
between process and product innovation, allows for a greater period of firms' longevity.

The endogenous firm size distribution is right skewed and approximated well by a log-
normal distribution. The conditional distributions of innovators are consistent with the data:
innovators are larger than non-innovators and in the case of product innovators also more right
skewed. Additionally, small firms do product innovation, intermediate firms do both product and
process innovation and large firms do process innovation. Hence, there is a non-monotonic
relation between firm size and innovation though firm size is still an indicator of the type of
innovation undertaken by firms. The industry growth

41
Notice

that when the entry cost is very high the industry is characterized by the absence of entering
and exiting firms. This generates the irregularities in the pictures. However, the discussion of the properties of this
scenario are not in the object of this paper.






Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 36


rate reacts positively to reductions in the innovation costs, however the model predicts
that its maximum is reached for a positive but small cost of process innovation. Though entry
barriers protect and stimulates innovation, growth is maximized for relatively low entry costs
which are accompanied by a more dynamic industry with a high turnover. As the industry
becomes more concentrated, the aggregate share of innovators increases however growth is
impacted less strongly.

These considerations leads to attractive policy recommendations aimed at fostering
growth and welfare. The next step is therefore to compute the optimal allocation and design
innovation policies that can implement the first best in the decentralized economy.




References


Aghion, P. and Howitt, P., (1992). A Model of Growth through Creative Destruction,
Econometrica, 60, 323-351.

Atkeson, A. and Burstein, A., (2007). Innovation, Firm Dynamic, and International
Trade, NBER Working Papers, 13326, National Bureau of Economic Research.

Bartelsman, E. J. and Doms, M., (2000). Understanding Productivity: Lessons from
Longitudinal Microdata, Journal of Economic Literature 38(3), 569-594.

Bartelsman, E. J., Haltiwanger, J. and Scarpetta, S. (2004). Microeconomic Evidence of
Creative Destruction in Industrial and Developing Countries, Tinbergen Institute Dis- cussion Paper,
04-114/3.

Bartelsman, E. J., Scarpetta, S. and Schivardi, F., (2003). Comparative Analysis of Firm
Demographics and Survival: Micro-Level Evidence for the OECD Countries, OECD Economics
Department Working Papers 348.

Bils, M. and Klenow, P., (2001). Quantifying Quality Growth, American Economic Re-
view, 91(4), 1006-1030. Farias, J. and Ruano, S., (2004). The Dynamics of Productivity: A
Decomposition Approach Using Distribution Functions, Small Business Economics, 22(3-4), 237-
251.

Cabral, L. and Mata, J., (2003). On the Evolution of the Firm Size Distribution: Facts
and Theory, American Economic Review, 93(4), 1075-1090.

Caves, R. E., (1998). Industrial Organization and New Findings on the Turnover and
Mobility of Firms, Journal of Economic Literature 36(4), 1947-1982.







Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 37


Cefis, E. and Marsili, O., (2005). A Matter of Life and Death: Innovation and Firm
Survival, Industrial and Corporate Change, 14(6), 1167-1192.

Cohen, W., and Klepper, S., (1996). Firm Size and the Nature of Innovation within
Industries: The Case of Process and Product R&D, The Review of Economics and Statistics 78(2),
232-243.

Doraszelski, U. and Jaumandreu, J., (2008). R&D and Productivity: Estimating Pro-
duction Functions when Productivity is Endogenous, CEPR Discussion Paper, 6636, C.E.P.R.
Discussion Papers.

Dorsey, R. E. and Mayer, W. J., (1995). Genetic Algorithms for Estimation Problems
with Multiple Optima, Nondiferentiability, and Other Irregular Featurs, Journal of Business and
Economic Statistics, 13(1), 53-66.

Eeckhout, J. and Jovanovic, B., (2002). Knowledge Spillovers and Inequality, American
Economic Review, 92(5), 1290-1307.

Foster, L., Haltiwanger, J. and Krizan, C., (2001). Aggregate Productivity Growth.
Lessons from Microeconomic Evidence, NBER Chapters, in: New Developments in Pro- ductivity
Analysis, National Bureau of Economic Research, 303-372.

Gabler, A. and Licandro, O., (2005). Endogenous Growth through Selection and Imita-
tion, mimeo, European University Institute.

Garcia, P. and Puente, S., (2006). Business Demography in Spain: Determinants of
Firm Survival, Bank of Spain Working Paper, 0608.

Garcia, P., Puente, S. and Gomez, A., (2008). Firm Productivity Dynamics in Spain,
Banco de Espana Working Paper, 0739.

Ghironi, F. and Melitz. M.J., (2005). International Trade and Macroeconomics Dynam-
ics with Heterogenous Firms, Quarterly Journal of Economics, 120(3), 865-915.

Grossman, G. M. and Helpman, E., (1991). Innovation and Growth in the global Econ-
omy, MIT Press, Cambridge MA.

Hallak, J. C. and and Sivadasan, J., (2008). Productivity, quality and Exporting Be-
havior Under Minimum Quality Requirements, mimeo.

Harrison, R., Jaumandreu, J., Mairesse, J. and Peters, B., (2008). Does Innovation
Stimulate Employment? A Firm-Level Analysis Using Micro-Data from Four European
Countries, NBER Working Paper, 14216.








Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 38


Hopenhayn, H. A., (1992). Entry and Exit and Firm Dynamics in Long Run Equilib-
rium, Econometrica 60(5), 1127-1150.

Hopenhayn, H. A. and Rogerson, R., (1993). Job Turnover and Policy Evaluation: a
General Equilibrium Analysis, Journal of Political Economy 101(5), 915-938.

Huergo, E. and Jaumandreu, J., (2004). How does Probability of Innovation Change
with Firm Age?, Small Business Economics 22, 193-207.

Huergo, E. and Jaumandreu, J., (2004). Firms' Age, Process Innovation and Produc-
tivity Growth, International Journal of Industrial Organization 22, 541-559.

Jovanovic. B., (1982). Selection and the Evolution of Industry, Econometrica 50(3),
649-670.

Klette, T. J. and Kortum, S., (2004). Innovating Firms and Aggregate Innovation,
Journal of Political Economy 112:5, 986-1018.

Lenz, R. and Mortensen, D. T., (2008). An Empirical Model of Growth Through Product
Innovation, Econometrica, 76(6), 1317-1373.

Lutttmer, E., (2007). Selection, Growth, and the Size Distribution of Firms, Quarterly
Journal of Economics 122(3), 1103-1144.

Martinez-Ros, E., (1999). Explaining the Decisions to Carry Out Product and Process
Innovations: The Spanish Case, Journal of High Technology Management Research, 10(2), 223-242.

Melitz, M., (2003). The Impact of Trade on Intra-Industry Reallocations and Aggregate
Industry Productivity, Econometrica 71(6), 1695-1725.

Miravete, E., Pernias, J., (2006). Innovation Complementarity and the Scale of Produc-
tion, The Journal of Industrial Economics LIV(1).

Parisi, M., Schiantarelli, F. and Sembenelli, A., (2006). Productivity, Innovation and
R&D: Micro Evidence for Italy, European Economic Review 50, 2037-2061.

Poschke, M., (2006). Employment Protection, Firm Selection, and Growth, Economics
Working Papers, ECO2006/35, European University Institute.

Romer, P. (1990). Endogenous Technological Change, Journal of Political Economy 98,
71-102.

Smolny, W., (1998). Innovations, prices and Employment: A Theoretical Model and
an Empirical Application for West German Manufacturing Firms, Journal of Industrial Economics,
46(3), 359-381.





Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 39


Smolny, W. (2003). Determinants of Innovation Behavior and Investment Estimates
for West-German Manufacturing Firms, Economics of Innovation and New Technology 12(5), 449-463.

Sutton, J., (1997). Gibrat's Legacy, Journal of Economic Literature 35(1), 40-59.

Tauchen, G. (1986). Finite State Markov-Chain Approximations to Univariate and
Vector Autoregressions, Economic letters, 20, 177-181.

Verhoogen, E., (2008). Trade, Quality Upgrading, and Wage Inequality in the Mexican
Manufacturing Sectors, The Quartely Journal of Economics 123(2), 489-530.




Appendix


A Partitions and Innovation Cutof Functions


Define A
x
= {(a, q) : a e A, q e Q : a(q)< a
x
(q)} the exit support, A
P
= {(a, q) :
a e A, q e Q . v(a, q) = v
P
(a, q)} the production support, A
A
= {(a, q) : a e A, q e Q . v(a, q) = v
A
(a, q)} the process
innovation support, A
Q
= {(a, q) : a e A, q e Q . v(a, q) = v
Q
(a, q)} the product innovation support and A
AQ
= {(a, q) :
a e A, q e
Q . v(a, q) = v
AQ
(a, q)} the process and product innovation support.

Let B = {(a +?, q +?)} for ,?,> 0 arbitrarily small. The innovation cutof function are
defined as a
A
= {(a, q) : (a, q) e A
A
. (A
P
A
Q
A
AQ
) A
A
= ?}, a
Q
= {(a, q) : (a, q) e
A
Q
.(A
P
A
A
A
AQ
)A
Q
= ?} and a
AQ
= {(a, q) : (a, q) e A
AQ
.(A
P
A
A
A
Q
)A
AQ
=
?}.



B Aggregate Variables


Using the information contained in equation (19), the price index, the aggregate con-
sumption, and the aggregate profits can be rewritten as:

o÷1
P=


ax(q)


Q
p(a, q)
q (a, q )
o
o÷1
Iµ(a, q)dqda
o



1
o
=I
o÷1
o p(µ), (1.26)
o 1
X= q x(a , q ) Iµ(a, q)dqda = I
o
x(µ). (1.27)
ax(q) Q


H= t(a, q)Iµ(a, q)dqda = I t (µ ). (1.28)
ax(q) Q






Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 40


C Growth Rate Disaggregation


On the Balanced Growth Path, given that the number of firms is constant, the growth
factor of aggregate (X) and average (X) consumption coincides: ¯


G= X = X .
?
¯?
X
X
¯
(1.29)

Defining the firm's quality weighted output with ˆ(a, q), the growth factor can be rewrit- x
ten as: 1
o
ax(q) Q ˆ(a, q)
o
µ
?
(a, q)dqda x
G=

Rewrite µ
?
using its law of motion yields:
X
¯
.




1
(1.30)
G=
A
Q
ˆ (a , q ) x
o
u
xI
µ(a, q) +
M
¸ (a , q ) I
dqda
o
X
o
¯
, (1.31)


where u
xI
is the optimal transition function with the exit and innovation rules. Adding
and subtracting X
o
=
ax
(q)
Q
ˆ(a, q)
o
((1÷M/I)µ(a, q)+M/Iµ(a, q)) to the numerator
¯ x
and rearranging the equation gives:

1
G=
A
Q
ˆ (a , q ) x
o
u
xI
µ(a, q) ÷ 1 ÷
M
I

¯
µ(a, q) +
M
I
¸(a, q) ÷ µ(a, q)) dqda
+1
o
.
X
o

(1.32)
The last step to obtain the growth rate decomposition consists in taking the logarithm of both
terms of the equation and approximating them using the rule ln(G) ~ g, given
that g is a small number. This results in:


1
g~ ˆ(a, q)
o
u
xI
µ(a, q) ÷ 1 ÷ M µ(a, q) + M ¸(a, q) ÷ µ(a, q) x ,
oX
o
¯
A Q
I I
(1.33)
which is equation (29) in the main body of the paper.



D Algorithm


The state space A · Q is discretized. The grid chosen is of 30 points for each state yield-
ing 900 technology combinations, (a, q).
42
Firms' value function is computed through

42
The choice of 30 grid points for each state is due to the fact that the algorithm is computationally heavy given the
presence of two states and the endogenization of the dynamic choice of the innovation investment. Increasing the grid
size would improve the precision of the calibration but would not afect qualitatively the results. On the other hand, the
technology combination (a, q) available to firms would increase quadratically in the grid size and the code would
eventually become unfeasible. Hence, given






Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 41


value function iteration. The unknown variables are the growth rates g
a
and g
q
, which
combines in the growth rate of the aggregate technology g, and the aggregate expendi-
o
ture and price index summarized by k = P 1÷
o
E. The growth rate of labor productivity,
1
g, is fixed exogenously. For given g
a
, g
q
= (G/G
a
) 1÷
q
÷ 1, and k compute the stationary
profitt(a, q; g
a
, k) and then the firm value function v(a, q; g
a
, k).
43
While iterating the
value function, the optimal policies for the investment in process and product innova-
tion, z(a, q; g
a
, k) and l(a, q; g
a
, k), are computed and the random walk processes, that
govern the transition of firm productivity and product quality, are approximated using
the method explained by Tauchen (1987). This step is time consuming since each firm's problem
has to be solved via first order conditions for each single couple of states, (a, q), till convergence is
reached. Once the value function is approximated the algorithm com-
putes the cutof functions a
x
(q; g
a
, k), a
A
(q; g
a
, k), a
Q
(a; g
a
, k), and a
AQ
(q; g
a
, k). Then
the transition matrix u
xI
is computed. This is the final transition matrix which takes
into account the exit and the innovation decisions. After guessing an initial distribution
for entrant firms and normalizing its initial joint mean to zero, the expected value of entry is
computed. The free entry condition is used to pin down the equilibrium value of k resulting from
the first iteration of the algorithm. Using the equilibrium k, the firm value, the cutof functions,
and the transition matrix can be found for given initial
g
a
. The bivariate firm distribution is then determined using the formula for the ergodic
distribution µ = (I ÷u
xI
)
÷
1
I as proved by Hopenhayn (1992). The algorithm is closed
using the condition on the mean of the entrant distribution,¸
e
=¢
e
µ, and pinning down
the equilibrium growth rate, g
a
, that satisfies this equation. Once g
a
is determined, g
q
is
determined as well. All these steps are repeated until all conditions are jointly satisfied
and convergence is reached.



E Conditional Probabilities


The final transition function T
XI
(a
?
, q
?
,a, q) contains all the information to compute
the probability that tomorrow a firm will optimally decide to do action Y e A
?
given
that today it choses action X e A where A
?
={Exit, Not to Innovate, Do Process Innovation, Do Product
Innovation, Do Both Innovations} and A ={Not to Innovate, Do Process Innovation, Do Product
Innovation, Do Both Innovations}. Weighting these probabilities by the firm density in each state
allows to calculate the fraction of firms that today chose action X and tomorrow will switch to
action Y . Simplify the notation and define a vector of states, s, of all the possible combinations
of a and q couples.

that the results are not qualitatively afected by the grid size, a quality and productivity grid of 30 points is a reasonable
restriction.
43
Notice that all the variables depend on both g and g . However for notational convenience g is
omitted since it is a function of g
a
.
a q q







Chapter 1. Product and Process Innovation in a Growth Model of Firm Selection 42


Indicating with "?" the next period variables the conditional probabilities are computed
as follows
1
P (Y , X ) = |(s
?
,s)µ(s)dsds
?
. (1.34)
s:A=
X
µ(s)ds s?:A?=Y s:A=X


























































Chapter 2




Trade and Growth: Selection
versus Process and Product
Innovation




2.1 Introduction


A growing empirical literature based on firm level data has documented the impact of
trade in afecting industry dynamics and firm level productivity.
1
A robust prediction is that trade
increases on average firm level productivity through a mechanism of self- selection of both
unprofitable firms exiting the industry and exporters that on average are more productive than
domestic firms. A less clear answer is given when analyzing the dynamic efects of trade on firm
productivity growth and industry growth. In this respect a key point to investigate is the efect of
trade on firms' innovation investments and hence on productivity growth. A series of empirical
works find that exporting and innovation are complements. That is, firms are more likely to be
exporters if they innovate and are more likely to innovate when they can increase their market
quota
through trade.
2


Though innovation is a fundamental force through which trade policies can afect growth
one element that is disregarded by this literature is the possibility of firms to undertake diferent
types of innovation. Recent evidence coming from the availability of micro data emphasizes that
firms perceive diferently innovations aimed at reducing the production

1
See

Bernard et al. (2007) for a survey on this literature.
2
Complementarity is documented by Aw et al. (2009), Lileeva and Tre?er (2007), and Bustos (2007).




43



Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 44


costs or increasing the product quality.
3
Not only firms have diferent incentives to
undertake one or the other innovation investment, but also their impact on firms' pricing
strategies, productivity, and TFP growth is diferent.

Motivated by this empirical evidence this paper presents a theoretical model that at-
tempts to examine the impact of openness and trade liberalization on the decisions of
heterogeneous firms to invest in cost reducing innovations, process innovation, or in product
quality enhancing innovations, product innovation, and how this generates firm level- and aggregate
growth. At this scope a general equilibrium dynamic model in which firms are heterogeneous in
their production efciency and in their product quality is de- veloped. The competitive structure is
taken from Melitz (2003) but introducing industry dynamics as in Hopenhayn (1992). The
evolution of both efciency and quality is given by a stochastic permanent component and by an
endogenous component proportional to firms' innovation investments. In each period non
profitable incumbents exit the indus- try and new firms enter the market imitating the average
incumbent as in Gabler and Licandro (2005) and Luttmer (2007). In the closed economy
endogenous growth arises due to firms innovation and selection and is sustained by entrants
imitation. Opening to costly trade generates three main mechanisms that afect growth: (i) the
selection of inefcient firms becomes tougher; (ii) the mass of innovative firms decreases
eliminating the marginal innovators; but (ii) the average innovation intensity increases as the
share of innovators that is also exporting can enjoy a higher market share. The selection of
innovators is a general equilibrium result. When an economy is exposed to costly trade part of its
resources are used to pay the export costs increasing the labor demand and as a consequence the
wage rate. Innovation becomes more expensive and thus the marginal innovators are forced to
become non-innovators. Hence, the economy resources are re- allocated not only from less
efcient firms to more successful firms but also from less efcient innovators to more efcient
innovators and to exporters.

Calibrating the model parameters to match empirical moments related to the Spanish
manufacturing sector shows that the positive efects of trade completely of-set the neg- ative one
leading to a higher growth rate in the open economy. Moreover, the model yields several
interesting predictions that could be further empirically tested. In par- ticular, exposure to trade
results in a more concentrated industry and in a larger share of non innovators. In addition, in this
model firm efciency is not the only factor that determine the export decisions of firms. In fact,
also relatively less efcient firms can access the foreign market when their product is of high
quality. This is a result that derives from the assumption of two attributes of firms heterogeneity.

3
Harrison et al. (2008), Huergo and Jamandreu (2004), Fritsch and Meschede (2001), and Smolny (2003) are some
references studying the efects of cost reduction and quality improving innovations on firm dynamics in diferent
European countries.






Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 45


Another important result of this model concern the efects of trade liberalization on
economic growth. A reduction of the variable trade cost unambiguously promotes growth and
fosters the difusion of higher quality variety as the share of firms undertaking product
innovation increases. Instead, changes in the fixed cost of trade promote growth only when the
fixed cost is not too low ensuring a sustained self-selection of exporters. When the fixed export
cost is low all the firms gain access to the foreign market and hence the competition in both the
domestic and foreign market increases. More firms start innovating mainly in process challenged
by the tougher competition. However the intensity of the innovation investment is low given the
reduced market quota. This could also bring to a growth rate in the open economy that is lower
than the growth rate in the closed economy.

This model is related to several models in the literature that try to understand how
trade impacts on the innovation investments of heterogeneous firms. Bustos (2007), Yeaple
(2005), and Navas and Sala (2007) study the static gain of technology adoption in response to
changes in the trade costs. Costantini and Melitz (2007) introduce a one-of innovation that
results in a one-time stochastic jump in productivity and then they analyze the transitional
dynamics induced by trade reforms. Van Long et al. (2008) introducing oligopolistic
competition studies how openness afects the process innovation incentives in a static framework.
The main result of the literature is that, trade liberalization leads to two efects: a direct efect
through which cost reducing innovations afect firm level productivity and a selection efect due to
inefcient firms are forced to leave the market.
4
While the latter efect always increases firms
productivity the former can either rise or reduce productivity depending if the trade cost are high
or low. Generally, the overall efect of trade liberalization is positive.

More closely to my work, Atkenson and Burstein (2007) and Impullitti and Licandro
(2009) focus on the joint continuous decision of exporting and innovating in a dynamic set-up.
5

Atkenson and Burstein (2007)'s paper presents a general equilibrium dynamic model of firms
process and product innovation but without endogenous growth. While process innovation is
stochastic and if successful upgrades firms' productivity, product innovation is seen as the
creation of a new product and hence it is equivalent to firm entry. Their main finding is that
changes in the marginal trade costs do not impact on aggregate productivity though they generate
a substantial impact at the firm level.

4
Since

Melitz (2003) the selection efect is a feature of models with heterogeneous firm. Stoelting
(2009) extends the Melitz (2003)'s model introducing endogenous growth due to persistent productivity shocks and firm
selection. She finds that moving from a close economy to an open economy increases permanently the growth rate.
Bernard et al. (2009) introducing multi-product firms find that the selection channel works not only eliminating the
least efcient firms but also eliminating the marginal products in the firm's portfolio.
5
My model is also related to Klette and Kortum (2004) and Lenz and Mortensen (2008) that shed light on the link
between innovation, firm heterogeneity and the role of resource reallocation in the growth process of a closed
economy.





Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 46


Impullitti and Licandro (2009) studying process innovation in a oligopolistic framework
find that trade liberalization leads to a higher number of firms and lower markups. This in turns
generates a dynamic selection efect which afects positively aggregate growth. An ambiguous
efect of trade liberalization on growth is instead found by Boldwin and Robert-Nicoud (2008)
and Gustafsson and Segerstrom (2006). However, it relies on the nature of the knowledge
spillowers.

This model complements the work of Irarrazabal and Opromolla (2009) that extends
Luttmer (2007)'s model to an open economy set up. They show that the export decision of firms
becomes history dependent and that also small firms can be exporters when the export costs are
sunk.
6
This result is consistent to the empirical findings of Eaton et al. (2008) for Columbian
plants and by Hallak and Sivadasan (2008) for exporters in India,
U.S, Chile and Columbia.
7


In the following I present the open economy version of the model developed in Chapter
1.




2.2 Open Economy


The world economy is characterized by two symmetric countries with the same prefer-
ences, technologies, wage rate, and aggregate variables. The access to the foreign market
is costly: firms willing to export have to pay fixed export costs, c
ex
expressed in terms
of labor, and variable costs of the iceberg type,t> 1. The export fixed cost is necessary
to generate a partition of firms between domestic firms and exporters.

Households face the same problem as in the closed economy implying that the demand
for each variety i stays the same (equation (1.3)). The only diference arises in the composition of
the consumption basket which is now given by the varieties produced domestically plus the
varieties imported, I = I
D
+ I
EX
-
. From now on, the superscripts D, EX and EX- indicate the domestic
variables, the export of the domestic country, and the imports of the domestic country, respectively. Firms
face a more complicated problem: after drawing their technology level they have to evaluate the
choice of entering or not the export market. This is a per-period choice that impacts on the
dynamic choices of innovation.

6
A
similar result is shown also in Arkolakis (2008) in which the rational for the existence of small
firms is given by per-consumer access costs. Firms can decide the fraction of the market they want to serve and the
fixed entry costs increases with the number of consumers reached.
7
This paper is also related to the trade literature that focuses on vertical diferentiation and hence on the prominent
role of quality in shaping the intra-industry trade patterns. Few examples are Schott (2004), Hallak (2006) and Hallak
and Sivadasan (2008).







Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 47


2.2.1 Production and Innovation


Firms that serve the domestic market face the same maximization problem as in the
closed economy. Thus, the optimal monopolistic price for the domestic products, p
D
(a, q), is given
by equation (1.7) and the optimal domestic profits,t
D
(a, q), by equation (1.10) . On the other hand,
when firms access the foreign market they have to pay fixed and
variable trade costs that afect the export profits and prices. It follows that:

o

t
E
X
(a , q ) =
a
t
q
1
÷
q
ot
t
1÷o o
(1 ÷o)P
t
1÷
o
E
t
÷ c
ex
(2.1)


and:


q
p
E
X
( a , q ) =t q
t
.
t
o a
t
(2.2)
The total profits that a firm with technology level (a, q) receives in period t are given by
the profits obtained selling in the domestic market and the profits obtained by serving
the foreign market but only if it is profitable. That is:


t
t
(a, q) =t
D
(a, q) + max{t
EX
(a, q), 0}. (2.3)



The export decision does not afect the modeling strategies of innovation and of the
evolution of firms production efciency and product quality. Hence, the evolution of
log a
t
and log q
t
are the same in both the closed and the open economy.



2.2.1.1 Firm Dynamic Optimization


In the open economy, the maximization of the expected discounted value of firms is
slightly more complicated as also the export choice needs to be considered. A firm with
technology (a, q) will export only if the value of exporting is higher than the value of
non exporting:
v(a, q) = max{v
D
(a, q), v
EX
(a, q)}. (2.4)

Notice that the return functions of v
D
(a, q) and v
EX
(a, q) are diferent: in v
D
(a, q) the
profits come only from the domestic market while in v
EX
(a, q) the profits come from both the
domestic and the foreign market. Diferent return functions imply diferent dynamic paths for the
innovation decisions. After drawing a technology (a, q) a firm decide whether to produce only
for the domestic market or also for the foreign market. Then within this decision a firm optimally
innovate. Hence, nested within the export









Chapter 2. Trade and Growth: Selection versus Process and Product Innovation


decision there are the diferent innovation strategies:


v
D
(a, q) = max{v
DP
(a, q), v
DA
(a, q), v
DAQ
(a, q), v
DQ
(a, q)},


for the producers that supply only the domestic market and:


v
EX
(a, q) = max{v
EXP
(a, q), v
EXA
(a, q), v
EXAQ
(a, q), v
EXQ
(a, q)}
48





(2.5)




(2.6)


for the producers that supply both the domestic and the foreign market. Again v
DP
(a, q),
v
DA
(a, q), v
DAQ
(a, q), and v
DQ
(a, q), (v
EXP
(a, q), v
EXA
(a, q), v
EXAQ
(a, q), and v
EXQ
(a, q))
are the value when a firm do not innovate, innovate in process, in both process and product, or
only in product, and serves only the domestic market (and serves both the domestic and the
foreign market). Trade afects the innovation choices of the firms since firms face diferent profits
and hence diferent incentives to innovation. In the Appendix the several components of the value
function are shown.



2.2.2 Exit, Entry, and the Cutof Functions


The entry and exit conditions are the same as in the closed economy: firms exit when
their continuation value is negative and firms enter until the free entry condition is satisfied. The
innovation and the exit cutof functions are defined as before. Upon these cutofs another cutof
function related to the export decisions can be introduced. That
is, a
ex
(q) such that a
ex
(q)> a
x
(q) and v
D
(a
ex
(q), q) = v
EX
(a
ex
(q), q). Hence, the export
cutof function is given by all the technology levels such that firms stay in the industry
and are indiferent between exporting or not exporting. Every firm with a(q) > a
ex
(q)
choses to produce also for the foreign market. Also the export cutof is decreasing in
the quality dimension. For given productivity, a firm producing a high quality variety has a easier
access to the export market.

Opening the model to trade slightly modify the transition function that summarizes
all firms' decisions and the corresponding supports. Define u
Open
: A A
Open
· Q ÷
xI x
(A
Open
A
Open
A
Open
A
Open
A
Open
)·Q where the support of efciency is partitioned
P A Q AQ x
into A
Open
= {a e A . q e Q : a(q)< a
x
(q)} (exit support), A
Open
= {a e A . q e
x P
Q : v(a, q) = v
DP
(a, q) v v(a, q) = v
EXP
(a, q)} (production support), A
Open
= {a e A
A . q e Q : v(a, q) = v
DA
(a, q) v v(a, q) = v
EXA
(a, q)} (process innovation support),
A
Open
= {a e A.q e Q : v(a, q) = v
DQ
(a, q)vv(a, q) = v
EXQ
(a, q)} (product innovation Q
support), and A
Open
= {a e A . q e Q : v(a, q) = v
DAQ
(a, q) v v(a, q) = v
EXAQ
(a, q)} AQ
(process and product innovation support).








Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 49


2.2.3 Firm Distribution


Firm density function is still shaped by the entry, exit and innovation decisions of firms
and similarly as the closed economy is given by:


I
D
?
µ
?
( a
?
, q
?
) = I
D



A
Open
P



Q


µ(a, q)|(a
?
, q
?
,a, q)dqda +


(2.7)


A
Open
A


Q
µ(a, q)|(a
?
, q
?
,a, q, z)dqda +


A
Open
AQ


Q
µ(a, q)|(a
?
, q
?
,a, q, z, l)dqda

+


A
Open
Q


Q

µ(a, q)|(a
?
, q
?
,a, q, l)dqda

+ M
?
¸ (a
?
, q
?
).

The support of each integral is corrected to take into account that the innovation deci-
sions are now taken by both exporters and non-exporters. In the open economy the mass of
domestic firms is denoted by I
D
. This measure of firms includes also the fraction of domestic
firms that export.

Finally, the output weighted mean adjusted by quality is a weighted average between
the output weighted average of the domestic firms and the output weighted average of the
exporters. This last term includes only the exporting market shares and re?ects the technology
gains obtained by the additional market share enjoyed by exporters corrected
by the output loss due to the iceberg cost,t . That is:

1÷oo
I
D
µ
D
1o
o
+ I
EX
µ=
t
I
t
t
÷
t
I
t
µ
E
X
t
t
1÷o o
(2.8)


where I
EX
= I
D


aex(q)
Q
µ(a, q)


is the mass of domestic firms that export and I is the
total mass of firms selling in the domestic market, and in both the domestic and the
foreign market.
8
Hence I represents the mass of available varieties in each country. The
weighted mean that considers only the domestic production is given by:

1÷o
o
o
µ
D
t
=
ax(q)

Q
aq
1
÷q
1÷o
µ
t
(a, q)dqda , (2.9)


while the weighted mean related to the exporters production is given by:


µ
E
X
= t




aex(q)


1
Q
µ
t
(a, q)dqda




aex(q)




Q


aq
1
÷q


o
1÷o



µ
t
(a, q)dqda

1÷o
o



.



(2.10)

8
Given the symmetry between the two countries, I
EX
is also the mass of foreign firms that import.









Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 50


2.2.4 Equilibrium and Balanced Growth Path


A stationary equilibrium in this economy is a collection of sequences of prices {p
D
}· 0, t t=
{p
EX
}· 0, {P
t
}· 0, real numbers {I
D
}· 0, {I
EX
}· 0, {M
t
}· 0,
t t= t= t t= t t= t=
{X
t
}· 0, functions t=
n(a, q; µ), z(a, q; µ), l(a, q; µ), v(a, q; µ), cutof functions a
x
(q), a
A
(q), a
AQ
(q), a
Q
(q),
and a
ex
(q), and probability density function {µ
t
}· 0 such that consumers maximize their t=
utility given their budget constraints, active firms maximize their expected discounted
value, the free entry condition holds, the exit and the export decisions are optimal, the good and
the labor markets clear, the firm distribution evolves as described before, and the stability
condition is satisfied.

The BGP is found similarly as in the closed economy. The economy admits a BGP
along which the shape of the firms' distribution is invariant but its mean, the mean of
the entering firms, and the aggregate consumption grow at a rate G = G
a
G
1
÷
q
, the q
price index decreases at the same rate G = G
a
G
1
÷
q
, the domestic and exported output q
distributions grow at a rate G
a
/G
q
, the domestic and export price distributions grow q
at a rate G
q
/G
q
and the number of firms, the number of exporters, the number of a
entrants, the aggregate expenditure, the aggregate profits, the profit distribution, the
labor distributions are constant.

The model along the BGP can be stationarized as in the closed economy and then it
can be solved numerically.




2.3 Quantitative Analysis


2.3.1 Calibration


Table 1 lists all the parameters used in the open economy. Fourteen parameters are cal-
ibrated to match empirical targets related to the Spanish manufacturing sector and five are fixed
accordingly to the literature or to directly match their empirical counterpart. These last
parameters are the discount factor, the preference parameter, the imitation parameter, the growth
rate of labor productivity, and the iceberg cost of trade.| is set equal to 0.95 to analyze a yearly
time period. Accordingly to Ghironi and Melitz (2003),o is set equal to 0.73, so that the price mark-up
charged by the monopolistic
firm is of 36% over the marginal cost.
9
The imitation parameter¢
e
is chosen such that

9
A

mark-up of 36% over the marginal cost could be seen high and at odds with the macro literature
that delivers a standard mark-up of around 20% over the marginal/average cost. In this model, a higher mark-up is
justified by the presence of the fixed costs. In fact, given the free entry condition firms on average break even: on
average firms price at the average cost leading to reasonable high mark-ups over the average cost.





Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 51


the average size of entrants is 38% of the size of incumbent firms as estimated by Gracia
and Puente (2006). From the European Innovation Scoreboard (2001) the growth rateof labor
productivity is fixed to 0.042, measured in terms of value added per-worker as average over the
nineties. Fixing g enables to distinguish endogenously the growth con-
tributions of efciency, g
a
, and quality, q
q
. Once these growth contributions are assesed
it is possible to fixed them and to evaluate the impact of trade on the aggregate growth
rate. Finally,t is set equal to 1.099 accordingly to Dovis and Milgram-Baleix (2009), who find that the
average trade tarif of the Spanish manufacturing sector is 9.9%.

Table 2.1: Calibration


Parameter
Calibrated Parameters
c
e

c
f
c
a
c
q

c
ex

q
o
a

o
az

o
q

o
q
lo
ea
o
eq
ì
a
ì
q

Parametrization
|
o
u
t
g


Value


36.72%
1.61%
8.21%
2.42%
11.27%
0.75
0.15
0.9
0.32
1.2
0.40
0.32
0.083
0.025


0.95
0.73
0.38
1.099
0.042


Description


Entry cost, % of average firm size
Fixed cost, % of average firm size
Process innovation cost, % of average firm size
Product innovation cost, % of average firm size
Export cost, % of average exporting firm size
Quality parameter
Variance of productivity shock
Variance of productivity shock with innovation
Variance of quality shock
Variance of quality shock with innovation
Variance of log productivity distribution of entrants
Variance of log quality distribution of entrants
Scale coefcient for process innovation Scale
coefcient for product innovation


Discount factor
Preference Parameter
Relative entrant mean
Iceberg cost of exporting
Growth rate of labor productivity



The remaining parameters are calibrated using a genetic algorithm as described by
Dorsey and Mayer (1995).
10
These parameters are: the ratio among the fixed costs,
c
e
/c
f
, c
a
/c
f
, c
q
/c
f
, and c
ex
/c
f
, the quality parameterq, the four variances of the in-
cumbent random walks,o
a
,o
az
,o
q
, ando
ql
, the two variances of the entrant random

10
The

aim of the algorithm is to jointly calibrate the parameters such that the mean relative squared
deviation of thirteen model moments with respect to the corresponding moments in the data is minimized. Since the
problem is highly non-linear, this optimization can be characterized by many local minima and the genetic algorithm
used has the nice feature to increase the probability of choosing the global minimum.






Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 52


Table 2.2: Empirical Targets and Model Statistics


Targets
Targets for Calibration
Share process innovation
Share product innovation
Share process and product innovation
Product innovation intensity
Process innovation intensity
2 year survival rate 5
year survival rate Firm
turnover rate
Firm below average productivity
Job creation due to entry
Size entrants wrt exiting firms
Productivity spread
Share of exporters
Targets for Parametrization
Entrant size/incumbent size
Mark-up over marginal cost
Average tarif


Data


12.2%
12.4%
20%
0.44%
1.26%
0.8
0.58
0.09
0.83
0.03
1.23
[2, 3]
33%


0.38
0.37
0.09


Model


10.38%
13.17%
16.32%
0.47%
1.41%
0.76 0.57
0.10 0.75
0.03 1.37
2.21
28.38%


0.38
0.37
0.09



walks,o
ea
, ando
eq
and the two parameters that scale the innovation drifts into the
stochastic processes,ì
a
andì
q
. These parameters jointly determine the shape, the
truncation functions of firm stationary distribution, and the partition of firms among
the diferent innovation strategies and among exporters and non exporters. They are calibrated
using as targets both static and dynamic empirical moments that are infor- mative about the
industry characteristics, the innovation decisions, and firms' export status.

A first group of moments refers to a set of targets traditionally used in the firm dynamic
literature. These are firms' survival rates after two and five years upon entry, firms' yearly
turnover rate, the job creation rate due to entry, the fraction of firms below average productivity,
the productivity spread, and the size of entrants with respect to exiting firms which calibrate the
six variances of the model and the entry cost. Accordingly to Garcia and Puente (2006), the two
and five year survival rates for Spanish manufacturing firms are estimated equal to 82% and 58%,
respectively.
11
They report also a yearly firm

11
Those numbers are aligned to the one reported by other developed countries as UK, Germany and Nederland
(Bartelsman et al. (2003)).







Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 53


turnover rate of 9% and a job creation rate due to entry equal to 3%.
12
Moreover they
show that entrants firms are 23% bigger than exiting firms in terms of employment. Bartelsman
et al. (2004) estimate that the fraction of Spanish firms below average productivity is equal to
83%, highlighting a right skewed firm size distribution. The last moment is the productivity
spread between the 85
th
and 15
th
percentile which is widely accepted to be between 3 and 4.

A second set of empirical moments gives information related to the innovation behavior
of firms: the share of firms performing process innovation, product innovation, both process and
product innovation, and the intensity of the innovation investments in both process and product.
These are new statistics coming from European and national surveys at the firm level. In the
scope of this paper these are relevant moments that help to calibrate the fixed cost of process and
product innovation, the quality parameter
q,ì
a
, andì
q
. Harrison et al. (2008), working on data derived from the CIS, report
that 12.2% of Spanish firms in the manufacturing sector declared a process innovation
between 1998 and 2000, while 12.4% declare a product innovation and 20% decleare both
process and product innovation. These numbers are close to the one published by the National
Statistics Institute (www.ine.es) using the ESEE. The innovation intensity of the Spanish
manufacturing sector, computed as the aggregate innovation expenditure over the aggregate
sales, in the 1998, is of 1.71%. Process innovation intensity accounts for 1.26% while product
innovation intensity accounts for the remaining 0.44%.

Finally, the last parameter to calibrate is the fixed cost of export. The empirical mo-
ment used as target is the share of exporting firms set equal to 33% as Dovis and Milgram-
Baleix (2009) reported. This moment represent the natural candidate given the fundamental role
played by the fixed cost of export in determining the partition of firms between exporters and non
exporters.

Table 2 shows the value assigned to the targets and the corresponding model moments.
Despite the large number of parameters to calibrate, the model statistics match closely the data.
Hence, this model seems to reproduce accurately the Spanish manufacturing sector.

For a given growth rate of labor productivity the model generates an average production
efciency growth rate, g
a
, equal to 3.27% and an average product quality growth rate,
g
q
, equal to 3.64%, (Table 3). That is, 77.90% of aggregate growth is due to firms level
efciency growth.
13
This figure is very close to the estimates reported by Huergo and
12
Firm turnover is computed as the sum of the number of entering and exiting firms over the total
number of firms while job creation rate is computed as the total amount of labor employed by entering firms in a year
divided by the total employment in the same year.
13
In equilibrium the growth rate can be approximated using a logarithmic transformation which yields
g ~ g
a
+(1÷q)g
q
. From this equation is then possible to distinguish the growth contribution of efciency
from the growth contribution of quality.





Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 54


Jamandreu (2004) confirming the validity of the model in explaining the dynamics of
the Spanish manufacturing sector.
14


Table 2.3: Growth Rates in the Open Economy


g g
a
g
q

4.2% 3.27% 3.64%




2.3.2 Closed and Open Economy


The object of this section is to study the efects of openness on firms' innovation decisions
and hence on aggregate growth. To achieve this aim the closed economy is simulated using the
parameters listed in Table 1 and fixing the share of growth due to efciency and quality
accordingly to what discussed in the previous section. Appendix C explains the algorithm used to
solve for the stationary solution in both the closed and the open economy.

Opening up to trade increases unambiguously the aggregate growth rate. The growth
rate in the closed economy is equal to 3.81% while the growth rate in the open economy is equal
to 4.2% (Table 4).

Table 2.4: Growth Rates in the Closed and Open Economy


Closed Economy Open Economy
Growth Rate 3.81% 4.2%



This positive growth diferential induced by costly trade results from the combination
of tougher selection of unprofitable firms, tougher selection of marginal innovators, and higher
innovation intensity as Appendix E shows. On the one hand, trade induces a higher turnover
rate which afects positively and permanently growth shifting to the
right the exit cutof function, a
x
(q). On the other hand, in the open economy innovation
is more costly and hence less firms find optimal to innovate. However, mostly exporting
firms are also innovators. Since they enjoy a larger market share and larger profits due to both
domestic and foreign sales, their incentives to invest in both product and process R&D increase.
The two positive growth efects completely ofset the negative efect of
the selection of innovators.
15

14
The
model can be equivalently solved fixing the growth contribution of productivity equal to 77.9%
and obtaining endogenously an aggregate growth rate, g, equal to 4.2%.
15
It should be noticed that tougher selection afect growth also indirectly leading to better entrants imitation.





Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 55


2.3.2.1 Firms Partition and Distributions





÷a
(q)Q






÷a
Q(q)
A


FirmPa
rtitino



Process&
Product
Prod
uct
Proc
ess
Produ
ction
E
xit




÷
a
(
Q
)q





÷a
AQ
(
q)


FirmP
artitino



Process&
Product
Produ
ct
Proce
ss
Producti
on
Exit
Exportc
utof




÷a
(q)x



÷a
(q)A




÷
a(
x
)q



÷
a
ex
(
q)




÷a(
A
q)


Productivtyi Productivyit




Figure 2.1: Firms Partition, Closed (Left) vs. Open (Right)


Figure 1 shows the partition of firms among exiting firms (in black), non-innovators (in
green), product innovators (in pink), process innovators (in blue), and both process and product
innovators (in yellow), and the corresponding cutof functions in the closed (left) and open
economy (right) for diferent combination of efciency (x-axis) and quality (y- axis).
16
Moreover,
in the left panel the export cutof function can be identified. In the open economy there are less
innovators. These are taken from process and from both process and product innovation but not
from product innovators. In fact, trade advantages product innovators which represent only
27.01% of the innovators in autarchy and 33.03% of the innovators in the open economy. Due to
lower product innovation fixed cost, the benefit-cost ratio of the R&D investments is such that
improvements in quality are prefered to improvements in efciency leading to a higher product
quality. Less innovators but relatively more product innovators generate a firm distribution over a
and q which is more concentrate towards the quality dimesion (Figure 2). This higher weight on
quality shapes a univariate firm distribution over a technology index aq
1
÷q
that is more concentrated in the open economy (Figure 3, left).
17


Product quality and the diferent innovation investments generates a non-monotonic
relation between quality weighted labor productivity and export status. Figure 3 (right panel)
shows that also firms with low labor productivity can become exporters. These

16
See

Benedetti Fasil (2009) for more details on the composition of the partition among the diferent
choices faced by firms.
17
While in the closed economy this distribution maps one-to-one to the firm size distribution, in the open economy it
needs to be corrected by the additional labor used by exporting firms to serve the foreign market. Hence, no direct
conclusion on the firm size distribution in the open economy can be driven.





Q
u a l i t y
Q
u a l i t y


Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 56


FirmDistibutionr FirmDistibr
utions


0.
0
5

0.
0
4

0.
0
3

0.
0
2

0.
0
1

0
2
5



0.05

0.04

0.03

0.02

0.01

0
25
2
0


1
5





Produ
ctivtyi

1
0



5



0



0


5


1
0


Qu
ality

1
5


2
0

2
5

2
0

1
5


1
0


Prod
uctiv
yit


5


00


5

1
0



Qu
ality

1
5

2
0

2
5



Figure 2.2: Bivariate Firms Distribution, Closed (Left) vs. Open (Right)


are firms characterized by a relatively low a (but still higher than the export cutof) but
high product quality.
18



0
.
4


FirmDist
ibutionsr



ClosedE
conomy



0
.
9


Conditi
nalDist
ibutionsor



DomesticFir
ms

0.
3
5

0
.
3

0.
2
5

0
.
2

0.
1
5

0
.
1

0.
0
5
OpenE
conomy

0
.
8

0
.
7

0
.
6

0
.
5

0
.
4

0
.
3

0
.
2

0
.
1
Exporti
gFirmsn

1 2 3 4 5 6 7 8 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
aq
1÷
q aq
1÷
q



Figure 2.3: Firms Distribution, Closed vs. Open (Left), Non Exporters vs. Exporters
(Right)



2.3.3 Trade Liberalization


This section studies the impact of trade liberalization on economic growth. Trade liber-
D
e n s i t y
D
e n s i t y
alization calls for a reduction of the trade costs. Firstly, the attention is focused on the efects of
changes in the iceberg cost of trade,t . Figure 4 plots the growth diferential

18
Through the innovation investments the export decision becomes history dependent. Firms with relatively low
labor productivity, caused mainly by high quality, choose to become exporters as they can benefit from higher profits
opportunities. These better opportunities are also generated by the expectation on future R&D investments.






Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 57


between the open and the closed economy. In general, as trade liberalizes the growth
diferential rises. However, for hight it is negative while for intermediate and low level oft it is positive. Hence,
when trade liberalization is at an early stage it leads to a growth rate in the open economy that is lower than
the growth rate in autarchy.


6

5

4

3

2

1

0

÷
1

x
10
÷3

Growth Differential
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
t

Figure 2.4: Growth Diferential for diferentt



Whent is high the exported varieties are very expensive and their demand is low. Hence,
only few firms serve the foreign market profitably shifting to the right the export cutof,
a
ex
(q). This implies a low labor demand and a low wage rate which relaxes the exit cutof,
a
x
(q). Selection is weak and many marginal firms survive in the market. A lower wage
rate eases R&D increasing the share of innovative firms which is higher than in the closed
economy. However, the majority of innovators serves only the domestic market and this reduces
the innovation intensity. The consequence is a negative growth diferential. The result reverses
when the iceberg cost of trade decreases. The export cutof shifts to the left and more firms enter
successfully into the export market demanding more labor. As a result the wage rate increases and
the selection of unprofitable firms becomes tougher. Innovation is more expensive and attracts
less firms. However the innovation intensity of these firms is higher given that many of them
export. Interestingly, a reduction in the iceberg cost of trade together with asymmetries in the
innovation costs favor product innovation. This results in a range of exported varieties
characterized by higher quality and by a better quality-price ratio. Figure 6 in Appendix D plots
the comparative statics discussed.

The scenario changes when trade liberalization is implemented through a reduction of
the fixed export cost, c
ex
. As can be seen from Figure 5 the growth diferential between
the open and the closed economy is not monotonically related to c
ex
and it sharply
declines up till it becomes negative for low fixed costs.
19

19
Notice

that the export cost is expressed as a percentage of the average firm size and that the x-axis
is cut for c
ex
= 100. After this point the growth diferential does not change substantially. The same is






g
o
p
e
n
÷
g
c
l o
s
e

Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 58



5

4

3

2

1

0

÷
1


x
10
÷3












0














1
7














3
4


GrowthDifferential÷c
ex
(%of
averagefirmsize)











51














6
8














8
6














100
c
ex

Figure 2.5: Growth Diferential for diferent c
ex




When trade liberalization starts (high value of c
ex
) the mechanism of resources real-
location from exiting and domestic firms to innovators and exporting firms works as
discusses in the previous paragraph. Hence higher selection, higher innovators selection,
higher investment intensity, and higher growth are the result. However, as c
ex
declines
a sustained selection is fostered mainly by an increasing number of innovators than by
an increasing number of exporters. In fact, lower export cost, though accompanied by
more exporters, reduces the demand of labor and hence the wage rate as c
ex
declines
more rapidly than the rate at which the share of exporters increases. Innovation be-
comes cheaper and the composition of the pool of innovative firms changes. The share of product
innovators progressively diminishes in favor of the share of process and both process and product
innovators. Since process innovation is more expensive than prod- uct innovation the wage rate is
sustained and firm selection is tough. This together with more innovators and higher intensity,
particularly by process innovators, results in a
high growth diferential. However, if c
ex
declines further many inefcient firms are able
to enter the foreign market. This together with a higher competition in the domestic
market, due to the introduction of many imported products, reduce the market share of each
domestic and exporting firm. Challenged by this increasing competition, more firms undertake
process innovation. However, though the number of innovator increases their investments
reduces and also the demand of labor declines weakening selection. The result is a decline in the
growth diferential until it becomes negative. A too strong trade liberalization, when implemented
through changes in the fixed cost of trade, leads to a growth rate in the open economy that is
lower than the growth rate in autarchy.


not true for the comparative statics displayed in Figure 7 in the Appendix. In this case the maximum c
ex
is set equal to
240% of the average firm size.









g
o
p
e
n
÷ g c l o s e
Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 59


2.4 Final Remarks


This paper studies the efects of intra-industry trade on firms' exit, process and product
innovation decisions and how these firm level dynamics impact on aggregate growth. At this
scope a general equilibrium model with endogenous growth is developed. Firms difer in their
production efciency and product quality. Both factors evolve through per- manent shocks but
incumbent firms endogenously afect their evolution through process and product innovations.

Calibrating the model parameters to match the Spanish manufacturing sector allows
several interesting implications. Costly trade unambiguously increases growth not only through
the standard tougher selection of inefcient firms but also through the selection of inefcient
innovators. In fact, when an economy is exposed to trade some labor is reallocated from exiting
and innovative firms to the payment of the export costs. Hence, the share of innovators
decreases. However, the remaining innovators are often also exporters and given the higher
market quota, domestic and foreign, the intensity of their investments increases. Moreover, the
resulting more concentrated industry favors product innovation and the average quality of the
varieties produced increases. The inter-temporal link between export and product innovation
determines that small firms with a product of high quality have an easier access to the export
market than large firms with a low product quality.

Concerning the debate on the efects of free-trade agreements on growth this model pro-
vides the following contribution. As long as trade liberalization is implemented through a
reduction of the variable cost of trade it is beneficial for growth and for the production and
difusion of high quality products. More attention has to be paid when freer trade is obtained
reducing the fixed cost of export. In this case, a too sharp liberalization could cause a decline of
the growth rate that could become even lower than the growth rate obtained in autarchy. This
decline would be accompanied by a reduction of product quality in favor of cheaper varieties.

These long run predictions are obtained by analyzing the economy at its steady state. A
complete understanding of their implications on growth and also on consumers' welfare requires
the study of the transitional dynamic of the model. The research agenda is therefore concentrated
on this point.













Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 60


References


Aghion, P. and Howitt, P., (1992). A Model of Growth through Creative Destruction,
Econometrica, 60, 323-351.

Arkolakis, C., (2008). Market Penetration Cost and Trade Dynamics, Manuscript, Yale
University, New Haven, CT.

Atkeson, A. and Burstein, A., (2007). Innovation, Firm Dynamic, and International
Trade, NBER Working Paper, 13326.

Aw, B. Y., Roberts, M. J. and Xu, D., (2009). R&D Investment, Exporting, and
Productivity dynamics, NBR Working Paper, 14670.

Bartelsman, E. J., Haltiwanger, J. and Scarpetta, S. (2004). Microeconomic Evidence of
Creative Destruction in Industrial and Developing Countries, Tinbergen Institute Dis- cussion Paper,
04-114/3.

Bartelsman, E. J., Scarpetta, S. and Schivardi, F., (2003). Comparative Analysis of Firm
Demographics and Survival: Micro-Level Evidence for the OECD Countries, OECD Economics
Department Working Papers 348.

Baldwin, R. E. and Robert- Nicoud, F., (2008). Trade and Growth with Heterogeneous
Firms, Journal of International Economics, 74(1), 21-34.

Bernard, A. B., Redding, S. J. and Schott, P. K., (2007). Firms in International Trade,
Journal of Economic Perspective, 21(3), 105-130.

Bernard, A. B., Redding, S. J. and Schott, P. K., (2009). Multi -Product Firms and
Trade Liberalization, Manuscript, Dartmouth College, Hanover, NH.

Bustos, P., (2007). The Impact of Trade on Technology and Skill Upgrading: Evidence
from Argentina, Manuscript, University Pompeu Fabra, Barcelona.

Bustos, P., (2007). Multilateral Trade Liberalization, Exports and Technology Upgrad-
ing: Evidence on the Impact of MERCOSUR on Argentinean Firms, Working Paper, CREI,
University Pompeu Fabra, Barcelona.

Costantini, J, and Melitz, M. J., (2008). The Dynamics of Firm Level Adjustment to
Trade Liberalization, in Helpman, E., Marin, D. and Verdier, T, (eds.), The Organization of Firms in
a Global Economy, 107-141, Harvard University Press, Cambridge, MA.

Dorsey, R. E. and Mayer, W. J., (1995). Genetic Algorithms for Estimation Problems
with Multiple Optima, Nondiferentiability, and Other Irregular Featurs, Journal of Business and
Economic Statistics, 13(1), 53-66.





Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 61


Dovis, M. and Milgram-Baleix, J., (2009). Trade, Tarifs and Total Factor Productivity:
The Case of Spanish Firms, The World Economy, Blackwell Publishing, 32(4), 575-605.

Eaton, J. and Kortum, S., (2001). Technology, Trade, and Growth: A Unified Frame-
work, European Economic Review: Papers and Proceedings, 45(4-6), 742-755.

Eaton, J., Eslava, M., Kugler, M. and Tybout, J., (2008). Export Dynamics in Colombia:
Transactions Level Evidence, Borradores de Economia, 004748, Banco de la Republica de
Colombia.

Eeckhout, J. and Jovanovic, B., (2002). Knowledge Spillovers and Inequality, American
Economic Review, 92(5), 1290-1307.

Gabler, A. and Licandro, O., (2005). Endogenous Growth through Selection and Imita-
tion, Manuscript, European University Institute, Florence.

Garcia, P. and Puente, S., (2006). Business Demography in Spain: Determinants of
Firm Survival, Bank of Spain Working Paper, 0608.

Ghironi, F. and Melitz, M.J., (2005). International Trade and Macroeconomics Dynam-
ics with Heterogenous Firms, Quarterly Journal of Economics, 120(3), 865-915.

Grossman, G. M. and Helpman, E., (1991). Innovation and Growth in the Global
Economy, MIT Press, Cambridge MA.

Gustafsson, P. and Segerstrom, P., (2006). Trade Liberalization and Productivity
Growth, CEPR Discussion Paper, 5894.

Hallak, J. C. and and Sivadasan, J., (2009). Productivity, quality and Exporting Be-
havior Under Minimum Quality Requirements, NBER Working Papers, 14928.

Harrison, R., Jaumandreu, J., Mairesse, J. and Peters, B., (2008). Does Innovation
Stimulate Employment? A Firm-Level Analysis Using Micro-Data from Four European
Countries, NBER Working Paper, 14216.

Hopenhayn, H. A., (1992). Entry and Exit and Firm Dynamics in Long Run Equilib-
rium, Econometrica 60(5), 1127-1150.

Impullitti, G. and Licandro, O., (2009). Trade, Firms Selection, and Innovation: the
competition Channel, Manuscript, European University Institute, Florence.

Irarrazabal, A. and Opromolla, L. D., (2008). A Theory of Entry and Exit into Export
Markets, Working Paper, 2008-20, Banco de Portugal, Lisbon.

Huergo, E. and Jaumandreu, J., (2004). Firms' Age, Process Innovation and Produc-
tivity Growth, International Journal of Industrial Organization 22, 541-559.





Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 62


Jovanovic. B., (1982). Selection and the Evolution of Industry, Econometrica 50(3),
649-670.

Klette, T. J. and Kortum, S., (2004). Innovating Firms and Aggregate Innovation,
Journal of Political Economy 112:5, 986-1018.

Lenz, R. and Mortensen, D. T., (2008). An Empirical Model of Growth Through Product
Innovation, Econometrica, 76(6), 1317-1373.

Lileeva, A. and Tre?er, D., (2007). Improved Access to Foreign Markets Raises Plant-
Level Productivity for Some Plants, NBER Working Paper, 13297.

Lutttmer, E., (2007). Selection, Growth, and the Size Distribution of Firms, Quarterly
Journal of Economics 122(3), 1103-1144.

Melitz, M., (2003). The Impact of Trade on Intra-Industry Reallocations and Aggregate
Industry Productivity, Econometrica 71(6), 1695-1725.

Navas, A. and Sala, D., (2007). Technology Adoption and the Selection Efect of Trade,
Economics Working Paper, ECO2007/58, European University Institute.

Poschke, M. (2006). Employment Protection, Firm Selection, and Growth, Economics
Working Papers, ECO2006/35, European University Institute.

Romer, P. (1990). Endogenous Technological Change, Journal of Political Economy 98,
71-102.

Schott, P. K., (2004). Across-product Versus Within-product Specialization in Interna-
tional Trade, The Quarterly Journal of Economics, 119(2), 646-677.

Stoelting, S., (2009). International Trade and Growth: the Impact of Selection and
Imitataion, Economics Working Papers, ECO2009/21, European University Institute.

Smolny, W. (2003). Determinants of Innovation Behavior and Investment Estimates
for West-German Manufacturing Firms, Economics of Innovation and New Technology 12(5), 449-463.

Tauchen, G. (1986). Finite State Markov-Chain Approximations to Univariate and
Vector Autoregressions, Economic letters, 20, 177-181.

Van Long, N., Raf, H. and Staehler, (2008). Innovation and Trade with Heterogenous
Firms, Kiel Working Paper, 1430, Kiel institute for the World Economy, Kiel, Germany.

Verhoogen, E., (2008). Trade, Quality Upgrading, and Wage Inequality in the Mexican
Manufacturing Sectors, The Quartely Journal of Economics 123(2), 489-530.






Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 63


Yeaple, S. R., (2005). A Simple Model of Firm Heterogeneity, International Trade, and
Wages. Journal of International Economics, 65(1), 1-20.



Appendix


A Innovation Cutof Functions


Define A
P
= {(a, q) : a e A, q e Q . v(a, q) = v
P
(a, q)} the production support,
A
A
= {(a, q) : a e A, q e Q . v(a, q) = v
A
(a, q)} the process innovation support, A
Q
= {(a, q) : a e A, q e Q .
v(a, q) = v
Q
(a, q)} the product innovation support and A
AQ
= {(a, q) : a e A, q e Q . v(a, q) = v
AQ
(a, q)} the process
and product innovation support a
A
(q). Moreover, let B = {(a +?, q +?)} for ,?,> 0 arbitrarily small.
The innovation cutof function are defined as a
A
= {(a, q) : (a, q) e A
A
. (A
P
A
Q
A
AQ
) A
A

= ?}, a
Q
= {(a, q) : (a, q) e A
Q
. (A
P
A
A
A
AQ
) A
Q
= ?} and a
AQ
= {(a, q) : (a, q) e A
Aq
. (A
P
A
A

A
Q
) A
AQ
= ?}. The innovation cutofs in the
open economy case are defined in a similar way though the required notation becomes
heavier.



B Value Function in the Closed Economy


A firm with technology (a, q) has the following value function:


v(a, q) = max{v
P
(a, q), v
A
(a, q), v
AQ
(a, q), v
Q
(a, q)}. (2.11)


Defining with prime the next period variables:


1
v
P
(a, q) = maxt(a, q) + 1 + r max p

O
v(a
?
, q
?
)|(a
?
, q
?
,a, q)da
?
dq
?
, 0 (2.12)


is the Belman equation when no innovation investments occurred and a firm takes only
the static decision about pricing and production. The profit function includes the fixed
operational cost and the inner max operator indicates the option to exit the market.
Next:

1
v
A
(a, q) = maxt(a, q)÷z(a, q)÷c
a
+ 1 + r max p,z

O
v(a
?
, q
?
)|(a
?
, q
?
,a, q, z)da
?
dq
?
, 0 ,
(2.13)
is the firm value when a firm produces and innovates in process aiming at increasing next period
productivity. The fixed cost and the variable cost related to process innovation are







Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 64


c
a
and z(a, q), respectively. Analogously, the value function when, besides production,
both process and product innovation occur reads:


v
AQ
(a, q) = maxt(a, q) ÷ (z(a, q) + l(a, q)) ÷ c
a
÷ c
q
+ (2.14)
p,z,l


+

1 max
1+r



O


v(a
?
, q
?
)|(a
?
, q
?
,a, q, z, l)da
?
dq
?
, 0


.


This time the fixed cost are given by the sum of c
a
+ c
q
and the variable costs by
z(a, q) + l(a, q). Finally,


1
v
Q
(a, q) = maxt(a, q) ÷ l(a, q) ÷ c
q
+ 1 + r max p,l

O
v(a
?
, q
?
)|(a
?
, q
?
,a, q, l)da
?
dq
?
, 0 .
(2.15)
is the value function when a firm optimally specializes only in product innovation.



C Value Function in the Open Economy


A firm with technology (a, q) has the following value function:


v(a, q) = max{v
D
(a, q), v
EX
(a, q)},


where:
v
D
(a, q) = max{v
DP
(a, q), v
DA
(a, q), v
DAQ
(a, q), v
DQ
(a, q)},

and:


v
EX
(a, q) = max{v
EXP
(a, q), v
EXA
(a, q), v
EXAQ
(a, q), v
EXQ
(a, q)}.





(2.16)



(2.17)




(2.18)


v
D
(a, q) is the value if a firm produce only for the domestic market. Hence the profit
function is given by only the first part of equation (3),t(a, q) =t
D
(a, q). Using these profits in the value
functions listed above and consistently changing the superscripts gives the values for the
domestic firms in the open economy. Similarly, v
EX
(a, q) is the value of a firm that operates both
domestically and abroad. Its profits are given by both components of equation (3),t(a, q) =t
D
(a, q)
+t
EX
(a, q). Substituting these profits in the previous value functions and accordingly changing the
superscripts yield the values for the exporting firms.












Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 65


D Algorithm


The state space A · Q is discretized. The grid chosen is of 25 points for each state
yielding 625 technology combinations, (a, q).
20


In the closed economy the unknown variables are the growth rates, g
a
and g
q
, the ag-
o
gregate expenditure, and price index summarized by k = P 1÷
o
E. The growth rate of
1
labor productivity, g, is fixed exogenously. For given g
a
, g
q
= (G/G
a
) 1÷
q
÷ 1, and k
compute the stationary profitt(a, q; g
a
, k) and then the firm value function v(a, q; g
a
, k).
Firms' value function is computed through value function iteration. While iterating the
value function, the optimal policies for the investment in process and product innovation,
z(a, q; g
a
, k) and l(a, q; g
a
, k), are computed. The random walk processes, that govern the
transition of a and q, are approximated using the method explained by Tauchen (1987).
This step is time consuming since a firm's problem has to be solved via first order con- ditions for
each single couple (a, q), till convergence is reached. Once the value function
is approximated the algorithm computes the cutof functions a
x
(q; g
a
, k),a
A
(q; g
a
, k),
a
Q
(a; g
a
, k), and a
AQ
(q; g
a
, k). Then the transition matrix u
xI
is computed. After
guessing an initial¸ and normalizing its initial joint mean to zero, compute the ex-
pected value of entry. The free entry condition pins down the equilibrium value of k. Using the
equilibrium k then compute the firm value, the cutof function and the tran-
sition matrices for given initial g
a
. The binomial firm distribution is then determined
using µ = (I ÷ T
xI
)
÷
1
G as proved by Hopenhayn (1992). The algorithm is closed using
the condition on the mean of the entrant distribution,¸
e
=¢
e
µ, and pinning down the
equilibrium growth rate, g
a
, that satisfies this equation. Once g
a
is determined, g
q
can
be computed. All these steps are repeated until all conditions are jointly satisfied and
convergence is reached.

In the open economy case, the algorithm needs to consider also the export decisions
and hence in the value function iteration the export and domestic profits are evaluated nesting in
each of them the innovation decisions. Again this step yields the innovation policy functions and
all the cutof functions that are then used to compute the final
transition matrix u
xI
. The remaining part of the algorithm is the same as the one used
for the closed economy.





20
This discretization is due to the fact that the algorithm is computationally heavy given the presence of two states
and the endogenization of the innovation choice. On the one hand, increasing the grid size would improve the precision
of the calibration but would not afect qualitatively the results. On the other hand, the (a, q) combinations available
would increase quadratically in the grid size and the code would eventually become unfeasible. Hence, given t hat the
results are not qualitatively afected by the grid size, a quality and productivity grid of 25 points is a reasonable
restriction.





Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 66


E Closed vs. Open Economy and Trade Liberalization


Table 2.5: Model Statistics in the Closed and Open Economy




Turnover Rate
Process Innovation
Product Innovation
Process and Product Innovation
Non Innovators
Process Innovation Intensity
Product Innovation Intensity


Closed Economy
7.95%
13.47%
11.40%
18.50%
57.08%
1.21%
0.42%


Trade
Liberalization÷t


Open Economy
10.26%
10.38%
13.17%
16.32%
60.13%
1.41%
0.47%
0.
35

0.
3

0.
25

0.
2

0.
15
0.
06

0.05
5

0.
05

0.04
5

0.
04

0.65

0.6

0.5

0.45
0.1


0.
16

0.
15

0.
14

0.
13

0.
12

0.
11
1








1
1.
2








1.
2
1.
4








1.
4

t








t
1.
6








1.
6
1.
8








1.
8
2








2


0.
15

0.
14

0.
13

0.
12

0.
11

0.
1
1








1
1.
2








1.
2
1.
4








1.
4

t








t
1.
6








1.
6
1.
8








1.
8
2








2


0.
22

0.
20

0.
18

0.
16

0.
14
1








1
1.
2








1.
2
1.
4








1.
4

t








t
1.
6








1.
6
1.
8








1.
8
2








2


Figure 2.6: Trade Liberalization -t





















S
h
o
f N
o
I n
n
o
v
a
t o
r s


S
h
a
r e
o
f E
x
p
o
r t e
r s


E
x
i t R
a
t e


S
h
o
f P
r o
d
u
c
t I n
n
o
v
a
t o
r s


S
h
o
f P
r o
c
e
s
s
I n
n
o
a
v
t o
r s


S
h
o
f B
o
t h
I n
n
o
a
v
t o
r s






Chapter 2. Trade and Growth: Selection versus Process and Product Innovation 67





















1

0.
8

0.
6

0.
4

0.
2

0





















0.0
55

0.
0
5

0.0
45

0.
0
4




















TradeLiberalization÷ c
ex
(% of
average firm size)





















0.7

0.65

0.6

0.55

0.5


0.
1
8

0.
1
6

0.
1
4

0.
1
2

0.
1
0








0
3
4








3
4
6
8








6
8
100137171206240
c
ex








100137171206240
c
ex


0.
2
5

0.
2

0.
1
5

0.
1

0.
0
5
0








0
3
4








3
4
6
8








6
8
100137171206240
c
ex








100137171206240
c
ex


0.
2
2

0.
2
0

0.
1
8

0.
1
6

0.
1
4

0.
1
2
0








0
3
4








3
4
6
8








6
8
100137171206240
c
ex








100137171206240
c
ex


Figure 2.7: Trade Liberalization - c
ex


















S
h
o
f N
o
I n
n
o
v
a
t o
r s


S
h
a
r e
o
f E
x
p
o
r t e
r s


E
x
i t R
a
t e


S
h
o
f P
r o
d
u
c
t I n
n
o
v
a
t o
r s


S
h
o
f P
r o
c
e
s
s
I n
n
o
a
v
t o
r s


S
h
o
f B
o
t h
I n
n
o
a
v
t o
r s









Chapter 3




World Trade Patterns and Prices:
The Role of Cost and Quality
Heterogeneity




joint work with Teodora Borota



3.1 Introduction


World trade patterns and their relation to the technological development and income per
capita levels of the trading partners have been studied extensively in the theoretical and empirical
literature. In several recent studies, data on export and import prices has been exploited as
evidence of countries' technological development (particularly as the ability to produce higher
quality), trade specialization and demand schedules.
1
On the export side, Schott (2004) presents
evidence on positive variation of US import prices depend- ing on the exporter's income per
capita, suggesting positive relation between prices and exporters income per capita within the
same product category. Fieler (2007) finds that export prices increase with income per capita of
the origin country. On the import side, the same paper reports that import prices are positively
related to income per capita, as well as that countries of diferent income per capita import goods
of diferent prices from the same exporter. To the extent that prices may be used as a proxy for
quality, this evidence suggests that rich countries not only specialize in the production and
export of relatively higher quality goods, but that they devote larger share of income on higher

1
We

focus on empirical evidence that refers to product-level trade prices, and also the aggregate
prices. Manova and Zhang (2009) analyze the firm-level prices and relate the quality dimension of firm's productivity to
it's export status, import and export prices, trade values and the choice of trading partners, which also relates to the
present study.

68



Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 69

quality imports and possibly high quality total consumption.
2
Most of the literature that
proposes a theoretical basis for this analysis starts from either non-homothetic prefer- ences,
where diferent income levels generate diferent demand structures, or standard preferences with
arbitrarily imposed diferent "love for quality" parameters in the North and the South. The supply
side mechanisms result in a comparative advantage in the production of goods that are in high
domestic demand.
3
Non-homothetic preferences might be the immediate natural assumption for
explaining reported increase in tradedgoods' prices with income per capita, but are certainly not
the only factor. Although the arbitrary parametrization of preferences might be regarded as a way
around modeling the black box of demand heterogeneity across countries, non-homothetic
preferences do have some empirical support in the micro-level data. The purpose of this paper is
not to contradict these findings, but to show that when the attention is shifted from modeling
preferences to modeling technology more closely, standard preferences model with fixed
operational and trade cost can yield the stated predictions as well.

We wish to give more weight to the supply side mechanisms and their role in shaping the
demand structure and therefore, we use homothetic preference structure. Specifically, the focus is
on the technology endowments of the North and the South which are the main determinants of
the production and export specialization, and the relative income per capita of the two regions.
The North has a higher level of technological development, while the South lags behind the North
and uses a lower level of technology. Firms in each region are heterogeneous in two technology
(productivity) dimensions: product quality and labor efciency which together determine the firms'
domestic and foreign market profitability. Existing models of trade and heterogeneous firms that
introduce only one productivity dimension, such as Melitz (2003), predict a negative relation
between ex- port prices and income per capita since higher technological development implies
higher income but also higher cost efciency and thus lower prices. Empirical evidence on ex- port
prices calls for the introduction of a diferent productivity dimension in a way that it generates
positive relation between productivity and price. Several papers introduce the quality dimension
of firm heterogeneity. In this sense, Northern technology allows this region to produce relatively
higher productivity-higher price varieties, while the South specializes in the production of lower
quality-lower price varieties.

Baldwin and Harrigan (2007) develops a model of trade and heterogeneous firms in the
quality dimension. They assume that quality rises faster than marginal cost and thus high
quality-high cost varieties are the most profitable ones. Therefore, export prof- itability is
increasing in quality (and price) monotonically. Johnson (2010) introduces

2
These

findings, however, should not be taken as a straightforward support for the diferences in
expenditure distribution over quality in the North and the South, as traded goods might present only a minor share of
total consumption.
3
See Fajgelbaum, Grossman and Helpman (2009) for a recent discussion.





Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 70


two dimensions of firm heterogeneity, but for the purpose of empirical analysis, two
dimensions again collapse to a single by assuming that quality is mechanically related to
capability (quality-cost ratio). Using this set-up for the analysis of the North-South trade,
counterfactual predictions are derived. Lower aggregate expenditure of the South implies that
only the most profitable, so highest price firms can cover the fixed cost of trade and export to
the South, while the pool of exporters to the North is larger. This prediction does not match the
empirical evidence, as it results in the negative relationship between import prices and income
per capita conditional on exporter.

We wish to separate the quality and efciency dimensions and introduce a measure of
cost efciency which afects the marginal cost independently of the quality. Each firm (variety) is
characterized by a quality level which afects positively both utility and the cost of production,
and by a labor efciency level which decreases the marginal cost. These two dimensions together
determine the productivity level of the firms, which are distributed across quality-efciency pairs,
with the Southern joint distribution having a lower mean due to its technological lag behind the
North. In this framework, the export decision of any firm depends on its productivity pair which
determines the profitability and thus the ability to cover the fixed cost of exporting. Less
profitable firms that export only to the North, also include those with highest quality but lower
efciency, and therefore a higher price. This contributes to a rise in the average import price with
income per capita conditional on exporter. In this sense, Northern average import price is higher
not because it consumes higher quality than the South, but due to the fact that it consumes also
the high priced - high quality varieties. Given the right-skewed distribution of firms in
equilibrium, varieties of this type are relatively numerous and this amplifies the efect on the
average import price and insures that North imports higher price varieties on average.

Two dimensions of firm productivity have been identified also in the industry surveys.
Several empirical studies document that firms distinguish between two diferent types of
investment in R&D - process or product innovation, which raise the firms' efciency or product
quality, respectively. Huergo and Jaumandreu (2004a) report a survey of Spanish firms while
Parisi et al. (2006) present a classification of Italian firms based on their R&D strategy (process,
product, both or none). Similar data are also avail- able for Germany, Great Britain and
Nederlands. Moreover, Huergo and Jamandreu (2004b) estimate that process and product
innovation have diferent contributions to firms' growth.

An important justification for the introduction of two productivity dimensions is found
in the recent debates in the literature on how valid unit values actually are as a proxy for the
product quality. Hallak and Schott (2010) oppose the large literature that associates






Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 71


cross-country variation in export unit-values with variation in product quality, implicitly
assuming away cross-country variation in quality-adjusted prices. They allow for price variation
induced by factors other than quality, e.g., comparative advantage or currency misalignment, and
find that observed unit value ratios can be a poor approximation for relative quality diferences,
that quality is converging more rapidly than income levels across countries, and that countries
difer in growth strategies - high-quality versus low- price. These findings directly provide
support for our modeling of firms' productivity.
4


In aggregate terms, the greater income of the North compared to the South implies not
only a greater expenditure on any good that is available in both regions, but higher levels in equal
proportion across goods, due to homothetic preferences. However, with fixed cost of export only
a subset of varieties is exported to foreign markets, and the resulting expenditure shares on
certain quality are not equal across regions. The North spends a lower share of income on low
quality varieties originated from the South, while the South spends a lower share on high quality
produced in the North, both relative to the other region's share of expenditure on those varieties.
If the income diference between the regions is sufciently large, the statement above holds also in
absolute terms.

The analysis of trade intensities within and across regions refers to the Linder hypothesis.
Linder (1961) argues that on the demand side, countries with high (low) income per capita spend
a larger fraction of their income on high (low) quality goods. On the supply side, countries
develop a comparative advantage in the goods that are in high domestic demand, so high (low)
income countries produce high (low) quality goods. Both these premises are predicted by our
model, but Linder's hypothesis goes further. The demand and supply premises are combined in
order to argue that the overlap of production and consumption patterns between countries of
similar income per capita should induce them to trade more intensively with one another. Rich
trade more with rich, while poor trade with poor. Our model predicts the highest intensity and
value of the North- North trade. The ordering of the South-South and the North-South trade
depends on the fixed and/or variable costs of trade, in particular on their asymmetries that are
conditional on the origin and destination country. With symmetric costs, North-South trade is of
higher value, but the result is reversed when stronger restrictions on Southern exports to the
North are imposed. However, there is no robust empirical support of the Linder hypothesis.
Namely, it is important to ascertain the level of aggregation at which the "Linder" mechanism
might operate. Hallak (2008) shows that the trade intensities prediction is valid on both sides of
income per capita distribution at the sectoral level (for some sectors), but is strongly rejected
when data is aggregated over sectors.

4
See

also Khandelwal (2010) who estimates the quality of U.S. imports using a procedure that relaxes
the strong quality- equals-price assumption.







Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 72


The rest of the paper is organized as follows, Section 2 presents the closed economy
model set-up, Section 3 present the open versions of the model with symmetric and asymmetric
countries, Section 4 discusses the results of the numerical exercise with a 4-country North-South
scenario, while Section 5 concludes.




3.2 The Model Set-up


3.2.1 Consumers


Consumers have homothetic preferences and every period they choose consumption and
supply labor inelastically at the wage rate w. The aggregate measure of population (labor) is L.
Consumers allocate optimally the aggregate consumption X across difer- entiated varieties
produced by operating firms. The utility function is given by a quality
augmented Dixit-Stiglitz utility function,

1
o
U (t) = (q(i)x(i, t))
o
di , (3.1)
ieI

where x(i, t) is the quantity and q(i) is the quality of a variety i e I consumed at time t.
The standard CES utility index is augmented to account for the quality variation across products
where quality acts as a utility shifter: a consumer prefers high quality over low quality products.
The elasticity of substitution between any two goods is constant and equal too = 1/(1 ÷o)> 1,
witho e (0, 1).

Consumers derive the optimal demand for each good, maximizing their utility subject
to the individual budget constraint E(t) =

ieI
p(i, t)x(i, t)di, where E(t) presents total
expenditure in the country and p(i, t) is the price of variety i e I at time t. The demand
for product x(i, t) is given by


x(i, t) =

P (t)q(i)
o

p(i, t)

1
1÷o


X(t) =

q (i )
o

p(i, t)

1
1÷o


o
P (t) 1÷
o
E(t)


(3.2)

with P (t) as the price-quality index defined by

o




o÷1
o
P (t) =
ieI
p(i, t)
q(i, t)
o÷1
di and X
t
= U
t
. (3.3)


Given the aggregates, the optimal expenditure (r(i, t)) decision across varieties is

o
r(i, t) =
P (t)q(i)
p(i, t)
1÷o
E(t). (3.4)





Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 73


This paper focuses on the analysis of the steady-state equilibrium in which all variables
are constant and we omit the time subscripts in the further text.



3.2.2 Firms


Firms difer in two dimensions of heterogeneity. The first source of heterogeneity is
labor efciency (in further text, efciency), a(i) e R++, which increases the marginal
productivity of labor, as in the seminal paper of Hopenhayn (1992). The second source is
quality of a firm's variety, q(i) e R++ (0, 1), which decreases the marginal productivity
of labor. In this respect, a higher quality variety implies a higher variable cost as
in Verhoogen (2008), but contributes positively to consumers' utility. The production
technology has the following form

x(i ) = a (i )
q
n(i ), _
q (i )


(3.5)

where n(i) is the production labor employed by firm i and_, q e (0, 1). Firms distribute
over quality and efciency, and we assume that each firm produces only one variety so that the
index i identifies both the firm and the corresponding variety it produces. Firms enter and exit
the market and the industry is characterized at the steady-state equilibrium.



3.2.2.1 Production Decision


Each firm is the monopolistic producer of its own variety. Firms pay a fixed operational
cost, c
f
, expressed in terms of labor in order to produce and this cost is responsible for
firms' exit from the market. Solving the standard monopolistic problem, firms charge a
price p(i), that is
p(i) = wa(i)
_
, q
q

o (i )
(3.6)
where common wage rate, w, is hereafter normalized to one. Substituting the expression
for prices in the demand function,


1 o
x(i) = (a(i)
_
q(i)
o
÷
q
o)1÷
o
P1÷
o
E, (3.7)


it follows that x(i) is increasing in a and it is decreasing in q if q>o. We restrict our
attention to the specification when this condition holds.

Firms revenues and profits are then given by








Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 74




o o
r(a, q) = (a
_
q
1
÷
q
)1÷
o
(oP )1÷
o
E (3.8)
o o
t(a, q) = (1 ÷o)(a
_
q
1
÷
q
) 1÷o(o P ) 1÷oE ÷ c
f
,


where the ratio of the revenues of any two firms is a function of the ratio of their
productivities,
o
r ( a
i
, q
i
) =
a
_
q
1
÷qii
1÷o
. (3.9)
r (a
j
, q
j
)
a
_
q
1
÷qjj


It is important to note here that profitability of a firm is increasing with its productivity
(in either dimension), but it is not a monotonous function of the price. Price is increas- ing in
quality but decreasing in efciency, while profits increase in both productivity dimensions. In this
sense the patterns present in previous literature, monotonously neg- ative (Melitz 2003) or
positive (Baldwin and Harrigan 2007) relation between price and profitability, is broken in this
paper. This relationship will become crucial for shaping the average price pattern across the firm
partitioning space, particularly concerning the exporter/non-exporter partitioning in the open
economy scenario. The most profitable firms are the most productive in both dimensions, so
their varieties have neither the highest nor the lowest price. Less productive firms have lower
efciency and/or quality, and they include both the firms that charge lower price compared to the
most produc- tive, but also those with the highest prices (high quality-low efciency firms).
Therefore, in the context of the closed economy, the average price of the exiting firms may as
well be higher than the average price of the surviving varieties.

On the other hand, the specification of_ andq afects the concavity of profits and the
price function in the two productivity dimensions, but also the ratio of the elasticities with respect
to each dimension. With_ bigger (smaller) than 1 ÷q the profits increase faster along the efciency
(quality) dimension, which shapes the isoprofit curves in the (a, q) space and thus the exit
productivity threshold functions.



3.2.2.2 The Exit Decision


Every firm faces an exogenous probability of a bad shocko which forces the firm to exit
the market. Besides this exogenous exit, firms exit the market when their profits are not
enough to cover the fixed operational cost, c
f
. The two sources of firm heterogeneity
imply that the thresholds that characterize the border between exit and survival in the
market are given by the infinite combinations of the (a,q) couples. For this reason, it becomes
convenient to express the reservation values in terms of efciency as a function







Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 75

of quality
5
, a(q), and to obtain a cutof function rather than cutof values as in one
factor heterogeneous firm models. For a given q e Q it is possible to define the following
exit cutof functions




a
x
(q ) =



c
f




o


1÷o
o



11


1
_




.




(3.10)
(1 ÷o)P1÷
o
E o q
1
÷q


The exit cutof functions are decreasing in quality produced: high quality allows for
an easier survival. A firm characterized by a low level of efciency but a high quality may still
find it optimal to produce. However, with_> 1 ÷q, the cutof efciency is decreasing in quality at a
decreasing rate. We assume this condition holds, as it captures the idea of increasing difculty in
keeping the market shares for the firms that produce high quality varieties with low efciency
which results in a high price. In other words, this assumption represents minimum (cost)
efciency requirements for survival. This also relates to the literature on the types of R&D
investment and their contributions to firms' profitability and growth. Huergo and Jamandreu
(2004b) estimate that process innovation contributes for about 77% of the yearly growth rate of
aggregate productivity, while product innovation can account for about 23%. The estimates do not
apply directly to our specification, but may point to higher returns to firm's efciency then
product quality.



3.2.2.3 Firms Entry


Each period, M firms enter the industry and pay a sunk entry cost, c
e
, expressed in
terms of labor. After paying the entry cost they draw the product quality and efciency
level (productivity vector (a,q)) from a bivariate distribution G(a, q), with corresponding density
g(a, q).

We assume that the free entry condition holds in equilibrium. Firms enter the industry
until the expected value of the firm, v, is equal to the entry costs. With the value of the firm given
as the discounted future ?ow of profits, and with no time discounting as in
Melitz (2003), the free entry condition reads



v=




ax(q)




Q


t(a, q) g(a, q)dqda = c . e
o



(3.11)

5
It is equivalent to express product quality as a function of efciency, q(a). Using a specific formulation for the cut-of
function does not afect the implications of the model.









Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 76

3.2.3 Cross Sectional Distribution and Aggregates


The density of firms conditional on successful entry is computed as


µ(a, q Pin
g(a,q
)
if a > a
x
(q)
(3.12)
0 otherwise
where P
in
=
ax(q)
Q
g(a, q)dqda
is the ex-ante probability of firm survival.

The average productivity measure as a function of the exit cutof is computed as

1÷o
o
o
µ˜=
ax(q)

Q
(a
_
q
1
÷
q
)
1÷o
µ(a, q)dqda . (3.13)


The average productivity level is determined by the cutof function, a
x
(q), and thus the
average revenue and profit, as the functions of the average productivity, also depend on
the cutof function. Using (3.9), for any given q, we obtain

o
r = r( ˜) = µ
˜µ
a
x
(q)
_
q
1
÷q
1÷o


o
r (a
x
(q ), q ) (3.14)
t =t ( ˜) = µ
˜µ
a
x
(q)
_
q
1
÷q
1÷o
(1 ÷o )r (a
x
(q ), q ) ÷ c
f
.

As the profit of a cutof firm equals zero and it's revenue is equal to

cf
1÷
o
,

it follows
that the relationship between the average profits and the exit cutof function can be
expressed as


o
t=
˜µ
a
x
(q)
_
q
1
÷q
1÷o
÷ 1 c
f
.


3.2.4 Steady-State Equilibrium


The free entry condition also represents a relation between the average profits and the
cutof productivity, i.e. cutof efciency for any given level of quality. Therefore, the
two equilibrium conditions,

o
t=


t=
˜µ
a
x
(q)
_
q
1
÷q
o c
e

1 ÷ G(a
x
(q, q))
1÷o
÷ 1 c
f
Zero Cutof profit


Free Entry,
(3.15)








Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 77


define the equilibrium average profits and the cutof productivity. The aggregate stability
condition requires that the mass of successful entrants in the market equals the mass of
exiting firms, i.e. P
in
M =oI. The labor market clearing condition assumes that the
total labor is used either in production, where aggregate income equals the diference
between aggregate revenue and aggregate profits, or to pay the fixed cost of entry, M c
e
.
Therefore, using the stability and free entry conditions,

L = (R ÷H) + M c
e
= (R ÷H) + PI c
e
= (R ÷H) + It = (R ÷H) + H = R. o
in

The mass of operating firms is then derived as

I = R = Lt1+ co) (÷
r
f


which in turn determines the equilibrium price-quality index as P =

1
1
Io÷1 . o
closes the characterization of the steady-state equilibrium.
o˜µ
This




3.3 Equilibrium in the Open Economy


3.3.1 Symmetric Countries


We now assume that there are two regions open to trade, home and foreign (denoted
by -), which are symmetric in all preference and technology dimensions except that they produce diferent
varieties. Consumers have the same homothetic preferences and they supply labor inelastically at
the wage rate w, with w = w
-
. Labor is not mo- bile across regions and the aggregate measure of
population in a region is L, L = L
-
. Consumers now allocate consumption X across diferentiated
varieties produced by do- mestic firms and those imported from abroad. The measure of available
goods is hence given by domestic goods of measure I
D
and imports from abroad I
-
X
, and similarly
for the foreign region, I
-
= I
-
D
+ I
X
. Although consumer preferences are the same in both regions, the
bundles of varieties consumed are diferent. Due to firm selection into exporters and non-
exporters firms, a subset of varieties in each country is not ex- ported, resulting in a diferent
consumption composition. However, due to symmetry in technology, productivity levels and
prices of non-exported and exported goods will be the same across countries, and thus the price-
quality indices will be the same, although relating to diferent bundles. This also assumes that we
abstract from the variable trade costs which may difer across origin and destination market and
thus distort the relative prices of tradables, and compared to non-tradables. Namely, we are
interested in trade patterns and prices that are a result of regions' technologies and firm
partitioning, and





Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 78


thus we assume no trade cost except for the fixed cost of becoming an exporting firm.
Therefore, conditional on being exporter, a firm charges the same price in domestic and foreign
market.

Firms still pay a fixed operational cost, c
f
, expressed in terms of labor in order to
produce, but now also incur a fixed export cost c
ex
, expressed in terms of labor, in
order to export. The fixed export cost generates the partition between exporter and non
exporter firms and it is assumed to be the same across regions.

Firms total profits are the sum of the profits obtained in the domestic market and the
profits from the foreign markets when it is profitable to export. The optimal profits for
home region are given by




t(a, q) =t
D
(a, q) + max{0, t
X
(a, q)} (3.16)
o
t
D
(a , q ) =
a
_
q
1
÷
q
o
w
a
_
q
1
÷
q
o
1÷o

o
1÷o
o
(1 ÷o)P1÷
o
E ÷ wc
f


o
t
X
(a , q )
=
w
(1 ÷o)P
-
1÷
o
E
-
÷ wc
ex


The max operator int indicates the choice of each firm to specialize only in the domestic
market, or to open to foreign markets when the profits derived from exporting exceed the
fixed cost of export, c
ex
. As the specification of_ andq shapes the isoprofit curves in the
(a, q) space, this also has implications for the export productivity threshold functions.

Similarly to the closed economy cutof functions, it is convenient to express the export
reservation value in terms of efciency as a function of quality, a(q). For a given q e Q
it is possible to define the following export cutof function for the home region,



a
ex
(q) =



wc
ex




o


1÷o
o



1w


1
_



(3.17)
(1 ÷o)P
-
1÷
o
E- o q
1
÷q


As in the case of exit cutof, the export cutof function is decreasing in quality which
implies that a firm characterized by a low level of efciency but a high quality may still find it
optimal to export. With_> 1 ÷q, the cutof efciency is decreasing in quality at a decreasing rate which
represents the minimum (cost) efciency requirements for exporting.

The cutof functions are increasing in the wage as higher wage implies higher fixed cost
of export and higher export price, while they decrease in the total expenditure and the price
index. Higher expenditure (income) of the destination market implies higher





Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 79


purchasing power of the market, while higher price index represents lower competition
pressures on the exporting firm. As the total expenditure depends on the size of the population
in the destination country, it follows that a larger export market implies higher profitability and
lower cutof productivity levels.

With symmetric wages and technology level of exporters and non-exporters across re-
gions, and thus price-quality indeces and expenditures, the optimal profits and cutof functions are
symmetric and the - superscript can be dropped. The export cutof func-
tion difers from the exit cutof function only in the fixed cost term, c
ex
and c
f
. With
c
ex
> c
f
, the exit cutofs are associated with lower productivity levels than the export
cutofs.



3.3.1.1 Cross Sectional Distribution and Aggregates


The density of firms conditional on successful entry is computed as in the closed economy
scenario, equation (3.12). The ex-ante probability of firm survival is still given by
P
in
=
ax(q)
Q
g(a, q)dqda, and we define the ex-ante probability that a successful firm
exports as P
ex
=
1
÷G(aex(q),q
)
. To compute the weighted mean of productivity, we P in
define the mass of incumbents in each country. Hence, I
D
also represents the measure
of varieties produced in each country, so I
ex
= P
ex
I
D
is the mass of exporting firms
and exported varieties. This means that the mass of available varieties in each region is
given by the mass of varieties produced domestically plus the mass of varieties imported:
I = I
D
+ I
-
. With symmetry, I
ex
= I
-
.
ex ex

The average weighted productivity is computed taking into account not only the output
share of the domestic firms, but the additional export share of the more productive
firms:

1÷o
I
D

˜
x
1÷
o
+ (I
D
I+xI ) ˜
e
1÷o


where
˜= µ
( I
D
+ I
ex
)
µ
o
e ex
o
µ
x
o
(3.18)


˜
x
= µ



ax(q)



Q


(a
_
q
1
÷
q
)


o
1÷o


µ(a, q)dqda

1÷o
o


(3.19)


˜
ex
= µ



aex(q)



Q


(a
_
q
1
÷
q
)

o
1÷o


µ
ex
(a, q)dqda
1÷o
o


,


with µ
ex
(a, q) as the conditional distribution of exporting firms, given that the firm
survives in the market. Zero cutof profit and free entry conditions determine the steady
state equilibrium in open economy, but also taking into account the partitioning of firms





Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 80


into exporters and non-exporters and the associated export cutof function. The model
is solved in the same manner as described in the closed economy section.



3.3.2 Asymmetric Countries


We now assume two asymmetric regions, home and foreign, which have the same pref-
erence structure but difer in two technology dimensions and produce diferent varieties. The
consumers allocate their expenditure on domestic and foreign varieties, but due to asymmetry in
productivity levels and thus the wages and prices of goods, the resulting consumption
composition and price schedules will be diferent across regions. This yields diferent price indices
as averages of the quality weighted prices of all varieties consumed by a region, domestically
produced and imported.

Firms in both regions distribute over quality and efciency, and since the regions' asym-
metry takes the form of diferent level of productivity, we refer to the regions as North (N ) and
South (S), the technologically developed and the developing region, respec- tively. Firms in the
North lead in both productivity dimensions while firms in the South lag behind the more
advanced Northern technology.

The wage rate is w
N
in the North and w
S
in the South, with w
N
> w
S
. Labor is not
mobile across regions and the aggregate measure of population in each country in the North and
the South regions is L
N
and L
S
, respectively. The fixed operational cost incurred by firms
triggers firm exit while the fixed export cost generates the partition between exporter and non
exporter firms. Given the same labor requirement for the fixed cost of operation and export in
the North and the South, it follows that both costs are higher in the North due to its higher wage.



3.3.2.1 Firms Entry


After paying the entry cost, firms in both regions draw the product quality and efciency
level (productivity vector (a,q)) from a bivariate distribution G
J
(a, q), J = {N, S}, with
corresponding density g
J
(a, q). The density function in the North, g
N
(a, q), is assumed to be log-
normal and exogenous while g
S
(a, q,µ
N
) is log-normal but its mean, g
S
, is determined as au fraction
of the incumbents joint mean in the North, µ
N
.
6
The assumption attempts to capture the idea of imitative
R&D in the South which copies the technology of the North at a certain lag due to high difculty
of copying the advanced goods. As we don't model the R&D process endogenously, we might
justify

6
This

specification is similar to the one used in Gabler and Licandro (2005).







Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 81


this assumption by the evidence on diferences in North-South TFP levels documented
in the literature.
7


When solving the model, we define another equilibrium condition besides the zero cutof
profit and free entry conditions. This is the trade balance requirement which equates the values
of Northern and Southern exports. At the same time, it is the third equa- tion linking the relative
South-North wage (Southern wage when Northern is taken as numeraire and normalized to one)
and the parameter measuring the technological lag of the South,u. This allows for solving the model for
the South-North relative wage.



3.3.3 Four Countries, Open Economy Model


We wish to analyze the trade patterns and prices of tradables at the regions' aggregate
level but also conditional on importer/exporter GDP per capita, and thus we construct a four
countries scenario. We propose a two region North-South trade model where each region, the
North and the South, consists of two symmetric countries (two symmetric North and two
symmetric South).
8
The measure of available goods in each country is hence given by domestic
goods of measure I
JD
, imports from the other country of the same region, I
JJ
, and from the two
countries of the other region, I
JK
, with J, K = {N, S}, J = K. Thus, I
N
= I
ND
+ I
NN
+ 2I
SN
for the
North and similarly for the South, I
S
= I
SD
+ I
SS
+ 2I
NS
. We use the same index to represent both
the region and the country of a particular region, as we assume symmetry in all environment
dimensions of the countries within a region. However, the varieties they produce are perceived as
diferent by the consumers and thus are all in demand, i.e. each country's consumers demand
varieties from the other country of the same region as well as the goods of both countries of the
other region.



3.3.3.1 Production and Export


Firms total profits are the sum of the profits obtained in the domestic market and the
profits from the foreign markets when it is profitable to export. Hence the optimal

7
See

for example, Cordoba and Ripoll (2008), Jerzmanowski (2007), Hall and Jones (1999).
8
With four countries, we can analyze the diference in variables concerning e.g. Northern exports
to both Southern and other Northern country, as well as its imports from countries at diferent income level. In other
words, this model specification at the same time represents both a North-North and a North-South trade model.












Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity

profits with J, K = {N, S}, J = K are given by


t
J
(a, q) =t
JD
(a, q) + max{0, t
JJ
(a, q)} + 2 max{0, t
JK
(a, q)}
o

82




(3.20)
a
_
q
1
÷
q
o 1÷o o
t
J
D
(a , q ) = (1 ÷o)P
J
1÷
o
E
J
÷ w
J
c
f

w
J

o
t
J
J
(a , q )


t
J
K
(a , q )
=t


=t
o
o÷1

o
o÷1
a
_
q
1
÷
q
o
w
J

a
_
q
1
÷
q
o
w
J
1÷o

o
1÷o
o
(1 ÷o)P
J
1÷
o
E
J
÷ w
J
c
ex


o
(1 ÷o)P
K
1÷
o
E
K
÷ w
J
c
ex

where superscript JJ denotes exports to the symmetric country of the same region,
while JK stands for export to a country of the other region.

Since export profits depend on the aggregate variables of the foreign region, this is the
channel through which the aggregate economy of the foreign region afects the profitabil- ity of the
domestic firms.

For a given q e Q we define the following export cutof functions for the North and the
South,





a
J
J
(q ) = ex




w
J
c
ex





o




1÷o
o




1 w
J
t



1
_





(3.21)
(1 ÷o)P
J
1÷
o
E
J


w
J
c
ex

1÷o
o
o q
1
÷q

1 w
J
t

1
_
a
J
K
(q ) = ex
o
(1 ÷o)P
K
1÷
o
E
K
o q
1
÷q
.


The order of the cutofs for export to diferent regions is determined by the ratio of
o
the aggregates of the two regions, P 1÷
o
E. However, the exit cutofs depend only on
the domestic aggregates. For a given quality firm partition in both the North and the South is
such that firms with low level of efciency (a) exit the industry, firms with intermediate levels
produce only for the domestic market, while the most efcient firms produce for both the domestic
and the foreign markets, first for the market in the North and then for the foreign markets in both
regions. The stated order of the firm partition
is assured by the conditions on the fixed costs of operation and export.
9

9
See

Appendix A. for the discussion on exit and export cutofs.













Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 83

3.3.3.2 Cross Sectional Distribution and Aggregates


The density of firms conditional on successful entry is computed as

g
N
(a,q)
NP
in
i f a > a
N
(q ) x
µ
N
( a , q
0 otherwise (3.22)
for the North firms and similarly for the South firms,

g
S
(a,q)
SP
in
i f a > a
S
(q ) x
µ
S
( a , q
0 otherwise, (3.23)
where P
in
= N aN (q)
Q
g x
N
(a, q)dqda
and P
in
= S aS (q)
Q
g x
S
(a, q,µ
N
)dqda
are the ex-
ante probabilities of surviving for the firms in the North and the South, respectively.
In a similar way we can define the ex-ante probability that a successful firm exports.
That is, P
ex
N
= N

1÷G(a
NN
(q),q
)
, ex

P
ex
S
= N

1÷G(a
NS
(q),q
)
, ex

P
ex
N
= S
1÷G(a
SN
(q),q)ex
and P
ex
S
= S
1÷G(a
SS
(q),q)ex
P
i
N
n
for North and South.
P
i
N
n
P
i
S n
P
i
S n
I
ND
and I
SD
represent the measure of varieties produced in each country of the North
and the South, so I
NN
= P
ex
N
I
ND
, I
NS
= P
ex
S
I
ND
, I
SN
= P
ex
N
I
SD
and I
SS
=
ex N ex N ex S ex
P
ex
S
I
SD
are the masses of exporting firms and exported varieties in the North and the S

South, respectively. This means that the mass of available varieties in each country is
given by the mass of varieties produced domestically plus the mass of varieties imported:
I
N
= I
ND
+ I
NN
+ 2I
SN
for the North, and I
S
= I
SD
+ I
SS
+ 2I
NS
for the South.
ex ex ex ex

The average weighted productivity for the North is given by


˜
J


I
JD


o


JJ


o
µ =
JD + I
JJ
+ 2I
JK
) ˜
JD
1÷
o
+ (I
JD
+ IIJex + 2I
JK
) ˜
JJ
1÷o
(I
ex

2I
JK
ex
µ
x


o

1÷o
o
J
ex
ex
µ
ex
(3.24)
+
(I
JD + I
JJ
+ 2I
JK
) ˜
ex
ex
ex

w
h
e
re J, K = {N, S}, J=K and
ex
µ
J
K

1
÷
o



µ
x
˜
J
D
=




aJ (q) x




Q


(a
_
q
1
÷
q
)


o
1÷o



µ
J
(a, q)dqda

1÷o
o



(3.25)


˜
J
J
µ
ex



˜
J
K


=



aJJ (q) ex



Q


(a
_
q
1
÷
q
)

o
1÷o


o


µ
JJ
(a, q)dqda ex
1÷o
o


1÷o
o
µ
ex
=
aJK (q) ex Q
(a
_
q
1
÷
q
)
1÷o
µ
JK
(a, q)dqda ex
.






Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 84

Variables µ
JJ
(a, q) and µ
JK
(a, q) are the conditional distributions of firms exporting
ex ex
to the North and of firms exporting to both regions, respectively, given that the firm
survives in the market.



3.3.3.3 Steady-State Equilibrium


The steady state equilibrium is characterized by prices (p
JD
, p
JX
), wages (w
J
), exit and
export cutof functions (a
J
(q), a
JJ
(q), a
JK
(q)), firm distributions (µ
J
, µ
JJ
and µ
JK
),
x ex ex ex ex
number of firms in each region (I
JD
) and the aggregate expenditure and price indices
(E
J
, P
J
) such that


• consumers choose consumption optimally and firms choose prices to maximize their
profits

• exit and export cutof functions satisfy the conditions given by (3.10) and (3.21)

• entry and exit are such that the stability conditionoI
JD
= P
in
M
J
and the free J

entry condition are satisfied

• distribution of firms in the North and the South are given by (3.25)

• number of operating firms is such that the labor markets clear, i.e. total labor
is used for domestic and export production and also for the fixed cost of entry,
operation and export


L
J


=



aJ (q) x



Q


n(a, q)µ
J
(a, q)I
JD
dqda +



aJJ (q) ex



Q


n(a, q)µ
J
(a, q)I
JD
dqda 26) (3.
+

n(a, q)µ
J
(a, q)I
JD
dqda + c
e
M
J
+ c
ex
(P
ex
J
+ P
ex
K
)I
JD
+ c
f
I
JD
aJK (q) ex Q J J


• the trade balance condition is satisfied, implying that the bilateral North-North,
South-South, North-South and South-North trade is balanced.
10



We solve the model numerically using the value of parameters which are calibrated to
match the recent data on the aggregate trade values (shares of North-North, North- South and
South-South exports in the total world exports, relative wage of the South compared to the
North) and the firm-level variables.

10
Due

to symmetry between the countries of the same region, trade balance depends only on the values
of export ?ows between countries of diferent regions in equilibrium.










Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 85

3.3.4 Calibration


In our quantitative exercise we choose the preference parameter,o, exponents on pro-
ductivity and quality in the production function,_ andq, exogenous exit probability,o, the size of the
countries, L
N
and L
S
, and the mean of the entrants in the North, g
N
.o is set equal to 0.73 to match
a mark-up over the marginal cost of 36%.
11
_ andq are equal to 0.5 and 0.86, respectively. The
results do not change qualitatively if_ andq change as long as the conditions on these two exponent
are satisfied.
12
The exogenous death probability is fixed equal to 0.5% and hence firms's life
expectancy is a priori of 200 years.
13
Finally, L
N
, L
S
, and g
N
scale and locate the economy in the
space (a, q). The population is assumed to be the same in both the North and the South and
normlized to one while g
N
is set equal to 4.

The remaining parameters are the technological gap between the North and the South,u,
the fixed cost of entry, c
e
, the fixed operational cost, c
f
, the fixed cost of export, c
ex
, and
the entrants distribution variance for the North and the South (assuming equal variance
over productivity and quality and across countries). These parameters are calibrated to match a
number of salient features related to the 2006 data on the within and across region export shares
in the total world exports, exit and entry rates in the manufacturing industry and the South-North
relative wage. The data on export shares are taken from The OECD Policy Brief "South-South
Trade:Vital for Development", August 2006, available at:
www.oecd.org/publications/Policybriefs and Goksel (2008). The reported export shares are
52.69% for the North-North trade, 40.86% for the North-South and 6.45% for the South-South
exports. Bartelsman et al. (2004) compute that the average firms exit rate in the data for the
North is around 10%, while it is slightly higher in the South, 20%. Accordingly to the World
Bank, International Comparison Program database, online edition, 2009 the relative South-North
wage in the manufacturing sector is on average 0.4.

Table 2 in Appendix B summarizes the parameters values both exogenously set and
calibrated, the empirical targets used for the calibration and the corresponding model moments.


11
For


more details on mark-ups in models with heterogenous firms and fixed costs see Ghironi and
Melitz 2005.
12
This also includes the specification with_ =q> 0.5
13
Atkeson and Burstein (2007) and Luttmer (2007) find the same value calibratingo.












Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 86
3.4 Four-Country Scenario Results


This section presents the numerical results of the North-South trade model with four
countries, two symmetric Norths and two symmetric Souths. Given the productivity lag of the
entrants in the South behind the incumbents in the North, the selection of the firms in the
equilibrium results in the distribution of operating firms over productivity vectors in the North
and the South as presented in Figure 1. The equilibrium productivity lag of the South results in
the positive North-South wage diferential in equilibrium.























Figure 3.1: Incumbents Distribution over Productivity and Quality


When the North and the South are open to trade, the South produces the low productiv-
ity varieties that are demanded domestically but also by the North whose international
competitiveness in this portion of the distribution is weakened due to lower produc- tion cost in
the South. On the other hand, Northern firms are more spread out on the whole remaining area of
the productivity space, higher efciency and higher quality. Few firms in the South reach these
productivity levels and thus the North specializes in the production and export of higher (a, q)
varieties.

Figure 2. presents the partitioning of the firms across the (a, q) space into exiting
firms, domestic producers and exporters of two types, those that export only to the North and
those that export both to the North and the South. Analyzing the partition over the efciency
dimension, the lowest a firms exit the industry in both regions, but the exit cutof in the North is
higher than in the South due to higher absolute value of the fixed operational cost. Therefore, it
can be observed that the low efciency






Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 87


varieties are consumed exclusively by the South as the North exits this market, and as the
South does not export due to low profitability. The North-South head-on competition occurs in
the intermediate efciency range of varieties. Southern varieties are more competitive and are
exported to the North, while the North produces them only for the domestic consumption at a
reduced scale. At even higher levels of efciency, the numberof Southern firms (varieties)
decreases. This is principally the market for Northern exporters who employ a large share of the
total labor force in the North. Details on labor (size) distribution of firms and the values of
average productivities across diferent areas of the (a, q) space in the North and the South are
presented in Appendix C.


Export to North and South
NORTH
150 Export to North
Domestic
Exit
100

50

0
0 20 40 60 80 100 120 140 160 180
productivity

SOUTH
150

100

50

0
20 40 60 80 100 120 140 160 180
productivity


Figure 3.2: Firms Partition


Bearing in mind the price schedule over the (a, q) space, the partitioning graph provides
a graphical explanation for positive relationship between the average export and import prices on
one side and income per capita on the other. With_> 1 ÷q the profits increase faster along the
efciency dimension, which shapes the isoprofit curves (cutof functions) in the (a, q) space as
presented in Figure 3.

The shape of the cutof functions determines the quality and price composition of the
domestic and import bundles of the two regions. The most profitable firms export both to the
North and the South, while less profitable export only to the North. With _> 1 ÷q, the bigger share of
the relatively higher priced varieties (high q and low a)
are not exported to the South and are shipped only to the North.
14


Thus, the resulting average import price is higher for the North. This result holds for
all exporter, and also conditional on a particular exporting country. Northern imports

14
As

opposed to the case with_< 1 ÷q when relatively low priced varieties are excluded from exports
to the South in a larger share than the high priced varieties.






q
u
a
l
i
t
y


q
u
a
l
i
t
y


Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 88


180

160

140

120

100

80

60

40

20

0









Exit





20









Domestic
market





40















60









Export
to
North




80















100









Export to
North and
South




120















140















160















180















200
productivity

Figure 3.3: Distribution of Prices


are of higher average price relative to the imports of the South as more high quality-low
efciency varieties are included in its import bundle. In other words, it imports goods of higher
average price not as it consumes higher quality than the South but due to the fact that it
additionally consumes the high priced high quality varieties. The analogue reasoning applies to
the imports from the South.This efect is not present with only one dimension of firms
heterogeneity as the profits are just a monotonic transformation of the price and the unique
productivity measure.

On the export side, the North abandons the export of low price varieties due to compe-
tition from the South, which results in higher export prices of the North. Average prices of export
and import are presented in Table 1.


Average Price
Exports
Imports
Imports from North
Imports from South


North
4.0739
1.0072
4.2514
1.0008


South
0.9495
0.9101
3.9861
0.9054


Table 3.1: Average Import Prices


The following graph (Figure 4.) presents the expenditure shares distribution of the
two regions across diferent levels of quality for a given efciency of the firm. Northern demand is
relatively higher for the varieties produced by the high quality firms, and the South is
demanding relatively more of the goods in the lower quality portion of the distribution, which is
the efect of the fixed cost of trade. With no fixed cost, the homothetic preferences would result in
a lower demand from the South but still in levels exactly proportional to those of the North. Once
the fixed cost of export is introduced






q
u
a
l
i
t
y


Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 89


in both the North and the South, this results in subsets of firms with only domestic
sales, which subsequently distorts the proportionality of the consumption shares of the two
regions across varieties.


5

4.5

4

3.5

3

2.5

2

1.5

1

0.5

0


x 10
5


Expenditure share per variety over quality



North
South
0 20 40 60 80 100 120 140 160 180 200
quality


Figure 3.4: Expenditure Shares Distribution over Quality


Figure 5. shows the total trade values within and across two groups of countries with no
asymmetries in the variable costs of trade. The model implies that larger shares of North- ern
export revenue is coming from the North due to higher profitability requirements for the export
to the South and low absolute expenditure of the South. This implies higher trade intensity
between countries of the North. As a result, the North-North trade is the largest compared to the
other trade ?ows, North-South and South-South. In this set-up North-South trade is of higher
value than the South-South trade, but the ranking reverses when the asymmetric variable costs of
trade are introduced, with the highest cost imposed on Southern exports to the North. Some
empirical evidence points to these asymmetries in the form of higher export barriers imposed on
the exporters from the South (such as iceberg trade cost, quality requirements, tarifs). In sectors
with these asymmetries, our model's results might support the final conjecture of the Linder
hypothesis, besides predicting the demand and supply premises.




3.5 Conclusions


This paper analyzes the role of efciency and quality in shaping the trade patterns and
trade intensities within and across two groups of countries, the developed and richer North and
the developing South. We employ a four country North-South trade model






Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 90



16

14

12

10

8

6

4

2

0



x 10
4



Value of total trade




N÷N
S÷S
N÷S
0 20 40 60 80 100 120 140 160 180 200
quality




Figure 3.5: Total Trade Values Within and Across Regions


with two dimensions of firm heterogeneity. Matching the empirical values of within and
across region export shares in the total world exports, we show that the equilibrium results
support the ranking of the average prices of tradables within and across regions as found in the
data. This result is not previously found in the literature since using only one technology
dimension does not simultaneously allow for increasing relation between export prices, import
prices and import prices conditional on exporter on one side and income per capita on the other.

Furthermore, we find diferences in the consumption bundles across regions even though
the preferences are of standard, homothetic form. Namely, the resulting total expendi- ture
allocation across quality shows that the North spends a larger share of its income on high quality
while the South allocates more of its expenditure on low quality varieties. Therefore, we wish to
stress that the trade patterns in this model are not determined by the non-homotheticity of
preferences and therefore do not originate exclusively from the demand structures. The results
mainly come from the supply side through the pro- ductivity distribution of incumbents and its
efect on prices. This in turn allows the fixed cost of exporting to act in a way that the empirically
observed trading pattern is replicated. In other words, it is not that the consumers alone have
diferent preferences over qualities based on their income but diferences in productivity and
income (coming endogenously from the productivity level) are the principal deciding factors.

The future research agenda calls for the development of an endogenous R&D mechanism
which will determine technology level of the North and the South in equilibrium. In this
hypothetical set-up, firm would choose the level of their investment in technology, which would
afect the initial productivity draw through the innovation in the North






Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 91


and technology adoption in the South. R&D incentives would come partly from the
domestic demand structure but also as a response to foreign demand, which would together
shape the comparative advantage of each region over quality segments. This allows for the
analysis of several issues such as trade liberalization, income inequality and R&D subsidies to
promote welfare. Furthermore, it should be noted that the set-up is easily extendable to include n
countries which allows for more empirically testable predictions.




References


Aghion, P. and Howitt, P., (1992). A Model of Growth through Creative Destruction,
Econometrica, 60, 323-351.

Baldwin, R. and Harrigan, J., (2007). Zeros, Quality and Space: Trade Theory and
Trade Evidence, CEPR Discussion Paper No. 6368.

Bartelsman, E., Haltiwanger J. and Scarpetta S., (2004). Microeconomic Evidence of
Creative Destruction in Industrial and Developing Countries Eric Bartelsman, Tinbergen Institute
Discussion Paper, 04-114/3.

Bernard, A.B., Redding, S.J. and Schott, P.K., (2009). Products and Productivity,
mimeo

Brooks, E.L., (2006). Why don't firms export more? Product quality and Colombian
plants, Journal of Development Economics, 80, 160- 178.

Choi, Y.C., Hummels, D. and Xiang, C., (2006). Explaining Import Variety and Quality:
The Role of the Income Distribution, NBER Working Paper 12531.

Coibion, O., Einav, L. and Hallak, H.C., (2007). Equilibrium demand elasticities across
quality segments, International Journal of Industrial Organization, 25, 13-30.

Cordoba, J.C. and Ripoll, M., (2008). Endogenous TFP and cross-country income
diferences, Journal of Monetary Economics, 55, 11581170.

Fajgelbaum, P.D., Grossman G.M. and Helpman E. (2009). Income Distribution, Prod-
uct Quality, and International Trade, NBER Working Paper Series, Working Paper 15329.

Fieler, C., (2007). Non-Homotheticity and Bilateral Trade: Evidence and a Quantitative
Explanation, New York University, mimeo.






Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 92


Fieler, C., (2007). Quality Diferentiation in International Trade: Evidence from the
Demand and Supply Sides, New York University, mimeo.

Flam, H. and Helpman, E., (1987). Vertical Product Diferentiation and North-South
Trade, The American Economic Review, 77(5), 810-822.

Fontagne, L. and Freudenberg, M., (2002). "Long-term Trends in IIT", Chapter 8 of
Frontiers of Research on Intra-industry Trade, Peter Lloyd & Hyun Lee eds, Palgrave, 131-158.

Fontagne, L., Guillaume, G. and Zignago, S., (2008). Specialization across varieties and
North-South competition, Economic Policy, 23 (53), 51-91.

Gabler, A. and Licandro, O., (2005). Endogenous Growth through Selection and Imita-
tion, European University Institute, mimeo.

Ghironi, F. and Melitz. M.J., (2005). International Trade and Macroeconomics Dynam-
ics with Heterogenous Firms, Quarterly Journal of Economics, 120(3), 865-915.

Goksel, T., (2008). Income, Trade Barriers, and International Trade, University of
Minnesota, mimeo.

Grossman, G. M. and Helpman, E., (1991). Innovation and Growth in the Global
Economy, MIT Press, Cambridge MA.

Hall, R.E. and Jones, C.I., (1999). Why Do Some Countries Produce So Much More
Output Per Worker Than Others?, The Quarterly Journal of Economics, MIT Press, 114(1), 83-116.

Hallak, J.C., (2006). A Product-Quality View of the Linder Hypothesis, NBER Working
Paper No.12712.

Hallak, J.C., (2006). Product Quality and the Direction of Trade, Journal of Interna-
tional Economics, 68(1), 238-265.

Hallak, J.C. and Schott, P. (2010). Estimating Cross-Country Diferences in Product
Quality, Quarterly Journal of Economics (forthcoming).

Hallak, J. C. and and Sivadasan, J., (2008). Productivity, quality and Exporting Be-
havior Under Minimum Quality Requirements, International Policy Center, Working Paper, 88.

Hopenhayn, H. A., (1992). Entry and Exit and Firm Dynamics in Long Run Equilib-
rium, Econometrica 60(5), 1127-1150.







Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 93


Hummels, D. and Klenow, P.J., (2005). The Variety and Quality of a Nation's Exports,
American Economic Review, 95(3), 704-723.

Hummels, D. and Skiba, A., (2004). Shipping the Good Apples Out? An Empirical
Confirmation of the Alchian-Allen Conjecture, Journal of Political Economy, 112(6), 1384-1402.

Jerzmanovwski, M., (2007). Total factor productivity diferences:Appropriate technol-
ogy vs. efciency, European Economic Review, 51, 20802110.

Johnson, R.C., (2010). Trade and Prices with Heterogeneous Firms, Dartmouth College,
mimeo.

Khandelwal, A., (2010). The Long and Short (of) Quality Ladders, Review of Economic
Studies (forthcoming).

Krugman, P., (1979). A Model of Innovation, TechnologyTransfer, and the World Dis-
tribution of Income, Journal of Political Economy, 87(2), 253-266.

Linder, S., (1961). An Essay on Trade and Transformation, Stockholm: Almqvist &
Wiksell.

Manova, K. and Zhang, Z. (2009). Quality Heterogeneity across Firms and Export
Destinations, NBER Working Paper Series, Working Paper 15342.

Meliz, M., (2003). The Impact of Trade on Intra-Industry Reallocations and Aggregate
Industry Productivity, Econometrica 71(6), 1695-1725.

Romer, P. (1990). Endogenous Technological Change, Journal of Political Economy 98,
71-102.

Schott, P. K., (2004). Across-product Versus Within-product Specialization in Interna-
tional Trade, The Quarterly Journal of Economics, 119(2), 646-677.

Segerstrom, P. and Dinopoulos, E., (2006). North-South Trade and Economic Growth,
Stockholm School of Economics, mimeo.

Verhoogen, E., (2008). Trade, Quality Upgrading, and Wage Inequality in the Mexican
Manufacturing Sectors, The Quarterly Journal of Economics 123(2), 489-530.














Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 94
Appendix


A Conditions on Fixed Costs and Technological Lag


The setup of the model requires that the exit cutof in any region, a
J
(q), is lower than x
the export cutof, a
JK
(q), in order to rule out the possibility of firms not operating ex
domestically, and producing only for the export market. To insure this we impose con-
ditions on the fixed costs of production and export, and on the level of the technological
lag of the South behind the North. With fixed export cost c
ex
higher than the fixed
operational cost c
f
, the cutof for exporting to the other country of the same region
(North-North and South-South trade) will be higher than the exit cutof. However, to
insure higher cutof for exporting to the other region (North-South trade) than the exit
cutof, the following condition is required

o
c
f
< P
N
1÷
o
L
N
w
N
< c
ex
o
(3.27)
c
ex
P
S
1÷
o
L
S
w
S
c
f

As the equlibrium wage and price indices are functions of the technological lagu, it
follows that the three parameters together determine whether the condition above holds. The
relative size of the population in the two regions afects the relative size of the aggregates and
therefore the ratio of exit cutofs in the North and the South, and the ordering of export cutofs
conditional on the destination country. In general, if the South is sufciently larger than the North,
the aggregates of the South might be larger than those of the North even with the relative wage
smaller than one. However, the calibration exercise shows that such a large South would neither
match the data on the actual size of trading partners in the North and the South nor the model
could be considered as the model of North-South trade as the share of the Southern firms
exporting to the North would be approaching zero. Therefore, without the loss of generality, we
assume equal
sizes of the regions. We find that under the wide range of c
f
, c
ex
andu that satisfy
the stated condition, the resulting ordering of the cutofs is such that the exit cutof
is higher in the North than in the South. Moreover, the exporters of relatively lower productivity
export only to the North, while the highest productivity firms export also to the South.
















Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 95

B Calibration

Table 3.2: Targets and Parameters


Targets
North-North Export Share
North-South Export Share
North Exit Rate
South Exit Rate


Data
52.69%
40.86%
10%
20%


Model
54.95%
42.49%
10.43%
23.43%
Wage Ratio w
s
/w
N
0.4 0.41
Calibrated Parameters
u
o
c
f

c
ex

c
e

Other Parameters
o
çqo
t
g
N

L
N
= L
S


0.18
0.5
11.42%
29.51%
38%


0.73
0.5
0.86
0.5%
1
4.1
1





of avg North domestic employment
of avg North domestic employment of
avg North domestic employment




C Size Distribution and Average Productivities


Table 3.3: Weighted Average Technology Across Firm Partition


Weighted Average Technology
Total
Domestic
Export to North
Export to N and S


North
16.76
15.01
17.23
19.79


South
8.38
8.05
13.29
16.18













Chapter 3. World Trade Patterns and Prices: The Role of Cost and Quality
Heterogeneity 96























0.
5

0.4
5

0.
4

0.3
5

0.
3

0.2
5

0.
2

0.1
5

0.
1

0.0
5

0



































5



































1
0



































1
5



































2
0























ConditionalonbeingSouthNonExporter
ConditionalonbeingNorthNon
Exporter
ConditionalonbeingNorthExporter
ConditionalonbeingSouth
Exporter










25



































30
Technology

Figure 3.6: Conditional Labor Distribution over Technology























L
a
b
o
r










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