Essays on endogenous technological progress

MISSING IMAGE

Material Information

Title:
Essays on endogenous technological progress
Physical Description:
xi, 169 leaves : ill. ; 29 cm.
Language:
English
Creator:
Petsas, Iordanis, 1974-
Publication Date:

Subjects

Subjects / Keywords:
Economics thesis, Ph.D   ( lcsh )
Dissertations, Academic -- Economics -- UF   ( lcsh )
Genre:
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph.D.)--University of Florida, 2002.
Bibliography:
Includes bibliographical references (leaves 164-168).
Statement of Responsibility:
by Iordanis Petsas.
General Note:
Printout.
General Note:
Vita.

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 029223622
oclc - 51024075
System ID:
AA00017638:00001


This item is only available as the following downloads:


Full Text










ESSAYS ON ENDOGENOUS TECHNOLOGICAL PROGRESS


By

IORDANIS PETSAS


















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA
2002



























Copyright 2002

by

Iordanis Petsas




























This dissertation is dedicated to my mother, Stavroula. Without her love and
support I would not have started my studies. During my graduate studies, while seriously
ill, she always supported me in an extraordinary way and encouraged me to finish my
dissertation. I dedicate this work to her with all my love.














ACKNOWLEDGMENTS

My biggest heartfelt thanks go to my mother, Stavroula, who provided me with

continuous encouragement. To my deepest sorrow, my mother passed away while I was

working on this dissertation. 1 am extremely sorry that she can not have the chance to see

my achievement.

In writing this dissertation, I have benefited from the guidance, encouragement,

and knowledge of many people and I offer them my thanks. I would like to thank my

parents Stavroula and Nikos Petsas and the rest of my family, Panagiotis and Maria, for

supporting my studying abroad and patiently waiting during the long spells of separation.

I am deeply indebted and grateful to Elias Dinopoulos for his guidance and

encouragement at every stage of the dissertation. Elias has contributed immensely to my

development as an individual, teacher, and researcher. I am very grateful for the role that

he has played so well as my great motivator and advisor. I also wish to recognize David

Figlio, Douglas Waldo, and Steven Slutsky for their helpful comments and advice. Their

keen eyes for detail and their astute comments always came at the right time.

I would also like to thank Panos Hatzipanayotou, my former undergraduate

teacher and advisor at the Aristotle University of Thessaloniki, who made me realize the

excitement of macroeconomics. He assured me that it is truly worthwhile to pursue a

Ph.D. in economics. I am also grateful to Manolis Loukakis, George Papachristou, Nikos

Varsakelis, and Chrisoula Zacharopoulou for their dedicated teaching.








My life in Gainesville would have been miserable had I not had wonderful

friends. I greatly acknowledge the friendship of Huseyin Yildirim and Hsiu-Chuan Yeh. I

also thank Sofia Vidalis for her support and for sharing my path despite her own

challenges as a Ph.D. student. This dissertation is dedicated to my mother, who has been

the best teacher of my life.















TABLE OF CONTENTS
page

ACKNOW LEDGM ENTS ............................................................... ...................... iv

A B ST R A C T ................................................................... ............. ............................ x

CHAPTER

I IN T R O D U C T IO N ........................................................................ ..........................

1.1 Process versus Product Innovation and Firm Size......................... ............ 1
1.2 General Purpose Technologies and Schumpeterian Growth ................................. 3
1.3 Sustained Comparative Advantage and Relative Wages....................................... 6

2 PROCESS VERSUS PRODUCT INNOVATION IN MULTIPRODUCT FIRMS.......9

2.1 Introduction........................................................................................................ 9
2.2 A Model of Process versus Product Innovation................... .................... .. 13
2.2.1 Demand for Differentiated Products...................... ...........................13
2.2.2 The Duopoly M odel....................................................... ............................. 15
2.3 Model of Product versus Process Innovation Considering the R&D Costs .......... 19
2.4 Implications and Extensions ............................... ... ....................... 24

3 THE DYNAMIC EFFECTS OF GENERAL PURPOSE TECHNOLOGIES ON
SCHUMPETERIAN GROWTH............................. .... ................ .....30

3.1 Introduction ...................................................... ............................................... 30
3 .2 T he M odel ............................................................................... .............. .......... 39
3.2.1 Industry Structure.......................... ........ .... .....................39
3.2.2 Diffusion of a New GPT...............................................40
3.2.3 H ouseholds............................................ .......................................... 42
3.2.4 Product M markets ...................................................... ....................... 44
3.2.5 R & D R aces ............................................................... ....................... 45
3.2.6 Labor M market ........................................................... ........................ 49
3.3 Long-Run Equilibrium .............................. ......................................................... 49
3.4 Transitional Dynamics.................... ................................... 54
3.4.1 Stock Market Behavior ................... ...................... 57
3.4.2 Aggregate Investment ...................... .... ....................... 61
3.5 Concluding Rem arks....................................................................... ............. 62









4 SUSTAINED COMPARATIVE ADVANTAGE IN A MODEL OF
SCHUMPETERIAN GROWTH WITHOUT SCALE EFFECTS..............................70

4.1 Introduction ...................................................... ............................................... 70
4.2 T he M odel ............................. ..... ......................................................... 78
4.2.1 Household Behavior........................... ........................... 79
4.2.2 Product M markets .................... ................................... 81
4.2.3 R & D R aces ............................................... ....................................... 83
4.2.4 Labor M arkets............................................................. ..................... 89
4.3 Steady-State Equilibrium Under the PEG Specification .................................. 90
4.4 Comparative Steady-State Analysis Under the PEG Specification.................... 94
4.5 Steady-State Equilibrium Under the TEG Specification.................................. 99
4.6 Comparative Steady-State Analysis Under the TEG Specification.................. 102
4.7 Conclusions............................. .. .............. ...................................... 106

5 C O N C LU SIO N .................................................................... ..................................122

APPENDIX

A PROOFS OF PROPOSITIONS IN CHAPTER 2...........................................127

B SUMMARY OF THE HISTORICAL EVOLUTION OF SEMICONDUCTOR
TECHNOLOGY AND PROOFS OF PROPOSITIONS IN CHAPTER 3 ...............134

C PROOFS OF PROPOSITIONS IN CHAPTER 4............................................. 149

R EFE R EN C E S ................................................................................ ....................164

BIOGRA PHICAL SKETCH ........................................................ ....................... 169















LIST OF FIGURES


Figure page

2-1 Marginal Profits from Process and Product Innovation Considering
R&D Costs as Sunk.................... ... .................... ..........................26

2-2 Net Marginal Profits from Process and from Product Innovations ..................27

2-3 Effect of an Increase in R&D Cost from Product Innovation on n*k...................28

2-4 Effect of an Increase in R&D Cost from Process Innovation on n*k.................29

3-1 Steady-State Equilibria................. .... ........... .................. 64

3-2 Stability of the Balanced-Growth Equilibrium..........................................65

3-3 Time Path of the Per Capita Consumption Expenditure After a GPT Arrives
in the Economy ....... ........... .... .............. .... ... .......................66

3-4 Time Path of the Market Interest Rate After a GPT Arrives in the Economy........66

3-5 Evolution of the Aggregate Investment During the Diffusion Path.....................67

3-6 Effects of a GPT on the Schumpeterian Growth Rate ..................................68

3-7 Effects of a GPT on the Stock M market ........... ..... .......... ... .................. 69

4-1 Steady-State Equilibrium Under the PEG Specification............................... 11

4-2 Ranking of the Global R&D Investment, I, Between Home and Foreign,
Under the PEG Specification.................................. ...............112

4-3 Effects of an Increase in the Foreign County's Relative Size or in the
Population Growth Rate (Under the PEG Specification)..............................113

4-4 Effects of an Increase in the R&D Difficulty Parameter, k, in the
Unit R&D Labor Requirement or in the Consumer's Subjective
Discount Rate (Under the PEG Specification).........................................114

4-5 Effects of an Increase in the Foreign's Unit Labor Requirement in
Manufacturing (Under the PEG Specification) .................................... 115








4-6 Effects of an Increase in Home's Unit Labor Requirement in
Manufacturing (Under the PEG Specification)........................................116

4-7 Steady-State Equilibrium Under the TEG Specification............................117

4-8 Effects of an Increase in the Foreign County's Relative Size in the
Consumer's Subjective Discount Rate or in the R&D Difficulty
Growth Parameter (Under the TEG Specification).................................. 118

4-9 Effects of an Increase in the Size of Innovations or in the Population
Growth Rate (Under the TEG Specification)........................................119

4-10 Effects of an Increase in Foreign's Unit Labor Requirement in Manufacturing
(Under the TEG Specification)................ ..... ...................120

4-11 Effects of an Increase in Home's Unit Labor Requirement in Manufacturing
(Under the TEG Specification)......... ................................ ................121














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

ESSAYS ON ENDOGENOUS TECHNOLOGICAL PROGRESS

By

lordanis Petsas

August 2002
Chair: Elias Dinopoulos
Major Department: Economics

This dissertation analyzes several issues involving the economics of endogenous

technological progress:

* The effects of firm size on the choice of R&D effort between process and product

innovation

* The transitional and long-run dynamic effects of general-purpose technologies on

Schumpeterian growth in a closed economy setting

* The interactions among endogenous technological change, the pattern of trade, and

income distribution within each country

Chapter 2 develops a differentiated-goods duopoly model in which firms engage

in Coumot-Nash quantity competition. I showed that an increase in a firm's efforts

devoted to product innovation (given that it is in the product R&D regime) increases its

incentives to switch from product to process innovation. Once the firm is in the process

R&D regime, it will perform process R&D indefinitely.








Chapter 3 builds a quality-ladders model of scale-invariant Schumpeterian

growth. The introduction of a new general-purpose technology increases Schumpeterian

growth and per-capita R&D investment in the final steady-state. During the transition

path from the initial to the final steady-state equilibrium, the measure of industries that

adopt the new general-purpose technology increases, consumption per capital falls, and

the interest rate increases. The growth rate of the stock market depends negatively on the

rate of the general-purpose technology diffusion process and the magnitude of the

general-purpose technology-ridden R&D productivity gains; and positively on the rate of

population growth. In addition, the model generates transitional growth cycles of

per-capita GNP.

Chapter 4 constructs a two-country (Home and Foreign) general equilibrium

model of Schumpeterian growth without scale effects. The scale effects property is

removed by introducing two distinct specifications in the knowledge production function:

the permanent effect on growth (PEG) specification, which allows policy effects on

long-run growth; and the temporary effects on growth (TEG) specification, which

generates exogenous long-run economic growth. Under the PEG specification, an

increase in the rate of population growth raises Home's relative wage and decreases its

range of goods exported to Foreign. Under the TEG specification, an increase in the rate

of population growth rate lowers Home's relative wage and increases its range of goods

exported to Foreign.













CHAPTER 1
INTRODUCTION

Economic historians have placed great weight on technology as a force of change.

The importance of technological progress has been increased dramatically in the last

decade. Many macroeconomic studies place technological progress at the center of the

growth process. This trend has been triggered by theoretical developments that allow

microeconomic aspects of the innovation process to be linked with macroeconomic

outcomes.

The search for causes and effects of technological progress has dominated the

recent literature in growth and international trade. In this dissertation, I consider these

causes and effects in the context of dynamic growth models. Chapter 2 provides an

analysis of two types of technological change, (process versus product innovations) and

examines the effects of the firm size on the choice of R&D effort between process and

product innovation. Chapter 3 analyzes the impacts of a certain type of drastic

innovations, termed general-purpose technologies (GPTs) on Schumpeterian growth.

Chapter 4 investigates interactions among endogenous technological change, the pattern

of trade, and income distribution within each country. Chapter 5 presents general

conclusions. The rest of Chapter 1 briefly describes the motivation, scope, and main

findings for each chapter of the dissertation.

1.1 Process versus Product Innovation and Firm Size

Numerous studies have tested the hypothesis about the advantages of size for

innovative activity. Kamien and Schwartz (1972), Baldwin and Scott (1987) and Scherer








(1980) reviewed the findings concerning the relationship within industries between firm

size and R&D effort. Cohen and Klepper (1996) summarized these findings in the form

of stylized facts that characterize this relationship within industries between firm R&D

effort and firm size. Some of their key findings are as follows:

* Among R&D performing firms, the number of patents and innovations per dollar of

R&D decreases with firm size or level of R&D.

* Among all firms, smaller firms account for a disproportionately large number of

patents and innovations relative to their size.

Scherer (1991) found that among manufacturing business units considered as a

whole, process R&D increases relative to product R&D as the size of the firm increases,

with each tenfold increase in business unit sales associated with a highly significant

ten-point increase in the percentage of R&D expenditures devoted to process innovation.

Cohen and Klepper (1996) proposed and tested a theory of how firm size

conditions the relative amount of process and product innovation undertaken by firms.

using patent data. They found that the share of process R&D undertaken by firms indeed

rises with firm size within most industries.

The motivation behind Chapter 2 was to examine the findings mentioned in the

studies above using a differentiated-goods duopoly model in which firms engage in

Cournot-Nash quantity competition. Firms optimally choose to engage either in product

or in process innovation.

The analysis generates several insights. An increase in the number of goods

produced by a firm and thus an increase in its size causes the firm to perform process

R&D regardless of the R&D regime in which it was located originally. Given that the








firm starts with product R&D, as the number of goods produced increases, the firm's

incentives to switch from product to process innovation increase. Once the firm is in the

process R&D regime, it continues to perform process R&D indefinitely. This constitutes

then a cost-based mechanism that links firm size to the type of R&D activity the firm

develops, which is not clear in the models mentioned earlier.

1.2 General Purpose Technologies and Schumpeterian Growth

The unusual combination of more rapid growth and slower inflation in the 1990s

initiated a strenuous debate among economists about whether improvements in America's

economic performance can be sustained. Many believe that the behavior of information

technology provides the key to the recent surge in economic growth. Jorgenson (2001)

provides plenty of evidence that the rise in structural productivity growth in the late

1990s in the United States can be traced to the introduction of personal computers and

semiconductors, which constitutes the necessary building blocks for the information

technology revolution. His estimates indicate that the importance of information

technology has steadily increased in the United States over the last 50 years. He estimates

that the contribution of information technology to the average growth rate of 3.46% for

the last 50 years is 0.4%. The information-technology products contribute 0.5 percentage

points to total factor productivity growth for 1995 to 1999, compared to 0.25 percentage

points for 1990 to 1995. This reflects the accelerating decline in relative price changes

resulting from shortening the product cycle for semiconductors.

Information technology is considered a drastic innovation. In recent years, the

literature on these types of drastic innovations has been initiated by Bresnahan and

Trajtenberg (1995), who coined the term, "General Purpose Technologies" (GPTs

henceforth). A drastic innovation qualifies as a GPT if it has the potential for pervasive








use in a wide range of sectors in ways that drastically change their modes of operation.

To quote from Bresnahan and Trajtenberg (1995):

[Most GPTs play the role of "enabling technologies," opening up new
opportunities rather than offering complete, final solutions. For example, the productivity
gains associated with the introduction of electric motors in manufacturing were not
limited to a reduction in energy costs. The new energy sources fostered the more efficient
design of factories taking advantage of the newfound flexibility of electric power.
Similarly, the users of micro-electronics benefit from the surging power of silicon by
wrapping around the integrated circuits their own technical advances. This phenomenon
involves what we call innovationall complementarities,"....These complementarities
magnify the effects of innovation in the GPT, and help propagate them throughout the
economy.] Bresnahan and Trajtenberg (1995, p. 84).

Even though the distinction between a drastic technological innovation and an

incremental one is needed to understand the proper roles of technological innovations as

engines of growth, economists have paid relatively less attention to the former.

Several empirical studies have documented the cross-industry pattern of diffusion

for a number of GPTs (For example, Helpman and Trajtenberg, 1998b). In addition, a

strand of empirical literature has established that the cross-industry diffusion pattern of

GPTs is similar to the diffusion process of product-specific innovations and it is governed

by standard S-curve dynamics (Griliches, 1957; Jovanovic and Rousseau, 2001). These

studies imply that the internal-influence epidemic model can provide an empirically-

relevant framework to analyze the dynamic effects of a GPT. During this diffusion

process, these drastic innovations could generate growth fluctuations and even business

cycles (Schumpeter, 1939, 1950).

Building an analytical model that incorporates all these key characteristics of

GPTs and examining their dynamic effects on Schumpeterian growth constitutes one

motivation of Chapter 3. The other motivation is to formalize relationships among GPTs,

stock market, and R&D investment that were empirically investigated by Jovanovic and








Rousseau (2001) using 114 years of U.S. stock market data. Therefore, I incorporate the

presence of a GPT into the standard quality-ladder framework of Schumpeterian growth

without scale effects that was developed by Dinopoulos and Segerstrom (1999), and

explore the impacts of GPTs on Schumpeterian growth, the stock market, and R&D

investment. It is a dynamic model of endogenous growth with endogenous determination

of innovation. Firms engage in R&D to discover higher-quality products.

In the presence of a GPT, the model has two steady-state equilibria: the initial

steady-state in which no industry has adopted the new GPT, and the final steady-state in

which all industries have adopted the new GPT and its diffusion process has been

completed. At the final steady-state relative to the initial steady-state: the long-run

growth rate is higher even though the per capital consumption expenditure is lower, due to

higher aggregate investment.

There are two additional findings of the model. First, there exists a unique

globally stable-saddle-path along which the measure of industries that adopt the new GPT

increases, the per capital consumption expenditure decreases, the market interest rate

increases, and the innovation rate of the industries that have adopted the new GPT

decreases at a higher rate than that of those that have not adopted the new GPT. Second,

the model exhibits transitional growth cycles of per capital GNP as a consequence of

S-curve dynamics.

The introduction of positive population growth in Aghion and Howitt's (1998b)

model of GPTs will make these growth cycles shorter and shorter as the size of the

economy increases, and in the long-run the GPT-induced cycles disappear. In the model

developed in Chapter 3, the fall in output comes from the reduction in per capital








consumption expenditure on final goods and the rise in the per capital R&D investment.

As the size of the economy increases (as a result of positive population growth) the

duration of the per capital GNP cycle remains the same. When all industries have adopted

the new GPT and the diffusion process has been completed, the economy experiences a

higher per capital income constant growth rate.

In addition, the growth rate of the stock market depends negatively on the rate of

GPT diffusion process and the magnitude of the GPT-ridden R&D productivity gains,

and positively on the rate of population growth.

Finally, the effect of the GPT diffusion on the aggregate investment during the

adoption process is ambiguous. In the initial stages of the diffusion process, only a

limited number of industries adopt the new GPT. These industries are called the early

adopters. As more industries adopt the new GPT, the aggregate investment increases.

1.3 Sustained Comparative Advantage and Relative Wages

Many models of endogenous growth and trade emphasize the role of continual

product innovation based on R&D investment in determining the pattern of trade between

countries (Grossman and Helpman, (1991a, b, c,), Taylor (1993)). All these studies

exhibit the scale effect property: if one incorporates population growth in these models,

then the size of the economy (scale) increases exponentially over time, R&D resources

grow exponentially, and so does the long-run growth rate of per-capita real output.

The scale effects property is a consequence of the assumption that the growth rate

of knowledge is directly proportional to the level of resources devoted to R&D. Jones

(1995a) argued that the scale effects property of earlier endogenous growth models is

inconsistent with post-war time series evidence from all major advanced countries that

shows an exponential increase in R&D resources and a more-or-less constant rate of








per-capita GDP growth.

Building a quality-ladders model of scale-invariant Schumpeterian growth and

examining interactions among endogenous technological change, the pattern of trade, and

income distribution within each country constitutes the motivation of Chapter 4. It

constructs a two-country (Home and Foreign) general equilibrium model. The scale

effects property is removed by introducing two distinct specifications in the knowledge

production function: The permanent effects on growth (PEG) specification which allows

policy effects on long-run growth; and the temporary effects on growth (TEG)

specification, which generates exogenous long-run economic growth.

My approach borrows from Taylor's work (1993) in that industries differ in

production technologies. In his model, industries also differ in research technologies and

in the set of technological opportunities available for each industry. The absence of

heterogeneity in research technologies in my model makes the removal of scale effects

more tractable, but eliminates the need for trade in R&D services between countries.

The main point of Chapter 4 is that the removal of scale effects affects the

comparative static properties of the model. Furthermore, the various comparative

steady-state results depend on the way that the scale effects property is removed. Under

the PEG specification, changes in the size of innovations do not affect Home's

comparative advantage and its relative wage, while under the TEG specification, an

increase in the size of innovations reduces Home's relative wage and raises its

comparative advantage.

Under the PEG specification, changes in the size of innovations do not affect

relative wages and comparative advantage, while under the TEG specification, an






8


increase in the size of innovations reduces Home's relative wage and raises its

comparative advantage. In addition, under the PEG specification, an increase in the rate

of population growth raises Home's relative wage and decreases its range of goods

exported to Foreign. On the other hand, under the TEG specification, an increase in the

rate of population growth rate lowers Home's relative wage and increases its range of

goods exported to Foreign.













CHAPTER 2
PROCESS VERSUS PRODUCT INNOVATION IN MULTIPRODUCT FIRMS

2.1 Introduction

There is heterogeneity among firms in the degree of product and process

innovation in which they engage. The percentage of total R&D dedicated to different

types of innovative activity differs greatly across industries. For example, in petroleum

refining, almost three-quarters of total R&D is dedicated to process innovation, whereas

less than one-quarter of pharmaceutical R&D is dedicated to process innovation. A large

part of such differences is due to differences in exogenous industry-level conditions that

systematically differentiate the returns to one sort of innovative activity versus another.

Link (1982), for example, finds that greater product complexity increases the fraction of

effort dedicated to process innovation.

There is an extensive empirical literature in industrial organization, investigating

at the industry level the relationship between firm size and the composition of R&D

effort, and hence, the nature of innovation. However, inadequate attention seems to have

been paid to modeling these two types of R&D activities and trying to support the

empirical papers.

The findings of Link (1982) all suggest that within industries, firm size, and, thus,

across industries, market structure, may also influence the composition of R&D. Scherer

(1991) finds that among manufacturing business units considered as a whole, process

R&D increases relative to product R&D as the size of the firm increases, with each








tenfold increase in business unit sales associated with a highly significant ten point

increase in the percentage of R&D expenditures devoted to process innovation.

Cohen and Klepper (1996) proposed and tested a theory of how firm size conditions the

relative amount of process and product innovation undertaken by firms. Their theory

explains the close and often proportional relationship within industries between firm size

and innovative activity. Their model generates predictions about the relationship between

firm size and the share of process R&D. They also tested these predictions using patent

data that distinguish between process and product innovation and business unit sales data

from the Federal Trade Commission's Line of Business Program. They found that the

share of process R&D undertaken by firms indeed rises with firm size within most

industries.

One critical question arises about how technologically progressive industries

evolve from birth through maturity. When industries are new, there is a lot of entry, firms

offer many different versions of the industry's product, the rate of product innovation is

high, and market shares change rapidly. Despite continued market growth, subsequently

entry slows, exit overtakes entry and there is a shakeout in the number of producers, the

rate of product innovation and the diversity of competing versions of the product decline,

increasing effort is devoted to improving the production process, and market shares

stabilize. This evolutionary pattern has come to be known as the product life cycle (PLC).

While numerous papers have contributed to this description, perhaps the most influential

one has been that of Abemathy and Utterback's (1978). In their paper, they stress that

when a product is introduced, there is considerable uncertainty about user preferences

and the technological means of satisfying them. As a result, many firms producing








different variants of the product enter the market and competition focuses on product

innovation. As users experiment with the alternative versions of the product and

producers learn about how to improve the product, opportunities to improve the product

are depleted and a defacto product standard, dubbed a dominant design, emerges.

Producers who are unable to produce efficiently the dominant design exit, contributing to

a shakeout in the number of producers. The depletion of opportunities to improve the

product coupled with locked-in of the dominant design leads to a decrease in product

innovation. This in turn reduces producers' fears that investments in the production

process will be rendered obsolete by technological change in the product. Consequently,

they increase their attention to the production process and invest more in capital-intensive

methods of production, which reinforces the shakeout of producers by increasing the

minimum efficient size firm.

Klepper (1996) summarized regularities concerning how entry, exit, market

structure, and innovation vary from the birth of technologically progressive industries

through maturity. He developed a model emphasizing differences in firm innovative

capabilities and the importance of firm size in appropriating the returns from innovation.

His model predicts that over time firms devote more effort to process innovation but the

number of firms and the rate and diversity of product innovation eventually wither.

One of the goals in this chapter is to examine these findings (within industries the

fraction of total R&D a firm devotes to process R&D will be an increasing function of the

firm's size) using a differentiated-goods duopoly model in which firms engage in

Courot-Nash quantity competition (in contrast to Klepper's model (1996), in which all








firms produce a standard product). Firms optimally choose to engage either in product or

in process innovation.

The present model differs from the ones in the studies mentioned above in a

number of respects. First, I consider multi-product firms that produce a number of

differentiated goods in a duopoly setting, and investigate the relationship between firm

size and R&D activity based on demand and cost functions. Second, labor is the only

primary factor of production: it can be used to produce the differentiated goods and R&D

services. R&D services result in discoveries of better production techniques, which

enhance the productivity of labor employed in the manufacturing of the differentiated

goods. R&D product services result in discoveries of new goods (adding or improving

product features).

The analysis generates several insights. For example, an increase in the number of

goods produced by a firm and thus an increase in its size (since in my model, the firm

size is measured by the firm's sales and the firm's sales are proportional to the number of

goods produced) causes the firm to perform process R&D regardless the R&D regime in

which it is located originally. Given that the firm starts with product R&D, as the number

of goods produced increases, the firm's incentives to switch from product to process

innovation increase. Once the firm is in the process R&D regime, it continues to perform

process R&D indefinitely. This constitutes a cost-based mechanism that links firm size to

the type of R&D activity the firm develops, which is not clear in the models mentioned

earlier.

This chapter is organized as follows. Section 2.2 develops the model, and shows

how it can explain Klepper's finding. Section 2.3 investigates the relationship between








firm size and innovative activity in different regimes. Section 2.4 considers the

implications of the analysis for the relationship between firm size and the types of

innovative activities undertaken by firms within industries as well as extensions of the

model are considered. The algebraic details and proofs of propositions in this chapter are

relegated to Appendix A.

2.2 A Model of Process versus Product Innovation

2.2.1 Demand for Differentiated Products

In this section, I develop a model to explain the influence of firm size on the

effort devoted to process relative to product innovation. I imagine an identifiable sectoral

structure of commodities. Thus, a pencil is a well-defined object and so are a refrigerator,

a personal computer, a restaurant meal, and a haircut. Each one of these goods is a

differentiated product, however, in the sense that there are many varieties of it available

in the market and many more varieties that could potentially be produced. There are red

and yellow pencils, soft and hard pencils, white and green refrigerators, 16MB memory

personal computers and 128 MB memory personal computers and so on.

Since products can be differentiated in many dimensions, one way to introduce

preferences for differentiated products is to assume that there are commodities that

individuals like to consume in many varieties, so that variety is valued in its own right.

The tastes of a representative individual are represented by the following utility function

(the economy is able to produce a large number of products, all of which enter

symmetrically into demand):

N
U = D, +xo, 0< a < 1, (1)









where D, is consumption of the i1h product, N is the number of available products and

x0 is an outside good.'

The demand for any individual product i can be derived by solving the following

maximization problem:

max U
D 1D2,. .,

N
subject to D,P, =I,


where I is the individual's income.

By forming the lagrangian function (L), the above problem is equivalent to:


maxL = max D, +Xo+ I- DP,-xo ,
D,,D,.D D D.D ..T )1

where X is the lagrangian multiplier.

The first order conditions to the above problem are the following:

aL
-- 0 aD-l -P, =0, Vii=,...N.
aD,

oL N
= 0 X, =I-JPiDi ,


aL
=0a =l.
ax,

Since k is fixed, the inverse demand functions for the differentiated goods are2:




See more on this in Dixit and Stiglitz (1977).

2In the monopolistic competition models, X is taken as fixed because it is assumed that
the number of goods produced is large and thus each firm's pricing policy has a
negligible effect on the marginal utility of income.








Pi =aD,-, Vi = ,...N. (2)

where D, is the quantity demanded per capital. As the total number of consumers is fixed,

I can set population at 1 without loss of generality. In this case, I do not have to

distinguish between total and per-capita quantities, so I let D, (i = l,...N)denote the

respective (total or per capital) quantities of the differentiated goods.

2.2.2 The Duopoly Model

I consider a duopoly in which each firm produces a range of differentiated goods.

Good i is produced with the following production function:

Xik =l"kL,k, Vi=l,...n, ifk=l, and Vi =n, +1,...N if k =2, (3)

where k denotes firm, Xik denotes the output of good i produced by firm k, and Lik

denotes the amount of labor used in the production of good i by firm k. Thus, production

functions are the same for all product varieties within each firm. The number of potential

varieties is assumed to be countably infinite, so that only a finite subset of the range is

actually produced. The parameter A (>1) is the quality increment per innovation, whereas

the parameters q, and q2 represent the number of innovations undertaken by firm I and

2 respectively (q e {0,1,2,....}) The total number of goods available in the economy is

n, + n, = N. Production of each product variety in such an industry will be undertaken

by only one producer, since the other firm can always do better by introducing a new

product variety than by sharing in the production of an existing product type.

Using labor as the numeraire, I can normalize the wage rate to unity. Then, the

marginal cost (the cost per unit) of good X,, is 1/pIq (Vi = l,...n,), when firm I knows

how to produce X, with the q, th process. The marginal cost of good X, is








1/(Ui (Vi= 1,...n2), when firm 2 knows how to produce X,, with theq2 th process. I

assume that both firms produce the quantities demanded of each good. Since each firm is

a multi-product firm, I measure the firm size by their sales. For example, sales for firm 1

are given by:


PiDi = nPD.


The above equation implies that the prices are the same for all goods produced

within each firm and the quantities produced are the same within each firm. Since the

sales of each firm are proportional to the number of goods produced by that firm, I can

use that number to measure the firm size.

In this section, I consider R&D costs as sunk (that is they already have been

incurred and they are fixed). The profit function for firm 1 for producing n, goods is as

follows:


, -~D, D, (4)


In the same way, the profit function for firm 2 for producing n, goods, is given by:

N IN
n, = YP,D D (5)


By differentiating equations (4) and (5), with respect to the quantities (D,), I obtain the

quantities produced of each good and then I can obtain the value profit functions. Since

the value profit functions are symmetric for both firms, I can generalize them and use k to

denote either firm (k = 1,2). By doing some comparative statics with respect to n k and

qk, I obtain the following two equations and Proposition 1:









Ak n*, kn+ 1 q k-g n- >0, (6)


where An ,k is the marginal profit of firm k from performing product innovation.


A, k,q =k(qk +l, nk)- Kk(qk nk)=nk I ) ( -1)>0, (7)


where Ackqk is the marginal profit of firm k from performing process innovation and

where k denotes firm (k= 1,2).

Proposition 1. Total profits for firm k (=1,2) depend positively on the number of

goods produced and the number ofprocess innovations it performs.

Proof. See Appendix A.

Equations (6) and (7) provide a basis for explaining why the firm size tends to

increase the marginal returns from process R&D, but not the marginal returns from

product R&D. In equation (6), the marginal returns to product R&D are independent of

the firm size, whereas in equation (7) the marginal returns to process R&D depend

positively on the firm size.

I can now solve explicitly for the number of goods (nk), at which the firm is

indifferent between performing one more product R&D and one more process R&D. By

equalizing equations (6) and (7), I obtain the following proposition:

Proposition 2. If n (1/11q )" '(, ..*.- ( -1)), then firm k is

indifferent between performing one more product innovation and performing one more

process innovation.

Proof. See Appendix A.








Proposition 2 provides a rationale for Scherer's (1991) finding that larger firms

devote a greater fraction of their R&D to process innovation. The intuition behind this

result is straightforward. The marginal returns to process R&D rise with the firm's size

(as it is measured with nk) while the marginal returns to product R&D are constant

(independent of nk). If n. > (l/ts ; (', t1 '" (. '-1)), then it is more

profitable for firm k (=1,2) to switch from product to process innovation.

Figure 2-1 shows the relationship between the marginal profits from process and

from product innovation considering the R&D costs as sunk costs. The marginal profit

from process innovation is an increasing function of the number of goods produced,

while the marginal profit from product innovation is independent of the number of goods

produced.

Point A in Figure 2-1 reflects a situation, in which the firm is indifferent between

performing one more process innovation and one more product innovation. For a small

number of goods produced (any point to the left of point A), the firm performs only

product R&D. The reason is that, when a firm develops a product innovation, it reaches

new buyers as well as raise price given some degree of transient monopoly power.

For a large number of goods produced (any point to the right of point A), the firm

performs only process innovation. The reason is that, when a firm develops a process

innovation, it lowers its average cost. Thus, the firm will increase its profits by the

decrease in average cost times the level of output of each good produced. Since, in the

model, whenever a firm develops a process innovation, it applies to all goods, the larger

the number of goods produced the greater the increase in the firm's profits.








Next, I consider the case, where the firm k is in the product R&D regime (any

point to the left of point A in Figure 2-1). I examine the effect of developing one more

product innovation on the incentives to switch from product to process innovation. Firm k

is in the product R&D regime if and only if


Akqk An knk .- / (n(tk /- )-)<0, (8)


or n < '-' ).

By differentiating equation (8) with respect to nk, and after rearranging, I obtain:

A(A4.,a -A1t ) -- )-i -) >0, (9)


since i > 1.

Proposition 3. Given that the firm k (=1,2) is in the product R&D regime, as each

firm produces more goods (develops more product innovations), its incentives to switch

from product to process innovations increase.

Proof. See Appendix A.

Proposition 3 explains the relationship between the firm size and the type of

innovative activity. The intuition behind this result is straightforward. The returns to

process R&D rise proportionally with the firm size while the returns to product R&D are

constant with the firm size. Consequently, an increase in the number of goods produced

must have a positive effect on process than product R&D, causing the firm to switch from

product to process R&D.

2.3 Model of Product versus Process Innovation Considering the R&D Costs

In this section, I examine how firms choose optimally their R&D effort between

process and product innovation. I assume for simplicity that firms develop either product








or process R&D, but not both of them at the same time. There are three regimes: product

R&D regime (in the area to the left of point A in Figure 2-1), process R&D regime (in the

area to the right of point A in Figure 2-1) and neutral R&D regime (point A in Figure 2-

1). Firms start with product R&D because of monopoly power and then they switch to

process R&D to exploit economies of scale.

In this section, I examine the decision of the firm to perform one more product

innovation or to perform one more process innovation for a given number of goods

produced and processes developed and given that the firm is in the process R&D regime

(any point to the right of point A in Figure 2-1).

This decision is based on the difference between the net marginal profit from

product innovations and the net marginal profit from process innovations. Net marginal

profit from process innovation includes the R&D cost for process innovation and net

marginal profit from product innovation includes the R&D cost for product innovation. If

the net marginal profit from process is larger than the net marginal profit from product

innovations, then it is more profitable for the firm to switch from product to process

innovations.

I assume that firms spend money on product R&D (R ) and process R&D (Rc).

Let's denote with Rpik the amount spent on product R&D for good i by firm k and Rck

the amount spent on process R&D for all goods by firm k. I assume that process R&D

applies to all goods, that is it reduces equally the average cost of all goods produced. I

further assume that the amount spent on product R&D is the same for all goods produced

within the firm.

Utilizing the assumptions mentioned above, I arrive at the following proposition:








Proposition 4.

(a+1) aqk a
If nk / 0- ) ( g(R k-R (1-) ( -) ) then firm k is


indifferent between performing one more product innovation and performing one more

process innovation.

Proof. See Appendix A.

Figure 2-2 depicts the net marginal profits from process and from product

innovations. At point A, firm k produces n~, and it is indifferent between performing

one more product innovation and performing one more process innovation.

Now, by differentiating n in Proposition 3 with respect to Rpk and Rk, I obtain

the following propositions:

Proposition 5. The number of goods produced byfirm k is a decreasing function

of the firm's R&D cost on product innovation.

Proof. See Appendix A.

Intuitively, as the firm's R&D cost on product innovation is higher, the net

marginal profit from product R&D decreases. Thus, at the original number of goods

produced at which the firm is indifferent between performing one more product and one

more process innovation, the net marginal profit from process innovation is greater than

the net marginal profit from product innovation causing the firm to produce fewer goods.

Figure 2-3 shows the effect of an increase in the R&D cost from product

innovation (Rpk) on n When Rpk increases, the net marginal profit from product

R&D line shifts down and the equilibrium moves from point A to point B. At point B, the

number of goods produced at which the firm is indifferent between developing one more








product innovation and developing one more process innovation is less than that of point

A (n*k < n'k).

Proposition 6. The number of goods produced byfirm k is an increasing function

of the firm's R&D cost on process innovation.

Proof. See Appendix A.

As the firm's R&D cost on process innovation increases, the net marginal profit

from process innovation decreases. Thus, at the original number of goods produced at

which the firm is indifferent between performing one more product and one more process

innovation, the net marginal profit from process innovation is lower than the net marginal

profit from product innovation causing the firm to produce more goods.

Figure 2-4 shows the effect of the increase in the R&D cost from process

innovation (Rck) on n When Rek increases, the net marginal profit from process

innovation shifts to the right and the equilibrium moves from point A to point B. At point

B, the number of goods produced at which the firm is indifferent between developing one

more product innovation and developing one more process innovation is higher than that

of point A (n*k > n*k).

Next, I consider the case, where the firm is at a point to the right of point A in the

Figures, so that it performs only process innovations, since the net marginal profit from

process is greater than the nets marginal profit from product innovations in this area.

The firm k is in the process R&D regime if and only if


Atkqk kAl.nk_ )-aqkl-(nk/'-) --1- 0.

This last expression implies the following:








[n;(a/"-a -1)-1] > 0. (10)

Suppose the firm has already developed nk product innovations and qk process

innovations. Given (nk ,qk), and given the fact that the firm is performing only process

innovations, I examine if it is more profitable for the firm to develop one more process

innovation (qk +1) or to develop one more product innovation (n k +1).

By developing one more process innovation, the difference between the marginal profit

from process and the marginal profit from product innovation increases by:

1-a .%,,(] -) I
A(A:.,, -An*,,), = ( ) ) (V '' -lI [nk(/- )-l], (11)

where A(A7n, An[,,, ), is the change in the difference between the marginal profit

from process and the marginal profit from product innovation due to change in the

number of process innovations by one.

If firm k is in the process R&D regime, equation (10) holds and implies that the

sign of equation (11) is positive. That is, the firm has an incentive to continue performing

process R&D. By developing one more product innovation, the difference between the

marginal profit from process and the marginal profit from product innovation increases

by:

A(A7t. A7t, ), (.o )(Li 0 -l) > o. (12)

The signs of equations (11) and (12) imply:

Proposition 7. Given that firm k (=1,2) is in the process R&D regime, it will

continue to perform process R&D indefinitely.

Proof. See Appendix A.








This finding suggests that large firms have no incentives to do product R&D,

reinforcing the conclusion of earlier studies on R&D effort and firm size (i.e., it supports

the idea of R&D cost spreading). The fraction of process R&D versus product R&D rises

monotonically with firm size. There is a critical point where the firm enters the process

R&D regime and its incentives to remain in this regime are high. Once the firm performs

only process R&D, its incentives to switch to product R&D disappear. That is, the firm

will find more profitable to find ways to produce its goods cheaper than to create higher

quality goods or more variety.

2.4 Implications and Extensions

The notion that the firm size and the choice between process and product

innovation follow a common pattern has become part of the folklore. My findings support

the basic idea that larger firms have an advantage in R&D because of the larger output

over which they can apply the results-and thus spread the costs-of their R&D (Cohen and

Klepper (1996)). Note, however, that once a firm switches from product to process, it

continues to develop only process (since the size of process innovation in my model is

greater than one). If the size of process innovation were small, by performing one more

product R&D in the process R&D regime would increase the incentives to switch from

process to product innovation. Indeed, if the size of process innovation is less than one,

process innovation is not profitable.

Two limitations of the model need to be brought to the forefront. First, my

conclusions depend on and are limited by the functional forms and the assumptions of my

model. Another production function, for example, can make the model conform better to

the real world. That is, once a firm is in the process R&D regime, after a critical number

of process innovations, it can be possible to switch from process to product innovations.





25

Second, the assumption that firms will not attend to the production process until product

innovation has slowed sufficiently is also restrictive. Yet the history of the automobile

industry and others, such as tires and antibiotics, indicates that great improvements were

made in the production process well before the emergence of any kind of dominant

design. Indeed, many of these improvements were based on human and physical

improvements that were not rendered obsolete by subsequent major product innovations.

One possible extension of the model is to relax this assumption and explore the

implications of this change on firm's optimal decision on choosing the fraction of process

and product innovation. This relaxation would change some of the results, but it would

also complicate the analysis of the model.


















A7M *k,q






R&D Regime


_r *k, n


0
n*k nk

Figure 2-1. Marginal Profits from Process and Product Innovation Considering R&D
Costs as Sunk
















AT*nk ,-Rpk


An *k,. -Rk


An,kq -R,,


*kn -Rpk


Figure 2-2. Net Marginal Profits from Process and from Product Innovations





















An*, -Rpk A *k, --Rck

An*kk -Rck


A
An *k,n -R'pk


An *k,%n -R2pk







-R n*k' n*k nk


Figure 2-3. Effect of an Increase in R&D Cost from Product Innovation on n*k


















k,n -Rpk, Ant,, -R'ck

An*kq k /R At*k, -R2k






A B
An*k,n -Rpk







R k nk *k" nk

R ck




Figure 2-4. Effect of an Increase in R&D Cost from Process Innovation on n*k












CHAPTER 3
THE DYNAMIC EFFECTS OF GENERAL PURPOSE TECHNOLOGIES ON
SCHUMPETERIAN GROWTH

3.1 Introduction

In any given economic "era" there are major technological innovations, such as

electricity, the transistor, and the Intemet, that have far-reaching and prolonged impact.

These drastic innovations induce a series of secondary incremental innovations. The

introduction of the transistor, for example, triggered a sequence of secondary innovations,

such as the development of the integrated circuit and the microprocessor, which are also

considered drastic innovations.3 These main technological innovations are used in a wide

range of different sectors inducing further innovations. For example, microprocessors are

now used in many everyday products like telephones, cars, personal computers, and so

forth.

In general, drastic innovations have three key characteristics. The first feature

refers to the generality of purpose, i.e., drastic innovations affect a wide range of

industries and activities within each industry. Consequently, Bresnahan and Trajtenberg

(1995) christened these types of drastic innovations "General Purpose Technologies"

(GPTs henceforth). Several empirical studies have documented the cross-industry pattern





SIn Appendix B, I provide a summary of the historical evolution of semiconductor
technology, from the birth of the transistor in 1947 invented by the Bell Labs to the
development of the microprocessor in 1971 by Intel. As a special case, I elaborate on the
computer and the Intemet to show how these important drastic innovations are based on a
previous drastic innovation, the transistor.








of diffusion for a number of GPTs.4 In addition, a strand of empirical literature has

established that the cross-industry diffusion pattern of GPTs is similar to the diffusion

process of product-specific innovations and it is governed by standard S-curve dynamics.5

In other words, the internal-influence epidemic model can provide an

empirically-relevant framework to analyze the dynamic effects of a GPT. During this

diffusion process, these drastic innovations could generate growth fluctuations and even

business cycles.

Schumpeter provides details on the connection between drastic innovations and

business cycles:






4 For example, Helpman and Trajtenberg (1998a) provide evidence for the diffusion of
the transistor. They state that transistors were first adopted by the hearing aids industry.
Later, transistors were used in radios followed by the computer industry. These three
industries are known as early adapters of the transistor GPT. The fourth sector to adopt
the transistor was the automobile industry, followed by the telecommunication sector.

5 For example, Griliches (1957) studied the diffusion of hybrid seed corn in 31 states and
132 crop-reporting areas among farmers. His empirical model generates an S-curve
diffusion path. Andersen (1999) confirmed the S-shaped growth path for the diffusion of
entrepreneurial activity, using corporate and individual patents granted in the U.S.
between 1890 and 1990. Jovanovic and Rousseau (2001) provide more evidence for an
S-shaped curve diffusion process by matching the spread of electricity with that of
personal computer use by consumers.

6 As Paul Saffo, founder and director of the Institute for the Future, in Palo Alto,
California, in his interview, Surfing the "S" Curve, in the News Link 1s Quarter (2001)
edition (Volume 9, No. 1), describes the S-curve dynamics for Internet: "In terms of the
Internet, we're at the bottom of the S-curve. Everything we've seen so far is just the
beginning." The vertical rise in the S-curve will depend on new technologies that are
going to advance in the future such as fiber optics, 3D chip arrays, DNA computing,
nanocomputers, and much more. For more information on emerging technologies see
"Taking Advantage of Technological Acceleration: Tracking Emerging Technologies and
Trends" by Manyworlds (2001, www.manyworlds.com) and Appendix B.








"It is by no means farfetched or paradoxical to say that "progress" destabilizes the
economic world, or that it is by virtue of its mechanism a cyclical process."
Schumpeter (1939, p. 138).

"These revolutions periodically reshape the existing structure of industry by
introducing new methods of production-the mechanized factory, the electrified factory,
chemical synthesis and the like; new commodities, such as railroad service, motorcars,
electrical appliances; new forms of organization."
Schumpeter (1950, p. 68).

"Times of innovation...are times of effort and sacrifice, of work for the future,
while the harvest comes after...The harvest is gathered under recessive symptoms and
with more anxiety than rejoicing... [During] recession...much dead wood disappears."
Schumpeter (1939, p. 143).

Second, the dynamic effects of these GPTs take a long period of time to

materialize. For instance, David (1990) argues that it may take several decades before

major technological innovations can have significant impact on macroeconomic activity.7

Third, these GPTs act as "engines of growth". As a better GPT becomes available, it gets

adopted by an increasing number of user industries and fosters complementary advances

that raise the industry's productivity growth. As the use of a GPT spreads throughout the

economy, its effects become significant at the aggregate level, thus affecting overall

productivity growth. In his presidential address to the American Economic Association,

Jorgenson (2001) documents the role of information technology in the resurgence of U.S.

growth in the late 1990s.8 There is plenty of evidence that the rise in structural



7 David (1990) describes a phase of twenty-five years in the case of the electric dynamo.
He argues that the observed productivity slowdown in the earlier stage of electrification
and computerization was due to the adjustment process associated with the adoption of a
new GPT.

8 At the aggregate level, information technology is identified with the output of
computers, communications equipment, and software. These products appear in the GDP
as investments by businesses, households, and governments along with net exports to the
rest of the world.








productivity growth in the late 1990s can be traced to the introduction of personal

computers and the acceleration in the price reduction of semiconductors, which

constituted the necessary building blocks for the information technology revolution.9

The growth effects of GPTs have been analyzed formally by Helpman and

Trajtenberg (1998b). In their model GPTs require complementary inputs before they can

be applied profitable in the production process. Complementary inputs developed for

previous GPTs are not suited for use with a newly arrived GPT. The sequential arrival of

GPTs generates business cycles. A typical cycle consists of two phases, a phase where

firms produce final goods with the old GPT and components are being developed for the

new GPT, and a second phase where final goods producers switch to the new GPT and

the development of components for that GPT continues. 1 Output declines in the first

phase of a cycle as workers switch from production to research to invent new inputs and

increases again in the second phase once the new technology is implemented.





9 Another study from OECD documents that U.S. investment in information processing
equipment and software increased from 29% in 1987 to 52% in 1999. The diffusion of
information and communication equipment accelerated after 1995 as a new wave of
information and communication equipment, based on applications such as the World
Wide Web and the browser, spread rapidly throughout the economy.

10 In the same paper, the authors also provide an extension of their model in which they
introduce a continuum of final-good sectors with different degrees of productivity gains
from GPTs and with the intermediate inputs being common to all sectors. As a result, a
GPT spreads gradually across the economy, first to sectors that stand to gain most from
its adoption and last to sectors that stand to gain least. Concerning output growth, it drops
right at the beginning of the cycle (as in the base case), but then it exhibits positive
growth during phase 1.

" There is a growing literature with this approach. See, for example, Helpman and
Rangel (1998), Aghion and Howitt (1998b) and the volume edited by Helpman (1998).








In this chapter, I analyze formally the effects of a GPT within a state-of-the-art

model of Schumpeterian growth without scale effects. Schumpeterian (R&D-based)

growth is a type of growth that is generated through the endogenous introduction of new

goods or processes based on Schumpeter's (1934) process of creative destruction, as

opposed to physical or human-capital accumulation.2

Earlier models of Schumpeterian growth assumed that the growth rate of

technological change depends positively on the level of R&D resources devoted to

innovation at each instant in time. As population growth causes the size of the economy

(scale) to increase exponentially over time, R&D resources also grow exponentially, and

so does the long-run growth rate of per-capita real output. In other words, long-run

Schumpeterian growth in these models exhibits scale effects. Two influential papers by

Jones ( 1995a, b) provided time series evidence for the absence of these scale effects. This

evidence led theorists to construct Schumpeterian growth models that exclude scale

effects. 3

My approach to modeling GPTs has the following features. First, the model

abstracts from scale effects and generates long-run growth, which is consistent with the

time-series evidence presented by Jones (1995a). Second, I take into consideration the

above mentioned evidence on long diffusion lags associated with the adoption of a new

GPT. I therefore analyze both the transitional dynamics and long-run effects of a new



12 There are two classes of scale invariant Schumpeterian growth models; endogenous
and exogenous. Endogenous [exogenous] Schumpeterian growth models are those in
which long-run growth can [cannot] be affected by permanent policy changes.

13 Dinopoulos and Thompson (1999) provide a survey of the empirical evidence on scale
and growth, and describe recent attempts to develop models that generate growth without
scale effects.








GPT. Third, I assume that a GPT is beneficial to all firms in each industry. Thus, when a

GPT is implemented in an industry, it affects the productivity of R&D workers, the size

of all future innovations in that industry and its growth rate. Finally, I assume that

although a GPT's rate of diffusion is exogenous, its diffusion path across a continuum of

industries is governed by S-curve dynamics.14

I incorporate the presence of a GPT into the standard quality-ladder framework of

Schumpeterian growth without scale effects that was developed by Dinopoulos and

Segerstrom (1999). In the model, there is positive population growth and one factor of

production, labor. Final consumption goods are produced by a continuum of structurally

identical industries. Labor in each industry can be allocated between two economic

activities, manufacturing of high-quality goods, and R&D services that are used to

discover new products of higher quality.

The arrival of innovations in each industry is governed by a memoryless Poisson

process whose intensity depends positively on R&D investments and negatively on the

rate of difficulty of conducting R&D. Following Dinopoulos and Segerstrom (1999), I

assume that R&D becomes more difficult over time in each industry. Specifically, I

assume that the productivity of R&D workers declines as the size of the market

(measured by the level of population) increases. This assumption captures the notion that

is more difficult to introduce new products and replace old ones in a larger market.15


14 This assumption can be justified by the empirical observation provided by David
(1991) that the measure of industries that adopted the dynamo and the number of
consumers that have adopted computers follow an S-curve.

is Several authors have developed microfoundations for this assumption. Young (1998),
Dinopoulos and Thompson (1998), and Aghion and Howitt (1998a, Chapter 12) have
combined tastes for horizontal and vertical product differentiation to generate models in
which absolute levels of R&D drive productivity growth at the firm-level, but aggregate








For any given measure of industries with the new GPT (i.e., in the absence of

S-curve dynamic diffusion of technology), the model generates a unique steady-state

equilibrium. In this equilibrium, per capital consumption expenditure is constant over

time, the aggregate stock value increases at the same rate as the constant rate of

population growth, and the long-run Schumpeterian growth is endogenous (Proposition

1).

In the absence a new GPT, the economy does not exhibit zero long-run growth as

in previous models of GPTs (see Helpman and Trajtenberg (1998b), Aghion and Howitt

(1998b), and Eriksson and Lindh (2000) among others). That is, the long-run growth rate

depends positively on the rate of innovation (which equals per capital R&D) and thus, any

policy that affects per capital R&D investment has long-run growth effects. In addition,

the removal of scale effects allows me to analyze the effects of changes in the rate of

growth of population that is absent from earlier models of GPTs.

In the presence of a GPT, the model has two steady-state equilibria: the initial

steady-state in which no industry has adopted the new GPT, and the final steady-state in



R&D in larger economies is diffused over a larger number of product lines or industries.
At the steady state, the number of varieties is proportional to the level of population. As
population grows, the number of varieties increases and aggregate R&D is diffused over
a larger number of product lines or industries, making R&D more difficult.
Dinopoulos and Syropoulos (2000) have provided microfoundations for this
specification in a model of Schumpeterian growth, where the discovery of higher quality
products is modeled as an R&D contest (as opposed to an R&D race) in which
challengers engage in R&D and incumbent firms allocate resources to rent-protecting
activities. Rent-protecting activities are defined as costly attempts of incumbent firms to
safeguard the monopoly rents from their past innovations. These activities can delay the
innovation of better products by reducing the flow of knowledge spillovers from
incumbents to potential challengers, and/or increase the costs of copying existing
products. Their model postulates that R&D may become more difficult as the size of the
economy grows because incumbent firms may allocate more resources to rent-protecting
activities.








which all industries have adopted the new GPT and its diffusion process has been

completed. At the final steady-state relative to the initial steady-state: the long-run

growth rate is higher, the aggregate investment is higher, the per capital consumption

expenditure is lower, and the market interest rate is equal to the subjective discount rate

(Proposition 2).

I use Mulligan and Sala-i-Martin's (1992) time-elimination method to study the

transitional dynamics of the model. This analysis generates several additional findings.

First, there exists a unique globally stable-saddle-path along which the measure of

industries that adopt the new GPT increases, the per capital consumption expenditure

decreases, the market interest rate increases, and the innovation rate of the industries that

have adopted the new GPT decreases at a higher rate than that of those that have not

adopted the new GPT. Second, the model exhibits transitional growth cycles of per capital

GNP as a consequence of S-curve dynamics (Proposition 3).

The introduction of positive population growth in Aghion and Howitt's (1998b)

model of GPTs will make these growth cycles shorter and shorter as the size of the

economy increases, and in the long-run the GPT-induced cycles disappear. In the present

model, the fall in output comes from the reduction in per capital consumption expenditure

on final goods and the rise in the per capital R&D investment. As the size of the economy

increases (as a result of positive population growth) the duration of the per capital GNP

cycle remains the same. When all industries have adopted the new GPT and the diffusion

process has been completed, the economy experiences a higher per capital income

constant growth rate.








I also analyze the effects of the adoption of the new GPT on the stock market. The

growth rate of the stock market depends negatively on the rate of GPT diffusion process

and the magnitude of the GPT-ridden R&D productivity gains, and positively on the rate

of population growth. It also follows a U-shaped path during the diffusion process of the

new GPT (Proposition 4).

During the transition period, there are two types of industries in the economy: one

that has adopted the new GPT and one that has not adopted it yet. The former type of

industries is more innovative in terms of discovering higher quality products than the

latter type of industries. In the initial stages of a GPT's diffusion, the aggregate stock

value decreases, since most of the industries belong to the latter type of industries. As

more industries switch to the new GPT, the aggregate stock value rises. This result is

consistent with the previous GPT-based models.16

However, the mechanism that links the growth rate of the stock market with the

GPT differs from these models. This mechanism allows the model to identify important

factors, such as the rate of the population growth, that affect the stock market, which

otherwise would have been ignored. In Helpman and Trajtenberg's (1998b) model, for



16 Jovanovic and Rousseau (2001) document empirically how technology has affected the
U.S. economy over the past century, using 114 years of U.S. stock market data. Their
estimates reveal evidence that entries to the stock market as a percentage of firms listed
in each year, were proportionately largest between 1915 and 1929, and that these levels
were not again approached until the mid-1980s. About half of American households and
most businesses were connected to electricity in 1920, and about one half of the
households and most businesses today own or use computers. Both expansions, therefore,
coincide with periods during which electricity and information technology saw
widespread adoption. During times of rapid technological change, the new entrants of the
stock market will grab the most value from previous entrants because the incumbents will
find hard to keep up. The downward trend in the starting values of the vintages reflects a
slowing down in the growth of the stock market.








example, during the first phase, the components of both the best practice GPT and of the

previous one have positive value. When the economy is in the second phase of a typical

cycle, only components of the best practice GPT are valuable because at that time it is

known that no component of older technologies will ever be used. Thus, the introduction

of a new GPT brings a sharp decline in the real value of the stock market during a

substantial part of phase one, but it picks up toward the end of the phase. In the second

phase, the stock market rises.

The effect of the GPT diffusion on the aggregate investment during the adoption

process is ambiguous (Proposition 5). In the initial stages of the diffusion process, only a

limited number of industries adopt the new GPT. These industries are called the early

adopters. As more industries adopt the new GPT, the aggregate investment increases.

The rest of this chapter consists of four parts. Section 3.2 develops the structure of

the model. Section 3.3 analyzes the long-run properties of the model and Section 3.4

deals with the transitional dynamics. Section 3.5 summarizes the model's key findings

and suggests possible extensions. Appendix B describes the evolution of semiconductor

technology. The algebraic details and proofs of propositions are also relegated to

Appendix B.

3.2 The Model

3.2.1 Industry Structure

I consider an economy with a continuum of industries indexed by 0 E [0, 1]. In

each industry 0, firms are distinguished by the quality j of the products they produce.

Higher values ofj denote higher quality and j is restricted to taking on integer values. At

time t = 0, the state-of-the-art quality product in each industry is j = 0, that is, some firm








in each industry knows how to produce aj = 0 quality product and no firm knows how to

produce any higher quality product. To learn how to produce higher quality products,

firms in each industry engage in R&D races. In general, when the state-of-the-art quality

in an industry is j, the next winner of an R&D race becomes the sole producer of aj+l

quality product. Thus, over time, products improve as innovations push each industry up

its "quality ladder", as in Grossman and Helpman (1991c).

3.2.2 Diffusion of a New GPT

The diffusion path of a new GPT is modeled as follows: The economy has

achieved a steady-state equilibrium, manufacturing final consumption goods with an old

GPT. I begin the analysis at time t = to, when a new GPT arrives unexpectedly. Firms in

each industry start adopting the new GPT at an exogenous rate.7

At each point in time, a fraction of industries, co, uses the new GPT and a fraction

of industries, (l-o), does not use the new GPT. For example, if the old GPT is the steam

power and the new GPT is electricity, c industries use electricity in their production and








17 Aghion and Howitt (1998b) model the spread of GPTs using a continuum of sectors. In
their model, the innovation process involves three stages. First, the GPT is discovered.
Then each sector discovers a "template" on which research can be based. Finally, that
sector implements the GPT when its research results in a successful innovation. They
have computed paths of the fraction of sectors experimenting with the new GPT and the
fraction using the new GPT and found that the time path of the later follows a logistic
curve (S-curve). Thus, they analyze the transitional dynamics of GPTs by endogenizing
the arrival rate of GPTs and running simulations. Endogenizing the rate of diffusion in
my model would be an interesting avenue for further research, although it would make
the analysis of the transitional dynamics complicated without adding much value on the
results.








(1-co) industries use steam power in their production.18 I use the epidemic model to

describe the diffusion of a new GPT across the continuum of industries.19 Its form can be

described by the following differential equation,

6=8(1-CO), (1)
O)

where 6) = 8ao/t denotes the rate of change in the fraction of industries that use the new

GPT and 8 > 0 is the rate of diffusion. Equation (1) states that the number of new

adoptions during the time interval dt, 6), is equal to the number of remaining potential

adopters, (l-(o), multiplied by the probability of adoption, which is the product of the

fraction of industries that have already adopted the new GPT, C, and the parameter 6,

which depends upon factors such as the attractiveness of the innovation and the

frequency of adoption, both of which are assumed to be exogenous.







18 Devine (1983) provides an excellent historical perspective on electrification where he
documents the transformation from shafts to wires. He states: "Until late in the nineteenth
century, production machines were connected by a direct mechanical link to the power
sources that drove them. In most factories, a single centrally located prime mover, such
as a water wheel or steam engine, turned iron or steel "line shafts" via pulleys and leather
belts...By the early 1890s then, direct current motors had become common in
manufacturing, but were far from universal. Mechanical drive was first electrified in
industries such as clothing and textile manufacturing and printing, where cleanliness,
steady power and speed, and ease of control were critical". Helpman and Trajtenberg
(1998a) explore the adoption of the transistor, an important semiconductor GPT by a
number of industries. As they state: The early user sectors were hearing aids and
computers. The prominent laggards were telecommunications and automobiles. These
examples indicate that the timing of adopting a new GPT differs across industries.

19 See Thirtly and Ruttan (1987, pp.77-89) for various applications of the epidemic model
to the diffusion of technology.








The solution to equation (1) expresses the measure of industries that have adopted

the new GPT as a function of time and yields the equation of the sigmoid (S-shaped)

logistic curve as follows:

CO (2)
[I + e-("' ]'

where y is the constant of integration. Notice that for t oo, equation (2) implies that all

industries have adopted the new GPT.20

3.2.3 Households

The economy is populated by a continuum of identical dynastic families that

provide labor services in exchange for wages, and save by holding assets of firms

engaged in R&D. Each individual member of a household is endowed with one unit of

labor, which is inelastically supplied. The number of members in each family grows over

time at the exogenous rate g, > 0. I normalize the measure of families in the economy at

time 0 to equal unity. Then the population of workers in the economy at time t is

N(t) = e8'.

Each household is modeled as a dynastic family2, which maximizes the

discounted utility

U= o e-'-"" logu(t)dt, (3)





20 Whent -oo, then =0. If one assumes that the new GPT arrives at time t=0, then
co > 0. That is, the new GPT is introduced in the economy by a given fraction of
industries co (i.e., the industry or industries that developed this particular GPT).

21 Barro and Sala-i-Martin (1995, Ch. 2) provide more details on this formulation of the
household's behavior within the context of the Ramsey model of growth.








where p > 0 is the constant subjective discount rate. In order for U to be bounded, I

assume that the effective discount rate is positive (i.e., p g, > 0). Expression log u(t)

captures the per capital utility at time t, which is defined as follows:

logu(t) f log[Xh(0)Jq(j,6,t)]d0. (4)
J

In equation (4), q (j, 0, t) denotes the quantity consumed of a final product ofqualityj in

industry 0 E [0, 1] at time t. Parameter X(0) measures the size of quality improvements

and is equal to

I if 0 e[0, m]
1(9) = (5)
,) = 1X0 if 0 E [o, 1], (5)


where > 0 > 1. At each point in time t, each household allocates its income to

maximize equation (4) given the prevailing market prices. Solving this optimal control

problem yields a unit elastic demand function for the product in each industry with the

lowest quality-adjusted price

q(j, 0, t) c(t)N(t)
p(jq(j t)(6)

where c(t) is per capital consumption expenditure, and p(j, 0, t) is the market price of the

good considered. The quantity demanded of all other goods is zero.

Given this static demand behavior, the inter temporal maximization problem of

the representative household is equivalent to

max o e -('**" logc(t)dt, (7)
(')








subject to the inter temporal budget constraint a(t) = r(t)a(t) + w(t) c(t)- g a, where

a(t) denotes the per capital financial assets, w(t) is the wage income of the representative

household member, and r(t) is the instantaneous rate of return. The solution to this

maximization problem obeys the well-known differential equation

c(t)
r(t) p, (8)
c(t)

According to equation (8), per capital consumption expenditure would increase over time

if the instantaneous interest rate exceeded the consumer's subjective discount rate p.

3.2.4 Product Markets

Every firm in each industry 0 uses labor L(0, t) as the sole input in its production

according to the following production function


Q(,t) L(t) (9)
ao

where aQ is the unit labor requirement. The monopolist engages in limit pricing, i.e., it

charges a price equal to unit cost of manufacturing a product times the quality increment

P = X()aQw. (10)

At each instant in time, the incumbent monopolist produces the state-of-the-art

quality product and earns a flow of profits


(,t)= (0) -Ic(t)N(t) (11)
X (o) )







3.2.5 R&D Races
Labor is the only input used to do R&D in any industry. Each firm in each

industry 0 produces R&D services by employing labor L R (, t) under the constant

returns to scale production function22

R(O,t) (0) LR(0,t), (12)
aR

In equation (12), aR/I(0) is the unit-labor requirement in the production of R&D

services and ji(0) is equal to

IT = if 0E[0, o]
p(0) = (13)
o = 1 if O [co, l],

where > 1. A firm k that engages in R&D discovers the next higher-quality product

with instantaneous probability Ikdt, where dt is an infinitesimal interval of time and

Ik(0, t) =R( (14)
X(t)

R (0, t) is firm k's R&D outlays and X(t) captures the difficulty of R&D in a typical

industry. I assume that the returns to R&D investments are independently distributed

across challengers, across industries, and over time. Therefore, the industry-wide




22 The empirical evidence on returns to scale of R&D expenditure is inconclusive.
Diminishing returns would make the analysis of the transitional dynamics more
complicated. Segerstrom and Zolnierek (1999) among others developed a model where
they allow for diminishing returns to R&D effort at the firm level and industry leaders
have R&D cost advantages over follower firms. In their model, when there are
diminishing returns to R&D and the government does not intervene both industry leaders
and follower firms invest in R&D.








probability of innovation can be obtained from equation (14) by summing up the levels of

R&D across all challengers. That is,


1(0, t) = Ik (0, t) R (15)
X(t)

where and R(6, t) denotes total R&D services in industry 0. Variable I(0, t) is the

effective R&D.23 The arrival of innovations follows a memoryless Poisson process with

intensity I, for the industries that have adopted the new GPT and I, for industries that

have not adopted the new GPT.

Early models of Schumpeterian growth considered X(t) to be constant over time.

This implied that the rates of innovation and the long-run growth increase exponentially

as the scale of the economy grows exponentially. This scale-effects property is

inconsistent with post-war time-series evidence presented in Jones (1995a).

A recent body of theoretical literature has developed models of Schumpeterian

growth without scale effects.24 Two approaches have offered possible solutions to the

scale-effects problem. The first generates exogenous long-run Schumpeterian growth

models.25 The second approach generates models that exhibit endogenous long-run




23 The variable 1(0, t) is the intensity of the Poisson process that governs the arrivals of
innovations in industry 0.

24 See Dinopoulos and Thompson (1999) for an overview of these models.

25 Jones (1995b), and Segerstrom (1998) have removed scale effects by assuming that
R&D becomes more difficult over time because "the most obvious ideas are discovered
first." The model that results from their specification is called the temporary effects of
growth (TEG) model. In these models, the growth rate does not depend on any measure
of scale. Increases in the steady-state level of R&D raise technology and income per
capital at any point in time, but they do not raise the growth rate.








Schumpeterian growth.26 Here I adopt the second approach and remove the scale-effects

property by assuming that the level of R&D difficulty is proportional to the market size

measured by the level of population,

X(t)=kN(t), (16)

where k > 0 is a parameter.27 Consumer savings are channeled to firms engaging in R&D

through the stock market. The assumption of a continuum of industries allows consumers

to diversify the industry-specific risk completely and earn the market interest rate. At

each instant in time, each challenger issues a flow of securities that promise to pay the

flow of monopoly profits defined in (11) if the firm wins the R&D race and zero

otherwise. Consider now the stock-market valuation of the incumbent firm in each

industry. Let V(t) denote the expected discounted profits of a successful innovator at time

t when the monopolist charges a price p for the state-of-the-art quality product. Because

each quality leader is targeted by challengers who engage in R&D to discover the next

higher-quality product, a shareholder faces a capital loss V(t) if further innovation occurs.

The event that the next innovation will arrive occurs with instantaneous probability Idt,

whereas the event that no innovation will arrive occurs with instantaneous probability



26 Young (1998), Aghion and Howitt (1998a, Ch..12), Dinopoulos and Thompson (1998),
Peretto (1998), and Peretto and Smulders (1998) remove the scale effects property by
essentially the same mechanism as the one developed by exogenous Schumpeterian
growth models. They introduced the concept of localized intertemporal R&D spillovers.
Dinopoulos and Syropoulos (2000) proposed a novel mechanism based on the notion of
innovation-blocking activities that removes the scale-effects property and generates
endogenous long-run Schumpeterian growth. Their model offers a novel explanation to
the observation that the difficulty of conducting R&D has been increasing over time.

27 Informational, organizational, marketing, and transportation costs can readily account
for this difficulty. Arroyo, et al. (1995) have proposed this specification under the name
of the permanent effects of growth (PEG) model, and have provided time-series evidence
for its empirical relevance.








1-Idt. Over a time interval dt, the shareholder of an incumbent's stock receives a dividend

7t(t)dt and the value of the incumbent appreciates by dV(t) = [aV(t)/Ot]dt = V(t)dt. The

absence of profitable arbitrage opportunities requires the expected rate of return on stock

issued by a successful innovator to be equal to the riskless rate of return r; that is,

V(, [1 I(, t)dt]dt + ( dt t)-0] I(0, t)dt = rdt. (17)
V(9, t) V(9, t) V(0, t)

Taking limits in equation (17) as dt -) 0 and rearranging terms appropriately gives the

following expression for the value of monopoly profits

n(6, t)
V(, t)= t) (18)
V((,, t) =t)
r(t) + I(, t) ,
V(0, t)

Consider now the maximization problem of a typical challenger k. This firm

chooses the level of R&D investment Rk (0, t) to maximize the expected discounted

profits

V(, t)Rk(t) dt-w RRk(0, t)dt, (19)
X(t) ()

where Ikdt = [Rk (0, t)/X(t)]dt is the instantaneous probability it will discover the next

higher-quality product and waRRk(0, t)/u(0) is the R&D cost of challenger k.

Free entry into each R&D race drives the expected discounted profits of each

challenger down to zero and yields the following equilibrium condition as follows:

waRkN(t)
V(0, t) = wakN(t) (20)
ko)e








3.2.6 Labor Market

All workers are employed by firms in either production or R&D activities. Taking

into account that each industry leader charges the same price p and that consumers only

buy goods from industry leaders in equilibrium, it follows from (9) that total employment

of labor in production is J Q(, t)dO. Solving (12) for each industry leader's R&D

employment LR (0, t) and then integrating across industries, total R&D employment by

industry leaders is j [R(0, t)g /p.(0)]dO. Thus, the full employment of labor condition

for the economy at time t is

N(t)= Q(,t)QdO+ d)d. (21)


Equation (21) completes the description of the model.

3.3 Long-Run Equilibrium

The dynamic behavior of the economy is governed by two equations that

determine the evolution of the per capital consumption expenditure, c, and the number of

industries that adopt the new GPT, o. To facilitate the interpretation and understanding

of my results, I begin by deriving expressions for long-run per capital real output and

long-run growth. Following the standard practice of Schumpeterian growth models, one

can obtain the following deterministic expression for sub-utility u(t), which is

appropriately weighted consumption index and corresponds to real per capital income28

log u(t) = log c log a, + I(, t)t log X(0) log (0) (22)


28 See Dinopoulos (1994) for an overview on Schumpeterian growth theory.








The economy's long-run Schumpeterian growth is defined as the rate of growth of

sub-utility u(t), g, = u(t)/u(t). By differentiating equation (22) with respect to time, I

obtain the following:

g, = I(0,t)log ( ), (23)
u(t)

which is a standard expression for long-run growth in quality-ladders growth models.

Because the size of each innovation becomes larger (i.e., Xi > Xo) after all industries have

adopted the new GPT (i.e., the diffusion process has been completed), long-run growth,

g,, can be affected not only through changes in the rate of innovation, but also through

the diffusion of the new GPT.

After substitution of equations (6) and (10) into the first integral of equation (21),

the demand for manufacturing labor is given by the following expression:

cN(t) ( ( -_ )
cN tl ( -l (24)

Substituting equation (12) into the second integral of equation (21), the demand

for R&D labor is given by:

oa R, +(1--)aRR. (25)

At this point it is useful to choose labor as the numeraire of the model and setting

w = 1. (26)

Combining equations (24) and (25) with equations (15) and (16) and taking into

account (26) yields the resource condition

l= c ( +kaR -,+(l-m)I, (27)
^, \, [f(9








which defines a negative linear relationship between per capital consumption expenditure,

c, and the effective R&D, I. The above resource condition holds at each instant in time

because by assumption factor markets clear instantaneously.

I now derive the differential equation that determines the growth rate of per capital

consumption expenditure, c/c, as a function of its level and the rate of innovation.

Equation (20) holds at each instant in time, so it yields 'V(, t)/V(0, t) = X(t)/X(t)= g,.

In other words, the values of expected discounted profits, V(t), and the level of R&D

difficulty, X(t), grow at the constant rate of population growth, gN, Combining equations

(18) and (20) (after substituting equation (11) into equation (18) and equation (26) into

equation (20)), I obtain

)(0)aRk
c= ) ][ p+I(0,t)-g ], (28)
(h(0) l)u(0)

which defines a positive linear relationship between per capital consumption expenditure,

c, and the effective R&D, I. It also implies the familiar condition that r = p, which means

that the market interest rate must be equal to the subjective discount rate in the steady-

state equilibrium. This property is shared by all Schumpeterian models where growth is

generated by the introduction of final consumption (as opposed to intermediate

production) goods.

Let a hat "A" over variables denote their market value in a steady-state

equilibrium. The resource condition (27) and the equilibrium R&D condition (28)

determine simultaneously the long-run equilibrium values of per capital consumption

expenditure, E, and the rates of innovation, i, and I,. Figure 3-1 illustrates the two

steady-state equilibria: the initial steady-state (point A) where no industry has adopted the








new GPT (i.e., o = 0) and the final steady-state (point B) where all industries have

adopted the new GPT (i.e., o = 1). When co = 0 the balanced-growth resource condition

is

1= +knaRl, (29)


and the balanced-growth R&D condition is given by equation (28) (when co = 0). The

vertical axis measures consumption per capital, c, and the horizontal axis measures the

rate of innovation, I. The resource condition is reflected by the negatively-sloped line

NoNo and the R&D equilibrium condition is represented by the positively-sloped line

RoRo. Their unique intersection at point A determines the long-run values c(0) and

Io (0), where c(0) denotes the per-capita consumption expenditure evaluated at o = 0

and i0 (0) denotes the innovation rate for industries that have adopted the new GPT

evaluated at co = 0. Therefore, I arrive at:

Proposition 1. For a given c e [0, I], where co is the measure of industries with a

new GPT, there exists a unique steady-state equilibrium such that the long-run

Schumpeterian growth, k, is endogenous and does not exhibit scale effects: it depends

positively on policies that affect the size of innovations, A, the labor productivity in R&D

services, pu()/a, and the rate of population growth, g.; it depends negatively on the

consumer's subjective discount rate, p. At each steady-state equilibrium, consumption

expenditure per capital, c, is constant, the interest rate, i(t), is equal to the constant

subjective discount rate, p, and the aggregate stock value, V, increases at the same rate

as the constant rate of population growth, g,.








Proof. See Appendix B.

The removal of scale effects from the long-run growth rate, g,, depends on the

assumption that the level ofR&D difficulty is proportional to the market size. At the

steady-state equilibrium, the level of R&D difficulty, X(t), increases exponentially at the

rate of population growth g, (i.e., X(t)/X(t) = g ) as can be seen from equation (16).

The absence of a new GPT does not result in zero long-run growth rate as in the Helpman

and Trajtenberg (1998b), Aghion and Howitt (1998b), and Eriksson and Lindh (2000)

models. That is, the long-run growth rate depends positively on per capital R&D and thus,

any policy that affects this variable has long-run growth effects. The following

proposition describes the long-run properties of the economy:

Proposition 2. If o is governed by S-curve dynamics, there are only two steady-

state equilibria: the initial steady-state equilibrium arises before the adoption of the new

GPT, where o = 0, and the final steady-state equilibrium is reached after the diffusion

process of the new GPT has been completed, where to = 1. At the final steady-state

equilibrium: aggregate investment is higher, I(1) > 1(0), long-run growth rate is

higher, g, (1) > g, (0), per capital consumption expenditure is lower, c(l) < C(0),

per- capital stock market valuation of the incumbent in each industry is lower,

V(1)/N < V(O)/N, relative to the initial steady-state equilibrium. In both steady states

the market interest rate is equal to the subjective discount rate, P = p.

Proof. See Appendix B.

These comparative steady-state properties can be illustrated with the help of

Figure 3-1. Before the introduction of the new GPT, the economy is in a steady state








(point A) where o = 0, with per capital consumption expenditure Z(0), and with

innovation rate i0. An increase in the measure of industries that adopt the new GPT

makes the R&D condition in Figure 3-1 shift downward from RoRa (where o = 0) to

RIRI (where o = 1) and the resource condition shift upward from NoNo to NINI, resulting

in higher long-run rate of innovation and in lower long-run consumption per capital. In

other words, when all industries have adopted the new GPT, the long-run Schumpeterian

growth rate increases. The new steady state is at point B, where o = 1, with per capital

consumption expenditure 8(1), and innovation rate i,.

3.4 Transitional Dynamics

I analyze the transitional dynamics of the model by adapting the time-elimination

method described by Mulligan and Sala-i-Martin (1992).29 The time-elimination method

enables me to construct a system of two differential equations that govern the evolution

of c and o. Since equation (28) holds at each instant in time (when the subjective

discount rate, p, is replaced by the interest rate, r), I can solve for the rates of innovation

for the two types of industries, Io and I,. After substituting these rates into the resource

condition (27), which holds at each instant in time, I can solve for the market interest rate

along any path and obtain

p(c-l1)
r) +gg. (30)


Substituting (30) into (8) yields the following differential equation:


-=r-p= +gs -P. (31)
c ckaR[-(-l) 1


29 See also Mulligan and Sala-i-Martin (1991) for more details on this method.








Equations (31) and (1) determine the evolution of the two endogenous variables

of the model, per capital consumption expenditure, c, and the number of industries that

have adopted the new GPT, o. Since the right-hand side of equation (31) is decreasing in

o, c = 0 defines the downward-sloping curve in Figure 3-2. Starting from any point on

this curve, an increase in co leads to c > 0 and a decrease in to leads to c < 0. The right-

hand side of equation (1) is independent of c, and therefore the 6 = 0 locus is a vertical

line. Starting from any point on this line, decrease in to leads to 6 > 0. The area to the

left of the vertical line (i.e., locus 6 = 0) identifies a region in which the potential

number of adopters is greater than one. Therefore, this region is not feasible. There exists

a downward-sloping saddle path going through the unique balanced-growth equilibrium

point B. Thus, I arrive at:

Proposition 3. Assume that 5 > (g, -p). Then, there exists a unique

negative-sloping globally stable-saddle-path going through the final unique

balanced-growth equilibrium point B. Along the saddle path, the measure of industries

that adopt the new GPT, co, increases, the per capital consumption expenditure, c,

decreases, the market interest rate, r, increases, the innovation rate of the industries that

have adopted the new GPT, I,, decreases at a higher rate than that of those that have not

adopted the new GPT, 10. In addition, there exist transitional growth cycles ofper-capita

GNP.


Proof. See Appendix B.








The analysis is predicated on the assumption of perfect foresight.30 When the new

GPT arrives, per capital consumption expenditure, c, jumps down instantaneously to

(point A' in Figure 3-2). This per capital consumption expenditure jump lowers the

interest rate to 7 (Figure 3-4) since there are more savings available. The downward

jumps on the per capital consumption expenditure and on the interest rate imply an

upward jump on the innovation rates of both types of industries; those that have adopted

the new GPT and those that have not adopted the new GPT ( I and I, in Figure 3-5).

Figure 3-1 illustrates that the R&D line RoRo will shift downwards and the

resource line NoNo will shift upwards with the arrival of the new GPT resulting in lower

per-capita consumption expenditure. Going back to Figure 3-2, the instantaneous

decrease in c is reflected by a movement from point A to point A'. The decrease in

per-capita consumption expenditure leads to a decrease in the market interest rate r (from

equation (30), which always hold). When the market interest rate r is lower than the

subjective rate p, per capital consumption expenditure decreases even further, until the

market interest rate approaches the subjective discount rate at the new steady state (point

B in Figures 3.1 and 3.2). During the transition dynamics (i.e., as the equilibrium moves

from point A' to point B in Figure 3-2), the interest rate increases leading to more

savings and a decrease in per capital consumption expenditure. At point B in Figure 3-2,

all industries have adopted the new GPT.


30 There also exists a degenerate equilibrium where the adoption of the new GPT is not
completed. Suppose that when a new GPT arrives, every potential consumer expects that
no one will decrease their consumption expenditure, in order to finance innovation. As a
result, it does not pay to decrease consumption expenditure of a single consumer, because
the new GPT will never be fully adopted. In this event, the pessimistic expectations are
self-fulfilling, and no new GPTs are fully adopted. I do not discuss these types of
equilibria in what follows.








Along the transition path, the aggregate investment may increase or decrease. One

possible path of the aggregate investment is shown in Figure 3-5 by the dotted curve.

There is an upward jump in the innovation rate of industries that have not adopted the

new GPT (from point Bo to point B in Figure 3-5).

Figures 3-3 and 3-4 show the time paths of per capital consumption expenditure

and the market interest rate (where to indicates the time when the new GPT arrives in the

economy and to indicates the time when all industries in the economy have adopted the

new GPT). Figure 3-6 shows the effect of a GPT on the Schumpeterian growth rate. The

adoption of the new GPT entails cyclical growth patterns.3 The growth rate decreases in

the initial stages of the adoption of the new GPT. There exist transitional growth cycles.

3.4.1 Stock Market Behavior

The fact that the adoption of a new GPT affects positively the productivity of

R&D together with free entry into each R&D race are the key factors in explaining the

behavior of the stock market. The probability of discovering the next higher quality

product in each industry increases with the adoption of the new GPT and so does the

probability that the incumbent in each industry will be replaced by a follower firm (i.e.,

the hazard rate). This link between the GPT adoption and higher risk for incumbent firms

captures the effects of creative destruction on the stock market valuation of monopoly

profits. In other words, during the diffusion of a GPT per capital consumption declines,

the market interest rate rises, and the hazard rate increases. These changes lower the



31 Earlier contributions on this issue include the macroeconomic model of Cheng and
Dinopoulos (1996) in which Schumpeterian waves obtain as a unique non-steady-state
equilibrium solution and the current flow of monopoly profits follows a cyclical
evolution.








per-capita expected discounted profits of the successful innovator and drives down its per

capital stock market valuation.32 Furthermore, the larger the productivity gains associated

with the new GPT, the larger the slump of the stock market. For example, it may be that

the productivity gains generated by the introduction of the new GPT are large not because

the new GPT is technologically very advanced at that initial stage, but because the

previous GPTs are particularly inadequate for the needs of these sectors.33 However, the

size of the slump in the stock market is more severe, when the new GPT is diffused at a

higher rate.

The aggregate stock value is given by the following equation:

V1 V5
V=[+o +(1- o) ]N(t), (32)
N(t) N(t)

where V, and V. are given by equation (20) after taking account equation (26). After

substitution of these values into equation (32) and taking logs and derivatives with

respect to time, I obtain the growth rate of the aggregate stock value:







32 Hobijn and Jovanovic (2001) argue that U.S. stock market decline in the early 1970s is
due to the arrival of information technology and the fact that the stock-market
incumbents were not ready to implement it. They state "Instead, new firms would bring
in the new technology after the mid-1980s. Investors foresaw this in the early 1970s and
stock prices fell right away." The U.S. stock market value relative to GDP plummeted to
0.4 in 1973,just after Intel had developed the microprocessor in late 1971. The decrease
of the stock market value relative to GDP did not recover until the mid-1980s, and it then
rose sharply. Leading OECD countries also experienced similar movements in their stock
markets, following a U-shaped path.

33 This was clearly the case for early computers, where even that valves had been getting
smaller for over a decade prior to the arrival of the transistor, the transistor was still an order
of magnitude smaller.








V (-1)o08(l o)
gv = =gN (33)
V [CO+(1- )C]

At the initial steady-state, where o = 0 and at the final steady-state, where o = 1, the

growth rate of the aggregate stock value is equal to the rate of the population growth.

That is,

v =g, (34)

The effects of a GPT on the stock market valuation of monopoly profits are summarized

in the following proposition:

Proposition 4. The growth rate of the stock market, g,, depends negatively on

the rate of GPT diffitsion process, 3, and the magnitude of the GPT-ridden R&D

productivity gains, p, and positively on the rate ofpopulation growth, g,. It also

follows a U-shaped path relative to the population growth rate during the diffusion

process of the new GPT.

Proof. See Appendix B.

These comparative properties, which differentiate the model from several others

in its class, can be illustrated with the help of Figure 3-7, which shows the growth rate of

stock market as a function of the measure of industries that have adopted the new GPT.

The initial adoption of the new GPT decreases the growth rate of the stock market below

the rate of the population growth. In the later stages of the adoption of the new GPT, the

growth rate of the stock market increases. When the diffusion process of the new GPT

has been completed, the growth rate of the stock market is equal to the rate of the

population growth. That is, it follows a U-shaped path relative to the population growth

rate during the diffusion process of the new GPT.








This last result can be seen from the second term of the right hand side in equation

(33).34 The free entry condition in each R&D race (equation 20) implies that the per

capital stock value in any industry 0 ( V /N(t)) is constant over time. It jumps down

instantaneously with the adoption of the new GPT, and it remains constant thereafter. The

aggregate stock value, which increases exponentially at the rate of the population growth,

jumps down with the arrival of the new GPT, and then increases again at the population

growth rate. The slump in the aggregate stock value is due to the realization of the R&D

productivity gain associated with the new GPT. The higher these R&D productivity gains

are, the higher is the jump in the per capital industry and aggregate stock value at the time

of the adoption of the new GPT.35

An increase in the GPT diffusion rate, 8, increases the economywide resources

devoted to R&D. Thus, the probability that the incumbent firm will be replaced by a

follower firm increases. This can be seen from equation (18), which gives the value of

monopoly profits. In other words, when the GPT diffusion process accelerates, the

decrease in per capital consumption expenditure is more severe, and the per capital R&D

investment increases. In this case, the U-shaped path of the growth rate of the stock

market sags down (this is shown by the dotted-shaped curve in Figure 3-7). That is, the





34 The numerator in equation (33), which is positive and it reflects the slope of a
truncated S-curve, is equal to 6r times a positive fraction that depends on the magnitude
of the GPT-ridden R&D productivity gains and on the number of the industries that have
adopted the new GPT.

35 This can be seen from equation (33), where the first term in the right-hand side gets
smaller when each industry adopts the new GPT relative to the second term of the right-
hand side of the same equation.








slope of the growth of the stock market gets steeper at the initial stages of the diffusion

process of the new GPT and it gets flatter at the final stages of this process.36

An increase in the productivity gains generated by the new GPT, 11, lowers the

cost of discovering the next higher quality product. This, in turn, will affect negatively

the stock market valuation of the incumbent firm (see equation (20)). An increase in the

rate of population growth, gs, shifts the U-shaped curve in Figure 3-7 upwards and

increases the growth rate of the stock market.

3.4.2 Aggregate Investment

Proposition 5. The effect of the GPT diffusion on the aggregate investment during

the adoption process is ambiguous.

Proof. See Appendix B.

The initial steady-state equilibrium is at point A in Figure 3-5. There is an upward

jump in the aggregate investment with the introduction of the new GPT (from I to 1).

Along the diffusion path, both innovation rates (I, and I,) decrease until the economy

reaches at the final steady-state equilibrium point B, where the aggregate investment is

higher relative to the initial steady-state equilibrium point A. There is an upward jump on


36 The first OPEC shock may also explain a part of the drop in the stock market in the
early 1970s, as well as a part of the productivity slowdown. Hobijn and Jovanovic (2001)
argue that there are several problems associated with the oil-shock explanation. One
problem is that a rise in oil prices should have lowered current profits more than future
profits, because of the greater ease of finding substitutes for oil on the long-run, perhaps
current output more than future output and, therefore, should have produced a rise in the
ratio of market capitalization to GDP, not a fall. This scenario also implies a constant
entry in the stock market, something that contradicts their evidence. Another problem that
is associated with the oil-price-shock explanation for the stock-market drop is that the
energy-intensive sectors did not experience the largest drop in value in 1973-1974. Their
evidence supports that the information-technology-intensive sectors experienced the
largest drop in 1973-1974.








the innovation rate of the industries that have not adopted the new GPT at the final steady

state (from point Bo to B). One possible picture of how the aggregate investment behaves

along the diffusion of the new GPT is shown in Figure 3-5. Along the transition path, the

aggregate investment decreases and then increases. In the initial stages of the diffusion

process, only a limited number of industries adopt the new GPT (see equation (1)). These

industries are called the early adopters. As more industries adopt the new GPT, the

aggregate investment increases.

3.5 Concluding Remarks

Previous models that have analyzed GPTs exhibit the scale effects property. The

present paper analyzed the effects of a GPT on short-run and long-run Schumpeterian

growth without scale effects. The absence of growth scale effects and the modeling of the

diffusion process through S-curve dynamics generate several novel and interesting

results.

First, the long-run growth rate of the economy depends positively on the

magnitude of quality innovations. Any policy that affects this magnitude has long-run

growth effects. However, the absence of the arrival of a new GPT in the economy does

not reduce the long-run growth rate to zero as in the previous GPTs-based growth

models. All the previous R&D-based models that analyze the effects of GPTs exhibit

scale effects.

The assumption that the diffusion of the new GPT follows an S-curve generates

two steady-state equilibria: one is the initial steady-state before the adoption of the new

GPT begins and the other is the final steady-state after the diffusion process of the new

GPT has been completed. At the final steady-state relative to the initial steady-state: the

long-run growth rate is higher, the aggregate investment is higher, the per-capita








consumption expenditure is lower, and the market interest rate is equal to the subjective

discount rate.

The growth rate of the stock market depends negatively on the rate of GPT

diffusion process, and the magnitude of the GPT-ridden R&D productivity gains, and

positively on the rate of population growth. It also follows a U-shaped path relative to the

population growth rate during the diffusion process of the new GPT. This is consistent

with the empirical evidence provided by Jovanovic and Rousseau (2001) who empirically

document that during times of rapid technological change the growth of the stock market

slows down, since the new entrants of the stock market will grab the most value from

previous entrants because the incumbents will find hard to keep up.

One could also develop a dynamic general equilibrium model to study the effects

of a GPT diffusion on a global economy that exhibits endogenous Schumpeterian growth.

As in this model, the adoption of a GPT by a particular industry can generate an increase

in the productivity of R&D workers and the magnitude of all future innovations and its

diffusion across industries can be governed by S-curve dynamics. The diffusion of the

GPT within an industry from one country to the other can occur with a time lag. Under

this framework, it would be interesting to analyze the long-run and transitional dynamic

effects of a new GPT on trade patterns, product cycles and (transitional) divergence in

per-capita growth rates between the two countries. This is a fruitful direction for future

research.



















Initial R&D Condition
/ Ro


Final R&D Condition


R, Initial Resource Condition


0 I(0) 1(1) No NI I

Figure 3-1. Steady-State Equilibria:
Point A: No industry has adopted the new GPT.
Point B: All industries have adopted the new GPT.






















do
=(1- )o =0
dt






B
dc 0
dt=0
dt


0 1 (


Figure 3-2. Stability of the Balanced-Growth Equilibrium


do)
=0
dt














c





a(0) ---.


C

) -----------------


to to Time


Figure 3-3. Time Path of the Per Capita Consumption Expenditure After a GPT Arrives
in the Economy


r














to t, Time


Figure 3-4. Time Path of the Market Interest Rate After a GPT Arrives in the Economy























II





\ ~ ~ ~ - -':-------,~-=





i() A ------ Bo



0 1
Figure 3-5. Evolution of the Aggregate Investment During the Diffusion Path:
The initial steady-state equilibrium is at point A. There is an upward jump in
the aggregate investment with the introduction of the new GPT. One possible
path of the aggregate investment, along the diffusion path, is depicted in the
Figure by the dotted curve IB.

























IllogXl -- -



Iologo






to t Time

Figure 3-6. Effects of a GPT on the Schumpeterian Growth Rate:
When all industries have adopted the new GPT, the economy experiences
higher steady-state Schumpeterian growth. There also exist transitional
growth cycles of per capital GNP.






























9N------------------1------ I




0o 0/(i+ i1

Figure 3-7. Effects of a GPT on the Stock Market:
The growth rate of the stock market depends on the rate of GPT diffusion
process, the magnitude of the GPT-ridden R&D productivity gains, and the
rate of population growth. It also follows a U-shaped path relative to the
population growth.













CHAPTER 4
SUSTAINED COMPARATIVE ADVANTAGE IN A MODEL OF SCHUMPETERIAN
GROWTH WITHOUT SCALE EFFECTS

4.1 Introduction

Many models of endogenous growth and trade emphasize the role of continual

product innovation based on R&D investment in determining the pattern of trade between

countries. Grossman and Helpman (1991a, b, c) have developed models where

innovations lead to either improvements in the quality of existing products ("quality

ladders" models) or increase in the variety of the goods ("love for variety" models).

Taylor (1993) has extended the continuum Ricardian model of Dombusch et al. (1977)

based on the "quality ladders" approach by Grossman and Helpman. All these studies

exhibit the scale effect property: if one incorporates population growth in these models,

then the size of the economy (scale) increases exponentially over time, R&D resources

grow exponentially, and so does the long-run growth rate of per-capita real output.

The scale effects property is a consequence of the assumption that the growth rate of

knowledge is directly proportional to the level of resources devoted to R&D. Jones

(1995a) has argued that the scale effects property of earlier endogenous growth models is

inconsistent with post-war time series evidence from all major advanced countries that

shows an exponential increase in R&D resources and a more-or-less constant rate of per-

capita GDP growth. Jones's criticism has stimulated the development of a new class of

models that generate growth without scale effects.37 However, the theoretical literature on


37 See Dinopoulos and Thompson (1999) for more details on this issue.








trade and growth without scale effects has focused either on closed economy models or

on structurally identical economies engaging in trade with each other.38 This chapter

develops a two-country general equilibrium framework without scale effects to determine

the equilibrium relative wages and the pattern of trade between countries.

My approach borrows from Taylor's work (1993) in that industries differ in

production technologies. In his model, industries also differ in research technologies and

in the set of technological opportunities available for each industry. In the presence of

heterogeneous research technologies (captured by different productivity in R&D

services), the pattern of R&D production and the pattern of goods production within each

country can differ. As a result, there is a case for trade between countries in R&D

services. The absence of heterogeneity in research technologies in my model makes the

removal of scale effects more tractable, but eliminates the need for trade in R&D services

between countries.

In the present model, there are two countries that may differ in relative size:

Home and Foreign. The population in each country grows at a common positive and

exogenously given rate and labor is the only factor of production. There is a continuum of

industries producing final consumption goods. Labor in each industry can be allocated

between the two economic activities, manufacturing of high-quality goods and R&D

services, which are used to discover new products of higher quality. As in Grossman and

Helpman 's (199 Ic) version of the quality-ladders growth model, the quality of each final




8Dinopoulos and Syropoulos (2001) have recently developed a two-country general
equilibrium model of endogenous Schumpeterian (R&D based) growth without scale
effects to examine the effect of globalization on economic growth when countries differ
in population size and relative factor endowments.








good can be improved through endogenous innovation. The arrival of innovations in each

industry is governed by a memoryless Poisson process whose intensity depends

positively on R&D investments and negatively on the rate of difficulty of conducting

R&D. I consider two alternative specifications regarding the difficulty of conducting

R&D in order to remove the scale effects property. The first specification is called the

permanent effects of growth (PEG) and it has been proposed by Dinopoulos and

Thompson (1996). According to this specification, R&D becomes more difficult over

time and the degree of R&D difficulty is proportional to the size of the world market.

The second specification is called the temporary effects of growth (TEG) and it

has been proposed by Segerstrom (1998). With this specification, R&D also becomes

more difficult over time but the degree of difficulty is an increasing function of

cumulative R&D effort in each industry.

The removal of scale effects property under either specification regarding the

R&D difficulty leaves some predictions in Taylor's (1993) model robust. A uniform

increase in Home's unit production costs reduces its relative wage and reduces its range

of goods that Home produces. A uniform increase in Foreign's unit production costs

increases Home's relative wage and increases Home's comparative advantage. In

addition, Home's relative wage and its comparative advantage are left unaffected by

equiproportionate changes in Home and Foreign production costs. Finally, factor price

equalization is not a generic property of the steady-state equilibrium. However, several

comparative-steady-state results in Taylor's (1993) model change with the removal of the

scale effects property. First, in his model, the direction of the effect of the size of

innovations (which can vary across industries) on the pattern of goods production, R&D








production, the pattern of trade, and the relative wage depends on the assumption that the

size of innovations is heterogeneous. Under the heterogeneity assumption, the increase in

the inventive step creates a deficit in the balance of payments for Home because it raises

the royalties' payments that Home has to pay for using the front-line technology.39

Balance of payments is maintained through two adjustments; Home raises its goods trade

balance by increasing the range of goods produced at Home and it reduces its reliance on

imported R&D by conducting more itself. Removing part of this heterogeneity in his

model, by eliminating Home's relative advantage in goods versus R&D, results in zero

trade in R&D and no effect of the size of innovations on the pattern of trade and Home's

relative wage.40 On contrast, in the present model, the direction of the effect of the size of

innovations on the pattern of trade and Home's relative wage depends on the way in

which the scale effects property is removed. Under the PEG specification, changes in the

size of innovations do not affect Home's comparative advantage and its relative wage,

while under the TEG specification, an increase in the size of innovations reduces Home's

relative wage and raises its comparative advantage.

Under the PEG specification, the increase in the size of innovations increases the

profitability of R&D activity. As a result, more firms enter into R&D races until the




39 Taylor (1993) divides the world's available technologies into two sets: the set of front
line technologies and the set of backward technologies. Frontline technologies are those
that are minimum cost given the prevailing wage rate. He further assumes that when an
innovator located in Foreign succeeds in the global R&D races and discovers the front
line technology, it has two options: it can either implement this improvement on the
foreign technology or it can go multinational and carry the innovation abroad to a wholly
owned subsidiary. This subsidiary would then pay the foreign firm a royalty.

40 Eliminating the across country heterogeneity in his model, results in factor price
equalization and indeterminate pattern of trade in both goods and R&D.








expected profits are driven back to zero. The adjustment to equilibrium requires an

increase in the level of global R&D investment, while it leaves Home's relative wage and

its comparative advantage unchanged. On contrast, the TEG specification implies that the

global level of R&D investment depends positively on the rate of population growth and

negatively on the R&D difficulty parameter, since the R&D difficulty grows at the

constant rate of population growth rate at the steady-state equilibrium. Therefore, an

increase in the size of innovations raises the rewards of innovating and thus it induces

more firms to engage in R&D. However, since the long-run level of R&D activity is

fixed by the unchanged parameters of the model, to maintain the equilibrium, the relative

wage has to decrease. The decrease in Home's relative wage raises its comparative

advantage.

Second, the direction of the effect of a change in R&D costs in Taylor's (1993)

model depends on the heterogeneous research assumption. A uniform increase in Home's

R&D costs reduces Home's relative wage and raises the measure of Home industries

active in production. A uniform increase in Foreign's costs increases Home's relative

wage and reduces the measure of Home industries active in production. However, if one

considers an equiproportionate changes in R&D costs in his model, then the effect of

these changes on Home's relative wage and its comparative advantage is ambiguous.41




41 This ambiguity arises because R&D technologies play two roles in Taylor's (1993)
model. First, R&D technologies determine the competitive margin for R&D production
within each country and the division of R&D across countries. Second, R&D
technologies determine, via the free entry process into the R&D, the value of a patent in
any industry. Equiproportionate changes in Home and Foreign unit R&D labor
requirements increase the value of patents and thus raise world expenditure levels. The
effect of the increased world expenditure on Home produced goods is ambiguous without
making further assumptions.








Eliminating the heterogeneous research technologies assumption, results in factor price

equalization in any equilibrium with both countries conducting R&D. In this case, an

equiproportionate changes in R&D costs in his model, has no effect on Home's relative

wage and its comparative advantage. Furthermore, if one assumes the absence of

heterogeneous size of innovations and unity budget share for products in Taylor's model,

then an equiproportionate changes in R&D costs makes Home conduct less R&D.

On contrast, in the present model, the direction of the effect of an

equiproportionate change of the unit R&D labor requirement depends on the way in

which the scale effects property is removed. Under the PEG specification, an increase in

R&D costs reduces Home's relative wage and raises its comparative advantage, while

under the TEG specification, changes in R&D costs do not affect Home's relative wage

and its comparative advantage.

Under the PEG specification, the increase in R&D costs decreases the profitability

of R&D activity. As a result, fewer firms enter into R&D races until the expected profits

are driven back to zero. The adjustment to equilibrium requires a decrease in the level of

Home's relative wage. The decrease in Home's relative wage raises its comparative

advantage. On contrast, under the TEG specification, since the long-run level of R&D

activity is fixed by the unchanged parameters of the model, an increase in R&D costs,

increases the population-adjusted difficulty of R&D and thus leaving Home's relative

wage and its comparative advantage unchanged.

The analysis in the present model generates new additional findings. Under both

specifications, the model generates a unique steady-state equilibrium in which there is

complete specialization in both goods and R&D production within each industry. Trade








between the two countries occurs only in goods and not in R&D services. In contrast to

the work of Grossman and Helpman (1991c), factor price equalization does not hold in

the steady-state equilibrium under either specification (Propositions 1 and 5).

Under the PEG specification, Home's relative wage depends positively on the

Foreign's relative size, Foreign's unit labor requirement in manufacturing, and the

population growth rate. It depends negatively on the R&D difficulty parameter, the unit

R&D labor requirement, the consumer's subjective discount rate, and Home's unit labor

requirement in manufacturing (Proposition 2). In contrast to previous models (Grossman

and Helpman (1991c), and Taylor (1993)), these results highlight the effects of

population growth and the R&D difficulty on relative wages.

Under the PEG specification, the range of goods produced in Home and exported

depends positively on the R&D difficulty parameter, the unit R&D labor requirement, the

consumer's subjective discount rate, and Foreign's unit labor requirement in

manufacturing. It depends negatively on Foreign's relative size, the population growth

rate, and Home's unit labor requirement in manufacturing (Proposition 3). These results

also highlight the importance of population growth and the R&D difficulty parameter on

the pattern of goods and R&D production, and the pattern of trade between the two

countries.

In addition, when the scale effects property is removed via the PEG specification,

the global innovation rate depends positively on Home's relative size measured by its

share of world's population, Foreign's relative size measured by its share of world's

population, and the population growth rate. It depends negatively on the R&D difficulty








parameter, the consumer's subjective discount rate, and the unit R&D labor requirement

(Proposition 4).

Some results that hold under the PEG specification analysis are reversed when the

TEG specification is introduced in the model. Home's relative wage depends positively

on the consumer's subjective discount rate and the R&D difficulty growth parameter. It

depends negatively on the population growth rate (Proposition 6). The range of goods

Home produces and exports depends positively on the population growth rate. It depends

negatively on the consumer's subjective discount rate and the R&D difficulty growth

parameter (Proposition 7).

The global level of R&D investment, under the TEG specification is completely

determined by the exogenous rate of population growth and the R&D difficulty growth

parameter. Specifically, the global innovation rate is higher when the population of

consumers grows faster or when R&D difficulty increases more slowly over time

(Proposition 8).

This chapter is organized as follows. Section 4.2 outlines the features of the

model. Section 4.3 describes the steady state equilibrium of the model under the PEG

specification and section 4.4 presents the comparative steady state results under the PEG

specification. Section 4.5 analyzes the steady state equilibrium of the model under the

TEG specification and section 4.6 presents the comparative steady state results under the

TEG specification. Section 4.7 concludes this chapter by summarizing the key findings

and suggesting possible extensions. The algebraic details and proofs of propositions in

this chapter are relegated to Appendix C.








4.2 The Model

This section develops a two-country, dynamic, general-equilibrium model with

the following features. Each country engages in two activities: the production of final

consumption goods and research and development. Each of the two economies is

populated by a continuum of industries indexed by 0 E [0, 1]. A single primary factor,

labor, is used in both goods and R&D production for any industry. In each industry 0

firms are distinguished by the quality j of the products they produce. Higher values ofj

denote higher quality and j is restricted to taking on integer values. At time t =0, the

state-of-the-art quality product in each industry is j=0, that is, some firm in each

industry knows how to produce a j=0 quality product and no firm knows how to

produce any higher quality product. The firm that knows how to produce the state-of-the-

art quality product in each industry is the global leader for that particular industry. At the

same time, challengers in both countries engage in R&D to discover the next higher-

quality product that would replace the global leader in each industry. If the state-of-the-

art quality in an industry is j, then the next winner of an R&D race becomes the sole

global producer of aj+ quality product. Thus, over time, products improve as

innovations such as push each industry up its "quality ladder," as in Grossman and

Helpman (1991c).

I assume for simplicity, that all firms in the global economy know how to produce

all products that are at least one step below the state-of-the-art quality product in each

industry. This assumption, which is standard in most quality-ladders growth models,

prevents the incumbent monopolist from engaging in further R&D, which is standard

assumption in most quality-ladder models.








For clarity, I adopt the following conventions regarding notation. Henceforth,

superscripts "h" and "f" identify functions and variables of "Home" and "Foreign"

countries, respectively. Functions and variables without superscripts are related to the

global economy, while functions and variables with subscripts are related to activities and

firms within an industry.

4.2.1 Household Behavior

Let N'(t) be country i's population at time t. I assume that each country' s

population is growing at a common constant, exogenously given rate

g, = N'(t)/N'(t) > 0. In each country there is a continuum of identical dynastic families

that provide labor services in exchange for wages, and save by holding assets of firms

engaged in R&D. Each individual member of a household is endowed with one unit of

labor, which is inelastically supplied. I normalize the measure of families in each country

at time 0 to equal unity. Thus, the population of workers at time t in country i is

N(t) = e"'

Each household in country i maximizes the discounted utility42

U= e '"" logu(t)dt, (1)

where p > 0 is the constant subjective discount rate. In order for U to be bounded, I

assume that the effective discount rate is positive (i.e., p g, > 0). Expression log u(t)

captures the per capital utility at time t, which is defined as follows:

logu(t) log[ 'q(j,0, t)]dO. (2)



42 Barro and Sala-i-Martin (1995, Ch. 2) provide more details on this formulation of the
household's behavior within the context of the Ramsey model of growth.








In equation (2), q (j, 0, t) denotes the quantity consumed of a final product of quality

(i.e., the product that has experienced j quality improvements) in industry 09 [0,1] at

time t. Parameter X > 1 measures the size of quality improvements (i.e., the size of

innovations).

At each point in time t, each household allocates its income to maximize (2) given

the pre' all.r mrrrkci prices. Solving this optimal control problem yields a unit elastic

demand function for the product in each industry with the lowest quality-adjusted price

c'(t)N'(t)
q'(j, t)= (t (3)
p'(t)

where c (t) is country i's per capital consumption expenditure, and p(t) is the market

price of the good considered. Because goods within each industry adjusted for quality are

by assumption identical, only the good with the lowest quality-adjusted price in each

industry is consumed. The quantity demanded of all other goods is zero. The global

demand for a particular product is given by aggregating equation (3) across the two

countries to obtain

q(j,a0, t)= ,q'(j,0,t). (4)
i=h.r

Given this static demand behavior, the intertemporal maximization problem of

country i's representative household is equivalent to

max je -"(-g, logc'(t)dt, (5)


subject to the intertemporal budget constraint (t)= r (t)a(t) + w'(t) c' (t) ga',

where a'(t) denotes the per capital financial assets in country i, w'(t) is the wage income

of the representative household member in country i, and r'(t) is country i's








instantaneous rate of return at time t. The solution to this maximization problem obeys

the well-known differential equation


(t) r'(t)- p, (6)
c'(t)

Equation (6) implies that a constant per-capita consumption expenditure is optimal when

the instantaneous interest rate in each country equals the consumer's subjective discount

rate p.

4.2.2 Product Markets

In each country firms can hire labor to produce any final consumption good

0 e[0,1]. Let L'(6, t) and Q'(6,t) respectively denote the amounts of labor devoted in

manufacturing of final consumption good 0 in country i and the output of final

consumption good 0 in country i. Then the production function of the final consumption

good 0 in country i is given by the following equation


Q'(, t)= L(,) (7)


where a'(0) is the unit labor requirement associated with the final consumption good 0

in country i. I assume that each vertically differentiated good must be manufactured in

the country in which the most recent product improvement has taken place. That is, I rule

out international licensing and multinational corporations.43




43 Taylor (1993) incorporates multinational corporations in a model of endogenous
growth and trade. In his model, innovations are always implemented on front line
production technologies (i.e., technologies that are minimum cost given the prevailing
wage rates) and when innovation and implementation occur at different countries, the
resulting transactions are considered as imports and exports of R&D.








Following Dombusch et al. (1977), the relative labor unit requirement for each

good 0 is given by


A(0)=- A'(0) <0. (A.1)
al(0)

The relative unit labor requirement function in (A. ) is by assumption continuous, and

decreasing in 0.

The assumptions that goods within an industry are identical when adjusted for

quality and Bertrand price competition in product markets imply that the monopolist in

each industry engages in limit pricing. The assumption that the technology of all inferior

quality products is public knowledge imply that the quality leader charges a single price,

which is times the lowest manufacturing cost between the two countries:

p =min a (0) wh,a (0)w ). (8)

I choose the wage of foreign labor, w', as the numeraire of the model by setting:

w'-l. (9)

I also assume that the wage of home labor, w h, which is also Home's relative wage, o, is

greater than one44

w =CO >1. (10)

Assumption (10) implies that the price of every top quality good is equal to

p=ka(09). (11)

It follows that the stream of profits of the incumbent monopolist that produces the state-

of-the-art quality product in Home will be equal to


44 In Propositions I and 5, I provide sufficient conditions under which this assumption
holds.









,(9,t)=[,, ., ; l- j) E(t), (12)

while the stream of profits of the incumbent monopolist that produces the state-of-the-art

quality product in Foreign will be equal to

7'(0, t) = [a (0)-a (0)]q = E(t), (13)


where E(t)[ch (t)N(t) + c (t)N (t)] is the world expenditure on final consumption

goods.

4.2.3 R&D Races

Labor is the only input engaged in R&D in any industry 0 e[0,1]. Let L' (0, t)

and R'(0, t) respectively denote the amounts of labor devoted in R&D services in

industry 0 in country i and the output of R&D services in industry 0 in country i. The

production function of R&D services in industry 0 in country i exhibits constant returns

and is given by the following equation45

R'(0,t) = L ) (14)
,R

where aR is the unit labor requirement in the production of R&D services. Note that the

absence of a superscript and the absence of the industry index 0 in the unit labor

requirement imply that they are the same across countries, industries and goods of



45 The empirical evidence on returns to scale of R&D expenditure is inconclusive.
Segerstrom and Zolnierek (1999) among others developed a model where they allow for
diminishing returns to R&D effort at the firm level and industry leaders have R&D cost
advantages over follower firms. In their model, when there are diminishing returns to
R&D and the government does not intervene both industry leaders and follower firms
invest in R&D.








different quality levels. The absence of heterogeneous research technologies allows me to

focus on the implications of assumption (A. 1) on the properties of the model.46

In each industry 0 there are global, sequential and stochastic R&D races that

result in the discovery of higher-quality final products. A challenger firm k that is located

in country i E {h,f }targeting a quality leader in country i E {h,f} engages in R&D in

industry 0 and discovers the next higher-quality product with instantaneous probability

1k (0, t)dt, where dt is an infinitesimal interval of time and


Ik'(6,t)- R(, (15)
X(t)

where R, (0, t) denotes firm k's R&D outlays and X(t) captures the difficulty of R&D in

industry 0 at time t. I assume that the returns to R&D investments are independently

distributed across challengers, countries, industries, and over time. Therefore, the

industry-wide probability of innovation can be obtained from equation (14) by summing

up the levels of R&D across all challengers in that country. That is,


I'(, t)= I ;( (0 t) (16)
k X(t)

where R' (, t) denotes total R&D services in industry 0 in country i. Variable I'(0, t) is

the effective R&D.47 The arrival of innovations in each industry follows a memoryless


46 Taylor (1993) has introduced heterogeneity in the research technologies and in the
technological opportunity for improvements in technologies. The presence of
heterogeneous research technologies makes trade in R&D services between countries
possible. The absence of heterogeneous research technologies in the present model,
makes the removal of scale effects more tractable, but eliminates the possibility of trade
in R&D services between the two countries.

47 The variable I'(0, t) is the intensity of the Poisson process that governs the arrivals of
innovations in industry 0 in country i. Dinopoulos and Syropoulos (2001) model the








Poisson process with intensity I(0,t)= ZR'(0,t)/X(t)which equals the global rate of


innovation in a typical industry. The function X(t) has been introduced in the endogenous

growth literature after Jone's (1995a) empirical criticism of R&D based growth models

generating scale effects.

A recent body of theoretical literature has developed models of Schumpeterian

growth without scale effects.48 Two alternative specifications have offered possible

solutions to the scale-effects property. The first specification proposed by Dinopoulos

and Thompson (1996) removes the scale-effects property by assuming that the level of

R&D difficulty is proportional to the market size measured by the level of population,

X(t)= kN(t), (17)

where k > 0 is a parameter.

This specification captures the notion that it is more difficult to introduce new

products and replace old ones in a larger market. The model that results form this

specification is called the permanent effects of growth (PEG) model because policies

such as an R&D subsidy and tariffs can alter the per-capita long-run growth rate.49

The second specification proposed by Segerstrom (1998) removes the scale





strategic interactions between a typical incumbent and its challengers as a differential
game for Poisson jump processes and derive the equilibrium conditions that govern the
solution to a typical R&D contest. They also provide an informal and intuitive derivation
of these conditions. In the present model, I follow their informal derivation to derive my
results.

48 See Dinopoulos and Thompson (1999) for an overview of these models.

49 Dinopoulos and Thompson (1998) provide micro foundations for this specification in
the context of a model with horizontal and vertical product differentiation.








effects property by assuming that R&D becomes more difficult over time because "the

most obvious ideas are discovered first." The model that results from this specification is

called the temporary effects of growth (TEG) model. In this model, the long-run growth

rate is proportional to the exogenous rate of population growth and it is not affected by

any standard policy instruments.

Under the TEG specification, R&D starts being equally difficult in all industries

(X(0,0)= 1 for all ), and the level of R&D difficulty grows according to

X(t) =_[lh(0,t)+If('i, i ]= =I(0,t), (18)
X(t)


where t > 0 is a constant.

In subsequent sections I will consider each specification separately to analyze the

steady-state equilibria and to derive their comparative-static properties.

Consider now the stock-market valuation of temporary monopoly profits.

Consumer savings are channeled to firms engaging in R&D through the stock market.

The assumption of a continuum of industries allows consumers to diversify the industry-

specific risk completely and earn the market interest rate. At each instant in time, each

challenger issues a flow of securities that promise to pay the flow of monopoly profits if

the firm wins the R&D race and zero otherwise.50 Consider now the stock-market

valuation of the incumbent firm in each industry. Let V'(t) denote the expected global

discounted profits of a successful innovator at time t in country i, when the global

monopolist charges a price p for the state-of-the-art quality product. Because each global



50 If the monopolist is located in Home, the monopoly profits are define by equation (12)
and if the monopolist is located in Foreign the monopoly profits are defined by equation
(13).








quality leader is targeted by challengers from both countries who engage in R&D to

discover the next higher-quality product, a shareholder faces a capital loss V'(t) if further

innovation occurs. The event that the next innovation will arrive occurs with

instantaneous probability Idt, whereas the event that no innovation will arrive occurs with

instantaneous probability 1-Idt. Over a time interval dt, the shareholder of an incumbent's

stock receives a dividend xt(t)dt and the value of the incumbent appreciates by

dV (t) = [aV'(t)/5t]dt = V (t)dt. Perfect international capital mobility implies that

rh = r' = r. The absence of profitable arbitrage opportunities requires the expected rate

of return on stock issued by a successful innovator to be equal to the riskless rate of

return r; that is,

V'( ,tdttdt (6,t)d~ [V'(6, t)-0]
t[1 I(0, t)dt]dt + dt t) 1(0, t)dt = rdt. (19)
v'(0,t) v'(0, t) v'(O, t)

Taking limits in equation (19) as dt -> 0 and rearranging terms appropriately gives the

following expression for the value of monopoly profits


VV ((6,,t)
r(t)+ I(0, t) V(0,
V'(0, t)

A typical challenger k located in country i chooses the level of R&D investment

Rk (0, t) to maximize the following expected discounted profits:

R (O, t)
V'(, t) --k tdt-w'aR (, t)dt, (21)
X(t)

where I dt = [Rk(0, t)/X(t)]dt is the instantaneous probability of discovering the next

higher-quality product and w'agRR (0,t) is the R&D cost of challenger k located in

country i.








Free entry into each R&D race drives the expected discounted profits of each

challenger down to zero and yields the following zero profit condition:

V'(t)= w'aRX(t). (22)

The pattern of R&D production across the two countries can be determined by utilizing

equations (20) and (22). Evaluating these equations on the competitive margin in R&D

production, I can obtain the R&D schedule (i.e., the schedule of relative labor

productivities in goods) as follows


co=RD(0)= (23)
a,(6)

where RD(6) is continuous and decreasing in 6 For low values of 0, Home has higher

relative labor productivity than Foreign, and thus it earns higher wage. Therefore, Home

has comparative advantage in producing and conducting R&D the final goods with lower

0 and Foreign has comparative advantage in producing and conducting R&D the final

goods with higher 0. The R&D schedule can be depicted in Figure 4-1.

Lemma 1. Under assumption (A.1) and for any given value of the relative wage,

ro e (, i',l/a (1), a (0)/ao (0)), there exists an industry 0 defined by equation (23)

such that

(a) firms are indifferent between conducting R&D in Foreign or in Home,

(b) for each industry 0 e [0, ), only Home conducts R&D,

(c) for each industry 0 e (, 1], only Foreign conducts R&D.

Proof. See Appendix C.








One can find the results from Lemma 1 in Dombusch et al. (1977). However, the

derivation of Lemma 1 differs between the present model and the one in Dombusch et al.

(1977). In their model, the results from Lemma 1 come from the assumption of perfect

competition in all markets. In the present model, the intuition behind Lemma 1 results

from the zero profit conditions regarding R&D. If in industry 0, R&D is undertaken by

Home, then the zero profit conditions for R&D imply that Foreign has negative profits in

this particular industry (see equations (20) and (22)). Thus, for all industries that Home

undertakes R&D, Foreign has negative profits and does not engage in R&D in these

industries. The reverse is true for those industries that Foreign undertakes R&D. Home

has negative profits in these industries, so it does not engage in R&D in those industries.

Thus, both countries sustain their comparative advantage.

4.2.4 Labor Markets

Consider first the Home labor market. All workers are employed by firms in

either production or R&D activities. Taking into account that each industry leader

charges the same price p and that consumers only buy goods from industry leaders in

equilibrium, it follows from (7) that total employment of labor in production in Home is

[I Q'(O,t)axd9. Solving equation (14) for each industry leader's R&D employment

L' (0, t) and then integrating across industries, total R&D employment by industry

leaders in Home is E R"(O,t)aRdO. Thus, the full employment of labor condition for

Home at time t is given by

N"(t)= J Q' .' I 1" ,idi+ EJ Rh(0,t)ad. (24)




Full Text
xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID E7LZK7IRR_9HNIHZ INGEST_TIME 2013-10-10T03:10:44Z PACKAGE AA00017638_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES