Endogenous Innovation in Neo- Classical Growth Models: A ... · Some recent literature in the neo-classical tradition dealing with the relation be- tween endogenous technological

f3ARTVERSPAGEN Maastricht Economic Research

Institute on Znnooation

and Technology

Unioersity of Limburg

Maastricht. The Netherlands

Endogenous Innovation in Neo- Classical Growth Models: A Survey*

Some recent literature in the neo-classical tradition dealing with the relation between endogenous technological change and economic growth is summarized. The main results of this “new” neo-classical approach to economic growth are compared to the basic (Solow) neo-classical growth model. Special attention is paid to the role of government in the process of economic growth and endogenous innovation. An assessment of the main achievements and limitations of the new models will be given.

1. Introduction The issue of economic growth received considerable attention

directly after the second world war. Contributions from different economic schools, such as the neo-Keynesian (the Harrod and Do- mar model), the post-Keynesian (Kaldor, Robinson) and the neo- classical school (Solow), all presented their own view on what determines (aggregate) economic growth paths and how stable these growth paths are.

One central element in growth theories must be technological change. A theory of economic growth abstracting from technological progress can hardly be imagined. In the basic neo-classical model, Solow (1956, 1957, 1970), it is assumed that technological change is exogenous to the economic process. Recently, the interest in technological change as an endogenous economic phenomenon has increased drastically (an overview is in Gomulka 1999). New in- sights from this literature have led to a reformulation of the assumptions on the nature of technological change in neo-classical macroeconomic growth models.

The aim of this paper is to give an overview of some of the most important contributions in recent neo-classical modeling of endogenous technological change and economic growth and to discuss

*I thank Thomas Ziesemer and an anonymous referee for helpful comments on an earlier version of this paper.

Journal of Macroeconomics, Fall 1992, Vol. 14, No. 4, pp. 631-662 631 Copyright 0 1992 by Louisiana State University Press 0164-0704/92/$1.50

Bart Verspagen

the main achievements and limitations. This latter purpose will hopefully provide some useful clues for future research. Although the set of papers in this field is already much richer than the few papers considered here, the basic ideas can be summarized by con- sidering only this limited set of contributions.

One could argue that the models surveyed are not neo-classical because they depart from some of the assumptions made in the basic neo-classical model of economic growth. But since these models also have some strong similarities with that model (the equilibrium notion and the rational behavior assumption of economic agents), they fit the neoclassical tradition quite well. In order to make a distinction between the basic neo-classical model and the newer models treating innovation as an endogenous phenomenon, the latter type of models will be called “new” neo-classical models here. ’

The main topic in this overview will be the relation between technological change and economic growth. Mathematical formulations will only be used to illustrate the model structure of the papers discussed. This means that the paper will not go into the mathematical detail of the solutions of the models under consid- eration, so that the emphasis is rather on the theoretical back- grounds of the models discussed than on the technical implemen- tation of it. The reader interested in the technicalities is referred to the original work discussed here. An explanation of the relation between endogenous innovation and economic growth has also been given in recent work in the evolutionary tradition. However, the character of this work is much less formal and more heterogenous (with regard to methods). than the neo-classical models surveyed here. Therefore, the evolutionary models will only briefly be considered.

The rest of this paper is organized as follows. In Section 2, the broad historical theoretical context of models on innovation and growth will briefly be recapitulated. This section serves as an introduction to Section 3, where the main contributions in new neo- classical growth theory will be reviewed. Subsections of Section 3 will in turn consider the role of externalities and increasing returns, the role of monopoly power and the appropriability of innovations, the characteristics of the optimal and equilibrium growth paths, the role of international trade in new neo-classical growth theory and

‘This terminology will be used in spite of the fact that it involves a double use of the proverb new. The term neo-classical on its own Falsely suggests that there is a clear-cut relation between classical and neo-classical economics.

Endogenous Znnouation in Neo-Classical Growth Models

the main differences between old and new neo-classical growth models. Section 4 will shortly summarize the main conclusions.

2. The Historical Theoretical Context The notion of endogenous technological progress was present

in the work of the classic school (especially Smith and Marx) and, from there, became prominent in the work by Schumpeter (for example, Schumpeter 1934). In the first neo-classical growth models, technological change was reduced to an exogenous phenomenon, basically for analytical convenience.

The assumptions in this model are 1) that the capital labor ratio depends on the factor price ratio (substitution); 2) that markets are assumed to clear and to be competitive; 3) that technological progress is exogenous and of the labor-augmenting type. The outcome of the model is that the rate of growth of output and the rate of growth of the capital stock are equal to the rate of growth of the labor force plus the rate of labor-augmenting technological progress.

pre-modern 1960 1970 1960 1990

Figure 1. An Interpretation of the Structure of the Literature on Technological Change and

Economic Growth

633

Bart Verspagen

It can be shown (Lucas 1988) that this growth path (established without government intervention) is not only a stable path, but also a socially optimal path.

Intuitive support for the assumption of exogenous technological change might be found in the public good characteristics of innovation. The user of technological change does not have to develop the innovation himself, but can (partly) rely upon other agents to develop the knowledge and then simply copy (or buy) it. This notion was introduced in the (neoclassical) literature by Arrow (1962). Still, the question remains why innovations would be “produced’ at all if one simply uses this explanation for the assumption of exogenous technological change.’ If technological change is a purely public good, there will be no incentive to produce and sell it on the market.

Possible answers to this problem are the following. First, Schumpeter argued that monopoly power is the principal means of appropriating an innovation. Second, a patent system might create legal protection from imitation. Third, a time-lead might give the innovator enough opportunities to earn back the innovation costs. All these possibilities have been developed in an analytical way in the literature on industrial organization (Kamien and Schwartz 1982; Scherer and Ross 1990).

Other neo-classical models of endogenous innovation have also been formulated. However, most of these models were mainly dealing with the character and pace of innovation itself, and not so much with economic growth. In contributions by, among others, Kennedy and Binswanger (for a survey and exact references see Thirtle and Ruttan 1987), the factor price ratio was identified as one of the main (endogenous) determinants of the character of innovation in models on endogenous biases of innovation. In another approach (started by the seminal work by Schmookler 1966), effective demand was considered as a main engine for the pace of innovation. However, the literature on endogenous technological change in growth models died out after a few early contributions by Uzawa (1965), Phelps (1966) and Shell (1967). Th ese papers specified models in which human capital formation is a main determinant of technological change.

The idea of endogenous innovation in a theory of economic

*Moreover, as has been recognized by Dosi (1988) and Cohen and Levinthal (1989), among others, imitation of technological knowledge developed elsewhere might be a costly activity.

634

Endogenous Innovation in Neo-Classical Growth Models

growth has also been a major source of inspiration for the evolutionary or neo-Schumpeterian literature that was initiated recently by authors like Nelson and Winter (1982) and Dosi et al. (1988). Out-of-equilibrium dynamics and bounded rational behavior are key concepts in this literature, which makes it quite different from the new neo-classical growth models. Therefore, these Schumpeterian theories will not be discussed extensively here. They will only be touched on on occasions where the relation to the models discussed here is quite strong.

Another novelty in the (neo-classical) literature, the use of nonlinear dynamics methods, will not be considered here. These models, of which examples are in Anderson, Arrow and Pines (1988) and Blanchard and Fisher (1989, ch. 5), provide interesting results, but usually do not take into account technological change in an explicit way, and therefore are beyond the scope of this survey.3

The new neo-classical growth models considered in the next section seem to be related to all this literature in the following way. The general setting of the model is taken from the basic neo-classical growth model (Solow). The attempts to endogenize innovation draw on the early papers on endogenous innovation and growth. The specific ways of modeling endogenous innovation draw on the literature of industrial organization.

3. New Neo-Classical Growth Models The central factor explaining economic growth in new neo-

classical growth theory is endogenous innovation. In order to endogenize innovation, these models have to deal with the public good features of technological progress, and the problems this poses with regard to appropriability of innovation. First, the role of externalities will be discussed. The presence of externalities is closely associated to increasing returns to scale in the production function. Second, the role of market structure (monopoly power) in the appropriability of innovation will be discussed.

Both the presence of increasing returns and monopoly power are important novelties in neo-classical growth theory. These features of the model shed a wholly different light upon the concept of perfect competition as a means to achieve a socially optimal growth path. Therefore, the characterization of socially optimal and equi-

3An exception is the chapter by Boldrin and Scheinkman in Anderson, Arrow and Pines (1988). which is an elaboration of the Lucas paper discussed below.

635

Burt Verspagen

librium growth paths will be the third and fourth issues in the survey. Fifth, the consequences for the international trade and the international distribution of growth will be discussed. The last topic will be the similarities and differences between old and new neo- classical growth models.

Innovation: Externalities and Zncreasing Returns New neo-classical growth models follow Arrow (1962) in as-

suming that there are important externalities concerned with the development of technical knowledge. In most cases, these externalities take the form of general technological knowledge which can be used to develop new methods of production and is available to all firms. An exception to this specification is Lucas (1988), where the externalities take the form of public learning, which increases the stock of human capital.

The existence of externalities in the innovation process is closely connected to an important novelty in new neo-classical growth models: the existence of increasing returns to scale in the aggregate production function. In the old neo-classical model, it is typically assumed that the production structure is characterized by constant returns to scale. Multiplying factor inputs by some (positive) number will also multiply output by that number. The presence of externalities, however, means that if one firm (say) doubles its inputs, the inputs of other firms will also increase. Hence a more than proportionate increase in aggregate output results.

In the case of constant returns to scale, a larger resource base can influence the level of output, but not the growth rate. In case of endogenous technological change, innovation itself is a factor of production. Since, as in the old model, innovation can influence the growth rate of production, the case of constant returns to scale no longer applies. Instead, the production function is characterized by increasing returns to scale.

Different approaches to incorporating externalities and increasing returns to scale have been proposed. An overview of the different models, as well as a more precise indication of the mathematical implication of the ideas discussed, is given in Table 1.

Perhaps the most clear and simple way of modeling the externalities involved in the innovation process is found in early papers like Romer (1986) and Lucas (1988). In this approach, technological change is treated as a separate factor in the (aggregate) production function. Individual agents (firms, laborers) invest in (some form) of technological change, and spillovers of this investment are

636


added to the inputs of all other firms. These models have no explicit microeconomic foundation for the production of knowledge (in a separate research sector) itself, and hence do not in an explicit way address the question of market structure and a market price for technological change. They only look at the consequences of investment in knowledge.

The general form of these models assumes that technological change enters the production function of an individual entrepreneur in two separate terms. The first term describes the outputs of private investments in knowledge, which have the normal characteristics (decreasing marginal returns). The second term describes the existence of knowledge spillovers. This term is related to the other firms’ investment in knowledge. In mathematical terms, this can be stated as follows.

Qi = Fi(Ti, Li, T) .

In this equation Q is output, L is some (conventional) production factor like labor, T represents the stock of investment in technological change (human capital in Lucas 1988) and i (1 . . . m) is an index representing the ith firm. The bar indicates a general volume, available to all firms in the economy. In Romer (1986), it indicates the sum of all individual Ts, while in Lucas (1988) it is the average level of human capital.

An obvious drawback of this simple approach is the lack of a clear microeconomic foundation explaining the working of the externalities, and the decision to invest in technological change. Later models following the early contributions of Romer (1986) and Lucas (1988) have tried to fill this gap. Most notable contributions are in Aghion and Howitt (1990), Romer (1990) and Grossman and Help- man (1989, 1990, 1991). Some of the implicit assumptions about (the output ol) the research sector made in the early approach are made explicit in this second approach. The general approach chosen in this second type of models is to make a distinction between a research sector and other sectors in the economy. Then technological change is explained from the perspective of market structure and price relations.

The research sector typically produces two types of goods: blueprints of new (intermediate) goods and (general) technological knowledge. A (first) difference between blueprints and general knowledge is with regard to the application in the production process. General technological knowledge cannot be applied directly in

637

Burt Verspagen

the production of goods, but has a more general nature. It adds to the productivity in the research sector, and thus is used in the production of blueprints. General knowledge is produced as a by-product of the innovation process. It can be used not only by the entrepreneur who develops it explicitly, but also by other firms in the research sector (non-appropriability). Its effect is thus completely public, so that this embodies the externalities in the innovation process.

Blueprints are specific. They provide the guidelines to produce a given type of intermediate good (or consumer good). Firms operating in the research sector principally devote their efforts to producing and selling these blueprints. The level of output (in the form of blueprints) in the research sector depends on employment input, general knowledge input and a (fixed) productivity parameter. Blueprints yield a positive price because they enable producers of consumer or intermediate goods to produce at lower cost or higher quality.

Two different approaches to modeling the advance in general knowledge are found. The first one is originally in Aghion and Howitt (1990). There, technological change increases the productivity in the production of intermediate goods. It is assumed that the development of production costs of intermediate goods over time takes the following form.

c,(i) = c, = c,y ’ , (2)

where c stands for production costs, y is a parameter indicating the size of the innovation (technological opportunity), and i denotes a specific intermediate good. A period t is specified as the time span during which one blueprint is used, so that each time an innovation occurs, the production costs are reduced.

Grossman and Helpman (1991) use the same type of relation, only they specify product innovation as steps up the quality ladder of a (fured) range of consumer goods, g. Similar to Equation (2), the highest quality version of each variant i of the consumer good is specified as follows:

g(i) = i.~j . (3)

In this equation, p, is a parameter, and j is an index for the highest attained position on the quality ladder.

638


These equations reflect the notion that each new innovation (blueprint) b ‘Id p UI s u on the previous one, so that the productivity (quality) of the intermediate (consumer) goods is always higher for the next innovation. This means that the impact of an innovation is not only to raise productivity (quality) in the present period, but also in the periods that follow. Since innovations in future periods may (and will) be sold by different firms, the value of an innovation to society as a whole goes beyond the value for the innovating firm in the present period. Thus there is a positive (intertemporal) externality in the innovation process.

However, there is also a negative externality involved in the production of innovation. This effect, which is called “creative destruction,” after Schumpeter, or alternatively, the “business stealing effect, ” is due to the fact that a new innovator, by bringing his innovation on the market, destroys the monopoly rents for the previous innovator. This is implicit in Equations (2) and (S), where each new innovation makes the previous one obsolete. This negative externality is not present in the other models of endogenous technological change considered below. This leads to a difference in the welfare properties of these two types of models which will be discussed in more detail below.

The second approach to modeling the research sector is found in Romer (1990) and Grossman and Helpman (1989, 1990). In these models, general knowledge (a by-product of the research process) is used as an input in the research sector. The following general form of the production function for blueprints is used.

ri = N(A,, H,, n) .

A is a productivity parameter, H is human capital input, n is the number of blueprints in the economy, a subscript n points to the research sector and dots above variables denote time deriva- tives. The presence of n itself in the (aggregate) production function for n points to the positive externality engaged in the production of blueprints. Each new blueprint generates general knowledge as a by-product, which again is a stimulus for the development of new blueprints by all firms in the research sector. This amount of general knowledge is measured by n itself, hence the presence of n in the rhs of (4).

These efforts to incorporate different aspects of technological innovation in a microeconomic framework on the one hand add to

639

Bar-t Verspagen

the level of realism of macroeconomic growth models, for endogenous technological change clearly is one of the most important driving forces for economic growth. Also, the specifications used allow for some of the typical characteristics of technological change (for example, cumulativeness; see Dosi 1988). On the other hand, however, the high degree of stylizedness of the models makes clear that one is still a long way from inclusion of endogenous technological change in models actually used for real world forecasts.

Innovation: Appropriability and Market Structure If innovation was a purely public good, obviously none of it

would be produced in a pure free market economy. Therefore, the new theory has to explain why some effects of technological change are appropriable. To do this, the models build to a large extent on work in the field of industrial organization, thus more or less incorporating this branch of literature in macroeconomic growth models. Monopolistic tendencies in the research market, enabling the producer to earn monopoly rents that cover its research costs, are an important issue in these models. An overview of the different approaches (and their mathematical details) to the appropriability of innovation are in Table 1 above.

The early models discussed above do not elaborate in a very explicit way on modeling the microeconomics of innovation. All markets (also the implicit one for technology) are competitive in these models. In Romer (1986) there is only an assumption about maximization of profits by means of investment in knowledge, which has its effect through a very general production function of technological knowledge. In the first version of the Lucas model, human capital is accumulated through explicit “production”: a part of (individual) working time is devoted to accumulation of skills. It is assumed that the growth rate of human capital is a linear function of the time devoted to accumulation:

il ; = 6(1 - U) ,

where u is the fraction of time devoted to productive (in a “direct” way) labor.

Lucas’s (1988) second model assumes a different structure of technological change. In this case all technological change (human capital accumulation) is related to endogenous learning by doing. Instead of assuming that the rate of accumulation of human capital

640

Endogenous Znnovation in Neo-Classical Growth Models

is dependent on the time explicitly devoted to this accumulation, it is assumed that the time devoted to (“direct”) production determines the rate of growth.

The process of innovation and the role of appropriability is more complex in the second (later) type of models. These models of endogenous technological change tackle the problem by assuming that part of the effects of the innovation can be appropriated by monopoly power. Thus, there will be an incentive to produce innovations (due to monopoly power), but there will also be a spillover effect (externality, see above).

Again, the distinction between blueprints and general knowledge is important. As already touched upon above, a (second) difference between blueprints and technological knowledge is the degree of appropriability. Blueprints can be appropriated completely (for example, by means of a patent) by the producer, who thus be- comes a monopolist (oligopolist if there are close substitutes). Gen- eral technological knowledge, as explained above, on the other hand, cannot be appropriated and directly flows over to the other producers of blueprints. Thus, the problem of the lack of incentive to produce technological change in the presence of public good features is solved by making the distinction between general technological knowledge (non-appropriable) and specific technological knowledge (appropriable).

A closer look at the different models reveals again a distinction between two types (this distinction corresponds to the one made in the first subsection of Section 3). A first approach to the modeling of the innovation sector is found in Aghion and Howitt (1990) and Grossman and Helpman (1991). In Aghion and Howitt, technological change enters the consumer goods sectors (indirectly) via the intermediate goods sector. A fixed continuum of intermediate goods i E [0 . . . l] exists, of which the production costs are influenced by innovation via Equation (2) above. Each period (only) one patented blueprint is sold by the patent holder (monopolist) to the (fixed) range of sectors ([0 . . . 11) which produce intermediate goods. Each innovation (blueprint) affects all intermediate sectors in the sense that it lowers costs of the intermediate good to the same extent. The value of a patent is thus determined by the profits in the intermediate sector. In Grossman and Helpman (199I), each new blueprint increases the quality of each consumer good in the fixed continuum.

Both in the case of this “quality ladder” approach and in the case of the Aghion and Howitt model of the research sector, tech-

641

TABL

E 1.

A

Sche

mat

ic

Des

crip

tion

of

the

Endo

geni

zatio

n of

Te

chno

logi

cal

Cha

nge

in Ne

w N

eo-C

lass

ical

G

row

th

Mod

els

Prod

uctio

n of

Effec

ts of

innov

- Se

ctors

in Ty

pe

of inn

o-

innov

ation

: at

ion:

mode

l Ex

terna

lities

Refer

ence

mo

del*

vatio

n pro

cess

mo

del

struc

ture

struc

ture

of inn

ovat

ion

Rom

er

(198

6)

one

cons

umer

pr

oces

s inn

ovat

ion

thro

ugh

f =

v(I/T

) in

cons

umer

go

od

know

ledge

sp

illove

rs

good

kn

owled

ge

accu

mul

atio

n v

boun

ded

sect

or:

(pos

itive)

fro

m

abov

e F,

(T.,

L 8

Ti)

Luca

s (1

988)

-I on

e co

nsum

er

hum

an

capi

tal

accu

mul

atio

n fi

in co

nsum

er

good

pr

oduc

tivity

st

imul

us

good

th

roug

h sa

ving

- =

6(1

- u)

H

sect

or:

F(A,

H,

fi)

from

av

erag

e hu

man

ca

pita

l (p

ositiv

e)

Luca

s (1

988)

-II

two

cons

umer

hu

man

ca

pita

l ac

cum

ulat

ion

h go

ods

thro

ugh

learn

ing

by

- =

6u

in co

nsum

er

good

pr

oduc

tivity

st

imul

us

H se

ctor

: F(

A)

horn

av

erag

e hu

man

do

ing

capi

tal

(pos

itive)

Aghio

n an

d re

sear

ch;

inter

- st

ocha

stic

(pois

son)

im

- c,

(i)

= co

q in

cons

umer

go

od

inter

tem

pora

l im

prov

e-

Howi

tt (1

990)

m

ediat

e pr

ovem

ents

in

bluep

rints

sect

or:

men

ts

(pos

itive)

; bu

si-

good

s;

con-

fo

r int

erm

ediat

e go

ods

ness

ste

aling

ef

fect

su

mer

go

od

(neg

ative

)

Gros

sman

an

d re

sear

ch

& in-

ad

dition

of

ne

w int

erm

edi-

ri =

N(A,

, H

,, n)

in

cons

umer

go

od

know

ledge

sp

illove

rs

in He

lpman

te

rmed

iate

at

e go

ods

(Eth

ier

pro-

se

ctor

: re

sear

ch

& int

erm

edi-

(198

9)

and

good

s;

con-

du

ctio

n fu

nctio

n)

ate

sect

or

(pos

itive)

ww

su

mer

go

od

Gros

sman

an

d re

sear

ch

& co

n-

impr

ovem

ents

in

qual

ity

of

g(i)

= t.r

,j via

ut

ility

func

tion

inter

tem

pora

l im

prov

e-

Helpm

an

sum

er

good

co

nsum

er

good

m

ents

, co

nsum

er

sur-

ww

plus

(pos

itive)

; bu

si-

ness

ste

aling

ef

fect

(n

egat

ive)

Rom

er

(199

0)

rese

arch

&

in-

addit

ion

of

new

inter

med

i- ri

= N(

A,,

H,,

n)

in co

nsum

er

good

kn

owled

ge

spillo

vers

in

term

edia

te

ate

good

s (E

thier

pr

o-

sect

or:

rese

arch

&

inter

med

i- go

ods;

co

n-

sum

er

good

s du

ctio

n fu

nctio

n)

m

H"L

@

x(i)‘-

“-@

di at

e se

ctor

(p

ositiv

e)

with

x(

i) =

0 fo

r i

>n

*Entr

ies

in thi

s co

lumn

not

sepa

rated

by

a

“;” sh

ould

be

inter

prete

d as

“in

on

e co

mbine

d se

ctor.”

Bart Verspagen

nological advances are essentially stochastic. In this case, stochastic innovation means that the chance of success of research efforts is represented by a Poisson distribution; that is, the arrival rate of research success in a given period depends upon the research efforts (intensity) and the parameters of the distribution.

Input in the innovation process is human capital. In these stochastic models of innovation, the more human capital is used, the bigger is the chance of research success. The (expected) rate of return to human capital is thus the main determinant of the wage rate (human capital is assumed to be the only form of labor input). Human capital is also used in the production of other (intermediate, consumer) goods, so that producers have to choose in which sector to use it.

Each producer of blueprints sells its products to the intermediate/consumer goods sector. Each blueprint is patented so that the producer can earn a monopoly profit as long as his blueprint is the most advanced one available. As soon as a new blueprint occurs, the current producer goes out of the market. The time span in which one blueprint is used is treated as one period (and is vari- able). Profit maximization and free entrance to the research sector ensures that expected (gross) profits are equal to the development costs of the blueprint (“limit pricing,” as it is called in Grossman and Helpman 1991).

This stochastic approach to innovation captures the basic notion of innovation as a search process with an uncertain outcome. In the evolutionary tradition, Dosi (1988) has pointed to this aspect of the innovation process. Dosi makes a distinction between weak uncertainty (the probability distribution of an event is known) and strong uncertainty (not even the probability distribution is known). He then argues that innovation involves a considerable degree of strong uncertainty. Of course, this latter notion is not captured in the stochastic model discussed above (where the probability distribution is known explicitly). However, modeling strong uncertainty is extremely difficult and involves a wholly different approach than the one used in the neo-classical tradition (see below).

A different approach to modeling the innovation sector is found in Romer (1990) and Grossman and Helpman (1989, 1990). There, each new blueprint leads to a new variety of the intermediate good used in the production of consumer goods. In these models, three sectors are present: a research sector, an intermediate goods sector and a final goods sector. The first two sectors can be thought of as combined in one. All sectors use human capital, while the final goods

644


sector also uses intermediate inputs produced in the other sector. The production function in the consumer goods sector has a hmc- tional form borrowed from Ethier (1982). In Grossman and Help- man (1989, 1990) it has the following form.

Q = F(Z+ [lx(iydi]l’a) , (6)

where x(i) is an intermediate good and CY is a parameter. All the other symbols have the meaning defined before. The Ethier functional form of the production function has the property that an increase in the number of varieties increases productivity. Thus, an increase in n through efforts in the research sector raises productivity in the consumer goods sector. The varieties of the intermediate good are not complete substitutes, since every new variety adds to the productivity in the consumer goods sector (product differentiation). Therefore, different producers (each producing one variety of the intermediate good and therefore having some degree of monopoly power) can co-exist in this sector without prices being driven to marginal production costs.

Assuming free entry in the research sector, price setting is done by a markup above marginal costs, as in the standard monopolistic competition (oligopoly) case. This markup just covers the research costs, so that net profits are equal to zero.

As in the stochastic models, human capital is also the (main) input in the research sector in the deterministic approaches to the innovation process. The more human capital is used, the larger is the research output. This is reflected in Equation (4) above. As in the stochastic models, the (certain) rate of return to innovation efforts determines the wage rate.

The framework of rationality used in the models discussed is usually strongly criticized in evolutionary theories (Dosi 1988; Dosi et al. 1988). In this type of theories, it is argued that firms, given the strong uncertainty they face, cannot optimize profits in the usual way. Instead, bounded rationality is used as the f&rework in which firms make decisions. Bounded rationality (Simon 1986) reflects the notion that agents only take into account some variables and relations in predicting the outcome of alternative behavioral patterns. Decision rules take the form of simple rules of thumb (like the pay back rule or the discounted cash flow method), which might yield sub-optimal (in the neo-classical sense) results. The first efforts to use the concept of bounded rationality in (growth) models have only

645

Burt Verspagen

recently been undertaken, and are still in the early phases of development (an example is in Silverberg et al. 1988).

Viewed in this way, one could see the neo-classical models discussed here as implicitly assuming the presence of rational technological expectations. As with “normal” rational expectations, it is likely that a lot of criticism to this assumption will be developed on the basis of the arguments of bounded rationality. Thus, the achievement of “neat” mathematical formulations (which are not so often found in, for example, the evolutionary approach) of optimiz- ing behavior only comes at the expense of some assumptions which are at least open to a long discussion.

Summarizing, it can be said that endogenization of technological change in neo-classical growth models basically comes down to assuming that there is a distinction between appropriable and non- appropriable effects in the production of innovation. In the neo- classical literature, this notion goes back to Arrow (1962). The distinction is necessary because the existence of externalities poses the problem of whether there is an incentive to produce innovation. It is typically assumed that some degree of monopoly power (patent protection, product differentiation) is necessary in order for appropriability.

Solving the Model: Equilibrium Growth Paths The explicit modeling of the externalities, increasing returns

and market structures in new neo-classical models would only be of limited use if the conclusions from the overall model would not differ from those drawn from the basic neo-classical model. In that case, the innovation-modeling exercise would merely have a cos- metic effect. There are, however, consequences for the equilibrium growth paths of an economy in case of endogenous technological change in neo-classical models. An overview of the results is given in Table 2.

In Romer (1986) and Lucas (1988), solving the model is simply done by maximizing the single objective function (utility). The solving procedure is more difficult in the later (more complex) models. The general way of solving these models is to assume equilibrium on the market for human capital (labor) (Aghion and Howitt 1990; Romer 1990; Grossman and Helpman 1989, 1990) or the markets for human capital and capital (Grossman and Helpman 1991). In the former papers, equating the reward for human capital in both (research & intermediate goods and consumer goods) sectors yields a single price for human capital inputs. This price is equal to the

646


marginal product of human capital in the two sectors, and thus, given the production functions in the two sectors, determines the allocation of human capital resources over the two sectors and the levels of (research) output. This yields an equilibrium growth path of the production and consumption of all goods.

In Grossman and Helpman (1991) equilibrium is found at the point where labor market equilibrium coincides with capital market equilibrium. The capital market equilibrium ensures that an equilibrium rate of interest is reached which both satisfies intertemporal consumer utility maximization and equals the rate of return of the “quality leading” firm which operates in the research sector and the consumer goods sector (arbitrage). Together with labor market equilibrium (as in the other models), this determines the equilibrium growth path.

The general characteristics of the growth paths found are as follows. The growth rate of the economy is a positive function of technological opportunities and the size of human capital (labor) endowment. Besides this, factors found in the basic growth model, like the time preference parameter, the interest rate and the intertemporal elasticity of substitution, affect the growth rate in their usual way.

Technological opportunities are reflected in the arrival rate parameter in the Poisson distribution for innovation and the size of innovations (y, II) in Aghion and Howitt (1990) and Grossman and Helpman (1991), or the productivity of research in Romer (1990) and Grossman and Helpman (1989, 1990). Their effect is intuitively plausible.

The role of increasing returns is reflected in the role of the supply of human capital in the equation for the growth rate. This role of human capital (functionally equal to labor) endowment as the factor responsible for increasing returns is a bit awkward. One would expect a factor more closely related to technical change to embody this effect.

Being as it is, the models lead to the conclusion that the larg- est countries (simply measured in terms of population) should also experience the highest growth rates, a hypothesis that is not only implausible, but also not in accordance with the empirical facts. As Aghion and Howitt (1990, 22) note when they discuss this result, “the positive effect of [the total supply of labor] on [the average growth rate] has the unfortunate implication . . . that larger economies should grow faster. . . . We accept the obvious implication that this class of models has little to say, without considerable mod-

647

TABL

E 2.

A

Sc

hem

atic

D

escr

iptio

n of

th

e C

hara

cter

istic

s of

th

e G

row

th

Path

in

N

ew

Neo

-Cla

ssic

al

Gro

wth

M

odel

s

Ref

eren

ce

Rom

er

(198

6)*

Luca

s (1

988)

**-I

Fact

ors

influ

enci

ng

Fact

ors

influ

enci

ng

grow

th

rate

gr

owth

ra

te

posi

tivel

y ne

gativ

e1 y

accu

mul

atio

n of

kn

owle

dge

disc

ount

ra

te

Diff

eren

ce

betw

een

optim

al

and

equi

libriu

m

grow

th

rate

oosi

tive

effe

ctiv

enes

s of

in

vest

men

t in

in

terte

mpo

ral

elas

ticity

of

po

sitiv

e hu

man

ca

pita

l; po

pula

tion

subs

titut

ion;

di

scou

nt

rate

gr

owth

; de

gree

of

ex

tem

al-

ity

from

in

vest

men

t in

hu

- m

an

capi

tal;

Aghi

on

and

How

itt

tech

nolo

gica

l op

portu

nity

(s

ize

inte

rest

ra

te

posi

tive

or

nega

tive,

de

pend

- m

m

of

inno

vatio

n an

d ef

ficie

ncy

ing

on

the

size

of

in

nova

- of

re

sear

ch);

popu

latio

n en

- tio

n an

d m

onop

oly

pow

er

dow

men

t; m

onop

oly

pow

er;

Gro

ssm

an

and

Hel

pman

(1

991)

te

chno

logi

cal

oppo

rtuni

ty

(siz

e di

scou

nt

rate

po

sitiv

e or

ne

gativ

e,

depe

nd-

of

inno

vatio

n an

d ef

ficie

ncy

ing

on

the

size

of

inno

va-

of

rese

arch

); po

pula

tion

en-

tion

dow

men

t

Rom

er

(199

6)

effic

ienc

y in

th

e re

sear

ch

sec-

in

ter-t

empo

ral

elas

ticity

of

po

sitiv

e to

r; hu

man

ca

pita

l en

dow

- su

bstit

utio

n;

disc

ount

ra

te

men

t;

*Rom

er’s

(198

6)

mod

el

is fo

rmul

ated

in

ve

ry ge

nera

l te

rms,

and

the

equa

tion

for

the

grow

th

rate

is

not

fully

sp

ecifie

d.

**Gr

owth

ra

te

is de

fined

as

th

e gr

owth

ra

te

of

effic

ient

hu

man

ca

pita

l in

th

is ca

se.


ification, about the relationship between population size and growth rate” (emphasis added).

The most obvious interpretation of this peculiarity is probably that it is the result of the stylized way of modeling the inputs into the innovation sector. A more realistic (but also more complicated) way to tackle the innovation process would be necessary to solve this deficiency and attribute the increasing returns argument more directly to innovation.

In addition to these general characteristics of the growth paths, each of the specific models discussed above has some specific factors influencing the growth paths. The most notable of these are the following. In Romer (1990), the value of the growth rate does not depend, like in other models, on the level of population. This is caused by the assumption that the amount of human capital is fixed. In Aghion and Howitt (1990) the degree of monopoly power has a positive influence on the growth rate. The role of monopoly power reflects the Schumpeterian notion that the appropriability of innovation rents spurs innovation efforts, and therefore economic growth. Moreover, in this paper, four types of equilibria are shown to be possible (a stationary equilibrium with positive growth, a stationary equilibrium with zero growth, a 2-period cycle and a no- growth trap). Since there is a stochastic element in the production function for innovation in this model, the average growth rate shows (random) variability (this also goes for Grossman and Helpman 1991). Thus, a measure of the average variability of the growth rate can be formulated.

Closely linked with the critique that can be given to the implicit assumption of rational technological expectations, the char- acteristic of equilibrium growth rates is likely to become subject to critique. If technological expectations are not rational, and the consequences of technological events cannot be calculated in advance, the equilibrium growth path predicted by the new growth models (perhaps with the exception of Aghion and Howitt) is much less likely to occur.

This has led evolutionary theorists to abandon the important role of market equilibrium. In general, these theories give much more attention to the out-of-equilibrium behavior of the economic system than to the state of equilibrium as such. Again, this requires a different way of modeling, since the market equilibrium concept can no longer be used to “close” the model. In “descriptive” (non- mathematical) evolutionary theories of economic growth (as, for example, in Freeman, Clark and Soete 1982) this is not a problem.

649

Bart Verspagen

However, when one tries to model the growth process, there is a need for an alternative “regulatory” process. Such a process can be found in the principle of economic selection (as the counterpart of natural selection). Examples of how this can be implemented in a mathematical way are in Silverberg (1988) and Silverberg, Dosi and Orsenigo (1988). However, this idea still has to be developed in much more detail to become a serious alternative to the neo-classical concept of market equilibrium.

In conclusion, it can be said that the basic driving factors behind the growth rate in the models discussed above are technological opportunity, as measured by the (average) size of innovation and the efficiency in the research sector, and population (human capital) endowment.

Optimality and the Market Process From welfare economics, it is generally known that the pres-

ence of externalities has important consequences for the distinction between the optimal and the equilibrium market result. This is also true for the new neo-classical growth models. An overview of the differences between the equilibrium and optimal growth path in the different models is given in Table 2 above.

The effect of externalities is perhaps made most clearly visible in the early aggregate models in Romer (1986) and Lucas (1988). The procedure followed there is simply to calculate the optimal rate of return by intertemporarily maximizing the aggregate utility4 function subject to the restriction of the production function (see also Blanchard and Fischer 1989 for an example of such a procedure). The outcome of this exercise is that the equilibrium growth rate is smaller than the optimal growth rate, due to the existence of externalities. This leads to the conclusion that government policies (subsidies) are necessary to increase the equilibrium growth rate up to the level of the optimal growth rate.

This procedure is repeated in more or less the same, although more detailed and thus more complicated, form in the other models. For the characterization of the differences between the optimal and the equilibrium growth paths of the economy, it is again useful to make the distinction between the models by Aghion and Howitt (1990) and Grossman and Helpman (1991) on the one hand and the

‘The choice of the functional form of the utility function is generally without discussion.

650


other models on the other hand. This is so because the first type of models takes into account the negative externality that is not taken into account in the other models, as explained above.

In the former two models, the difference between the equilibrium growth rate and the outcome of the “social planning exercise” is not unambiguous in sign. It is possible that too much is invested in research from a welfare perspective. The positive externality in the innovation process (that is, the effect that an innovation lowers production costs beyond the period of the current innovation) leads to underinvestment in innovation. However, the negative externality (the business stealing effect) leads to overin- vestment. Besides these two externalities in the innovation process, there is also a monopolistic distortion effect which creates a difference between the equilibrium and optimal growth rate: the presence of monopolistic market structures makes innovation possible, but reduces the consumer surplus. This effect can also work either way, and vanishes in case of some functional specifications of the production structure. No more attention to this effect will be paid here, as it is treated in another part of the literature more extensively.

The question of which of the two external effects will domi- nate, and hence the question whether the equilibrium growth rate is smaller or larger than the optimal growth rate, depends on the size of innovation and the degree of monopoly power. For large innovations (and little monopoly power), the social value of innovation is large relative to the private value to the monopolist, so that the optimal growth rate is larger than the equilibrium growth rate. When the size of innovation is small (and monopoly power large) the opposite case arises.

In the Grossman and Helpman (1991) paper based on the Aghion and Howitt approach, the positive externalities of innovation concern the intertemporal quality spillover, which is part of the consumer surplus due to innovation. Innovation is passed onto the consumer in the form of quality improvements with constant prices.5 The business stealing effect is also present in this model. This effect is relatively large for small and for large innovations, so that, only

‘The result that prices are independent of quality hinges on the functional specification of the quality hnction. It can be shown that, for different functional specifications than the one used in Grossman and Helpman (1991), prices change (rise) over time.

651

Burt Verspagen

for intermediately-sized innovations, the optimal growth rate ex- ceeds the equilibrium growth rate.

In Romer (1990) and Grossman and Helpman (1989), the socially optimal rate of growth is unambiguously larger than the equilibrium growth rate. This is caused by the presence of positive externalities and the absence of negative externalities. Thus, there is the opportunity for increasing the growth rate (and welfare) by sub- sidizing research efforts. This is a simple reproduction of the results in early models like Romer (1986) and Lucas (1988).

Thus, a major achievement of the new growth models is that they leave open serious possibilities for governmental (technology) policy. As with static welfare theory, however, this conclusion is of limited use in practice, since it does not provide a clue on the size of the subsidy (or tax). Moreover, the theoretical and practical significance of the result relies on the functional specification of (utility) functions and assumptions on maximizing behavior.

All of this, for reasons mentioned above, makes evolutionary economics reject welfare analysis as a concept for determining the outcome of the growth process. The policy conclusions drawn from evolutionary models would therefore not be based upon a formal welfare analysis, and first or second best situations cannot be identified. This leaves open the possibility that the policy conclusions might point in the same direction (encouragement of research efforts), especially if one realizes that the neo-classical models do not provide an operational quantification of the subsidy/tax.

International Trade and Growth The new growth theory also has important consequences for

international growth rate differentials and international trade. The relation between endogenous technological change, international trade and economic growth is addressed in Lucas (1988) and Grossman and Helpman (1989, 1990, 1991). An overview of the models is in Table 3.

One way of making some sort of classification of these models is by looking at the assumptions about differences between countries. Lucas (1988) and Grossman and Helpman (1990) assume that the only differences between countries are initial factor endowments.6 Grossman and Helpman (1989, 1990), on the contrary, as-

‘Note that the models from the papers discussed in this section are extensions of the models in the same papers discussed above.

652

TABL

E 3.

A

Sc

hem

atic

R

epre

sent

atio

n of

th

e M

ain

Argu

men

ts

Foun

d in

N

ew

Neo

-Cla

ssic

al

Gro

wth

Th

eorie

s on

In

tern

atio

nal

Trad

e an

d Ec

onom

ic

Gro

wth

Diff

eren

ces

Cha

ract

er

of

Trad

e an

d/or

be

twee

n te

chno

logi

cal

tech

nolo

gy

Ref

eren

ce

coun

tries

ch

ange

po

licy

effe

ctiv

e?

Luca

s (1

988)

-II

endo

wm

ents

lo

caliz

ed

lear

ning

at

di

ffere

nt

not

expl

icitl

y tre

ated

in

m

odel

ra

tes

in

diffe

rent

se

ctor

s

Gro

ssm

an

and

endo

wm

ents

st

ocha

stic

qu

ality

im

prov

e-

trade

po

licy

not

effe

ctiv

e;

Hel

pman

(1

991)

m

ents

te

chno

logy

po

licy

effe

ctiv

e

Gro

ssm

an

and

endo

wm

ents

; te

chno

logi

cal

new

va

rietie

s of

in

term

edia

te

poss

ibly

ef

fect

ive

(bot

h)

to

in-

Hel

pman

(1

990)

ca

pabi

litie

s go

ods

(Rom

er

1990

) cr

ease

gr

owth

ra

te

Gro

ssm

an

and

endo

wm

ents

; te

chno

logi

cal

new

va

rietie

s of

in

term

edia

te

Hel

pman

(1

989)

po

ssib

ly

effe

ctiv

e (b

oth)

to

in

- ca

pabi

litie

s go

ods

(Rom

er

1990

) cr

ease

w

elfa

re

Bart Verspagen

sume that there are also differences in technological capabilities between countries, an assumption quite common in evolutionary theories also.

In his analysis of learning by doing and comparative advantage, Lucas (1988) extends the one good aggregate production function with human capital as the main source of technological change to a two (consumption) goods setting. Human capital is the only production factor, and its effect is totally external (that is, only average skill levels matter). Human capital skills are only relevant for the production of one commodity; that is, there are two kinds of human capital (one for each sector). Moreover, the rate of accumulation of human capital is dependent on the amount of labor devoted to production, in order to represent learning effects.

The case considered by Lucas (1988) is the one of substitut- ability between the two consumer goods. This (and profit maximization) implies that relative prices are determined by the human capital endowments. For a number of open economies, each single economy will then specialize in the good for which its (initial) endowment of human capital is best suited. This state of specialization has a self-reinforcing tendency, since in each country learning only takes place in the sector in which it is specialized. If learning rates are then different among the two sectors, there will also be different growth rates between countries. This result (as well as the model structure) resembles the results obtained in the well-known Kal- dorian export-base models (Dixon and Thirlwall 1975; Kaldor 1970). These models today are a source of inspiration for evolutionary models of growth (see Dosi, Pavitt and Soete 1990).

Grossman and Helpman (1991) provide a different view on the process of international trade and endogenous innovation. They consider a 2 X 2 X 2 (country X factor X good) model, which is an extension of the quality ladder model of innovation discussed above. The extension lies in the introduction of a homogeneous consumer good and a separate factor called unskilled labor. As in Lucas (1988), factor endowments between countries are assumed to differ. The question they ask is whether the profit maximizing equilibrium in this setting can achieve the same result as the one 1 x 2 x 2 variant of the model (the integrated equilibrium).

The assumptions in the model (free trade, among others) lead to the outcome that the integrated equilibrium is repeated for val- ues of the endowments within certain limits. In this equilibrium, each country specializes in a certain range of differentiated consumer goods, performs an appropriate amount of R&D, and uses

654


the rest of its resources to produce an amount of the homogenous consumer good. Thus, the conclusion is that, under free trade, the world integrated equilibrium will be reached.

The approach in Grossman and Helpman (1989, 1990) is different. Here it is assumed that there are two countries (regions) which differ not only with regard to initial endowments, but also with regard to their technological capabilities. The structure of these models is basically the same as in Romer (1990), with the Ethier production function, and the positive externality of general technological knowledge as the most important concepts. Blueprints are not tradeable (obviously an unrealistic assumption), but intermediate and consumption goods are. Consumer goods from the two countries are imperfect substitutes in the utility function of the consumer. It is assumed that a country can face a comparative (dis-) advantage in manufacturing or research. These comparative advantages are measured by the ratios of the labor coefficients of the production of new intermediate goods (research) and manufacturing (of intermediate goods). Comparative advantages do not necessarily lead to complete specialization in this model, because even if a new intermediate good produced in a country with a comparative disadvantage in research is more expensive than an innovation from the other country, it can improve productivity due to the Ethier functional form of the production function for consumer goods (product differentiation).

The reduced form for the equilibrium growth rates in the model is found in more or less the same way as in Romer (1999) and has the following properties. In the case that no comparative advantages in research exist, the (aggregate world) outcome of the model is similar to the outcome in Romer (1999). This situation is more or less comparable to the integrated equilibrium in Grossman and Helpman (1991). The general equilibrium nature of the model is such that if comparative advantages do exist, however, the world growth rate is dependent upon the allocation of resources (human capital) between sectors or countries and the structure of demand. For example, relatively higher demand for the consumer good produced in the country with a comparative advantage in research will lower the world’s growth rate, since human capital is pulled out of research activities in that country. A rise in human capital resources (both total resources and resources in the country with comparative advantage in research) spurs research and therefore has a positive influence on the growth rate. Also, a reallocation of human capital resources can influence the growth rate (positively if the share in

Bart Verspagen

effective labor of the country with comparative advantage in research grows). Grossman and Helpman (1990) do not consider the welfare effects, in the sense of an aggregate analysis of welfare implications of policy measures. They do consider the effect of various trade and technology policies on the world growth rate, without making judgments about the desirability of such a change on the basis of welfare analysis. From the previous paragraph it is clear that an import tariff (export subsidy) on consumer goods in the country with comparative disadvantage in research stimulates research activity in the other country, and therefore stimulates world economic growth. Also, a subsidy for research in both countries (thus not altering the division of research) or in the country with a comparative advantage in research stimulates growth.

In Grossman and Helpman (1989), the above framework is ex- tended to include the aggregate welfare effects of policy measures suggested. The conclusions reached there more or less confirm the results from Grossman and Helpman (1999). The model shows that research subsidies and trade policy (tari& or quota) generally are necessary to reach the first best equilibrium growth rate (in the common welfare economics sense).

In light of the empirical experience in the postwar world, the new models describing international growth have important advantages over the old growth theory. They open up possibilities for unequal growth patterns, something which is obviously a realistic phenomenon. However, it is doubtful whether the models discussed go far enough in their description of technological change in order to be of any significance for the poorest countries. For these countries, the phenomenon of international diffusion of innovation (or technology transfer) is of course much more important than the movement of the world technological frontier by undertaking research. This aspect of development and catching up (see Verspagen 1991) is not being dealt with in the papers discussed.

In conclusion, it can be said that the application of models of endogenous technological change in an international context pro- vides interesting outcomes with regard to trade and technology policy. What can be learned from this exercise is that the well-known arguments in favor of free trade no longer bear unlimited (with re- spect to time and place) validity. In some specific cases trade policies, in the form of tariffs, or technology policies, in the form of research subsidies, may influence aggregate economic growth or welfare by changing the factor proportions devoted to research and/ or manufacturing. The exact outcomes of the policy measures are


not very clear-cut from the international perspective. A lot depends on the comparative advantages with regard to technology and manufacturing activities.

Old and New Neo-Clussical Growth Theories: Summing Up the Differences and Similarities

The differences between old and new neo-classical growth theories both concern assumptions and conclusions. With regard to the assumptions, the novelties in new theory are increasing returns to scale (due to externalities involved in the endogenous innovation process) and monopolistic market structures (which are necessary in order for innovation to occur at all). With regard to the conclusions, new theory stresses the effect of endogenous innovation, and points out that it is likely that the market generates a sub-optimal result.

The first assumption (endogenous innovation and its extemal- ities) is indeed an important modification to the basic neo-classical model. Both in new and old neo-classical theories, there is a direct relation between growth and technological change. In the old neo- classical model, the rate of technological change is given exoge- nously, whereas in new models, it is determined within the model itself. In the first place, this is a result that bears (theoretical) significance in its own right. Endogenous innovation obviously is more attractive from a theoretical point of view than imposing some exogenous trend to capture the effect of technological progress. Sec- ond, externalities in the innovation process lead directly to some important differences in further conclusions.

The second assumption (some degree of monopoly power is needed to generate innovation) sheds new light upon the conclusion reached by general equilibrium models and welfare analysis that perfect competition in all markets generates an optimal result (in the sense of allocation of goods). New neo-classical growth models explicitly assume that a monopolistic market structure is necessary for innovation, and therefore for economic growth. The role of the competitive market as a means of generating efficient prices is thus no longer obvious. Anti-trust policy as a form of government intervention is no longer obviously related to a better (compared to the monopolistic market) allocation of goods. This is not to say that anti-trust policy may not be necessary. The point is merely that it is no longer obvious to make the point for perfect competition ir- respective of what happens in the technological field.

An important aspect of endogenous innovation is that it leads to a new conclusion: the sub-optimality of the market. When mod-

Burt Verspagen

eling of the endogenous innovation process is done this way, externalities in the research sector lead to increasing returns: if one firm doubles its inputs, it will increase the inputs of all the other firms too (via the externality), and thus yield a more than proportionate rise in aggregate output.

Because of the increasing returns effect, the equilibrium rate of technological progress does not coincide with the optimal rate of growth. In the old model, where technological change is exogenous, a difference between the optimal and equilibrium rate of growth is not present, because the (exogenous) actual rate of growth is optimal. As explained above, in some models the equilibrium growth rate is always smaller than the optimal growth rate. In other models, the equilibrium growth rate might both be smaller or larger than the optimal rate.

This leads to the important implication that the policy conclusion reached in the old neo-classical model (“laissez faire”) is no longer valid in the new theories of growth. In these models, an active role for government is possible, and indeed desirable. Gov- ernmental technology policies (subsidies, or in some cases even taxes) or trade policy (tariffs or subsidies) will in general increase welfare. Together with the above conclusion that perfect competition is no longer the standard in theories of economic growth, one may say that the role of government and the role of the market have changed quite a bit in new neo-classical growth theories.

4. Summary and a First Assessment of Achievements and Limitations of New Neo-Classical Growth Models

In the so-called new neo-classical models of endogenous innovation, two main lines of procedure with regard to the modeling of innovation are found. A first type of model specifies knowledge accumulation as a separate factor in the aggregate production function, and points to the externalities involved in innovation.

A second type of model pays more specific attention to the phenomenon of innovation, and specifies a separate section of the model with its own price structure in which innovation is gener- ated. Here the generation of innovation is dependent upon the appropriability of part of the research output. Monopolistic market structures (patents, product differentiation) in the market for research output guarantees the appropriability. Besides the appropriable aspects of innovation, there is also a public part in the form of general technological knowledge.

658

Endogenous lnnovation in Neo-Classical Growth Models

Two main characteristics about endogenous growth paths arise, which are new to the neo-classical theory of economic growth. First, the externalities involved in the innovation process lead to increasing returns to scale. Second, the presence of increasing returns means that there is a difference between the equilibrium rate of growth and the optimal rate of growth, so that there is in general a role for the government to increase welfare by means of technology policy. In an international setting, trade policy (as well as technology policy) may (positively) affect the (world) growth rate. Another conclusion is that, because monopolistic price structures are necessary for innovation, the competitive market idea loses its central role.

The major achievements of the models discussed are as follows. First, identifying endogenous technological change as the main driving force for economic growth obviously adds to the level of realism of growth theory. The way in which this is done explicitly takes into account some of the inherent characteristics of the innovation process, as they have been identified by case studies at the microeconomic level. The possibility of increasing returns to scale associated with endogenous innovation leads to new conclusions with regard to national technology policy and international growth rate differentials. At the national level, the inclusion of endogenous innovation opens up possibilities for the government to increase growth performance by means of an active technology policy. The explicit welfare basis on which this conclusion is based adds importantly to its theoretical significance. In an international setting, increasing returns to scale lead to possibilities for unequal growth. From an empirical perspective, this is an important im- provement over old growth theory.

There are, however, also some limitations of the models, which (partly) may be resolved by undertaking further research. First, the modeling of technological change is still very stylized, which makes the use of these ideas in more realistic models (for example, for policy analysis) difficult. Second, the implicit assumption of rational technological expectations is at least open for discussion (like the

Burt Verspagen

countries. The fact that the models until now mostly look at research instead of international innovation diffusion makes them less useful for this purpose.

Receioed: October 1990 Final version: Nooember 1991

References Aghion, Philippe, and Peter Howitt. “A Model of Growth Through

Creative Destruction.” NBER Working Paper, no. 3223, Cam- bridge, Mass., 1990.

Anderson, Philip W., Kenneth Arrow, and David Pines, eds. The Economy as an Evolving Process. Redwood City: Addison-Wes- ley, 1988.

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Appendix

List of Used Symbols

= indicates a general volume, available to the economy as a whole.

ci, B, 6 = parameters. y, p, = parameters indicating the size of innovation,

A = parameter. c,(i) = production costs of intermediate i E [0 . . . l] in pe-

riod t. F, v = functions.

H = human capital input. I = investment in (fured) capital. i = as a subscript: indicating an individual entrepreneur. j = highest position attained on the quality ladder. L = some conventional production factor (labor). n = the number of (blueprints for) intermediates.

Q = output. T = the stock of investment in knowledge. u = fraction of time devoted to directly productive labor (note

that 1 - u indicates the fraction of time devoted to human capital accumulation).

x(i) = quantity of intermediate good; i E [0 . . . l] in Aghion and Howitt (1990) and Grossman and Helpman (1991); i E 10 . . . n] in Romer (1990) and Grossman and Helpman (1989, 1990).

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