Transcript Slides in

Scale Effects in Schumpeterian Growth Theory
By
Elias Dinopoulos
Lecture Organization
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Introduction
Anatomy of Scale Effects
Endogenous Schumpeterian Growth Models with Scale
Effects (Earlier endogenous growth models)
Exogenous Schumpeterian Growth Models without Scale
Effects (Semi-endogenous growth models)
Endogenous Scale-Invariant Schumpeterian Growth Models
(Fully-endogenous growth models).
An Assessment
Summary, conclusions and extensions
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 2
Introduction
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Schumpeterian growth is a particular type of growth
which is generated by the endogenous introduction of
product and/or process innovations.
The development of Schumpeterian growth theory
started in the early 1990s.
Until the mid 1990s the theory expanded rapidly
under the label of “endogenous” growth.
By mid 1990s the theory reached a blind intersection.
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 3
Introduction
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Jones (1995) criticized the scale-effects property: The
rate of technological progress is assumed to be
proportional to the level of R&D investment services.
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In the presence of positive population growth, the
presence of scale effects implies that per-capita growth
rate becomes infinite in the steady-state equilibrium.
Time-series evidence from developed countries is
inconsistent with the scale-effects property.
The Jones critique raises several fundamental
questions:
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 4
Introduction
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Is the scale-effects property empirically relevant?
Can one develop Schumpeterian growth models with
positive population growth and bounded long-run
growth?
Can one develop scale-invariant Schumpeterian growth
models that maintain the policy endogeneity of longrun growth?
Affirmative answers to the above questions are crucial
to the evolution of the theory for the following reasons:
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 5
Introduction
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Removal of scale effects enhances the empirical relevance of the
theory.
Scale-invariant Schumpeterian growth models can serve as
templates for a unified growth theory.
Scale-invariant endogenous Schumpeterian growth theory
improves its policy relevance and is closer to the spirit of
Schumpeter (1937):
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Elias Dinopoulos
“There must be a purely economic theory of economic change which
does not merely rely on external factors propelling the economic
system from one equilibrium to another. It is such theory that I have
tried to build…[that] explains a number of phenomena, in particular
the business cycle, more satisfactorily than it is possible to explain
them by means of either the Walrasian or Marshalian apparatus”
Schumpeterian Growth Theory
Slide - 6
An Anatomy of Scale Effects
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The scale-effects property arises from assumptions on an
economy’s knowledge production function and its resource
constraint.
Consider an economy producing final output by the
following production function:
Y (t )  A(t ) LY (t )
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The knowledge production function is
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A(t ) LA (t )
gA 

A(t ) X (t )
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 7
An Anatomy of Scale Effects
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Assumptions that govern the evolution of X(t) are crucial.
If the production of X(t) does not require any resources, the
model closes with the resource constraint
L(t )  LY (t )  LA (t )
L(t )  L0etgL
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Where
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Denote with s(t) the share of labor devoted to manufacturing
and notice that the economy’s income per capita is y(t) =
Y(t)/L(t) = A(t)s(t). Therefore, we have
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 8
An Anatomy of Scale Effects
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The economy’s long-run growth rate of output per capita is
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y (t ) A(t )
L( t )
gy 

 (1  s )
y (t ) A(t )
X (t )
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(1)
The per-capita resource condition can be written as
X (t )
s  (1  s ) g A
1
L( t )
Elias Dinopoulos
Schumpeterian Growth Theory
( 2)
Slide - 9
Endogenous Schumpeterian Growth Models
with Scale Effects
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They assumed that L(t )  L0 and that the R&D difficulty was
also constant X (t )  X 0 .
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y (t ) A(t )
L0
gy 

 (1  s)
y (t ) A(t )
X0
X0
s  (1  s ) g A
1
L0
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(1)
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Any policy that changes share of labor devoted to R&D (1 – s),
has long-run growth effects.
If L(t) increases exponentially, the long-run growth goes to
infinity.
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 10
Endogenous Schumpeterian Growth Models
with Scale Effects
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Jones (1995) tested directly the knowledge production
function
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A(t ) LA (t )
gA 

A(t )
X0
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He argued that the rate of TFP growth is roughly constant over
time, whereas the resources devoted to R&D increased
exponentially.
Models of this class include Romer (1990), Segerstrom, Anant,
Dinopoulos (1990), Grossman and Helpman (1991) and
Aghion and Howitt (1992).
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 11
United States per capita GDP
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 12
The evolution of number of scientists
and engineers
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 13
Exogenous Scale-Invariant Schumpeterian
Growth Models
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The first approach to the removal of scale effects property
employs the notion of diminishing technological opportunities.
The level of R&D difficulty is related to the level of
technology:
1/ 
X (t )  A(t )
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Substituting this expression into the two fundamental equations
yields:
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 14
Exogenous Scale-Invariant Schumpeterian
Growth Models
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y (t ) A(t )
L( t )
gy 

 (1  s )
y (t ) A(t )
A(t )1 / 
A(t )1/ 
s  (1  s) g A
1
L(t )
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(1)
(2)
These equations imply that the constant steady-state of growth
is proportional to the exogenous population growth rate:
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1 A(t ) L(t )

 A(t ) L(t )
Elias Dinopoulos

g A   gL
Schumpeterian Growth Theory
Slide - 15
Exogenous Scale-Invariant Schumpeterian
Growth Models
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Since the rate of population growth is not affected by policies,
this class of models generates exogenous scale-invariant
growth.
It should be emphasized that these models generate transitional
growth of technological progress that can be analyzed by
ranking the steady state values of per-capita R&D difficulty x
= X(t)/L(t).
These models are also very tractable and useful tools for
analyzing other dynamic dimensions (such as globalization,
wages, trade patterns etc).
Jones (1995), Segerstrom (1998), Kortum (1997), Li (2003),
Dinopoulos and Segerstrom (1999, 2006).
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 16
Endogenous Scale-Invariant Schumpeterian
Growth Models
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The second approach to removing the scale-effects property
uses a two dimensional framework with vertical and horizontal
product differentiation.
Variety accumulation removes the scale-effects property in the
same way as the exogenous growth approach.
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The level of R&D difficulty is a linear function of the level of
varieties.
The level of varieties is a linear function of the level of
population.
Quality improvements generate endogenous long-run
Schumpeterian growth.
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 17
Endogenous Scale-Invariant Schumpeterian
Growth Models
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Consider an economy consisting of n(t) industries producing
horizontally differentiated products, with each industry’s output
given by
z(t )  A(t ) Z
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The knowledge production function is a function of the
economy’s aggregate R&D and the R&D difficulty.
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gA 
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A(t ) n(t ) A

A(t )
X (t )
The R&D level of difficulty is given by
X ( t )  n ( t )   L( t )
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 18
Endogenous Scale-Invariant SchumpeterianGrowth Models
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Substituting X(t) into the knowledge production function yields
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A(t )
gA 
 A
A(t )
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The resource constraint is
 Z n ( t )   An ( t )  L( t ) 
Elias Dinopoulos
n(t )
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
Z   A 
Schumpeterian Growth Theory
1
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Slide - 19
Endogenous Scale-Invariant SchumpeterianGrowth Models
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Aggregate output is given by
Y (t )  z(t )n(t )  A(t ) Z n(t )  A(t ) Z L(t )
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Long-run growth of per-capita output is therefore
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y (t ) A(t )
gY 
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 A
y (t ) A(t )
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Models of this class include Peretto (1998), Young (1998), Aghion and
Howitt (1998), Dinopoulos and Thompson (1998), and Howitt (1999).
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 20
Endogenous Scale-Invariant SchumpeterianGrowth Models
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Dinopoulos and Syropoulos (2007) have proposed a different
approach to remove the scale-effects property based on
innovation contests.
We introduced explicitly the actions of incumbents to protect
their monopoly rents.
We call these actions rent-protecting activities (RPAs).
The level of R&D difficulty is assumed to be proportional to
the level of RPAs.
This approach has been used by Sener (2006) and Dinopoulos
and Syropoulos (2004) to address questions of globalization
and wage income inequality.
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 21
An Assessment
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Endogenous Schumpeterian growth models employ a
linear relationship between the level of R&D
difficulty and the level of population.
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Is this “knife-edge” property unsatisfactory?
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There are many knife edge properties in economics.
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The linear property is the result of market-based
mechanisms.
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Elias Dinopoulos
Constant returns to scale
Saddle-point stability path
Labor-augmenting technological progress
Under monopolistic competition the number of varieties is
proportional to the economy’s size measured by the number of
consumers.
Schumpeterian Growth Theory
Slide - 22
An Assessment
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In the case of RPAs, the level of R&D difficulty is chosen
optimally to maximize expected discounted profits.
Conjecture: For any scale invariant endogenous
growth mechanism, there exists a market based
mechanism that determines endogenously the
evolution of R&D difficulty.
The following remark on the issue of “functional
robustness” is borrowed from Temple (2003).
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 23
An Assessment
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Five obvious rules for thinking about long-run growth:
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Elias Dinopoulos
The long-run is a theoretical abstraction that is sometimes
of limited practical value.
Do not assume that a good growth model needs to have a
balanced growth, or that long-run growth have to be
endogenous.
Do not dismiss a model of growth because the long-run
outcomes depend on knife-edge properties.
Long-run predictions might be impossible to test.
Do not undervalue level effects.
Schumpeterian Growth Theory
Slide - 24
An Assessment
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I believe that all approaches to the removal of scale
effects are extremely useful.
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Exogenous Schumpeterian growth models are
analytically more tractable and have been used analyze
a variety of current issues.
Focus on steady-state analysis is very useful because
of its simplicity.
We should be analyzing the robustness of policy
effects by using a variety of scale-invariant growth
models.
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 25
An Assessment
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The development of exogenous scale-invariant growth
models necessitates the use of “Schumpeterian” as
opposed to “endogenous” growth.
The term “Schumpeterian growth” is policy neutral
and offers the well deserved recognition and credit to
Joseph Schumpeter.
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 26
Conclusions
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This paper offered an overview of recent
development and directions in Schumpeterian growth
theory.
Scale invariant growth models can be exogenous or
endogenous.
These models can serve as templates for a unified
growth theory that combines the insights of the
neoclassical model with endogenous thennological
progress and positive rate of population growth.
Elias Dinopoulos
Schumpeterian Growth Theory
Slide - 27